then the sum of the areas of the two smaller squares will be equal to the area of the largest square.
if three squares have sides that make an acute triangle, then the sum of the areas of the two small squares is equal to the area of the largest square. This is known as the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse). However, in an acute triangle, there is no side that is longer than the other two sides, and so the three squares cannot form a right triangle. Therefore, the sum of the areas of the two smaller squares cannot be determined from the information given.
If three squares have sides that make an obtuse triangle, then the sum of the areas of the two small squares is less than the area of the largest square. In an obtuse triangle, one of the angles is greater than 90 degrees, which means that the square with its side opposite the obtuse angle will have a larger area than the other two squares. Therefore, the sum of the areas of the two smaller squares will be less than the area of the largest square.
If three squares have sides that make a right triangle, then the sum of the areas of the two small squares is equal to the area of the largest square. This is the Pythagorean Theorem, as mentioned in the first answer. In a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore, if the squares are constructed with their sides equal to the lengths of the sides of the right triangle, then the sum of the areas of the two smaller squares will be equal to the area of the largest square.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
rylie is a newly hired cybersecurity expert for a government agency. rylie used to work in the private sector. she has discovered that, whereas private sector companies often had confusing hierarchies for data classification, the government's classifications are well known and standardized. as part of her training, she is researching data that requires special authorization beyond normal classification. what is this type of data called? group of answer choices
Compartmentalized is the type of data that is discussed in the problem researched by an employee rylie who is a newly hired cybersecurity expert for a government agency and has working experience in the private sector.
Data classification is the way of organizing data into different categories that make it easy to retrieve, sort and store for future use. In simple words, compartmentalization means to separate into isolated compartments or categories. In data language, A nonhierarchical grouping of information used to control access to data more finely than with hierarchical security classification alone is called Compartmentalization. Now, we have a rylie who is a newly hired cybersecurity expert for a government agency. She has working experience in the private sector. On basis of her experience she has discovered that, the private sector companies often had confusing hierarchies for data classification as compared to the government's classifications which are well known and standardized. During her training, she is researching data that requires special authorization beyond normal classification. The data type that she researched and that is authorization beyond normal classification is called compartmentalized data.
For more information about data classification, visit :
https://brainly.com/question/30580761
#SPJ4
Mia removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by f(x) = 10x2 −19x + 6, where x is time in minutes. Which of the following equations will reveal the time in minutes when the trough is empty?
Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.
To find the time in minutes when the trough is empty, we need to solve the equation f(x) = 0, since f(x) represents the volume of water in the trough.
So, we need to solve the quadratic equation:
[tex]10x^2 - 19x + 6 = 0[/tex]
To solve this equation, we can use the quadratic formula:
[tex]x = (-b ± \sqrt(b^2 - 4ac)) / 2a[/tex]
where a = 10, b = -19, and c = 6.
Plugging in these values, we get:
[tex]x = (-(-19) ± \sqrt((-19)^2 - 4(10)(6))) / 2(10)[/tex]
[tex]x = (19 ± sqrt(241)) / 20[/tex]
So, the two solutions are:
[tex]x = (19 + \sqrt(241)) / 20 \approx1.807 minutes[/tex]
[tex]x = (19 - \sqrt(241)) / 20 \approx0.313 minutes[/tex]
However, only the second solution makes sense in this context, since the trough cannot be empty before we start draining the water. Therefore, the time in minutes when the trough is empty is approximately 0.313 minutes.
To know more about quadratic visit:
https://brainly.com/question/22364785
#SPJ1
Question 11
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10, 16, 20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 14, with a median of 14
Bus 18, with a mean of 12
Bus 14, with a mean of 14
Bus 18, with a median of 12
Question 13
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Question 14
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 39.6°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
The lake activity with a central angle of [tex]39.6^\circ[/tex] is Wakeboarding.
What is the central angle?11. the number of tortilla sandwich wraps falling into each interval can be represented by the height or area of the bars. This allows for an easy visualization of the distribution of the data.
12. To determine which bus typically has the faster travel time, we need to compare the measures of center for each data set. Since there are outliers in both data sets, the median would be a more appropriate measure of center than the mean.
For Bus 14, the median is (10 + 12)/2 = 11.
For Bus 18, the median is (10 + 14)/2 = 12.
Therefore, Bus 18 typically has the faster travel time, with a median of 12 minutes.
13. The IQR (interquartile range) is the best measure of variability for the data because it is less sensitive to outliers than the range, and it gives us an idea of how spread out the middle 50% of the data is.
To find Q1, we need to find the median of the lower half of the data: (1+2)/2 = 1.5.
To find Q3, we need to find the median of the upper half of the data: (8+8+8)/3 = 8.
Therefore, the IQR = Q3 - Q1 = 8 - 1.5 = 6.5.
14. To determine the central angle of each lake activity, we need to calculate the percentage of campers who chose each activity and then multiply that percentage by 360 (the total degrees in a circle).
The percentage of campers who chose Kayaking is 15%, so the central angle would be 0.15 x 360 = 54°.
The percentage of campers who chose Wakeboarding is 11%, so the central angle would be 0.11 x 360 = 39.6°.
The percentage of campers who chose Windsurfing is 7%, so the central angle would be 0.07 x 360 = 25.2°.
The percentage of campers who chose Waterskiing is 13%, so the central angle would be 0.13 x 360 = 46.8°.
The percentage of campers who chose Paddleboarding is 54%, so the central angle would be [tex]0.54 x 360 = 194.4^\circ.[/tex]
Therefore, The lake activity with a central angle of [tex]39.6^\circ[/tex] is Wakeboarding.
Learn more about angle here:
https://brainly.com/question/16831377
#SPJ1
y+5=2(x+1) what is the X and Y intercept
50 POINTS!!!! Rewrite the function by completing the square f(x) = x^2 - 8x - 2
Answer:
The rewritten function by completing the square is:
[tex]f(x)=(x-4)^2-18[/tex]
The solutions of the function are:
[tex]x=4+3\sqrt{2},\;x=4-3\sqrt{2}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2-8x-2[/tex]
To rewrite the function by completing the square, begin by adding and subtracting the square of half the coefficient of the term in x. (Place these between the term in x and the constant).
[tex]f(x)=x^2-8x+\left(\dfrac{-8}{2}\right)^2-\left(\dfrac{-8}{2}\right)^2-2[/tex]
Simplify:
[tex]f(x)=x^2-8x+\left(-4\right)^2-\left(-4\right)^2-2[/tex]
[tex]f(x)=x^2-8x+16-16-2[/tex]
We have now created a perfect square trinomial from the first three terms: x² - 8x + 16.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{\sf \large Perfect Square Trinomial}\\\\\sf A perfect square trinomial is a polynomial of the form $a^2 + 2ab + b^2$ or $a^2 - 2ab + b^2$, where $a$ and $b$ are constants. \\\\When factored, a perfect square trinomial becomes the square of a binomial: $(a + b)^2$ or $(a - b)^2$. \\\end{minipage}}[/tex]
Factor the perfect square trinomial x² - 8x + 16.
[tex]f(x)=(x-4)^2-16-2[/tex]
Simplify by subtracting the numbers outside the parentheses:
[tex]f(x)=(x-4)^2-18[/tex]
Therefore, the given function rewritten by completing the square is:
f(x) = (x - 4)² - 18The solutions to a quadratic function are the x-values which satisfy the equation f(x) = 0. Therefore, to find the solutions, set the function equal to zero and solve for x.
[tex]\begin{aligned}f(x)&=0\\\implies (x-4)^2-18&=0\\(x-4)^2-18+18&=0+18\\(x-4)^2&=18\\\sqrt{(x-4)^2}&=\sqrt{18}\\x-4&=\pm\sqrt{18}\\x-4+4&=\pm\sqrt{18}+4\\x&=4\pm\sqrt{18}\\x&=4\pm\sqrt{3^2 \cdot 2}\\x&=4\pm\sqrt{3^2} \sqrt{2}\\x&=4\pm3 \sqrt{2}\end{aligned}[/tex]
Therefore, the solutions of the function are:
[tex]x=4+3\sqrt{2},\;x=4-3\sqrt{2}[/tex]
Huseyin was able to map quadrilateral EFGH onto EJGK using a vertical stretch
Huseyin used a vertical stretch, so the quadrilateral aren't similar. So correct option is A.
Describe Quadrilateral?A quadrilateral is a geometric shape that consists of four straight sides and four angles. It is a polygon because it is a closed shape with multiple straight sides.
There are various types of quadrilaterals, which are classified based on their properties. Some common types of quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.
A square is a quadrilateral with four equal sides and four equal right angles. A rectangle has four right angles but opposite sides are equal. A rhombus has four equal sides, but its angles are not necessarily right angles. A parallelogram has opposite sides that are parallel and equal in length, but its angles are not necessarily right angles. A trapezoid has only one pair of opposite sides that are parallel. A kite has two pairs of adjacent sides that are equal in length.
We know that that two quadrilateral are similar if corresponding angles are congruent and measures of their corresponding sides are proportional.
In the given transformation, angles that corresponding to each other are
∠fEH and ∠JEK
∠EHG and ∠EKG
∠HGF and ∠KGJ
and ∠GFE and ∠GJE
Here all four angles of EFGH are not congruent to other four angles of EJGK.
So,
Here Huseyin used a vertical stretch, so the quadrilateral aren't similar.
To know more about angles visit:
https://brainly.com/question/10462409
#SPJ1
The complete question is:
the area covered by the hour hand of a wall clock between time 4 : 26 and 6 : 50 is what percent of the area covered by it in 15 hours?
Step-by-step explanation:
From 4:26 to 6:50 is 2 hr and 24 in = 2 24/60 hrs = 2.4 hours
2.4 hrs is what percent of 15 hrs ?
2.4 / 15 * 100% = 16%
whats the answer to this question (Please help me)
The correct option is C, the skews are different.
Which is best supported for both dot plots¨?We have two dot plots and we want to see which statement is the best suported by these.
The right one is better distributed, so we can conclude that the correct statement is that the data have different skews.
The ranges may seem also to be different, but are the same ones, in the first one is:
20 - 12 = 8
In the second it is:
19 - 11 = 8
so the correct option is C.
Laern more about dot plots at:
https://brainly.com/question/15853311
#SPJ1
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)
Part A: A reasonable domain to plot the growth function would be from d = 0 to d = 11.
Part B: The y-intercept of the graph of the function f(d) is 7
Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.
Domine and y-intercept of a function:
The domain of a function represents the set of input values for which the function is defined and can produce a meaningful output.
The y-intercept of a function represents the value of the function when the input is equal to zero.
The average rate of change of a function from x = a to x = b is given by the slope of the secant line passing through the points (a, f(a)) and (b, f(b)).
Here we have
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
=> f(d) = 7(1.06)^d
Since it is given that the radius of the algae was approximately 13.29 mm when the biologist concluded her study, we can set f(d) = 13.29
=> 13.29 = [tex]7(1.06)^{d}[/tex]
=> ln(13.29/7) = d ln(1.06)
=> d = ln(13.29/7)/ln(1.06) ≈ 11
Therefore, A reasonable domain to plot the growth function would be from d = 0 to d = 11.
Part B: The y-intercept of the graph of the function f(d) represents the value of the function when d = 0.
Substituting d = 0 into the given equation, we get:
f(0) = 7(1.06)⁰ = 7
Therefore, The y-intercept of the graph of the function f(d) is 7
Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is given by the slope of the secant line passing through the points (4, f(4)) and (11, f(11)). Using the given equation, we can evaluate f(4) and f(11):
f(4) = 7(1.06)⁴ ≈ 8.84
f(11) = 7(1.06)¹¹ ≈ 13.29
The slope of the second line passing through these two points is:
Slope = (f(11) - f(4))/(11 - 4) = [ 13.29 - 8.84]/7 = 0.64
Therefore,
The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.
Learn more about Functions at
https://brainly.com/question/24839787
#SPJ1
which figure has exactly one line of symmetry ³³³³÷²³²×³
What is -3 4/5 converted to a decimal.
The solution is, -3 4/5 when converted to a decimal is -3.5.
We know that,
A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
here, we have,
given number is:
-3 4/5
= - (3 + 4/5)
= - 17/5
= -3.5
Hence, -3 4/5 when converted to a decimal is -3.5.
To learn more on decimal number click:
brainly.com/question/17429689
#SPJ1
An electrician charges $45 an hour for labor and an initial fee of $55. The total cost c equals 45 times the number of hours x plus 55. Enter an equation for the relationship and use the equation to complete the table.
So, for example, if the electrician works for 1 hour, the total cost would be $451 + $55 = $100. If the electrician works for 2 hours, the total cost would be $452 + $55 = $145, and so on.
What is cost?Cost refers to the amount of money or resources that are required to produce or acquire a good or service. It is often used to describe the expenses associated with a particular activity or project, including the materials, labor, overhead, and other expenses necessary to complete the task. Cost can also refer to the value or price that is paid or incurred for a particular item or service. In business and economics, cost is an important factor in determining profitability and efficiency, as it helps to evaluate the expenses and benefits of different options and make informed decisions about resource allocation.
The equation for the relationship between the total cost c and the number of hours x is:
c = 45x + 55
To complete the table, we need to plug in the given hours and calculate the total cost for each:
Number of hours (x) Total cost (c)
1 $100
2 $145
3 $190
4 $235
5 $280
So, for example, if the electrician works for 1 hour, the total cost would be $451 + $55 = $100. If the electrician works for 2 hours, the total cost would be $452 + $55 = $145
To know more about cost visit:
https://brainly.com/question/30045916
#SPJ1
An animal population N(t) is modeled by the differential equation:
dN/dt = -0. 001N(N - 110)(N - 99). If N(0)=A, where A is a positive integer, what is the maximum value of the positive integer A such that extinction will occur?
For the given integer, the maximum starting population size that will eventually lead to extinction is 98, since any larger value will result in the population either stabilizing at a positive value or growing indefinitely.
The equation in question is:
dN/dt = -0.001N(N - 110)(N - 99)
Here, N represents the population size, and dN/dt represents the rate of change of the population with respect to time. The right-hand side of the equation tells us how the population size changes over time, and it's determined by the current population size N, as well as the two constants 110 and 99.
We can do this by setting dN/dt equal to zero and solving for N:
dN/dt = -0.001N(N - 110)(N - 99) = 0
=> N = 0, N = 99, N = 110
We can then plot the direction field (i.e., arrows indicating the direction of change) on each interval, and use this to determine the behavior of the solution curve. In this case, we can see that the direction of the arrows changes at each critical point, indicating that the population behavior switches between growing and declining as we move from one interval to the next.
Specifically, we can see that if the initial population size A is less than 99, the population will decline to extinction. If the initial population size is between 99 and 110, the population will initially decline but then grow and eventually stabilize at N = 110. If the initial population size is greater than 110, the population will grow exponentially and tend towards infinity.
To know more about integer here
https://brainly.com/question/15276410
#SPJ4
will give brainliest!!
Answer:
Remember SOHCAHTOA
SOH- Sin= Opposite/Hypotenuse
CAH- Cosine= Adjacent/Hypotenuse
TOA- Tangent= Opposite/Adjacent
sin Θ is 24/25
cos Θ is 7/25
tan Θ is 24/7
Step-by-step explanation:
If using the SOHCAHTOA method all you have to do is memorize your Pythagorean triples
Ex: 3,4,5
7,24,25
5,12,13
If a book about airplanes costs $5.39, how much would it cost to buy 5 books about airplanes?
Answer:
$5.39 × 5 = $26.95
5 books about airplanes would cost $26.95.
The spinner shown is spun twice Use a tree diagram to record the sample space of the repeated experiment
Here is the tree diagram to represent the sample space of spinning the spinner twice:
sp1 - Possible outcomes of the first spin:
Red, Blue, Green
sp1 - Red
sp2 - Red Red, Red
sp2 - Blue Red, Blue
sp2 - Green Red, Green
sp1 - Blue
sp2 - Red Blue, Red
sp2 - Blue Blue, Blue
sp2 - Green Blue, Green
sp1 - Green
sp2 - Red Green, Red
sp2 - Blue Green, Blue
sp2 - Green Green, Green
So the full sample space would be:
{(Red, Red), (Red, Blue), (Red, Green),
(Blue, Red), (Blue, Blue), (Blue, Green),
(Green, Red), (Green, Blue), (Green, Green)}
Does this capture the correct sample space for spinning the spinner twice? Let me know if you need any clarification.
which of the following statements is false? a.) a larger sample size would increase the power of a significance test. b.) the significance level is the probability of making a type i error. c.) expanding the sample size can decrease the power of a hypothesis test. d.) the probability of rejecting the null hypothesis in error is called a type i error.
The statement C is false .
why the statement C is false ?a)A larger sample size would increase the power of a significance test because it provides more information, reduces random error, and increases the precision of the estimate.
b.) The significance level is the probability of making a type I error, which is rejecting the null hypothesis when it is actually true. It is usually denoted by α and is set before conducting a hypothesis test.
c.) Expanding the sample size cannot decrease the power of a hypothesis test. Power is the probability of rejecting the null hypothesis when it is false (i.e., correctly detecting a real effect). A larger sample size generally increases the power of a test, making it more likely to detect a true effect.
d.) The probability of rejecting the null hypothesis in error is called a type I error. It occurs when the null hypothesis is actually true but is rejected based on the sample data. The probability of making a type I error is equal to the significance level (α) of the test.
Learn more about significance test
brainly.com/question/30827627
#SPJ11
Nancy placed 3 red pins and 12 yellow pins on the cork board. What percentage of the pins were red pins?
Answer:
25%
Step-by-step explanation:
We Know
Nancy placed 3 red pins and 12 yellow pins on the corkboard.
What percentage of the pins were red pins?
We Take
(3÷12) x 100 = 25%
So, 25% of the pins were red pins.
at their highest rate, the wildfires which ravaged california were estimated to have consumed the equivalent of one football field per three seconds, over a 20-hour period. if a football field is 360 feet long and 160 feet wide, how many square inches per minute, was the fire burning at its highest rate? be sure to include units with your answer.
the fire was burning at its highest rate at approximately 165,888,000 square inches per minute.
To find the square inches per minute that the fire was burning at its highest rate, we need to first find the total square footage of a football field, which is 360 feet x 160 feet = 57,600 square feet.
Since there are 12 inches in a foot, we can convert the square footage to square inches by multiplying by 12^2 (or 144).
57,600 square feet x 144 square inches per square foot = 8,294,400 square inches in one football field.
Next, we can find how many football fields the fire consumed in 20 hours by dividing the number of seconds in 20 hours (20 x 60 x 60 = 72,000 seconds) by 3 seconds per football field:
72,000 seconds ÷ 3 seconds per football field = 24,000 football fields consumed.
Finally, we can find the total square inches consumed by multiplying the number of football fields by the square inches in one football field:
24,000 football fields x 8,294,400 square inches per football field = 199,065,600,000 square inches consumed in 20 hours.
To find the square inches per minute, we can divide the total square inches consumed by the number of minutes in 20 hours (20 x 60 = 1,200 minutes):
199,065,600,000 square inches consumed ÷ 1,200 minutes = 165,888,000 square inches per minute.
Therefore, the fire was burning at its highest rate at approximately 165,888,000 square inches per minute.
Units: square inches per minute.
learn more about square inches per minute
https://brainly.com/question/30100954
#SPJ11
At its highest rate, the fire was burning 16,588,800,000 square inches per minute.
First, find the area of one football field in square feet.
Area = length × width
Area = 360 feet × 160 feet
Area = 57,600 square feet
Convert the area to square inches. (1 foot = 12 inches)
Area = 57,600 square feet × (12 inches/foot) × (12 inches/foot)
Area = 829,440,000 square inches
Calculate the number of football fields burned per minute.
Since one football field was burned every 3 seconds,
we can find the number of football fields burned in a minute by dividing 60 seconds by 3 seconds.
Number of football fields burned per minute = 60 seconds / 3 seconds = 20 football fields
Calculate the total area burned per minute in square inches.
Area burned per minute = 20 football fields × 829,440,000 square inches/football field
Area burned per minute = 16,588,800,000 square inches.
For similar question on area.
https://brainly.com/question/25965491
#SPJ11
Any new purchases with a choice for exterior colors A, B, C, and D parentheses and three into your colors one, two, and three make an organized list unlock the first color combinations for the car
the first letter represents the exterior color, and the second number represents the interior color. So "A1" means exterior color A with interior color 1, "B2" means exterior color B with interior color 2, and so on.
A1
A2
A3
B1
B2
B3
C1
C2
C3
D1
D2
D3
Sure, here's an organized list of the first color combinations for the car with exterior colors A, B, C, and D, and interior colors 1, 2, and 3:
To learn more about combinations, visit
https://brainly.com/question/31596715
#SPJ1
The americans with disabilities act states that ramps must have an angle less than or equal to 4.8 degree angle in a right triangle has a 1:12 ratio for the legs. Select all designs of a ramp that meet the americans with disabilities act requirements. Answers to pick from : Right triangle with legs 3 meters and 33 meters. Right triangle with legs 1 meters and 15 meters. Right triangle with legs 12 meters and 140 meters. Right triangle with legs 12 meters and 150 meters. right triangle with legs 24 meters and 240 meters.
Answers are ,Right triangle with legs 3 meters and 33 meters, Right triangle with legs 1 meter and 15 meters, Right triangle with legs 12 meters and 140 meters, Right triangle with legs 12 meters and 150
what is Right triangle ?
A right triangle is a triangle that has one angle equal to 90 degrees (a right angle). The other two angles are acute angles (less than 90 degrees). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs.
In the given question,
The ratio of the legs of the right triangle for a ramp should be 1:12, which means that for every 1 inch of rise, there should be 12 inches of ramp length. To calculate the angle of inclination, we can use the inverse tangent function, which gives us the angle whose tangent is equal to the ratio of the legs. The angle of inclination should be less than or equal to 4.8 degrees.
Let's calculate the angle of inclination for each ramp design:
Right triangle with legs 3 meters and 33 meters:
The ratio of the legs is 3:33, which simplifies to 1:11. The length of the ramp is 11 times the height of the rise. The angle of inclination is:
arctan(1/11) ≈ 4.76 degrees
The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.
Right triangle with legs 1 meter and 15 meters:
The ratio of the legs is 1:15. The length of the ramp is 15 times the height of the rise. The angle of inclination is:
arctan(1/15) ≈ 3.81 degrees
The angle of inclination is less than or equal to 4.8 degrees, so this ramp design also meets the requirements of the Americans with Disabilities Act.
Right triangle with legs 12 meters and 140 meters:
The ratio of the legs is 12:140, which simplifies to 3:35. The length of the ramp is 35 times the height of the rise. The angle of inclination is:
arctan(3/35) ≈ 4.56 degrees
The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.
Right triangle with legs 12 meters and 150 meters:
The ratio of the legs is 12:150, which simplifies to 2:25. The length of the ramp is 25 times the height of the rise. The angle of inclination is:
arctan(2/25) ≈ 4.62 degrees
The angle of inclination is less than or equal to 4.8 degrees, so this ramp design meets the requirements of the Americans with Disabilities Act.
Right triangle with legs 24 meters and 240 meters:
The ratio of the legs is 24:240, which simplifies to 1:10. The length of the ramp is 10 times the height of the rise. The angle of inclination is:
arctan(1/10) ≈ 5.71 degrees
The angle of inclination is greater than 4.8 degrees, so this ramp design does not meet the requirements of the Americans with Disabilities Act.
Therefore, the ramp designs that meet the requirements of the Americans with Disabilities Act are:
Right triangle with legs 3 meters and 33 meters.
Right triangle with legs 1 meter and 15 meters.
Right triangle with legs 12 meters and 140 meters.
Right triangle with legs 12 meters and 150 meters.
To know more about Right triangle , visit:
https://brainly.com/question/6322314
#SPJ1
In ΔPQR, q = 77 inches, r = 38 inches and ∠P=57°. Find the area of ΔPQR, to the nearest square inch
To the nearest square inch, PQR has an area of about 1215 square inches.
We can apply the formula: to determine the area of PQR.
(1/2) * Base * Height = Area
where the height is the angle between any triangle side and the opposite vertex, and the base is any one of the triangle's sides.
The triangle's height can be determined using the angle and side lengths provided:
opposite/hypotenuse = sin(P)
Height divided by 77 is sin(57) times height, or 64.05 inches.
The formula can now be used to calculate the area:
The area is equal to (1/2) * QR * height, or 1215.19 square inches.
We obtain the result by rounding to the nearest square inch:
1215 square inches in size
Learn more about the similarity of triangles:
https://brainly.com/question/15367648
2. A teacher wants to determine whether his students have mastered the material in their statistics unit. Each student completes a pretest before
are in the table.
Student Prefest Score Posifest Score
2125
72
75
82
85
90
86
78
84
87
82
80
78
84
84
92
91
81
84
86
86
The teacher's null hypothesis is that #p=0 while his alternative hypothesis is >0. Based on the data in the table and using a significance
The P-value is 0.003, so he must reject the null hypothesis.
What is the correct P-value and conclusion?To determine the correct answer, we need to perform a statistical hypothesis test.
The null hypothesis is that the mean difference between pretest scores and posttest scores (μd) is equal to 0. The alternative hypothesis is that the mean difference is greater than 0.
To perform this hypothesis test, we can use a paired-sample t-test, since we have two sets of scores from the same students. The formula for the t-statistic is: t = (Md - μd) / (sd / sqrt(n))
Using the data from the table, we can calculate the mean difference, standard deviation, and t-statistic as follows:
Mean difference (Md) = 84.33 - 81.33 = 3
Standard deviation (sd) = 2.622
t-statistic = (3 - 0) / (2.622 / sqrt(18)) = 3.13
To find the p-value, we need to look up the t-distribution with 17 degrees of freedom (since we have 18 paired observations) and a one-tailed test (since the alternative hypothesis is one-tailed). At a significance level of 0.01 and 17 degrees of freedom, the critical t-value is 2.567.
The p-value is the probability of getting a t-statistic as extreme or more extreme than the observed t-statistic, assuming the null hypothesis is true. From the t-distribution table, we can see that the p-value corresponding to a t-statistic of 3.13 with 17 degrees of freedom is approximately 0.003.
Since the p-value is less than the significance level of 0.01, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean difference between pretest scores and posttest scores is greater than 0, indicating that the students have mastered the material in their statistics unit.
Read more about p-value
brainly.com/question/4621112
#SPJ1
What is the parabola of
The parabola representing the graph of the function y = 2x² + 3x + 1 is a concave up parabola.
How to classify a parabola as concave up or concave down?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The vertex is classified as a maximum or minimum depending on the term a, which multiplies x², as follows:
If a > 0, the vertex is a minimum, meaning that the parabola is concave up.If a < 0, the vertex is a maximum, meaning that the parabola is concave down.More can be learned about quadratic functions at https://brainly.com/question/1214333
#SPJ1
ANSWER ASAP AND PLEASE BE CORRECT FOR BRAINLIST
Question 12
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Question 13
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 14
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Answer:
1-There were about 483 principals in attendance.
2-The college will have about 640 students who prefer pie
3-histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
4-The correct option regarding which bus has the least spread among the travel times is given as follows:
Bus 18, with an median of 16
Hope you get them all right :)
a store sells 8 colors of balloons with at least 31 of each color. how many different combinations of 31 balloons can be chosen? apply the method of example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 31 balloons that can be chosen is 12620256 correct: your answer is correct. .
There are 12,620,256 different combinations of 31 balloons that can be chosen from the store's inventory of 8 colors, each with at least 31 balloons.
We can use the method of example 9.6.2, which involves using the combination formula. We know that there are 8 colors of balloons and at least 31 of each color. We have 8 options for the first balloon, 8 options for the second balloon, and so on, for a total of 8 options for each of the 31 balloons.
Using the combination formula, we can calculate the number of different combinations of 31 balloons that can be chosen as follows:
[tex]nCr = n! / (r! \times (n-r)!)[/tex]
where n is the total number of options (in this case, 8), and r is the number of items we are choosing (in this case, 31).
Plugging in these values, we get:
[tex]8C31 = 8! / (31! \times (8-31)!)[/tex]
[tex]= 8! / (31! \times (-23)!)[/tex]
= 87654321 / (313029...9(-23)(-24)(-25)...(-52))
= 12620256
Learn more about inventory here:
https://brainly.com/question/14184995
#SPJ4
air-usa has a policy of booking as many as 26 persons on an airplane that can seat only 25. (past studies have revealed that only 82% of the booked passengers actually arrive for the flight.) what is the expected number of passengers to arrive for the flight? expected number of passengers
For an AIR-USA flight which has a policy of booking as many as seat, With the past probability of the people to arrive for the flight, the expected number of passengers to arrive for the flight is equals to 21.32 ~ 21 persons.
Binomial distribution : From the name it's meaning comes out, (prefix 'bi' means two), so in a binomial distribution, there are two possible outcomes of an event. The expected value of a binomial distribution is the product of binomial parameters n and p. E[ X ] = n p --(1). We have a data of seat booking in air-usa. Number of seats available to seat in airplane = 25
Number of persons booked the seat in air USA = 26
On basis of past studies, probability that the booked passengers actually arrive for the flight = 82%
= 0.82
Let X be the number of people turning up for flight, for determining excepted number we will use above formula in equation(1). Here, binomial parameters are p = 0.82 and n= 26
Excepted number of passengers, E(X)
= n×p
= 26 × 0.82
= 21.32
Hence, the excepted number of passengers are 21.32.
For more information about excepted number , visit :
https://brainly.com/question/22383619
#SPJ4
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 49 is the most appropriate measure of variability to use to represent the spread of donations received by the charity in this data set.
what is statistics?
Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It involves the study of methods for designing experiments and surveys, analyzing and interpreting data, and making decisions based on data. Statistics plays an important role in a wide range of fields, including science, social science, economics, finance, engineering, and many others. It is used to draw conclusions, make predictions, and inform decision-making by providing a quantitative and objective approach to understanding and analyzing data.
The most accurate measure of variability to use for this data set is the range of 49. The range is the difference between the highest and lowest values in the data set, which in this case is 59 - 10 = 49. The range provides a simple and straightforward measure of the spread of the data and is useful when the data is not too skewed.
While the data in this set is skewed, the range is still an appropriate measure of variability because there are no extreme outliers that would significantly affect the range. The IQR (interquartile range) is another measure of variability that is useful for skewed data, but in this case, it would not be the most appropriate choice because the data set is not divided into quartiles and the IQR would not provide additional information beyond what the range already shows.
Therefore, the range of 49 is the most appropriate measure of variability to use to represent the spread of donations received by the charity in this data set.
To learn more about statistics from the given link
https://brainly.com/question/29093686
#SPJ1
a measure of association whose value may vary depending on which variable is considered the independent variable and which the dependent variable is called a(n) .
A measure of association whose value may vary depending on which variable is considered the independent variable and which is considered the dependent variable is called a directional measure of association.
This is because the value of the measure of association can change depending on the direction of the relationship between the two variables. Examples of such measures of association include regression coefficients, such as the slope coefficient in simple linear regression or the beta coefficients in multiple linear regression.
In these cases, the coefficient value will change if the direction of the relationship between the dependent and independent variables is reversed. Directional measures of association are statistical measures that are calculated based on the relationship between the dependent and independent variables. The value of the measure can vary depending on the direction of the relationship between the two variables.
For example, in simple linear regression, the slope coefficient represents the change in the dependent variable for each one-unit change in the independent variable. If the relationship between the two variables is positive (i.e., as the independent variable increases, the dependent variable also increases), the slope coefficient will be positive. However, if the relationship is negative (i.e., as the independent variable increases, the dependent variable decreases), the slope coefficient will be negative.
To know more about the Dependent variable, here
https://brainly.com/question/30665908
#SPJ4
please I need HELP!!!
Answer:
the answer is 0.77 yes that is the answer
Answer:
C. 0.64
Step-by-step explanation:
the answer is on the picture