Comparing the medians, we can see that the median length of alligators in Swamp A and Swamp B is the same, which suggests that the two swamps may have similar populations of alligators in terms of length.
What is median?
Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.
To compare the lengths of the alligators from two different swamps using medians, we need to collect data on the lengths of alligators from each swamp. Then we can calculate the median length of alligators in each swamp and compare them.
Let's say we have collected the following data on the lengths of alligators from Swamp A and Swamp B:
Swamp A: 4 feet, 5 feet, 6 feet, 7 feet, 8 feet
Swamp B: 3 feet, 5 feet, 6 feet, 7 feet, 9 feet
To find the median length of alligators in Swamp A, we need to arrange the lengths in order from smallest to largest: 4, 5, 6, 7, 8. The middle value is 6, so the median length of alligators in Swamp A is 6 feet.
To find the median length of alligators in Swamp B, we also need to arrange the lengths in order from smallest to largest: 3, 5, 6, 7, 9. The middle value is also 6, so the median length of alligators in Swamp B is also 6 feet.
Comparing the medians, we can see that the median length of alligators in Swamp A and Swamp B is the same, which suggests that the two swamps may have similar populations of alligators in terms of length. However, it is important to note that this comparison is based only on the median length and not on the full distribution of alligator lengths, so it is possible that there are other differences between the two populations of alligators that are not captured by this comparison.
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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]
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%
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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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
A science class is doing an experiment with a model rocket. The rocket shoots straight up in the air, and the students record the time it takes for the rocket to hit the ground. The height of the rocket at time t, in seconds, is given by the equation y = -2(t – 2)2 + 12, where y is in meters.
If the initial height of the rocket is the height of the rocket at time t = 0, what is the initial height of the rocket?
Answer:
To find the initial height of the rocket, we need to determine the height of the rocket when t = 0, since that is the initial time.
Substituting t = 0 into the given equation, we get:
y = -2(0 – 2)2 + 12
y = -2(-2)2 + 12
y = -2(4) + 12
y = 8
Therefore, the initial height of the rocket is 8 meters.
Step-by-step explanation:
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
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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.
If y=3, then -3+y2 =
Answer:
The answer is 6
Step-by-step explanation:
y=3
-3+y²
-3+(3)²
-3+6=6
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
a survey of an urban university showed that 1,010 of 1,500 students sampled supported a fee increase to fund improvements to the student recreation center. using the 95% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase
The 95% confidence interval for the proportion of students supporting the fee increase is (0.6453, 0.7013), indicating with 95% confidence where the true proportion of supporters is likely to fall based on the sample data.
How to find the confidence interval for the proportion?Using the given information, the sample proportion of students supporting the fee increase is 1,010/1,500 = 0.6733. To find the confidence interval for the population proportion, we can use the formula:
CI = p ± z*√(p(1-p)/n)
where p is the sample proportion, z is the z-score corresponding to the level of confidence (95% in this case), and n is the sample size.
Using a standard normal distribution table or calculator, the z-score for a 95% confidence level is approximately 1.96.
Plugging in the values, we get:
CI = 0.6733 ± 1.96 * √(0.6733*(1-0.6733)/1500)
CI = 0.6733 ± 0.028
Therefore, the 95% confidence interval for the proportion of students supporting the fee increase is (0.6453, 0.7013) to the nearest thousandth.
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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.
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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.
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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.
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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.
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The complete question is:
For his phone service, Omar pays a monthly fee of $28, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $97.65. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes, and solve your inequality for m.
Answer: 1393 m
Step-by-step explanation: Because first you are going to subtract the fee (28) and the least charged month (97.65) that is 69.65 and then you are going to divide that number by 0.05 to get the mins that is 1393
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.
In triangle ∆ABC, m<A = 33°, m<C = 58°, and AB = 25 in. What is AC to the nearest tenth of an inch?
1. 16.1 in.
2. 38.9 in
3. 42 in.
4. 12 in.
The value of AC to the nearest tenth is 29.5
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Angle B = 180-(33+58)
= 180-91 = 89°
using sine rule
represent AC by x
x/ sin89 = 25/sin 58
xsin58 = 25sin89
0.848x = 0.9998×25
0.848x = 24.995
x = 24.995/0.848
x = 29.5( nearest tenth)
therefore the value of AC is 29.5.
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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.
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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 :)
You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than 0. 16.
With H1 : p < 0. 16 you obtain a test statistic of z=−2. 683.
Use a normal distribution calculator and the tet statistic to find the P-value accurate to 4 decimal places. It may be left-tailed, right-tailed, or 2-tailed.
P-value =
The p-value for the given hypothesis test is 0.0037 (accurate to 4 decimal places)
To find the p-value, we need to use the standard normal distribution table or a calculator. Since the alternative hypothesis is left-tailed, we are interested in finding the area under the curve to the left of the observed test statistic z.
Using a standard normal distribution calculator, we find that the area to the left of z = -2.683 is 0.0037 (rounded to 4 decimal places). This represents the p-value for the hypothesis test.
Therefore, we can conclude that there is strong evidence to reject the null hypothesis at a significance level of 0.05, since the p-value of 0.0037 is less than the chosen significance level. The evidence suggests that the accuracy rate for fingerprint identification is significantly less than 0.16.
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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:
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i need the answer loololololololol
The standard format of the polynomial given in the image is given as follows:
0.5x^5 - x^4 - 5x² - 6.
How to obtain the standard format of the polynomial?The standard format of a polynomial is to write it in descending order of the exponents of the variable, with each term separated by a plus or minus sign. For example, the standard format of a polynomial with one variable (x) is:
a_nx^n + a_{n-1}x^{n-1} + ... + a_2x^2 + a_1x + a_0
The exponents of the polynomial in this problem are given as follows:
5, 0, 4, 2.
Hence the descending order is:
5, 4, 2, 0.
And the standard format of the polynomial is of:
0.5x^5 - x^4 - 5x² - 6.
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