The reduced exact values for the root of f(x) = x² + 10·x - 5, obtained using the quadratic formula are; x = (-5 + √(30)) and x = (-5 - √(30))
What is the quadratic formula?The quadratic formula is a formula that is used to find the roots of a quadratic equation, by plugging in the coefficients of a quadratic equation into the formula.
The roots of the quadratic function, f(x) = x² + 10·x - 5, can be obtained using the quadratic formula as follows;
The quadratic formula, which can be used to find the roots of the quadratic function, f(x) = a·x² + b·x + c is; x = (-b ± √(b² - 4·a·c))/(2·a)
The function f(x) = x² + 10·x - 5, indicates;
a = 1, b = 10, and c = -5, therefore;
x = (-10 ± √(10² - 4 × 1 × (-5)))/(2 × 1) = (-10 ± √(120))/2
(-10 ± √(120))/2 = (-5 × 2 ± 2 × √(30))/2
(-5 × 2 ± 2 × √(30))/2 = (-5 ± √(30))/2
The roots of the quadratic function are;
x = (-5 + √(30))/2, and x = (-5 - √(30))/2
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write an equation of the parabola that passes through the point (-5,2) and has vertex (7,-2)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=7\\ k=-2\\ \end{cases}\implies y=a(~~x-7~~)^2 + (-2)\hspace{4em}\textit{we also know that} \begin{cases} x=-5\\ y=2 \end{cases} \\\\\\ 2=a(-5-7)^2-2\implies 4=a(-12)^2\implies 4=144a\implies \cfrac{4}{144}=a \\\\\\ \cfrac{1}{36}=a\hspace{9em} {\Large \begin{array}{llll} y=\cfrac{1}{36}(x-7)^2-2 \end{array}}[/tex]
Check the picture below.
g you are dealt a hand of three cards from a standard deck of 52 cards. a. how many different combinations of 3 cards can you possibly have? b. how many different combinations of 3 aces can you possibly have?
a) There are 22,100 possible combinations of 3 cards that can be drawn from a standard deck of 52 cards.
b) There are only 4 possible combinations of 3 aces that can be drawn from a standard deck of 52 cards.
How to find the possible combinations of 3 cards?a) The number of different combinations of 3 cards from a deck of 52 cards is given by the combination formula:
C(52, 3) = 52! / (3! * (52-3)!) = 22,100
Therefore, there are 22,100 possible combinations of 3 cards from a deck of 52 cards.
How to find the possible combinations of 3 aces?b) Since there are 4 aces in a standard deck of 52 cards, the number of different combinations of 3 aces is given by the combination formula:
C(4, 3) = 4! / (3! * (4-3)!) = 4
Therefore, there are only 4 possible combinations of 3 aces from a deck of 52 cards.
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In circle C, FG and FE are tangent segments, m
Choose the two answers that represent the angle measures of the central and circumscribed angles.
The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
What is angle?Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.
The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.
In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
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you want to display data on average number of points scored by the top 5 uci basketball players in the history of uci. which type of graph would be best?
A The histogram is the best graph showing the average scores of 5 UCI volleyball teams in UCI history. Because it allows us to divide the data into as many or as few groups as we want and clarify the comparison between them.
We would like to view the average points data of the top 5 UCI basketball players in UCI history. There are two types of charts used to present data. The first is a histogram and the second is a scatterplot. We have to decide which picture is the best. Now, as we know, scatter charts are used to plot observations based on points to show the relationship between two data sets. A histogram is a type of bar chart in which all values are divided. Divides the range of results in the data into classes or groups. It can help identify outliers or gaps in the data. After discussing the features of the two graphs, shows the average score of 5 UCI basketball players in UCI history, the histogram is the best choice here because it allows us to divide and share the difference between clearly.
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complete question:
The above figure complete the question..
you want to display data on average number of points scored by the top 5 uci basketball players in the history of uci. which type of graph would be best?
Only write the number.
Find VZ
Answer:
VZ = 72
XW = 48VW = 24YZ = 36VZ = ?
FINDING VZ:
XW / VW = VZ / YZ
48 / 24 = VZ / 36
*Simplify:
48 / 24 = VZ / 362 = VZ / 36*Multiply both sides by 36:
2 × 36 = VZ / 36 × 3672 = VZI don't know how's that even possible, but I did the same formula and solutions the pictures below show.
How many 6-digit numbers can be found using the digits from 1 to 6 if the number is less than 400000 and the even digits occupy the even places in descending order, answer should be 4
Answer
Step-by-step explanation:
Answer
Answer step-by-step explanation
7. Suppose that there is a rumour going around
your school that next year all weekends will
be extended to three days. Initially, on day 0,
five students know the rumour. Suppose that
each person who knows the rumour tells two
more students the day after they hear about
it. Also assume that no-one hears the rumour
more than once.
a) How many people will learn about the
rumour
i) on day 1?
ii) on day 2?
On day 1, each of the 5 people tells 2 more people, so 5 x 2 = 10 people now know the rumor, including the original 5.
a) How many people will learn about the rumour
i) on day 1?a) Let's first consider how the number of people who know the rumor grows each day:
On day 0, 5 people know the rumor.
On day 1, each of the 5 people tells 2 more people, so 5 x 2 = 10 people now know the rumor, including the original 5.
On day 2, each of the 10 people tells 2 more people, so 10 x 2 = 20 people now know the rumor, including the original 5 and the 10 from day 1.
i) Therefore, on day 1, a total of 10 people will know the rumor.
ii) On day 2, a total of 20 people will know the rumor.
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What is the value of the expression 8w−4j2 when w=0. 25 and j=0. 5?
The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.
The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.
First, we substitute w = 0.25 and j = 0.5 in the expression:
8(0.25) - 4(0.5)²
Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:
= 2 - 1
= 1
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The given question is incomplete, the complete question is:
What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?
Between which two integers does 7/3 lie Answer A 4 and 5 Answer B 1 and 2 Answer C 2 and 3 Answer D 3 and 4
We can conclude that 7/3 lies between the integers 2 and 3. So, correct option is C,
To determine between which two integers 7/3 lies, we can use division and rounding.
Dividing 7 by 3 gives 2 with a remainder of 1. Therefore, we can express 7/3 as the sum of 2 and a fraction:
7/3 = 2 + 1/3
Since the fraction 1/3 is less than 1/2, we can round down to 2. Therefore, we can conclude that 7/3 lies between the integers 2 and 3.
This question requires us to determine between which two integers the fraction 7/3 lies. One approach to solving this is to perform long division, which gives us a quotient of 2 with a remainder of 1. We can express 7/3 as the sum of the quotient and the fraction 1/3. Since 1/3 is less than 1/2, we round down to the nearest integer, which in this case is 2.
Answer C, 2 and 3, is the correct answer.
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can yall help me with this question this would rlly help me out!
Answer:
59.5[tex]cm^{2}[/tex]
Step-by-step explanation:
You have two shape: a square and a triangle
Square:
The area of a square is the sides squared
a = [tex]s^{2}[/tex] The side length is 7 (7 x 7 = 49)
a = [tex]7^{2}[/tex]
a = 49
Triangle:
a [tex]\frac{bh}{2}[/tex] The base times the height divided by 2
The base is 7 and the height is 3.
a = [tex]\frac{7x3}{2}[/tex] = [tex]\frac{21}{2}[/tex] = 10.5
Add the two areas together: 49 + 10.5 = 59.5
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jackie converted the fallowing decimals to fractions.
explain plisssss
Answer:
Step-by-step explanation:
To convert a fraction to a decimal, you divide the numerator by the denominator. The line in the middle of a fraction is essentially a large division sign.
Let's check Jackie's work
1/200 = 0.005
3/10 = 0.3
7/8 = 0.875
4/5 = 0.8
Jackie listed 7/8 as 0.625, which is incorrect. 7/8 is 0.875
So, 0.625 is your answer.
I NEED HELP ASAP IT'S DUE IN 20MIN
Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 5
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 7
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sports 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 8
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
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 scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
2. The appropriate measure of center for the given data is the median, and it equals 19.
5. We can predict that there were about 169 principals in attendance at the conference.
6. The best graphical representation for the teacher's data would be a bar graph.
7. A histogram is used to display continuous data, while a bar graph is used to display categorical data.
8. The correct circle graph to represent the data is titled "New York City Visitor's Transportation"
9. We can predict that the college will need about 1440 scoops of ice cream.
Median, bar chart, histogramAnswer 2:
The appropriate measure of center for the given data is the median, and it equals 19. We can determine this from the box plot since the line inside the box represents the median of the data, and the box itself represents the middle 50% of the data. Since the box extends from 17 to 21, we know that half of the data falls below 19 and half above, making it the median. The mean is not a good measure of center for this data because it can be influenced by outliers, which are present in this dataset.
Answer 5:
Since we know that 15 out of 80 people in the exhibit room were principals, we can assume that about 15/80 (or about 0.1875) of the attendees were principals. To estimate the number of principals in attendance, we can multiply this fraction by the total number of attendees:
0.1875 x 900 ≈ 169
Therefore, we can predict that there were about 169 principals in attendance at the conference.
Answer 6:
The best graphical representation for the teacher's data would be a bar graph. A bar graph is a useful way to display categorical data, such as the subject preferences of the students. Each subject can be represented by a bar, with the height of the bar representing the frequency or percentage of students who prefer that subject.
Answer 7:
The correct graph to display the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The bars should be labeled "Basketball" with a value of 17, "Baseball" with a value of 12, "Soccer" with a value of 27, and "Tennis" with a value of 44. A histogram is used to display continuous data, while a bar graph is used to display categorical data.
Answer 8:
The correct circle graph to represent the data is titled "New York City Visitor's Transportation" and has five sections labeled "Walk" at 30%, "Bicycle" at 6%, "Car Service" at 11.25%, "Bus" at 7.5%, and "Subway" at 20.25%. To calculate the percentages, we can divide the number of visitors for each mode of transportation by the total number of visitors (i.e., 300), then multiply by 100% to get the percentage.
Answer 9:
To estimate the number of students who prefer ice cream, we can add up the number of students who chose ice cream, which is 81. Then, we can set up a proportion:
81/225 = x/4000
where x represents the number of students who prefer ice cream out of the total population of 4000. Solving for x, we get:
x = 81 x 4000 / 225 = 1440
Therefore, we can predict that the college will need about 1440 scoops of ice cream.
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Solve the triangle
A
B
C
Find the missing measures in each diagram.
Answer:
X = 65°
Y = 75°
Z = 65°
Step-by-step explanation:
Hello!
Angle Y and the angle measuring 75 degrees are corresponding angles, and corresponding angles are congruent to each other in degree measure.
There is also another set of corresponding angles, and those are Angle Z and Angle X.
Since Angle Y and 75° are corresponding, we can state that Angle Y is also 75°. We can now find Angle Z by subtracting 40° and 75° from 180°. This is because the sum of angles in a triangle is 180°.
Angle Z:180° - 40° - 75°180°-115°65°The measure of Angle Z is 65°. We know that Z and X are corresponding, so X is also 65°.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
The radius of the circle is 3 units.
The center of the circle lies on the y-axis.
Step-by-step explanation:
The circle equation is :
x² + (y-1)² = 3²
center: (0, 1) The center of the circle lies on the y-axis.
Radius: 3 The radius of the circle is 3 units.
Please help me with this homework
Answer:
14
Step-by-step explanation:
c = 2[tex]\pi r[/tex]
c = 2[tex]\pi[/tex]7
x = 14[tex]\pi[/tex]
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I WILL GIVE BRAINLIEST TO THE BEST/CORRECT ANSWER
Point U is located at (5,2) on the coordinate plane. Point U is reflected over the y-axis to create point U'. Point U' is the reflected over the x-axis to create point U". What ordered pair describes the location of U"?
Answer:
(-5,-4)
Step-by-step explanation:
i think this is correct because i tried to solve in paper.
Correct 0.00025 to one Significant figure
Answer:
0.0003
Step-by-step explanation:
u don't count the zeros as a significant figure
5 rounds 2 up to 3
3. In raising a 7000 N motorcycle with a pulley system, the workers note that for every 3 m of rope pulled down- ward, the piano rises 0. 3 m. Show that 700 N is required to lift the motorcycle
If workers note that for every "3 m" of rope pulled down-ward, the piano rises 0.3 m, then we have shown that 700 N is required force to lift the motorcycle.
The term "Mechanical advantage" (MA) is defined as ratio of "output-force" to "input-force" in a machine.
In this case, the output force is the weight of the motorcycle (7000 N) and the input force is the force applied to pull the rope downward.
We use the formula for mechanical advantage in a pulley system, which is given by:
⇒ MA = (distance moved by the effort) / (distance moved by the load),
In this case, the distance moved by the effort is 3 m, and
The distance moved by the load is 0.3 m,
Substituting the values,
We get,
⇒ MA = 3/0.3,
⇒ MA = 10,
So, mechanical advantage of "pulley-system" is 10.
Now, we use mechanical advantage to calculate the required force to lift the motorcycle.
Since mechanical advantage is defined as the ratio of output force to input force, we can rearrange the formula as:
⇒ Input force = (Output force)/(Mechanical advantage),
Substituting values for "output-force" as 7000 N and "mechanical-advantage" as 10,
We get,
⇒ Input force = 7000/10,
⇒ 700 N,
Therefore, the required force to lift motorcycle is 700 N.
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the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?
Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.
Explain about the bell-shaped curve:A bell curve is a form of graph that is used to show how a collection of selected values are distributed; it often has a peak at the centre that tends to be normal, with low and high extremes tapering out rather symmetrically on either side.
Given that:
Mean = 42 with standard deviation of 4.
Now,
If mean = 42,
1 standard deviation (+1σ) above that mean = 42 + 4 =48
1 standard deviation (-1σ) below that mean = 42 - 4 = 38
By the empirical rule 68-95-99.7 rule:
68% of the given normal distribution data lies between -1σ and +1σ: That is between 38 - 48 requests.
And,
In the range 42 - 50 requests (between that mean and +1σ) is half of the given 68% : 68/2 = 34%
Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.
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Correct question:
the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?
Evaluate: a = 3, b = 6, c = 4 a •b + c
Answer:
Step-by-step explanation:(3)(6)+(4) = 18+4= 22
To help determine what types of clubs to offer at harding middle school the principal surveyed fifty 8th grades. Does the sampl fairly represent the population ? explain
To determine if the sample fairly represents the population, we need to consider whether the sample is representative and whether there is any bias present in the sampling process.
If the principal surveyed fifty 8th graders in a way that ensures that each 8th grader in the population has an equal chance of being selected, then the sample can be considered representative. This means that the sample accurately reflects the characteristics of the population, and any conclusions drawn from the sample can be applied to the population.
However, if the sampling process was biased in some way, the sample may not be representative of the population. For example, if the principal only surveyed 8th graders in one class or in one particular group, the sample may not be representative of the entire 8th-grade population at Harding Middle School. In this case, any conclusions drawn from the sample may not accurately reflect the entire population.
Therefore, the key factor in determining whether the sample fairly represents the population is the sampling method used. If the sampling method is random and unbiased, then the sample can be considered representative of the population.
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Find the point that partitions segment AB in a 2:1 ratio when A(1,3)B(7,8)
Answer:
X2 - X1 = 7 - 1 = 6
Y2 - Y1 = 8 - 3 = 5
L = (6^2 + 5^2)^1/2 = 7.81
2/3 L = 5.21 length of segment
Tan θ = 5 / 6 = .833 slope of line
θ = 39.8 deg
5.21 * sin 39.8 = 3.34
5.21 * cos = 39.8 = 4.00 gives length of line segments
x2 = 1 + 4 = 5
y2 = 3 + 3.34 = 6.34
(5, 6.34) = point 2/3 up the line
Check (length of line)
[(5 - 1)^2 + (6.34 - 3)^2]^1/2 =
l = 5.21 correct length for line segmet
Determine the number of real solutions of the system
y=X^2 + 8
y= X + 15
Answer:
2
Step-by-step explanation:
Graphing the system shows that the lines intersect twice, meaning there are two real solutions.
Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. −9. 5 − (−8) − 6. 5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. Then, show your work, and represent the answer as a single rational number
The value of the expression as a single rational number is -8.
Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:
= -9.5 - (-8) - 6.5
= -9.5 + 8 - 6.5 (replacing -(-8) with its positive equivalent 8)
= (-9.5 - 6.5) + 8 (grouping like terms)
= -16 + 8 (simplifying)
= -8
Therefore, the value of the expression is -8, which is a single rational number.
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Calculate the area of each of the polygons with the following dimensions.
1. Triangles
B = 4in, H = 5in
B = 6ft, H= 10ft
B = 12m, H = 15m
Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?
2. Parallelogram (H = height) and (B = base)
H = 9in, B = 6in
H = 5 ft, B = 2ft
H = 7yds, B = 3yds
Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?
Hint: Use the formula. Substitute the given values and then solve as an equation.
3. Rectangle (L = length) and (w = width)
rect. DKIF with L = 8 ft and w = 6 ft
rect. AOPU with L = 13 ft and w = 5 ft
Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.
4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)
rhombus with d1 = 12 yds and d2 = 12 yds
rhombus with d1 = 10 ft and d2 = 25 ft
rhombus with d1 = 16 in and d2 = 22 in
Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?
5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)
b1 = 6 ft, b2 = 7 ft, H = 10 ft
b1 = 5 yds, b2 = 8 yds, H = 4 yds
c. b1 = 9 in, b2 = 11 in, H = 13 in
d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?
The total area of two triangle tablecloths for one table = 8ft²,
height = 6mm,
The total area of the den = 430ft²,
height of the rhombus = 12ft,
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Triangles:
a) Area of triangle = 1/2 * base * height = 1/2 * 4in * 5in = 10in²
b) Area of triangle = 1/2 * base * height = 1/2 * 6ft * 10ft = 30ft²
c) Area of triangle = 1/2 * base * height = 1/2 * 12m * 15m = 90m²
Total area of two triangle tablecloths for one table = 2 * 1/2 * 2ft * 4ft = 8ft²
Parallelogram:
a) Area of parallelogram = base * height = 6in * 9in = 54in²
b) Area of parallelogram = base * height = 2ft * 5ft = 10ft²
c) Area of parallelogram = base * height = 3yds * 7yds = 21yds²
height = Area/base = 78mm²/13mm = 6mm
Rectangle:
a) Area of rectangle = length * width = 8ft * 6ft = 48ft²
b) Area of rectangle = length * width = 13ft * 5ft = 65ft²
Total area of the den = (2 * 9ft * 15ft) + (2 * 8ft * 10ft) = 270ft²+ 160ft² = 430ft². Charles has enough paint because one gallon of paint will cover 440 square feet of wall space.
Rhombus:
a) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 12yds * 12yds = 72yds²
b) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 10ft * 25ft = 125ft²
c) Area of rhombus = (1/2) * diagonal1 * diagonal2 = (1/2) * 16in * 22in = 176in²
height of the rhombus = 2(area/diagonal1) = 2(72ft²/12ft) = 12ft
Trapezoid:
a) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (6ft + 7ft) * 10ft = 65ft²
b) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (5yds + 8yds) * 4yds = 26yds²
c) Area of trapezoid = 1/2 * (base1 + base2) * height = 1/2 * (9in + 11in) * 13in = 130.5in²
d) Height of trapezoid = 2(area/(base1 + base2)) = 2(32km²/16km) = 4km
Hence, the total area of two triangle tablecloths for one table = 8ft²,
height = 6mm,
The total area of the den = 430ft²,
height of the rhombus = 12ft,
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highway accidents: dui the u.s. department of transportation, national highway traffic safety administration, reported that 77% of all fatally injured automobile drivers were intoxicated. a random sample of 27 records of automobile driver fatalities in kit carson county, colorado, showed that section 8.3 testing a proportion p 479 15 involved an intoxicated driver. do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in kit carson county? use a 5 0.01.
The highway accident evidence to reject the null hypothesis that the population proportion is equal to 77%.
No, these data do not indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County.
The sample proportion of 15 out of 27 is 56.25%, which is not significantly different from the population proportion of 77%.
The p value for this test is 0.788, which is greater than the alpha level of 0.01.
The p value of this test indicates that the sample proportion of 15 out of 27 (56.25%) is not significantly different from the population proportion of 77%.
This means that there is not enough evidence to reject the null hypothesis that the population proportion is equal to 77%.
The p value of 0.788 is greater than the alpha level of 0.01, meaning that the results of this test are not statistically significant enough to support the alternative hypothesis that the population proportion is less than 77%.
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Please help ASAP!
A clinical trial is performed to test a new drug designed to lower blood sodium levels. One hundred fifty participants are randomly assigned to take the new drug, and 150 participants are randomly assigned to take a placebo. After 6 months of treatment, blood sodium levels are measured and compared to the starting levels. For those who took the new drug, the blood sodium levels had a mean reduction of 27 points with a standard deviation of 5.2, while for those who took the placebo, the blood sodium levels showed a mean reduction of 22 points with a standard deviation of 3.9. Assuming the standard deviations are true for the entire population, calculate 90% confidence intervals and evaluate whether there is evidence the new drug is working.
A: The interval for the new drug is from 26.168 to 27.832 points. The interval for the placebo is from 21.376 to 22.624 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is working.
B: The interval for the new drug is from 26.302 to 27.698 points. The interval for the placebo is from 21.476 to 22.524 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is not working.
C: The interval for the new drug is from 26.302 to 27.698 points. The interval for the placebo is from 21.476 to 22.524 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is working.
D: The interval for the new drug is from 26.168 to 27.832 points. The interval for the placebo is from 21.376 to 22.624 points. Since the interval for the new drug lies above the interval for the placebo, there is evidence that the drug is not working.
The answer to the question is C
Is the following a statistical question?
How tall are buildings in Manhattan?
PLEASE HELP,I HAVE A BAD MEMORY!!
Answer:
at least 115 feet (35m)
Step-by-step explanation:
Gia made a garden stone shaped like a regular octagon with the dimensions shown. Find the area of the octagon.
5.5 in.
4.6 in.that is the area of the octagon but what is the answer???
Area of the octagon is 85.5591 in².
What is octagon?
The fundamental characteristics of a regular octagon. There are 8 interior angles and 8 sides. Both the length of each side and the measurement of each angle are equal. A regular octagon has a total of 20 diagonals. Each inner angle is 135 degrees in length. This means that (135 x 8) = 1080 degrees is the total of all interior angles. An octagon is a polygon that has 8 sides. An octagon is referred to as a regular octagon if all 8 of its sides are equal in length and all of its angles are equal.
Area of rectangular octagon = 2a² (1 + √2) , where a is side
= 2 * (5.5)² ( 1+√2)
= 2 * 30.25(1+√2)
= 60.5 (1+√2)
= 60.25(1 + 1.4142)
= 60.25 * 2.4142
= 85.5591 in²
Therefore, Area of the octagon is 85.5591 in².
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