Given the set of data, we can calculate that the mean is 9.5, the variance is 17.58 and the standard deviation is 4.19
Mean, variance, and standard deviation
The concepts of mean, variance and standard deviation are very basic but very important in statistics.
Mean is the average of all data in a sample group, which is obtained by adding up all the data values, then dividing by the number of samples.
[tex]mean = \frac{sum all of the data}{size of data}[/tex]
Variance is a value that describes the variation of data, by measuring how far each piece of data is spread from the average of a data set.
[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]
Standard Deviation is a measure of the spread of observations in a data set relative to their mean. it measures how many observations in a data set differ from the mean and is the square root of the variance.
σ = [tex]\sqrt{variance}[/tex]
Now we can calculate the mean of the given data as follows:
[tex]mean = \frac{sum all of the data}{size of data}[/tex]
= (3 + 6 + 8 + 12 + 13 + 15) / 6
= 57 / 6
= 9.5
Then we can calculate the variance as follows:
[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]
= [tex]\frac{((3-9,5)^{2} + (6-9,5)^{2} + (8-9,5)^{2} + (12-9,5)^{2} + (13-9,5)^{2} + (15-9,5)^{2} )}{6}[/tex]
= (42,25 + 12,25 + 2,25 + 6,25 + 12,25 + 30,25) / 6
= 105.5 / 6
= 17.58
Standard deviation can be calculated from the variance:
σ = [tex]\sqrt{variance}[/tex]
= [tex]\sqrt{17.58}[/tex]
= 4.19
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Find the height and area of the polygon. Round your answer to the nearest thousandths (Use exact values until the end).
Answer:
height 6 radicAL 2 area: 120 radical 2
Step-by-step explanation:
9)
5.6 yd
5 yd
12 yd
Find the area. (A = 1/2 ( 61 + b2) h)
Answer:
Area, A = 63.6 square yards
Step-by-step explanation:
A trapezoid refers to a quadrilateral that is convex in shape; as such it has no equal sides and no parallel sides.
Let the height of a trapezoid be h.
Let the top base of a trapezoid be b1.
Let the bottom base of a trapezoid be b2.
[tex] Area \; of \; trapezoid = \frac {1}{2} * (Sum \; of \; nonparallel \; sides) * height [/tex]
Therefore, [tex] Area \; of \; trapezoid = \frac {1}{2} * (b_{1} + b_{2}) * h [/tex]
Given the following data;
Length, b1 = 5 yards
Width, b2 = 5.6 yards
Height, h = 12 yard
To find the area of geometrical shape (trapezoid), we would use the above formula;
A = 1/2 (b1 + b2) * h
Substituting into the formula, we have;
A = ½ * (5 + 5.6) * 12
A = ½ * (10.6)*12
A = 5.3 * 12
Area, A = 63.6 square yards
The U.S. and many other countries have recently tightened airport security. A sociologist is interested in estimating the proportion of the travelers who feel that airports are safe. The sociologist found that 375 of the 500 travelers randomly selected and interviewed indicated that the airports were safe. With an alpha level of 0.05, conduct a test to determine whether the true proportion of interest is higher than 0.7.
Answer:
0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.
Step-by-step explanation:
Conduct a test to determine whether the true proportion of interest is higher than 0.7.
This means that the null hypothesis is: [tex]H_{0}: p = 0.7[/tex]
And the alternate hypothesis is: [tex]H_{a}: p > 0.7[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that [tex]\mu = 0.7, \sigma = \sqrt{0.7*0.3}[/tex]
The sociologist found that 375 of the 500 travelers randomly selected and interviewed indicated that the airports were safe.
This means that [tex]n = 500, X = \frac{375}{500} = 0.75[/tex]
Value of the z-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.75 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{350}}}[/tex]
[tex]z = 2.44[/tex]
P-value of the test:
Probability of z being larger than 2.44, that is, a proportion larger than 0.75.
This is, looking at the z-table, 1 subtracted by the pvalue of Z = 2.44. S
Z = 2.44 has a pvalue of 0.9927
1 - 0.9927 = 0.0073
0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.
What is the surface area of the cylinder with height 5 mi and radius 6 mi? Round your answer to the nearest thousandth.
Step-by-step explanation:
Given
h = 5 mi
r = 6 mi
Surface Area of Cylinder =
[tex]2\pi \: rh + 2\pi {r}^{2} \\ = 2\pi(6)(5) + 2\pi ({6}^{2}) \\ = 2\pi(30) + 2\pi(36) \\ = 60\pi + 72\pi \\ = 132\pi \\ = 414.690 {mi}^{2} (nearest \: thousandth)[/tex]
Answer: 414.69 m2
Step-by-step explanation:
A square patio has a side length of (x − 8) feet. It is surrounded by a flower garden with a uniform width. The side length of the entire square area including the patio and the flower garden is (x + 8) feet. Enter an expression for the area of the flower garden.
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Answer:
32x ft²
Step-by-step explanation:
The area of the garden plus patio is ...
(x +8)² = x² +16x +64
The area of the patio is ...
(x -8)² = x² -16x +64
The area of the flower garden is the total area less the patio area:
(x² +16x +64) -(x² -16x +64) = 32x . . . area of the flower garden
Can someone help me pls
Answer:
Oops, didn't mean to answer because I already answered this one.
Step-by-step explanation:
4x+15 what is the value of X
Answer:
No solution
Step-by-step explanation:
4x+15 doesn't equal anything so it's impossible to solve.
Unless you forgot to add what it equals I can't solve it for you :(
subtract and simplify 1/6m - (-5/8 m +1/3)
show full work
Answer:
11/24
Step-by-step explanation:
first we work out the bracket -5/8+1/3= -7/24. then 1/6 - -7/24 two negatives means you will add to get the answer
I need to find the area, I just need to show my work any answers can help.
Vladimir hit a home run at the ballpark. A computer tracked the ball's trajectory in feet and modeled its flight path as a
parabola with the equation, y = -0.003(x – 210)2 + 138. Use the equation to complete the statements describing the
path of the ball.
Answer:
The vertex of the parabola is
✔ (210, 138)
The highest the ball traveled was
✔ 138
feet.
Step-by-step explanation:
Edge 2022
A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The highest the ball has travelled is 138 feet.
What is an equation of a parabola?A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.
y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower the parabola is, and the "-" or "+" that the parabola will open up or down.
A.) In the given quadratic equation, the vertex of the equation is y=-0.003(x-210)² + 138 is (210,138).
B.) Since the vertex is the highest point, therefore, The highest the ball has travelled is 138 feet.
The complete question is,
Vladimir hit a home run at the ballpark. A computer tracked the ball's trajectory in feet and modelled its flight path as a parabola with the equation, y = -0.003(x – 210)2 + 138. Use the equation to complete the statements describing the
path of the ball.
The vertex of the parabola is ?
The highest the ball travelled was? Feet
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Need help ASAP giving away 15 points will mark brainlyist as well
Answer:
1. < 11
2. < 5
3. < 1
4. x=38
5. x=25
6. x=6
7. x=18
8. x=52
9. x=15
10. x=12
Step-by-step explanation:
1. Vertical Angles
2. complementary angles= 90
3. vertical Angles
4. Supplementary Angles- 4x+28=180
5. vertical Angles :2x+5=55
6. Right Angle: 7x+8x=90
7. Supplementary Angles: 119+3x+7=180
8. vertical Angles: 3x=156
9. vertical angles: 8x-4=116
10. right angles: 3x+7+4x-1=90
Will give brainliest and 50 points to who ever gives me the answer and not a link
Find the surface area of the
triangular prism.
10 ft.
3 ft.
ft.
3 ft.
[?] sq ft.
A snowball has a diameter of 6 centimeters. How long would it take the snowball to melt if it melts at a rate of 1.8 cubic centimeters a minute.
Which point graphed below has an x-coordinate that is less than 0 and a y-coordinate that is greater than 0?
O Point L
O Point M
O Point N
O Point o
v=10 e=5
2v divided by e + 4
What is the tan M, sin M and Cos M?
I hope this helps you
tgM=39/80
sinM=39/89
cosM=80/89
Help please will mark brainliest
Answer:
SA = 638 mi²Steps:
SA = 2L² + 4(LH)
SA = 2×11² + 4(11×9)
SA = 2×121 + 4×99
SA = 242 + 396
SA = 638 mi²
A human resources manager selected a random sample of 200 workers who donate to charity. The following table shows the distribution of the 200 workers.
Count Type of worker Management Other white collar 96 50 S Blue collar 54
The manager conducts a goodness-of-fit test to determine whether the proportions of workers of these types are identical to the population proportions of workers donating to charity, which are 50 percent for management, 30 percent for other white-collar workers, and 20 percent for blue-collar workers. Which of the following statements must be true about the sample?
A. The expected number of blue-collar workers donating to charity is less than 30.
B. The expected number of management workers donating to charity is 100.
C. The expected numbers of other white collar and blue-collar workers donating to charity are the same.
D. The expected number of other white-collar workers donating to charity is 50
E. The combined expected numbers of other white collar and blue-collar workers donating to charity is greater than the expected number of management workers donating to charity.
Answer: B the expected # of management workers donating to charity is 100
Step-by-step explanation:
50% = management so, .50(200)=100
The difference between a blue-collar worker and a white-collar worker is Blue-collar workers are unskilled, manual laborers, and white-collar workers are professionals or semiprofessionals.
Thus the correct option is D.
What is a white-collar worker?White collar employees refer to individuals who work as a salaried employees in a professional workspace. They work on the managerial profile or executive profiles also clerical positions. This type of worker has a particular office setting in which they perform their task.
here, we have,
Blue collar employees refer to an individual who does not work on salaries instead they receive daily wages on the basis of the number of hours they spent. These refer to laborers or workers who do not have any qualifications or skills to perform the task.
Therefore, option D is appropriate.
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complete question:
What is the difference between a blue-collar worker and a white-collar worker? O White-collar workers must wear a shirt and tie to work, but blue-collar workers can dress casually. thing O White-collar workers keep their clothes clean during the course of the workday, and blue-collar workers do not. O Blue-collar workers have defined work clothes or protective attire, while white-collar workers wear white shirts. O Blue-collar workers are unskilled, manual laborers, and white-collar workers are professionals or semiprofessionals.
Choose all the weights that are equal to 1 ton 200 pounds.
A.
35,000 ounces
B.
1,200 pounds
C.
2,200 pounds
D.
1,200 pounds 100 ounces
E.
1 ton 100 pounds 1,600 ounces
PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS ANSWER IF U DONT I WONT RATE BRAINLYEST IF U DONT U DUM
C and E i did it and got it right and Np
Gabby draws a line segment to connect points (2,1) and (7,4). She draws a second lien segment that is parallel to the first one by connecting the points at (2,3) and (7,6). If she wants to draw a third line segment parallel to the ones she has already drawn, what ordered pairs could she use?
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Answer:
(2,5) and (7,8)
Step-by-step explanation:
Gabby has increased the y-coordinates by 2 units to get her first parallel line. She can do the same thing again to get the second parallel line.
(2, 3+2) = (2, 5)
(7, 6+2) = (7, 8)
Hello pleasee!!!!!!!!!!!!
Answer: go to I think it’s c but try a math solver to trust my answer
Step-by-step explanation:
Hope this helps
Sasha selected a random sample of bivariate data, with a sample size of 30, and calculated a slope of 3.6 for the sample slope of a regression model. Sasha constructed a 95 percent confidence interval to estimate the slope. Alex claims he can construct a confidence interval that is narrower by changing the sample size but keeping all other things the same. Which of the following sample sizes will make Alex's claim true?
A. 10
B. 15
C. 20
D. 25
E. 35
The sample size that will make the Alex's claim true is option E. 35.
What is Confidence Interval?Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.
This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.
Sample size of Sasha = 30
She took a confidence interval of 95%.
Alex claims he can construct a confidence interval that is narrower by changing the sample size but keeping all other things the same.
The relation between the sample size and confidence interval is that when the size of sample increases, the confidence interval becomes narrower.
So if the Alex's claim has to be true, sample size must increase.
He can use sample size of 35.
Hence the correct option is E.
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ale.
2 Emily saw an anaconda snake at the zoo
that was 24 feet 6 inches long. Which
equation can Emily use to find L, the length
of the snake in inches only?
QL = (24 + 12) + 6
QL = (24 x 10) + 6
L = (24 + 6) + 12
L = (24 * 12) + 6
eset in
5
Answer:
L=(24*12) + 6
Step-by-step explanation:
24 feet by 12 since each foot is 12 inches after that you'll need to add the rest of the inches you've already measured which is why you add 6
why does nobody talk to circles?
why does nobody talk to circles? :3
Answer:
Is this a joke
Step-by-step explanation:
I don’t know the answer
Maybe it’s “Because there is no point”
Evaluate the expression \dfrac{4^x}{2^x}
2
x
4
x
start fraction, 4, start superscript, x, end superscript, divided by, 2, start superscript, x, end superscript, end fraction for x=3x=3x, equals, 3.
Answer:
4
Step-by-step explanation:
(2)²ˣ/2ˣ is the expression equivalent to 4ˣ/2ˣ.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 4ˣ/2ˣ.
start fraction, 4, start superscript, x, end superscript, divided by, 2, start superscript, x, end superscript, end fraction for x=3x=3x, equals, 3.
In the given expression x is the variable and division is the operator.
Which means Four to the power of x and divided by two to the power of x.
4ˣ/2ˣ.
The numerator 4ˣ can be written as (2)²ˣ
(2)²ˣ/2ˣ
Hence, (2)²ˣ/2ˣ is the expression equivalent to 4ˣ/2ˣ.
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help lol don’t understand smart teacher math awesome simple lol geometry brainlyesy
Answer:
1. square, 28cm^2
2. triangle, 60ft^2
3. trapezoid, 21ft^2
4. pentagon, 30cm^2
Step-by-step explanation:
The length of a rectangle is 5 centimeters less than twice its width. Its area is 63 square centimeters.
Find the dimensions of rectangle
Answer:
I think the Length is 5 cm and the width is 7 cm
Step-by-step explanation:
The library has allotted $480 for spring landscaping and has decided
to spend the money on flowering bushes. There is room to plant a total
of 36 bushes. Rose bushes cost $25 each and lavender bushes cost $5
each.
a. (2 PTS) Define your variables.
b. (3 PTS) Write an equation to represent the total number of bushes you
can purchase.
c. (3 PTS) Write an equation to represent the total cost of the bushes.
d. (3 PTS) How many of each type of bush should you purchase?
Answer:
a. x = roses
y= lavender
b. x + y=36
c. 25x + 5y = 480
d. 19 rose bushes and 1 lavender bush
evaluate the intergral2x(xsquared+3)exponent 4
Answer:
(x^2+3)^5/5 + C
Step-by-step explanation:
Here substitute u = x^2 + 3 , du/dx = 2x ---> dx= 1/2x du
Then: integral (u^4) du
Apply power rule: u^5/5
Then replace the substitution u=x^2+3 in u
= (x^2+3)^5/5 + C
Find the value of "x"