An alien empire is considering taking over planet Earth, but they will only do so if the portion of rebellious humans is less than 10 % 10%10, percent. They abducted a random sample of 400 400400 humans, performed special psychological tests, and found that 14 % 14%14, percent of the sample are rebellious. Let's test the hypothesis that the actual percentage of rebellious humans is 10 % 10%10, percent versus the alternative that the actual percentage is higher than that. The table below sums up the results of 1000 10001000 simulations, each simulating a sample of 400 400400 humans, assuming there are 10 % 10%10, percent rebellious humans. According to the simulations, what is the probability of getting a sample with 14 % 14%14, percent rebellious humans or more?'

Answer:

Step-by-step explanation:

Hello!

Given the variables

X₁: Weight of a safety helmet for racers

X₂: Price of a safety helmet for racers

Note, there is n= 17 observed values for each variable so for all calculations I'll use this number and disregard the 18 mentioned in the text.

a) Scatterplot in attachment.

b) If you look at the diagram it seems that there is a negative linear regression between the price and the weight of the helmets, meaning, the higher the helmet weights, the less it costs.

c) The estimated regression equation is ^Yi= a + bXi

n= 17; ∑Y= 6466; ∑Y²= 3063392; ∑X= 1008; ∑X²= 60294; ∑XY= 367536

Y[bar]= 380.35; X[bar]= 59.29

[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{367536-\frac{1008*6466}{17} }{60294-\frac{(1008)^2}{17} } = -30.18[/tex]

[tex]a= Y[bar]- bX[bar]= 380.35-(-30.18)*59.29= 2169.77[/tex]

The estimated regression equation for the price of the helmets as a function of their weight is:

^Yi= 2169.77 -30.18Xi

I hope it helps!

Answer: pi/3

Step-by-step explanation:

correct on edge 2020

The equivalent value of trigonometric relation sin⁻¹ ( √3/2 ) = π/3

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

sin⁻¹ ( √3/2 ) = θ

Now , the value of θ is calculated by

In a triangle , sin θ = opposite / hypotenuse

So , sin θ = √3/2

The value of θ = 60°

So , the measure of 60° in radians is θ = π/3

Hence , the value of θ from the trigonometric relation is π/3

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Answer:

0.416667

Step-by-step explanation:

divide the length value by 12

happy to help:) mark me as brainliest pls

Answer:

B; {x|x<-8}

Step-by-step explanation:

Answer:

the answer is either x=√3+5 or -√ 3+5

Step-by-step explanation:

split it into 2 equations

Answer:

(x-5)(x-5) =3

X^2 -5x -5x +25 = 3

x^2 -10x +22 = 0

x1 = (-b + sqrt(b^2 - 4ac))/2a

a=1

b=-10

c= 22

x1 = (10 +sqrt((-10)^2- 4(1)(22))/2(1)

x1 = (10 + sqrt(100-88))/2

x1= (10 + sqrt(22))/2

x1= (10 + sqrt(4) x sqrt(3))/2

x1=(10 + 2 x sqrt(3))/2

x1 =5 +sqrt(3)

x2 = (-b - sqrt(b^2 - 4ac))/2a

x2 = 5 - sqrt(3)

Answer is C

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

Answer:

height = 140.875m

Step-by-step explanation:

Volume of first pyramid= base * height /3 = 230*147/3= 11270

if the base is 240, volume is remain -> height = volume *3 /base

                                                                            = 11270*3/240 =140.875m

Answer:

0.13

Step-by-step explanation:

1/10 + 3/100 =

10/100 + 3/100 =

13/100

Hope that this helps you and have a great day:)

Answer:

Height  = 5

Step-by-step explanation:

3.

[tex]y=\sec^3x+\cot^2(2x)[/tex]

Use the chain rule:

[tex]y'=(\sec^3x)'+(\cot^2(2x))'[/tex]

[tex]y'=3\sec^2x(\sec x)'+2\cot(2x)(\cot(2x))'[/tex]

[tex]y'=3\sec^2x(\sec x\tan x)-2\cot(2x)\csc^2(2x)(2x)'[/tex]

[tex]y'=3\sec^3x\tan x-4\cot(2x)\csc^2(2x)[/tex]

4.

[tex]y=\sin(cos(3x))[/tex]

Same as before:

[tex]y'=(\sin(\cos(3x)))'[/tex]

[tex]y'=\cos(\cos(3x))(\cos(3x))'[/tex]

[tex]y'=-\cos(\cos(3x))\sin(3x)(3x)'[/tex]

[tex]y'=-3\cos(\cos(3x))\sin(3x)[/tex]

Answer:

The athlete will run 200 kilometers.

A atleta percorrerá 200 quilômetros no total.

Step-by-step explanation:

She will run x kilometers.

She has already run 5/8 of the distance(5/8 of x), and still needs to run 75 kilometers.

So

[tex]\frac{5x}{8} + 75 = x[/tex]

[tex]x - \frac{5x}{8} = 75[/tex]

[tex]\frac{8x - 5x}{8} = 75[/tex]

[tex]3x = 8*75[/tex]

[tex]x = \frac{8*75}{3}[/tex]

[tex]x = 200[/tex]

The athlete will run 200 kilometers.

A atleta percorrerá 200 quilômetros no total.

Answer:

  see below for a graph

Step-by-step explanation:

To draw a graph on a grid, locate the point (4, -2) and use the slope to find another point. One such point will be 1 to the left and up 3*, at (3, 1). With two points, you can draw the line through them to complete the graph.

__

For a graphing tool that requires an equation, the point-slope form of the equation can be used:

  y -k = m(x -h) . . . . . a line of slope m through point (h, k)

For the given slope and point, the equation of the line is ...

  y +2 = -3(x -4)

  y = -3x +10

_____

* The slope is "rise" over "run". The slope of -3 means that a run of +1 will result in a rise of -3. The given point is already below the x-axis, so we don't really want to find more points farther down. In order to go up on a line with negative slope, we must choose a point to the left of the given one.

Domain (infinity,infinity)

Range (infinity,[tex]\sqrt{7}[/tex])

Answer:

6 inches per 1/2 of an hour

Step-by-step explanation:

in between 4 pm and 5 pm, the water level grows by 12 inches. in between 3:30 pm and 4 pm, the water level grows by 6 inches.

Answer:

173.15 yards is the distance from tee to hole.

Step-by-step explanation:

Please refer to the image attached.

Let A is the position of tee and where the golfer is standing.

C is the position of hole.

CB is the vertical distance between greens and tee.

Angle of elevation, [tex]\angle BAC = 12^\circ[/tex]

To find: side AC.

Using trigonometric functions, we know that value of sine is:

[tex]sin\theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]

Here [tex]\theta = \angle BAC = 12^\circ[/tex]

Perpendicular is side CB.

Hypotenuse is side AC.

[tex]sin12^\circ = \dfrac{\text{CB}}{\text{AC}}\\\Rightarrow \text{CB} = \dfrac{36}{sin12^\circ}\\\Rightarrow \text{CB} = 173.15\ yards[/tex]

Hence, 173.15 yards is the distance from tee to hole.

Answer:

Y=x-3/4

Step-by-step explanation:

slope intercept form

(slope=x)(1x=x)

Answer:

The common factors of 45 and 72 are 9, 3, 1

Step-by-step explanation:

Answer:

The GCF of these two numbers is nine.

Step-by-step explanation:

They share three common factors: 1, 3 and 9. The greatest out of all of those is 9. Hope this helps!

Answer:

  7(5 +2)

Step-by-step explanation:

From our knowledge of times tables, we know that ...

  35 = 5·7

  14 = 2·7

so the greatest common factor of 35 and 14 is 7. Factoring that out, we have ...

  35 +14 = 7(5 +2)

Answer:

200; 80% of 250 is 200

Answer:

Step-by-step explanation:

200

Answer:-1

Step-by-step explanation:

2(3x-4)+x-1=-16

Open brackets

6x-8+x-1=-16

Collect like terms

6x+x=-16+1+8

7x=-7

Divide both sides by 7

7x ➗ 7=-7 ➗ 7

x=-1

Answer:

x = -1

Step-by-step explanation:

Answer:

The graph of g(x) = |x - h| + k is a translation of h units horizontally and k units vertically of the graph of f(x) = | x |.

Hope this helps.

Answer:

H units horizontally, k units vertically

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer:

should be 20

Step-by-step explanation:

yes

Answer: She had added the Denominator, instead of finding the LCM.

Explanation: She should've multiplied them by a common number to equal a common Product, and replace the Denominator with the Product. (The correct denominator is 20, because 4 x 5 = 20, and 5 x 4= 20)

Answer:

2621440

Step-by-step explanation:

The 9th term of the geometric sequence 10, 40, 160, .........  will be 655,360.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The sequence is given below.

10, 40, 160, .........

The first term is 10 and the common ratio of the sequence will be given as,

r = 40 / 10

r = 4

Then the equation of the geometric sequence is given as,

aₙ = 10 · (4)ⁿ⁻¹

The 9th term of the geometric sequence will be given as,

a₉ = 10 · (4)⁹⁻¹

a₉ = 10 · 65,536

a₉ = 655,360

The 9th term of the geometric sequence 10, 40, 160, .........  will be 655,360.

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Answer:

9 times

Step-by-step explanation:

hope this helps

Answer:

9

Step-by-step explanation:

Mathematically, 9, although reality wise, you could flip the coin and get heads every time, or the opposite.

I think you mean mathematically though, so yes, it would be 9.

Step-by-step explanation:

a. 81 ÷ 9 = 9

b. 40 ÷ 5 = 8

c. 21 ÷ 3 = 7

d. 54 ÷ 6 = 9

e. 42 ÷ 7 = 6

f. 63 ÷ 9 = 7

g. 36 ÷ 4 = 4

h. 45 ÷ 9 = 5

i. 39 ÷ 3 = 12

j. 24 ÷ 6 = 4

Answer:

4x - 5y = 10

Step-by-step explanation:

Any line parallel to 4x - 5y = 35 will have the same equation EXCEPT that the constant will be different.

Starting with 4x - 5y = 35, replace x with the given x-coordinate -5 and the given y-coordinate -6, and finally the given 35 with the constant C:

4(-5) - 5(-6) = C, or

-20 + 30 = C.  Thus, C = 10, and the equation of the new line is

4x - 5y = 10

The equation of line is 4x - 5y = 10

A straight line's general equation is y = mx + c, where m is the gradient. On the y-axis, this number c is referred to as the intercept. Key Point y = mx + c is the equation for a straight line with a gradient of m and an intercept of c on the y-axis.

Given the points (-5,-6)

and parallel to line 4x - 5y = 35...…..(1)

the equation of line is (y - y₁) = m( x - x₁)

for parallel line condition the value of m is equal to both equations

converting eq. 1 in the form of y = mx + c

4x - 5y = 35

we get y = 4/5x -7

here m = 4/5 and c = -7

substitute the value of m in  equation of line

where y₁ = -6; x₁ = -5

(y - (-6)) = 4/5(x - (-5))

y +6 = 4/5(x+5)

simplify above eq. we get

4x - 5y = 20

Hence the equation of  the line that passes through the point (- 5, - 6) is  4x - 5y = 20

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Answer:B. Between 62​% and 78​% of all orders arrive on time. State whether the conclusion is correct or not and explain why. Choose the correct answer below.

Step-by-step explanation:

A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 90% confidence interval for the proportion of all orders that arrive on time is 89% ± 6%.

a) The correct answer is A

b) The correct answer is B

c) The correct answer is C

d) The correct answer is D.

e) The correct answer is B.

Here, we have,

a) Between 83% and 95% of all orders arrive on time.

The correct answer is A. This statement is correct.

b) 90% of all random samples of customers will show that 89% of orders arrive on time.

The correct answer is B. This statement is not correct. It implies certainty, but in reality, the statement refers to the confidence interval estimate for the proportion of orders that arrive on time based on the sample.

c) 90% of all random samples of customers will show that 83% to 95% of orders arrive on time.

The correct answer is C. This statement is not correct. No more than 95% of all orders arrive on time. The confidence interval represents the range within which the true proportion is estimated to fall, but it doesn't guarantee that all intervals will cover the true proportion.

d) The company is 90% sure that between 83% and 95% of the orders placed by the customers in this sample arrived on time.

The correct answer is D. This statement is not correct. The confidence interval provides an estimate of the proportion of orders that arrive on time, not a measure of the company's certainty.

e) On 90% of the days, between 83% and 95% of the orders will arrive on time.

The correct answer is B. This statement is not correct. It implies certainty about the proportion of orders arriving on time, but the confidence interval only provides an estimate based on the sample data and does not guarantee the exact proportion for every day.

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complete question:

A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 90% confidence interval for the proportion of all orders that arrive on time is 89% ± 6%. What does this mean? Are the conclusions below correct? Explain.

a) Between 83% and 95% of all orders arrive on time.

b)90% of all random samples of customers will show that 89% of orders arrive on time. c) 90% of all random samples of customers will show that 83% to 95% of orders arrive on time.

d) The company is 90% sure that between 83% and 95% of the orders placed by the customers in this sample arrived on time. e) On 90% of the days, between 83% and 95% of the orders will arrive on time.

a) Choose the correct answer below.

A. This statement is correct.

B. This statement is not correct. It implies certainty.

C. This statement is not correct. No more than 95% of all orders arrive on

D. This statement is not correct. At least 83% of all orders arrive on time.

The null and alternative hypothesis for the tests are:

H0: μ = 20

Ha: μ < 20

Given data:

In this situation, the null and alternative hypotheses can be formulated as follows:

Null Hypothesis (H0): The average weight loss of consumers who take the "fat-burner" pill is equal to 20 pounds.

Alternative Hypothesis (Ha): The average weight loss of consumers who take the "fat-burner" pill is less than 20 pounds.

In symbolic notation:

H0: μ = 20

Ha: μ < 20

where μ represents the population mean weight loss of consumers who take the "fat-burner" pill.

The null hypothesis assumes that the claim made by the company is accurate and that the average weight loss is indeed 20 pounds. The alternative hypothesis challenges this claim and suggests that the actual average weight loss may be less than 20 pounds, implying that the "hype" around the pill's effectiveness might be exaggerated.

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Answer:

I would love to help you but all I see is dots