A graduate student believes that people consider faces with more contrast between eye color and skin tone as more feminine. She identifies the null and alternative hypotheses as:
H₀: The level of contrast between eye color and skin tone does not affect how feminine a face is considered.
H₁: The level of contrast between eye color and skin tone affects how feminine a face is considered.

She chooses a significance level of 0.01. After she collects the data and computes the sample statistics, it is time for her to make a decision about H₀.
Check the two possible decisions that the graduate student can make given her choices of H₀ and H₁. Check all that apply.

There is not enough evidence to reject the hypothesis that the contrast between eye color and skin tone affects how feminine a face is considered.
There is not enough evidence to reject the hypothesis that the contrast between eye color and skin tone does not affect how feminine a face is considered.
There is enough evidence to reject the hypothesis that the contrast between eye color and skin tone affects how feminine a face is considered.
There is enough evidence to reject the hypothesis that the contrast between eye color and skin tone does not affect how feminine a face is considered.

What decision should the graduate student make if the test statistic is not inside the critical region?

A. The graduate student should reject the alternative hypothesis.
B. The graduate student should reject the null hypothesis.
C. The graduate student cannot reject the null hypothesis.


Suppose that the test statistic is 3.29 and the boundary to the critical region is 2.576. The test statistic is ____ the critical region. Therefore, the graduate student _____ reject the null hypothesis, and she _____ conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered.

Answer:

(-1, 5)

Step-by-step explanation:

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

Substitute the defined points into the formula:

[tex]\begin{aligned}\implies \textsf{Midpoint} & =\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ & =\left(\dfrac{0+(-2)}{2},\dfrac{9+1}{2}\right)\\\\& =\left(\dfrac{-2}{2},\dfrac{10}{2}\right)\\\\& =\left(-1,5\right)\end{aligned}[/tex]

Therefore, the midpoint of the segment with endpoints (-2, 1) and (0, 9) is (-1, 5).

Answer:

c. 12km/hr

Step-by-step explanation:

Speed = distance/time

Coffee shop: Divide distance traveled by time taken to get the speed in km/min, then convert minutes to hours, and finally simplify to calculate the speed in km/hr

4km/20min * 60min/1hr = 240km/20hr = 12km/1hr = 12km/hr

Other shop: Same task, in the question it already says he is traveling at the same rate so this is only useful to check your answer

10km/50min * 60min/1hr = 600km/50min = 12km/1hr = 12km/hr

The set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°

"It is a geometric transformation where all the points of an object are reflected on the line of reflection."

For the given question,

The Rectangle ABCD is formed by ordered pairs A at (-4, 2), B at (-4, 1), C at (-1, 1), D at (-1, 2)

The Rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at   (-4, -1), C" at (-1, -1) and D" at (-1, -2)

We can observe that the coordinates of ABCD are of the form (-x, y)  where x, and y, are positive numbers

The form of the ordered pair of the vertices of the A″B″C″D″ will be (-x, -y)

The coordinates of the point (-x, y) after a reflection over the y-axis would be of the form (x, y)

And after rotation of 180°, the coordinates would be (-x -y).

Hence, the set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°.

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The environmental threat in Japan and Korea that threatens food security is: B. soil erosion.

Soil erosion can be defined as the washing away of the top soil that supports plants growth and also contains vital nutrients for plants growth.

Crops are grown majorly on land. The disruption of soil nutrients by soil erosion poses a serious environmental threat to food security in both Japan and Korea. Therefore, the answer is: B. soil erosion.

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Answer:

27 cubic inches

Step-by-step explanation:

A cube by definition has all the side lengths equal to each other. Kind of like how a square has all equal sides, except with a cube, there's depth. So the volume of the cube would be the width*length*depth, but since the width=length=depth, you only need one side, and you just cube it, or raise it to the third power. So you have the equation: [tex]A=(3\text{ inches})^3=27\text{ inches}^3[/tex] which is read as 27 cubic inches

After calculation, the composite function f(g(0)) returns the value 2 as the response.

Given, the values of the functions are:

f(x) = √₋x₊1 and g(x) = ₋x₋3

we need to find f(g(0)) = ?

F of g of x is another name for a composite function. Normal representations include f(g(x)) or (f g)(x), which denote that x = g(x) should be used in place of f(x). While the function g (x) is referred to as an inner function, the function f (x) is referred to as an outer function.

It means that every instance of an x in the function f is replaced with the function g(x).

∵ g(x) = ₋x₋3  so we can substitute this in the following expression:

  g(0) = -(0) ₋ 3

    g(0) = ₋3

Now in place of g(0) we can write ₋3, hence the changed expression becomes:

f(g(0)) = f(₋3)

          = √₋(₋3)₊1

          = √4

∴ f(g(0)) = 2

Hence we get the calculated function value as 2.

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Answer:

How about 100 adults and 100 students?

Step-by-step explanation:

Could you respond?

Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

Given that:-

The time will be calculated by using the relative speed concept.

Relative speed = Speed of father - Speed of Tommy

Relative speed = 1.65 - 1.35

Relative speed = 0.3 meter per second

Relative speed = Distance / Time

0.3 = 720 / Time

Time = 720 / 0.3

Time = 2400 seconds = 2400/ 60 = 40 minutes

We know that both departed at 3 pm they will meet at 3:40 pm.

Therefore Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.

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The value of g(x) = 2[f(x)]² - 1 is g(x) = 8x² + 8x + 1

f(x) = 2x+1

Find

g(x) = 2[f(x)]² - 1

Hence,

g(x) = 2[2x + 1]² - 1

g(x) = 2[4x² + 4x + 1] - 1

g(x) = 8x² + 8x + 2 - 1

g(x) = 8x² + 8x + 1

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One of the two equations required in the system of equations needed to determine the dollar amount of phone and computer sales Houa made is y = x + 600.

Let x represents the dollar amount of phone sales Houa made, and y represents the dollar amount of computer sales she made.

Therefore, a system of equations that could be used to determine x and y can be written as follows:

y = x + 600 ........................................................... (1)

0.04x + 0.05y = 129 ......................................... (2)

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There are 36 possible combinations that can occur when 2 dice are rolled. For the sake of this question, we'll count instances where dice 1 = 3/dice 2 = 2 and dice 1 = 2/dice 2 = 3.

Now, let's think about all of the possible ways a total of 5 could be rolled.

1 + 4

2 + 3

3 + 2

4 + 1

That's 4 possibilities to roll a total of 5 out of 36 possible outcomes.

4 / 36 = ? / 180

---Now, we need to use a proportion in order to figure out the possibilities out of 180.

36x = 720

x = 20

If you rolled a pair of fair dice 180 times, you would expect to roll a total of 5, 20 times.

Hope this helps!

The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2

An equation is an expression that shows the relationship between two or more numbers and variables.

Dilation is the increase or decrease in size of a figure by a scale factor.

The scale factor of the image = K'T'/KT = 1/2 ÷ 1 = 1/2

The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2

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The account that yields the highest annual interest rate is account 2.

In order to determine the account that yields the highest interest, the effective annual interest has to be calculated. The effective annual interest is the interest rate that an account actually earns when compounding is accounted for.

Effective annual rate = (1 + APR / m ) ^m - 1

M = number of compounding

Account 2: (1 + 0.0325/12)^12 - 1 = 3.3%

Account 3 : (1 + 0.0310 / 52)^52 - 1 = 3.15%

Account 4: (1 + 0.0315 /365)^365 - 1 = 3.2%

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The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the function f(x) = -5(x + 7)

When x = -2; f(-2) = -5(-2 + 7) = -25

When x = -1; f(-1) = -5(-1 + 7) = -30

When x = 0; f(0) = -5(0 + 7) = -35

When x = 1; f(1) = -5(1 + 7) = -40

When x = 2; f(2) = -5(2 + 7) = -45

The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).

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Answer: 80.28 square feet

Step-by-step explanation:

[tex]2(6.1\cdot 3+3\cdot 2.4+2.4 \cdot 6.1)=80.28[/tex]

Answer:

a) 24 [cm]; b) 30°.

Step-by-step explanation:

a) the length of full the circle is: min_arc(AB)+maj_arc(AB)=π(22+2)=24π [cm]. Then the radius is: r=L/π; ⇒ r=24π/π=24 [cm];

b) if the full circle is 360° (L=24π), then m(∠AOB):2=360°:24 and the required measure of the acute angle AOB is:

m(∠AOB)=360*(1/12)=30°.

Answer:

second graph

Step-by-step explanation:

looking at the y intercept. 12 is y int

Answer:

Second line

Step-by-step explanation:

our equation rearranged is y=-3x+12

meaning that y-intercept is 12, that is where the line cuts the y axis

we find that the second line cuts the y axis around that 12 therefore it is the most relevant line here

Answer:

(-5-5x)/(4x+3

Step-by-step explanation:

Replace x with y to get (-3y-5)/(4y+5). Solve for y to get (-5-5x)/(4x+3).

By applying Cathetus theorem, the value of x is equal to 10 units.

In order to determine the value of x, we would apply Cathetus theorem (leg rule), which states that each leg of a right-angled triangle is the geometric mean that's directly proportional between the hypotenuse and the part of the hypotenuse that's directly below the leg.

In this context, we have:

x² = m × a

x² = (21 + 4) × 4

x² = 25 × 4

x² = 100

x = √100

x = 10 units.

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Using a calculator, the quadratic regression equation that fits the data is:

C. y = 2.13x² + 0.13x + 6.39

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are:

(-4,40), (-3,28), (-2, 10), (-1, 8), (0,7), (1,10), (2,16), (3,26), (4,40).

Hence the equation is:

C. y = 2.13x² + 0.13x + 6.39

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Answer:

Possibly 3

Step-by-step explanation:

Lets say

g=girls

b=boys

1st option: gbbbg

2nd option: bbbgg

3rd option: ggbbb

Answer:

9. 3 acute angles

10: a) Acute Isosceles

     b) Acute Scalene  

Step-by-step explanation:

9:  Sum of Interior angle theorem: Sum of the interior angles of a Triangle = 180°

An Acute angle is a angle that is less than 90°

the sum of the two acute angles must be less than 180°

The base angles of an isosceles triangle are congruent.

So For example,

the base angles of the isosceles are ∠1 and ∠2

Lets make the three angle measure closer:

if ∠1 = 46° then ∠2 also have to be 46° and ∠3 = 88°

all three angle are less than 90° and two angles are congruent.

Step-by-step explanation:

hggggggggggggggggggggg

Answer:

Step-by-step explanation:

[tex]\huge\boxed{\textsf{A.}\ 78.5\ \text{in}^2}[/tex]

Correction to your question text: diameter, not radius.

The area of a circle is given by:

[tex]A=\pi r^2[/tex]

The radius is half of the diameter.

[tex]A=\pi\cdot\left(\dfrac{10}{2}\right)^2[/tex]

Substitute and solve.

[tex]\begin{aligned}A&=\pi\cdot\left(\frac{10}{2}\right)^2\\&=\pi\cdot5^2\\&=\pi\cdot25\\&\approx\boxed{78.5}\end{aligned}[/tex]

Using the normal distribution and the central limit theorem, we have that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the parameters are given as follows:

[tex]\mu = 60, \sigma = 11, n = 12, s = \frac{11}{\sqrt{12}} = 3.1754[/tex].

Hence:

The probabilities are given by the p-value of Z when X = 61.2 subtracted by the p-value of Z when X = 59.3, hence, for a single individual:

X = 61.2:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{61.2 - 60}{11}[/tex]

Z = 0.11

Z = 0.11 has a p-value of 0.5398.

X = 59.3:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{59.3 - 60}{11}[/tex]

Z = -0.06

Z = -0.06 has a p-value of 0.4761.

0.5398 - 0.4761 = 0.0637.

0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.

For the sample of 12, we have that:

X = 61.2:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{61.2 - 60}{3.1754}[/tex]

Z = 0.38

Z = 0.38 has a p-value of 0.6480.

X = 59.3:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{59.3 - 60}{3.1754}[/tex]

Z = -0.22

Z = -0.22 has a p-value of 0.4129.

0.6480 - 0.4129 = 0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.

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Answer:

use a sin cos tan calculator.

Step-by-step explanation

on calculator

2nd tan

tan x = 30/8

there's ur answer

The regression equation of the table is y = 5.71x + 27.6

From the table of values, we have the following parameters:

[tex]\sum x = 1193[/tex]

[tex]\sum y = 6950[/tex]

[tex]\sum x^2 = 346337[/tex]

[tex]\sum xy = 2010500[/tex]

Calculate A using

[tex]A = \frac{\sum y * \sum x^2 - \sum x * \sum xy}{n\sum x^2 - (\sum x)^2}[/tex]

This gives

[tex]A = \frac{6950 * 346337 - 1193 * 2010500}{5 * 346337 - (1193)^2}[/tex]

Evaluate

[tex]A = \frac{8515650}{308436}[/tex]

Divide

A = 27.6

Calculate B using

[tex]B = \frac{n\sum xy - \sum x * \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

This gives

[tex]B = \frac{5 * 2010500 - 1193 * 6950}{5 * 346337 - (1193)^2}[/tex]

Evaluate

[tex]B = \frac{1761150}{308436}[/tex]

Divide

B = 5.71

The regression equation is represented as:

y = Bx + A

So, we have

y = 5.71x + 27.6

Hence, the regression equation of the table is y = 5.71x + 27.6

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let width be 'x'

according to the question,

length = 4x

perimeter = 100 cm

we know ,

perimeter of rectangle = 2(l+b)

100= 2(4x+x)

100= 10x

x= 10

then length = 4x = 4×10= 40

and , area of rectangle = l×b

= 40 × 10 = 400

area of rectangle is 400cm

Answer:

Step-by-step explanation:

let width=x

length=4x

2(x+4x)=100

2×5x=100

x=100/10=10

width=10 cm

length=4×10=40 cm

area=l×b=40×10=400 cm²