Many students brag that they have more than 150 friends on a social media website. For a class​ project, a group of students asked a random sample of 13 students at their college who used the social media website about their number of friends and got the data available below. Is there strong evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150?

Required:
a. Find and interpret the test statistic value.
b. Report and interpret the P-value and state the conclusion in context. Use a significance level of 0.05.
c. What does the test statistic value represent?

1. The test statistic value is the difference between the sample mean and the null hypothesis value.
2. The test statistic value is the number of standard errors from the null hypothesis value to the sample mean.
3. The test statistic value is the expected mean of the differences between the sample data and the null hypothesis value.
4. The test statistic value is the number of standard deviations from the null hypothesis value to the sample mean.

Answer:

y = 3x + 9

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 4 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation of the parallel line

to find c substitute (1, 12 ) into the partial equation

12 = 3 + c ⇒ c = 12 - 3 = 9

y = 3x + 9 ← equation of parallel line

Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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For statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

If the slope of the triangles is equal then triangle A is similar to triangle B.

In the statement  when we simplify

(5/3)=(15/9),

(5/3)=(5/3),

Then the reason for this statement is "If the slope of triangles are equal"

And the definition of slope in general is m = y/x.

Therefore, for statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

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Answer:

1

Step-by-step explanation:

Perpendicular lines always have the opposite slope (meaning that you have to switch the numerator and denominator) and sign when comparing to the given equation.

To start off, convert the equation to be formatted into y=. You do this by first subtracting the 3x from both sides of the equation so that it now reads 3y=-3x-273y=−3x−27 . Now, divide the whole equation by three in order to get rid of the value attached to the y. The equation should now read to be: y=-x-9y=−x−9 . Now, just switch the the slope into its opposite (which is the reciprocal) and switch the negative sign into a positive.

Answer:

3:6

Step-by-step explanation:

8:16 is a 1/2 ratio

A point that represents the ordered pair (0, -3) is: D. Point G.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the ordered pair (0, -3), we can logically deduce that the coordinates would be located in quadrant IV as shown in the image attached below.

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Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

here is the answer please mark me bainliest

The expand form will be;

⇒ 28x² - 44x

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 4x (7x - 11)

Now,

Solve the expression as;

⇒ 4x (7x - 11)

⇒ 4x × 7x - 4x × 11

⇒ 28x² - 44x

Thus, The expand form will be;

⇒ 28x² - 44x

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Answer:

$275.40

Step-by-step explanation:

Add 444+523+410=1377

divide 1377 by 5 and u get 275.4

Answer:

n = -3

Step-by-step explanation:

P E M D A S

10 x 7n = 70n

10 x 10 = 100

10n + 70n + 100 = -10(11 - n )

80n + 100 = -10(11 - n )

80n + 100 = 10n - 110

80n + 100 - 100 = 10n - 110 - 100

80n = 10n - 210

80n - 10n - 10n - 210 - 10n

70n = -210

70n ÷ 70 = -210 ÷ 70

n = -3

Answer:

78.5

Step-by-step explanation:

A=πr^2 is the formula. Since you're using pi as 3.14, 3.14 times 5^2 is 78.5 (5^2 is 25 because 5x5=25)

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Answer:

65/100 that is the answer to this question

Answer:

at the end of the day the temperature would be -26° F

Answer:

G)

Step-by-step explanation:

3% of 8000 is 240

now multiply it by 4 (years) and you get 940

Answer:

see in pdf the solution is there.

Step-by-step explanation:

Answer:

\(5\sqrt{5}\left(ab\right)^{\frac{3}{2}}=\sqrt{\left(5ab\right)^3}\)

Step-by-step explanation:

Let us consider the expression

\(5\sqrt{5}\left(ab\right)^{\frac{3}{2}}\)

Writing the expression as a radical

But, let us revise some rules:

\(\sqrt{a}=a^{\frac{1}{2}}\)

\(\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\)

\(\left(a\cdot \:b\right)^n=a^nb^n\)

let us solve now

\(5\sqrt{5}\left(ab\right)^{\frac{3}{2}}\)

\(=5^{\frac{3}{2}}\left(ab\right)^{\frac{3}{2}}\)         ∵  \(\:5^{\frac{3}{2}}=5\sqrt{5}\)

\(=\left(5ab\right)^{\frac{3}{2}}\)

\(=\left(5ab\right)^{3\cdot \frac{1}{2}}\)

\(=\left(\left(5ab\right)^3\right)^{\frac{1}{2}}\)

\(\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}=a^{\frac{1}{2}}\)

\(=\sqrt{\left(5ab\right)^3}\)

Thus,

\(5\sqrt{5}\left(ab\right)^{\frac{3}{2}}=\sqrt{\left(5ab\right)^3}\)

I believe the answer is D. Nonlinearity is a mathematical term describing a situation where the relationship between an independent variable and a dependent variable is not predictable from a straight line. I hope this helps.

Answer:

Step-by-step explanation:

(enlarges height)/(original height) = 13.5/2.7 = 5

The enlarged rectangle is 5 times the original.

enlarged width = 5(original width) = 5(3.7) = 18.5 in

Answer:

t = I/(Pr)

Step-by-step explanation:

We divide P*r on both sides to isolate t and we get t=I/(P*r)

Let's assume x gallons of milk containing 8% butterfat and y gallons of milk containing 2% butterfat are used.

The total amount of milk is x + y gallons, and we want it to be equal to 258 gallons.

To determine the amount of butterfat in the mixture, we can multiply the volume of each type of milk by its respective butterfat percentage and sum them up.

For milk containing 8% butterfat, the amount of butterfat is 0.08x (8% is equivalent to 0.08 as a decimal).

For milk containing 2% butterfat, the amount of butterfat is 0.02y (2% is equivalent to 0.02 as a decimal).

Since we want the final mixture to contain 7% butterfat, we can set up the following equation:

0.08x + 0.02y = 0.07(258)

Simplifying the equation, we have:

0.08x + 0.02y = 18.06

To solve for x and y, we need another equation. Since the total amount of milk is x + y = 258, we can rearrange it to y = 258 - x.

Substituting this value into the equation above, we get:

0.08x + 0.02(258 - x) = 18.06

Solving this equation will give us the values of x and y, which represent the gallons of milk containing 8% butterfat and 2% butterfat, respectively, needed to obtain the desired 258 gallons.

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Answer:

After 15 days he has earned $7.50

Step-by-step explanation:

Hello there!

Answer:

16

Step-by-step explanation:

\( |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0\)

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

The choice that had statements that are all true is (a) Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The number line

On the number line, we have the following

A = -4

B = -2 1/2

C = 1

D = 1 3/4

When the above values are compared with the list of options, we have

Option (A) = true

This is so because in (a)

Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2

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Answer:

$983.45

Step-by-step explanation:

Given data

Principal= $700

Rate= 1.2%

Time= 3 years

The compound interest expression is given as

A= P(1+r)^t

A= 700(1+0.12)^3

A= 700(1.12)^3

A= 700*1.404928

A=$983.45

Hence the balance will be $983.45

The correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

We know that there are 40 students at summer camp who are divided into two groups for either swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking. The outcome frequency for swimming is 16 and for hiking is 24.
To compare the probabilities, we need to first understand the difference between theoretical probability and experimental probability. Theoretical probability is the expected probability of an event occurring based on mathematical calculations and assumptions, whereas experimental probability is the actual observed probability of an event occurring based on data from experiments or observations.
Option 1 states that the theoretical probability of swimming is one half, but the experimental probability is 24 over 40. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is false.
Option 2 states that the theoretical probability of swimming is one half, but the experimental probability is 16 over 40. This statement is correct because the theoretical probability of swimming is 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is true.
Option 3 states that the theoretical probability of swimming is 16 over 24, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 16 over 24, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
Option 4 states that the theoretical probability of swimming is 24 over 40, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 24 over 40, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
In conclusion, the correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

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