In a study, researchers wanted to measure the effect of alcohol in the development of the hippocampal region in adolescents. The researchers randomly selected 30 adolescents with alcohol use disorders to compare the hippocampal volumes in the alcoholic adolescents to the normal volume of 9.08 cubic centimeters. An analysis of the sample data revealed that the hippocampal volume was distributed normally with a mean of 8.25 cm^3 and a standard deviation of 1.67 cm^3.
a. The researchers wanted to determine if the hippocampal values in the alcoholic adolescents were different from the normal volume of 9.08 cm. Write the null and alternative hypotheses for this question. Use a t critical value of 2.045.
b. What are the assumptions (conditions) of this test? Are the assumptions met for this sample?
c. Perform the appropriate test including the formula that you used, the calculated value of the t-statistic, and the t-critical you compared your t-statistic to using a significance level of .05. Then, state your conclusion to the test.
d. Calculate and interpret the 95% confidence interval for the test. Use a t critical of 2.045.

In the two period consumer model , the net effect from a decrease in the interest rate for a net borrower is increase in present consumption (C1 increases) , future consumption decreases (C2 decreases) and savings decreases.

What is two period consumer model?

Hence, the net effect from a decrease in the interest rate for a net borrower is increase in present consumption (C1 increases) , future consumption decreases (C2 decreases) and savings decreases.

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\(P(B|A) = \frac{P(AandB)}{P(A)}\)

Answer:

0.3324

Step-by-step explanation:

The probability of the event for the given odds in favor (4 to 7) is found as 4/11.

To continue solving, we must represent the ratio as a fraction.

Thus, we have the depiction shown below.

Odds ratio equals 4/7

We use the following equation to translate the aforementioned odd's expression into a probability expression.

This is displayed as

P = (Odds + 1)/(Odds).

Replace the unknown values in the equation above.

The following equation is what we have.

P = (4/7)/(4/7 + 1)

Analyze the amount

This results

P = (4/7)/(11/7)

Put the quotient in product form.

P = (4/7) * (7/11)

Evaluate

P = 4/11

Thus, the probability of event for the given odds in favor (4 to 7) is found as 4/11.

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Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

Answer:

y = - \(\frac{1}{2}\) x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

y = - \(\frac{1}{2}\) x + 6 ← is in slope- intercept form

with slope m = - \(\frac{1}{2}\)

• Parallel lines have equal slopes , then

slope of parallel line = - \(\frac{1}{2}\)

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - \(\frac{1}{2}\) x - 2 ← equation of parallel line

Answer:

just do it urself

Step-by-step explanation:

ANSWER:

\( {2}^4\)

REASON:

1.multiply the terms with the same base by adding thier exponents.

2.add the numbers.

Answer:

S₇ = 514.75

Step-by-step explanation:

the nth term of a geometric sequence is

\(t_{n}\) = a\(r^{n-1}\)

where a is the first term and r the common ratio

given t₂ = 24 and t₅ = 81 , then

ar = 24 → (1)

a\(r^{4}\) = 81 → (2)

divide (2) by (1) to eliminate a

\(\frac{ar^{4} }{ar}\) = \(\frac{81}{24}\)

r³ = \(\frac{81}{24}\) ( take cube root of both sides )

\(\sqrt[3]{r^{3} }\) = \(\sqrt[3]{\frac{81}{24} }\)

r = 1.5

substitute r = 1.5 into (1) and solve for a

a × 1.5 = 24 ( divide both sides by 1.5 )

a = 16

the sum to n terms of a geometric sequence is

\(S_{n}\) = \(\frac{a(r^{n}-1) }{r-1}\) , then

S₇    = \(\frac{16((1.5)^{7}-1)) }{1.5-1}\)

      = \(\frac{16(17.0859375-1)}{1.5-1}\)

     = \(\frac{16(16.0859375)}{0.5}\) ( divide 16 by 0.5 )

     = 32 × 16.0859375

     = 514.75

Answer:

B. 4 square feet

Step-by-step explanation:

The formula for area of a triangle is length x height / 2 so 4 x 2 is 8 then divided by 2 is 4.

Answer: 4

Base 4

hight 2

4x2=8 ÷ 2 or 1/2 Equals 4

Formula L x W ÷ 2 or 1/2

The equation  set up is:

0.5x² - 40x + 15300 = 0

Cost, C(x) = 35x + 300

Revenue, R(x) = 75x - 0.5x²

Profit, P(x) = 15000

Profit = Revenue - Cost

P(x) = R(x) - C(x)

15000 = 75x - 0.5x² - (35x + 300)

15000 = -0.5x² + 40x - 300

0.5x² - 40x + 15000 + 300 = 0

The quadratic equation to get the number of items sold is shown below:

0.5x² - 40x + 15300 = 0

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Answer:

33

Step-by-step explanation:

48 - 15 = 33

Answer:

33??

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

to find the perimeter of a trapezoid you add all the sides together

therefore we do it backwards

24-3-6-9=6

Solution :-

We know that perimeter is the sum of all sides, and here we have been provided with perimeter and the length of three sides. Now, we can assume the length of other side as any variable, say x. And develop a linear equation, and solve it. Thus,

A/Q,

→ 3yd + 6yd + 9yd + x = 24yd

→ 18yd + x = 24yd

→ x = 24yd - 18yd

→ x = 6yd

Thus, the length of the fourth side is 6yd.

Hope that helps :)

Answer:

Jiri is 25 years old.

Step-by-step explanation:

1)Pamela =Jiri-9 ( Pamela is 9 years younger than Jiri)

2)Pamela +Jiri=41

Substitute equation 1 into equation 2

(J-9)+J= 41

2J-9=41

Add 9 to both sides:

2J=41+9

Divide by 2:

2J=50

J=25

the required Jiri's age is 25 years.

Pamela is 9 years younger than Jiri and the sum of their ages is 41. What is Jiri's age is to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Let the age of Pamela and Jiri is x and y respectively
Pamela is 9 years younger than Jiri. so,
y = x + 9   - - - - (1)
the sum of their ages is 41
x +  y = 41  - - - - (2)

From equation 1 put y in equation 2
x + x + 9 = 41
2x + 9 = 41
2x = 41 - 9
2x = 32
x = 32/2
x = 16
Now put this x =16 in equation 1
y = 16 + 9
y = 25

Thus, the required Jiri age is 25 years

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Answer:

(A) For this research we made use of the paired t test.

(B) For the t test, we conclude that in the null Hypothesis H₀, there was no difference between the average labor force participation rate for women between the years of 1968 and​ 1972 as against the alternate Hypothesis Hₐ.

From the output data we have, since the P value is 0.024 and  is lesser than the alpha value of 0.05, we will accept the alternate Hypothesis instead of the null Hypothesis.

Note:Kindly find an attached copy of the complete question below.

Step-by-step explanation:

Solution

Recall that:

The U.S of Bureau of Labor Statistics have published Values for the labor force participation rate of women​ (LFPR).

We are more interested in if there was a difference between female participation 1968 and​ 1972, a rapid change in women.

so we will check values for 19 randomly selected cities for 1968 and​ 1972,

Now,

(a) Which of this test is most appropriate for this data

The test which will be more suitable for these data will be paired to test t.

Because the data is for labor force participation for two different years, we apply the t test. now that we are making a comparison of two different year times, we will apply the t test in this research.

In this case, the sample size for both the years evaluated should be same, since we need to pair each and all the data.

(b)By using the test you selected, explain your conclusion

Now, to test the data paired t test, we have already the null Hypothesis  H₀: In this case there  is no difference between the average labor force participation rate for women between the years of 1968 and​ 1972 as compared with the alternate Hypothesis Hₐ: there was a significant difference between the average labor force participation rate for women between the years of 1968 and​ 1972.

However, from the output, we have that the P value is 0.024 which is lower than the alpha value of 0.05.

In conclusion, the alternate Hypothesis accepted while the null Hypothesis is rejected.

Note: kindly find an attached copy of the complete question to this solution

below.

The area of the composite figure is equal to 71.07 in² square yards.

The composite figure is made up of a trapezium and a quarter of a circle, so we shall calculate for the areas of the two figures and then add the result to get the total area of the composite figure as follows:

area of the trapezium = [(6 + 10)/2] yd × 8 yd

area of the trapezium = (16/2) yd × 8 yd

area of the trapezium = 8 yd × 8 yd

area of the trapezium = 64 yd²

area of circle = πr²

area of circle = 22/7 × 3 × 3

area of circle = 198/7

a quarter area of the circle = 198/7 ÷ 4

a quarter area of the circle = 7.07 square yard

total area of the composite figure = 64 yd² + 7.07 yd²

total area of the composite figure = 71.07 yd²

Therefore, the area of the composite figure is equal to 71.07 yd² square yard.

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The first blank is BAL and FGH

The second blank is AL

The third blank is CE and KI

The fourth and final blank is GH

According to the statement

we have given a diagram in which there are some angles and from these angles we have to find that the

Which opposite angles are congruent

The opposite side of AB

With GF angle which angle are congruent

Two angles are which are opposite to each other.

So, from a diagram it is clear that The angles which are congruent with each other is BAL and FGH. Because there positions are perfectly opposite and same  to each other.

And The opposite side of AB is AL because it is present at opposite position to each other.

And with GF angle GH are congruent angles.

So, The first blank is BAL and FGH

The second blank is AL

The third blank is CE and KI

The fourth and final blank is GH

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DISCLAIMER: This question is incomplete.Please see the complete question below.
QUESTION:
Select the correct answer from each drop-down menu.

For the figure shown, point D is a midpoint of , and point J is a midpoint in figure.

Since reflecting the points C, B, A, L, and K across line maps these points onto E, F, G, H, and I, respectively, the opposite angles

are congruent. Since reflecting the points L, K, J, I, and H across line maps these points onto B, C, D, E, and F, respectively, the opposite sides are congruent.

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Answer:

The surface of the rectangular prism is 42

l × w × h

The length is 3 width is 2 and the height is 3.

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\(3\frac{1}{4}\)  cups of chocolate chips is 19.5 ounces.

If one cup of chocolate chips weighs about 6 ounces

we can find out the weight of \(3\frac{1}{4}\) cups by multiplying it by the weight of one cup.

\(3\frac{1}{4}\) cups = 3 cups + 1/4 cup

= 3 + 0.25

= 3.25 cups

Weight of 3.25 cups = 3.25 cups × 6 ounces/cup

Weight of 3.25 cups = 19.5 ounces

Therefore, \(3\frac{1}{4}\)  cups of chocolate chips is 19.5 ounces.

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Answer:

A. 2564 cm^2

Step-by-step explanation:

There are two triangles (Which both are the same) and three different rectangles.

1. Let's solve the area of the triangles first!

Formula: bh(1/2)

10(26)(1/2)

130

2. Now, let's multiply by 2 since there's two of them:

130(2) = 260

3. So, we got 260. Let's find the area of the three rectangles!

Formula: bh

Rectangle A: 28(36) = 1008

Rectangle B: 10(36) = 360

Rectangle C: 26(36) = 936

4. Add the area of the triangles and the rectangles!

260 + 1008 + 360 + 936 = 2564

So the surface area is 2564 cm^2

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Using linear function concepts, it is found that the slopes and intercepts of the functions are given as follows:

a) -4.

b) P = 25.

c) 2.

d) P = 5.

A linear function is modeled by: y = mx + b

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The demand is given by:

D = 100 - 4P.

Hence the slope is -4. The demand is equals to zero when:

100 - 4P = 0 -> P = 25.

The supply is given by:

QS = -10 + 2P.

Hence the slope is 2. The supply is equal to zero when:

-10 + 2P = 0 -> P = 5.

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Answer:

34 mph Is correct answer

Step-by-step explanation:

Average speed = total distance / total time

Total distance = ( 40 × 2 + 30 × 3 )

= 170 miles

Total time = 5 h

So, avg speed = 170/5 = 34 mph

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Answer:

systematic random sample

Step-by-step explanation:

Answer:

acute angle

Step-by-step explanation:

Answer:

Acute Angle!

Step-by-step explanation:

Picture in 1st answer! <3