In each case below, we describe a study to determine whether exercise helps increase certain mood enhancing chemicals in the brain. Indicate whether each describes an experiment or an observational study.
a). Using a random sample of 100 people, we randomly assign half of them to participate in a regular exercise program for a six-week period while the other half makes no changes. At the end of the time period, we measure the brain chemicals.
b). We contact a random sample of 100 people and record how much each person exercises and also measure the chemicals in the brain for each person.

Answer:

HERE

Step-by-step explanation:

The answer you're looking for is 0.1587

Answer:

116.4545454545455

Step-by-step explanation:

Answer:

The equations for each situation are

A = 36 + 6t

B = 21 + 9t

After 3 years, Tree A is taller.

Step-by-step explanation:

From the question,

Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and

Tree A grew by 6 inches per year and Tree B grew by 9 inches per  year after planting.

For Tree A,

Given a period of t years after planting, the height would have increased by 6t

∴ A = 36 + 6t

For Tree B,

Given a period of t years after planting, the height would have increased by 9t

∴ B = 21 + 9t

To determine, which tree is taller after 3 years,

t = 3

For Tree A

A = 36 + 6t

A = 36 + 6(3)

A = 36 + 18

A = 54 inches

For Tree B

B = 21 + 9t

B = 21 + 9(3)

B = 21 + 27

B = 48 inches

Hence, After 3 years, Tree A is taller.

The distance from point A to point B is 2744.1 feet.

Define Trigonometric ratio

The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

Given, horizontal distance = 1357 feet

Let h  = height of the lighthouse

tan(A) = perpendicular / base

where, perpendicular = h

base = 1357 feet

Angle is 9°

so now, put these value in trigonometric ratio

tan(9) = h / 1357

where, tan(9) = 0.1584

h = 1357 * 0.1584

h = 214.9 feet

Let d = distance from point B to the Lighthouse base

Angle is 3°

h = 214.9 feet

so, tan(3) = 214.9 / d

where, tan(3) = 0.0524

0.0524 = 214.9 / d

d = 214.9 / 0.0524

d = 4101.1 feet

Distance between point A to B = 4101.1 - 1357

                                                    = 2744.1 feet

Therefore, the distance from point A to point B is 2744.1 feet

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Answer:

this might be the answer..

Step-by-step explanation:

m²+6m+9

To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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Answer:

Mexico

Step-by-step explanation:

It’s in Spanish

Thus, the given sequence of found to be in Arithmetic as the common difference comes out to be same.

The difference between two successive words in an arithmetic progression sequence, often known as A.P., is always the same. The common difference is the term for the constant.

The difference between the two consecutive numbers in an arithmetic progression (AP) is always the same amount. In other words, "A mathematical series when the variance between two subsequent terms is always a constant" is how arithmetic progression is defined.

The given sequence is-

-7, -13, -19, -25,...

First term a1 = -7

second term a2 = -13

third term a3 = -19

Common difference: d1 = a2 - a1

d1 = -13 + 7 = -6

Now,

d2 = a3 - a2

d2 = -19 + 13 = -6

As,  d1 = d2  (Arithmetic)

Thus, the given sequence of found to be in Arithmetic as the common difference comes out to be same.

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Answer:  4.17 steps

Step-by-step explanation:

Draw a point to use as the center and then sketch 50 units north (up) and 25 units west (left) and 315° which creates a right triangle that has an angle of 360° - 315° = 45°

Use Pythagorean Theorem to find the length of the hypotenuse.

50² + 25² = hypotenuse²   --> hypotenuse = 55.9 units

Since Musah only walked 50 units along the hypotenuse, he is 5.9 units from the center.

Create another right triangle using the remaining 5.9 units as the hypotenuse.  You can use 45°-45°-90° rules OR sin 45° to find the horizontal distance from the center to be 4.17.

see attachment for sketch

1. We can see that the number in the bottom box is: 13.5yd.

2. The number in the top box is: 7.5yd.

3. The area of the table = 78.75yd²

A trapezoid, also known as a trapezium in some countries, is a quadrilateral shape that has only one pair of parallel sides. The parallel sides of a trapezoid are called the bases of the trapezoid, and the non-parallel sides are called the legs.

We see here that in order to get the number in the bottom box, we discover that the number in the top box is a square which means that all the sides are equal to 7.5yd.

Thus, the number in the bottom box = 3 + 7.5 + 3 = 13.5yd.

Thus, the area of the table, a trapezoid = 1/2(a + b)h

Where a = 7.5yd

b = 13.5yd

height, h = 7.5yd.

Thus, A = 1/2(7.5 + 13.5) 7.5 = 157.5/2 = 78.75

∴ Area of the table, A = 78.75yd²

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The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230.

Now, WE get;

the probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 1 - P (snowfall)

P (no snowfall) = 1 - 0.230

P (no snowfall) = 0.770

Thus, The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

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Answer:

-13/-5 is the opposite of 13/5. Hope this helps :)

Answer: \(\frac{4^{9} }{4^{3} }\)=4096

Steps:

\(\frac{4^{9} }{4^{3} }\)

\(\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\)

\(\frac{4^9}{4^3}=4^{9-3}\)

\(=4^{9-3}\)

\(4^{9} -^{3}\)

=4096

The Simplifying the expression 4 ^ 9 / 4 ^ 3 will be 4096.

Simplification is the process of replacing a mathematical expression with an equivalent one, that is simpler (usually shorter), for example.

Simplification of algebraic expressions, in computer algebra.

Simplification usually involves making the expression simple and easy to use later.

We need to Simplifying the expression

4 ^ 9 / 4 ^ 3 .

Now,  4 ^ 9 / 4 ^ 3

Using exponent formula;

= 4 ^ ( 9 - 3 )

= 4 ^ 6

= 4096

Therefore, the Simplifying the expression 4 ^ 9 / 4 ^ 3 will be 4096.

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Answer:

160 inches

Step-by-step explanation:

47+33+47+33=160inches

Therefore, the value of f(m-2) is 5/(m-2) + 2, and the value of function g(1/2) is 2.

In mathematics, a function is a rule or correspondence between two sets, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function is often represented by a formula, equation, or graph.

Here,

1. To find f(m-2), we substitute (m-2) for x in the expression for f(x):

f(m-2) = 5/(m-2) + 2

So the value of f(m-2) is 5/(m-2) + 2.

2. To find g(1/2), we substitute 1/2 for x in the expression for g(x):

g(1/2) = -2(1/2) + 3

So the value of g(1/2) is -1 + 3, which simplifies to 2.

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Answer:

The answer is option D.

Hope this helps you

, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: The fraction 3/9

Now we can simplify the fraction further by dividing both the numerator and denominator by 3

let p=3/9

then p=3/3 / 9/3

       p= 1/3

Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

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The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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Answer:

I think it's about 3840 in.^2

Step-by-step explanation:

The shape is a half circle and a parallelogram

Area of a half circle is 1/2 x pi x r ^2

R is half the diameter(8in), r = 4

Area of half circle = 1/2 x 3.14 x 4^2

Area of half circle = 25.12 square in.

Area of parallelogram = length x height

Area of parallelogram = 10 x 6 = 60 square in.

Total area = 25.12 + 60 = 85.12 square inches

Answer: 85.12 square inches

A) , the firm will run out of retained earnings at a capital structure size of $560 million for the first capital structure, $60 million for the second capital structure, and $800 million for the third capital structure.

B)  there will be a change in the cost of debt at a capital structure size of approximately $19.95 million.

A) To determine the size of the capital structure at which the firm will run out of retained earnings, we need to calculate the retained earnings limit. Retained earnings are expressed as a percentage of the common equity (Ke). From the given information, the retained earnings are 7.5%, 70, and 5.25 for the three different capital structures. Let's assume the size of the capital structure as "x" million dollars.

For the first capital structure (7.5% Ke), the retained earnings limit is given by:

0.075x = 42

x = 42 / 0.075

x ≈ 560

For the second capital structure (70 Ke), the retained earnings limit is given by:

0.70x = 42

x = 42 / 0.70

x ≈ 60

For the third capital structure (5.25 Ke), the retained earnings limit is given by:

0.0525x = 42

x = 42 / 0.0525

x ≈ 800

Therefore, the firm will run out of retained earnings at a capital structure size of $560 million for the first capital structure, $60 million for the second capital structure, and $800 million for the third capital structure.

B) The 8.5% cost of debt applies only to the first $14 million of debt. After that, the cost of debt will go up. To find the capital structure size at which the cost of debt changes, we need to consider the different debt levels and their associated costs.

Assuming the capital structure size as "y" million dollars, we can calculate the change in cost of debt:

For the first $14 million of debt, the cost of debt is 8.5%. Therefore, we have:

0.085(14) = 1.19

Once the debt exceeds $14 million, the cost of debt will change. From the given information, the cost of debt increases to 20% after $14 million. So, we have:

0.20(y - 14) = 0.20y - 2.8

To find the size of the capital structure at which the cost of debt changes, we need to equate the two expressions:

1.19 = 0.20y - 2.8

0.20y = 1.19 + 2.8

0.20y = 3.99

y = 3.99 / 0.20

y ≈ 19.95

Therefore, there will be a change in the cost of debt at a capital structure size of approximately $19.95 million.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Oliver's number is bigger than that of Chen.

It is a number equal to 10 times 10.

Given is that Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds, my number must be bigger.

Oliver number can be written as follows -

8 x 10 x 10

Chens number can be written as follows -

3 x 10 x 10

It can be concluded that Oliver's number is bigger than that of Chen.

Therefore, Oliver's number is bigger than that of Chen.

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Answer:

-$130

Step-by-step explanation:

\( - 780 \div 6 = - 130\)

Each owner of the company suffers a $130 loss.

Answer:

increases by 30

Step-by-step explanation: its right

1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

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Yes,1/2 of an answer is zero answer.

D. I and IV are the quadrants the cosine function is positive

To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.

The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.

Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.

Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.

Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.

It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.

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Answer:

-

you write the answer here

Step-by-step explanation:

and explain here