(15. 28) Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6. 4. Suppose that (unknown to you) the mean score of those taking the MCAT on your campus is 26. In answering the following, use z-scores rounded to two decimal places. If you choose one student at random, what is the probability (±0. 0001) that the student's score is between 20 and 30?

Answer:500

Step-by-step explanation:

√250000=500

Answer:

\( \sqrt{250000} \\ \sqrt{500} \times \sqrt{500 } \\ { \sqrt{500 } }^{2} \\ 500\)

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Answer:

second choice

Step-by-step explanation:

Answer:

I THINK it would be 11.

Answer:75

Step-by-step explanation:

since there are 15 students and they each need 5 plates you just do 15x5 and get 75

Answer:

F

Step-by-step explanation

If there is 4 months and every month $32 is added you count $32 for every month.

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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The graph of the function over the interval -2 ≤ x ≤ 2 is given below:

What do you mean by step function?

A piecewise function is one that is broken up into smaller functions, each of which has its own equation. A very particular (and much simpler) type of piecewise function is called a step function (or staircase function), and it has parts that resemble steps or the stairs of a staircase.

The graph of the function over the interval -2 ≤ x ≤ 2 is given below:

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\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Considering the data:

Dilation by a scale factor of 4 from the origin in the form of an A'B'C' reflection over x = 1

<=> The two triangles are comparable to one another since triangles can have the same shape but differ in size, so A′′B′′C′′ is 4 times larger than ABC.

=> the connection between "ABC" and "A"B"C" .

\(\frac{AB}{A"B"} = \frac{1}{4}\)

We settle on C.

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

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Answer:

.

Step-by-step explanation:

The given inequality: y < 0.5x + 2

The coordinates of they satisfy the given inequality than they are the solutions of the inequality y < 0.5x + 2

Plot the given points on the given line, The points which are passes through the line is the solution of the given inequality:

The point (-1,2)

The points doenot pss through the line and lie in the shaded region

So, (-1,2) are not the solution of the given inequality:

Solution are :(-2, 1)

(1, -2)​

Answer :

(-2, 1)

(1, -2)​

Answer:

58%

Step-by-step explanation:

47/81 x 100%

≈ 58%

Hope it helps : )

Given information:Position of a particle moving along the x-axis varies in time according to the expression x = 3t², where x is in meters and t is in seconds.

To determine the position at the following times. a. t = 3.30 s, b. t = 3.30 s + Δt xf and c. Evaluate the limit of Δx/Δt as Δt approaches zero to find the velocity at t = 3.30 s. a. To find the position when t = 3.30 s, substitute t = 3.30 s in x = 3t².x = 3t² = 3(3.30)² = 32.67 metersTherefore, the position at t = 3.30 s is 32.67 meters.

b. To find the position when t = 3.30 s + Δt, substitute t = 3.30 s + Δt in x = 3t².x = 3t² = 3(3.30 s + Δt)² = 3(10.89 + 6.6Δt + Δt²) = 32.67 + 19.8Δt + 3Δt²Therefore, the position when t = 3.30 s + Δt is 32.67 + 19.8Δt + 3Δt².c. Velocity is given by Δx/Δt.Δx/Δt = [x(t + Δt) - x(t)]/ΔtBy substituting the given values, we have;Δx/Δt = [x(3.30 + Δt) - x(3.30)]/Δt= [3(3.30 + Δt)² - 3(3.30)²]/Δt= 19.8 + 6ΔtTaking the limit of Δx/Δt as Δt → 0, we have;Δx/Δt = 19.8 + 6(0)Δt = 19.8Therefore, the velocity at t = 3.30 s is 19.8 m/s.

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The correct option is (d) i.e. the correct notation of given series is ∑2n where n=1 is the lower notation and n=10 is the higher notation.

What is Series?

A series in mathematics has constant term differences. By multiplying the number of times the average of the final and first terms, we may determine the sum of the terms in an arithmetic series.

Given series : 2 + 4 + 6 + 8 + ... for 10 terms

Here, we can see that the first term is 2 and the difference btw the two terms is 2.

Similarly, the notation for lower limit is 1 and the notation for higher limit is 10 which is given.

We can write the given series as ∑2n.

When we put n=1, we get 2 which is the first term.

hence, verified too.

So, The notation of given series is ∑2n where n=1 is the lower notation and n=10 is the higher notation.

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(a) The profit of the firm at the current employment levels of 25 units of labor and 50 units of capital can be calculated by subtracting the total cost from total revenue.

The total revenue is given by the output multiplied by the market price, which is $2. The total cost is the sum of the wage cost (W) and the rental cost of capital (R), multiplied by their respective quantities.

Profit = Total Revenue - Total Cost

Profit = (Output * Price) - (Wage * Labor + Rental * Capital)

Given that the output is determined by the production function Y = 100K^(1/2) + 40L^(1/2), the profit can be calculated as follows:

Profit = (100K^(1/2) + 40L^(1/2)) * $2 - ($8 * 25 + $10 * 50)

(b) The profit-maximizing quantity of capital for this firm can be determined by setting the marginal revenue product of capital (MRPK) equal to the rental cost of capital (R). MRPK represents the additional revenue generated by employing an additional unit of capital.

MRPK = R

The marginal revenue product of capital can be calculated as the partial derivative of the production function with respect to capital (K), multiplied by the market price (P):

MRPK = (∂Y/∂K) * P

Using the production function Y = 100K^(1/2) + 40L^(1/2), we can calculate the marginal revenue product of capital as follows:

MRPK = (∂Y/∂K) * P = (50K^(-1/2)) * $2

Setting this equal to the rental cost of capital (R) of $10, we have:

(50K^(-1/2)) * $2 = $10

Simplifying the equation, we find:

K^(-1/2) = 1/5

Squaring both sides of the equation, we get:

K = 25

Therefore, the profit-maximizing quantity of capital for this firm is 25 units.

(c) To raise profits, the firm should decrease its capital employment from 50 to 25 units. This is because the profit-maximizing quantity of capital is determined to be 25 units, as calculated in part (b). By employing fewer units of capital, the firm can reduce its rental cost while still maintaining the optimal level of capital for production. As a result, the firm can lower its total cost and increase its profit. Employing more capital beyond the profit-maximizing level would lead to diminishing returns, where the additional costs outweigh the additional revenue generated. Therefore, reducing capital employment to the optimal level of 25 units would be the most favorable decision for the firm to maximize its profits.

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By comparing the heights and distances of the surveyor and the cliff, we can set up a proportion and solve for the height of the cliff. Therefore, the height of the cliff is approximately 4.57 feet.

Let's denote the height of the cliff as h. The surveyor's height is 4 feet, and he is standing 32 feet away from the base of the cliff.

We can set up a proportion using the similar triangles formed by the surveyor and the cliff. The ratio of the surveyor's height to his distance from the cliff should be equal to the ratio of the cliff's height to the total distance from the surveyor to the cliff.

Mathematically, we have:

4 feet / 32 feet = h / (32 feet + h)

To solve for h, we can cross-multiply and solve the resulting equation:

4 * (32 feet + h) = 32 feet * h

128 feet + 4h = 32h

128 feet = 28h

h = 128 feet / 28

h ≈ 4.57 feet

Therefore, the height of the cliff is approximately 4.57 feet.

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For this problem the universe is the number of raspberry plants which has a total of 340 possible outcomes. The event of the problem is "The raspberry are ready for picking" and it has 181 favorable outcomes; now, the complement of this event will be "The raspberry are not ready for picking" and to get its outcomes we subtract the number of plants that are ready to the total number of plants:

Therefore, the number of outcomes for the complement is 159

9514 1404 393

Answer:

  C.  8%

Step-by-step explanation:

The tax rate is the ratio of tax to the before-tax sale amount:

  tax rate = $14.39/$179.92 ≈ 0.07998 ≈ 8.00% . . . matches C

  The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.

The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.

    So, the option c is most suitable option.

Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.

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The correct option is B, A hypothesis is a conjecture by the researcher about the connection between multiple fluctuating factors.

A hypothesis is a proposed explanation or prediction for a phenomenon or set of phenomena based on limited evidence or initial observations. It is a tentative explanation that must be tested and evaluated before it can be accepted or rejected.

A good hypothesis is testable, falsifiable, and based on available evidence or prior knowledge. It should also be specific, clear, and able to be repeated by other researchers to verify the results. Hypotheses are used in scientific research to guide the design of experiments or studies, and to help researchers determine the most effective ways to test their ideas. Once a hypothesis has been formulated, it can be tested through experimentation or observation.

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Complete Question : -

A hypothesis is

a. a lie that needs to be exposed by researchers and is independent of the variables.

b. a conjecture by the researcher about the connection between multiple fluctuating factors.

c. a truth that needs to be proven by researchers and is dependent on the variables.

d. a proven explanation for the relationship between known variables.

\(a=-1\)

Using the midpoint formula directly from the topic meaning

\(\frac{x_{1}+x_{2} }{2} or \frac{y_{1}+y_{2} }{2}\)

so

\(\frac{a+a+4}{2} =1\\a=-1\)

Answer:

235

Step-by-step explanation:

Answer:

253 Students chose pizza

Step-by-step explanation:

To find the number of students who chose pizza you must multiply 500 x .47

The decimal point of 47% is moved two times to the left

500 x .47 = 235

Answer:

1. The fraction converts into a repeating decimal.

Step-by-step explanation:

1/3=0.33333333333

Answer

516,901

Step-by-step explanation:

36,700/7.1%

you have to change the 7.1% to a decimal so its now

36,700/0.071= 516,901.4084507

round it to the nearest whole number is 516,901

Kirk must earn an annual rate of return of approximately 6.07% on his investment to accumulate enough money to pay for the ring.

To calculate the annual rate of return Kirk must earn on his investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount (the cost of the ring, which is $13,000 in 9 years)
P = initial amount (the amount Kirk currently has, which is $4,532)
r = annual interest rate (what we need to solve for)
n = number of times interest is compounded per year (assuming it's compounded annually, n = 1)
t = number of years (9 years)

Plugging in the given values:
$13,000 = $4,532(1 + r/1)^(1*9)
Next, simplify the equation:
(1 + r)^(9) = 13000/4532
Take the ninth root of both sides:
1 + r = (13000/4532)^(1/9)
Solve for r:
r = (13000/4532)^(1/9) - 1
Now, plug the value into a calculator to find r:
r = 0.0607

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Answer: 0.02291666

Step-by-step explanation:

divide 55 by 60 (minutes)

then by 60 again (seconds)

multiply by 1.5

there you go

The person travelled for 0.0229167 miles.

To calculate the distance, we have to multiply the speed by the time taken.

Distance = Speed × Time

Speed = 55 miles per hour.

Time taken = 1.5 seconds = 0.0004167 hours

Note that 3600 seconds = 1 hour

Therefore, 1.5 seconds = 0.0004167 hours

Then, the distance will be:

= Speed × Time

= 55 × 0.0004167

= 0.0229167 miles

The person travelled for 0.0229167 miles.

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The factored form of the quadratic equation 4x² + 7 + 25 is 4(x² + 8).

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.

Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors

Therefore, let's factorise the quadratic equation as follows:

4x² + 7 + 25

4x² + 32

Hence, using the common factor,

4x² + 32 = 4(x² + 8)

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Answer:

No, because 20 x 6 = 120 and 120 is bigger than 102

Step-by-step explanation:

Answer:

4    1    1/8

Step-by-step explanation:

(1/2)^-2 = 2^2 = 4

(1/2)^0 = 1

(1/2)^3 = 1/(2^3) = 1/8

Answer:

At x=-2:
y=16

At x=0:
y=1

At x=3:
y=1/64

Step-by-step explanation:

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