A college admissions officer evaluates potential students for acceptance based on many qualities, one of which is high school GPA.

(a) Student A has a high school GPA of 3.75. The high school GPA of students applying to this college is approximately Normal with a mean of 3.8 and a standard deviation of 0.08. Calculate and interpret the z-score for Student A.

(b) Student B’s high school GPA has a z-score of z = –0.875. If all else were equal and Student A and Student B were contending for the last open spot, which student should be offered admission?

(c) Student C’s high school GPA is at the 99th percentile among students applying to this college. What is the student’s high school GPA?

A polynomial in which the degrees of all the variables is 0 is called a zero degree polynomial .

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

For example- 6 x 0 , − 9 a 0.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division .

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial .

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10) Using the equation 98.4 = (12.3)8, it costs $12.30 (cost per unit) per uniform.

11) Using the equation 26.70 = k6, the cost of one bag of apples (unit rate) is $4.45.

The unit rate is the quotient of the total cost divided by the number of items contained.

The unit rate is the same as the average or mean of a data set.

We describe the unit rate as the slope of a linear equation.

The unit rate shows the constant rate of change in an equation.

The total cost of 8 uniforms = 98.4 = (12.3)8

The cost per uniform = 12.30 (98.4/8)

The total cost of 6 bags of apples = 26.70

The cost per unit = 4.45 (26.70/6)

Thus, the unit rate or cost is also described as the variable unit cost.

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Answer:

E is the answer

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

(4, 6), (8, -8), (4, -4)

Step-by-step explanation:

Answer:

(4, 6), (8, -8), (4, -4)

Step-by-step explanation:

Hope this helps

Answer:

a/8 or a over 8 hope this helps

Step-by-step explanation:

Answer:

n

8

→

I used

n

as the unknown number

Explanation:

The quotient is the result of division between two numbers.

The quotient of a number (I used

n

) and

8

would be

n

8

The factoring of the equation is 6x(x + 8).

It should be noted that based on the information given, we have to factor the expression that's given.

The expression given is:

6x² + 48x

The common factor is 6x

6x(x + 8)

Therefore, the factoring of the equation is 6x(x + 8).

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Answer:

37

Step-by-step explanation:

Good Luck! I double checked my answer!

Answer:

37

Step-by-step explanation:

Hey There!

They want us to find the hypotenuse using the Pythagorean Theorem

The Pythagorean Theorem says

\(a^2+b^2=c^2\)

or that the two legs ( shorter side) square, added together equal the hypotenuse square

Note: This only works with right triangles

so basically

\(hypotenuse^2=35^2+12^2\\35^2=1225\\1262=144\\144+1225=1369\\\sqrt{1369} =37\)

Therefore the missing side length equals 37

hope this helps!

The total surface area of the television is 21,584 square centimeters.

To find the total surface area of the television, we need to calculate the area of all six sides and add them up.

The front and back sides have the same dimensions and area, so we can find the area of one and multiply it by two. The same goes for the left and right sides.

The area of the front/back sides is:

120 cm x 68 cm = 8160 sq cm

Multiplying by 2 gives us the total area of both front/back sides:

2 x 8160 sq cm = 16,320 sq cm

The area of the left/right sides is:

68 cm x 14 cm = 952 sq cm

Multiplying by 2 gives us the total area of both left/right sides:

2 x 952 sq cm = 1904 sq cm

The area of the top and bottom sides is:

120 cm x 14 cm = 1680 sq cm

Multiplying by 2 gives us the total area of both top/bottom sides:

2 x 1680 sq cm = 3360 sq cm

Adding up all six sides, we get:

16,320 sq cm + 1904 sq cm + 3360 sq cm = 21,584 sq cm

Therefore, the total surface area of the television is 21,584 square centimeters.

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Answer:

d

Step-by-step explanation:

it is opened up because the voeff of X^2 tetm is positive

Answer:

(8,4)

Step-by-step explanation:

The rule is (x,y) becomes (-y,x)

Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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The nervous system works to generate a reaction by sensory receptors in the arteries detecting low oxygen levels, then sensory neurons generate an impulse, and then the central nervous system relays an impulse to certain brain regions. The brain then sends signals through motor neurons, causing Isabel's breathing rate to increase.

This response is an automatic, unconscious process called reflexive or autonomic control. Isabel's nervous system will continue to regulate her breathing and heart rate until her oxygen levels return to normal. The nervous system is responsible for generating the reaction in the body of Isabel by detecting the levels of oxygen in the blood to regulate breathing. When Isabel is running in a marathon and is near the finish line, she feels out of breath, her nervous system works to regulate the oxygen levels in the blood.

The sensory receptors in the arteries detect low oxygen levels, and this detection leads to sensory neurons generating an impulse. The central nervous system relays an impulse to certain brain regions. The brain then sends signals through motor neurons, causing Isabel's breathing rate to increase. This response is an automatic, unconscious process called reflexive or autonomic control. The nervous system controls the respiratory system by using the respiratory centers in the brain, the medulla oblongata, and the pons. These centers receive and interpret information from the respiratory system, such as carbon dioxide and oxygen levels, and then send out appropriate signals to regulate breathing. Isabel's nervous system will continue to regulate her breathing and heart rate until her oxygen levels return to normal. In conclusion, the nervous system plays a vital role in the body, regulating breathing, heart rate, and other vital functions, which helps to keep the body healthy and functioning properly.

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Answer:

0.001? or -299.7

Step-by-step explanation:

so i don't have idea what do you meaning so

0,3:300=0.001 or 0,3-300=-299.7

so i think i help

The probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times is 0.370

The given parameters are:

The probability is represented using the following binomial formula

\(P(x) = ^nC_x * p^x * (1 - p)^{n - x}\)

Using the above formula, we have:

\(P(x \le 15) = 0.370\)

Hence, the probability is 0.370

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The probability is 0.3845.The probability of anything occurring is known as probability.

Explanation:

2/52 * 10/52  = 20/52 = 0.3845.

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90 minutes he spend walking .

The greatest power of a variable in a linear equation is always equal to 1. A one-degree equation is another name for it. A linear equation with one variable is typically expressed as Ax + B = 0. Here, the variables x and A and B are constants and coefficients, respectively. A linear equation with two variables often has the form Ax + By = C. Here, the variables are x and y, the coefficients are A and B, and the constant is C. Equations with a degree of 1 are regarded as linear equations. This demonstrates that there are no variables in a linear equation with an exponent bigger than one.

System of equations!

Let x equal minutes walking,

y equal minutes biking.

First equation will be (4.2)x + (5.1)y = 531 for the total amount of calories. Second equation will be x + y = 120 (converted 2 hours into minutes for convenience). Solve for y in the second equation to get y = 120 - x.

You can then plug (120 - x) in for y in the first equation.

Solve for x

4.2x + 5.1(120 - x) = 531

4.2x + 612 - 5.1 x = 531

612 - 531 = 0.9 x

x = 81 / 0.9

x = 90 min.

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Answer:

3/32

Step-by-step explanation:

The first question should be 3/8 as there are 3 "1"s on the spinner. The answer to the last one is "3/32". You take the 3/8 chances to get a one and multiply that by 1/4 to get a "B". Once you multiply you get .09375 which is 3/32 when converted. Please let me know if this is incorrect.

Answer:

I think its AM not sure tho

Step-by-step explanation:

In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

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Using Lagrange Interpolating Polynomial, f(x) at x = -1 is 106.2, at x = 6 is -31.7, and at x = 17 is -272.4.

Lagrange Interpolating Polynomial is a type of interpolation method that fits a polynomial through given data points. It is used to find the value of a function at a point where there is no value available in the data. Fit the data points given in the table using Lagrange Interpolating Polynomial:

 X     f(x)2     -1.13.2   1317    

Applying the Lagrange's Interpolation formula, the polynomial can be written as follows:

f(x) = {(x - x1)/(x0 - x1)} f(x0) + {(x - x0)/(x1 - x0)} f(x1)f(x)

= {(x - 3.2)/(2 - 3.2)} (-1.1) + {(x - 2)/(3.2 - 2)} (3.2) + {(x - 2)/(13 - 2)} (13)f(x)

= 1.5625x² - 22.75x + 82.1

Therefore, the required Lagrange Interpolating Polynomial is

1.5625x² - 22.75x + 82.1

Now, to find the value of f(x) at x = -1, 6, and 17, substitute the values in the polynomial.

f(-1) = 1.5625(-1)² - 22.75(-1) + 82.1f(-1)

= 106.2f(6)

= 1.5625(6)² - 22.75(6) + 82.1f(6)

= -31.7f(17)

= 1.5625(17)² - 22.75(17) + 82.1f(17)

= -272.4

Therefore, f(x) at x = -1 is 106.2, at x = 6 is -31.7, and at x = 17 is -272.4.

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Answer:

HE IS CORREECT

Step-by-step explanation:

THROUGH BOTH EQUASIONS HE IS CORRECT

Answer:

division property of equality

Step-by-step explanation:

The property used in the last step to find x = 10 in the expression is the division property of equality.

      8(x-2) = 64

      8x-18 = 84

        8x = 80

         x = 10

In 8x = 80 ;

 Division property of equality was used to find the value of x.

The property states that when we divide both sides by a non-zero value, the two sides remains the same.

The volume of the triangular prism is 30 mm³ (option 1).

To calculate the volume of a triangular prism, you'll need to use the formula: Volume = (Area of base) × Height. The base of a triangular prism is a triangle, so we first need to find the area of the triangle using the formula: Area = (Base × Height) / 2.

In your given measurements, it's unclear which dimensions represent the base and height of the triangle, and which is the height of the prism. I'll assume that the base and height of the triangle are 2 mm and 3 mm, respectively, and that the height of the prism is 10 mm.

First, let's find the area of the base triangle: Area = (2 mm × 3 mm) / 2 = 3 mm².

Now, we can use this area to find the volume of the prism: Volume = (Area of base) × Height = (3 mm²) × (10 mm) = 30 mm³.

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The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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The metric system is defined as the decimal system of units based on the meters, kilograms, and second as the units of length, mass, and time respectively. The imperial system is defined as the measurement system used in countries like the UK, Liberia, Myanmar, etc. that uses units like an inch, pound, ton etc.

The Metric and Imperial systems are both systems of measurement. That is, they are not just one unit of measure, but are correlated systems of many units of measure – measuring length and area, weight and mass, volume, force, temperature etc.

The imperial system of measurement is defined as a system that originated in Britain and came to formal use in the early 19th century with the Weights and Measures Act of 1824 and 1878. It uses some of the commonly used units there like an inch, ton, pound, gallon, pint, etc.

Most countries use the metric system which uses the measuring units such as meters and grams, and adds prefixes like kilo, milli, and centi to count orders of magnitude.

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The area of the polygon containing the given triangle and rectangle is 45 square units.

What exactly is a rectangle?

A rectangle is a quadrilateral having four straight sides, four right angles, and parallel and equal-length opposing sides. A rectangle's opposing sides are also congruent, which implies they have the same length.

The formula A = lw gives the area of a rectangle, where A is the area, l is the length, and w is the width. A rectangle's perimeter is determined by the formula P = 2l + 2w, where P is the perimeter.

Now,

To find the area of the polygon containing the triangle and rectangle, we need to find the individual areas of the triangle and rectangle, and then add them together.

The area of a triangle

A = (1/2)bh

where b= base and h = height. Substituting the given values, we get:

A_triangle = (1/2)(9)(6) = 27 square units

The area of a rectangle is

A = lw

where l = length and w = width. Substituting the given values, we get:

A_rectangle = (9)(2) = 18 square units

Therefore, the total area of the polygon is:

A_polygon = A_triangle + A_rectangle

A_polygon = 27 + 18

A_polygon = 45 square units

Therefore, the area of the polygon containing the given triangle and rectangle is 45 square units.

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Answer:

use tiger math and use the camera feature it shows steps also I know teachers can be a pain in the butt i go to high school this year so yeah

(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

The Fourier transform pair for a function f(x) is defined as follows:

F(k) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

f(x) = (1/2π) ∫[-∞,∞] F(k) \(e^{2\pi iyx}\) dk

Now let's prove the given properties:

(i) If f is an even function, then f(y) = 2∫[0,∞] f(x) cos(2πxy) dx.

To prove this, we start with the Fourier transform pair and substitute y for k in the Fourier transform of f(x):

F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

Since f(x) is even, we can rewrite the integral as follows:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[-∞,0] f(x) \(e^{2\pi iyx}\) dx

Since f(x) is even, f(x) = f(-x), and by substituting -x for x in the second integral, we get:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[0,∞] f(-x) \(e^{2\pi iyx}\)dx

Using the property that cos(x) = (\(e^{ ix}\) + \(e^{- ix}\))/2, we can rewrite the above expression as:

F(y) = ∫[0,∞] f(x) (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dx

Now, using the definition of the inverse Fourier transform, we can write f(y) as follows:

f(y) = (1/2π) ∫[-∞,∞] F(y) \(e^{2\pi iyx}\) dy

Substituting F(y) with the expression derived above:

f(y) = (1/2π) ∫[-∞,∞] ∫[0,∞] f(x) \(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\)/2 dx dy

Interchanging the order of integration and evaluating the integral with respect to y, we get:

f(y) = (1/2π) ∫[0,∞] f(x) ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy dx

Since ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy = 2πδ(x), where δ(x) is the Dirac delta function, we have:

f(y) = (1/2) ∫[0,∞] f(x) 2πδ(x) dx

f(y) = 2 ∫[0,∞] f(x) δ(x) dx

f(y) = 2f(0) (since the Dirac delta function evaluates to 1 at x=0)

Therefore, f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx, which proves property (i).

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

The proof for this property follows a similar approach as the one for even functions.

Starting with the Fourier transform pair and substituting y for k in the Fourier transform of f(x):

F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

Since f(x) is odd, we can rewrite the integral as follows:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx - ∫[-∞,0] f(x) \(e^{-2\pi iyx}\) dx

Using the property that sin(x) = (\(e^{ ix}\) - \(e^{-ix}\))/2i, we can rewrite the above expression as:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) - \(e^{2\pi iyx}\)/2i dx

Now, following the same steps as in the proof for even functions, we can show that

f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx

This completes the proof of property (ii).

In summary:

(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

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