Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.57 and a standard deviation of 0.44. Using the empirical rule, what percentage of the students have grade point averages that are at least 1.69? Please do not round your answer.

The correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

In such a fraction, the value that appears above the horizontal line is referred to as the numerator.

It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.

The error in the reasoning is that it assumes that multiplying the second fraction by "x" will result in an equivalent expression to 5/a. However, this is not necessarily true.

To correct the error, we can use the property of reciprocals, which states that if a/b = c/d, then b/a = d/c. Using this property, we can rewrite the given equation as:

a/5 = b/3

5/a = 3/b (multiplying both sides by 5/a)

5/a = (b/3) * (3/b) (multiplying both sides by the reciprocal of b/3)

5/a = 1

Therefore, the correct expression is 5/a = 1. There is no need to introduce an additional variable "x".

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The value of cosC is equal to 0.866025.

Value is the worth of something in terms of the amount of money or goods for which it can be exchanged or in terms of its importance or usefulness. It can also refer to the moral principles or qualities that are seen as desirable and important in life. It is an important concept in economics, philosophy, and psychology.

The value of cosC is equal to the cosine of the angle C, which is the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle. CosC is a trigonometric function, which is commonly used in mathematics to solve problems involving angles and triangles. For instance, if the angle C is 30 degrees, then the value of cosC is equal to 0.866025.

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Answer:

1.05

Step-by-step explanation:

Because 30% of 70 is \(30\% \times 70 = \frac{30}{100} \times 70 = 0.3 \times 70 = 21\), so the question becomes "21 is what percent of 2000?"

To answer this, we can solve for \(x\) in the equation \(21 = x\% \times 2000\), which is:

\(21 = x\% \times 2000\\21 = \frac{x}{100} \times 2000\\21 = 20x\\x=\frac{21}{20}=1.05\)

So the answer is 1.05 percent.

Using Altitude/leg Theorem. The solution for x are:

No.3: x = 12 units

No. 4: x = 8√3 units

What is Altitude/Leg Theorem?

Leg-acute is referred to in the LA theorem. It says that if the leg and acute angle of one right triangle match the leg and acute angle of another right triangle, the triangles are congruent.

No. 3

Using the altitude theorem:

x = √(16*9)

x = 12 units

The Leg Rule states that the length of each leg of a right triangle can be found by taking the square root of the product of the hypotenuse and the adjacent segment on that leg.

In mathematical notation, if we have a right triangle with legs a and b, and hypotenuse c, then we have:

a² = bc or a = √(bc) and

b² = ac or b = √(ac)

No. 4

hypotenuse = 12 + 4 = 16

x = √(16 * 12)

x = 8√3 units

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The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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Answer:

4, or it could be 8 but mostly 4

Step-by-step explanation:

The base angles a and b have their measures to be 45 degrees each

If the diagonal of a square produces an isosceles right triangle, then the two legs of the right triangle are congruent, meaning the two base angles are congruent as well.

Since the triangle is a right triangle, one of the base angles must be 45 degrees (which is half of the right angle).

Therefore, both base angles are 45 degrees.

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The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Step-by-step explanation:

How do you write the vertex of an absolute value equation?

f (x) = - | x + 2| + 3 In general, the graph of the absolute value function f (x) = a| x - h| + k is a "V" with vertex (h, k), slope m = a on the right side of the vertex (x > h) and slope m = - a on the left side of the vertex (x < h).

How do you write an absolute value equation?

Image result for Write an equation of an absolute value that has a vertex of (6,2) and x intercepts of 3 and 9

More generally, the form of the equation for an absolute value function is y=a| x−h |+k.

Answer:

Step-by-step explanation:

The quantities specified in a recipe are intended to be proportional. In order to maintain the proportions, all values in the recipe must be multiplied by the same constant.

Stan's pantry holds 1 cup of raisins, which is 4 times the 1/4 cup needed for the recipe. If Stan uses the entire supply of raisins, he can make 4 times the quantity the recipe would normally produce. To maintain the proportions, each quantity in the recipe must be multiplied by 4.

  4 × 1/4 cup raisins = 1 cup raisins

  4 × 5/8 cup chocolate chips = 5/2 cup = 2 1/2 cups chocolate chips

  4 × 1 1/2 cups almonds = 4 +4/2 cups = 6 cups almonds

Answer:

Below

Step-by-step explanation:

Instead of x , I assume you want the angle.    

  For RIGHT triangles, remember

cos (angle ) = adjacent leg / hypotenuse

cos ( angle ) = 5 /12    

     angle = arccos( 5/12) = 65 °

You could also use pythagorean theorem to calculate the misssing side....then use cos law to calculate the angle.

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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1. An equation that represents "the amount of tax on an item of price p",

t = p x X / 100

2. Marta does pay on an item whose price is $20, $1.6

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

Tax rate = 8%

1. Let's assume that the sales tax rate is X%.

Then, the equation that represents the amount of tax (t) Marta pays on an item whose price is p can be written as:

t = p x X / 100

2. If the price of the item is $20, the amount of tax Marta pays can be calculated as follows:

t = $20 x X / 100

t = $20 x 8 / 100

t = $1.6

So, Marta pays $1.6 in sales tax on an item whose price is $100.

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Answer:

y^-1= x +8

Step-by-step explanation:

this may be helpful for you

Answer:

x=5    y=3      z=5

Step-by-step explanation:

The coefficient is the number in front of the variable

Answer:

Step-by-step explanation:

The coefficient in an expression is the multiplier of a designated part of a term of the expression.

__

The given expression is

  5z -2 +6x +3y

It consists of four (4) terms, added together. One term is a constant, -2. The others each have a single variable that is multiplied by a constant. When we ask for the coefficient of the variable, we are asking for the value of that constant multiplier.

The term containing x is 6x. The multiplier of x in that term is 6, so we say ...

  the coefficient of x is 6.

The term containing y is 3y. The multiplier of y in that term is 3, so we say ...

  the coefficient of y is 3.

The term containing z is 5z. The multiplier of z in that term is 5, so we say ...

  the coefficient of z is 5.

__

In an expression such as πr²h, different parts of the expression will have different coefficients. If we ask for the coefficient of the expression, we are generally asking for the constant: π. (The Greek letter pi is the symbol used to represent the irrational constant ratio between the circumference and diameter of a circle. Is is about 3.1415926535....)

If we ask for the coefficient of h, we are asking for the product (πr²) that multiplies h in this expression. Similarly, the coefficient of r² is (πh). Note that we have specified a "designated part" of the expression for which we want the coefficient. This is important when we are solving equations.

__

The commutative property of multiplication means that parts of a product can be written in any order. That is, 5·z is the same product as z·5. When the constant and variable parts of the expression can be unambiguously identified, the order does not matter. In some cases, a constant coefficient may come in several parts: 3z·5·2 has a z-coefficient of 30, for example.

See below for a case where there may be some ambiguity.

__

In the expression r², the constant 2 that comes after the variable, written as a superscript, is called an "exponent," not a coefficient. Often on Brainly, and sometimes in curriculum materials, you will see this written as r2, because superscripts do not get properly rendered. If you're writing this in plain text, the form r^2 is preferred.

Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm,  An award for creating the monster causes these feelings.

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Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm,  An award for creating the monster causes these feelings.

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Answer:

q = 6

Step-by-step explanation:

|q - 8| = 14

The negatives within an absolute value turn positive so it's really:

q + 8 = 14

q = 6

Answer:

B.

Step-by-step explanation:

Not another one! ;)

A can be eliminated because the numbers don‘t match. B seems like a possible answer, let’s first check the others out. C and D can be slim instead because the variable, g, should be next to the 1.5 and 2.5. C and D both change the variable location. So, B.

The rise and the run of the line is shown in the diagram below.

The slope = rise/run = 1/4.

The rise of a line is the vertical distance along the line, which is equal to the number if units you move up or down from one point to another, while the run is the horizontal distance along the line, which is the number of units you move from left or right from a point to another.

The slope of any line (m) = rise of the line/run of the line.

Given the graph shown above:

Red line = rise of the line = 1 unit

Blue line = run of the line = 4 units

Slope of the line = 1/4

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Yes because 6x_____=42 hours

Answer:

Step-by-step explanation:

No explanation is needed because there is no question.

Answer:

you got it

Step-by-step explanation:

no explanation needed

Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.

The answer to this problem: 2

Answer:

$56 million

Step-by-step explanation:

8% x 5 = 40%

40% of 40 = 16

40 + 16 = 56

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

2t + 9

Step-by-step explanation:

5 and 4 are like terms. 3t and -t are like terms

= 2t + 9

or 9 + 2t

Answer:

2t + 9

Step-by-step explanation:

5 + 4 = 9

3t - 1t = 2t

The factored expressions (x + 3)(x + 27), (x + 9)(x + 9),and (x - 3)(x + 27) can matched to the quadratic expressions x² + 30x + 81, x² + 18x + 81, and x² + 24x - 81 respectively.

Factor is a number or an expression that divides another without a remainder. That is if multiplying two expressions gives us a product, then the expressions we are multiplying are factors of the product.

(x + 3)(x + 27) = x² + 27x + 3x + 81

(x + 3)(x + 27) = x² + 30x + 81

(x + 9)(x + 9) = x² + 9x + 9x + 81

(x + 9)(x + 9) = x² + 18x + 81

(x - 3)(x + 27) = x² + 27x - 3x - 81

(x - 3)(x + 27) = x² + 24x - 81

Therefore, the factored expressions (x + 3)(x + 27), (x + 9)(x + 9),and (x - 3)(x + 27) can matched to the quadratic expressions x² + 30x + 81, x² + 18x + 81, and x² + 24x + 81 respectively.

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Answer:

n²+1

2n²

Step-by-step explanation:

We can see that 2, 5, 10, and 17 becomes 1, 4, 9, and 16 when we subtract 1.

So it adds 1. The nth will be n² + 1.

2, 8, 18, and 32 is the double of n². 1, 4, 9, and 16 are their half.

So the nth term becomes 2n².

The value of the equation is

a) The nth term of the equation is Aₙ = n² + 1

b) The nth term of the equation is Bₙ = 2n²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

a)

Let the nth term of the equation be represented as Aₙ

Now , the sequence is

P = { 2 , 5 , 10 , 17 , .. }

when n = 1 , P₁ = 2

when n = 2 , P₂ = 5

So , the equation for the nth term is Aₙ = n² + 1

b)

Let the nth term of the equation be represented as Bₙ

Now , the sequence is

Q = { 2 , 8 , 18 , 32 , .. }

when n = 1 , P₁ = 2

when n = 2 , P₂ = 8

So , the equation for the nth term is Bₙ = 2n²

Hence , the equations are solved

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Answer:

Below

Step-by-step explanation:

As in my other post:

Acceleration = change in velocity / change in time

                        = (7 - 70) m/s / 30 s = -63/30 m/s^2 = -  2.1 m/s^2