a blanket measures 1 1/4 yards on each side. how many square yards does the blanket cover?

We can conclude that cosh2x−sinh2x=1.

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

To show that cosh2x−sinh2x=1, we can use the identities for cosh2x and sinh2x. The identity for cosh2x is cosh2x=2cosh2x−1 and the identity for sinh2x is sinh2x=2sinh2x−1.

Substituting these identities into the equation cosh2x−sinh2x=1 yields 2cosh2x−1−2sinh2x−1=1. Simplifying this equation yields cosh2x−sinh2x=1, as required. Thus, we can conclude that cosh2x−sinh2x=1.

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Simplifying this equation yields [tex]\cosh^2x-sinh^2x=1[/tex], as required. Thus, we can conclude that [tex]\cosh^2x-sinh^2x=1[/tex].

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

We will show that [tex]\cosh^2x-sinh^2x=1[/tex].

Let us consider the expression [tex]\cosh^2x-sinh^2x.[/tex]

Then, [tex]\cosh^2x=(e^2x+e^{-2}x)/2[/tex] and [tex]sinh^2x=(e^2x+e^{-2}x)/2[/tex]

Substituting, we get [tex]\cosh^2x -\sinh^2x=(e^2x+e^{-2}x)/2\ -(e^2x+e^{-2}x)/2[/tex]

Simplifying, we have [tex]\cosh^2x -\sinh^2x=e^2x+e^{-2}x-e^2x+e^{-2}x[/tex]

[tex]=2e^{-2}x\\\\=2(e^{-2}x)\\\\=2[/tex]

Hence, [tex]cosh^2x-sinh^2x=1[/tex]

Therefore, we have shown that [tex]cosh^2x-sinh^2x=1[/tex]

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The correct form of question is Show that cosh2x−sinh2x=1 .

The equation for the sinusoidal function that represents Jane's motion would be d(t) = 25 x sin(π/4 x (t + 4)) - 5

Let d(t) be the distance Jane is from the bank (in feet) at time t (in seconds). Since Jane's motion is sinusoidal, we can express it as:

d(t) = A x sin(B x (t - C)) + D

We need to find the values of A, B, C, and D that satisfy these conditions.

Since the amplitude is half the peak-to-peak amplitude, we have:

A = 50 / 2 = 25

The vertical shift (D) is the average of the maximum and minimum distances:

D = (20 + (-30)) / 2 = -10 / 2 = -5

Since the sine function is -1 at 3π/2 (270 degrees), we have:

π/4 x (2 - C) = 3π/2

2 - C = 6

C = -4

So, the equation of the sinusoidal function representing Jane's motion is:

d(t) = 25 x sin(π/4 x (t + 4)) - 5

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The question is:

Find the sinusoidal function that represents Jane's motion.

Answer:

6 examinations

Step-by-step explanation:

We Know

A doctor can complete 3 examinations in 2 hours.

How many examinations can the doctor complete in 4 hours?

We see

4 hours is 2 hours times 2

We take

3 x 2 = 6 examinations

So, the doctor can complete 6 exams in 4 hours.

The next four equivalent fractions of 8/13 are:

Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.

In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.

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The solution to the system of equations is (23, -72).

The first equation is y = -72, which means that whatever the value of x is, the value of y will always be -72.

Substituting y = -72 in the second equation, we get:

7x + 2(-72) = 20

Simplifying this equation, we get:

7x - 144 = 20

Adding 144 to both sides, we get:

7x = 164

Dividing both sides by 7, we get:

x = 23.428571...

So the solution to the system of equations is the ordered pair (x, y) = (23.428571..., -72).

However, we usually express solutions as ordered pairs of integers, so we can round x to the nearest integer to get:

(x, y) = (23, -72)

Therefore, the solution to the system of equations is (23, -72).

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Lin plans to swim 12 laps and has already swum 9.75 laps, so the number of laps she has left to swim can be found by subtracting 9.75 from 12:

y = 12 - 9.75

Simplifying the right side:

y = 2.25

Therefore, Lin has 2.25 laps left to swim.

Answer:

A. February 26th

B. $3,500 - Balance ≈ $6,697.26

C. $2,500 - Balance ≈ $4,263.46

D. $4,284.81

Step-by-step explanation:

a) What is the due date of the loan?

The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.

April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days

Subtracting 48 days from April 15th, we get:

Due date = February 26th (of the following year)

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

First, we need to calculate the number of days between April 15th and October 12th:

April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days

Now, we will calculate the interest for 180 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $10,000 × 0.04 × (180 / 365)

Interest ≈ $197.26

Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $10,000 + $197.26 - $3,500

Balance ≈ $6,697.26

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.

First, we need to calculate the number of days between October 12th and January 11th:

October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days

Now, we will calculate the interest for 91 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $6,697.26 × 0.04 × (91 / 365)

Interest ≈ $66.20

Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $6,697.26 + $66.20 - $2,500

Balance ≈ $4,263.46

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

First, we need to calculate the number of days between January 11th and February 26th:

January (20 days) + February (26 days) = 46 days

Now, we will calculate the interest for 46 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $4,263.46 × 0.04 × (46 / 365)

Interest ≈ $21.35

Finally, we will calculate the final payment Peter must pay on the due date:

Final payment = Principal + Interest

Final payment = $4,263.46 + $21.35

Final payment ≈ $4,284.81

Answer: 6 3/7

Step-by-step explanation:

9/1 x 5/7

If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.

Answer:

[tex]\frac{45}{7}[/tex] or 6.4285

Step-by-step explanation:

First, multiply 9 and 5, which gives you 45.

9(5)=45

Then, divide 45 by 7.

45/7=6.4285

That gives  you  [tex]\frac{45}{7}[/tex] or 6.4285

Hope this helps!

The number of atoms in 8.500 moles of chlorine atoms can be calculated using Avogadro's number, which is approximately 6.022 × 10²³ atoms/mole.

So, the number of atoms in 8.500 moles of chlorine atoms would be:

8.500 moles × 6.022 × 10²³ atoms/mole = 5.12 × 10²⁴ atoms of chlorine.

The molar mass of oxygen is approximately 16.00 g/mol. Therefore, the mass of 15.50 moles of oxygen would be:

15.50 moles × 16.00 g/mol = 248 g of oxygen.

The molar mass of helium is approximately 4.00 g/mol. Therefore, the number of moles of helium in 1.953 x 10^8 g of helium would be:

1.953 x 10^8 g / 4.00 g/mol = 4.88 x 10⁷ moles of helium.

The molar mass of sulfur is approximately 32.06 g/mol. Therefore, the number of moles of sulfur in 147.82 g of sulfur would be:

147.82 g / 32.06 g/mol ≈ 4.61 moles of sulfur.

The molar mass of cobalt (Co) is approximately 58.93 g/mol.

The formula mass of Ca₃(PO₄)₂ can be calculated by adding the molar masses of all the individual atoms in the formula.

The molar mass of calcium (Ca) is approximately 40.08 g/mol, the molar mass of phosphorus (P) is approximately 30.97 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.

Therefore, the formula mass of Ca₃(PO₄)₂ would be:

3 × 40.08 g/mol (for Ca) + 2 × (2 × 30.97 g/mol + 4 × 16.00 g/mol) (for P and O) = 310.17 g/mol.

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Answer:

  -3

Step-by-step explanation:

You want the graphical solution to x² +6x +9 = 0.

The graph of the expression on the left shows it has a value of 0 when x = -3.

The solution is x = -3.

__

Additional comment

A graphing calculator is very helpful when you want a graphical solution.

If you want to graph this by hand, you can rewrite it as ...

  (x +3)² = 0

The graph of (x +3)² is a graph of the parent function y = x² after it has been shifted left 3 units. The graph will go through points (-5, 4), (-4, 1), (-3, 0), (-2, 1), (-1, 4). Of course the point at (-3, 0) indicates the solution is x=-3.

The height of the parabolic balloon arch for the prom is 12.25 feet.

Using these assumptions, we can find the equation of the parabola that the arch follows as x = a(y-k)² + h, where (h,k) is the vertex and a is a constant that determines the shape of the parabola. We can find the value of a by using one of the points that the arch passes through, say (3,0):

3 = a(0-k)² + h h = 3 - a(k²)

Similarly, using the other point that the arch passes through, say (7,0):

7 = a(0-k)² + h h = 7 - a(k²)

Equating the expressions for h, we get:

3 - a(k²) = 7 - a(k²) a = -1/4

Substituting this value of a into one of the equations for h, say h = 7 - a(k²), we get:

h = 7 + 1/4(k²)

So the vertex of the parabola is at (h,k) = (7,0), and the equation of the parabola is x = -1/4(y² - 28y + 49).

To find the height of the arch, we need to find the y-coordinate of the vertex, which is k = 0. So the height of the arch is given by the distance between the vertex and the lowest point of the arch, which is the x-intercept of the parabola. To find the x-intercept, we set y = 0 in the equation of the parabola:

x = -1/4(0² - 28(0) + 49)

x = -1/4(49) = -12.25

However, since we are dealing with a physical object, the height cannot be negative. Therefore, we take the absolute value of the x-intercept, which gives us:

| -12.25 | = 12.25 feet

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The value of x, in the image given is calculated by applying the intersecting chords theorem, which is: x = 16.

The Intersecting Chords Theorem, also known as the Ptolemy's Theorem, states that in a circle, if two chords intersect, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

In mathematical terms, if two chords, AB and CD, intersect at point E inside a circle, then:

AE × EB = CE × ED

Applying the theorem, we have:

5(x) = (x - 6)8

5x = 8x - 48

5x - 8x = -48

-3x = -48

x = 16

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Answer:2/3

Step-by-step explanation:

its the only possible answer because it needs to have a scale factor below one as A'B'C'D' is smaller than ABCD

Answer: 2/3

Step-by-step explanation:

The corresponding side of AD is A'D'.

AD = 30

A'D' = 20

Scale factor = 2/3 because AD * 2/3 = A'D'

If I'm wrong, please tell me.

In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).

The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.

The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)

Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).

Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).

The point (2,5) will change to if it is reflected across the line y=x (5,2).

Therefore, the correct option is 1. (-2, 5).

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The leg measurement will make a right triangle is 21 cm.

The longest side of a right-angled triangle, i.e. the side opposite the right angle, is called the hypotenuse in geometry.

Pythagorean theorem :

If p be the length of the hypotenuse of a right-angled triangle, q and r be the lengths of the other two sides, then

p² = q² + r²

The lengths of the other two sides of the given right-angled triangle are 20 cm and 21 cm. Put these values in the above theorem to get the desired result.

Now, p² = (20)² + (21)²

= 400 + 441 = 841

i.e. p = √(841) = 29

Therefore the length of the hypotenuse is 29 cm. The right angle traingle is 21 cm.

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Answer:

below

Step-by-step explanation:

26. yes because a straight line is formed

27. domain - -2 to 2

range -2 to 1

Answer:

Yes, the graph is a linear function.

Domain: x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Step-by-step explanation:

A linear function is an expression that will form a straight line when graphed (or a graph that forms a straight line). These points form a straight line, so the function is linear.

The domain of the function is everything that x can be equal to. We can see here that the ordered points are:

(-2, -1.5), (-1.5, -1), (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), (1.5, 2)

So, the domain of the function is all of the x values of the ordered pairs, or:

x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

(the symbol next to the x means "belongs to.")

As for the range, it is everything that y can be equal to. Let us look once again at the ordered pairs. The range of the function is equal to the y coordinates of these ordered pairs, or:

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Keep in mind that if the function contains more than one value for x or y, it is listed ONLY ONCE in the domain/range.

The values of trigonometric-ratios in the given triangle whose legs are 4 and [tex]4\sqrt{3}[/tex] are:

a)sinθ=0.5

b)cosθ=0.866

c)tanθ=0.577

What is trigonometric-ratios ?

A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.

Given sides of triangle: 4 and [tex]4\sqrt{3}[/tex]

hypotenuse=[tex]\sqrt{perpendicular^{2}+base^{2} }[/tex]

                  =[tex]\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }[/tex]

                  =[tex]\sqrt{16+48}[/tex]

                  =8

a)Sin θ=[tex]\frac{side opposite to the given angle}{hypotenuse}[/tex]

Sin θ=[tex]\frac{4 }{8}[/tex]

Sin θ=[tex]\frac{1}{2}[/tex]

Sin θ=0.5

b)Cos θ=[tex]\frac{side adjacent to the given angle}{hypotenuse}[/tex]

            =[tex]\frac{4\sqrt{3} }{8}[/tex]

            =[tex]\frac{\sqrt{3} }{2}[/tex]

            =[tex]\frac{1.732}{2}[/tex]

Cos θ=0.866

c)tan θ=[tex]\frac{side opposite to the given angle}{side adjacent to the given angle}[/tex]

            =[tex]\frac{4}{4\sqrt{3} }[/tex]

            =[tex]\frac{1}{\sqrt{3} }[/tex]

tan θ=0.577

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Answer: Using the given information and the formula ab = cd, we can write:

d = (ab) / c

We are given b = 12 cm and c = 6 cm. To find ab, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

where a is the unknown length we want to find. Substituting the given values, we get:

a^2 + 12^2 = 6^2

a^2 + 144 = 36

a^2 = -108 (which is not a possible solution)

This means that the given values do not form a valid triangle. Therefore, we cannot find the length of segment d using the given information.

Step-by-step explanation:

1. The expression √b means "the square root of b".

2. The radical symbol (√) stands for the exponent 1/2.

3. The number or expression under the radical symbol is called the radicand.

A radicand is the number or expression underneath a radical symbol (√). It is the number or expression that is being operated on by the root. The square root of the radicand is the result of the operation.

The expression √6 represents the square root of 6. This is the value of x that, when multiplied with itself, results in 6.

The square root of 6 is equal to 2.44948974, which is the positive solution to the equation x² = 6.

The radical symbol (√) indicates that the expression is a root and the number or expression under the radical symbol is called the radicand, which is 6 in this case.

The exponent of the radical symbol is 1/2, which implies that the expression is a square root.

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Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.

Annual data frequency refers to data that is collected and reported on an annual basis. This means that the data points in the dataset represent a full year's worth of data, with one data point for each year. Annual data is often used in economic indicators, such as gross domestic product (GDP) or unemployment rates, and can provide insights into long-term trends and changes over time.

GDP stands for Gross Domestic Product, which is a measure of the total value of goods and services produced within a country's borders during a specific time period, typically a year. It is used as an indicator of a country's economic health and growth. GDP is calculated by adding up the total spending on consumption, investment, government spending, and net exports (exports minus imports) during the period.

Seasonality may still be a problem for data frequencies of monthly, weekly, daily, and quarterly as certain patterns or fluctuations may occur within each of these time intervals. Seasonality may be less of a problem for annual data frequency as there may be less variation due to the longer time interval.

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Okay, here are the steps to find the minimum value of P:

1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)

|z+w|=sqrt(2)

Find z and w such that these conditions are satisfied.

Possible solutions:

z = 1, w = i (or vice versa)

z = i, w = 1 (or vice versa)

2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

For the cases:

z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5

z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5

3) The minimum value of P is 5.

So in summary, the minimum value of

P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|

is 5.

Let me know if you have any other questions!

Answer:

x = 10

Step-by-step explanation:

Angle form is = 90°

therefore

5x + 25 + x + 5 = 90

6x + 30 = 90

6x = 90-30

6x = 60

6x/6 = 60/6

x = 10

Answer:

565.486677646 inches squared

Step-by-step explanation:

Let's recall the formula for the surface area of a cylinder:

[tex]A=2\pi rh+2\pi r^2[/tex]

Where r is the radius and h is the height.

We are given that the radius is 6 inches and the height is 9 inches.

Substitute the values and solve the equation, like so:

[tex]A=2\pi (6)(9)+2\pi (6)^2=\\A=2\pi (54) +2\pi(36)=\\A=108\pi +72\pi =\\A=180\pi[/tex]

Thus, in terms of pi, the surface area is equal to [tex]180\pi[/tex].

180 times pi is equal to approximately 565.486677646 inches squared.

We must first convert the given information into an equivalent fraction. The answer is 56%.

Equivalent fractions have the same value or represent the same portion of a whole even though they may have different numerators and denominators.

To do this, we must multiply both the numerator (14) and denominator (25) by the same number so that the denominator equals 100.

To do this, we must multiply both 14 and 25 by 4.

This gives us 14*4/25*4 = 56/100.

To convert this fraction to a percent, we can simply divide the numerator by the denominator and multiply the result by 100.

Therefore, 56/100 * 100 = 56%.

This result can also be found by setting up a proportion. We can set up the proportion as follows:

14/25 = x/100.

To solve for x, we must multiply both sides by 100. This gives us 14*100/25 = x.

Hence, x = 56. Therefore, 56% of swimmers finished the race in less than 47 minutes.

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The height of the kite is approximately 68.4 ft.

To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:

tan(46°) = height / 94

Solving for height, we get:

height = 94 * tan(46°)

Using a calculator, we get:

height ≈ 68.4 ft

Therefore, the height of the kite is approximately 68.4 ft.

We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.

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Complete Question:

A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.

It will take 10 years to double the amount.

Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,

[tex]A = P(1+r/n)^{nt}[/tex]

[tex]2800 = 1400(1+0.0058)^{12t}[/tex]

[tex]2= (1.0058)^{12t[/tex]

㏒ 2 = 12t ㏒ (1.0058)

0.03 = 12t (0.0025)

12t = 120

t = 10

Hence, it will take 10 years to double the amount.

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The two options that represent circles with diameter 12 units and center on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

The diameter of a circle is a straight line segment that passes through the center of the circle and connects two points on its circumference. It is twice the length of the circle's radius.

The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

Explanation:

For a circle with diameter 12 units, the radius is half of the diameter, which is 6 units.

Since the center of the circle lies on the y-axis, the x-coordinate of the center is 0.

The general equation for a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².

Using the given information, we substitute h = 0, k = ±6, and r = 6 to get the two equations:

(x - 0)² + (y - 6)² = 6² => x² + (y - 6)² = 36

(x - 0)² + (y + 6)² = 6² => x² + (y + 6)² = 36

Therefore, the two options that represent circles with diameter 12 units and center on the y-axis are:

x² + (y - 6)² = 36

x² + (y + 6)² = 36

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Answer:

y = -4

Step-by-step explanation:

13 - y = 17

y = 13 - 17 = -4

Answer:

y = -4

Step-by-step explanation:

Alright so you shift the y to the other side:
13 = 17 + y

Now you shift the 17 to the other side,
y = 13 - 17 = -4

Hence, y = -4

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Sharon's desired percentile rank of 0.78.

To determine the goal Sharon set for herself, we need to understand the relationship between standardized scores and percentile ranks.

In a standardized test, such as Sharon's Statistics final, the standardized score represents how well a student performed relative to the average score of the test-takers.

The percentile rank, on the other hand, indicates the percentage of test-takers that scored below a particular student.

In Sharon's case, she wants her standardized score to be equal to her percentile rank.

Therefore, her goal is to achieve a standardized score of 0.78 (written as a decimal) on her Statistics final.

This means she aims to score better than approximately 78% of her classmates, as indicated by her desired percentile rank of 0.78.

Hence her desired percentile rank of 0.78.

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