The total surface area of a
rectangular prism is 1,060 cm². The
prism's base has measurements 8
centimeters and 10 centimeters.
What is the height of the prism?

Answer:

[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\sinh(2)x+6[/tex]

Step-by-step explanation:

Given:

    [tex]\phantom{ww} \bullet\;\;\;f''(x)=x^3+\sinh(x)[/tex]

    [tex]\phantom{ww} \bullet\;\;\;f(0)=6[/tex]

    [tex]\phantom{ww} \bullet\;\;\;f(2)=7.6[/tex]

To find f'(x), integrate f''(x):

[tex]\begin{aligned}\displaystyle f'(x)=\int f''(x)\; \text{d}x&=\int \left(x^3+\sinh(x)\right)\; \text{d}x\\\\&=\int x^3\;\text{d}x+\int \sinh(x)\; \text{d}x\\\\&=\dfrac{1}{4}x^4+\cosh(x)+\text{K}\end{aligned}[/tex]

To find f(x), integrate f'(x):

[tex]\begin{aligned}\displaystyle f(x)=\int f'(x)\; \text{d}x&=\int \left(\dfrac{1}{4}x^4+\cosh(x)+\text{K}\right)\;\text{d}x\\\\&=\int \dfrac{1}{4}x^4\; \text{d}x+\int \cosh(x) \; \text{d}x + \int \text{K}\; \text{d}x\\\\&=\dfrac{1}{20}x^5+\sinh(x)+Kx+\text{C}\end{aligned}[/tex]

Substitute f(0) = 6 to determine the value of the constant C:

[tex]\begin{aligned}f(0)=\dfrac{1}{20}(0)^5+\sinh(0)+K(0)+\text{C}&=6\\\\0+0+0+\text{C}&=6\\\\\text{C}&=6\end{aligned}[/tex]

Substitute f(2) = 7.6 and C = 6 to determine the value of the constant K:

[tex]\begin{aligned}f(2)=\dfrac{1}{20}(2)^5+\sinh(2)+K(2)+6&=7.6\\\\1.6+\sinh(2)+2K+6&=7.6\\\\\sinh(2)+2K&=0\\\\2K&=-\sinh(2)\\\\K&=-\dfrac{1}{2}\sinh(2)\end{aligned}[/tex]

Therefore, function f(x) is:

[tex]\boxed{f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\sinh(2)x+6}[/tex]

[tex]\textsf{As}\;\;\sinh(2)=\dfrac{e^4-1}{2e^2},\;\textsf{we can also write the equation as:}[/tex]

[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\left(\dfrac{e^4-1}{2e^2}\right)x+6[/tex]

[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\left(\dfrac{e^4-1}{4e^2}\right)x+6[/tex]

The log expression in single equation is   log 12 - log 3 + log 2.

The solution of the log equation is calculated by applying the following method.

log 12 - ¹/₂log 9  +  ¹/₃log 8

we can simplify the equation as follows;

log 12 - log 3 ⁽² ˣ ¹/₂⁾ +  log 2 ⁽³ ˣ ¹/₃⁾

= log 12 - log 3¹ + log 2¹

=  log 12 - log 3 + log 2

Thus, the log equation or expression has been simplified in the form of single equation.

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There is 1 smaller can that will be put on the shelve.

Given that, a clerk is placing cans of soup on an 8-ft long shelf, we need to find how many more of the smaller cans will fit on the shelf than the larger cans,

Volume of small cans = 127.2 in³

Therefore,

127.2 = 3.14 × 4.5 × r²

r² = 127.2 / 14.13

r² = 9

r = 3

Similarly, the volume of the large can = 301.6 in³

301.6 = 3.14 × 6 × r²

r² = 16

r = 4

The number of small cans that can be out on the shelve = 8/3 ≈ 9

The number of larger cans that can be out on the shelve = 8/4 = 2

Hence, there is 1 smaller can that will be put on the shelve.

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The painted area of the sign is approximately 324 square inches. This was calculated by finding the area of the pole, square signboard, and triangle portion of the signboard and adding them together.

To find the painted area, we need to find the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard.

Area of pole

The pole is a rectangular prism with height 60in and width 4in. Therefore, the area of the pole is:

60in x 4in = 240 sq. in.

Area of square signboard

The square signboard has a side length of 8in. Therefore, the area of the square signboard is:

8in x 8in = 64 sq. in.

Area of triangular portion of the signboard

The triangular portion of the signboard has a base of 8in and a height of 5in. Therefore, the area of the triangular portion of the signboard is:

(1/2) x 8in x 5in = 20 sq. in.

Total painted area

The total painted area is the sum of the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard. Therefore, the painted area is:

240 sq. in. + 64 sq. in. + 20 sq. in. = 324 sq. in.

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--The given question is incomplete, the complete question is given

" clara is running a bakery she has made a street sign to direct people to her bakery . She painted one of the post and sign. What is the painted area?8in,8in,5in, 60in, 4in "--

Mary has the qualities of being a team leader.

Here, we have,

Team leaders upload any other stage of control. They’re employed to persuade and construct relationships, to make matters happen. Team chief’s to-do lists may be vast, however through categorizing them, it’ll come up with readability approximately the reason of your job.

A group chief has an outline of a set of humans, motivates, offers guidance and video display units performance. It is probably an professional identify alternate or a delegation exercising out of your management, however both way, being a group chief separates you out of your friends as a depended on individual to manipulate a assignment or institution of humans.

Team leaders and executives have exceptional responsibilities. Unlike managers, group leaders won’t have the authority to direct, alternate plans, put in force or construct their groups via hiring and firing. Their position is mostly a motivational and inspirational one inside an organization. They’re professional dating developers and mediators, liaising among the humans and management.

Thus this are the qualities of team leader.

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complete question;

Mary is a perfectionist . She loves participating on teams and often takes on too many tasks because she wants to ensure that they are done on time and on budget.

The experimental probability of the rolling a 6 is 13%.

Probability is the likelihood of a desired event happening. Experimental probability is a probability that relies mainly on a series of experiments.

From the table:

The total number of times all the numbers appear is:

total number of times = 7 + 4 + 4 +  5 + 6 + 4 = 30

The number six (6) occurred 4 times.

Experimental probability = (occurrence of 6 / total number of times)

Experimental probability = 4/30 * 100

Experimental probability = 13%

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The correct graph of the system of equations 3x + y = 12 and x - 4y = 4 is:

The graph shows a line with an x-intercept at (4, 0) and a y-intercept at

(0, -1). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 12).

We have,

To graph the system of equations 3x + y = 12 and x − 4y = 4, we first need to rearrange them in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept:

3x + y = 12 => y = -3x + 12

x - 4y = 4 => y = (1/4)x - 1

Now we can see that the first equation has a slope of -3 and a y-intercept of 12, while the second equation has a slope of 1/4 and a y-intercept of -1.

Now,

The x-intercept is when y = 0.

So,

3x + y = 12

3x = 12

x = 4

And,

x - 4y = 4

x = 4

Thus,

The correct graph of the system of equations 3x + y = 12 and x - 4y = 4 is:

The graph shows a line with an x-intercept at (4, 0) and a y-intercept at

(0, -1). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 12).

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Answer: - None of the above.

Step-by-step explanation:

The median is the middle value of the data set when arranged in order. In this case, we have an even number of values, so we need to take the average of the middle two values to find the median. The middle two values are 80 and 85. Therefore, the median student score is:  (80 + 85) / 2 = 82.5

The closest answer choice to this value is C. 85, but it is not the correct answer. Therefore, the correct answer is none of the above.

Answer: All of them

Step-by-step explanation:

All of them can be divided into two equal halves.

The figures that show axis symmetry are 1, 2, and 3.

The axis of symmetry is a line, plane, or other axis that divides a geometric figure into two mirror-image halves that are congruent to each other.

A figure has axis symmetry if it looks the same after being rotated around an axis.

Out of the given figures, the ones that have axis symmetry are:

The figures that do not have axis symmetry are:

So, the figures that show axis symmetry are 1, 2, and 3.

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Amelia  can make inferences by using

Inferences from data on student heights include range determination based on minimum and maximum values, indicating greater variability with a larger range.

The average height of students can be determined using measures like mean, median, and mode. The distribution's shape can be determined by the histogram or box plot, indicating how the heights are distributed. inferences can be made by the use of height samples to gain insight into school population.

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The surface area of the rectangular prism is 82 square cm.

Given that:

Length, L = 3 cm

Width, W = 7 cm

Height, H = 2 cm

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as,

SA = 2(LW + WH + HL)

The surface area of the rectangular prism is calculated as,

SA = 2 x (3 x 7 + 7 x 2 + 2 x 3)

SA = 2 x (21 + 14 + 6)

SA = 2 x 41

SA = 82 square cm

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The points are not at a distance of 6 units from each other.

Given that the distance between point (2, 2) and point (8, 2) is 6 units a coordinate plane.

We need to find which other pairs of points are also 6 units apart.

The distance between two points (x₁, y₁), (x₂, y₂) are 6 if and only if either

( x₂ - x₁ = 6 and y₂ = y₁ )or ( x₂ = x₁ and y₂ - y₁ = 6 ).

If either of the conditions is satisfied, then only we can say that the two points has distance of 6 units between them.

Now, As given

Let (x₁, y₁) = ( 2, 2) , (x₂, y₂) = (8, 2)

Check whether the conditions are satisfied or not .

Here x₁ = 2 , x₂ = 8, y₁ = 2, y₂ = 2

Now,

x₂ - x₁ = 8 - 2 = 6 , y₂ - y₁ = 2 - 2 = 0

∴ we get

1st condition is satisfied, So the points have a distance of 6 units between them.

Now,

Let us suppose another point (x₁, y₁) = ( 4, 3) , (x₂, y₂) = (3, 3)

Here x₁ = 4 , x₂ = 3, y₁ = 3, y₂ = 3

Now,

x₂ - x₁ = 4 - 3 = 1 , y₂ - y₁ = 3 - 3 = 0

Here neither of the conditions are satisfied.

So, the points are not at a distance of 6 units from each other.

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The ratio of a:b in 5a-3b=7b is 4:5.

We know that,

A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are equal to each other. For example, if there are 2 boys and 6 girls, you can write the ratio as: 1 : 3 (for every boy there are 3 girls).

Ratios compare two numbers obtained by dividing. If one data point (A) is compared to another data point (B), it is expressed as A/B. It means that we are partitioning information A from information B. For example, if A is five and B is 10, your ratio would be 5/10, or 1/2.

For above information,

5a - 3b =  7b

5a = 7b- 3b

5a= 4b

So, a/b= 4/5

a:b  is 4:5

Thus, the ratio of a:b in 5a-3b=7b is 4:5.

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The solution and graph of each of the inequalities is shown below:

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Next, we would determine the solution for each of the inequalities as follows;

k + 7 ≥ 11

k ≥ 11 - 7

k ≥ 4

5 > v - 12

5 + 12 > v

17 > v

v < 17 (flip).

-5x ≤ -30

x ≤ 6

y/4 > 2

y > 2(4)

y > 8

10g + 19 > 49

10g > 49 - 19

10g > 39

g > 3.9

-w - 7 > 0

-w > 7

w > -7

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The measure of the missing angle is 20 degrees.

The figure in the image is a right triangle.

To solve for the missing angle. we use trigonometric ratio.

Note: Tangent = Opposite / Adjacent

Plug in the values and solve for the angles:

tanθ = 8/20

Take the tan inverse

θ = tan⁻¹( 8/20 )

θ = 21.8°

θ ≈ 20°

Therefore, the angle is 20 degrees.

Option B)20° is the correct answer.

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The requried value of x that satisfies the problem is 4.5,

Let's start by finding the side length of the square tabletop, which is equal to the square root of its area. We have:

Area = 9x² - 30x + 25

Side length = √(Area) = √(9x² - 30x + 25)

To find x, we need to use the fact that the perimeter of the table top is 34 feet. The perimeter of a square is given by 4 times the length of one of its sides, so we can write:

Perimeter = 4 * Side length

34 = 4 * √(9x² - 30x + 25)

8.5 = √(9x² - 30x + 25)

9x² - 30x - 47.25 = 0

We can solve this quadratic equation by using the quadratic formula gives,

x = 4.5 and -1.16

Therefore, the value of x that satisfies the problem is approximately 4.5, since the other solution is negative and not meaningful in this context.

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a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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a) Based on the exponential function, p(t)=1200 (1.026)^t, the item's current price with a rate of inflation of 2.6% per year is $1,200.

b) In 8 years, the future price of the item would be $1,473.53.

An exponential function is a mathematical equation depicting the relationship between one variable and another with a periodic constant rate of growth or decline.

Exponential functions are classified into two:

Let the number of years from today = t

Annual inflation rate = 2.6%

Current price = $1,200

Time in years = 8 years

p(t)=1200 (1.026)^t

p(8) = 1,200(1.026)^8

= $1,473.53

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The area of the border is 105.53 feet².

We have,

The swimming pool is a combination of two shapes.

Rectangle:

Length = 60 feet

Width = 30 feet

Area = 60 x 30 = 1800 feet²

Semicircle:

Diameter = 30 feet

Radius = 15 feet

Area = π/2 r² = 1/2 x 3.14 x 15 x 15 = 353.25 feet².

Now,

The area of the swimming pool.

= 1800 + 353.25

= 2153.25 feet²

Now,

Without the border.

Area of the swimming pool.

= rectangle area + semicircle area

= 60 x (30 - 1) + 1/2 x π x (15 - 1)²
= 60 x 29 + 1/2 x 3.14 x 14 x 14

= 1740 + 307.72

= 2047.72 feet²

Now,

The area of the border.

= 2153.25 - 2047.72

= 105.53 feet²

Thus,

The area of the border is 105.53 feet².

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We need to sample at least 18 wine bottles to construct a 90% confidence interval for the mean volume of the population, with a margin of error of at most 0.1 ounces.

To determine the sample size required for a given confidence interval and margin of error, we need to use the following formula:

[tex]n = (Z^2 * \sigma^2) / E^2[/tex]

Where:

n = sample size

Z = the z-score associated with the desired confidence interval (for 90% confidence, Z = 1.645)

σ = the standard deviation of the population (0.5 ounces in this case)

E = the desired margin of error (0.1 ounces in this case)

Plugging in the values, we get:

[tex]n = (1.645^2 * 0.5^2) / 0.1^2[/tex]

n = 17.1

Thus, we need to sample at least 18 wine bottles to create a 90% confidence interval for the population's mean volume, with a margin of error of no more than 0.1 ounces.

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We need to sample at least 69 bottles to construct a 90% confidence interval for the mean volume of the wine bottles with a margin of error at most 0.1 ounces.

We have,

To construct a confidence interval for the mean volume of the wine bottles, we need to use the formula:

Confidence interval = sample mean ± margin of error

Where,

Margin of error = z (σ/√(n))

Here, we want to construct a 90% confidence interval with a margin of error at most 0.1 ounces.

This means that the margin of error should be less than or equal to 0.1, and the confidence level is 90%, so the critical value of z is 1.645

(using a standard normal table or calculator).

We are given that the standard deviation is σ = 0.5 ounces.

We don't know the sample mean or the sample size (number of bottles), so we'll use the worst-case scenario to find the sample size that gives the largest margin of error.

The worst-case scenario is when the sample mean is equal to the population mean (μ) plus the margin of error (0.1 ounces), and the sample size is as small as possible (which gives the largest margin of error).

So, we have:

0.1 = 1.645 x (0.5/sqrt(n))

Solving for n, we get:

n = (1.645 x 0.5/0.1)²

n = 68.225

Rounding up to the nearest whole number, we get:

n = 69

Therefore,

We need to sample at least 69 bottles to construct a 90% confidence interval for the mean volume of the wine bottles with a margin of error at most 0.1 ounces.

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The function type of f(x) = √3x + 2 is A. square root

From the question, we have the following parameters that can be used in our computation:

f(x) = √3x + 2

In the above function, we have the notation √

The notation √ is a square root notation

This means that the function type of f(x) is A. square root

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The measure of the unknown angles in the parallel lines AC and DF with transversal HJ are as follow,

m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.

Two lines AC and DF are parallel to each other  in the attached figure

Transversal HJ cut  lines AC and DF at point B and E respectively.

Measure of ∠ABE = 63°.

Using the result based on corresponding angles, alternate interior angles , and vertically opposite angles of a parallel lines we get,

Measure of ∠ABE ≅ Measure of ∠DEH ( corresponding angles)

⇒Measure of ∠DEH = 63°

Measure of ∠ABE ≅ Measure of ∠BEF ( alternate interior angles)

⇒Measure of ∠BEF = 63°

Measure of ∠ABE ≅ Measure of ∠CBJ ( vertically opposite angles)

⇒Measure of ∠CBJ = 63°

Using the result of linear pair angles,

Measure of ∠ABE + Measure of ∠CBE = 180°

⇒ Measure of ∠CBE = 180° -63°

⇒  Measure of ∠CBE = 117°

Measure of ∠CBE ≅ Measure of ∠FEH ( corresponding angles)

⇒Measure of ∠FEH = 117°

Measure of ∠CBE ≅ Measure of ∠BED ( alternate interior angles)

⇒Measure of ∠BED = 117°

Measure of ∠CBE ≅ Measure of ∠ABJ ( vertically opposite angles)

⇒Measure of ∠ABJ = 117°

Therefore, the measure of the seven unknown angles formed in the parallel line are given by m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.

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The above question is incomplete, the complete question is:

Lines AC and DF are parallel. They are cut by transversal HJ with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E.

In the attached figure.

The measure of side DF is 15cm

Similar triangles are triangles that have the same shape, but their sizes may vary. For two traingles to be similar, the corresponding angles of the triangles must be equal.

And also, the ratio of corresponding sides of Similar triangles are equal

This means;

15 /25 = 9/DF

representing DF by x

15/25 = 9/x

15x = 25×9

15x = 225

divide both sides by 15

x = 225/15

x = 15cm

Therefore the measure of DF is 15cm

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Answer:

32.13

Step-by-step explanation:

The value of c in the equation 15.3 = c/2.1 is 32.13. To solve for c, you can cross-multiply and simplify the equation to c = 15.3 x 2.1 = 32.13.

The solution to the equation "the quotient of a number and 8 is 16" is 128. To solve for the number, you can multiply both sides by 8 to get "the number is 16 x 8 = 128."

To translate the sentence "the quotient of a number and 8 is 16" into an equation, you can use "x" to represent the number and write x/8 = 16.

Answer:

c or a

Step-by-step explanation:

i thing a

Answer:

2700

Step-by-step explanation:

20 inches x 15 inches x 9 inches! <3

also get some sleep lol

Answer:

If we are looking at 100th it is 176 if it's tens look at 7 and 9

Each of the graphs should be matched with the appropriate function as follows;

Graph 1: D. f(x) = (x - 2)² + 3

Graph 2: C. f(x) = -(x - 2)² - 3

Graph 3: B. f(x) = -(x - 3)² - 2

Graph 4: C. f(x) = (x - 3)² + 2

In Mathematics and Geometry, the standard or general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Mathematically, the vertex form of a quadratic function is modeled by this equation:

f(x) = a(x - h)² + k

Where:

In conclusion, we can logically deduce that each of the given quadratic function were either vertically translated or horizontally translated.

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Two other categories of data that could be used to better understand the physical fitness levels of students are:

Body composition data:

Cardiovascular fitness data:

We have,

Two other categories of data that could be used to better understand the physical fitness levels of students are:

Body composition data:

This data can include measurements such as body mass index (BMI), body fat percentage, and waist circumference.

By collecting body composition data for students, we can better understand their overall physical health and identify potential risk factors for chronic diseases related to physical fitness.

Cardiovascular fitness data:

This data can include measurements such as resting heart rate, maximal oxygen uptake (VO2 max), and cardiovascular endurance test results.

By collecting cardiovascular fitness data for students, we can better understand their cardiovascular health and fitness levels, as well as identify potential risk factors for heart disease and other related conditions.

Thus,

Two other categories of data that could be used to better understand the physical fitness levels of students are:

Body composition data:

Cardiovascular fitness data:

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The percentage of the questions she got wrong is 15%

What is a Percentage?

Percentage is a number or ratio by dividing the value by the total value and then multiplying the result by 100.

How to determine this

Out of 20 questions, Claire got 17 questions

i.e the questions she got right = 17

The questions she got wrong = 20 - 17 = 3

To get the percentage she got wrong

= 3/20 *100%

= 300/20%

= 15%

Therefore, the percentage she got wrong is 15%

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