Can someone show me step by step correctly for a better grade
There are approximately 7.48 liquid gallons in a cubic foot. If a cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet, what is the approximate height of the water tank? Approximate using π = 3.14 and round to the nearest tenth.

4.6 feet

14.4 feet

46.0 feet

147.1 feet

Let the speed in still water be [tex]x[/tex] miles per hour.

The speed upstream will be slower than the speed downstream.

Speed upstream [tex]= x-4[/tex] miles per hour and speed downstream will be [tex]x+4[/tex] miles per hour.

[tex]\text{Time Taken}=\dfrac{\text{Distance}}{\text{Speed}}[/tex]

The time taken for the trip upstream and the trip downstream are the same:

[tex]\text{time}_{\text{up}}=\dfrac{3}{x-4}[/tex]

[tex]\text{time}_{\text{down}}=\dfrac{11}{x+4}[/tex]

[tex]\dfrac{11}{x+4} =\dfrac{3}{x-4} \ \ \ \ \ \ \ \leftarrow \ \text{cross multiply}[/tex]

[tex]11(x-4)=3(x+4)[/tex]

[tex]11x-44=3x+12[/tex]

[tex]11x-3x=12+44[/tex]

[tex]8x=56[/tex]

[tex]\bold{x=7}[/tex] miles per hour

The first option, "one half," corresponds to the scale factor of 0.5.

Scale factor = Dimensions of the new shape Dimensions of the original shape is the fundamental formula used to calculate it. The formula is expressed as Scale factor = Larger image dimensions Smaller figure dimensions in the event that the original figure is enlarged.

We can contrast the side lengths of triangles D and D′ to determine the scaling factor.

Let's contrast the side lengths for the two triangles.

Triangle D has sides that are 4.2 in length, and triangle D′ has sides that are 2.1 in length.

Scale factor = (Side length of triangle D′) / (Side length of triangle D)

Scale factor = 2.1 / 4.2

Scale factor = 0.5

The first option, "one half," corresponds to the scale factor of 0.5.

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None of the descriptive alternatives are correct.

What is the null hypothesis?

In statistical hypothesis testing, null and alternate hypotheses are utilized. The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

Here, we have

Given:  if obtained from an experiment, would lead to rejecting the null hypothesis if a = .01.

for 1st choice ; p-value =fdist(5,3,18)= 0.0107

for 2nd choice : p-value =fdist(4.08,3,8)=0.0496

for 3rd choice : p-value =fdist(150,1,1)=0.052

since none of the choices have p value less than 0.01; none of these would lead to a rejected null hypothesis.

Hence, none of the descriptive alternatives are correct.

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Answer:

To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:

z = (x - μ) / σ

Where:

x = ACT score of 31

μ = mean of ACT scores (28)

σ = standard deviation of ACT scores (2)

z = number of standard deviations away from the mean

Substituting the values, we get:

z = (31 - 28) / 2

z = 1.5

Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.

True, r² is a metric that expresses how much of a variable is accounted for by a basic linear regression model.

Calculate the sum of squares for the regression model (SSR):  SSR = Σ (predicted values - mean of the dependent variable)²

Calculate the sum of the squares of the residuals (SSE): SSE = Σ (observed values - predicted values)²

Calculate the coefficient of determination (r²): r² = SSR/ (SSR + SSE)

The coefficient of determination (r²) is then a percentage measure of the proportion of the variation explained by the simple linear regression model.

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the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."

How to solve the question?

To calculate the overall gain or loss, we need to first find the total cost of buying the shares and the total revenue from selling them.

For the 40 shares of Zycodec purchased at its lowest price of 29.39, the total cost would be:

40 shares x $29.39/share = $1,175.60

For the 95 shares of Unix purchased at its highest price of 16.12, the total cost would be:

95 shares x $16.12/share = $1,531.40

The total cost of purchasing both stocks would be:

$1,175.60 + $1,531.40 = $2,707

Now, we need to find the total revenue from selling the shares. The closing price of Zycodec is 34.95, so the revenue from selling 40 shares would be:

40 shares x $34.95/share = $1,398

The closing price of Unix is 15.78, so the revenue from selling 95 shares would be:

95 shares x $15.78/share = $1,499.10

The total revenue from selling both stocks would be:

$1,398 + $1,499.10 = $2,897.10

The overall gain or loss would be the difference between the total revenue and total cost:

Overall gain/loss = total revenue - total cost

Overall gain/loss = $2,897.10 - $2,707

Overall gain/loss = $190.10

Since the overall gain is positive, we can conclude that the stockholder made a profit of $190.10. Therefore, the correct answer is: "The overall gain is $190.10."

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Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

we get the coordinates of Q' as (2,3) after rotation of the triangle.

What is rotation of axis?

Rotation of axes is a transformation in which the coordinate axes are rotated by a certain angle with respect to the original axes. This transformation can be used to simplify the equations of curves and to make it easier to solve problems involving them. The rotation is usually done by finding the angle of rotation, which is the angle between the original x-axis and the new x-axis. The formulae for converting coordinates from the old system to the new system can then be applied.

In the given problem, we are given that triangle PQR is located in the xy-plane with coordinates of Q being (2,-3). The task is to find the coordinates of Q' when triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R'.

To start, we apply the 180 degree clockwise rotation about the origin transformation rule to the coordinates of Q (2,-3) which gives us (-2,3).

Next, we reflect the point (-2,3) across the y-axis. Reflecting across the y-axis involves changing the sign of the x-coordinate while leaving the y-coordinate unchanged. Applying this rule,

Hence, we get the coordinates of Q' as (2,3) after rotation of the triangle.

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The probability for the possibility on a failing the exam is  1/3 , shown on the scale.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Any collection of results constitutes an event. Events are represented by capital letters, such as A and B. For instance, if the experiment involves flipping a single fair coin, event A might only receive one head. P(A) represents the probability of an event A.

Given that-

probability = number of favourable outcome / total outcome

number of favourable outcome = 1

number of total outcome = 3

probability = 1/3

Thus, the probability for the possibility on a  failing exam is 1/3 , shown on the scale.

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The value of the given expression is 31/6.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

We can simplify the given expression using the order of operations (PEMDAS):

First, we evaluate the expression inside the parentheses:

9 - 3/4 = 35/4

Next, we simplify the multiplication by 2/3:

2/3 * 35/4 = 35/6

Now we substitute the above values in the expression and simplify:

-1/6 + 35/6 - 1/2 = (-1 + 35 - 3)/6

= 31/6

Therefore, the value of the given expression is 31/6.

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Answer:

999,000,000 bytes

Step-by-step explanation:

if you subtract the total of the gigabytes from the total of the megabytes you get this answer.

The average size of the 15 diameters is 25.00mm. Using the concept of percentages, the mass of copper, lead, and tin in the bronze bearing are 140 kg, 40 kg, and 20 kg, respectively.

To find the average size of the 15 diameters, we need to calculate the sum of all the dimensions and then divide by 15 (the total number of diameters).

The sum of the dimensions can be calculated as follows:

(5 x 24.99mm) + (6 x 25.01mm) + (4 x 25.00mm)

= 375.01mm

Now, we can calculate the average size by dividing the sum by 15:

Average size = 375.01mm / 15

= 25.00mm (rounded to 2 decimal places)

Therefore, the average size of the 15 diameters is 25.00mm.

b.

To find the mass of each metal, we need to determine how much of each metal is present in the bronze bearing. This can be done using the concept of percentage

Let's start by finding the mass of copper in the bearing:

Mass of copper = 70% of 200 kg = 0.7 x 200 kg = 140 kg

Next, let's find the mass of lead in the bearing:

Mass of lead = 20% of 200 kg = 0.2 x 200 kg = 40 kg

Finally, let's find the mass of tin in the bearing:

Mass of tin = 10% of 200 kg = 0.1 x 200 kg = 20 kg

Therefore, the mass of copper, lead, and tin in the bronze bearing are 140 kg, 40 kg, and 20 kg, respectively.

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Complementary angles are two angles whose sum is equal to 90 degrees. In other words, if you add the measures of two complementary angles, you get 90 degrees. Complementary angles are often referred to as "complements" for short. For example, if one angle is 30 degrees, its complement would be 60 degrees.

Supplementary angles, on the other hand, are two angles whose sum is equal to 180 degrees. In other words, if you add the measures of two supplementary angles, you get 180 degrees. Supplementary angles are often referred to as "supplements" for short. For example, if one angle is 120 degrees, its supplement would be 60 degrees.

Answer:

Step-by-step explanation:

Evaluate the expression

Divide 18 by 3 = 6

Then add the 6 to the 8

then subtract 7 from 14

answer=7

The value of the identities are;

1. sin M = 3√39/20

2. sin M = √3/5

3. sin M = 3√19/14

4. sin M = √3/2

The different trigonometric identities and their ratios are written as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

1. opposite = 3√39

Hypotenuse = 20

Then, sin M = 3√39/20

2. Opposite = 4√3

Hypotenuse = 20

sin M =  4√3/20

Divide the values

sin M = √3/5

3. The Opposite side = 3√19

Hypotenuse = 14

sin M = 3√19/14

4. Opposite = 6√3

Hypotenuse = 12

sin M =  6√3/12

Divide the values

sin M = √3/2

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The area of the parallelogram is[tex]39\sqrt(15)[/tex] square units.

In the preceding diagram, we must determine the height of the parallelogram in order to determine its area. The length of the perpendicular line segment drawn from vertex A to side BC determines the parallelogram's height. We'll refer to this line segment as AD. Since AD is perpendicular to BC, we can calculate its length using the Pythagorean theorem:

[tex]AD^2 = AC^2 - CD^2[/tex]

[tex]AD^2 = 12^2 - 3^2[/tex]

[tex]AD^2 = 135[/tex]

[tex]AD = \sqrt(135) = 3\sqrt(15)[/tex]

Now that we know the height of the parallelogram, we can use the formula for the area of a parallelogram:

Area = base x height

The base of the parallelogram is the length of side AB, which is 13 units. Therefore, the area of the parallelogram is:

[tex]Area = 13 \times 3\sqrt(15)[/tex]

[tex]Area = 39\sqrt(15) square units[/tex]

Therefore, the area of the parallelogram is [tex]39\sqrt(15)[/tex] square units.

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Answer:

Based on the information, the probability of rolling a number less than a 3 (that is, a 1 or a 2) is 56/200 = 7/25 = 28%.

The correct answer is (a) a = 0, b = two-thirds, c = 3.

This can be seen by comparing the given equation, y = two-thirds x squared + 3, to the general form of a quadratic equation, y = ax^2 + bx + c.

In the given equation, the coefficient of x^2 is two-thirds, so a = two-thirds. The coefficient of x is 0, so b = 0. And the constant term is 3, so c = 3.

Therefore, the correct answer is (a) a = 0, b = two-thirds, c = 3.

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The value of the variables are x = -2 and y = 4

From the information given, we have that the simultaneous equations are;

4x-5y=-28

-9x-2y=10

Make 'x' the subject from equation 1

4x = -28 + 5y

x = -28 + 5y/4

Now, substitute the value in equation 2, we get;

-9(-28 + 5y/4) - 2y = 10

expand the bracket

252 - 45y/4 - 2y = 10

find the lowest common multiple

252 - 45y - 8y/4 = 10

cross multiply

252 - 45y -8y = 40

collect the like terms

-53y = -212

Make y the subject

y = 4

substitute the value

x = -28 + 5y/4

x = -28 + 20/4

x = -8/4

x = -2

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For a continuous random variable X, which is uniformly distributed on an interval [4,9], the probability density function of [tex]f_Y( y)[/tex] is equals to

[tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise\ \ \end{cases}[/tex]. So, option(5) is correct.

We have a continuous random variable X is uniformly distributed on the interval [4,9]. The PDF is a probability that a random variable acquire a value exactly same or equal to the random variable but in case of CDF, this probability values is less than or equal to the random variable. The probability density function for X is defined as [tex]f_X(x) = \frac{1}{b - a} [/tex] so, we can write it as [tex]f_X ( x) =\begin{cases} \frac{1}{5},\quad 4≤ x ≤ 9 \\ 0, \quad otherwise \\ \end{cases}[/tex].

We have to determine the probability density function [tex]f_Y(y)[/tex]. For this first we have to calculate the cumulative distribution function for f(x) is written as [tex]F_X(x) = \int_{4}^{x} f(x) dx [/tex]

[tex]= \int_{4}^{x} \frac{1}{5} dx [/tex]

[tex]= \frac{1}{5} [ x]_{4}^{x} [/tex]

[tex]F_X(x) = \frac{x - 4}{5}[/tex]

Now, we have, [tex] Y = \sqrt{X}[/tex]

when X = 4 => Y = 2 and X = 9 => Y = 3

Also, X = Y²

Differentiating X = Y² with respect to Y

=> dX = 2Y dY

=> dX/dY = 2Y

Now, pdf of Y is written as [tex]f_Y(y) = f_X(x)|\frac{dX}{dY}| [/tex]

[tex] = \frac{ 1}{5} × 2y[/tex]

[tex]= \frac{ 2y}{5}[/tex]

So, [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex]. Hence, required value is [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex].

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Complete question:

The above figure complete the question.

A government structure that is authoritarian or dictatorial in nature would be threatened by debate over public policy.

In such a system, the government exercises complete control over decision-making and any opposition or dissent is not tolerated.

Open debate and discussion over public policy would challenge the authority of the government and its ability to maintain control over the population.

Democracies, on the other hand, thrive on healthy debate and discussion over public policy, as it allows for diverse perspectives and ideas to be heard and considered.

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The zeros of the function f(x) are:

For a function y = f(x), the zeros are the values of x such that:

f(x)= 0

Here we have:

f(x)= (4x-3) (2x-1)

The zeros are the values such that any of the coefficients are zero, then we have:

4x - 3 = 0

x = 3/4

And:

2x - 1 = 0

x = 1/2

These are the zeros.

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If the circumference of the circle is 153.86 units, then the radius of that  circle is 24.5 units.

The "Circum-ference" of circle is defined as "total-length" of boundary of the circle. The formula for circumference is = 2 × π × Radius,

The "Radius" of circle is the distance from center of circle to its outer edge. It is half of "diameter" of circle, and it is a measure of size of circle.

We know that, circumference of circle is 153.86 units,

So, the circumference equation becomes,

⇒ 2 × 3.14 × Radius = 153.86,

⇒ 153.86/(2 × 3.14) = Radius,

⇒ Radius ≈ 24.5

So, the radius of the circle is approximately 24.5 units.

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The given question is incomplete, the complete question is

What is the radius of the circle if it has a circumference of 153.86 units?

The value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

Expanding the determinant using the first row, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a | b c 7d + 7e b 7f + g h i| - b |a c 7d + 7e c 7f + g h i| + c |a b 7d + 7e 7f + g h i|

= a | b c 7d + 7e b 7f + g h i| + b |a c 7d + 7e c 7f + g h i| - c |a b 7d + 7e 7f + g h i|

Now, we can expand each of the three determinants on the right-hand side using the first row and simplify:

| b c 7d + 7e b 7f + g h i| = b | c 7f h i| - 7e |b 7f h i| + g |b c h i|

= -7e b |7f h i| + g |b c h i| - h |b c 7f i| + i |b c 7f h|

= -7e bi + gh - bhf + chi

|a c 7d + 7e c 7f + g h i| = a |c 7f h i| - 7e |c 7d h i| + g |c 7d 7f i|

= 7e ac - gci + chd - ahf

|a b 7d + 7e 7f + g h i| = a |b 7f h i| - 7e |b 7d h i| + g |b 7d 7f i|

= -7e ab + ghi - bgd + aef

Substituting these expressions back into the expanded determinant and simplifying, we get:

| a b c 7d + a 7e + b 7f + c g h i|

= a(-7e bi + gh - bhf + chi) + b(7e ac - gci + chd - ahf) + c(-7e ab + ghi - bgd + aef)

= -7abe - 7bdf - 7cfg + 7aef + bch + cgi + ahk - ceh - afg - bdi

= -7(abe + bdf + cfg - aef) + (bch + cgi + ahk - ceh - afg - bdi)

Since |a b c d e f g h i| = 5, we have:

abe + bdf + cfg - aef = 5

Therefore, we can simplify the expression further:

| a b c 7d + a 7e + b 7f + c g h i|

= -7(5) + (bch + cgi + ahk - ceh - afg - bdi)

= -35 + b(ch - di) + c(gi - eh) + a(hk - fg)

Hence, the value of | a b c 7d + a 7e + b 7f + c g h i| is given by -35 + b(ch - di) + c(gi - eh) + a(hk - fg).

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The simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

First, factor out the 7 from the second row:

| a b c 7(d + e + f) g h i| = 7| a b c d + e + f g h i|

Expand the second row using the property of determinants that allows us to break up a row sum:

7(| a b c d g h i| + | a b c e g h i| + | a b c f g h i|)

Now, use the property of determinants that allows us to switch rows and multiply by -1:

7(| a b c d g h i| + | a b c e g h i| - | d e f a b c g h i|)

Recognize that the third determinant is equivalent to the given determinant, but with rows 1 and 3 switched, which

gives us:

7(| a b c d g h i| + | a b c e g h i| - 5)

Finally, multiply 7 by the expression inside the parentheses:

7| a b c d g h i| + 7| a b c e g h i| - 35

So, the simplified expression for | a b c 7d + a 7e + b 7f + c g h i| is 7| a b c d g h i| + 7| a b c e g h i| - 35.

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The correct answer is D. Trapezoid EFGH is congruent to Trapezoid ABCD after undergoing transformation D.

Let's first define the transformations:

A. Translation down, followed by rotation of 90°, followed by dilation by a scale factor of 3.

B. Rotation of 45°, followed by a reflection, followed by a translation left.

C. Dilation by a scale factor of 12, followed by a translation up, followed by a reflection.

D. Reflection, followed by a dilation of a scale factor of 1, followed by a rotation of 180°.

To determine if Trapezoid EFGH is congruent to, an enlargement of, or a reduction of Trapezoid ABCD, we need to analyze the effects of each transformation on the trapezoid.

A. Translation down, followed by rotation of 90°, followed by dilation by a scale factor of 3.

This transformation involves moving the trapezoid down, rotating it 90 degrees clockwise, and then increasing its size by a scale factor of 3. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.

B. Rotation of 45°, followed by a reflection, followed by a translation left.

This transformation involves rotating the trapezoid 45 degrees clockwise, reflecting it across a line of reflection, and then moving it left. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.

C. Dilation by a scale factor of 12, followed by a translation up, followed by a reflection.

This transformation involves increasing the size of the trapezoid by a scale factor of 12, moving it up, and then reflecting it across a line of reflection. This transformation does not preserve angles or side lengths, so Trapezoid EFGH is not congruent to Trapezoid ABCD.

D. Reflection, followed by a dilation of a scale factor of 1, followed by a rotation of 180°.

This transformation involves reflecting the trapezoid across a line of reflection, then increasing its size by a scale factor of 1 (i.e., not changing its size), and then rotating it 180 degrees. This transformation preserves angles and side lengths, so Trapezoid EFGH is congruent to Trapezoid ABCD.

Therefore, the correct answer is D. Trapezoid EFGH is congruent to Trapezoid ABCD after undergoing transformation D.

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The statement "The least expensive animal to feed may not be the favorite animal for a pet" explains why Katie asked the wrong question.

What is graphs?

Graphs are used by mathematicians to logically express or chart facts and values visually. A graph point typically depicts the relationship between several things.

While the cost of feeding an animal may be an important consideration for some people when choosing a pet, it is not necessarily the only or even the most important factor. Many people choose pets based on factors such as their personality, behavior, and the amount of attention and care they require.

Therefore, the animal that is least expensive to feed may not necessarily be the animal that people consider to be their favorite pet.

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The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0680. So, the correct answer is option d.

Calculate the sample proportion:

The formula (p) = x/n, where x is the sample size (163) and n is the number of successes (96), yields the sample proportion.

Therefore, the sample proportion is 96/163 = 0.5896.

Calculate the standard error:

The formula SE(p) yields the sample proportion's standard error = √[p(1-p)/n], where n is the sample size, and p is the sample proportion.

Consequently, the sample proportion's standard error is as follows:

SE(p) = √[0.5896(1-0.5896)/163] = 0.037

Calculate the margin of error:

The margin of error is given by the formula ME = z × SE(p), where SE(p) is the standard error of the sample proportion and z is the z-score corresponding to the desired level of confidence.

The z-score for a 95% confidence interval is 1.96.

As a result, the error margin is:

ME = 1.96 × 0.037 = 0.0680

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Answer:

the diameter of the softball is approximately 4.72 inches.

Step-by-step explanation:

The formula to calculate the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.

We can rearrange the formula to find the radius of the softball:

r = cube root of [(3V)/(4π)]

r = cube root of [(3 x 33.5)/(4π)]

r ≈ 2.36 inches

The diameter is twice the radius:

d = 2r

d ≈ 4.72 inches

Therefore, the diameter of the softball is approximately 4.72 inches.

Answer: the diameter of the softball is approximately 4.22 inches.

Step-by-step explanation: The volume of a sphere can be calculated using the formula:

V = (4/3)πr^3

where V is the volume of the sphere, r is the radius of the sphere, and π is the mathematical constant pi.

To find the diameter of the softball, we can use the formula:

d = 2r

where d is the diameter of the sphere.

We know that the volume of the softball is 33.5 in^3. So, we can solve for the radius as follows:

33.5 = (4/3)πr^3

r^3 = (3/4)(33.5/π)

r^3 = 8.9375

r = ∛(8.9375)

r ≈ 2.11 inches

Now, we can find the diameter of the softball:

d = 2r

d = 2(2.11)

d ≈ 4.22 inches