If the height of this prism is 10 cm, what is the surface area
of the rectangular prism?
Surface Area = 2lw + 2lh + 2wh
5 cm
5 cm

The resulting histogram would show the distribution of the grades on the exam, with the bins and frequency of data points clearly displayed. The title, axis labels, and scales would provide context for the graph and make it easy to interpret the data.

In mathematics and computer science, a graph is a collection of points, called vertices or nodes, that are connected by lines, called edges or arcs. Graphs can be used to model and analyze relationships between objects or data, such as social networks, transportation systems, or web pages.

Here,

Part A:

The best graphical representation to display the given data is a histogram. A histogram is a bar graph-like representation of data that divides the data into intervals or bins and shows the frequency of each interval. Histograms are appropriate for displaying continuous data, which the grades on the exam can be considered as, and can also show the distribution of the data.

Part B:

To create a histogram of the given data, follow these steps:

Choose the number of bins or intervals. In this case, we can choose a reasonable number of bins, such as 6-8, to display the distribution of the grades.

Determine the range of the data. The lowest grade is 60 and the highest is 99, so the range is 99-60 = 39.

Calculate the bin size. The bin size is calculated by dividing the range by the number of bins. For example, if we choose 6 bins, the bin size would be 39/6 ≈ 6.5. Since it is difficult to have bins that are fractions of a point, we can round the bin size up to the nearest whole number to get a bin size of 7.

Create the bins. Starting from the lowest grade, create intervals or bins of size 7 that cover the range of the data. For example, the first bin would be 60-66, the second bin would be 67-73, and so on.

Count the frequency of data points that fall into each bin. For example, there are 2 data points in the first bin, 3 data points in the second bin, and so on.

Draw the histogram. On the horizontal axis, label and scale the bins. On the vertical axis, label and scale the frequency of data points in each bin. Draw a rectangle above each bin with a height equal to the frequency of data points in that bin.

Title: Grades on Recent 8th Grade Mathematics Exam

X-axis label: Grades

Y-axis label: Frequency

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If the noon class has a symmetric distribution, the median would be 15.

From the given table,

a) Evening class has the highest average age, that is 22 years.

b) Morning class has age that are the most spread out, that is 2.4.

c) If the noon class has a symmetric distribution, the median would be 15 (which is equal to the mean).

Therefore, if the noon class has a symmetric distribution, the median would be 15.

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Answer: 3.610^5+4.810^4 in scientific notation is 4.08*10^5.

Step-by-step explanation: The initial step to convert 3.610^5+4.810^4 into scientific notation is to combine the two values.

The sum of 3610 multiplied by 10 to the power of 5 and 4810 multiplied by 10 to the power of 4 is equal to adding 3610 multiplied by 10 to the power of 4 and 4810 multiplied by 10 to the power of 4, resulting in 40.8 multiplied by 10 to the power of 4.

We can convert 40.8*10^4 to scientific notation by shifting the decimal point to the left until there is only one non-zero digit to the left of the decimal, and denoting the number of decimal places moved with a 10 exponent.

Rewording: When you raise 40.810 to the power of 4, the result is 4.0810 to the power of 5 when you add 1 to the exponent. This is equivalent to multiplying 4.08 by 10 and raising it to the power of 5.

Let's assume that Mr. and Mrs. Johnson bought x adult tickets and y children's tickets.

Since there are three children, we know that:

y = 3x

The total cost of the parents' tickets is 7x, and the total cost of the children's tickets is 4y. Substituting y = 3x, we get:

total cost of parents' tickets = 7x

total cost of children's tickets = 4(3x) = 12x

Therefore, the ratio of the total cost of the parents' tickets to the total cost of the children's tickets is:

(7x) / (12x) = 7/12

So the answer is 7/12, which cannot be simplified further. Therefore, the ratio is 7/12, which can be written in the form aib as 0+7/12i.

Answer: 7:6

Step-by-step explanation:

1. There are two adults (Mr. and Mrs. Jonhson) and three children. So let's make adults = y and children = x

2. Adult tickets cost $7. So we are going to multiply 7 x 2y = $14

3. Children's tickets cost $4. So we are going to multiply 4 x 3x = $12

4. The last step is to fully reduce [tex]\frac{14}{12}[/tex] = [tex]\frac{7}{6}[/tex]

5. So the answer is 7:6

Using circle theorems CD =  9.17

Circle theorems are theorems that govern circle properties.

Given that form the figure EF = 8, ON = 3 and OM = 2, we need to find CD.

From the figure using Pythagoras' theorem

OE² = ON² + EN²

= ON² + (EF/2)²

= 3² + (8/2)²

= 3² + 4²

= 9 + 16

= 25

OE = √25

= 5

Also, OD² = OM² + DM²

Making DM subject of the formula, we have that

DM² = OD² - OM²

DM = √(OD² - OM²)

Now OD = OE = 5

So, we have that

= √(OD² - OM²)

= √(OE² - OM²)

= √(5² - 2²)

= √(25 - 4)

= √(25 - 4)

= √21

= 4.58

Now CD = 2DM

= 2 × 4.58

= 9.17

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The quadratic formula x = (-b ± √ ( [tex]b^2[/tex] - 4ac)  / (2a) is used to find the solutions (or roots) of a quadratic equation of the form [tex]ax^2[/tex] + bx + c = 0.

In this formula, "a", "b", and "c" are coefficients of the quadratic equation, and the ± symbol indicates that there are two possible solutions, one with a positive square root and one with a negative square root. By plugging in the values of "a", "b", and "c" from the given quadratic equation, one can use the quadratic formula to calculate the solutions for x that satisfy the equation.

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x = (-b ± √(b² - 4ac)) / (2a) is the formula x=-b±b2-4ac2a, used to find the solutions to a quadratic equation of the form ax2+bx+c=0.

The formula x = (-b ± √(b² - 4ac)) / (2a) is known as the Quadratic Formula, used to find the solutions to a quadratic equation of the form ax² + bx + c = 0.

The formula x=-b± b2 -4ac2a, is called the quadratic formula, which is used to find the solutions (or roots) to a quadratic equation of the form ax2+bx+c=0,

where a, b, and c are coefficients of the equation.

The term under the square root sign (b2-4ac) is called the discriminant and can tell you whether the quadratic equation has two real solutions (if the discriminant is positive), one real solution (if the discriminant is zero), or two complex conjugate solutions (if the discriminant is negative).

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The simplification that accurately explains the statement 73 = 713A is A = 73/713

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

7 3 = 7 1 3 A.

Express properly

So, we have

73 = 713A

Divide both sides of the equation by 713

So, we have

A = 73/713

Hence, the simplification that accurately explains the statement is A = 73/713

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Answer: 228.8cm

Step-by-step explanation:

Hope this helps! :)

the value of c is 11.165 lbs. This was calculated using the z-score formula, assuming a normal distribution with a mean weight of 10 lbs and a standard deviation of 0.5 lbs. This ensures that 99% of all parcels are at least 1 lb under the surcharge weight.

To find the value of c, we need to use the standard normal distribution and the z-score formula. Since we know that 99% of all parcels are at least 1 lb under the surcharge weight, we can use the z-score associated with the 99th percentile, which is 2.33 (from a z-score table).

The formula for the z-score is:

z = (x - μ) / σ

where x is the weight of the parcel, μ is the mean weight, and σ is the standard deviation.

In this case, we want to find the weight of the parcel that is at the 99th percentile, which is 1 lb under the surcharge weight. Let's call this weight x. We know that the surcharge weight is c, so the weight of the parcel that is 1 lb under the surcharge weight is (c - 1).

Using the z-score formula and substituting the values we know, we get:

2.33 = ((c - 1) - μ) / σ

We want to solve for c, so we need to rearrange the equation:

c - 1 = 2.33σ + μ
c = 2.33σ + μ + 1

We don't know the values of μ and σ, but we can use the fact that the distribution is normal to estimate them. We can assume that the distribution is centered at the mean weight of all parcels, and that the standard deviation is equal to the average difference between the weight of each parcel and the mean weight.

Let's say that the mean weight is 10 lbs, and the standard deviation is 0.5 lbs. Then, we can plug these values into the equation for c:

c = 2.33(0.5) + 10 + 1
c = 11.165

So, the value of c that ensures that 99% of all parcels are at least 1 lb under the surcharge weight is approximately 11.165 lbs.

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The probability that a congressman selected at random supports Bill A or Bill B is 0.83.

The probability that a congressman selected at random supports Bill A but not Bill B is 0.21.

The probability that a congressman selected at random supports neither Bill A nor Bill B is 0.17.

P(Bill A or Bill B) = P(Bill A) + P(Bill B) - P(Bill A and Bill B) = 0.35 + 0.62 - 0.14 = 0.83

ii. The probability that a congressman selected at random supports Bill A but not Bill B is the probability in the Bill A circle that is not in the overlap:

P(Bill A but not Bill B) = P(Bill A) - P(Bill A and Bill B) = 0.35 - 0.14 = 0.21

iii. P(neither Bill A nor Bill B) = P(not Bill A and not Bill B) = 0.17

Therefore, the probability that a congressman selected at random supports neither Bill A nor Bill B is 0.17.

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The average rate of change in revenue as the number of bluetooth speakers sold increases from 20 to 40 units is $34.50 per unit.

To find the average rate of change in revenue, we need to calculate the change in revenue over the change in units sold.

First, let's calculate the revenue for 20 and 40 units sold:

R(20) = 35(20) - 0.01(20)^2 = $670

R(40) = 35(40) - 0.01(40)^2 = $1360

Now we can calculate the change in revenue:

ΔR = R(40) - R(20) = $1360 - $670 = $690

And the change in units sold:

Δx = 40 - 20 = 20

Finally, we can calculate the average rate of change in revenue:

ΔR/Δx = $690/20 = $34.50

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The biggest effect of electing so many public officials is that it can be difficult for voters to make informed decisions.

With so many candidates to choose from, voters may not have the time or resources to thoroughly research each candidate and their qualifications. This can lead to uninformed voting, where voters may simply choose a candidate based on their name recognition, party affiliation, or other superficial factors.

Additionally, contested elections can also lead to an increase in negative campaigning and attack ads, which can further cloud voters' perceptions of the candidates and the issues at stake. Ultimately, electing a large number of public officials can make it harder for voters to feel confident in their choices and can undermine the democratic process.

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Answer: the exact value of tan(13π/12) is √3 + 2.

Step-by-step explanation: The trigonometric equation demonstrating the equality between the tangent of 13π/12 and the tangent of 3π/4 added to π/3 may be expressed in the formal and technical tone often employed in academic writing as follows: tan(13π/12) = tan(3π/4 + π/3).

Through utilization of the identity, tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)*tan(b)), the given expression may be rendered more concise.

The trigonometric expression tan(13π/12) can be represented as (tan(3π/4) + tan(π/3)) divided by (1 - tan(3π/4) multiplied by tan(π/3)).

It is established that:

it can be observed that the value of the trigonometric function of tan(3π/4) is -1.

The mathematical expression "tan(π/3) = √3" signifies that the trigonometric tangent function of the angle π/3 is equivalent to the square root of three.

Upon substitution of the aforementioned values, the resulting output is obtained.

The trigonometric function of tan(13π/12) can be expressed as a quotient between two real numbers. Specifically, it can be represented in the form (-1 + √3) / (1 + (-1) * √3).

By utilizing the conjugate of the denominator and performing the operation of multiplication on both the numerator and denominator, the resulting expression is obtained:

The trigonometric function of tangent evaluated at 13π/12 is expressed as the product of two fractions. The numerator of the first fraction is comprised of the difference of the values -1 and the positive square root of 3, while the denominator is the sum of the value 1 and the product of -1 and the square root of 3. The numerator of the second fraction is the sum of the values 1 and the positive square root of 3, while the denominator is the sum of the same values.

The trigonometric identity expressed as tan(13π/12) has been rendered in symbolic form, wherein the numerator is the summation of -1, √3, √3, and -3. The denominator is the product of (1 + √3) and (1 - √3).

The mathematical expression tan(13π/12) can be represented as (-2√3 - 4) / (-2).

The mathematical expression tan(13π/12) is equivalent to the value of √3 + 2.

The ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.

What is the scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Let h1 and h2 be the heights of the two similar prisms, and let A1 and A2 be the areas of their respective bases.

Also, let k be the scale factor that relates the smaller prism to the larger prism.

a. We know that the volumes of the two similar prisms are proportional to the cubes of their corresponding side lengths, so we have:

(kh1)³ / (kh2)³ = 135 / 5000

Simplifying this expression, we get:

h1³ / h2³ = 135 / 5000

Taking the cube root of both sides, we get:

[tex]h1 / h2 = (135 / 5000)^{(1/3)}[/tex]

Using a calculator, we find:

h1 / h2 ≈ 0.405

Therefore, the ratio of the heights of the two similar prisms is approximately 0.405 to 1.

b. The ratio of the areas of the bases of two similar prisms is equal to the square of the scale factor. That is:

A1 / A2 = k²

To find the scale factor k, we can use the fact that the volumes of the two prisms are proportional to k³. Therefore:

k³ = 5000 / 135

k ≈ 5.091

Using this value of k, we get:

A1 / A2 = k² = (5.091)² ≈ 26

Therefore, the ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.

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The correct answer is (a) 114 standard hours.

To find the measured capacity of the work center, we need to add up the standard hours of work produced over the previous three weeks.
36 + 43 + 35 = 114
Therefore, the measured capacity of the work center is 114 standard hours.
The answer is (a) 114 standard hours.

To determine the measured capacity of the work center, you need to sum up the standard hours of work produced over the three weeks.

Here's the calculation:

36 standard hours (week 1) + 43 standard hours (week 2) + 35 standard hours (week 3) = 114 standard hours
So, the measured capacity of the work center is 114 standard hours. The correct answer is (a) 114 standard hours.

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The measured capacity of the work center is 114 standard hours. The correct answer is (a) 114 standard hours.

The correct answer is (a) 114 standard hours.

We must tally up the standard hours of work completed during the preceding three weeks in order to determine the measured capacity of the work center

36 + 43 + 35 = 114

Therefore, the measured capacity of the work center is 114 standard hours.

You must total the standard hours of work completed over the course of the three weeks in order to calculate the measured capacity of the work center.

Here's the calculation:

36 standard hours (week 1) + 43 standard hours (week 2) + 35 standard hours (week 3) = 114 standard hours

So, the measured capacity of the work center is 114 standard hours. The correct answer is (a) 114 standard hours.

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Answer:

2.15g + 0.75w = 20.35

Step-by-step explanation:

(no explanation needed)

The solution to the equation -2/(x - 8) = (x - 1)/(x + 2) is x = 3 after checking for extraneous solutions.

To solve the equation

-2/(x - 8) = (x - 1)/(x + 2)

We can start by cross-multiplying to eliminate the fractions

-2(x + 2) = (x - 1)(x - 8)

Simplifying both sides, we get

-2x - 4 = x² - 9x + 8

Bringing all the terms to one side, we get

x² - 7x + 12 = 0

Now we can factor the quadratic equation to get

(x - 3)(x - 4) = 0

So the solutions are x = 3 and x = 4. However, we need to check for any extraneous solutions that may have been introduced by the original equation.

Plugging in x = 3 to the original equation, we get

-2/(3 - 8) = (3 - 1)/(3 + 2)

Which simplifies to

2/5 = 2/5

Therefore, x = 3 is a valid solution.

Plugging in x = 4 to the original equation, we get

-2/(4 - 8) = (4 - 1)/(4 + 2)

Which simplifies to

1/2 = 3/6

Therefore, x = 4 is not a valid solution.

So the only solution to the equation is x = 3.

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An expression that represents the amount of money Henry would have saved in w weeks is $95 + ($5 x w)

Henry already has $95, and he can save an additional $5 per week. So after one week of saving, Henry would have a total of $100 ($95 + $5). After two weeks, he would have $105 ($100 + $5), and so on.

To find out how much total money Henry would have after 10 weeks of saving, we can use the same method. After 10 weeks, Henry would have saved a total of $145 ($95 + ($5 x 10)). So, Henry would have a total of $145 after 10 weeks of saving.

Now, let's talk about an expression that represents the amount of money Henry would have saved in w weeks. We can use the formula:

Total amount saved = $95 + ($5 x w)

This formula takes into account the $95 that Henry already has, and the additional $5 he can save each week. The "w" in the formula represents the number of weeks Henry has been saving for. By plugging in different values of "w", we can determine how much money Henry would have saved at different points in time.

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Answer:

y= 7/3x -7

Step-by-step explanation:

Slope is 7/3 (rise/run or up seven over 3) and when you continue the graph the line will eventually hit your y-intercept at -7

To find the area of the resulting surface when the given curve y = 1/4x^2 - 1/2 ln(x) is rotated about the y-axis, we can use the Surface of Revolution formula:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from a to b

Here, a = 3 and b = 5.

First, we need to find the derivative of y with respect to x (dy/dx):

y = 1/4x^2 - 1/2 ln(x)
dy/dx = (1/4 * 2x) - (1/2 * 1/x) = x/2 - 1/(2x)

Now, let's plug this into the Surface of Revolution formula:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (x/2 - 1/(2x))^2)] dx from 3 to 5

We will now integrate the expression within the brackets with respect to x from 3 to 5. This might be challenging to solve analytically, so we may need to use a numerical integration method or a calculator to find the exact value.

Once the integration is completed, you will obtain the surface area of the curve when rotated about the y-axis.

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To determine whether the normal approximation can be used to study the proportion of students in the population who go home every weekend, we need to check if the sample size is large enough and if the success-failure condition is met.

Sample size: A commonly used rule of thumb is that the sample size should be at least 10 times the number of successes and failures combined. In this case, the number of students who go home every weekend in the sample is 18, and the number who do not is 82. So the sample size is 100, which is greater than 10 times the number of successes and failures combined.

Success-failure condition: Another assumption for the normal approximation is that the sample proportion is not too close to 0 or 1. In this case, the sample proportion of students who go home every weekend is 18/100 = 0.18, and the proportion who do not is 0.82. Both proportions are between 0.1 and 0.9, so the success-failure condition is met.

Therefore, we can use the normal approximation to study the proportion of students in the population who go home every weekend.

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Answer:

a) What is her GROSS pay for a week? 1,400

b) What is her GROSS pay for a year? 67,200

c) What are her TOTAL DEDUCTIONS for a week? 351.39

d) What is her NET pay for a week? 1,048.61

e) What is her NET pay for a year? 50,333.28

f) What does she pay in Income Tax per YEAR? 13,535.52

g) What does she pay in CPP contributions per YEAR? 2,537.28

h) What does she pay in El contributions per YEAR? 793.92

i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%

Step-by-step explanation:

 GROSS

 NET

 There are 4 weeks in a month, 52 weeks in a year.

a) What is her GROSS pay for a week? 1,400

b) What is her GROSS pay for a year? 67,200

c) What are her TOTAL DEDUCTIONS for a week? 351.39

d) What is her NET pay for a week? 1,048.61

e) What is her NET pay for a year? 50,333.28

f) What does she pay in Income Tax per YEAR? 13,535.52

g) What does she pay in CPP contributions per YEAR? 2,537.28

h) What does she pay in El contributions per YEAR? 793.92

i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%

Answer:

for the following question the answer will be

1/5=0.2 given as example

60%=0.6

50%=1/2

3/4=0.75

for 1/6 there os no answer for it the answer is 0.166

Answer:

Vertical translation

Step-by-step explanation:

Let's compare each point to its corresponding point in the image.

First, look at point A. Look at point A'.

With respect to the shapes ABCD and A'B'C'D', they are in the same position (in between B/B' and D/D'; across from C/C').

If you look at the image again, you'll find that the shape A'B'C'D' is not a rotated version of ABCD.

Thus, we can rule out the option "90° clockwise rotation."

A reflection across the x-axis indicates that A'B'C'D' and ABCD would be symmetrical across the x-axis (a horizontal line).

Because ABCD and A'B'C'D' are not symmetrical across a horizontal line, we can also rule out "Reflection across the x-axis."

Now, look at the position of A'B'C'D' with respect to ABCD. It's directly next to ABCD. In other words, it was shifted sideways.

Translations are basically just shifts.

Recall that horizontal means up and down, while vertical means side to side.

Since this is a sideways shift, we can conclude that the translation was:

a vertical translation.

The thief stole 22 oranges using algebraic equations.

To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.

According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.

We also know that the thief was left with only 9 oranges. So we can set up the equation:

x - [(1/2)x + 2] = 9

Simplifying this equation:

(1/2)x - 2 = 9
(1/2)x = 11
x = 22

Therefore, the thief stole 22 oranges.

The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.

To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.

In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.

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Answer:

20 tables

Step-by-step explanation:

12a is the small tables and 8b is the 8 large tables so they are adding it together and getting 20 tables.

The volume of the given cone with a height of 17.3 and a diameter of 10.4 is  489.87 cubic cm

The volume of any cone can easily be determined by the formula (pi*r*r)*(h/3) where pi has the value of 3.14, 'r' is the radius of the cone, and 'h' is the given height of the cone.

Here in the given question, we can see that the height(h) given here is 17.3cm and the diameter is 10.4cm with which we can find the radius because we know the radius is the half of diameter so 'r' will be 5.2cm.

Now just putting the values of 'h' and 'r' in the given formula (pi*r*r)*(h/3)  we get the volume of the cone which is 489.87 cubic cm.

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Answer:

Step-by-step explanation:

here,

height h= 17.3cm

diameter= 10.4cm

therefore, radius r will be 5.2cm

pi= 3.14

solution:

volume v of cone= 1/3*pi*r2*h

= 1/3*3.14*5.2*5.2*17.3 cm3

= 489.7 cm3

explanation:

here, it is given that the height is 17.3cm and the radius is 5.2cm. we know that the formula for finding the volume of a cone is 1/3*pi*r2*h.

Answer:48

Step-by-step explanation:

Answer:

The numbers in order from biggest to smallest are: 0.925, 0.9, 0.871, 0.87, 0.637, 0.62, 0.125, 0.012, and 0.01.

Step-by-step explanation:

To order these numbers from biggest to smallest, I compared the digits in each decimal place starting from the tenths place. For example, the number with the largest digit in the tenths place is 0.9. If two or more numbers have the same digit in the tenths place, I then compared the digits in the hundredths place and so on until I found which number was larger.

Answer:

Hello thanks for submitting here is the equation commonly known for this type of thing!

Equation y = 12.50x. 2

If you need the answer let me know!