Two similar cones have volume of 343pi cubic centimeters and 512pi cubic centimeters. The height of each cone is equal to 3 times its radius. Find the radius and height of both cones

Answer:

Find the five number summary of the data:

Minimum = x

Quartile 1 = x

Quartile 2 (median) = x

Quartile 3 = x

Maximum = x

Then, make the plot based on that information. If you are provided with a list of data, you should be able to use a calculator to find out that information.

Final answer:

A box-and-whisker plot is graphed by organizing data, finding the five key data points (minimum, Q1, median, Q3, maximum), plotting a box from Q1 to Q3 with a median line, drawing whiskers to the minimum and maximum values, and indicating outliers if any.

Explanation:

To graph a box-and-whisker plot, start with organizing the data in ascending order and then identify the five key data points: the minimum value, the first quartile (Q1), the median (the second quartile or Q2), the third quartile (Q3), and the maximum value. Follow these steps:

Answer:

13

Step-by-step explanation:

Answer:

They predict 1350 renters will buy liability insurance.

The answer is 1350 renters.

Step-by-step explanation:

Given:

A car rental company at the local airport estimates they sell liability insurance to 45% of their customers.

If they rent 3,000 cars next month.

Now, to find the renters they predict will buy liability insurance.

So, the rate of the car rental company which estimates of selling liability insurance to their customers is 45%.

And, the cars they rent next month = 3,000.

Now, to get the renters they predict of buying liability insurance by getting the rate of the cars they rent next month:

[tex]45\%\ of\ 3,000\\\\=\frac{45}{100}\times 3,000\\\\=0.45\times 3,000\\\\=1350.[/tex]

Hence, they predict 1350 renters will buy liability insurance.

Therefore, the answer is 1350 renters.

Answer:

The answer is

D. 8 inches

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cylinder this time.

Given data

Volume of cylindrical shape v=

56.52 inch³

Diameter of cylindrical glass d= 3

inch

But raduis r =diameter/2=3/2= 1.5

inch

We know that the the expression for the volume of a cylinder is given as

v= πr²h

Substituting our given data to solve for the height h

56.52= 3.14*(1.5)²*h

56.52= 7.065h

h= 56.52/7.065

h= 8 inches

To calculate the height of the cylindrical glass, use the volume formula with the radius from the diameter, and solve for the height. The final calculation shows that the glass is 8 inches tall, corresponding to option D.

To find the height of a cylindrical drinking glass given its volume and diameter, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, π (pi) is a constant approximated as 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

Since the diameter is given as 3 inches, the radius r is half of that, which is 1.5 inches. By substituting the values into the formula and solving for h, we get:

V = πr²h

56.52 = 3.14 × (1.5)² × h

56.52 = 3.14 × 2.25 × h

56.52 = 7.065 × h

h = 56.52 / 7.065

h = 8 inches

Therefore, the height of the drinking glass is 8 inches, which corresponds to choice D.

Answer:

Compounded Semiannually: $17,574.89

Compounded Quarterly: $17,588.68

Compounded Monthly: $17,597.98

Compounded Continuously: $17,602.66

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

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

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 4% into a decimal:

4% -> [tex]\frac{4}{100}[/tex] -> 0.04

Now, plug in the values to the equation:

Compounded Semiannually:

[tex]A=15,000(1+\frac{0.04}{2})^{2(4)}[/tex]

[tex]A=17,574.89[/tex]

Compounded Quarterly:

[tex]A=15,000(1+\frac{0.04}{4})^{4(4)}[/tex]

[tex]A=17,588.68[/tex]

Compounded Monthly:

[tex]A=15,000(1+\frac{0.04}{12})^{12(4)}[/tex]

[tex]A=17,597.98[/tex]

To find the value if compounded continuously, use the following formula:

[tex]A = Pe^{rt}[/tex]

[tex]A=15,000e^{0.04(4)}[/tex]

[tex]A=17,602.66[/tex]

The accumulated value of an investment is calculated differently depending on the compounding period - semiannually, quarterly, monthly or continuously. This involves the compound interest formula and understanding of how interest rates work.

The subject of this question is about calculating the accumulated value of an investment at a given interest rate with various compounding periods i.e., semiannually, quarterly, monthly, and continuously. We first need to understand that compound interest is calculated on the principal plus the accumulated interest.

To calculate the future value of the investment, we use the compound interest formula: P*(1+r/n)^(nt), where P is the principal (or initial investment), r is the annual interest rate (in decimal form), n is the number of compounding periods per year, and t is the time in years.

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Step-by-step explanation:

Science book weighs = 2 1/2 = 2.5 pounds

Library books weigh = 3/8 = 0.375 pounds

Math book weighs = 2.5 ÷ 2 = 1.25 pounds

Total weight of the books = 2.5 + 0.375 + 1.25 = 4.125 pounds

Answer:

1 and 5

Step-by-step explanation:

The squares have a side length of 10 and 1 square side is the radius of the half-circles. Since there are two half-circles, find the circumference for one full circle:

[tex]C=2\pi r[/tex]

Insert the radius:

[tex]r=10\\C=2\pi *10[/tex]

Simplify pi:

[tex]C=2*3.14*10[/tex]

Simplify multiplication:

[tex]C=6.28*10\\C=62.8[/tex]

The circumference of the circles is 62.8. Now find the perimeter of the exposed squares with side length 10. There are 4 exposed sides, which equals one square. Find the perimeter:

[tex]P=10+10+10+10\\P=10+10+20\\P=10+30\\P=40[/tex]

Add the perimeter of the circle and the square together:

[tex]P=62.8+40=102.8[/tex]

Now see which of the options gives you the perimeter:

1. [tex]40+20\pi =102.8[/tex]  ****

2. [tex]unavailable[/tex]

3. [tex]120+20\pi =182.8[/tex]

4. [tex]300+100\pi =614.2[/tex]

5. [tex]10+10+10\pi +10+10+10\pi =102.8[/tex] ****

Finito.

The expression . 40 + 20π and 10 + 10 + 10π + 10 + 10 + 10π gives the correct value of the perimeter is 102.8 .

We have to determine, the perimeter of the given shape in the question.

According to the question,

The squares have a side length of 10 and 1 square side is the radius of the half-circles.

There are two half-circles,

To find the circumference for one full circle:

[tex]C = 2\pi r[/tex]

Where radius = 10

[tex]C = 2\times 3.14 \times 10\\\\C = 62.8[/tex]

The circumference of the circles is 62.8.

To find the perimeter of the exposed squares with side length 10.

There are 4 exposed sides, which equals one square.

Therefore, perimeter p is given as,

[tex]P = 10+10+10+10\\\\P = 40[/tex]

On adding  the perimeter of the circle and the square together:

[tex]P = 62.8+ 40 = 102.8[/tex]

Check all the statement which give perimeter of the shape,

[tex]40+20\pi = 40+ 20\times3.14 = 102.8\\\\20\pi = 20 \times 3.14 = 62.8\\\\120+20\times \pi = 120+20\times3.14= 182.8\\\\300 + 100\times\pi = 300+100\times3.14 = 614\\ \\10+10+10\times\pi +10+10+10\times\pi = 40+ 20\times3.14 = 102.8[/tex]

Hence, The expression . 40 + 20π and 10 + 10 + 10π + 10 + 10 + 10π gives the correct value of the perimeter is 102.8 .

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Answer:

C≈157.08ft

Solution

C=2πr=2·π·25≈157.07963ft

Answer:

157.0796327 is my answer

The simplified expression for the number of moons of Neptune, based on the variable for Mars' moons m, is 6m + 2, meaning Neptune has twice as many moons as Mars plus two more.

The student has asked to write and interpret a simplified expression that represents the number of moons of Neptune, based on the information that Mars has m moons, Pluto has one more than twice the number of moons of Mars, and Neptune has one less than three times the number of moons of Pluto.

Let's denote the number of moons of Mars as m. According to the information, Pluto has 2m + 1 moons. Therefore, Neptune would have 3(2m + 1) - 1 moons. Simplifying this expression:

Neptune's moons = 3(2m + 1) - 1

= 6m + 3 - 1

= 6m + 2

The simplified expression 6m + 2 represents the number of moons of Neptune, which means that Neptune has twice as many moons as Mars plus an additional two moons.

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Answer:

Quentin made a total of 4 shots

Step-by-step explanation:

The complete question is as follows;

Quentin was challenged to a half-court shooting completion. For every half-court shot he makes, he will earn 20 points. For each half-court shot he misses, he will lose five points. After 20 half-court shots, Quentin has zero points. How many half-court shots did he make?

Now let's answer;

Let the number of shot he makes be x and the number of shot he misses be y

For every shot made, we have +20, for every shot missed, we have -5

Firstly we know that adding both numbers would give 20.

Mathematically;

x + y = 20        (i)

Now, we add the number of points he made to the number of points he missed to give a total of 0

Mathematically, that would be;

+20x -5y = 0  (ii)

from i, y = 20-x

Substitute this in ii

20x -5(20-x) = 0

20x - 100 + 5x = 0

25x = 100

x = 100/25

x = 4

This means that he made 4 shots

Answer:

65 quarts of water and 39 quarts of juice are required to make 104 quarts of banana berry smoothies

Step-by-step explanation:

Given:

Ratio of water and juice in banana berry smoothies = [tex]5:3[/tex]

To find:

Amount of water and juice required to make 104 quarts of banana berry smoothies

Solution:

Amount of water required to make 104 quarts of banana berry smoothies = [tex]\frac{5}{8}[/tex]×104 = 5×13 = 65 quarts

Amount of juice required to make 104 quarts of banana berry smoothies = [tex]\frac{3}{8}[/tex]×104 = 3×13 = 39 quarts

So,

65 quarts of water and 39 quarts of juice are required to make 104 quarts of banana berry smoothies.

To make 104 quarts of banana berry smoothies with a water to juice ratio of 5:3, Just Juice should mix 65 quarts of water with 39 quarts of juice.

To make banana berry smoothies with a mix of water and juice in a ratio of 5 to 3, and to create a total of 104 quarts, we need to find the amount of water and juice separately. Since the total parts of the ratio is 5 parts water plus 3 parts juice, which equals 8 parts, we can calculate the amount of each as follows:

Therefore, Just Juice should mix 65 quarts of water with 39 quarts of juice to make 104 quarts of banana berry smoothies.

Answer:

A = [tex]8\sqrt{110}[/tex] [tex]inches^{2}[/tex]

Step-by-step explanation:

In this question, we are tasked with calculating the area of a triangle given the length of its three sides

Mathematically, we can calculate this using the Heron's formula

For Heron's formula, A = [tex]\sqrt{S(S-A)(S-B)(S-C)}[/tex]

WHERE S = [tex]\frac{A+B+C}{2}[/tex]

we take the lengths of the triangle as A,B and C respectively as given

S = (12 + 14 + 18)/2 = 22

Plugging the values into the equation, we have;

A = [tex]\sqrt{22(22-12)(22-14)(22-18)}\\ \\\sqrt{22(10)(8)(4)} \\\\\sqrt{7040}[/tex]

A = [tex]8\sqrt{110}[/tex] [tex]inches^{2}[/tex]

Answer:

8*sqrt(110)

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

if you are really stuck just go through each possible answer to see if its right

here is some help for solving:

area is equal to length times width or   A = L x W

perimeter is equal to length plus width plus length plus width or L+W+L+W

perimeter is just adding up all the sides of the square or rectangle

so if you try with answer a you get:

2 x 6 = 12   and   2 + 6 + 2 + 6 = 16

the answer is A

Answer:

4

Step-by-step explanation:

When M varies inversely P squared rhen this is represented as

[tex]M=\frac {k}{P^{2}}[/tex]

Here, k is a constant of proportionality

Now when M is 9 and P is 2, P squared will be 4. Now substituting the value of P squared and M into the equation we can find the xonstant of proportionality as

K=9*4=36

Now that we have k, when P is 3 then we substitute the value of P as 3 and k as 36 into the first equation hence

[tex]M=\frac {36}{3^{2}}=4[/tex]

Therefore, M=4

Answer:

g(x) = 1

Step-by-step explanation:

Answer:

15 feet

Step-by-step explanation:

1 yard = 3 feet

2 yards = 6 feet

3 yards = 9 feet

4 yards = 12 feet

5 yards = 15 feet

Answer:

15 feet.

Step-by-step explanation:

Hello there!

First calculate how many feet are in a yard, then multiply it by 5.

[tex]1*3=3\\3*5=15 ft[/tex]

;)

Answer:

Yes, it does

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

12*12=144

Answer:

2(e^2+6e+11) is the GCF

Answer:

4quarters and 14dimes

Step-by-step explanation:

Answer:

The answer is x=10

Step-by-step explanation:

Answer:

the answer to the equation is x=10

Answer:

c

Step-by-step explanation:

Answer:

C.                                                  

Step-by-step explanation:

Step-by-step explanation:

21x/7x = 21/7    (The x cancel out)

          = 3

The square root of a positive number cannot be negative, all positive numbers have two square roots, and 25 = 5 because 52 = 25.

The statements that are true about square roots are:

These statements are correct because the square root of a positive number will always be positive, every positive number has two square roots (one positive and one negative), and the square root of 25 is 5 because 5 multiplied by itself is equal to 25.

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Answer:

money they will have saved for his 16th birthday = $18,926

Step-by-step explanation:

This is a geometric series problem.

The sum of a geometric series is given by the formula;

Sn = a1•(rⁿ - 1)/(r - 1)

Where;

a1 is the first term

n is the number of terms

r is the constant ratio

Now, in this question, they started saving since he was born till his 16th birthday. That's 16 years. Thus number of terms; n = 16

Also, the first money saved was $800, thus the first term; a1 = 800

They save 5% more each year than the previous year. That's an increase of 1.05 each year. Thus, the common ratio; r = 1.05

The amount of money they will have by his 16th birthday will be;

S_16 = 800•(1.05^(16) - 1)/(1.05 - 1)

S_16 = 800(1.18287458838/0.05)

S_16 = $18,926

S16 = $800·(1.05^16 -1)/(1.05 -1)

Answer:

[tex]\sigma=547.1125[/tex]

Step-by-step explanation:

-The margin of error is calculated using the formula:

[tex]ME=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\\\[/tex]

-We substitute the values, n=900 and ME=30 in the formula to solve for standard deviation:

[tex]ME=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\\\\\30=1.645\times\frac{\sigma}{\sqrt{900}}\\\\\sigma=\frac{30^2}{1.645}\\\\=547.1125[/tex]

Hence, the population standard deviation is 547.1125

Answer: it is the last one

Step-by-step explanation:

If you were to plot the point (4,-12), the correct method is to plot the point 4 units right, then 12 units down

Option D is correct

If a point is expressed in the form (x, y), the coordinate x represents the location of the point on the horizontal axis while the coordinate y represents the location of the point on the vertical axis

If x is positive, it means that the point is plotted on the right hand side of the horizontal axis. If x is negative, it means that the point is plotted on the left hand side of the horizontal axis

If y is positive, it means that the point is plotted on the  top region of the vertical axis. If y is negative, it means that the point is plotted on the bottom region of the vertical axis

For the point (4, -12)

x = 4, and y = -12

Since x = 4 is positive, the graph is plotted 4 units to the right

Since y = -12 is negative, the graph is plotted 12 units down

Therefore, If you were to plot the point (4,-12), the correct method is to plot the point 4 units right, then 12 units down

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Answer:

3 fold or 3 times

Step-by-step explanation:

The rate of increase of the house is 200%.

To calculate the rate of increase of the house, we can use the formula:

Rate = ((Final Value - Initial Value) / Initial Value) * 100

Using the given values, the rate of increase of the house is: ((150000 - 50000) / 50000) * 100 = 200%

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Answer:

A = Quartile 1 = 74.725

B = Median (quartile 2) = 80.25

C = Quartile 3 = 82.125

D = Minimum = 74.1

E = Maximum = 82.7

Step-by-step explanation:

The values for the data for the average life expectancy are as follows;

North Carolina                    79.6  

Oregon                                82  

District of Columbia           77.9

Nevada                               81.3  

New York                           82.5  

Colorado                            80.9  

Alaska                                74.9  

Connecticut                       82.7  

Montana                            74.1  

Mississippi                         74.2  

Sorting the data we have;

74.1

74.2

74.9

77.9

79.6

80.9

81.3

82

82.5

82.7

The minimum value is 74.1

The maximum value is 82.7

The 1st quartile is the [tex]\frac{10 + 1}{4} th[/tex] term or 74.725

The median 2nd quartile is the [tex]\frac{10 + 1}{2} th[/tex] term and the value is 80.25

Third quartile value is the[tex]\frac{3\times (10 + 1)}{4} th[/tex] term or 82.125.

Answer:

11.43 gallons used exactly per week asuming not changes in schedule or any other reasons to drive and that a one way trip is 24 miles.

Step-by-step explanation:

48 as total for two trips

five of these need to be done, so 240 miles a week assuming no other reason to drive

240 / 21 = 10 with remainder 30

so 11 and remainder 9

9/21 = nearly .43 gallons, which means as a minimum she shouldn't go below 11.5 and better yet 12 gallons.

Candace drives 240 miles each week (48 miles per day * 5 days). Given her car's fuel efficiency is 21 miles per gallon, she would therefore need approximately 11.43 gallons of gas (240 miles / 21 miles per gallon) for her weekly commute.

To answer the question of how many gallons of gas Candace needs to get to work and back home each week, you need to first know how many miles she is driving in total for that week.

First, let's find the total miles she drives weekly. We know she drives 48 miles each day to work and back home and she works 5 days a week. So, miles per week = 48 miles per day * 5 days per week = 240 miles per week.

Next, we know her car gets 21 miles per gallon of gas. To find the gallons required, we divide the weekly miles by the miles per gallon. So, Gallons used per week = 240 miles per week / 21 miles per gallon ≈ 11.43 gallons per week.

So, she needs approximately 11.43 gallons of gas to drive to work and back home each week.

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