Rewrite the following as a mix numbers 17/3

9) Volume of the cone: [tex]9152 mm^3[/tex]

10) New volume of the cone: [tex]339 mm^3[/tex]

11) The volume of the cone shrinks by a factor of [tex]3^3=27[/tex]

12) Volume of the composite  figure: [tex]15 ft^3[/tex]

Step-by-step explanation:

9)

The volume of a cone is given by the equation

[tex]V=\frac{1}{3}\pi r^2 h[/tex]

where

[tex]\pi r^2[/tex] is the area of the base, where

r is the radius of the cone

h is the height of the cone

For the cone in this problem, we have:

r = 18 mm (radius)

h = 27 mm (height)

Therefore, the volume of this cone is

[tex]V=\frac{1}{3}\pi (18)^2 (27)=9152 mm^3[/tex]

10)

In this second exercise, the radius and the height of the cone are divided by 3. Therefore we have:

[tex]r'=\frac{r}{3}=\frac{18}{3}=6 mm[/tex] is the new radius of the cone

[tex]h'=\frac{27}{3}=9 mm[/tex] is the new height of the cone

Therefore, the new volume of the cone is

[tex]V=\frac{1}{3}\pi r'^2 h'[/tex]

And substituting, we find

[tex]V=\frac{1}{3}\pi (6)^2 (9)=339 mm^3[/tex]

11)

We can understand what happened to the volume of the cone after dividing its dimensions by 3 by calculating the ratio of the original volume to the new volume:

[tex]\frac{V}{V'}=\frac{9152}{339}=27[/tex]

This means that the new volume of the cone is 27 times smaller than the original volume.

We see that this "factor of shrinking" corresponds to the total factor of shrinking ofits dimensions, to the power of 3. In fact:

- Each the radius and the height of the cone has shrunk by a factor of 3

- However, the cone is a figure in 3  dimensions, so the total factor of shrinking of its volume is [tex]3^3 = 27[/tex]

12)

The composite figure consists of a squared pyramid + a parallelepiped.

The volume of the square pyramid is given by:

[tex]V_1 = \frac{1}{3}Lwh[/tex]

where

L = 5 ft is the length of the base

w = 1 ft is the width of the base

h = 6 ft is the height of the pyramid

Substituting,

[tex]V_1 = \frac{1}{3}(5)(1)(6)=10 ft^3[/tex]

The volume of the parallelepiped is given by

[tex]V_2=Lwh[/tex]

where

L = 5 ft is the length of the base

w = 1 ft is the width of the base

h = 1 ft is the height

Substituting,

[tex]V_2 = (5)(1)(1)=5 ft^3[/tex]

So, the total volume of the composite figure is

[tex]V=V_1+V_2=10+5=15 ft^3[/tex]

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Answer:

9) Volume of the cone: 9152 mm^3

10) New volume of the cone: 339 mm^3

11) The volume of the cone shrinks by a factor of 3^3=27

12) Volume of the composite  figure: 15 ft^3

Step-by-step explanation:

Answer:

8:36

Step-by-step explanation:

Factors: 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36

GCF: 4

8 ÷ 4 = 2 36 ÷ 4 = 9

Answer:

The fraction less than  [tex]\frac{3}{5}[/tex] is   [tex]\frac{3}{10}[/tex]

Step-by-step explanation:

Given fractions are

[tex]\frac{3}{5} ,\frac{3}{10} ,\frac{3}{4}, \frac{2}{3}, \frac{5}{3}[/tex]

[tex]\frac{3}{5} =0.6\\\\\frac{3}{10}= 0.3\\\\\frac{3}{4} =0.75\\\\\frac{2}{3}=0.66 \\\\\frac{5}{3}=1.66[/tex]

Arranging the fraction in increasing order of their value

     [tex]\frac{3}{10}= 0.3<\frac{3}{5} =0.6<\frac{2}{3}=0.66<\frac{3}{4} =0.75<\frac{5}{3}=1.66[/tex]

So,the fractions less than  [tex]\frac{3}{5}[/tex] is   [tex]\frac{3}{10}[/tex]

Answer: 95 sold



Step-by-step explanation:

995 horses and cows - 510 horses and 390 cows left = 95 sold

Answer:

95

Step-by-step explanation:

add 510 + 390 to find out the total number of horses and cows he has left. this equals 900

then you subtract the total of horses and cows he started with by what he has left to find out how many he sold

995-900=95

Answer: 90 tarts

Step by Step: 150/5 = 30

30 multiplied times 3 = 90

Final answer:

Jake initially had 750 tarts, sold 450 of them, and had 150 tarts remaining after giving some to his friends.

Explanation:

Jake initially had a total number of tarts. He sold 3/5 of them and then gave 1/4 of the remainder to his friends. If he had 150 tarts left, we need to calculate the number he sold. Let's denote the total number of tarts as T. After selling 3/5 of T, Jake would have 2/5T left. Then, he gives away 1/4 of 2/5T, which means he's giving away 1/4 * 2/5T = 1/10T. So, he is left with 2/5T - 1/10T = 1/5T. We know that 1/5T equals 150, so T equals 150 * 5 = 750. Jake sold 3/5 of these, which is 3/5 * 750 = 450 tarts.

there is not any slope for this mathematical equation

To find one-third of the tank's maximum volume, multiply the maximum volume by one-third: 1/3 * 3rs/4 = 3rs/12.

To find one-third of the tank's maximum volume, we can multiply the maximum volume by one-third:

1/3 × 3rs/4 = 3rs/12

So, one-third of the tank's maximum volume is 3rs/12 liters.

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Answer:

[tex]4\frac{1}{2}[/tex]

Step-by-step explanation:

The sequence is [tex]3\frac{1}{2}, 3\frac{5}{6}, 4\frac{2}{12}, .... , 4\frac{5}{6}[/tex].

So, we have to find the missing term.

The sequence can be written in improper fraction as [tex]\frac{7}{2}, \frac{23}{6}, \frac{25}{6}, ... , \frac{29}{6}[/tex].

Therefore, the sequence is in A.P. as the consecutive numbers in the sequence are increasing by [tex]\frac{1}{3}[/tex].

As, [tex](\frac{23}{6} - \frac{7}{2}) = \frac{1}{3} = (\frac{25}{6} - \frac{23}{6})[/tex].

Therefore, the missing number is [tex](\frac{25}{6} + \frac{1}{3}) = \frac{27}{6} = \frac{9}{2} = 4\frac{1}{2}[/tex]. (Answer)

Answer:

$883.40

Step-by-step explanation:

Calculate the amount of money needed to pay after the discount.n

$1049 × 88% = $923.12

Calculate the amount of money needed to pay after the tax.

$923.12 × 104.5% = $883.3684210526

=$883.40(rounded off to nearest cents)

hope  this helps

To find the final price of the television on sale, calculate the discount amount, subtract it from the original price, and then add the sales tax amount.

To find the final price of the television, we first need to find the discount amount by multiplying the original price ($1,049) by the discount percentage (12%).

Discount amount = $1,049 × 0.12 = $125.88

Next, subtract the discount amount from the original price to get the sale price:

Sale price = $1,049 - $125.88 = $923.12

Finally, add the amount of sales tax to the sale price. To find the sales tax amount, multiply the sale price by the sales tax rate (4.5%):

Sales tax amount = $923.12 × 0.045 = $41.54

Final price = Sale price + Sales tax amount = $923.12 + $41.54 = $964.66

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The height of living room ceiling is 15 feet.

Step-by-step explanation:

Given,

Height of ceiling in bedroom = 10 feet

This is 2/3 height of living room ceiling.

Let,

x be the height of living room ceiling.

2/3 of x = 10

[tex]\frac{2}{3}x=10[/tex]

Multiplying both sides by 3

[tex]3*\frac{2}{3}x=10*3\\2x=30[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{30}{2}\\x=15[/tex]

The height of living room ceiling is 15 feet.

Keywords: fraction, division

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The height of the living room ceiling is 15 feet.

To find the height of the living room ceiling, we can start by letting 'x' represent the height of the living room ceiling.

Since the bedroom ceiling is 2/3 as high as the living room ceiling, we can write the equation:

10 = (2/3)x

To solve for x, we can multiply both sides of the equation by 3/2:

(3/2)(10) = (3/2)((2/3)x)

15 = x

Therefore, the height of the living room ceiling is 15 feet.

Answer:

Therefore the volume of the box is 13824 in³

Step-by-step explanation:

Given:

A spherical ball with is packaged in a box that is in the shape of a cube.

Volume of ball = 2304π in³.

Let 'r' be the radius of sphere

To Find:

Volume of Cube = ?

Solution:

Volume of sphere is given by

[tex]\textrm{Volume of sphere}=\dfrac{4}{3}\pi r^{3}[/tex]

Substituting the values we get

[tex]2304\pi=\dfrac{4}{3}\pi r^{3}\\\\\therefore r^{3}=1728\\\\Cube\ Rooting\\\\r=12\ in[/tex]

Now we know that diameter is given by

[tex]diameter=2\times r=2\times 12=24\ in[/tex]

it is given that,

The edge length of the box is equal to the diameter of the ball.

Therefore the length of cube = 24 in

Now the volume of the cube is given by

[tex]\textrm{Volume of cube}=(edge)^{3}[/tex]

substituting the values we get

[tex]\textrm{Volume of cube}=(24)^{3}=13824\ in^{3}[/tex]

Therefore the volume of the box is 13824 in³

Answer: tenth place

Step-by-step explanation:

Answer:

The tens place.

Step-by-step explanation:

In order, the numbers would go as follows:

7 would be in the ones place.

4 would be in the tens place.

3 is in the hundreds place.

2 is in the thousands place.

6 is in the hundred thousands place.

5 is in the millions place.

Answer:

30 meters away

Step-by-step explanation:

each second is equal to 5 meters, hence meters per second

Answer:

30%?

Step-by-step explanation:

im not really sure but 30 percent of 280 is 84 and i couldnt find anything else

since 280-129=88 i thought 84/30% was closest

Answer:

Dealer B

Step-by-step explanation:

Maintenance cost per year = 75$

Dealer "A' wants $4.995.00.

Dealer "B" wants 55,595.00 with free maintenance cover for a year.

It is obvious that the best deal is what dealer B is offering, with free maintenance cover per year. for example, if i pick dealer A, calculate the maintenance cover for 3years = $2700

whereas for dealer B, a whole year maintenance cost is free, it implies that one will start paying the next coming year i.e a year lesser than dealer A. by that time the one who picked dealer A must have paid $3600 for maintenance while the one who picked dealer B will about to pay $1800.

The best deal is what dealer B is offering coupled with the free maintenance cover for 1year.

Final answer:

After calculating the total costs for one year, Dealer B offers a better deal on the Jeep by saving $300, as it includes free maintenance, contrasting with Dealer A which results in higher overall costs after adding maintenance payments.

Explanation:

To determine which car deal from the dealers is the better option, we need to calculate the total cost of each option over the course of one year, including the average monthly maintenance cost on a used car. According to AAA, this cost is $75 per month.

For Dealer A, the cost of the car is $4,995 with no free maintenance, so the total cost after one year is the price of the car plus 12 months of maintenance:

Cost of the car: $4,995

12 months of maintenance: 12 * $75 = $900

Total cost for Dealer A after one year: $4,995 + $900 = $5,895

For Dealer B, the car costs $5,595 but comes with free maintenance for one year, which means:

Total cost for Dealer B after one year: $5,595

Comparing these totals, we see that Dealer B offers the better deal, with the overall savings being:

Savings: $5,895 - $5,595 = $300

Answer:

b. 8 ft

Step-by-step explanation:

We use the formula for the circumference of a circle to find the length of  each loop.

Circumference of a circle    = 2πr or Dπ

Where:                                π =  pi

                                           r   = radius of the circular loops

                                           D  = Diameter

                                             π  = [tex]\frac{22}{7}[/tex]

                                             D  =  30 inches

Use Circumference of a circle = Dπ

Circumference of a circle         = 30 x (22/7)

                                                   = 30 x 3.142857143

                                                   =  94.28571429 inches

Convert 94.28571429 inches to feet (ft)

                                  12 inches  = 1 ft

                94.28571429 inches  =  94.28571429/12

                                                    =  7.857142858 ft

                                                    ≈  8 ff                  

Answer:2

Step-by-step explanation: 1/2=0.5   0.5x4=2

Answer:jennie has 536 songs and diamond has 359

Step-by-step explanation:

Answer:

Step-by-step explanation:

When you talk about "unit price," you need to define the unit of interest. Unit prices on grocery store shelves don't always use the same unit, even for like items. Here it might be convenient to use any of the following as the "unit":

The "unit price" is computed as ...

  unit price = (price for some number of units)/(the number of units)

The "number of units" may be larger, smaller, or equal to 1.

Then the price per cup (8 ounces) would be ...

  unit price = (price for 15 oz)/(15/8 cups) = ($2.79)(8/15)

  = $1.488 per cup

__

The price per ounce would be ...

  unit price = ($2.79)/(15 oz) = $0.186/oz

__

We assume that the unit of interest is probably 1 ounce, but it could be something else. Your grader may expect the value to be rounded to the nearest cent, $0.19 per ounce.

The unit price of shampoo is approximately $0.186 per ounce.

To find the unit price of shampoo, divide the cost of the bottle by the number of ounces it contains. In this case, the cost is $2.79 and the bottle is 15 ounces. So, the unit price can be calculated as $2.79 divided by 15 ounces, which gives us approximately $0.186 unit price per ounce.

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Answer:

27 > b

Step-by-step explanation:

7 > -20 + b

7 + 20 > -20 + 20 + b

27 > b

Answer:

ocho es 8

Step-by-step explanation:

si quieres a saver mas solo necesitas a preguntar ;)

solo estoy jugando no mi mesajas yo no te quiero solo estoy jugando otra ves si te quiero como un amigo

Answer:

Step-by-step explanation:

5 pinks =9 greens

x pinks = 27 greens

Cross multiply

5pinks × 27 greens =x pinks × 9greens

Divide both side by 9green

5 pinks × 27 greens / 9greens =x pinks

Then green cancel greens

x pink = 15 pinks

Then, 27 greens implies 15 pinks

Answer:

Identify the input and output values.

convert the data to do coordinate pairs.

find the slope.

write the linear model.

use the model to make a prediction by evaluating the function at the given x-value.

use the model to identify an x value that results in a given y value.

The quotient of 987 divided by 47 is found to be 21 using estimation and step-by-step long division.

The question asks to find 987 divided by 47 using an efficient strategy and show the work. To solve this, we can perform long division.

The final answer is 21 because 47 goes into 987 exactly 21 times. The most efficient strategy here was to use estimation and subtraction to find the quotient step-by-step.

Answer:

If you're supposed to be multiplying the first four numbers, the answer is going to be 13.

Step-by-step explanation:

The equation formed by the given problem statement is 0.5*x + 4 = 20, solving this gives x = 32. Hence, there are 32 students in Bryan’s homeroom.

The problem statement says that 'Four more than half of the students in Bryan’s homeroom have tickets to attend the school’s musical' and '20 students have tickets'. If we denote the total number of students in Bryan’s homeroom by x, we can write the statement as an equation: 0.5*x + 4 = 20. Simplifying this equation gives us 0.5*x = 20 - 4 = 16, so x = 16 * 2 = 32. Hence, there are 32 students in Bryan’s homeroom.

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Answer:

5b²-1b-2

Step-by-step explanation:

-3b and +2b are like terms so you combine them together -3b+2b= -1b

+2 and -4 are like terms so +2-4= -2

5b² has no like terms

then you put your answers together to simplify the equation

5b²-1b-2

The polynomials added together give the result 5b^2 - b - 2. The addition is done by combining like terms in the given polynomials.

To add these polynomials, you combine like terms. Like terms are the terms in the polynomial that have the same variable and exponent. Here, our terms are 5b^2, -3b, 2, 2b, and -4.

The term 5b^2 does not have a like term, so it remains as is. The terms -3b and 2b add up to -b because -3b + 2b = -b. And finally, the constants 2 and -4 add up to -2. When we combine these results, we have the final answer: 5b^2 - b - 2.

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Answer:

A I think is the right one

Answer: 44! Hope this helps :D

Step-by-step explanation:

Answer:

Step-by-step explanation:

56 - 12 is 44

Answer:

3 11/16

Step-by-step explanation:

7 1/2 - 2 3/16 - 1 5/8

turn all to same fractions using multiplication

by this i mean to only multiply the fractions (both numerator and denomenator)

7 8/16 - 2 3/16 - 1 10/16

Turn them into improper fractions

120/16 - 35/16 - 26/16 =

And solve

3 11/16

Answer:

If two parallel lines  [tex]p[/tex] and [tex]q[/tex] are cut by a transversal, then the alternate interior angles are congruent.

Below is the prove of this.

Step-by-step explanation:

As we know that Alternate interior angles are two angles that are on the interior of [tex]p[/tex] and [tex]q[/tex], but on opposite sides of the transversal.

In other words,  If two parallel lines  [tex]p[/tex] and [tex]q[/tex] are cut by a transversal, then the alternate interior angles are congruent.

Lets prove this.

Given: p ║ q

Prove: ∠1 ≅ ∠2

Statement                                  Reasons

1. p ║ q                                        1. Given

2. ∠1 ≅ ∠3                                  2. Corresponding Angles Postulate

3. ∠3 ≅ ∠2                                 3. Vertical Angles Congruence Theorem

4. ∠1 ≅ ∠2                                  4. Transitive Property of Congruence