The cross-sectional area parallel to the bases of the two figures above is the same at every level. Find the volume of the cone, to the nearest tenth.
A.
26.5 cm3
B.
44.2 cm3
C.
79.5 cm3
D.
132.5 cm3

Final answer:

To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, divide the weight of the 5 pound bag by the weight of each 3/4 pound bag.Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.

Explanation:

To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, we need to divide the weight of the 5 pound bag by the weight of each 3/4 pound bag. We can use the division operation to solve this.

5 pounds ÷ 3/4 pounds = 5 ÷ 3/4

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3.

5 ÷ 3/4 = 5 × 4/3 = 20/3

Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.

Answer:

Options B and D

Step-by-step explanation:

we have

[tex]y=\frac{1}{x-3}[/tex] -----> equation A

[tex]y=3-x^{3}[/tex] -----> equation B

Solve the system of equations by graphing

The solution of the system of equations is the intersection point both graphs

The solutions are the points (1.545,-0.687) and (2.956,-22.835)

see the attached figure

The approximate solutions are

(1.5,-0.7) and (2.9,-22.8)

Answer:

Options B and D

Step-by-step explanation:

Use the law of sines:

Sin(angle) = Opposite Leg / Hypotenuse

Sin(30) = 14 / x

x = 14/sin(30)

x = 28

Answer:

One

Step-by-step explanation:

It is one because each spoke has one space in the middle. However some people think it's 64 because they read the question wrong.

Answer:

the number (x) is 120.

Explanation:

100% + 60% = 160% = 1.6

(just multiply it by 1.6 because it is equal to 60%)

The equation for the problem can be expressed as x + 0.6x = 192. To solve for x, you simplify the equation and isolate x, resulting in the answer of 120.

This problem is a simple algebraic problem in which we're trying to find a number that satisfies a given condition. To solve this, we need to express the problem as an equation. Let's assume the number we're looking for is denoted as x.  So, according to the problem, we have the following equation:

x + 0.60x = 192

The steps to solve this equation are as follows:

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Answer:

4 1/8 pieces

Step-by-step explanation:

Since you are using a string that is 100 ft. long then and you need exactly 24 3/8 ft. sections, you would do these calculations:

3/8 = 0.375

100/24.375 = 4.1026

.1026 = 1/8

4 1/8 ft long pieces

Answer:

The string is cut into 4.1025 pieces.

Step-by-step explanation:

We are given the following information:

Length of the string =  100 feet

Length of one piece = [tex]24\displaystyle\frac{3}{8} = \displaystyle\frac{195}{8} ~feet[/tex]

Number of pieces =

Formula:

[tex]\text{Number of pieces} = \displaystyle\frac{\text{Length of string}}{\text{Length of one piece}}[/tex]

Number of pieces =

[tex]\displaystyle\frac{100}{\frac{195}{8} } = \displaystyle\frac{100\times 8}{195}\\\\=\displaystyle\frac{800}{195} = 4\displaystyle\frac{4}{39} = 4.1025[/tex]

Thus, the string is cut into 4.1025 pieces.

Answer:

-9

Step-by-step explanation:

Answer:

slope = - 9

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (5, - 6) and (x₂, y₂ ) = (4, 3)

m = [tex]\frac{3+6}{4-5}[/tex] = [tex]\frac{9}{-1}[/tex] = - 9

To find the length of the radius, use the formula for the circumference of a circle. Divide the circumference by 2π to get the radius. In this case, the radius is approximately 59 cm.

In order to find the length of the radius, we can use the formula for the circumference of a circle: C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 367 cm, so we can plug in the values to solve for r.

367 = 2πr

To isolate r, divide both sides of the equation by 2π: r = 367 / (2π)

Using a calculator to approximate π as 3.14, we can calculate the radius: r ≈ 367 / (2 * 3.14) ≈ 58.598

Therefore, the length of the radius, rounded to the nearest centimeter, is approximately 59 cm.

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Answer:

a=9

Step-by-step explanation:

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

Get a common denominator for the left hand side

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

3/(2a) = 1/ (a-3)

Using cross products

3 * (a-3) = 1 * 2a

Distribute

3a -9 = 2a

Subtract 3a from each side

3a-3a-9 = 2a-3a

-9 = -a

Multiply by -1

-1*-9 = -1 *-a

9 = a

Answer:

36

Step-by-step explanation:

The 10 part of the ratio represents 120 chickens. Divide 120 by 10 to find the value of one part of the ratio.

120 ÷ 10 = 12 ← value of 1 part of the ratio, hence

3 parts = 3 × 12 = 36 ← number of horses

The number of horses on the farm is​ 36.

Given that, the ratio of chicken to pigs to horses on a farm is 10:2:3 and the number of chickens on the farm is 120.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

We can write the given ratio 10:2:3 as 10x: 2x: 3x.

So, 10x=120

⇒x=12

Then, the number of horses=3x=36

Therefore, the number of horses on the farm is​ 36.

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Answer:

C) angle 2 and angle 8

Step-by-step explanation:

Answer:

6%

Step-by-step explanation:

To solve this you need to subtract 607000 by 572000 to see how many people in the population decreased.

607,000- 572,000= 35,000

Then you put 35,000 over 607,000

also you need x over 100

35000/607,000 x/100

Then do cross product property

35,000*100=3,500,000

607,000* x= 607,000x

3,500,000= 607,000x

Then do 3,500,000 divided by 607,000

You get 5.76%

Round to the nearest percent and get 6%

Final answer:

The rate of decrease of the population from the 2000 census to the 2010 census is 6% when rounded to the nearest percent.

Explanation:

To calculate the rate of decrease of the city's population, we use the population values from the 2000 and 2010 censuses. The population in 2000 was 607,000, and in 2010 it was 572,000. To find the population decrease, subtract the 2010 population from the 2000 population:

Population decrease = Population in 2000 - Population in 2010

Population decrease = 607,000 - 572,000

Population decrease = 35,000

Next, to find the rate of decrease as a percent, we divide the population decrease by the original population (in 2000) and then multiply by 100:

Rate of decrease (%) = (Population decrease / Population in 2000) × 100

Rate of decrease (%) = (35,000 / 607,000) × 100

Rate of decrease (%) = 0.0577 × 100

Rate of decrease (%) = 5.77%

Round this to the nearest percent, and you get a 6% decrease.

you have a 1/12.5 chance of getting a white egg. so the theoretical possibility of getting only two white eggs is 1/156.25. so it is very unlikely to get two white eggs

Answer:

0.029

Step-by-step explanation:

Last year, the porgs laid 30 dotted eggs, 40 grey eggs, and 15 white eggs.

Total eggs = 30+40+15 = 85 eggs

White eggs = 15

So, probability of getting 1 white egg = [tex]\frac{\text{No. of white eggs}}{\text{Total no. of eggs}}[/tex]

                                                              = [tex]\frac{15}{85}[/tex]

Remaining white eggs = 14

Total eggs remaining = 84

Probability of getting 1 white egg on second draw   = [tex]\frac{14}{84}[/tex]

So, the probability that you would only collect 2 white eggs =[tex]\frac{15}{85} \times \frac{14}{84}[/tex]

                                                                                                   =0.029

Hence the probability that you would only collect 2 white eggs is 0.029.

Answer:

80

Step-by-step explanation:

60%=48

10%=8

8*10=80

Answer:80

Step-by-step explanation:

60/100*x=48

60/100=3/5 so,

3/5*x=48

3x=48*5

x=240/3

x=80

therefore the maximum capacity is 80 people

Answer:

Step-by-step explanation: it’s c

Answer:

C. a rotation about point L

Step-by-step explanation:

Answer:

145

step by step explanation:

perimeter definition:

perimeter definition:the continuous line forming the boundary of a closed geometrical figure.

add up the length of the sides:

80+20+45=145

Answer:

b. 4+7x-2

Explanation:

when you add like terms for the first equation it becomes 7x-6

the second one becomes 7x+2

the third one becomes 7x-6

and the last one is also 7x-6

which means the second one is not equivalent

Answer:

B. 4 + 7x – 2

Step-by-step explanation:

Answer:

128/15 min or 8.5 min

Step-by-step explanation:

By using unitary method,

Time required to paint 5/8 of wall = 16 min.

Time required to paint 1/1 of wall = 16×8/5

Hence, Time required to paint 1/3 of wall = 16×8/5×1/3

Answer:

8 8/15

Step-by-step explanation:

simplify the two fractions you have to make them have the same denominater

enthen you can determine the answer.

Check the picture below.

Answer:

x=6.9 inches

Step-by-step explanation:

If a tangent and a secant are draw to a circle from the same exterior point, the square of the length of the tangent is equal to the product of the total length of the secant and the length of the external segment of the secant.

From the given diagram,

(8+4)×4=x²

12×4=x²

x²=48

x=6.9 inches

Answer:

Distance = 3r

Step-by-step explanation:

We are to write an algebraic expression and then simplify it for the given situation:

The distance traveled by a train in three hours with a constant speed of r miles per hour.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

Answer:

-7.2

Step-by-step explanation:

The value of expression A•D²/C² is 1.8 x 10⁻⁷ / D².

To find the value of A•D²/C², we can first rearrange the given equations and then manipulate them to get the desired expression.

Given equations:

A • B² = 1.8 x 10⁻⁷

C • B/D = 7.2 x 10⁻⁴

Let's manipulate the second equation to get C by itself:

C • B/D = 7.2 x 10⁻⁴

C = (7.2 x 10⁻⁴) • (D/B)

Now, substitute the expression for C from the second equation into the first equation:

A • B² = 1.8 x 10⁻⁷

A = (1.8 x 10⁻⁷) / B²

Now, we have expressions for both A and C:

A = (1.8 x 10⁻⁷) / B²

C = (7.2 x 10⁻⁴) • (D/B)

Now, let's find the value of A•D²/C²:

A•D²/C² = ((1.8 x 10⁻⁷) / B²) • (B/D)²

Since (B/D)² = B²/D²:

A•D²/C² = ((1.8 x 10⁻⁷) / B²) • (B²/D²)

Now, B² in the numerator and denominator cancel out:

A•D²/C² = 1.8 x 10⁻⁷ / D²

Thus, the value of A•D²/C² is 1.8 x 10⁻⁷ / D².

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Answer:

Each quart is 1.31 to the customer.

Step-by-step explanation:

Cost of 1 quart to  Wong = 0.75

Cost to you or I = 0.75 * 175/100 = 1.31

He sells each quart for 1.31 dollars.

Answer:

41.79%

Step-by-step explanation:

To be on the swim team, we look at the right most (total) number int he table of "on the swim team" row. That is 28.

The grand total is the bottom-rightmost. That is 67.

Hence, probability of being on swim team is 28/67 = 41.79%

Answer:

5

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/ (x2-x1)

   = (-3-3)/(4-1)

  =-6/3

  = -2

Then we can use point slope form to make the equation

y-y1 = m(x-x1)

y-3 = -2(x-1)

Distribute

y-3 = -2x+2

Add 3 to each side

y-3+3 = -2x+2+3

y = -2x+5

Since this is in slope intercept form, y = mx +b, the y intercept is 5

Answer: D. 5

Step-by-step explanation: First we need to find the slope

m = (y2-y1)/ (x2-x1)

  = (-3-3)/(4-1)

 =-6/3

 = -2

Then we can use point slope form to make the equation

y-y1 = m(x-x1)

y-3 = -2(x-1)

Distribute

y-3 = -2x+2

Add 3 to each side

y-3+3 = -2x+2+3

y = -2x+5

Since this is in slope intercept form, y = mx +b, the y intercept is 5

Answer:

A

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, - 4) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0+4}{4+4}[/tex] = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]

Using (a, b) = (- 4, - 4), then

y - (- 4) = [tex]\frac{1}{2}[/tex] (x - (- 4)), that is

y + 4 = [tex]\frac{1}{2}[/tex] (x + 4) → A

Answer:

2

Step-by-step explanation:

2:1  win / loss ratio

1 = 4 loses

4 x 2 = 8

the team has 6 wins it would need to win a total of 8 to have a 2:1 ratio

The baseball team must win 2 more games to achieve a win:loss ratio of 2:1, assuming they have no additional losses.

The student's baseball team currently has a record of 6 wins to 4 losses. The question asks how many more games the team must win to achieve a win:loss ratio of 2:1, assuming no more losses occur. To achieve a 2:1 win:loss ratio, the number of wins must be twice the number of losses. Since the losses are fixed at 4, the team needs 2 times 4 (which equals 8) wins to attain this ratio. The team has already won 6 games, so they need 8 - 6, which equals 2 more wins to reach a 2:1 ratio.

Answer:

6^8=6*6*6*6*6*6*6*6

=1679616

Step-by-step explanation:

In this expression the exponent shows that how many times 6 will be multiplied.

6^8=6*6*6*6*6*6*6*6

=1679616

Answer:

The sum is a binomial with a degree of 6

Step-by-step explanation:

we have

[tex](3x^{2}y^{2}-2xy^{5})+(-3x^{2}y^{2}+3x^{4}y)[/tex]

Group terms that contain the same variable

[tex](3x^{2}y^{2}-3x^{2}y^{2})-2xy^{5}+3x^{4}y[/tex]

[tex]0-2xy^{5}+3x^{4}y[/tex]

[tex]-2xy^{5}+3x^{4}y[/tex]

The sum is a binomial ( two terms) with a degree of 6  

[tex]-2xy^{5}[/tex] has a degree of 6 (x has an exponent of 1, y has 5, and 1+5=6)

The sum of the polynomial is a binomial with a degree of 6. The correct option is D) and this can be determined by using arithmetic operations.

Given :

Polynomials --   [tex]3x^2y^2-2xy^5[/tex] and [tex]-3x^2y^2+3x^4y[/tex]

The following steps can be used to determine the sum of the given polynomials:

Step 1 - Write the sum of the given polynomials.

[tex]3x^2y^2-2xy^5-3x^2y^2+3x^4y[/tex]

Step 2 - Subtract [tex]3x^2y^2[/tex] from [tex]3x^2y^2[/tex] in the above expression.

[tex]-2xy^5+3x^4y[/tex]

The above expression cannot be further simplified. Therefore, this is the final expression of the sum of the given polynomials.

The sum of the polynomial is a binomial with a degree of 6. Therefore, the correct option is D).

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Answer:

5/4 hope this helps

Step-by-step explanation:

ANSWER

The correct answer is D.

EXPLANATION

The given exponentiial expression is

[tex] {5}^{ \frac{7}{3} } [/tex]

Recall that:

[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]

We put a=5, n=3 and m=7

This implies that,

[tex]{5}^{ \frac{7}{3} } = \sqrt[3]{ {5}^{7} } [/tex]

The correct answer is D.

The last option is correct.

Answer:

1 mi/1.61 km

Step-by-step explanation:

we know that

1 mile= 1.61  kilometers

To convert 1 kilometer to miles

use proportion

so

1/1.61 mi/km=x/1 mi/km

x=1 mi/1.61 km

Answer:

[tex]\frac{1 mi}{1.61km}[/tex]

Step-by-step explanation:

We are given the unit values of inch, foot and mile to convert into centimeters.

Using these conversion units, we are to determine whether which expression in the answer options can be used as the conversion factor to convert kilometers to miles.

So using the given conversion units, we can see that the following is the conversion factor to convert kilometers to miles.

[tex]\frac{1 mi}{1.61km}[/tex]