How many different three person relay teams can be chosen from six students?

The expression that represents the volume of the composite figure is 16/3πr³ + r³

The given parameters are:

The volume of a cube is:

V = l³

So, we have:

V = r³

The volume of a hemisphere is:

V = (2/3)πr³

So, we have:

V = (2/3)π(2r)³

Evaluate

V = (2/3)π * 8r³

This gives

V = 16/3πr³

Add both volumes

Volume = 16/3πr³ + r³

Hence, the expression that represents the volume of the figure is 16/3πr³ + r³

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Answer:

Step-by-step explanation:

Beth's position over time is constant, which makes the problem a lot easier. You are asked for the rate of position versus time, so begin by doing that. Since the rate is constant, clearly from the table, you can take any two data points and take their ratio. Her rate would be 11 feet every 5 seconds, or equivalently 2.2 feet every second. To graph the data, put position on the x-axis and time on the y-axis. The slope will be 2.2 at every point along her bike ride.

Moving on to the third part. If Amy traveled at a rate of 75 feet every 30 seconds, then she would be traveling 2.5 feet every second. Amy's rate is larger than Beth's rate. Since the rate corresponds to the slope of the postion vs. time graph, Amy's graph will have a steeper incline since the slope is 2.5

Answer:

Your answer is C, 14ft

Step-by-step explanation:

Your Given Measurements (in feet):

Height = 5 1/2 ; Width = 1 1/2

___________________________________________________

The Perimeter Formula:

L + W + L + W = P

In this case, the "L" which is length going to get substituted as Height.

5 1/2 is 5.5 because if you do 1/2 on the calculator, you get 0.5 which you can add 5 to get 5.5.

1 1/2 is 1.5 which is the same as the 5 1/2.

____________________________________________________

Now do 5.5 + 1.5 + 5.5 + 1.5 = perimeter

5.5 + 1.5 = 7

7 + 7 = 14ft

Your answer is C: 14 ft

Answer:

Answer is csc(x)

Step-by-step explanation:

I convert tan(x)= sin(x)/cos(x) and cot(x)= cos(x)/sin(x).

Then distribute the cos(x).

Then turn it into fractor that has same denominator.

Simplified the numerator sin^2(x)+cos^2(x)=1

[tex]cos(x)*\((tan(x)+cot(x))\\\\cos(x)*(\frac{sin(x)}{cos(x)} +\frac{cos(x)}{sin(x)})\\\\sin(x)+\frac{cos^2(x)}{sin(x)}\\\\sin(x)*\frac{sin(x)}{sin(x)}+\frac{cos^2(x)}{sin(x)}\\\\\frac{sin^2(x)}{sin(x)}+\frac{cos^2(x)}{sin(x)}\\\\\frac{sin^2(x)+cos^2(x)}{sin(x)}\\\\\frac{1}{sin(x)}\\\\csc(x)[/tex]

Answer:

→cosecx

Step-by-step explanation:

[tex]\hookrightarrow cosx(tanx+cotx)\\\\\hookrightarrow cosx(\frac{sinx}{cosx} +\frac{cosx}{sinx} )\\\\\hookrightarrow cosx(\frac{sinx \times sinx + cosx \times cosx}{cosx*sinx} )\\\\\hookrightarrow cosx(\frac{sin^{2}x+cosx^{2}x}{cosx*sinx} )\\\\\hookrightarrow cosx(\frac{1}{cosx*sinx} )\\\\\hookrightarrow cosx \times \frac{1}{cosx} \times \frac{1}{sinx} \\\\\hookrightarrow 1\times\frac{1}{sinx} \\\\\hookrightarrow \frac{1}{sinx} \\\\\hookrightarrow cosecx[/tex]

Answer:

Step-by-step explanation:

Vertically opposite angles are congruent.

-2x - 6 = 40

Add 6 to both sides

-2x = 40 + 6

-2x = 46

Divde both sides by (-2)

x = 46/(-2)

x = -23

Answer:

15/4= 3.75

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

since you have 84/42, and you are supposed to convert the improper fraction to a mixed number, the easiest place to start is to divide the two numbers and find the remainder. In this case, however, there is no remainder, as 84 divided by 42 is exactly 2. Therefore, the most simplified fraction would be 2 (although it does not look like a fraction the most simplified form of the fraction is 2/1 --> which is just 2). Hope this helps!

Answer:

On Knewton May 15,2022 $510.14

Step-by-step explanation:

One way we can organize a linear equation is in standard form:

[tex]Ax+By=C[/tex]

Another way we can organize a linear equation is in point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We're given:

We only need the point-slope form equation to find the stand form of the equation for this line. All we have to do is rearrange the numbers to get them in the right places.

[tex]y+7=-\dfrac{5}{2}(x-10)[/tex]

⇒ First, multiply both sides by 2 to get rid of the fraction:

[tex]2y+14=-5(x-10)[/tex]

⇒ Now, open up the parentheses:

[tex]2y+14=-5x+50[/tex]

⇒ Move -5x to the other side:

[tex]5x+2y+14=50[/tex]

⇒ Move 14 to the other side:

[tex]5x+2y=50-14[/tex]

⇒ Combine like terms:

[tex]5x+2y=36[/tex]

[tex]5x+2y=36[/tex]

Answer:

Step-by-step explanation:

This is a permutation of 6 out of 8

Use formula

Find the number of starting positions

If we were getting 60% discount early and then again we are receiving 20% discount for using credit card then it means that we are getting 80% discount.

Discount means the amount which is deducted by sellers from the amount to be payable by buyers.

Let the total price to be paid by us to store is $100.

Discount received because on purchase on sale day=100*60%

=60

Discount received due to use of credit card=100*20%

=20

Total discount received from store=60+20

=80

Percentage=80/100*100

=80%

Hence the total discount received by us from store is 80%.

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Answer:

B and E

Step-by-step explanation:

A. -7 ÷ (-4) = -7/-4 = 7/4 = 1.75

B. -(3 ÷ 2) = -(1.5) = -1.5

C. -8/5 * (-5/8) = (8/5) * (5/8) = 1

D. -5/-3 = 5/3 ≈ 1.667

E. -9 ÷ 6 = -9/6 = -1.5

Answer:

Step-by-step explanation:

To solve this problem, first, you have to use the order of operations.

PEMDAS stands for:

Use the fractional rule.

[tex]\Longrightarrow: \sf{n!= 1*2*3*4}[/tex]

First, multiply.

1*2=2

2*3*4

2*3=6

6*4=24

[tex]\Longrightarrow: \boxed{\sf{24}}[/tex]

I hope this helps. Let me know if you have any questions.

Answer:

3/4

Step-by-step explanation:

Prob to pick a club is 13/52

Prob not to pick a club is 1 - 13/52

1 - 13/52 = 3/4

Step-by-step explanation:

First we need to get his speed:

speed = distance / time

If he travelled 24 miles in 20 mintues, his speed is 24 / 20 = 1.2 miles per minute

If he travelled 18 miles in 15 minutes, his speed is 18 / 15 = 1.2 miles per minute

Those two should give us the same answer since it says that the distance varies linear with time, which means that his speed is constant.

Then after 30 minutes he will have traveled: 1.2 x 30 = 36 miles

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[tex]~~~~~7e^{xy} +2x^2 -4y^2 =13\\\\\\\implies \dfrac{d}{dx}\left(7e^{xy} +2x^2 -4y^2\right) =\dfrac d{dx} (13)\\\\\\\implies 7\left[e^{xy} \dfrac{d}{dx} ( xy)\right] +2 \cdot 2x -4\cdot 2y \dfrac{dy}{dx} = 0\\\\\\\implies 7e^{xy} \left( x \dfrac{dy}{dx} +y\right) +4x -8y \dfrac{dy}{dx} =0\\\\\\\implies 7xe^{xy}\dfrac{dy}{dx} + 7ye^{xy} +4x -8y\dfrac{dy}{dx} = 0\\\\\\\implies \left(7xe^{xy} -8y \right) \dfrac{dy}{dx}=-7ye^{xy} -4x\\\\\\[/tex]

[tex]\implies \dfrac{dy}{dx} = \dfrac{-7ye^{xy} -4x}{7xe^{xy} -8y }[/tex]

14 miles

Let "Candler" be known as "C" and "Oteen" as "O"

Given:

3.5 ------> 3.50

Comparing the rate (inches/mile) and the distance:

Multiplying both sides by 100:

Clearly, 350 is divisible by 25 as "50" is divisible by 25.

Divide both sides by 25 to isolate x:

The actual distance between the two cities is 14 miles.

Answer:

14 miles

Step-by-step explanation:

Given:

Let [tex]x[/tex] be the distance between Candler and Oteen in miles.

[tex]\implies \dfrac14:1=3 \frac12:x[/tex]

[tex]\implies \dfrac{\frac14}{1}=\dfrac{\frac72}{x}[/tex]

[tex]\implies \dfrac14x=\dfrac72[/tex]

[tex]\implies x=\dfrac72 \div \dfrac14[/tex]

[tex]\implies x=\dfrac72 \times \dfrac41[/tex]

[tex]\implies x=\dfrac{28}{2}[/tex]

[tex]\implies x=14[/tex]

Answer:

$ 383 854.28  per pound  ====>   See below !!

Step-by-step explanation:

Increases 10.2 % per WEEK   (??  Per WEEK?))  

  2 years is 104 weeks    (this is going to be a HUGE number)

15.75 (1+.102)^104 =

If increase is YEARLY

15.75 ( 1 + .102)^2 = $ 19.13 per pound    <<<<after two years

A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot. The weight of the tabletop, in pounds, is 1032.

The volume of the rectangular tabletop is the product of the length, breadth, and height of the given tabletop.

Volume of rectangular tabletop= (length x width x height)

The tabletop will have a length of eight feet, a width of three feet, and a thickness of one inch.

Volume of rectangular tabletop= (length x width x height)

                                                 = [tex]8 \times 3 \times 1\\\\24[/tex]

A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot.

The weight of the tabletop, in pounds = 43 x 24

                                                              = 1032 pounds

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x = 10

hope it helps...!!!

Answer:

60%

Step-by-step explanation:

If you look through the data, it is clear that 46, 59, 63, 68, 72, 76, 78, 85, and 89 are all less than 90. There are 9 elements total that are less than 90.

For percentages, you take the number you have and divide by the total. Since we know that there are 15 students, we can do 9 / 15. This gives us 0.6 which is 60%

Answer:

6300in

Step-by-step explanation:

vol=base area x height

210x30

=6300in

Answer:

The 5 is in the thousandths place

8 is the 'ones'

7 is the tenths

6 is the hundredths

5 is the thousandths

Step-by-step explanation:

Answer:

answer = 3(a +b)

Step-by-step explanation:

[tex] log(2) = a \: log(3) = b \: \: \\ log(216) = log(2 \times 2 \times 2 \times 3 \times 3 \times 3) \\ = log( {2}^{3} \times {3}^{3} ) \\ = log(2^{3} ) + log( {3}^{3} ) \\ = 3 log(2) + 3 log(3) \\ = 3(a) + 3(b) \\ = 3(a + b) \\ \\ log(216) = 3(a + b)[/tex]

Answer:

odd

Step-by-step explanation:

take example of 2^3 +3^3 it's odd

now others try yourself

Answer:

yes multiply the 3 sides 3 times together with the number 2

[tex]2 \ln x+ 3 \ln y - \ln z\\\\=\ln x^2 + \ln y^3 - \ln z\\\\=\ln(x^2 y^3) - \ln z\\\\=\ln \left( \dfrac{x^2y^3}{z} \right)[/tex]