Use the Pythagorean’s theorem to calculate the length of the hypotenuse of a right triangle with 17 as the length and 15 as the width

Step-by-step explanation:

Let's first consider a rotation about a vertical axis (x=0 or x=a).

Using washer method, the volume is:

∫ᵧ₁ᵞ² π (x₂² − x₁²) dy

∫ᵧ₁ᵞ² π ((x₂ − a)² − (x₁ − a)²) dy

Using shell method, the volume is:

∫ₓ₁ˣ² 2π x (y₂ − y₁) dx

∫ₓ₁ˣ² 2π (x − a) (y₂ − y₁) dx

First, notice that with washer method, the differential dy is parallel to the axis of rotation.  With shell method, the differential dx is perpendicular to the axis of rotation.

Also, notice that the limits of integration must match the differential.

Choosing the best method will depend on the function.

If x² can be written in terms of y, and integrated, then washer method is the one to use.

If y can be written in terms of x, and integrated, then shell method is the one to use.

In other words, use washer method if x = f(y) is simple to integrate.  Use shell method if y = f(x) is simple to integrate.

If instead we rotate about a horizontal axis (y=0 or y=a), the volume with washer method is:

∫ₓ₁ˣ² π (y₂² − y₁²) dx

∫ₓ₁ˣ² π ((y₂ − a)² − (y₁ − a)²) dx

Using shell method, the volume is:

∫ᵧ₁ᵞ² 2π y (x₂ − x₁) dy

∫ᵧ₁ᵞ² 2π (y − a) (x₂ − x₁) dy

We choose washer method when y² = f(x) is easy to integrate.

We choose shell method when x = f(y) is easy to integrate.

So here's the takeaway:

If the axis of rotation is x = 0 or x = a, and x² = f(y) is easy to integrate, use washer method.

If the axis of rotation is y = 0 or y = a, and y² = f(x) is easy to integrate, use washer method.

Otherwise, use shell method.

The correct answer is 5460 cubic feet or 5460 [tex]ft^{3}[/tex]

Explanation:

The silo has a cylindrical shape, in this context, the volume of the silo or any other cylinder can be calculated by using the formula [tex]Volume =\pi r^{2} h[/tex]. In this formula the symbol [tex]\pi[/tex] refers to the number 3.1415..., the letter [tex]r[/tex] refers to the radius of the base and the letter [tex]h[/tex] refers to the height.

Moreover, in this case, it is known the heigh (21 feet) and the area of the base (260 square feet). Additionally, this area of the base is the result of the formula [tex]Area = \pi r^{2}[/tex], which is exactly the first section of the formula to find the volume. This implies that by multiplying the area of the base by the height the volume is known. Here is the process:

[tex]Volume = \pi r^{2} h[/tex]  or  [tex]Volume = Ah[/tex]   (Area of the base × height)

[tex]V = 260 square feet[/tex] × [tex]21 feet[/tex]

[tex]V = 5460 cubic feet[/tex]

Answer:

its ten dimes are equal to 40 pennies. :)

Step-by-step explanation:

Answer:

your anwser is D.4

Step-by-step explanation:

you count by tens till you get to 40 so 10 20 30 40            count that and that gives you 4

Answer:

Step-by-step explanation:

for IV you do 40^2+30^2=c, or 1600+ 900=c. c= 2500 and unsquare that you get 50

Answer:

the ans of III is 50 and IV is12

Answer:

5

Step-by-step explanation:

13 + (-8) = 5

Answer:

Hi there!

Your answer is:

1. f(-2) Means the function of y when x is equal to -2. You plug in -2 for x!

2. f(-2) = 65

Step-by-step explanation:

6(8-(-2)) +5

6(8+2) +5

6(10)+5

60+5

65

Hope this helps!

Blue whales, about 80 feet in length and over 250,000 pounds in weight, are much bigger than whale sharks.

The blue whale is 1  × 10^1 times heavier than a white rhinoceros.

The number is written in the form  [tex]a \times 10^b[/tex] where we have it [tex]1 \leq a < 10[/tex]. The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. Scientific notations have some of the profits as Better readability due to compact representation. Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.

The weight of the animals can be written in scientific notation.

To determine that how much heavier the blue whale is, we need to divide the weight of the blue whale by the weight of the white rhinoceros.

The division operation that is used to group a number into equal parts using another number.

Weight of the blue whale ÷ weight of the white rhinoceros

2 x [tex]10^5[/tex] ÷ 2 x [tex]10^4[/tex]

(2 ÷ 2) x ([tex]10^{5-4}[/tex])

1  × 10

Hence, The blue whale is 1  × 10^1 times heavier than a white rhinoceros.

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Hey there! I'm happy to help!

We have 2 thousand dollar bills.

2000

4 hundred dollar bills...

2000+400

and 6 ten dollar bills

2000+400+60=2460

We multiply this amount by 10.

2460(10)=24600

This car costs $24,600

Have a wonderful day! :D

Answer:

The car costs 24,600

Step-by-step explanation:

You have to add 2000 + 400 + 50 =2460 and the multiply 2460 x 10 = 24600

Answer:

$324

Step-by-step explanation:

We need to make a proportion:

[tex] \frac{259.20}{x} = \frac{80}{100} [/tex]

[tex]25920 = 80x[/tex]

[tex]x = 324[/tex]

x is 1%. So 100% = 324*100 = 32400 cents = $324

Hope I helped :)

Answer:

24

Step-by-step explanation:

Answer:

[tex]A = [\frac{32}{3}][/tex]

Step-by-step explanation:

Given

[tex]y_1 = 2x - x^2[/tex]

[tex]y_2 = 2x - 4[/tex]

Required

Determine the area bounded by the curves

First, we need to determine their points of intersection

[tex]2x - x^2 = 2x - 4[/tex]

Subtract 2x from both sides

[tex]-x^2 = -4[/tex]

Multiply through by -1

[tex]x^2 = 4[/tex]

Take square root of both sides

[tex]x = 2[/tex]   or    [tex]x = -2[/tex]

This Area is then calculated as thus

[tex]A = \int\limits^a_b {[y_1 - y_2]} \, dx[/tex]

Where a = 2 and b = -2

Substitute values for [tex]y_1[/tex] and [tex]y_2[/tex]

[tex]A = \int\limits^a_b {(2x - x^2) - (2x - 4)} \, dx[/tex]

Open Brackets

[tex]A = \int\limits^a_b {2x - x^2 - 2x + 4} \, dx[/tex]

Collect Like Terms

[tex]A = \int\limits^a_b {2x - 2x- x^2 + 4} \, dx[/tex]

[tex]A = \int\limits^a_b {- x^2 + 4} \, dx[/tex]

Integrate

[tex]A = [-\frac{x^{3}}{3} +4x](2,-2)[/tex]

[tex]A = [-\frac{2^{3}}{3} +4(2)] - [-\frac{-2^{3}}{3} +4(-2)][/tex]

[tex]A = [-\frac{8}{3} +8] - [-\frac{-8}{3} -8][/tex]

[tex]A = [\frac{-8+ 24}{3}] - [\frac{8}{3} -8][/tex]

[tex]A = [\frac{-8+ 24}{3}] - [\frac{8-24}{3}][/tex]

[tex]A = [\frac{16}{3}] - [\frac{-16}{3}][/tex]

[tex]A = [\frac{16}{3}] + [\frac{16}{3}][/tex]

[tex]A = [\frac{16 + 16}{3}][/tex]

[tex]A = [\frac{32}{3}][/tex]

Hence, the Area is:

[tex]A = [\frac{32}{3}][/tex]

the answer is -72

i checked on a calculator

Answer:

x=2(m+n+1)

Step-by-step explanation:

I am assuming you mean: (X-2)/2 =m+n

X-2 =2(m+n)

X =2m+2n+2

x=2(m+n+1)

Answer:

It’s 3.5 percent

Step-by-step explanation:

Population increases by 3.6% every year.

The population in question doubles every 20 years and you need to find out the annual rate of increase.

You can use the rule of 72 which allows you to calculate the doubling time of a variable by the formula:

Time to double = 72 / Rate

As we already have the time the double, the rate is:

20 = 72 / Rate

Rate x 20 = 72

Rate = 72/20

Rate = 3.6%

The population therefore increases by 3.6% every year.

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The largest number of groups she can have is c) 8

Given:

104 nickels

88 dimes.

Now let determine  the largest number of groups she can have

2×2×2×3=104

2×2×2×11=88

Based on the above the greatest common divisor will be:

Greatest common divisor=2×2×2

Greatest common divisor=8

Inconclusion The largest number of groups she can have is 8

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Answer:

im honestly not sure but to help out a little bit im sure its either negatively skewed or constant

Step-by-step explanation:

Answer:

It is C. Negatively skewed.

Step-by-step explanation:

If the bigger portion of the data is to the right, then the data is negatively skewed.

Answer:

found this i think this should help with your question

Step-by-step explanation:

Answer:

sixteen or 1.6 X 10E2

Step-by-step explanation:

Answer: 2^4

Step-by-step explanation:

2•2•2•2=

4 • 4=

16

Answer:

4140

Step-by-step explanation:

when u multiply the measurements for the first one you get 300 and the second measurement you get 546 then u put it in the ratio form

If 300= 2,275

546=x

then you cross multiply

The expirmental probability us 28/50

Theoretically the probability is 25/50 because that would be half :)

The relative frequency of getting a tail on the next toss will be 0.40.

Relative frequency is the ratio of the considered subgroup's count to the whole count.

A coin is tossed 50 times, and it lands on tails 20 times.

Then the relative frequency of getting a tail on the next toss will be

The probability of getting tail is 1/2.

Then the relative frequency will be

⇒ 20/50

⇒ 0.40

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Answer:

9

Step-by-step explanation:

72 pieces divided by 6 pieces/pie = 12 pies

3 were donated by the cafeteria

thus 12-3 = 9 pies made by the club

Answer:

Step-by-step explanation:

Here is the complete question.

Dominique, Marco, Roberto , and John work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company decides that the two individuals who get to attend will have their names drawn from a hat. This is like obtaining a simple random sample of size 2. (a) Determine the sample space of the experiment. That is, list all possible simple random samples of size n = 2. (b) What is the probability that Dominique and Marco attend the conference? (c) What is the probability that John attends the conference?  ​(d) What is the probability that John stays​ home?

Since there are four employees to select the two to send from. then for us to get the sample space for the experiment we need to merge all possible two employees and represent them as set.

Let D = Dominique, M = Marco, R = Roberto and J = John

a) The sample space for the experiment is the total number of possible outcomes that we can have. It is as given below

S = 4C2 = 4!/(4-2)!2! (Selecting 2 out of 4 employees)

Total sample space = 4!/2!2!

Total sample space = 4*3*2!/2!2

Total sample space = 12/2 = 6

The sample space are S = {DM, DR, DJ, MR, MJ, RJ}

b) Probability is the ratio of number of event to the sample space.

P = n(E)/n(S)

Given n(S) = 6

n(E) is the event of Dominique and Marco attending the conference.

E = {DM}

n(E) = 1

P(D and M) = 1/6

Hence  the probability that Dominique and Marco attend the conference is 1/6

c) For John to attend the conference, the event outcome will be given as;

E = {DJ, MJ, RJ}

n(E) = 3

n(S) = 6

Probability for John to attend the conference is 3/6 = 1/2

d) Probability that John stays at home = 1 - Prob (John attends the conference)

Probability that John stays at home = 1 - 1/2

Probability that John stays at home = 1/2

Answer:Anthony

Step-by-step explanation:

Answer:

Find the measure of what?

Step-by-step explanation:

Next time please write the entire equation. Thank you!

Answer:

the consumer price index is a measure of the average change over time in the prices paid by the consumers for a market basket of consumer goods and services.

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

36 houses  = (x) houses

  30 min            7.5 min.

cross multiply:

30x = 36 (7.5)

x = 270 / 30

x = 9