The volume, V, of a sphere in terms of its radius, r, is given by , V(r)=4/3(pie)r^3. Express r as a function of V, and find the radius of a sphere with volume of 150 cubic feet. Round your answer for the radius to two decimal places.

r(V)=

A sphere with volume 150 cubic feet has radius
_________ feet.​

Answer:

width is also "inches"

Step-by-step explanation:

Answer:

It could be a solution

Step-by-step explanation:

This depends on what equation you are solving. It could be a solution for a quadratic or even a transformation problem.

Answer:

2/7

Step-by-step explanation:

d=2n+3

 [tex]\frac{d-7}{2n-4} = \frac{4}{13}[/tex]

13(2n+3) -91 =8n - 16

26n+39 -91 = 8n-16

18n=36

n=2

d=7

Answer:

Rewrite in vertex form and use this form to find the vertex  

(

h

,

k

)

.

(

2

,

3

)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

Total no. of cards = 52

No. of 2 of spades cards = 1

Therefore,

Probability of getting 2 of spades

[tex] = \frac{no. \: of \: required \: outcomes}{total \: outcomes} [/tex]

[tex] = \frac{1}{52} (ans)[/tex]

Answer:

yes , This is an example of the associative property.

Step-by-step explanation:

Answer:

so the answer is 0.16339

Answer:

C) x = ± 4

Step-by-step explanation:

12x² - 288 = 0

12x ² = 288

[tex] \small \sf \: x {}^{2} = \frac{288}{12} \\ [/tex]

[tex]\small \sf x {}^{2} = \frac{ \cancel{288 }}{ \cancel{12}} \\ [/tex]

x² = 24

[tex] \small \sf \: \sqrt{x {}^{2} } = ± \sqrt{ 24} [/tex]

[tex] \small \sf \: x_1, _2 = ± \sqrt{ 24} [/tex]

[tex] \small \sf \: x_1, _2 = ± 4.899 [/tex]

Answer:

c is answer

Step-by-step explanation:

yes

Answer:

C

Step-by-step explanation:

took test

Answer:

compound interest

Step-by-step explanation:

compound interest yields higher profit than simple interest

Answer:

the simple interest function will be greater in the beginning, but the

compound interest equation will overtake the simple after a while.

it appears that the 4% compound equation will overtake the simple at about 10 years

Step-by-step explanation:

[tex]1 + .05t = 1(1.04)^t[/tex]

Answer:

Step-by-step explanation:

commission = 0.7% of $12,500

= 0.007×$12,500

= $87.5

Looking at Point A to A', the rectangle moves 5 places to the left which is the x value + 5 and it shifts 1 place down which would be the y value - 1

This gets written as:

(x+5, y-1)

Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet

2. 3ft 8in = 3 8/12 or reduced to 3 2/3  12ft 3in = 12 3/12 or reduced to 12 1/4   The fractional part is referring to a fraction of a foot.

3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3  P= 31 5/6 feet

4. The estimate and the actual are very close. They are 1/6 of a foot apart.

5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.

5b. Take the total and divide it by 8ft  = 29 7/12 divided by 8= 3.7  You are not buying a fraction of a board so you would need 4 boards.

Answer:

decrease

Step-by-step explanation:

Answer:

comparing with ax²+bx+c=0

a=3, b=1 , c= -5

Solve using the formula now ,,

Answer:

The length of the rectangle is 10 inches, and the width is 4 inches.

Step-by-step explanation:

Given that the length of a rectangle is 6 inches more than the width, and the perimeter is 28 inches, the following calculation must be performed to find the length and the width:

(X + X + 6) x 2 = 28

2X + 2X + 12 = 28

4X = 28 - 12

X = 16/4

X = 4

Therefore, the length of the rectangle is 10 inches, and the width is 4 inches.

The cost of the cereal if the grocery store buys 250 boxes is $475

Functions are written in terms of variables. If the cost function that represents the cereal is given as C(n), the equivalent expression if the grocery store buys 250 boxes is 1.9n

Substitute n = 250 into the function to have:

C(250) = 1.9(250)

C(250) = $475

Hence the cost of the cereal if the grocery store buys 250 boxes is $475

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Answer:

[tex]\sqrt[3]{x^5 \ y } = (x^5 y)^\frac{1}{3} = x^{ \frac{5}{3}} \ y^ { \frac{1}{3}}[/tex]

Answer:

[tex] {x}^{ \frac{5}{3} } {y}^{ \frac{1}{3} } [/tex]

Step-by-step explanation:

A cube root is equivalent to the power of 1/3, so by taking the powers of the exponents and multiplying them by 1/3, you get your answer.

She gets a 4% raise so her new pay is 100% + 4% of her previous pay.

104% = 1.04 as a decimal.

Divide her new pay by 1.04:

24,960 / 1.04 = 24,000

Her previous pay was $24,000

Answer:

ur answer is correct

A =xy

A = 1.6×0.3 = 0.48

Answer:

4

Step-by-step explanation:

Since this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees.

We can see that this is a 30-60-90 degree triangle.

The rules of 30-60-90 degree triangles are that the side opposite the 90 degree angle, or the hypotenuse can be measured with the variable [tex]2a[/tex]. The side opposite the 30 degree angle can be measured with [tex]a[/tex], and the side opposite the 60 degree angle will be measured with [tex]a\sqrt{3}[/tex].

We can see that 8 represents [tex]2a[/tex] because it is the hypotenuse. Since the side marked [tex]x[/tex] is separated by the hypotenuse by an angle of 60 degrees, we note that side marked [tex]x[/tex] is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked [tex]a[/tex], and since we already know that 8 is equal to [tex]2a[/tex], we realize that the side marked x is equal to [tex]a[/tex], or 4.

The value of x in the triangle is 4.

What is the Pythagorean theorem ?

The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

It is given this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees. By the sum of all the three interior angles of a triangle is 180 degrees

The side opposite the 90 degree angle, or the hypotenuse can be measured with the variable '2a' . The side opposite the 30 degree angle can be measured with 'a' , and the side opposite the 60 degree angle will be measured with 'a√3'.

8 represents '2a' because it is the hypotenuse. Since the side marked x is separated by the hypotenuse by an angle of 60 degrees, we note that side marked x is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked 'a', and since we already know that 8 is equal to '2a', we realize that the side marked x is equal to

'a' , or 4.

2a=8

a=4

x=a=4

so, the the value of x in the triangle is 4.

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Answer:

Step-by-step explanation:

[tex]\frac{tan^2t}{sint}=\frac{tan t\times tant}{sin t} =\frac{tan t}{sint} \times \frac{sin t}{cos t} =\frac{tan t}{cos t} =tan t ~sec t[/tex]

Answer:

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Step-by-step explanation:

The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Fleet of 17 means that [tex]N = 17[/tex]

4 are carrying nucleas weapons, which means that [tex]k = 4[/tex]

9 are destroyed, which means that [tex]n = 9[/tex]

What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?

This is:

[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]

In which

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294[/tex]

[tex]P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412[/tex]

[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588[/tex]

0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed

Answer:

652 cases

Step-by-step explanation:

The formula for percentage increase is 100 times the final-initial/final value. If we plug the numbers in and calculate, we get 652 cases. Have a great day!

Step-by-step explanation:

let y = x+5/4

Interchanging x and y , we get ;

x = y+5/4

or, 4x = y+5

or, 4x-5 = y

or, g(x) -1 = 4x-5

Answer:

In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:

4x-5

Answer:

Solution given:

B.g(x)=[tex]\frac{x+5}{4}[/tex]

let

g(x)=y

y=[tex]\frac{x+5}{4}[/tex]

Interchanging role of x and y

we get:

x=[tex]\frac{y+5}{4}[/tex]

doing crisscrossed multiplication

4x=y+5

y=4x-5

So

g-¹(x)=4x-5

Answer:

Part 1)

1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.

2) Dylan is perfectly correct.

3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.

Part 2)

Only Skyler's approach was incorrect. When Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.

Step-by-step explanation:

Part 1)

We want to simplify the expression:

[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7}[/tex]

We can divide. Recall that xᵃ / xᵇ = xᵃ ⁻ ᵇ. Hence:

[tex]\displaystyle =0.88\times 10^{-11-7}=0.88\times 10^{-18}[/tex]

In scientific notation, the coefficient is always between 1 or 10.

So, we can multiply 0.88 by 10. To keep the equality, we need to divide 10⁻¹⁸ by 10. Hence:

[tex]\displaystyle =0.88(10)\times \frac{10^{-18}}{10}[/tex]

(You can see that the 10s can cancel out, giving us our original expression.)

Simplify. Thus:

[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7} = 8.8\times 10^{-19}[/tex]

Therefore, as we can see:

1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.

2) Dylan is perfectly correct.

3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.

Part 2)

Reviewing their work, we can see that only Skyler's approach was incorrect.

729 is indeed 3⁶. However, when Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.

Both Robert and Kevin are correct, having set each exponent equal to each other after their bases are equivalent and solving for x.

Answer:

( x - 3.5)² - 29/4

Step-by-step explanation:

Given :-

Writing in ( x - a)² - b form ,

Answer:

(f • g) (x) = [tex]x^{3}[/tex] - 3[tex]x^{2}[/tex] - 16x - 12

Step-by-step explanation:

(x-6)([tex]x^{2}[/tex] + 3x + 2)

[tex]x^{3}[/tex] + 3[tex]x^{2}[/tex] + 2x - 6[tex]x^{2}[/tex] - 18x -12

[tex]x^{3}[/tex] - 3[tex]x^{2}[/tex] - 16x - 12