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The value of [tex]n[/tex] such that [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex] is [tex]280[/tex].

In this question we need to find the root of the radical function [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex], which must be simplified by algebraic means.

First, we need to elevate each side of the expression by third power:

[tex]\left(\sqrt[3]{n+\sqrt{n^{2}+8}} + \sqrt[3]{n+\sqrt{n^{2}+8}} \right)^{3} = 512[/tex]

[tex]2\cdot n + 3\cdot \sqrt[3]{(n+\sqrt{n^{2}+8})^{2}\cdot (n-\sqrt{n^{2}+8})} + 3\cdot \sqrt[3]{(n-\sqrt{n^{2}+8})^{2}\cdot (n+\sqrt{n^{2}+8})} = 512[/tex]

[tex]2\cdot n -6\cdot (\sqrt[3]{n+\sqrt{n^{2}+8}} + \sqrt[3]{n-\sqrt{n^{2}+8}}) = 512[/tex]

[tex]2\cdot n - 6\cdot (8) = 512[/tex]

[tex]n = 280[/tex]

The value of [tex]n[/tex] such that [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex] is [tex]280[/tex]. [tex]\blacksquare[/tex]

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Answer:

155

Step-by-step explanation:

Based on the number of families that left and the number in total on that block, the expected number of families gone on the other block is 25 families.

On the first block, the proportion of families that is gone is:

= Number of families gone / Total number of families on block

= 5 / 12

If there are 60 families on a block, the number gone would be:

= Proportion of families gone x Total number of families

= 5/12 x 60

= 25 families

In conclusion, 25 families would be gone

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Answer:

what's the question that you need answered?

Step-by-step explanation:

?

Answer:

3.

2x^3+10x^2+14x+6

Step-by-step explanation:

according to figure,

v=w•l•h

(2x+2)(x+1)(x+3)

=(2x+2)x(x+1)+3(X+1)

=(2x+2)(x^2+4x+3)

=2x(x^2+4x+3)+2(x^2+4x+3)

=2x^3+10x^2+14x+6

The volume of the figure as a polynomial in standard form is

V = 2x³ + 10x² + 14x + 6.

A closed three-dimensional geometric shape called a cuboid is surrounded by six rectangular plane sections.

The given figure is a cuboid with dimensions (2x + 2), (x + 1), and (x + 3).

The volume of the cuboid is the multiplication of its dimension, therefore, the volume of the cuboid is:

V = (2x +2)(x + 1)(x + 3)

V = (2x² + 2x +2x + 2)(x + 3)

V = (2x² + 4x + 2)(x + 3)

V = 2x³ + 6x² + 4x² + 12x + 2x + 6

V = 2x³ + 10x² + 14x + 6

Hence, the volume of the figure as a polynomial in standard form is

V = 2x³ + 10x² + 14x + 6.

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Using the binomial distribution, it is found that there is a 0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.

For each free throw, there are only two possible outcomes, either he makes it, or he misses it. The results of free throws are independent from each other, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

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

The parameters are:

In this problem:

The probability that he makes exactly 1 is P(X = 1), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{3,1}.(0.9)^{1}.(0.1)^{2} = 0.027[/tex]

0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.

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Answer:

0.03

Step-by-step explanation:

I just did it on Khan

Answer:

Well add up the sides you can make the curving part into a full circle and calculate for the circumference.

So if the half of the circle straight part is 62 you times it by π. But π (pi) can be a fraction and a decimal: 22/7 or 3.14 although (pi) is 3.14 that is because after .14 there is ton of number so it constantly continues.

Method:

C = 2πr

or

C = πr

I hope this gives you a hint.

Answer:

394.68 m

Step-by-step explanation:

The 2 ends are half circles, so together they make a circle.

The diameter is 62 m, so the circumference is pi x diameter, or 3.14 x 62 = 194.68.

The top and bottom parts of the track are each 100 m, so add 2 of them = 200 m.

Add all 3 parts 194.68 + 200 = 394.68 m.

Answer:

Abby will earn $510 if she works 60 hours.

Step-by-step explanation:

8 hrs --> $68

1 hr --> 68 × 1/8 = $8.5

So, 60 hrs

= 8.5 × 60

= $510

Step-by-step explanation:

As it's a product, just multiply each number! We notice there are 2 identical square roots multiplied, and we know that: [tex]\sqrt{x} * \sqrt{x} = x\\[/tex].

So we'll remain with: 5 * 2 * 3 = 30.

:)

Answer:

30

Step-by-step explanation:

First multiply 2 square root with 2 square root and since they are identical the answer will be 2.

Now multiply 3 and 5:

3×5= 15

Now we have two numbers 15 and 2, we will multiply 15 with 2 and we get 30

I couldn't explain well but I hope you understand

The another number is divider to pi 22/7

The another number is divider to pi 22/7

Answer:

dont now

Step-by-step explanation:

Answer:

Name:

Grade & Section:

Date Submitted: 12/14/2021

Advent: Use it

Christmas: Open gifts under the tree left by Santa

Ordinary Time:

Lent: Celebrate Jesus.

Paschal Triduum: The Proper day to Celebrate Jesus

Easter: It is a Holiday where you celebrate a bunny and get candy.

Step-by-step explanation:

So is what you do here is you enter your Name, Grade & Section, and Date which i've already given you. So your assignment is about how you will participate in the seasonal activity. So Advent looks like it would be a Advent Calendar.

Christmas You wanna open gifts

Now I left Ordinary Time blank because you need to put what time you would regularly open gifts or if you do not celebrate Christmas put what time you'd like to open gifts at.

Lent: is where you celebrate Jesus and what he did on his time being on Earth.

Paschal Triduum is basically the same as Lent but it is the proper day you celebrate Jesus Which starts April 13 & Ends Saturday, April 16

Easter: Is where you usually get candy but it is in a hunt form

Answer:

[tex]{ \rm{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }} \\ [/tex]

Answer:

  (b)

Step-by-step explanation:

The hundredths place is immediately to the left of the thousandths place. In our base-10 number system, moving a digit to the left one place increases its value by a factor of 10.

The value of 7 in the hundredths place is 10 times the value of 7 in the thousandths place.

Answer:

The value of the 7 in the hundredth place is 10 times​ the value of the 7 in the thousandth place.

Step-by-step explanation:

Answer:

It's B

And Prime Factorization is when 2 numbers have the same answer.

Example: 3x8=24 and 4x6=24

Step-by-step explanation:

Answer:

Step-by-step explanation:

11

Answer:

Which graph?

Step-by-step explanation:

Answer:

where is the graph

Step-by-step explanation:

umm i dont know how to answer

Answer:

1:Cubic

2:5a and the value in the 2a is a exp.

3:Quintic

Step-by-step explanation:

Im sure this answer is correct

An expressions equated to another expression is called an equation

An equation is an expression that is used to show the relationship between two or more variables and numbers.

Given that a = 5, hence:

2a + 5

substituting values:

2(5) + 5 = 10 + 5 = 15

2a + 5 = 15

The sum of twice and four times of the variable x is 2x + 4x = 6x

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Answer:

28.9 m

Step-by-step explanation:

First, we can draw a picture. The statue is on the right, with the top of the statue representing the top right corner of the triangle. The angle of elevation to the sun is 78 degrees, so the angle between the shadow and the top of the statue must be 78 degrees as well. Assuming there is no angle of elevation between the shadow and the statue, we can say that the shadow and statue form a 90 degree angle because the shadow is perfectly horizontal and the statue is perfectly vertical.

We are trying to find the hypotenuse of the triangle, or the length from the top of the statue to the end of the shadow. To do this, we can utilize the fact that

cos(x) = adjacent / hypotenuse

cos(78°) = 6 / hypotenuse

divide both sides by cos(78°) and multiply both sides by hypotenuse to solve for the hypotenuse

hypotenuse = 6/cos(78°) ≈ 28.9 m

Answer:

121 inches

Step-by-step explanation:

See the attached diagram.  We can form a right triangle as shown.  The base and sides of the right triangle can be computed by adding the 10 steps of horizonal distance 9.5" (95" for the base) and the 10 vertical distances of 7.5" (75" total) for the height.  Use the Pythagorean Theorem to calculate the hypotenuse, which will be the same as the railing length.

Answer:

the nominator could be any number here

Step-by-step explanation:

what do you need ? the equation itself is true, if you put the same number in both places above 21.

any number is possible there, it will not change the equation.

so, again, I am not sure, what you need here.

let's write it with a variable to make my statements clearer :

9 + 1 x/21 = 10 x/21

that is true, because we can combine the whole numbers first giving us 9 + 1 = 10.

and then we add the fraction again (x/21).

again, you can put any number instead of x, and it will always be true.

example

9 + 1 4/21 = 10 4/21

Answer:

static electricty

Step-by-step explanation:

it is preserved charge

Answer:

its electroboom not boy

Step-by-step explanation:

lol its static

Answer:

m∡B = 120°

Step-by-step explanation:

base angles are equal

adjacent angles are supplementary so:

4x+20 + 3x-15 = 180

7x + 5 = 180

7x = 175

x = 25

∡B = 4(25) + 20

∡B = 120°

Answer:

39.6

Step-by-step explanation:

(3x-15)+(4x+20)+2x=360

9x+5=360

9x=355

*Divide each side by 9*

X=39.4

*SUBSTITUTE X*

3(39.4)-15=103.2

4(39.4)+20=177.6

*ADD THE TOTALS FROM ABOVE*

103.2+177.6= 280.8

360-280.8=79.2

*DIVIDE THE TOTAL BY 2*

79.2/2=39.6

*CHECK*

3(39.4)-15=103.2

4(39.4)+20=177.6

103.2+177.6+39.6+39.6=360 IS CORRECT.

Hope this helps! :)

Answer:

[tex]3x^3 - 5x + 1 - \frac{10}{x + 3}[/tex]

or

3x^3 - 5x + 1

Remainder: -10

Step-by-step explanation:

Please see attached image for full explanation!

1.) Write the coefficient of each term.

2.) Beginning with 3, multiply by -3, or x + 3 = 0 (the divisor.)

3.) Add the product to the next coefficient and repeat until you get to the last number, -7.

4.) You should have the numbers 3, 0, -5, 1, and -10.

5.) Rewrite this quotient as an equation:

3x^3 - 5x + 1

Note that the highest power is 3, one less than that of the highest power in the original equation.

6.) Don't forget the remainder!

You can include this in the equation or not, depending on the instructions.

Therefore, the final answer is 3x^3 - 5x + 1 - 10/x+3 or 3x^3 - 5x + 1 R: -10.

the 1st and 2nd ones r correct

Step-by-step explanation:

hope this helps

The number of quarts of shampoo does Elena need to order, When she wants to order for the year, is 64.8.

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation form using the variable in place of unknown numbers.

Elena’s Hair Salon uses an average of 5.4 quarts of shampoo per month. Let suppose that she needs to order n quarts of shampoo in a year.

As it is known that there are total 12 months in a year and Elena’s Hair Salon uses an average of 5.4 quarts of shampoo per month. Thus, the number of quarts of shampoo does she need to order is,

[tex]n=5.4\times12\\n=64.8\\[/tex]

Thus, the number of quarts of shampoo does Elena need to order, When she wants to order for the year, is 64.8.

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