A group of 13 friends all want to ride a roller coaster. The coaster seats 15 in a single file row from front to back. How many ways can they arrange themselves?

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

Given the following data:

Translating the word problem into an algebraic expression;

[tex]W = 3 + L[/tex]  ......equation 1

[tex]H = 4 + L[/tex]  ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

[tex]Volume = length * width * height[/tex]  .....equation 3.

Substituting the values into equation, we have;

[tex]224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}[/tex]

Rearranging the polynomial, we have;

[tex]L^{3} + 7L^{2} + 12L - 224 = 0[/tex]

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

[tex](x - 3) = 0\\x = 3[/tex]

[tex]P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0[/tex]

We would try with 4;

[tex]P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0[/tex]

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: https://brainly.com/question/10689855

Answer:

3 ft per minute

Step-by-step explanation:

Take the distance and divide by the time

3/4 ft ÷ 1/4 minute

Copy dot flip

3/4 * 4/1

Rewriting

3/1 * 4/4

3/1 *1

3 ft per minute

Answer:

D. Positively skewed

Step-by-step explanation:

Answer:

16x^2 + 24x + 9  

Step-by-step explanation:

perfect square trinomial is of the form

a^2 + 2 * a * b + b^2

9x^2 + 9x + 1   = (3x)^2 + 3*3x*1 + 1^2  not a perfect square trinomial

36b^2 − 24b + 8  = ( 6b)^2  -2 * 6b *2 + ( 2 sqrt(2)) ^2  not a perfect square trinomial

16x^2 + 24x + 9  = ( 4x) ^2 + 2 * ( 4x) * 3 + 3^2 = perfect square trinomial

4a^2 − 10a + 25 = ( 2a) ^2 -  1 * 2a *5 + 5^2   not a perfect square trinomial

Answer:

The third answer listed:

[tex]16x^2+24x+9[/tex]

Step-by-step explanation:

The trinomial:  

[tex]16x^2+24x+9[/tex]

can be factored out as follows:

[tex]16x^2+24x+9\\(4x)^2+24x+3^2\\(4x)^2+12x+12x+3^2\\4x(4x+3)+3(4x+3)\\(4x+3)\,(4x+3)\\(4x+3)^2[/tex]

which as can be seen,is the perfect square of a binomial, so this trinomial is what is called a perfect square trinomial.

Answer:

8a^3-64p^3-36a^2+54a-27

Step-by-step explanation:

since it no common variable so it can not be further solved

3x²–243=0 —> 3 (x²–81) = 0 —>

x²–81=0 —> (x-9)(x+9)=0

x-9=0 —> x=9

x+9=0 —> x=–9

I hope I helped you^_^

Answer:

b. The science students

Step-by-step explanation:

If you count the dots, they are the same for both class (9 people) but the range of the science students' scores are higher than the range for the math students, which means that the sum of their scores will be larger than the math students' and since they have the same number of people, the number being divided for the average would be the same, so the science students' average would be greater than the math's.

I hope this helped! ;D

Answer:

  GH = 16; CH = 12

Step-by-step explanation:

First of all, you need to understand the meaning of "perpendicular bisector." It means that GH is divided into two equal parts by line AC, and that AC makes a right angle to GH.

The right angle is marked.

(a) The length of one of the halves of GH is marked as being 8 units long, so the other half will also be 8 units long. Of course, the length of GH is the sum of its two halves:

  GH = GB +BH = 8 + 8

  GH = 16

__

(b) Triangles CBG and CBH share side CB, so have that length in common. They have equal lengths BG and BH because BC bisects GH. They have a right-angle at B in common, so can be considered congruent by SAS, the fact that two congruent sides have a congruent angle between them.

Since triangles CBG and CBH are congruent, their corresponding sides CG and CH are also congruent. Side CG is marked 12 units long, so CH will be 12 units long, also.

  CH = 12

You could shortcut all of the congruent triangle logic by recognizing that an altitude (CB) is a perpendicular bisector of the base (GH) if and only if the triangle is isosceles. The sides of an isosceles triangle are always congruent, so CG = CH = 12.

__

In part (c), you're supposed to choose possible theorems for demonstrating the congruence of the triangles we described above.

Answer:

8

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = z₁(6, 2) and (x₂, y₂ ) = z₂(6, 10)

d = [tex]\sqrt{(6-6)^2+(10-2)^2}[/tex]

   = [tex]\sqrt{0^2+8^2}[/tex]

   = [tex]\sqrt{64}[/tex] = 8

Answer:

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= 2000π unit³

Volume= 6284 unit³

Step-by-step explanation:

The decimal value of the volume already given= 600π

The decimal value of the volume already given= 600*3.142

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= πr²h/3

Volume= 11²*12/3 *π

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume = πr²h/3

Volume= 4²*6/3(π)

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= πr²h/3

Volume= 20²*15/3(π)

Volume= 2000π unit³

Volume= 6284 unit³

Here's the right answer.

Answer:

Karen jogged 2.32 kilometers more than Morgan.

Step-by-step explanation:

Calculate the difference:

53.52 - 51.2 = 2.32

Answer:

2.32 km

Step-by-step explanation:

Take the amount that Karen jogged and subtract the amount that Morgan jogged

53.52 - 51.2

2.32

Answer:

113 degrees

Step-by-step explanation:

Measure of arc ADCB = 58+108+60 = 226 degrees

Measure of angle B = 226/2 = 113 degrees

Answer:50

Step-by-step explanation:

Answer:

k=10BY DPING PROCESS IT BECOME

Answer:

Given,  

The ratio of the three numbers are 1:2:3 . Let the numbers are x , 2x and 3x.

According to the question,

x³+(2x)³+(3x)³=4,500  

⟹x³+8x³+27x³=4,500  

⟹36x³=4500  

⟹x³=4,50036  

⟹x³=125  

⟹x=125−−−√3  

⟹x=5  

So the numbers are 5,5×2=10,5×3=15  

Therefore, 5 is the smallest number.

https://www.quora.com/Three-numbers-are-in-the-ratio-1-2-3-and-the-sum-of-their-cubes-is-4-500-What-is-the-smallest-number

Answer:

mean is adding up all the numbers.

range means the difference between the Lowest and highest value.

Step-by-step explanation:

when we add the answer is 240.6.

divide it to 12..do the final answer is 20.05

range is 25.4_16.3

9.1

Answer:

Mean: 20.05

Range: 9.1

Step-by-step explanation:

To find the mean in this problem, first you add all the following numbers together then subtract by the quantity.

20.1 + 19.6 + 18.0 + 17.8 + 25.2 + 18.7 + 21.9 + 16.3 + 25.4 + 20.5 +17.8 + 19.3

= 240.6

Now, divide by the quantity which is 12 since there's 12 numbers.

240.6 divided by 12 = 20.05.

The mean is 20.05.

To find the range in the problem, you must subtract the smallest value from the largest value.

In this case, 16.3 is the smallest value and 25.4 is the largest.

25.4 - 16.3 = 9.1

9.1 is the range.

Hope this helps you!

Answer:

31

Step-by-step explanation:

Given

x² + 5x - 3 = 0

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

sum of roots x₁ + x₂ = - [tex]\frac{b}{a}[/tex] = - [tex]\frac{5}{1}[/tex] = - 5

product of roots = [tex]\frac{c}{a}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

Now

(x₁ + x₂)² = x₁² + 2x₁x₂ + x₂² , that is

(- 5)² = x₁² + 2(- 3) + x₂²

25 = x₁² - 6 + x₂² ( add 6 to both sides ), then

x₁² + x₂² = 31

Answer:

B

Step-by-step explanation:

it is defined for all values so D=R

also we can get any value

so Range =R

Answer:

B

Step-by-step explanation:

because that's odd power function it can take both, negative and positive values

Answer:

(x-12)² + (y-6)² = 36 (Option C)

Step-by-step explanation:

use circle formula

(x-h)² + (y-k)²= r²

h= 12 and k= 6 and r= 6

(x-12)² + (y-6)² = 6²

6 squared = 36 (6·6)

(x-12)² + (y-6)² = 36

( − 2 ) ( 3+ 2 2 − − 2 )

Hope this helps, have a great day!

Answer:

8 pipes

Step-by-step explanation:

given that when height increases also time increases and automatically no of pipes will be decreased Mathematically;

h∝t•1/p

remove proportionality symbol and we will get

h=kt

p

make k as subject and we'll get

k=hp

t

find the value ok k

k=3×5

4

k=15

4

k=3.75

from h=kt. make p as subject and the answer should be

p=kt. find p

h

p=3.75×10

5

p=37.5

5

p=7.5 or 8

hence 8 pipes should be used

Answer:

[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1[/tex]

And we want to find:

[tex]\displaystyle (s-r)(x)[/tex]

This is equivalent to:

[tex]\displaystyle (s-r)(x) = s(x) - r(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}[/tex]

In conclusion:

[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]

Answer:

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

Step-by-step explanation:

Factor top and bottom.

The numerator is a difference of two squares, and the denominator is a quadratic.

[tex] \frac{ {9x}^{2} - {(x}^{2} - 4)^{2} }{4 + 3x - {x}^{2} } [/tex]

= [tex]\frac{ (3x+x^2-4)(3x-x^2+4) }{(1+x)(4-x)}[/tex]

= [tex] \frac{ (x-1)(x+4) (1+x)(4-x) }{(1+x)(4-x)} [/tex]

If x does not equal -1 and does not equal 4, we can cancel the common factors in italics to give

= [tex] { (x-1)(x+4)} [/tex]

= [tex] { x^2+3x-4} [/tex]

Answer:

The answer is

Step-by-step explanation:

[tex] \frac{9 {x}^{2} - ( { {x}^{2} - 4})^{2} }{4 + 3x - {x}^{2} } [/tex]

To solve the expression first factorize both the numerator and the denominator

For the numerator

9x² - ( x² - 4)²

Expand the terms in the bracket using the formula

( a - b)² = a² - 2ab + b²

(x² - 4) = x⁴ - 8x² + 16

So we have

9x² - (x⁴ - 8x² + 16)

9x² - x⁴ + 8x² - 16

- x⁴ + 17x² - 16

Factorize

that's

(x² - 16)(-x² + 1)

Using the formula

a² - b² = ( a + b)(a - b)

We have

(x² - 16)(-x² + 1) = (x + 4)(x - 4)( 1 - x)(1 + x)

For the denominator

- x² + 3x + 4

Write 3x as a difference

- x² + 4x - x + 4

Factorize

That's

- ( x - 4)(x + 1)

So we now have

[tex] \frac{(x + 4)(x - 4)( 1 - x)(1 + x)}{ - (x - 4)(x + 1)} [/tex]

Simplify

[tex] \frac{ - (x + 4)(1 - x)(1 + x)}{x + 1} [/tex]

Reduce the expression by x + 1

That's

-( x + 4)( 1 - x)

Multiply the terms

We have the final answer as

Hope this helps you

Answer:

x^2+3x-4

Step-by-step explanation:

(x-1)(x+4)

x^2+4x-x-4

x^2+3x-4

Hope this helps ;) ❤❤❤

Answer:

y = x² + 3x -4

Step-by-step explanation:

we can use the FOIL formula

(x-1) (x+4)

x² + 4x - x -4

x² + 3x -4

therefore, the standard form would be y = x² + 3x -4

Answer:

Step-by-step explanation:

2(75)=150 that's the amount due in total for two months so

400-150= 250 they will owe $250 after two months payment

Answer:

A,B,C

explanation:

i got it right on edge

Answer:

1 : 400

Step-by-step explanation:

[tex]\frac{3.5 x 10^{3} }{3.5 x 10^{3} } : \frac{1.4 x 10^{6 } }{3.5 x 10^{3} }[/tex]

1 : .4 x [tex]10^{3}[/tex]

1 : 4 x [tex]10^{2}[/tex]

1 : 400

Answer:

Step-by-step explanation:

4 person =  1575 bags

1 person  = 1575:4 = 393.75 bags

40 min = 1 bag

393,75 bags = 40 min•393,75 = 15 750 min