All categories

3 years ago

What expression is equal to 6(-3m) times 4

Mathematics

1 answer:

ololo11 [35]3 years ago

8 0

Answer:

-18x4

Step-by-step explanation:

You might be interested in

John Calipari, head basketball coach for the 2012 national champion University of Kentucky Wildcats, is the highest paid coach i

MrRissso [65]

Answer:

A) sample mean = $1.36 million

B) standard deviation = $0.9189 million

C) confidence interval = ($1.93 million , $0.79 million)

*since the sample size is very small, the confidence interval is not valid.

Step-by-step explanation:

samples:

$2.7 million
$2.4 million
$2.2 million
$2 million
$1.5 million
$1.5 million
$0.5 million
$0.5 million
$0.2 million
$0.1 million

sample mean = $1.36 million

the standard deviation:

$2.7 million - $1.36 million = 1.34² = 1.7956
$2.4 million - $1.36 million = 1.04² = 1.0816
$2.2 million - $1.36 million = 0.84² = 0.7056
$2 million - $1.36 million = 0.64² = 0.4096
$1.5 million - $1.36 million = 0.14² = 0.0196
$1.5 million - $1.36 million = 0.14² = 0.0196
$0.5 million - $1.36 million = -0.86² = 0.7396
$0.5 million - $1.36 million = -0.86² = 0.7396
$0.2 million - $1.36 million = -1.16² = 1.3456
$0.1 million - $1.36 million = -1.26² = 1.5876
total $8.444 million / 10 = $0.8444 million

standard deviation = √0.8444 = 0.9189

95% confidence interval = mean +/- 1.96 standard deviations/√n:

$1.36 million + [(1.96 x $0.9189 million)/√10] = $1.36 million + $0.57 million = $1.93 million

$1.36 million - $0.57 million = $0.79 million

7 0

3 years ago

Identify the volume of the composite figure rounded to the nearest tenth.

Verdich [7]

Answer:

Step-by-step explanation:

The volume of a composite figure can be found by decomposing it into figures whose volumes are easy to compute. Here, the figure can be nicely represented as a cube and a square pyramid.

The volume of the cube on the left is given by ...

V = s³

V = (4.2 ft)³ = 74.088 ft³

<h3>Pyramid</h3>

The volume of the pyramid on the right is given by ...

V = 1/3Bh . . . . . where B is the area of the square base

V = 1/3(s²)h = (4.2 ft)²(7 ft) = 41.16 ft³

<h3>Total</h3>

The volume of the composite figure is the sum of these volumes:

cube volume + pyramid volume = 74.088 ft³ +41.16 ft³ = 115.248 ft³

The volume of the composite figure is about 115.2 ft³.

6 0

2 years ago

I really need it to be sold in imaginary numbers

Yuliya22 [10]

Solving a 5th grade polynomial

We want to find the answer of the following polynomial:

$x^5+3x^4+3x^3+19x^2-54x-72=0$

We can see that the last term is -72

We want to find all the possible numbers that can divide it. Those are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

We want to factor this polynomial in order to find all the possible x-values. In order to factor it we will have to find some binomials that can divide it using the set of divisors of -72.

We know that if

(x - z) is a divisor of this polynomial then z might be a divisor of the last term -72.

We will verify which is a divisor using synthetic division. If it is a divisor then we can factor using it:

Let's begin with

(x-z) = (x - 1)

We want to divide

$\frac{(x^5+3x^4+3x^3+19x^2-54x-72)}{x-1}$

Using synthetic division we have that if the remainder is 0 it will be a factor

We can find the remainder by replacing x = z in the polynomial, when it is divided by (x - z). It is to say, that if we want to know if (x -1) is a factor of the polynomial we just need to replace x by 1, and see the result:

If the result is 0 it is a factor

If it is different to 0 it is not a factor

Replacing x = 1

If we replace x = 1, we will have that:

$\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ 1^5+3\cdot1^4+3\cdot1^3+19\cdot1^2-54\cdot1-72 \\ =1+3+3+19-54-72 \\ =-100 \end{gathered}$

Then the remainder is not 0, then (x - 1) is not a factor.

Similarly we are going to apply this until we find factors:

(x - z) = (x + 1)

We replace x by -1:

$\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ \downarrow \\ (-1)^5+3\cdot(-1)^4+3\cdot(-1)^3+19\cdot(-1)^2-54\cdot(-1)-72 \\ =-1+3-3+19+54-72 \\ =0 \end{gathered}$

Then, (x + 1) is a factor.

Using synthetic division we have that:

Then:

$x^5+3x^4+3x^3+19x^2-54x-72=(x+1)(x^4+2x^3+x^2+18x-72)$

Now, we want to factor the 4th grade polynomial.

Let's remember our possibilities:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

Since we verified ±1, let's try with ±2 as we did before.

(x - z) = (x - 2)

We want to divide:

$\frac{x^4+2x^3+x^2+18x-72}{x-2}$

We replace x by z = 2:

$\begin{gathered} x^4+2x^3+x^2+18x-72 \\ \downarrow \\ 2^4+2\cdot2^3+2^2+18\cdot2-72 \\ =16+16+4+36-72 \\ =0 \end{gathered}$

Then (x - 2) is a factor. Let's do the synthetic division:

Then,

$x^4+2x^3+x^2+18x-72=(x-2)(x^3+4x^2+9x+36)$

Then, our original polynomial is:

$\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =\mleft(x+1\mright)\mleft(x^4+2x^3+x^2+18x-72\mright) \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \end{gathered}$

Now, let's prove if (x +2) is a factor, using the new 3th grade polynomial.

(x - z) = (x + 2)

We replace x by z = -2:

$\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-2)^3+4(-2)^2+9(-2)+36 \\ =-8+16-18+36 \\ =26 \end{gathered}$

Since the remainder is not 0, (x +2) is not a factor.

All the possible cases are:

{±1, ±2, ±3, ±4, ±6, ±8, ±9, ±12, ±18, ±36, ±72}

let's prove with +4

(x - z) = (x + 4)

We want to divide:

$\frac{x^3+4x^2+9x+36}{x+4}$

Let's replace x by z = -4 in order to find the remainder:

$\begin{gathered} x^3+4x^2+9x+36 \\ \downarrow \\ (-4)^3+4(-4)^2+9(-4)+36 \\ =-64+64-36+36 \\ =0 \end{gathered}$

Then (x + 4) is a factor. Let's do the synthetic division:

Then,

$x^3+4x^2+9x+36=(x+4)(x^2+9)$

Since

x² + 9 cannot be factor, we have completed our factoring:

$\begin{gathered} x^5+3x^4+3x^3+19x^2-54x-72 \\ =(x-1)(x-2)(x^3+4x^2+9x+36) \\ =(x-1)(x-2)(x+4)(x^2+9) \end{gathered}$

Now, we have the following expression:

$(x-1)(x-2)(x+4)(x^2+9)=0$

Then, we have five posibilities:

(x - 1) = 0

or (x - 2) = 0

or (x + 4) = 0

or (x² + 9) = 0

Then, we have five solutions;

x - 1 = 0 → x₁ = 1

x - 2 = 0 → x₂ = 2

x + 4 = 0 → x₃ = -4

x² + 9 = 0 → x² = -9 → x = ±√-9 = ±√9√-1 = ±3i

→ x₄ = 3i

→ x₅ = -3i

<h2><em>Answer- the solutions of the polynomial are: x₁ = 1, x₂ = 2, x₃ = -4, x₄ = 3i and x₅ = -3i</em></h2>

7 0

1 year ago

A box with a volume of 40 cubic inches holds 10 balls. A box with a volume of 60 cubic inches holds 15 of the same kinds of ball

lesya692 [45]

Pretend these are coordinates that you can use to find the slope of the line.
(10, 40) and (15, 60). Fit these into the slope formula to find the slope of the line you are looking for:
$m= \frac{60-40}{15-10}$ and the slope is 4. Now use one of the points and the slope of 4 to solve for b, the y-intercept:
40 = 4(10) + b so b = 0. The equation of the line then is y = 4x + 0 or just
y = 4x

6 0

3 years ago

Fernando has gathered details about his finances to create a financial assets and liabilities record. Which represents one of hi

Bingel [31]

<span>
C.
His college savings account has a balance of $13,700.</span>

4 0

3 years ago