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3 years ago

Please helpppppp :((

Mathematics

2 answers:

nasty-shy [4]3 years ago

3 0

Answer:

$4^{21}$

Step-by-step explanation:

kkurt [141]3 years ago

3 0

$\frac{4^{12}}{4^{-9}}\\$

Given 4 = a

From the properties of exponents for the example...

$\frac{a^4}{a^{-2}} = \frac{a*a*a*a}{\frac{1}{a^2} } = (a*a*a*a)*a^2 = a^4 * a^2 = a^{4+2} = a^6$

Therefore, the answer is....

$4^{12}*4^{9} = 4^{12+9} = 4^{21}$

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3 years ago

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A job fair was held at the Student Union. 25% of the students who attended received job offers. Of all of the students at the jo

vovangra [49]

Answer:

A) Both events are not independent.

B) Both events are not mutually exclusive

C) 8.33%

D) 80%

Step-by-step explanation:

A) Both events are not independent. This is because, If B occurs it means that it is very likely that J will occur as well.

B) Both events are not mutually exclusive. This is because it is possible for both events J and B to occur at the same time.

C) we want to find the probability that Joe who is not a business student will receive the job offer.

This is;

P(J|Not B) = P(J & Not B)/P(Not B)

Now,

P(J & Not B) = P(J) – (P(B) × P(J | B))

25% of the students who attended received job offers. Thus; P(J) = 0.25

40% were from the College of Business. Thus;

P(B) = 0.4

Among the business students, 50% received job offers. Thus;

P(J|B) = 0.5

Thus;

P(J & Not B) = 0.25 - (0.4 × 0.5)

P(J & Not B) = 0.25 - 0.2

P(J & Not B) = 0.05

Since P(B) = 0.4

Then, P(Not B) = 1 - 0.4 = 0.6

Thus;

P(J|Not B) = 0.05/0.6

P(J|Not B) = 0.0833 = 8.33%

D) This probability is represented by;

P(B | J) = P(B & J)/P(J)

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3 years ago

What is the quotient when 4x3 + 2x + 7 is divided by x + 3?

Arte-miy333 [17]

Answer:

The quotient of this division is $(4x^2 -12x + 38)$ . The remainder here would be $-26$ .

Step-by-step explanation:

The numerator $4x^3 + 2x + 7$ is a polynomial about $x$ with degree $3$ .

The divisor $x + 3$ is a polynomial, also about $x$ , but with degree $1$ .

By the division algorithm, the quotient should be of degree $3 - 1 = 2$ , while the remainder shall be of degree $1 - 1 = 0$ (i.e., the remainder would be a constant.) Let the quotient be $a\,x^2 + b\, x + c$ with coefficients $a$ , $b$ , and $c$ .

$4x^3 + 2x + 7 = \left(a\,x^2 + b\, x + c\right)(x + 3)$ .

Start by finding the first coefficient of the quotient.

The degree-three term on the left-hand side is $4 x^3$ . On the right-hand side, that would be $a\, x^3$ . Hence $a = 4$ .

Now, given that $a = 4$ , rewrite the right-hand side:

$\begin{aligned}&\left(4\,x^2 + b\, x + c\right)(x + 3) \cr =& \left(4x^2 + (b\, x + c)\right)(x + 3) \cr =& 4x^2(x + 3) + (bx + c)(x + 3) \cr =& 4x^3 + 12x^2 + (bx + c)(x + 3)\end{aligned}$ .

Hence:

$4x^3 + 2x + 7 = 4x^3 + 12x^2 + (b\,x + c)(x + 3)$

Subtract $\left(4x^3 + 12x^2\right$ from both sides of the equation:

$-12x^2 + 2x + 7 = (b\,x + c)(x + 3)$ .

The term with a degree of two on the left-hand side has coefficient $(-12)$ . Since the only term on the right hand side with degree two would have coefficient $b$ , $b = -12$ .

Again, rewrite the right-hand side:

$\begin{aligned}&\left(-12 x + c\right)(x + 3) \cr =& \left(-12 x+ c\right)(x + 3) \cr =& (-12x)(x + 3) + c(x + 3) \cr =& -12x^2 -36x + (bx + c)(x + 3)\end{aligned}$ .