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2 years ago

Simplify the monomials

Mathematics

1 answer:

Zielflug [23.3K]2 years ago

7 0

Answer:

$(4a)^{-3}*^{-4}$

$x^m*x^n=x^{m+n}$

$(4a)^{-3}*a^{-4}$

$(-4)^{-3}\: a^{-3}*a^{-4}$

$4^{-3}\:a^{-3-4}$

$\cfrac{1}{4^3} \:a^{-7}$

$\boxed{\frac{1}{64a^{7}} }$

$(3xy)^2*(-4x^3y^2)^3$

$9x^2y^2*(64x^9y^6)$

$\boxed{-576x^{11}y^8}$

$(4a^{-1}b^5c^{-3})^3$

$(4)^3(a^{-1})^3(b^5)^3(c^{-3})^3$

$(4*4*4)\:a^{-1*3}\:b^{5*3}\:c^{-3*3}$

$64\:a^{-3}b^{15}c^{-9}$

$\boxed{\frac{64b^{15}}{a^3c^9}}$

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What is the quotient when x3 − 5x2 + 3x − 8 is divided by x − 3?

brilliants [131]

X^3 - 5x^2 + 3x - 8/x - 3
Steps
First, divide x^3 - 5x^2 + 3x - 8/x - 3: x^3 - 5x^2 + 3x - 8/x - 3 = x^2 + -2x^2 + 3x -8/x - 3
= x^2 + -2x^2 + 3x - 8/x - 3
Second, divide -2x^2 + 3x - 8/x - 3: -2x^2 + 3x - 8/x - 3 = -2x + -3x - 8/x - 3
= x^2 - 2x + -3x - 8/x - 3
Third, divide -3x - 8/x - 3: -3x - 8/x - 3 = -3 + -17/x - 3
= x^2 - 2x - 3 + -17/x - 3
Lastly, simplify
= x^2 - 2x - 3 - 17/x - 3

6 0

3 years ago

It has been determined that 60% of the people in a certain midwest city who are responsible for preparing the evening meal have

natali 33 [55]

Answer:

Random sample, $np \geq 10$ and $n(1-p) \geq 10$ , so yes, both conditions were satisfied.

Step-by-step explanation:

60% of the people in a certain midwest city who are responsible for preparing the evening meal have no idea what they are going to prepare as late as 4PM in the afternoon.

This means that $p = 0.6$

A recent survey was conducted from 1000 of these individuals.

This means that $n = 1000$

Also, a random sample, so the first condition was satisfied.

The sample size must be large (so that at least 10 or more successes and failures).

$np = 1000*0.6 = 600 \geq 10$

$n(1-p) = 1000*0.4 = 400 \geq 10$

So yes, both conditions were met.

4 0

3 years ago

An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a d

anygoal [31]

Answer:

The probability of event A is $\frac{7}{11}$ .

The probability of event B is $\frac{6}{11}$ .

Step-by-step explanation:

The sample space of rolling a fair six-sided dice is as follows:

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Now consider the experiment of the computing the sum of the two rolls as follows:

X = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Number of total outcomes, N = 11.

The probability of an event E is the ratio of the number of favorable outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

The event A is defined as the sum is greater than 5.

The sample space of A is:

A = {6, 7, 8, 9, 10, 11, 12}

n (A) = 7

Compute the probability of event A as follows:

$P(A)=\frac{n(A)}{N}=\frac{7}{11}$

Thus, the probability of event A is $\frac{7}{11}$ .

The event B is defined as the sum is an even number.

The sample space of B is:

B = {2, 4, 6, 8, 10, 12}

n (B) = 6

Compute the probability of event B as follows:

$P(B)=\frac{n(B)}{N}=\frac{6}{11}$

Thus, the probability of event B is $\frac{6}{11}$ .

7 0

3 years ago

Suppose x is a uniform random variable with values ranging from 40 to 90. Find the probability that a randomly selected observat

maxonik [38]

ok, so x is a number ranging from 40-90 which is 50 meaning that x has 50 different possibilities. But what are the chances that x is 75? well the chances of x being 75 is 1 out of 50.

so that means there is a 2% chance of x being 75

brainliest is appreciated

6 0

3 years ago

I had help but still don't understand plz help

erica [24]

Two parallel lines are intersect by the same line, and the angles shown lie on the same orientation about the intersection so the angles are equal to each other...which means:

9x+21=10x+10 subtract 21 from both sides

9x=10x-11 subtract 10x from both sides

-x=-11 divide both sides by -1

x=11

7 0

3 years ago