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aleksandr82 [10.1K]
2 years ago
10

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 <em>A</em> is \frac{7}{11}.

The probability of event <em>B</em> 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, <em>N</em> = 11.

The probability of an event <em>E</em> is the ratio of the number of favorable outcomes to the total number of outcomes.

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

The event <em>A</em> is defined as the sum is greater than 5.

The sample space of <em>A</em> is:

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

n (A) = 7

Compute the probability of event <em>A</em> as follows:

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

Thus, the probability of event <em>A</em> is \frac{7}{11}.

The event <em>B</em> is defined as the sum is an even number.

The sample space of <em>B</em> is:

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

n (B) = 6

Compute the probability of event <em>B</em> as follows:

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

Thus, the probability of event <em>B</em> 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
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