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2 years ago

Find the product. (-5a ^2)^3·a ^5 A)-15a10 B)-125a11 C)15a6 D)-125a10

Mathematics

2 answers:

Ber [7]2 years ago

5 0

Answer:

B) -125a^11

Step-by-step explanation:

(-5a^2)^3·a^5 = (-5)^3·a^6·a^5

= (-5)^3·a^(2·3)·a^5

= (-5)^3·a^6·a^5

= -125·a^(6+5)

= -125·a^11 . . . . matches choice B

_____

The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

(a^b)^c = a^(bc)

seropon [69]2 years ago

3 0

Answer:

B) -125a^11

Step-by-step explanation:

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Suppose that 75% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection. Consider grou

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b) 0.2961

c) 0.2251

d) Mean = 11.25, Standard deviation = 1.667

Step-by-step explanation:

We are given the following information:

We treat trucks undergoing a brake inspection passin as a success.

P( trucks undergoing a brake inspection passes the test) = 75% = 0.75

a) Conditions for binomial probability distribution

There are n independent trial.
Each trial have a success probability p
The probability of success is same for all trials.

Then the number of trucks undergoing a brake inspection follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 15

b) P(proportion of groups will between 8 and 10 trucks pass the inspection)

We have to evaluate:

$P(8\leq x \leq 10) = P(x = 8) + P(x = 9) + P(x = 10)\\= \binom{15}{8}(0.75)^8(1-0.75)^7 + \binom{15}{9}(0.75)^9(1-0.75)^6 + \binom{15}{10}(0.75)^{10}(1-0.75)^5\\= 0.0393 + 0.0917 + 0.1651\\= 0.2961$

c) P( exactly 3 trucks fail the inspection)

p = 0.25

$P(x = 3)\\= \binom{15}{3}(0.25)^3(1-0.25)^{12}\\=0.2251$

d) Mean and standard deviation

$\mu = np = 15(0.75) = 11.25\\\sigma = \sqrt{np(1-p)} = \sqrt{15(0.75)(1-0.75)} = 1.667$

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3 years ago