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lorasvet [3.4K]
2 years ago
6

If fx()=8-10x and g(x)=5x+4, what is the value of (fg)(-2)

Mathematics
1 answer:
lyudmila [28]2 years ago
7 0

So, we are looking for F of G of 2. So, we need to work backwards and find G(x) first.


g(-2)=5(-2)+4\\g(-2)=-6

So we know that g(-2) = -6, now we take thatt -6 and plug in into f(x)

f(g(-2))=f(-6)\\f(-6)=8-10(-6)\\f(-6)=8+60\\f(-6)=68


68 is the answer

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Step-by-step explanation:

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3 years ago
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Consider randomly selecting a single individual and having that person test drive 3 different vehicles. Define events A1, A2, an
zmey [24]

a. Use the inclusion/exclusion principle.

P(A_1\cap A_2)=P(A_1)+P(A_2)-P(A_1\cup A_2)=0.55+0.65-0.80=0.40

b. By definition of conditional probability,

P(A_2\mid A_3)=\dfrac{P(A_2\cap A_3)}{P(A_3)}=\dfrac{0.50}{0.70}\approx0.7143

4 0
2 years ago
) One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million. Suppose a samp
Nutka1998 [239]

Answer:

Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

Step-by-step explanation:

We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.

Suppose a sample of 400 major league players was taken.

<em>Let </em>\bar X<em> = sample average salary</em>

The z-score probability distribution for sample mean is given by;

                 Z = \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = mean salary = $1.5 million

            \sigma = standard deviation = $0.9 million

             n = sample of players = 400

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P(\bar X > $1.1 million)

    P(\bar X > $1.1 million) = P( \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} } >  \frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} } ) = P(Z > -8.89) = P(Z < 8.89)

<em>Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.</em>

Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

4 0
2 years ago
Ean: jenny wants to make three pillow cases using fourteen feet of fabric. She plans to use an equal amount of fabric for each p
Veseljchak [2.6K]

Answer:

Approximately 4.67 feet of fabric is required for one pillow case.

Step-by-step explanation:

We are given the following in the question:

Number of pillow cases to be made by Jenny = 3

Amount of fabric Jenny has = 14 feet

Each pillow case use same amount of fabric.

Amount of fabric used to make 1 pillow case =

=\dfrac{\text{Amount of fabric}}{\text{Number of pillow cases}}\\\\=\dfrac{14\text{ feet}}{3}\\\\\approx 4.67\text{ feet}

Thus, approximately 4.67 feet of fabric is required for one pillow case.

5 0
3 years ago
40 employees increased by 15% use the percent of change to find new amohnt
Neko [114]
Answer=46 employees

40 employees
15% increase

100%+15%=115%

115%=1.15

40*1.15=46 employees



6 0
2 years ago
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