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3 years ago

Let f(x)=x^2+2 and g(x)=1-3x. Find each function value: (fg)(-1)

Mathematics

1 answer:

Verizon [17]3 years ago

6 0

Answer:

Step-by-step explanation:

$f(x)=x^2+2$

$g(x)=1-3x$

$(fg)(x)=f(x) \times g(x)$

$\implies (fg)(x)=(x^2+2)(1-3x)$

$(fg)(-1)=((-1)^2+2)(1-3(-1))$

$\implies (fg)(-1)=(1+2)(1+3)$

$\implies (fg)(-1)=12$

Extra:

If you were looking for f[g(-1)], then:

$f[g(-1)]=f(4)=4^2+2=18$

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The American Management Association is studying the income of store managers in the retail industry. A random sample of 49 manag

VashaNatasha [74]

Answer:

a) The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.

b) The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.

Step-by-step explanation:

Question a:

We have to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a p-value of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{2050}{\sqrt{49}} = 574$

The lower end of the interval is the sample mean subtracted by M. So it is 45420 - 574 = $44,846.

The upper end of the interval is the sample mean added to M. So it is 45420 + 574 = $45,994.

The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.

Question b:

The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.

5 0

3 years ago

The sum of 3 times a number and 5 is equal to 9.

tiny-mole [99]

Answer:

Let x equal “a number”

3x+5=9

4 0

3 years ago

Read 2 more answers

What is two filths plus one eighth

pantera1 [17]

Answer: 21/40

Step-by-step explanation:

25+18=?The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(2/5, 1/8) = 40

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(25×88)+(18×55)=?

Complete the multiplication and the equation becomes

1640+540=?

The two fractions now have like denominators so you can add the numerators.

Then:

16+540=2140

This fraction cannot be reduced.

Therefore:

25+18=2140

4 0

4 years ago

Which graph the linear inequality <_ 4x —3 ?

kykrilka [37]

Answer:

Step-by-step explanation:

6 0

3 years ago

R/10+4=5 two step equations with integers

Kamila [148]

Answer:

So we have this equation:

r/10 + 4 = 5

FIrst, we can substract 4 in both sides

r/10 + 4 - 4 = 5 - 4

r/10 = 1

Now, we can multiply both sides per 10:

r/10 * 10 = 1 * 10

r = 10

And we know that r = 10, and that's the result of the equation.

7 0

3 years ago