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3 years ago

If f(x) = 3x2 and g(x) = x+2, find (f•g)(x).

1 answer:

5 0

Since you have provided me with • symbol I must assume it's about function multiplication, but since standard keyboard doesn't have the function composition symbol $\circ$ I must assume you meant either.

1. Case you meant multiplication.

$(f\cdot g)(x)=3x^2\cdot(x+2)=\boxed{3x^3+6x^2}$

2. Case you meant composition.

$(f\circ g)(x)=f(g(x))=f(x+2)=3(x+2)^2=\boxed{3x^2+12x+12}$

Hope this helps. Next time please use LaTeX to format your equations so that others can give you answers as well.

You might be interested in

If f(x) = -2x^2 + x–5, what is f(3)?

yan [13]

Answer:

-20

Step-by-step explanation:

Replace X by 3

f(3) = -2(3)^2+ (3)-5 = -20

7 0

3 years ago

According to a Washington Post-ABC News poll, 331 of 502 randomly selected U.S. adults interviewed said they would not be bother

k0ka [10]

Answer:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124$

$p_v =P(z>7.124)=5.24x10^{-13}$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.

Step-by-step explanation:

Data given and notation

n=502 represent the random sample taken

X=331 represent the adults that said they would not be bothered if the NAtional security agency

$\hat p=\frac{331}{502}=0.659$ estimated proportion of people who would not be bothered if the NAtional security agency

$p_o=0.5$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than the majority of 0.5:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>7.124)=5.24x10^{-13}$

4 0

3 years ago

You work a part-time job at $7.85/hr for 10 hours per week. Your deductions are FICA (7.65%), federal tax withholding (9.8%), an

Dmitrij [34]

Here, My initial salary = 7.85

FICA deduction amount = 7.85 * 7.65% = 7.85 * 0.0765 = 0.60
Federal Tax amount = 7.85 * 9.8% = 7.85 * 0.098 = 0.77
State tax amount = 7.85 * 5.5% = 7.85 * 0.055 = 0.43

So, Total deducted amount = 0.60 + 0.77 + 0.43 = 1.80
Net hourly wage = 7.85 - 1.80 = 6.05

In short, Your Answer would be $6.05

Hope this helps!

4 0

2 years ago

What is the annual interest rate if $1600 is invested for 6 years and $456 in interest is earned

sergij07 [2.7K]

Use the formula i = p*r*t:
$456
$456 = $1600*r*6. Solving for r, r = ----------------- = 0.0475, or 4 3/4%
($1600)(6)

6 0

3 years ago

A recipe for sugar cookies requires 2 cups of flour for every 2/3 cups of sugar at this rate how many cups of sugar should be us

maks197457 [2]

The answer would be 5/3 or 1 2/3

4 0

3 years ago