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2 years ago

If f(x) = 2x - 4 and g(x) = x^2+3, find each value. 19. (f - g)(x) 20. (f • g)(x)

Mathematics

1 answer:

just olya [345]2 years ago

5 0

Step-by-step explanation:

$(f - g)(x) = f(x) - g(x) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2x - 4) - ( {x}^{2} + 3) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2x - 4 - {x}^{2} - 3 \\ \red{ \boxed{\therefore (f - g)(x) = - {x}^{2} + 2x - 7}}$

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An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry ou

Katyanochek1 [597]

Answer:

$t=\frac{29.35-30}{\frac{1.365}{\sqrt{6}}}=-1.17$

$p_v =P(t_{(5)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense

Step-by-step explanation:

Data given and notation

The mean and sample deviation can be calculated from the following formulas:

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)}{n-1}}$

$\bar X=29.35$ represent the sample mean

$s=1.365$ represent the sample standard deviation

$n=6$ sample size

$\mu_o =30$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 30 or no, the system of hypothesis are :

Null hypothesis: $\mu \geq 30$

Alternative hypothesis: $\mu < 30$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{29.35-30}{\frac{1.365}{\sqrt{6}}}=-1.17$

P-value

We need to calculate the degrees of freedom first given by:

$df=n-1=6-1=5$

Since is a one-side left tailed test the p value would given by:

$p_v =P(t_{(5)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense

5 0

2 years ago

a man pays 330 each month for his gym membership what is the change in the amount of money in his account after two thirds of a

olasank [31]

$\dfrac{\$330}{1\,month}\times\dfrac{12\,month}{1\,year}\times\dfrac{2}{3}\,year\\\\=\$2640$

The account will have decreased by $2640 after 2/3 year.

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3 years ago

Which of the following waves allows us to see colors?

topjm [15]

Gamma rays are radiation.
Radio waves are sound.
Visible light is color.
X-Rays allow us to see bones.

//Your answer is Visible Light.\\

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2 years ago

Read 2 more answers

In a certain Algebra 2 class of 29 students, 7 of them play basketball and 14 of them

Mariulka [41]

Answer:

<em>Two possible answers below</em>

Step-by-step explanation:

<u>Probability and Sets</u>

We are given two sets: Students that play basketball and students that play baseball.

It's given there are 29 students in certain Algebra 2 class, 10 of which don't play any of the mentioned sports.

This leaves only 29-10=19 players of either baseball, basketball, or both sports. If one student is randomly selected, then the propability that they play basketball or baseball is:

$\displaystyle P=\frac{19}{29}$

P = 0.66

Note: if we are to calculate the probability to choose one student who plays only one of the sports, then we proceed as follows:

We also know 7 students play basketball and 14 play baseball. Since 14+7 =21, the difference of 21-19=2 students corresponds to those who play both sports.

Thus, there 19-2=17 students who play only one of the sports. The probability is:

$\displaystyle P=\frac{17}{29}$

P = 0.59

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3 years ago

In triangle ABC, an altitude is drawn from vertex C to the line containing AB. The length of this altitude is h and h=AB. Which

adoni [48]

Answer:

II. Angle C cannot be a right angle.

III. Angle C could be less than 45 degrees.

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If f(x) = 2x -­ 4 and g(x) = x^2+3, find each value. 19. (f -­ g)(x) 20. (f • g)(x)

If f(x) = 2x - 4 and g(x) = x^2+3, find each value. 19. (f - g)(x) 20. (f • g)(x)