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Zina [86]
3 years ago
7

If ƒ(x) = x + 2 and g(x) = 3x2 + 7x, find ....

Mathematics
1 answer:
Tamiku [17]3 years ago
7 0

Answer:

The correct answer is option C

(f o g)(x) = 3x² + 7x + 2

Step-by-step explanation:

<u>Points to remember</u>

<u>Composite functions</u>

Let f(x) and g(x) be the two functions then (f o g)(x) can be written as

(f o g)(x) = f(g(x))

<u>To find the value of (f o g)(x)</u>

Here f(x) =x + 2  and g(x) = 3x² + 7x

(f o g)(x) = f(g(x))

 = f(3x² + 7x)

 = 3x² + 7x + 2

Therefore the correct answer is option C

(f o g)(x) = 3x² + 7x + 2

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A random sample of 850 births included 434 boys. Use a 0.10 significance level to test the claim that 51.5​% of newborn babies a
Molodets [167]

Answer:

A

Null hypothesis: H0: p = 0.515

Alternative hypothesis: Ha ≠ 0.515

z = -0.257

P value = P(Z<-0.257) = 0.797

Decision; we fail to reject the null hypothesis. That is, the results support the belief that 51.5​% of newborn babies are​ boys

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 90% confidence interval) ---- reject Null hypothesis

Z score < Z(at 90% confidence interval) ------ accept Null hypothesis

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

Null hypothesis: H0: p = 0.515

Alternative hypothesis: Ha ≠ 0.515

Given;

n=850 represent the random sample taken

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 850

po = Null hypothesized value = 0.515

p^ = Observed proportion = 434/850 = 0.5106

Substituting the values we have

z = (0.5106-0.515)/√(0.515(1-0.515)/850)

z = −0.256677

z = −0.257

To determine the p value (test statistic) at 0.10 significance level, using a two tailed hypothesis.

P value = P(Z<-0.257) = 0.797

Since z at 0.10 significance level is between -1.645 and +1.645 and the z score for the test (z = -0.257) which falls with the region bounded by Z at 0.10 significance level. And also the one-tailed hypothesis P-value is 0.797 which is greater than 0.10. Then we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that at 10% significance level the null hypothesis is valid.

5 0
3 years ago
Which number is not a member of the solution set of the inequality 4x ≥ 18
lapo4ka [179]

Answer:

4.4

Step-by-step explanation:

4 (4.4) ≥ 18 does not make sense. 4 x 4.4 = 17.6, which is not more than or equal to 18.

6 0
2 years ago
Read 2 more answers
Select the correct answer.
Umnica [9.8K]
I believe this would be a contingent discount. Contingent discounts are granted to a buyer when they satisfy certain requirements. In this case, the requirement is to have a minimum purchase of $500. Thus, that would make it a contingent discount.
The other's are incorrect.
A membership discount requires you to have a membership. 
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8 0
3 years ago
Read 2 more answers
Which graph shows the solution to the inequality -3x-7&lt;20
Anestetic [448]

Answer:

-9 < x

Step-by-step explanation:

-3x - 7 < 20

+ 7 + 7

___________

-3x < 27

___ ___

-3 -3

x > -9 [Whenever you <em>divide</em><em> </em>or <em>multiply</em><em> </em>by a negative, reverse the inequality symbol.]

The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

6 0
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Jillian measured the distance around a small fish pond as 27 yards. Which would be a good estimate for the distance across the p
Anton [14]
14 because it is half of the width around the pond.
8 0
3 years ago
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