MATHEMATICS COLLEGE

Identify the exponent in the term –3x 2 . A. 3 B. x C. 2 D. minus sign (–)

Answers

Answer 1

Answer:

Answer:

Correct option is:

C. 2

Step-by-step explanation:

We have to find the exponent in the term -3x²

An exponent refers to the number of times a number is multiplied by itself.

Here, x is multiplied to itself 2 times

i.e. $x* x=x^2$

Hence, exponent in the term -3x² is:

So, the correct option is:

C. 2

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Answers in Scientific Notation.

Over the interval [-3, 0[, the local minimum is

Answers

Answer:

-16

Step-by-step explanation:

If f(x) = 2x – 5 and g(x) = x +4, then f(g(2)) =

Answers

Answer:

Step-by-step explanation:

f(g(2))

f(x+4) and you would replace x with two, so you would get

f(2+4) = f(6)

You would then plug in 6 for the x in the f(x) equation:

2(6) - 5 = 12-5 = 7

Some parts of California are particularly earthquake- prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with proba bility (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.] b. Draw the corresponding probability histogram. c. What is the most likely value for X

Answers

Answer:

a. Binomial random variable (n=4, p=0.25)

b. Attached.

c. X=1

Step-by-step explanation:

This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).

a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:

$P(x=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\n\n\nP(x=k) = \dbinom{4}{k} 0.25^(0)\cdot0.75^(4)$

The sample space for X is {0,1,2,3,4}

The associated probabilties are:

$P(x=0) = \dbinom{4}{0} p^(0)(1-p)^(4)=1*1*0.3164=0.3164\n\n\nP(x=1) = \dbinom{4}{1} p^(1)(1-p)^(3)=4*0.25*0.4219=0.4219\n\n\nP(x=2) = \dbinom{4}{2} p^(2)(1-p)^(2)=6*0.0625*0.5625=0.2109\n\n\nP(x=3) = \dbinom{4}{3} p^(3)(1-p)^(1)=4*0.0156*0.75=0.0469\n\n\nP(x=4) = \dbinom{4}{4} p^(4)(1-p)^(0)=1*0.0039*1=0.0039\n\n\n$

b. The histogram is attached.

c. The most likely value for X is the expected value for X (E(X)).

Is calculated as:

$E(X)=np=4\cdot0.25=1$

In a survey of 125 people, it was found that 60 people like chocolate ice cream, 25 people like vanilla ice cream, and 20 people like both chocolate and vanilla ice cream. Create a Venn diagram to represent this data and answer the following questions: a) How many people like only chocolate ice cream? b) How many people like only vanilla ice cream? c) How many people don't like either chocolate or vanilla ice cream? d) How many people like either chocolate ice cream or vanilla ice cream or both?

Answers

To create a Venn diagram for this data, we need to represent the number of people who like chocolate ice cream, vanilla ice cream, and both.

Let's start by drawing two overlapping circles. The left circle represents chocolate ice cream, the right circle represents vanilla ice cream, and the overlapping region represents people who like both.

To find the number of people who like only chocolate ice cream (a), we subtract the number of people who like both from the total number of people who like chocolate ice cream. So, 60 - 20 = 40 people like only chocolate ice cream.

To find the number of people who like only vanilla ice cream (b), we subtract the number of people who like both from the total number of people who like vanilla ice cream. So, 25 - 20 = 5 people like only vanilla ice cream.

To find the number of people who don't like either chocolate or vanilla ice cream (c), we subtract the total number of people who like chocolate or vanilla ice cream from the total number of people surveyed. So, 125 - (60 + 25 - 20) = 60 people don't like either flavor.

To find the number of people who like either chocolate ice cream or vanilla ice cream or both (d), we add the number of people who like only chocolate ice cream, the number of people who like only vanilla ice cream, and the number of people who like both. So, 40 + 5 + 20 = 65 people like either chocolate ice cream or vanilla ice cream or both.

In summary:

a) 40 people like only chocolate ice cream.

b) 5 people like only vanilla ice cream.

c) 60 people don't like either chocolate or vanilla ice cream.

d) 65 people like either chocolate ice cream or vanilla ice cream or both.

Select each polynomial that is a perfect square.Question 5 options:

x2−10x−25

4x2−12x+9

9x2+12x+16

16x2+16x+1

Answers

Answer:

4x^2−12x+9

Step-by-step explanation:

The form of a perfect square trinomial is ...

(a +b)² = a² +2ab +b²

The first and last terms must be positive and perfect squares. The middle term must be twice the product of their roots (possibly with a minus sign).

x^2 -10x -25 . . . . -25 is not a positive perfect square

4x^2 -12x +9 . . . . 12x = 2√(4x^2·9) = 2·6x . . . . perfect square

9x^2 +12x +16 . . . 12x ≠ 2√(9x^2·16) = 2·12x

16x^2 +16x +1 . . . 16x ≠ 2√(16x^2·1) = 2·4x

What is .5 ( 5 repeating) in a fraction ?

Answers

Hey there! I'm happy to help!

Let's say that our fraction is x.

x=0.5555555...

Let's get rid of the repeating stuff. If you multiplied x by 10, the fraction would be equal to 5.5555555.....

x=0.55555555....

10x=5.5555555.....

What if we subtracted the first equation from the second? Then all of the repeating stuff would be gone!

9x=5

We divide both sides by 9.

x=5/9.

Have a wonderful day! :D

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You are on the market for a new car. You want to check whether there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars. You sample 17 domestic car makes and find an average fuel economy of 34.904 MPG with a standard deviation of 4.6729 MPG. For imports, you sample 15 cars and find an average MPG of 28.563 MPG with a standard deviation of 8.4988. Construct a 90% confidence interval for the difference between the true average fuel economies in question. Assume the difference will represent (domestic - import). You can also assume that the standard deviations are statistically the same between the two populations.

What is the answer to the problem?