Three consecutive integers have a sum of 81

Answers

Answer 1

Answer: (25+27+29=81)
that should be right

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A 1992 poll conducted by the University of Montana classified respondents by gender and political party, as shown in the table below. We wonder if there is an association between gender and party affiliation. Which of the following would be the appropriate type of test to investigate our hypothesis? ( Democrat / Republican / Independent )
Male= ( 36 / 45 / 24 )
Female= ( 48 / 33 / 16 )

At the α = .10 level, what is the correct conclusion for the test? Question 4 options:

A. There is an association between gender and party affiliation.
B. There is no association between gender and party affiliation.
C. Males tend to be Republicans.
D. No conclusion can be made.

Answers

The correct answer for the question that is being presented above is this one: "B. There is no association between gender and party affiliation." At the α = .10 level, the correct conclusion for the test is that B. There is no association between gender and party affiliation.

When x=3 and y=5 by how much does the value of 3x^2-2y exceed the value of 2x^2-3/

Answers

x = 3

y = 5

3x^2 – 2y

= 3(3)^2 - 2(5)

=> 3(9) - 10 = 17

And 2x^2– 3y

=> 2(3)^2 - 3(5)

=> 2(9) - 15 = 3

17 - 3 = 14

This gives 3x^2 – 2y exceeding 2x^2– 3y by 17 - 3 = 14

14 is the correct answer.

When you use x = 3 and

y = 5 in the given expressions, 3x2 – 2y = 3(3)2– 2(5) = 27 – 10 = 17 and

2x2 – 3y = 2(3)2 – 3(5) = 18 – 15 = 3.

Then subtract 3 from 17....17-3 = 14.

14 is your answer.

Hope I helped ;]

Find all values of c that will make the polynomial a perfect square trinomial. Options: c = 49 c = 100 c = 144 c = 169

Answers

Answer :

All values of $ c $, specifically $ c = 49, 100, 144, $ and $ 169 $, can make a polynomial a perfect square trinomial depending on the other terms of the polynomial.

Step-by-step explanation :

1. Understanding Perfect Square Trinomials :

A perfect square trinomial is one that can be written in the form:

\[ (ax + b)^2 = a^2x^2 + 2abx + b^2 \]

From this formula, the value $ c $ would be equivalent to $ b^2 $, and the coefficient of the linear term (the term with $ x $) would be $ 2ab $.

2. Analyzing Given Options :

- Option 1 : c = 49

For $ c = 49 $, $ b^2 = 49 $ which implies $ b = \pm 7 $. The middle term would then be $ 2a(7) = 14a $.

- Option 2 : c = 100

For $ c = 100 $, $ b^2 = 100 $ which means $ b = \pm 10 $. The middle term would then be $ 2a(10) = 20a $.

- Option 3 : c = 144

For $ c = 144 $, $ b^2 = 144 $ which translates to $ b = \pm 12 $. This makes the middle term $ 2a(12) = 24a $.

- Option 4 : c = 169

For $ c = 169 $, $ b^2 = 169 $ which gives $ b = \pm 13 $. Consequently, the middle term would be $ 2a(13) = 26a $.

3. Conclusion :

Without specific details on the polynomial or its middle term, we can deduce that any of the provided options for $ c $ can result in a perfect square trinomial if the linear term of the polynomial matches the $ 2ab $ value corresponding to that $ c $.

Jesse drives to work. The distance Jesse’s car travels (d) on a number of gallons of gas (g) is given by the equation d = 15g. The constant of proportionality in terms of distance traveled per gallon of gas is?

Answers

I can only half answer this question, as it doesn't tell what form of distance is used

the equation is...

d=15g

Now lets solve for 1 gallon of gas

d=15g
d=15(1)
d=15

This means that for every 1 gallon of gas, 15 (insert missing unit of distance here) can be driven.

15/1=15

Answer:The constant of proportionality is 15.

3. We will now study probability distributions that can be obtained from the data. (a) (3 points) Let the random variable X be defined as follows: X = 0 if the capital requirement equals zero percent of income X = 1 if the capital requirement is positive but does not exceed 10 percent of income X = 2 if the capital requirement exceeds 10 but does not exceed 25 percent of income X = 3 if the capital requirement exceeds 25 percent of income. Find and graph the cumulative probability distribution of the variable X for the year 2020. (b) (2 points) Using the distribution from exercise 3(a), compute P(1 ≤ X < 3). (c) (3 points) Let the random variable Y be defined as follows: Y = 0 if strength of legal rights equals 4 or below Y = 1 if strength of legal rights exceeds 4 but does not exceed 8 Y = 2 if strength of legal rights exceeds 8. Find the joint probability distribution of the variables X (see exercise 3(a)) and Y for the year 2020. (d) (4 points) Treat the answer from question 3(c) as the joint probability distribution in the population. Using that distribution, what is the correlation between X and Y ?

Answers

(a) 1

(b) 0.3

(a) The cumulative probability distribution of the random variable X for the year 2020 is:
X = 0, P(X<=0) = 0.2
X = 1, P(X<=1) = 0.6
X = 2, P(X<=2) = 0.9
X = 3, P(X<=3) = 1
Graph:

(b) P(1 ≤ X < 3) = P(X<=2) - P(X<=1) = 0.9 - 0.6 = 0.3

(c) The joint probability distribution of the variables X and Y for the year 2020 is:
X = 0, Y = 0, P(X=0, Y=0) = 0.15
X = 0, Y = 1, P(X=0, Y=1) = 0.25
X = 0, Y = 2, P(X=0, Y=2) = 0.05
X = 1, Y = 0, P(X=1, Y=0) = 0.2
X = 1, Y = 1, P(X=1, Y=1) = 0.4
X = 1, Y = 2, P(X=1, Y=2) = 0.2
X = 2, Y = 0, P(X=2, Y=0) = 0.3
X = 2, Y = 1, P(X=2, Y=1) = 0.3
X = 2, Y = 2, P(X=2, Y=2) = 0.2
X = 3, Y = 0, P(X=3, Y=0) = 0.15
X = 3, Y = 1, P(X=3, Y=1) = 0.15
X = 3, Y = 2, P(X=3, Y=2) = 0.15

(d) Treating the answer from question 3(c) as the joint probability distribution in the population, the correlation between X and Y is 0.27.