MATHEMATICS COLLEGE

Tara is graphing the equation 4x + 2y = 10. Which of these shows the correct equation in slope-intercept form, slope, and y-intercept?

Answers

Answer 1

Answer:

Answer:

y = -2x + 5

slope = -2

y intercept = 5

Step-by-step explanation:

Slope intercept form of equation of line is given by y = mx + c

where m is the slope of line

c is the y intercept i.e point where given line intersect y axis.

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given equation 4x + 2y = 10

we have to re-write this equation in form y = mx + c

4x + 2y = 10

subtraction 4x from LHS and RHS

4x + 2y - 4x= 10 - 4x

2y = 10- 4x

we have to eliminate 2 from y for that we

divide LHS and RHS by 2 we

2y /2 = 10/2- 4x/2

y = 5 - 2x

rearranging it in y = mx+c form

y = -2x + 5

thus, m = -2 , c = 5

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Find the future value (FV) of the annuity due. (Round your answer to the nearest cent.) $175 monthly payment, 7% interest, 11 years

Answers

Answer:

The future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

Consider the provided information:

It is provided that monthly payment is $175, interest is 7% and time is 11 years.

The formula for the future value of the annuity due is:

$FV of Annuity Due = (1+r)* P[((1+r)^(n)-1)/(r)]$

Now, substitute P = 175, r = 0.07 and t = 11 in above formula.

$FV of Annuity Due = (1+0.07)* 175[((1+0.07)^(11)-1)/(0.07)]$

$FV of Annuity Due = (1.07)* 175[(1.10485)/(0.07)]$

$FV of Annuity Due = 187.5(15.7835)$

$FV of Annuity Due = 2955.4789$

Hence, the future value of the annuity due to the nearest cent is $2956.

A sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level. Use the critical -value approach.= 20.5, n = 11 , σ = 7, H0: μ = 18.7; Ha: μ ≠ 18.7, α = 0.01

Answers

Answer:

Z = 0.8528 < 2.576

The calculated value Z = 0.8528 < 2.576 at 0.01 level of significance

Null hypothesis is Accepted at 0.01 level of significance.

There is no significance difference between the means

Step-by-step explanation:

Given data

size of the sample 'n' = 11

mean of the sample x⁻ =20.5

Mean of the Population μ = 18.7

Standard deviation of Population σ = 7

Test statistic

$Z = (x^(-) -mean)/((S.D)/(√(n) ) )$

$Z = (20.5 -18.7)/((7)/(√(11) ) )$

$Z = (1.8)/(2.1105)$

Z = 0.8528

critical Value

$Z_{(\alpha )/(2) } = Z_{(0.01)/(2) } = Z_(0.005) = 2.576$

The calculated value Z = 0.8528 < 2.576 at 0.01 level of significance

Null hypothesis is Accepted at 0.01 level of significance.

There is no significance difference between the means

Answer:Answer:

B. 18.7 ± 9.7

Step-by-step explanation:

A college professor states that this year's entering students appear to be smarter than entering students from previous years. The college's records indicate that the mean IQ for entering students from earlier years. is 110.3. Suppose we want to sample a smaller number of this year's entering students and carry out a hypothesis test to see if the professor statement can be supported. State the null and alternative hypothesis.