Mr.ward and mr. heskey are racing toy cars and Mr. heskey wants to give mr. ward an 8 ft head start because his car is 2 seconds slower. mr. ward's car travels 4 feet per second and mr. he's key's car travels 6 ft per second.which inequality could be used to determine after how many seconds, 's mr. heskey's car will be head of mr. ward's car?

please show how you got the answer.

Answers

Answer 1

Answer:

Answer:

F. 6s > 4s +8

Step-by-step explanation:

From a reference point at the beginning of the track, Ward's car will be located 4s+8 feet down the track after s seconds. That is, it starts 8 feet down the track, and increases its distance by 4 feet every second.

From the same reference point, Heskey's car will be located 6s feet down the track after s seconds. Its distance starts from zero and is increasing at the rate of 6 feet every second.

For Heskey's distance to exceed Ward's distance you want ...

6s > 4s +8 . . . . . . matches choice F

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You have just received a windfall from an investment you made in a friend's business. He will be paying you $10,000 at the end of this year, $20,000 at the end of the following year, and $30,000 at the end of the year after that (three years from today). The interest rate is 3.5% per year. a.What is the present value of your windfall? b.What is the future value of your windfall in three years (on the date of the last payment)?

Answers

Answer:

a. $55,390.29

b. $61,412.20

Step-by-step explanation:

a. To find the present value of your windfall, each value must be brought back to the present year at a rate of 3.5% per year. The present value is:

$PV = (10,000)/(1.035)+(20,000)/(1.035^2)+(30,000)/(1.035^3)\nPV = \$55,390.29$

The present value of your windfall is $55,390.29.

b. To find the future value of your windfall at the date of the last payment, simply compound the preset value amount obtained on the previous item for three years at a rate of 3.5%:

$FV =55,390.29*(1.035)^3\nFV=\$61,412.20$

The future value of your windfall is $61,412.20.

Final answer:

The present value and future value of an investment are calculated using formulas that account for the interest rate and the period. The present value is calculated by dividing each year's payout by the increment of the interest rate for that year and summing these values. The future value in this scenario would be the sum of the payouts.

Explanation:

This question deals with the financial concepts of present value and future value in relation to an investment payout structure over time.

a. The present value is a measure of the current worth of a future sum of money given a specified rate of return. The formula to calculate present value is PV = CF / (1 + r)^n, where CF is cash flow, r is interest rate and n is the period. To calculate the present value of your windfall:

End of Year 1: PV = $10,000 / (1+0.035)^1
End of Year 2: PV = $20,000 / (1+0.035)^2
End of Year 3: PV = $30,000 / (1+0.035)^3

Add all these present values together to get the total present value.

b. The future value is how much an investment is worth at a certain time in the future. The formula to calculate future value is FV = CF * (1 + r)^n. But in this case since the last cash flow coincides with the period, the future value in three years would simply be the sum of all cash flows which is $60,000 ($10,000+$20,000+$30,000).

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Is (2,3) a solution of y + 1 > 1/2x + 3?

Answers

Answer:

No, it is not.

Step-by-step explanation:

You graph the inequality by finding the boundary line, then shading the appropriate area.

If 2/3x+1/2y=5 what is the value of 4x+3y

Answers

Final answer:

To find the value of 4x + 3y, the given equation can be solved by clearing the fractions and simplifying the expression. The value of 4x + 3y is 30.

Explanation:

To find the value of 4x + 3y, we need to first solve the given equation for either x or y. Let's solve the equation for x:

2/3x + 1/2y = 5

Multiplying both sides of the equation by 6 to clear the fractions gives us:

4x + 3y = 30

Therefore, the value of 4x + 3y is 30.

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Slope=
2.000
2.667

=1.333
x−intercept=
4
30

=
2
15

=7.50000
y−intercept=
−3
30

=
−1
10

=−10.00000

*8. Consider a LTI system with unit impulse response, h(t) = e-3tu(t). Using direct integration technique for finding convolution, find its zero-state response due to an input, x(t) = u(t) (which is called unit step response of the system). Also, from your answer above, write down its response due to an input of the form, x(t) = 2δ(t) – 4u(t). [Hint: Use principle of superposition]