Annuities
Suppose a fixed investment R is done every fixed number of periods m per year for t years at a constant rate r.
a.
The final value of the investments plus the interest is calculated as follows:
Where:
n = number of total periods of the investment.
n = m*t
The company invests R = $13,000 for t = 10 years at the end of every quarter (3 months), thus m = 4. The interest rate is r = 9% = 0.09.
The interest rate compounds quarterly.
Calculate:
n = 4*10 = 40
i = 0.09 / 4 = 0.0225
Calculating:
FV = $829,220
The company will have $829,220 in scholarship funds
b. The interest can be found by subtracting the final value and the initial value. We have to calculate the latter:
Thus, the interest is:
welcI = $829,220 - $340,516
I = $488,704
The interest is $488,704
Answer:
The 99% confidence interval for the proportion of ASD in Arizona is (0.014, 0.018).
Step-by-step explanation:
The information provided is as follows:
The sample proportion is:
The critical value of <em>z</em> for 99% confidence level is, <em>z</em> = 2.56.
Compute the 99% confidence interval for the proportion of ASD in Arizona as follows:
Thus, the 99% confidence interval for the proportion of ASD in Arizona is (0.014, 0.018).
<h3>
Answer: A) Dashed line, shaded below</h3>
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Explanation:
2x + 4y < 16 solves to y < -0.5x+4 when you isolate y. The inequality sign does not change direction because we divided both sides by a positive value (in this case, 4).
The graph of y < -0.5x+4 will be the same as the graph of 2x+4y < 16
To graph y < -0.5x+4, we graph y = -0.5x+4 which is a straight line that goes through the two points (0,4) and (2, 3). This is the boundary line of the inequality shaded region. The boundary line is a dashed line because we are not including points on the boundary that are part of the solution set. We only include these boundary points if the inequality sign has "or equal to".
We then shade below the dashed boundary line to indicate points below the boundary line. The shading is done downward due to the "less than" sign.
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Perhaps another method to find what direction we shade is we can try out a point like (0,0). The point cannot be on the boundary line.
Plug those coordinates into either equation. I'll pick the second equation
y < -0.5x+4
0 < -0.5*0+4
0 < 0+4
0 < 4
The last inequality is true, so the first inequality is also true when (x,y) = (0,0). Therefore, the point (0,0) is in the shaded region. The point (0,0) is below the boundary line y = -0.5x+4
So this is another way to see that the shaded region is below the boundary line.
The digit in the hundred thousands place is the 2
