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3 years ago

Gordon invested $77,000 into a CD compounded quarterly with an annual interest

Mathematics

1 answer:

erastovalidia [21]3 years ago

3 0

Answer:

$135,150.18

Step-by-step explanation:

We're gonna use the quarterly compound interest formula: P = A(1 + r/4)⁴ⁿ

P = final amount (?)

A = starting amount (77,000)

r = rate (0.063)

n = years (9)

P = 77000(1 + 0.063/4)⁴ ˣ ⁹

P = 77000(1 + 0.063/4)³⁶

P = 77000(1.01575)³⁶

P = 77000(1.7551972)

P = 135,150.1844

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Lee Wine bought pizza from Pizza Hut for her son's party. The owner of the store said it would feed eight. Assuming six children

lidiya [134]

Answer : 2/8 of the pizza would be left of Lee Wine’s pizza.

Solution: 8/8 (1) - 6/8 = 2/8

Hope this helps!!

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3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

kondor19780726 [428]

Answer:

The equation of the regression line is:

$y~=~234.56158 ~-~ 2.95835 \cdot x$

Step-by-step explanation:

The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance.

We have the following data:

$\begin{array}{c|ccccccccc}X&50&55&50&79&44&37&70&45&49\\Y&152&48&22&35&43&171&13&185&25\end{array}$

To find the line of best fit for the points:

Step 1: Find $X\cdot X$ and $X\cdot Y$ as it was done in the table

Step 2: Find the sum of every column:

$\sum{X} = 479 ~,~ \sum{Y} = 694 ~,~ \sum{X \cdot Y} = 32784 ~,~ \sum{X^2} = 26897$

Step 3: Use the following equations to find a and b:

$\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 694 \cdot 26897 - 479 \cdot 32784}{ 9 \cdot 26897 - 479^2} \approx 234.56158 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 9 \cdot 32784 - 479 \cdot 694 }{ 9 \cdot 26897 - \left( 479 \right)^2} \approx -2.95835\end{aligned}$

Step 4: Assemble the equation of a line

$\begin{aligned} y~&=~a ~+~ b \cdot x \\y~=~234.56158 ~-~ 2.95835\cdot x\end{aligned}$

The graph of the regression line is:

5 0

4 years ago

Please help!! <br> Find A

Triss [41]

Answer:

(5/2)√13 ≈ 9.0139

Step-by-step explanation:

The longer hypotenuse is found using the Pythagorean theorem as ...

$\sqrt{8^2+12^2}=\sqrt{208}=4\sqrt{13}$

The right triangles are AA similar, and vertical sides correspond. Their ratio, smaller/larger is 5/8. That means the hypotenuse of the smaller triangle, A, is 5/8 of the hypotenuse of the larger one.

$A=\dfrac{5}{8}\cdot 4\sqrt{13}= \dfrac{5\sqrt{13}}{2}$