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melomori [17]
2 years ago
5

Jennifer opened a savings account with $750. She earned $75 in interest after 2 years. What is the interest rate?

Mathematics
1 answer:
balu736 [363]2 years ago
4 0

Answer:

5%

Step-by-step explanation:

Solving our equation

r = 75 / ( 750 × 2 ) = 0.05

r = 0.05

converting r decimal to a percentage

R = 0.05 * 100 = 5%/year

The interest rate required to

accumulate simple interest of $ 75.00

from a principal of $ 750.00

over 2 years is 5% per year.

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Arm Span(x) Height(y)
natita [175]

Answer:

Here's what I get.

Step-by-step explanation:

1. Representation of data

I used Excel to create a scatterplot of the data, draw the line of best fit, and print the regression equation.

2. Line of best fit

(a) Variables

I chose arm span as the dependent variable (y-axis) and height as the independent variable (x-axis).

It seems to me that arm span depends on your height rather than the other way around.

(b) Regression equation

The calculation is easy but tedious, so I asked Excel to do it.

For the equation y = ax + b, the formulas are

a = \dfrac{\sum y \sum x^{2} - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\b = \dfrac{n\sumx y  - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}

This gave the regression equation:

y = 1.0595x - 4.1524

(c) Interpretation

The line shows how arm span depends on height.

The slope of the line says that arm span increases about 6 % faster than height.

The y-intercept is -4. If your height is zero, your arm length is -4 in (both are impossible).

(d) Residuals

\begin{array}{cccr}&\textbf{Arm Span} & \textbf{Arm Span}&\\\textbf{Height/in} &\textbf{Actual} & \textbf{Predicted}&\textbf{Residual}\\25 & 19 & 22.3 & -3.3\\40 & 41 & 38.2 & 2.8\\55 & 51 & 54.1 & -3.1\\65 & 67 & 62.6 & 4.4\\ \end{array}

The residuals appear to be evenly distributed above and below the predicted values.

A graph of all the residuals confirms this observation.  

The equation usually predicts arm span to within 4 in.

(e) Predictions

(i) Height of person with 66 in arm span

\begin{array}{rcl}y& = & 1.0595x - 4.1524\\66 & = & 1.0595x - 4.1524\\70.1524 & = & 1.0595x\\x & = & \dfrac{70.1524}{1.0595}\\\\& = & \textbf{66 in}\\\end{array}\\\text{A person with an arm span of 66 in  should have a height of about $\large \boxed{\textbf{66 in}}$}

(ii) Arm span of 74 in tall person

\begin{array}{rcl}y& = & 1.0595x - 4.1524\\& = & 1.0595\times74 - 4.1524\\& = & 78.4030 - 4.1524\\& = & \textbf{74 in}\\\end{array}\\\text{ A person who is 74 in tall should have an arm span of $\large \boxed{\textbf{74 in}}$}

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Find a rational and irrational number between 9.5 and 9.7.
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20 = 5(-3 + x)     Multiply 5 into (-3 + x)

20 = -15 + 5x       Add 15 on both sides

35 = 5x         Divide by 5 on both sides to get x by itself

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Step-by-step explanation:

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