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NARA [144]
2 years ago
14

Michelle borrows a total of $2500 in student loans from two lenders. One charges 4.4% simple interest and the other charges

Mathematics
1 answer:
Inessa [10]2 years ago
5 0

The amount borrowed from the  the lender that charges 4.4% interest is $1000.

The amount borrowed from the  the lender that charges 5.7% interest is $1500.

<h3>What are the linear equations that can be derived from the question?</h3>

a + b = $2500 equation 1

0.088a + 0.114b = $246 equation 2

Where:

a = amount borrowed from the lender that charges 4.4% interest

b =  amount borrowed from the lender that charges 5.7% interest

<h3>How much was borrowed from the lender that charges 5.7% interest?</h3>

Multiply equation 1 by 0.114

0.114a + 0.114b = 285 equation 3

Subtract equation 2 from equation 3

39 = 0.026b

b = $1500

<h3>How much was borrowed from the lender that charges 4.4% interest?</h3>

Substitute for b in equation 1

a + $1500 = $2500

a = $2500 - $1500

a = $1000

To learn more about simultaneous equations, please check: brainly.com/question/25875552

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8090 [49]

Answer:

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

3 0
3 years ago
Identify the graph of f(x)=4^x
Wittaler [7]

Answer:

the first one

Step-by-step explanation:

The correct one is the one in the top left corner.


A great website to find out things like this is

https://www.mathpapa.com/algebra-calculator.html


5 0
3 years ago
Helpppppppppppppppppppp pretty please im very desperate
laila [671]

Answer:

the first one is no it's nonproportional

and the second one it yes its proportional

7 0
2 years ago
Read 2 more answers
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