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2 years ago

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Jessica is selling books during the summer to earn money for college. She earns a commission on each sale but has to pay for her

own expenses.
After a month of driving from neighborhood to neighborhood and walking door-to-door, she figures out that her weekly earnings are approximately a linear function of the number of doors she knocks on.

She writes the equation of the function like this: E(x) = 7x - 25, where x is the number of doors she knocks on during the week and E(x) is her earnings for the week in dollars.

What does the slope of Jessica's function represent?

2 answers:

kap26 [50]2 years ago

7 0

The slope of her function represents the amount she earns per door that she knocks on.

Gelneren [198K]2 years ago

6 0

In other words for every door she knocks on she will make $7

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Part A: Rhett made $250 washing cars with his mobile car wash company. He charges $70 per car and earned $50 in tips. Write an e

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Total Amount made = $250

Amount charged = $70 per car

Tips earned = $50

Equation 1 to represent the above

(Amount charged per car × number of cars) + tips earned = total amount made

Let number of cars = c

Hence,

$70c + $50 = $250

Part B:

Total Amount made = $250

Amount charged = $75 per car

Tips earned = $35

Cost of supplies per car washed = $5

Equation 2:

(Amount charged per car × number of cars) + tips earned - (cost of supplies × number of cars) = total amount made

$75c + $35 - $5c = $250

$70c + $35 = $250

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Find c1 and c2 such that M2+c1M+c2I2=0, where I2 is the identity 2×2 matrix and 0 is the zero matrix of appropriate dimension.

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The question is missing parts. Here is the complete question.

Let M = $\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]$ . Find $c_{1}$ and $c_{2}$ such that $M^{2}+c_{1}M+c_{2}I_{2}=0$ , where $I_{2}$ is the identity 2x2 matrix and 0 is the zero matrix of appropriate dimension.

Answer: $c_{1} = \frac{-16}{10}$

$c_{2}=\frac{-214}{10}$

Step-by-step explanation: Identity matrix is a sqaure matrix that has 1's along the main diagonal and 0 everywhere else. So, a 2x2 identity matrix is:

$\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

$M^{2} = \left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]$

$M^{2}=\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]$

Solving equation:

$\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+c_{1}\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right] +c_{2}\left[\begin{array}{cc}1&0\\0&1\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right]$

Multiplying a matrix and a scalar results in all the terms of the matrix multiplied by the scalar. You can only add matrices of the same dimensions.

So, the equation is:

$\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+\left[\begin{array}{cc}6c_{1}&5c_{1}\\-1c_{1}&-4c_{1}\end{array}\right] +\left[\begin{array}{cc}c_{2}&0\\0&c_{2}\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right]$

And the system of equations is:

$6c_{1}+c_{2} = -31\\-4c_{1}+c_{2} = -15$

There are several methods to solve this system. One of them is to multiply the second equation to -1 and add both equations:

$6c_{1}+c_{2} = -31\\(-1)*-4c_{1}+c_{2} = -15*(-1)$

$6c_{1}+c_{2} = -31\\4c_{1}-c_{2} = 15$

$10c_{1} = -16$

$c_{1} = \frac{-16}{10}$

With $c_{1}$ , substitute in one of the equations and find $c_{2}$ :

$6c_{1}+c_{2}=-31$

$c_{2}=-31-6(\frac{-16}{10} )$

$c_{2}=-31+(\frac{96}{10} )$

$c_{2}=\frac{-310+96}{10}$

$c_{2}=\frac{-214}{10}$

<u>For the equation, </u> $c_{1} = \frac{-16}{10}$ <u> and </u> $c_{2}=\frac{-214}{10}$ <u />

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2 years ago

The Office of Student Services at UNC would like to estimate the proportion of UNC's 34,000 students who are foreign students. I

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Answer:

Mean is 3.05

Standard deviation is 1.69.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they are foreign, or they are not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The probability of x sucesses on n repeated trials, with p probability.

In this problem, we have a sample of 50 students, so $n = 50$ . The proportion of all UNC students that are foreign students is 0.061, so $p = 0.061$ .

The mean is given by the following formula:

$E(X) = np = 50*0.061 = 3.05$

The standard deviation is given by the following formula:

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