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Nataliya [291]
3 years ago
11

Johnathan and Darius both tutor students part time on the weekends to earn extra money. Johnathan starts tutoring at 9:00am and

earns $80.00 for every 3 hours he tutors. Darius starts at 10:30am and earns $30.00 every hour he tutors.
If they keep on tutoring until Darius has earned the same amount of money as Johnathan, how much will they each earn?

If Darius earned $25.00 for every hour he tutored instead of $20.00 per hour, how would that change the answer to question 3?
Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0
$1,000. lbdgdiha anosksnsbbdjduxbx. frnosmsnwvauainf t
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Consider the simple linear regression model Yi=β0+β1xi+ϵi, where ϵi's are independent N(0,σ2) random variables. Therefore, Yi is
Virty [35]

Answer:

See proof below.

Step-by-step explanation:

If we assume the following linear model:

y = \beta_o + \beta_1 X +\epsilon

And if we have n sets of paired observations (x_i, y_i) , i =1,2,...,n the model can be written like this:

y_i = \beta_o +\beta_1 x_i + \epsilon_i , i =1,2,...,n

And using the least squares procedure gives to us the following least squares estimates b_o for \beta_o and b_1 for \beta_1  :

b_o = \bar y - b_1 \bar x

b_1 = \frac{s_{xy}}{s_xx}

Where:

s_{xy} =\sum_{i=1}^n (x_i -\bar x) (y-\bar y)

s_{xx} =\sum_{i=1}^n (x_i -\bar x)^2

Then \beta_1 is a random variable and the estimated value is b_1. We can express this estimator like this:

b_1 = \sum_{i=1}^n a_i y_i

Where a_i =\frac{(x_i -\bar x)}{s_{xx}} and if we see careful we notice that \sum_{i=1}^n a_i =0 and \sum_{i=1}^n a_i x_i =1

So then when we find the expected value we got:

E(b_1) = \sum_{i=1}^n a_i E(y_i)

E(b_1) = \sum_{i=1}^n a_i (\beta_o +\beta_1 x_i)

E(b_1) = \sum_{i=1}^n a_i \beta_o + \beta_1 a_i x_i

E(b_1) = \beta_1 \sum_{i=1}^n a_i x_i = \beta_1

And as we can see b_1 is an unbiased estimator for \beta_1

In order to find the variance for the estimator b_1 we have this:

Var(b_1) = \sum_{i=1}^n a_i^2 Var(y_i) +\sum_i \sum_{j \neq i} a_i a_j Cov (y_i, y_j)

And we can assume that Cov(y_i,y_j) =0 since the observations are assumed independent, then we have this:

Var (b_1) =\sigma^2 \frac{\sum_{i=1}^n (x_i -\bar x)^2}{s^2_{xx}}

And if we simplify we got:

Var(b_1) = \frac{\sigma^2 s_{xx}}{s^2_{xx}} = \frac{\sigma^2}{s_{xx}}

And with this we complete the proof required.

8 0
4 years ago
A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’
xz_007 [3.2K]

When the ball is in the ground, its height is basically equal to zero thus making our equation,

<span>    -16t^2 + 272t + 1344 = 0</span>

Simplifying the equation will give us,

<span>  - t^2 + 17t + 84 = 0 or t^2 – 17t – 84 = 0</span>

Factoring out the equation will give us,

<span>   (t – 21)(t + 4) = 0</span>

Thus, t = 21 or t = -4. -4 is an extraneous root. Thus, the answer is t = 21.

<span>Answer: 21 seconds</span>

5 0
3 years ago
The _______ is the point where the x axis and y axis intersect <br> HURRY PLEASE
Alex_Xolod [135]

Answer:

the answer is origin

8 0
3 years ago
Read 2 more answers
Please help me out with this please!!
Monica [59]
It will be close to 15 days but don’t take my word for it
5 0
3 years ago
A = b + rb, for r<br> Please help me..
kifflom [539]

Answer:

r=(a/b)-1

Step-by-step explanation:

a=b(1+r)

a/b = 1+r

r=(a/b)-1

6 0
3 years ago
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