Is 4286 divisible by 6

Jason earns 20 per game as a referee in youth soccer games. Write an expression to find how much money Jason will earn for refer

prisoha [69]

$20 per n games

When n = 6

20(6) = 120

Jason will earn $120 for refereeing 6 games.

5 0

4 years ago

If the ratio of purple bikes to red bikes is 8 to 12 and there are a total of 100 bikes how many of them are purple

Ulleksa [173]

Answer:

Step-by-step explanation:

Tbh bro u need to use photo math

8 0

4 years ago

at a maximum speed, an airolane travels 1680 miles against the windin 5 hours. Flying with the wind, the plane can travel the sa

Licemer1 [7]

Answer:

Plane Speed (x) = 378 mph

Step-by-step explanation:

Equation

d = r * t

Givens

With the wind

d = 1680 miles
t = 4 hours
r = x + y

Against the wind

d = 1680
t = 5 hours
r = x - y

Equation

The distances are the same, so you can solve for x in terms of y and then deal with the actual distance.

(x + y)*4 = (x - y)*5 Remove the brackets on both sides

Solution

4x + 4y = 5x - 5y Subtract 4x from both sides
4y = -4x + 5x - 5y Combine
4y = x - 5y Add 5y to both sides
5y + 4y = x
x = 9y

Solution part 2

Now take one of the distance formulas and solve for x first then y.

(x - y)*5 = 1680 Substitute 9y for x
(9y - y)*5 = 1680 Subtract on the left
8y * 5 = 1680 Multiply on the left
40y = 1680 Divide by 40
y = 1680/40
y = 42 That's the speed of the wind.

(x - y)*5 = 1680 Substitute the wind speed for y
(x - 42)*5 = 1680 Divide both sides by 5
(x - 42) = 1680 / 5 Do the division on the right
(x - 42) = 336 Add 42 to both sides.
x = 336 + 42
x = 378 mph Plane's speed

7 0

4 years ago

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

What is the common differences or common ratio in the sequence

siniylev [52]

Answer:

Use the formula for Arithmetic only if it is Arithmetic: a1+ (n-1)d

a represents the first number in the sequence, n represents the number, and d represent common difference

Use the formula for geometric sequence: an=a1r the exponent of r to n-1

an represents the nth term you are trying to find, a1 represents the first number, r represents the common ratio, and n-1 is just the nth term minus 1.

Once you figure out if the sequence is arithmetic or geometric you one of those formulas.

8 0

3 years ago