$26.53 is what percent of $75.80 ?

Exhibit 15-2A regression model between sales (y in $1000s), unit price (x1 in dollars) and television advertisement (x2 in dolla

Semmy [17]

Answer:

Sales are expected to increase positively.

Step-by-step explanation:

The model is y =7-3*X1+5*X2

Here, y is the depended variable and X1 and X2 are independent variable.

Holding the unit price constant X2 (television advertisement) is increase by $1 dollar

SSR= 3500

SSE=1500

So, TSS = SSR+SSE = (3500+1500) = 5000

Now r^2= 1 - (SSR/TSS) = 1 - (3,500/5,000) = 1 - 0.70 = 0.30

So, the sample correlation coefficient (r) = (0.3)^(1/2) = 0.547

We can conclude that sample correlation indicates a strong positive relationship.

7 0

4 years ago

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

4 years ago

Prove algebraically that 0.5 recurring = 5/9

weeeeeb [17]

Answer:

see explanation

Step-by-step explanation:

We require 2 equations with the recurring part after the decimal point.

Let x = 0.555..... → (1)

Multiply both sides by 10, then

10x = 5.555..... → (2)

Subtract (1) from (2) thus eliminating the recurring decimal

(10x - x) = (5.5555 - 0.5555 ), that is

9x = 5 ( divide both sides by 9 )

x = $\frac{5}{9}$

5 0

3 years ago

if 7 dancers were at a dance and 46 more came in and h left and there was 13 dancers left how many was h

TEA [102]

<span>If 7 dancers were at a dance and 46 more came in and h left and there was 13 dancers left how many was h
</span>- h is 70.

5 0

4 years ago

Use the elimination method to solve the system of equations.2x + 3y = 183x – 3y = 12

weeeeeb [17]

Answer:

The solution would be (6, 2)

Step-by-step explanation:

In order to solve this using elimination, simply add the two equations together.

2x + 3y = 18

3x - 3y = 12

-----------------

5x = 30

x = 6

And now that we have the value for x, we can solve for y.

2x + 3y = 18

2(6) + 3y = 18

12 + 3y = 18

3y = 6

y = 2

7 0

3 years ago

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