What is the area of the trapezoid shown below??

Find the slope of a line perpendicular to y = 3x + 7.

avanturin [10]

To create the perpendicular of a given slope, you use the negative of the slope's reciprocal.

The negative reciprocal of 3 is -1/3.

Therefore, the new slope would be -1/3.

5 0

4 years ago

Read 2 more answers

What is the volume of the doorstop below?

MArishka [77]

The answer is 27 inches

5 0

3 years ago

Read 2 more answers

What is the solution to this system of linear equations?

sp2606 [1]

The solution to the system of linear equations is (-1,3). Here's how I got my answer step by step using the substitution method.

Step 1: Solve for either x or y in one of the two equations.

y - 4x = 7
+ 4x   + 4x
-----------------------
y = 4x + 7

Step 2: Plug in the value that you got for x or y into the equation that you haven't worked with yet.

2(4x + 7) + 4x = 2
8x + 14 + 4x = 2

12x + 14 = 2
    - 14   - 14
-----------------------
12x = -12
------- -------
12 12

  x = -1

Step 3: Plug in the number you got for y or x into either of the two equations.

y - 4(-1) = 7
y + 4 = 7
- 4    - 4
-------------------
y = 3

The final answer is (-1,3). If you want to check to make sure that this coordinate is a solution to the system of equations, all you have to do is plug in -1 for x and 3 for y into both equations.

Equation 1: y - 4x = 7
Equation 2: 2y + 4x = 2

3 - 4(-1) = 7 2(3) + 4(-1) = 2
3 + 4 = 7 6 - 4 = 2
7 = 7        2 = 2

I hope all of this makes sense to you :)

3 0

3 years ago

Read 2 more answers

The following table summarises the data from a survey on the ownership of iPods among families with different levels of income.

AURORKA [14]

The two nominal variables are related.

The following table summarises the data from a survey on the ownership of iPods among families with different levels of income.

Ownership C1 C2 C3

No 40 32 48

Yes 30 48 52

The first thing to do in order to determine if they are related or not is to state our null and alternative hypothesis

Null hypothesis

$\mathbf{H_o: Two \nomial \ variables \ are \ related}$

Alternative hypothesis

$\mathbf{H_a: Two \nomial \ variables \ are \ not \ related}$

Using the Chi-square test statistics which can be expressed by using the formula

$X ^2 = \sum \dfrac{(O-E)^2}{E}$

Ownership C1 C2 C3 Total

No 40 32 48 120

Yes 30 48 52 130

Total 70 80 100 250

The expected values are calculated as:

$\mathsf{E_{a,b} = \dfrac{(row \ total \times column \ total )}{grand \ total }}$

$\mathsf{E_{1,1} = \dfrac{(70 \times120 )}{250 }}$

$\mathsf{E_{1,1} = 33.6}$

$\mathsf{E_{1,2} = \dfrac{(70 \times130 )}{250 }}$

$\mathsf{E_{1,2} = 36.4}$

$\mathsf{E_{2,1} = \dfrac{(80 \times120 )}{250 }}$

$\mathsf{E_{2,1} = 38.4}$

$\mathsf{E_{2,2} = \dfrac{(80 \times 130 )}{250 }}$

$\mathsf{E_{2,2} = 41.6}$

$\mathsf{E_{3,1} = \dfrac{(100 \times120 )}{250 }}$

$\mathsf{E_{3,1} = 48}$

$\mathsf{E_{3,2} = \dfrac{(70 \times130 )}{250 }}$

$\mathsf{E_{3,2} = 52}$

∴ Using the Chi-square test statistics, we have:

$X ^2 = \sum \dfrac{(O-E)^2}{E}$

$X ^2 = \Bigg( \dfrac{(40-33.6)^2}{33.6}+ \dfrac{(30-36.4)^2}{36.4}+ \dfrac{(32-38.4)^2}{38.4}+ \dfrac{(48-41.6)^2}{41.6} + \dfrac{(48-48)^2}{48}+ \dfrac{(52-52)^2}{52} \Bigg)$

$X ^2 = \Bigg( \dfrac{40.96}{33.6}+ \dfrac{40.96}{36.4}+ \dfrac{40.96}{38.4}+ \dfrac{40.96}{41.6} + \dfrac{0}{48}+ \dfrac{0}{52} \Bigg)$

$X ^2 = \Bigg( 1.2190+ 1.1253+ 1.0667+ 0.9846+0+ 0 \Bigg)$

$\mathbf{X ^2 =4.3956}$

The degree of freedom df = ((r - 1) × (c - 1))

= (3 - 1) (2 -1 )

= 2 × 1

= 2

∴

Assuming the level of significance = 5%

The p-value of the Chi-square test statistics at df of 2 is:

= $\mathbf{P(X^2 > 4.3956) \implies 0.111}$

Therefore, we can conclude that since the p-value (0.111) is greater than the level of significance (0.05), we fail to reject the null hypothesis.

Hence, the two nominal variables are related.

Learn more about Chi-square test statistics here:

brainly.com/question/2365682?referrer=searchResults

7 0

3 years ago

Choose the answer with the correct missing numbers and the correct expression to describe the conversion.

ahrayia [7]

I need points homie but 7 is 7000 8 is 8000 9 is you baby

8 0

3 years ago