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Pavel [41]
3 years ago
10

Factor 2pq - 5qr + 10r - 4p.

Mathematics
1 answer:
Tresset [83]3 years ago
5 0
The answer is B) <span>(q - 2)(2p - 5r) 

</span>2pq - 5qr + 10r - 4p = 2pq - 4p - 5qr + 10r
                                 = 2pq - 4p - (5qr - 10r)
                                 = 2p(q - 2) - 5r(q - 2)
                                 = (q - 2)(2p - 5r)
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The National Transportation Safety Board publishes statistics on the number of automobile crashes that people in various age gro
ra1l [238]

Answer:

a) Null hypothesis:p\leq 0.12  

Alternative hypothesis:p > 0.12  

b) z_{\alpha}=1.64

c) z=\frac{0.134 -0.12}{\sqrt{\frac{0.12(1-0.12)}{1000}}}=1.362  

d) p_v =P(z>1.362)=0.0866  

e) For this case since the statistic is lower than the critical value and the p value higher than the significance level we have enough evidence to FAIL to reject the null hypothesis so then we don't have information to conclude that the true proportion is higher than 0.12

Step-by-step explanation:

Information given

n=1000 represent the random sample selected

X=134 represent the number of young drivers ages 18 – 24 that had an accident

\hat p=\frac{134}{1000}=0.134 estimated proportion of young drivers ages 18 – 24 that had an accident

p_o=0.12 is the value that we want to verify

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic

p_v{/tex} represent the p valuePart aWe want to verify if the population proportion of young drivers, ages 18 – 24, having accidents is greater than 12%:  Null hypothesis:[tex]p\leq 0.12  

Alternative hypothesis:p > 0.12  

The statistic would be given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Part b

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the right and we got:

z_{\alpha}=1.64

Part c

For this case the statistic would be given by:

z=\frac{0.134 -0.12}{\sqrt{\frac{0.12(1-0.12)}{1000}}}=1.362  

Part d

The p value can be calculated with the following probability:

p_v =P(z>1.362)=0.0866  

Part e

For this case since the statistic is lower than the critical value and the p value higher than the significance level we have enough evidence to FAIL to reject the null hypothesis so then we don't have information to conclude that the true proportion is higher than 0.12

8 0
3 years ago
Graph XY with endpoints X(5,−2) and Y(3,−3) and its image after a reflection in the x-axis and then a rotation of 270 degrees ab
DerKrebs [107]

Answer:

  X''(2, -5), Y''(3, -3)

Step-by-step explanation:

You know that reflection in the x-axis changes the sign of the y-coordinate. Points that used to be above the axis are now below by the same amount, and vice versa.

Rotation counterclockwise by 270° is the same as clockwise rotation by 90°. That maps the coordinates like this:

  (x, y) ⇒ (y, -x)

The two transformations together give you ...

  (x, y) ⇒ (x, -y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection across y=-x.

Using this mapping, we have ...

  X(5, -2) ⇒ X''(2, -5)

  Y(3, -3) ⇒ Y''(3, -3) . . . . . . on the equivalent line of reflection, so invariant

_____

The attachment shows the original segment in red, the reflected segment in purple, and the rotated segment in blue. The equivalent line of reflection is shown as a dashed green line.

8 0
3 years ago
The area of a rectangular patio is 31 7/8 square meters. The width of the patio is 4 1/4 meters. What is the length? ( in simple
Allushta [10]

Answer:

it is good and people need to do math problems

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she
Sergeeva-Olga [200]
A) .10 d + .25 q = 7.75
B) d + q = 40

Multiplying B) by -.10
B)  -.10d -.10q = -4.0
Then adding this to A)
A) .10 d + .25 q = 7.75
.15q = 3.75

Quarters = 25
Therefore, dimes = 15
***************************************************
Double-Check
A) .10 d + .25 q = 7.75
A) .10 * 15 d + .25 * 25 = 7.75
A) 1.50 + 6.25 = 7.75

Correct!!


6 0
3 years ago
The triangles shown below must be congruent. right awnsers only please.
tankabanditka [31]
It is true. The triangles are congruent.
8 0
3 years ago
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