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2 months ago

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Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16). Wha

t is the y-value of P'?

1 answer:

Svet_ta [12.7K]2 months ago

6 0

The y-coordinate of P' is -10.

Step-by-step explanation:

It is given that triangle PQR has vertices at P(–2, 6), Q(–8, 4), and R(1, –2).

The translation rule is

$(x,y)\to (x-2,y-16)$ To determine the image of point P, referred to as P', we must substitute the coordinates of P(-2,6) to arrive at;

$P(-2,6)\to P'(-2-2,6-16)$

$P(-2,6)\to P'(-4,-10)$

Thus, the y-coordinate of P' is -10.

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Response:

1/6

Detailed explanation:

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2 months ago

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Answer:

$y>\frac{2}{3}x+3$

Step-by-step explanation:

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Calculate the slope of the dashed line

The slope between two points is computed with the formula:

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We consider

(-3,1) and (0,3)

and substitute into it:

$m=\frac{3-1}{0+3}$

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Step 2

Determine the equation of the dashed line in slope-intercept form:

$y=mx+b$

The equation we established is:

$m=\frac{2}{3}$

$b=3$ ---> associated problem

Substituting yields:

$y=\frac{2}{3}x+3$

Step 3

Establish the inequality corresponding to the graph

Given that it is represented by a dashed line, the area to the left of this line is shaded.

Thus,

$y>\frac{2}{3}x+3$

Refer to the attached diagram for enhanced understanding of the problem.

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According to a survey by Bankrate, of adults in the United States save nothing for retirement (CNBC website). Suppose that adult

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Complete Question

The complete question appears in the first uploaded image

Answer:

a) Yes, selecting 15 corresponds to a binomial experiment

b)

c)

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Step-by-step explanation:

Regarding question a:

For an experiment to qualify as binomial

the trials have to be independent

each trial must yield one of two possible outcomes

Given that the selection of 15 individuals is random, we ascertain that the trials are independent and the outcomes are “either the individual saves for retirement or does not save for retirement.”

Therefore, we conclude that the selection of 15 people at random is indeed a binomial experiment.

In question b:

The probability that all selected adults do not save for retirement is mathematically modeled as

$P(r = n) = ^nC_r * p^r * q^{n-r}$

Here C signifies combination

r = 15 implies all selected adults

n refers to the population size equating to 15

From the problem, p = 0.20

and q can be calculated as

=>

=> $q = 1 - p$

Thus

$P(r = 15) = ^{15}C_{15} * p^{15} * q^{15-15}$

$P(r = 15) = 3.2768 *10^{-11}$ Regarding question c:

The probability that exactly five of the selected adults do not save for retirement is mathematically modeled as

$P(r = 5) = ^{15} C_5 * (0.20)^5 * (0.80)^{15}$

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In relation to question d:

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$P(r \ge 1 ) = 1 - P (r = 0 )$

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It is stated that a full-time electrician will put in 40 hours weekly.

Hence, we should determine the total hours he could work in a year, which consists of twelve months.

Thus, a year consists of 365 days.

To find the number of weeks in these twelve months:

Number of weeks = Total days in a year / 7 days of the week

⇒ 365 / 7

⇒ 52.14 (approximately 52 weeks)

It translates to 52 weeks within twelve months.

Out of these 52 weeks, three weeks are designated for vacation.

The total weeks the electrician will work = 52 weeks - 3 weeks

⇒ 49 weeks.

Thus, the electrician worked for 49 weeks.

To find his total worked hours = 49 weeks × 40 hours

⇒ 1960 hours.

So, the total hours the electrician worked amounts to 1960 hours, which corresponds to option b).

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