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Verizon [17]
2 years ago
8

On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R On a coordinate plane, a line goes thr

ough (negative 4, 0) and (4, negative 4). A point is at (2, 3). What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x + 2y = 4 x + 2y = 8 2x + y = 4 2x + y = 8
Mathematics
2 answers:
Nitella [24]2 years ago
8 0

Answer:

x + 2y = 8.

Step-by-step explanation:

Line goes through (-4, 0) and (4, -4).

The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.

Since we are looking for the equation of the line parallel to that line, the slope will be the same.

We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.

3 = (-1/2) * 2 + b

b - 1 = 3

b = 4.

So, we have y = -1/2x + 4.

1/2x + y = 4

x + 2y = 8.

Hope this helps!

lianna [129]2 years ago
7 0

ANSWEAr

x + 2y = 8

because it is

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Julio takes a multivitamin and a calcium vitamin every day. One at a time, he randomly
RUDIKE [14]

Answer:

21 / 400

Step-by-step explanation:

Given 8 cherry, 5 grape, and 7 orange gummy vitamins out of the multivitamin container.

The probability that Julio will select an orange  multivitamin is

   7 ÷ 8 + 5 + 7 = 7/20

Also, given 11 berry, 3 lemon, and 6 pineapple  gummy vitamins out of the calcium container

The probability that Julio will select a lemon calcium is

3 ÷ 11 + 3 + 6 = 3/20

Therefore, since the event of selecting are independent of each other

probability that Julio will select an orange  multivitamin and a lemon calcium vitamin is

7/20 × 3/20

= 21 / 400

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2 years ago
Caden has an offer to buy an item with a sticker price of $7400 by paying
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Answer:

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Step-by-step explanation:

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A sapling, or young tree, is planted in a garden. After 3 years, it is 180 cm tall. After 7 years, it is 368 cm tall. How tall w
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2 years ago
In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. In the survey,
balandron [24]

Answer:

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}

And for this case the confidence interval is given by: (0.275, 0.305)

We can estimate the proportion difference as:

\hat p_D = \frac{0.275+0.305}{2}=0.29

And the margin of error would be:

ME=0.305-0.29=0.015

So then for this case the possibl two options are:

We are 95% confident that the true difference in proportion of Latinos who view global warming as a serious problem and whites who view global warming as a serious problem is 27.5% to 30.5%.

We are 95% confident that the difference between Latino and white opinions about the severity of global warming is 29% with a margin of error of 1.5%.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p_A represent the real population proportion of Latinos who view global warming as a serious problem

\hat p_A=0.75 represent the estimated proportion Latinos who view global warming as a serious problem

n_A is the sample size required of Latinos who view global warming as a serious problem

p_B represent the real population proportion of white who view global warming as a serious problem

\hat p_B =0.46 represent the estimated proportion  of whitewho view global warming as a serious problem

n_B is the sample size required of white

z represent the critical value for the margin of error  

Solution to the problem

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}

And for this case the confidence interval is given by: (0.275, 0.305)

We can estimate the proportion difference as:

\hat p_D = \frac{0.275+0.305}{2}=0.29

And the margin of error would be:

ME=0.305-0.29=0.015

So then for this case the possibl two options are:

We are 95% confident that the true difference in proportion of Latinos who view global warming as a serious problem and whites who view global warming as a serious problem is 27.5% to 30.5%.

We are 95% confident that the difference between Latino and white opinions about the severity of global warming is 29% with a margin of error of 1.5%.

4 0
2 years ago
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babunello [35]

For this case, the first thing we are going to do is write the generic equation of motion for the vertical axis.

We have then:

h = \frac {1} {2} gt ^ 2 + vo * t + h0

Where,

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  • <em>vo: initial speed </em>
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For the first body:

h1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21

For the second body:

h2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

By the time both bodies have the same height we have:

h1 = h2\\

\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

Rewriting we have:

\frac {8} {12} * t + 21 = - \frac {11} {12} * t + 50

\frac {8} {12} * t + \frac {11} {12} * t = 50 - 21

\frac {19} {12} * t = 29

Clearing time:

t = 29 (\frac {12} {19})\\t = 18.31s

Answer:

 it takes 18.31s for the two window washers to reach the same height

6 0
2 years ago
Read 2 more answers
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