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olga_2 [115]
3 years ago
7

Y = -x + 4 y = 2x - 8

Mathematics
2 answers:
Y_Kistochka [10]3 years ago
8 0

Answer:

x = 4, y = 0 or (4, 0)

Step-by-step explanation:

<u>Part 1:</u>

2x - 8 = -x + 4

3x - 8 = 4

3x = 12

x = 4

<u>Part 2:</u>

y = -(4) + 4

y = -4 + 4

y = 0

Mrac [35]3 years ago
7 0

Answer:

Step-by-step explanation:

2x - 8 = -x + 4

3x - 8 = 4

3x = 12

x = 4

y = -4+4 = 0

(4,0)

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Suppose we have a population whose proportion of items with the desired attribute is p = 0:5. (a) If a sample of size 200 is tak
crimeas [40]

Answer:

a. If a sample of size 200 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 41.26%.

b. If a sample of size 100 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 30.5%.

Step-by-step explanation:

This problem should be solved with a binomial distribution sample, but as the size of the sample is large, it can be approximated to a normal distribution.

The parameters for the normal distribution will be

\mu=p=0.5\\\\\sigma=\sqrt{p(1-p)/n} =\sqrt{0.5*0.5/200}= 0.0353

We can calculate the z values for x1=0.47 and x2=0.51:

z_1=\frac{x_1-\mu}{\sigma}=\frac{0.47-0.5}{0.0353}=-0.85\\\\z_2=\frac{x_2-\mu}{\sigma}=\frac{0.51-0.5}{0.0353}=0.28

We can now calculate the probabilities:

P(0.47

If a sample of size 200 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 41.26%.

b) If the sample size change, the standard deviation of the normal distribution changes:

\mu=p=0.5\\\\\sigma=\sqrt{p(1-p)/n} =\sqrt{0.5*0.5/100}= 0.05

We can calculate the z values for x1=0.47 and x2=0.51:

z_1=\frac{x_1-\mu}{\sigma}=\frac{0.47-0.5}{0.05}=-0.6\\\\z_2=\frac{x_2-\mu}{\sigma}=\frac{0.51-0.5}{0.05}=0.2

We can now calculate the probabilities:

P(0.47

If a sample of size 100 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 30.5%.

8 0
3 years ago
Find the equation of the line with a slope of 3/4 and passes through (4-2)
Ira Lisetskai [31]

Answer:

y = 3/4x - 5

Step-by-step explanation:

An equation of a line can be written in slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

Let's plug in what we know.

The slope is 3/4.

y = 3/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the point (4, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 3/4(4) + b

To find b, multiply the slope and the input of x(4)

-2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-5 = b

Plug this into your standard equation.

y = 3/4x - 5

This is your equation. It has a slope of 3/4, and passes through (4, -2)

Hope this helps!

5 0
2 years ago
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ELEN [110]

Answer:

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Step-by-step explanation:

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timama [110]

Answer:

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Step-by-step explanation:

We are given that the temperature started at 35°F. The temperature went down 4°F and then up 2°F.

Firstly, the original temperature = 35°F

Now, it is stated that the temperature went down 4°F, this means that the temperature decreases by this amount.

So, the new temperature = 35°F - 4°F = 31°F

Now, the temperature went up by 2°F, this means that the temperature increases by this amount.

So, the final temperature = 31°F + 2°F = 33°F

Now, the final temperature difference relative to the high temperature is given by = 33°F - 35°F = -2°F.

{Here, the maximum temperature is 35°F}

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Answer:

4/42 = 2/21 when simplified down

Step-by-step explanation:

Cancel the common factor: 2

=2/21

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