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andrew-mc [135]
2 years ago
9

What is the solution of the system? Use any method. 3x + 2y = 7 y = –3x + 11

Mathematics
1 answer:
Gnom [1K]2 years ago
6 0

Answer:

(5,-4)

Step-by-step explanation:

SOLVE BY SUBSTITUTION:

STEP 1: Replace all occurrences of y with -3x+11 in each equation.

-3x+22=7\\y=-3x+11

STEP 2: Solve for x in the first equation.

x=5\\y=-3x+11

STEP 3: Replace all occurrences of x with 5 in each equation.

y=-4\\x=5

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A rectangle is four times as long as it is wide. If its length were diminished by 6 meters and its width were increased by 6 met
valkas [14]

Answer:

Length equals 16 and Width equals 4

Step-by-step explanation:

First let us create an equation. We can use L and W for length and width.

If the length is 4 times the width, then we end up with: L = 4W

It then says, " If its length were diminished by 6 meters and its width were increased by 6 meters, it would be a square."

Since a square has an equal length and width then we end up with:

L - 6 = W + 6

Knowing this we can just substitute the first equation into the second one leaving us with: 4W - 6 = W + 6

We then remove a W from both sides so that the right side is left with a 6, and add 6 to both sides to remove the -6 from the left one.

This leaves us with 3W = 12

W = 4, and if we put that into our first equation, L = 4W, then Length equals 16, and Width equals 4. We can check this by putting it into the 2nd equation. 16 - 6 = 4 + 6.

7 0
1 year ago
On Saturday, Nikki and Tyler walked to the local farmer’s market. Nikki bought 8 apples for $6. Tyler bought 3 fewer apples than
Tems11 [23]

Answer:

$3.75

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
math problme After hearing of the national result that 44% of students engage in binge drinking (5 drinks at a sitting for men,
natali 33 [55]

Answer:

According to the result of the hypothesis test, there is no significant difference between the true population proportion of students who binge drink according to the results of the Professor's survey and the national standard of 0.44.

So, the Professor shouldn't be surprised by this result.

Step-by-step explanation:

- The known standard proportion of students for binge drinking is 44% = 0.44.

- In the Professor's random sample, 96 out of 244 students admitted to binge drinking in the past week.

- So, we need to check if the result of the random sample is in keeping with the known national standard.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that there is no significant difference between the true population proportion of students who binge drink according to the results of the Professor's survey and the national standard of 0.44.

The alternative hypothesis will now be that there is significant difference between the true population proportion of students who binge drink according to the results of the Professor's survey and the national standard of 0.44.

Mathematically,

The null hypothesis is represented as

H₀: p = 0.44

The alternative hypothesis is given as

Hₐ: p ≠ 0.44

To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ)/σₓ

x = sample proportion of the Professor's poll = (96/244) = 0.393

μ = p₀ = the national standard = 0.44

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 244

σₓ = √[0.393×0.607/244] = 0.0313

t = (0.393 - 0.44) ÷ 0.0313

t = -1.50

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 244 - 1 = 243

Significance level = 0.05 (most tests are performed at 5% significance level)

The hypothesis test uses a two-tailed condition because we're testing in the two directions.

p-value (for t = -1.50, at 0.05 significance level, df = 243, with a two tailed condition) = 0.134913

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.134913

0.134913 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there is not enough evidence to conclude that there is a significant difference between the true population proportion of students who binge drink according to the Professor's survey and the national standard.

That is, there is no significant difference between the true population proportion of students who binge drink according to the results of the Professor's survey and the national standard of 0.44.

Hope this Helps!!!

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Answer:

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Step-by-step explanation:

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The answer is H. positive non-linear, because the dots are gradually increasing in height but not in a strait line so its not linear
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