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blagie [28]
3 years ago
12

Which system of equations has the same solution as the system below?

Mathematics
1 answer:
zepelin [54]3 years ago
6 0
2x + 2y = 16 ⇒ 2x + 2y = 16
3x -  1y =   4 ⇒ 6x -  2y =   8
                                 8x = 24
                                  8      8
                                   x = 3
                         2x + 2y = 16
                       2(3) + 2y = 16
                           6 + 2y = 16
                         - 6           - 6
                                 2y = 10
                                  2      2
                                   y = 5
                             (x, y) = (3, 5)
The systems of equations that has the same solution as the system is one common solution.
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A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000
Vinil7 [7]

Answer:

The 95% confidence interval for the difference between the proportion of women who drink alcohol and the proportion of men who drink alcohol is (-0.102, -0.014) or (-10.2%, -1.4%).

Step-by-step explanation:

We want to calculate the bounds of a 95% confidence interval of the difference between proportions.

For a 95% CI, the critical value for z is z=1.96.

The sample 1 (women), of size n1=1000 has a proportion of p1=0.494.

p_1=X_1/n_1=494/1000=0.494

The sample 2 (men), of size n2=1000 has a proportion of p2=0.552.

p_2=X_2/n_2=552/1000=0.552

The difference between proportions is (p1-p2)=-0.058.

p_d=p_1-p_2=0.494-0.552=-0.058

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{494+552}{1000+1000}=\dfrac{1046}{2000}=0.523

The estimated standard error of the difference between means is computed using the formula:

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.523*0.477}{1000}+\dfrac{0.523*0.477}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.000249+0.000249}=\sqrt{0.000499}=0.022

Then, the margin of error is:

MOE=z \cdot s_{p1-p2}=1.96\cdot 0.022=0.0438

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.058-0.0438=-0.102\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.058+0.0438=-0.014

The 95% confidence interval for the difference between proportions is (-0.102, -0.014).

7 0
3 years ago
A car has a full tank with 13 and 1/2 gallon of gas .Over the course of two days the amount of gas decreased by 6.25 write and e
aleksklad [387]

Answer: 7.25 gallons

Step-by-step explanation:

Convert 13¹/₂ to a whole number with a decimal:

= 1/2 = 0.5

= 13.5 gallons of gas

If the gas reduces by 6.25 gallons, the amount of gas remaining will be:

= Starting amount - Amount reduced by

= 13.5 - 6.25

= 7.25 gallons

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Answer:

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Step-by-step explanation:

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10 times for thousands equals blank thousand equals blank
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10×4,000=40,000 because all u do is add an extra zero everything you multiple something by ten
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