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3 years ago

What is the equation of the line that is parallel to y-3x=2 and that passes through (6,1)?

Mathematics

2 answers:

Rudik [331]3 years ago

8 0

Slope-intercept form: y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be parallel, they need to have the same slope.

y - 3x = 2 Add 3x on both sides to change the equation to slope-intercept form

y - 3x + 3x = 2 + 3x

y = 3x + 2 The slope is 3, so the parallel line's slope is also 3.

Now that you know the slope, substitute/plug it into the equation

y = mx + b

y = 3x + b To find "b", plug in the point (6, 1) into the equation, then isolate/get the variable "b" by itself

1 = 3(6) + b

1 = 18 + b Subtract 18 on both sides to get "b" by itself

1 - 18 = 18 - 18 + b

-17 = b

y = 3x - 17 Your answer is the 1st option

Sauron [17]3 years ago

6 0

Answer:

y=3x-17

Step-by-step explanation:

You first get y by its and you do this by adding 3x to both sides of the equal sign. You should then get y=3x+2 and then to find the parallel line, the x should stay the same as the first equation so that takes out the -3x. Then you continue to draw the line down until you get a y-intercept which turns out to be 17. You also know that the y-intercept is going to be negative so that takes out the two 19's.

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Waqas wishes to distribute 128 bananas and also 176 apples equally among a certain number of children. find the highest number o

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Answer:
The maximum number of children = 16

Explanation:
The greatest number of students who can get the fruit in this way (equally) will be equal to the highest common factor between the number of bananas and the number of apples.

Number of bananas = 128 = 2 * 2 * 2 * 2 * 2 * 2 * 2
number of apples = 176 = 2 * 2 * 2 * 2 *11

We can note that:
the highest common factor = 2 * 2 * 2 * 2
the highest common factor = 16

This means that the maximum number of children to get both equally is 16

Hope this helps :)

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3 years ago

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cupoosta [38]

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3 years ago

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2 years ago

A College Alcohol Study has interviewed random samples of students at four-year colleges. In the most recent study, 494 of 1000

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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:

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