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Delicious77 [7]
3 years ago
11

Given a line with equation 3x +7y = 21. write an equation in point-slope form of the line parallel to the given line through the

point (4, -5).
Mathematics
1 answer:
guapka [62]3 years ago
8 0

Answer:

The equation of the line is y = -3/7x - 23/7

Step-by-step explanation:

To start we need to find the slope of the original line. We can do this by solving the equation for y.

3x + 7y = 21

7y = -3x + 21

y = -3/7x + 3

Now we know the slope to be -3/7. Since parallel lines have same slopes, we know the new line also will have a -3/7 slope. We can now use that along with the given point in point-slope form to find the equation.

y - y1 = m(x - x1)

y + 5 = -3/7(x - 4)

y + 5 = -3/7x + 12/7

y = -3/7x - 23/7

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Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a
spin [16.1K]

Answer:

Mean = 68.9

s^2 =18.1 --- Variance

Step-by-step explanation:

Given

\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5

For 59 - 66

x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5

For 67 - 74

x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5

For 75 - 82

x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5

For 83 - 90

x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5

So, the table becomes:

\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}

The mean is then calculated as:

Mean = \frac{\sum fx}{\sum f}

Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}

Mean = \frac{2547.5}{37}

Mean = 68.9 -- approximated

Solving (b): The sample variance:

This is calculated as:

s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}

So, we have:

s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}

s^2 =\frac{652.8}{36}

s^2 =18.1 -- approximated

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3 years ago
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A furnace was originally priced at $907.07 but went on sale for 33% off. If Omar bought the furnace and paid 9% sales tax, how m
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Answer:

662.433221

Step-by-step explanation:

907.07 × 1.09 × 0.67

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2 years ago
Shirley spelled 12 of her 16 spelling words correctly on the test. What percent grade did shirley get on the test
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Answer:

75%

Step-by-step explanation:

percent = part/whole * 100%

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3 years ago
Need help with school
Scorpion4ik [409]

Answer:

x = 7.2m

Step-by-step explanation:

Because it is a right triangle, you can use the Pythagorean theorem:

4^2+6^2 = x^2

16+36 = x^2

52 = x^2

sqrt52 = x

7.2 = x

5 0
3 years ago
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