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2 years ago

Supoose y varies directly with x. If y=6 when x=-2, find x when y=15

Mathematics

1 answer:

kirill [66]2 years ago

7 0

Answer:

When y = 15, x = -5.

Step-by-step explanation:

"y varies directly with x" signifies the linear relationship y = kx, where k is the constant of proportionality.

Substituting 6 for y and -2 for x into this equation yields the value of k:

6 = k(-2), or k = -6/2, or k = -3

Then the proportional relationship is y = -3x.

If y = 15, then we can write 15 = -3x, or x = -15/3, or x = -5.

When y = 15, x = -5.

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2 years ago

Find the midpoint of the segment with the given endpoints. (-10.2) and (0,-7)

iris [78.8K]

Answer:

$=\left(-5,\:-\frac{5}{2}\right)$

Step-by-step explanation:

$\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(-10,\:2\right),\:\left(x_2,\:y_2\right)=\left(0,\:-7\right)\\\\=\left(\frac{0-10}{2},\:\frac{-7+2}{2}\right)\\\\= (\frac{-10}{2} , \frac{-5}{2})\\ \\=\left(-5,\:-\frac{5}{2}\right)$

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2 years ago

A sample of small bottles and their contents has the following weights (in grams): 4, 2, 5, 4, 5, 2, and 6. What is the sample v

Inessa05 [86]

Answer:

What is the sample variance of bottle weight 2.33

Step-by-step explanation:

First find the mean. The mean of the bottle weight is obtained by taking the ratio of the sum of ages and total number of ages.

Mean = (4+2+5+4+5+2+6) / 7

= 28 / 7

= 4

Sample Variance = $\frac{\left[\begin{array}{ccc}(4-4)^{2} +(2-4)^{2} +\\(5-4)^{2} + (4-4)^{2} +\\(5-4)^{2} + (2-4)^{2} +\\(6-4)^{2}\end{array}\right]}{7-1}$

= $\frac{0+4+1+0+1+4+4}{6}$

= 2.33

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