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3 years ago

Find the constant of proportionality.

Mathematics

1 answer:

avanturin [10]3 years ago

3 0

Answer as a fraction = 4/3

Answer in decimal form = 1.33 approximately

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Explanation:

x = number of days

y = number of inches

For instance, on day x = 3, we have y = 4 inches of flood water. This is shown by the point (x,y) = (3,4) on the diagonal line.

Divide y over x to get the value of k, which is the constant of proportionality.

k = y/x

k = 4/3

k = 1.33 which is approximate

You could also pick a point like (x,y) = (6,8) to find that

k = y/x

k = 8/6

k = 4/3

k = 1.33

Which is the same as earlier.

We can pick any point on the diagonal line as long as it's not the origin point (0,0).

The equation of this direct variation line is y = (4/3)x. It has a slope of 4/3 and a y intercept of 0. The slope of 4/3 means that each time we move up 4 on the y axis, we move to the right 3 units on the x axis.

In short, slope = rise/run = 4/3. So rise = 4 and run = 3.

For any direct variation linear equation, the slope and constant of proportionality are the same thing.

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Vsevolod [243]

Translation by h (right) and k (up)
g(x)=f(x-h)+k
=f(x-4)^2+2
so h=4, k=2
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3 years ago

Marine scientists categorize signature whistles of bottlenose dolphins by typelong dash—type a, type b, type c, etc. In one s

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Answer:

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Step-by-step explanation:

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$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

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For this problem, we have that:

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95% confidence level

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The lower limit of this interval is:

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The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 + 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.6123$

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

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3 years ago

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umka2103 [35]

to write 98 as a product of its prime factors we have to first find the prime factors of 98

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98 we have to keep dividing it by prime numbers

98 is an even number so we can first divide by 2

98 / 2 = 49

49 is a multiple of 7 which too is a prime number so we can divide 49 by 7

49/7 = 7

7 can be divided again by 1

7/7 = 1

98 is divisible by 2 and 7

so 98 written as a product of prime factors is

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3 years ago

Read 2 more answers

A stereo system is being installed in a room with a rectangular floor measuring 13 feet by 11 feet and a 7-foot ceiling. The st

zhuklara [117]

Answer:

about 22.2 feet

Step-by-step explanation:

The wire can run diagonally across the floor and, from the intersection with the wall, diagonally up the wall. The total length is computed per the hint to be ...

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If the wire were to go up the short wall, its length would be ...

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_____

<em>Comment on the attachment</em>

The red represents the floor; the green represents the long wall.

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3 years ago