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3 years ago

9

What is the equation, in standard form, of a parabola that contains the following points? (-2,18),(0,4),(4,24)

1 answer:

nydimaria [60]3 years ago

6 0

Y=ax² + bx + c and A(-2,18), B(0.4), C(4,24) given

1)Let's determine 1st the value of c in using the pair of B
4= a(0)² + b(0) + c , c=4 and y=ax²+bx+4

2) Use the pair of A: 18 = 4a -2b + 4===> 4a-2b=14

3) Use C pair: 24 = 16a+4b+4 ==> 16a+4b=20

4) solve the system equation in 2) and 3) and you'll find a=2 and b=-3

Hence the equation is y =2x²-3x+4

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8 minutes

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7:18 - 7:10 = 8 minutes

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3 years ago

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kotegsom [21]

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3 years ago

A bicycle company is designing women's bicycle frames The frames can accommodate any woman taller than 54.5 inches. Given that t

mariarad [96]

Using the normal distribution, it is found that 0.13% of American women CANNOT use the bicycles designed by this company.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 65, \sigma = 3.5$

The proportion of women that cannot use the bikes(smaller than 54.5 inches) is the <u>p-value of Z when X = 54.5</u>, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{54.5 - 65}{3.5}$

Z = -3

Z = -3 has a p-value of 0.0013.

0.0013 = 0.13% of American women CANNOT use the bicycles designed by this company.

More can be learned about the normal distribution at brainly.com/question/27850813

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2 years ago