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3 years ago

Given: f(x) = x - 7 and h(x) = 2x + 3 Write the rule for f(h(x)).

Mathematics

1 answer:

Lena [83]3 years ago

3 0

Answer:

f(h(x))= 2x-4

Step-by-step explanation:

f(h(x))=f(2x+3)=2x+3-7= 2x-4

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Simplify 7x + 2y = -23 Solving 7x + 2y = -23 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 7x + 2y + -2y = -23 + -2y Combine like terms: 2y + -2y = 0 7x + 0 = -23 + -2y 7x = -23 + -2y Divide each side by '7'. x = -3.285714286 + -0.2857142857y Simplifying x = -3.285714286 + -0.2857142857y

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Considering the number of questions incorrect from classmates on a quiz {10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19,

IrinaK [193]

Answer:

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

Step-by-step explanation:

We are given the following data in the question:

10, 11, 12, 13, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{225}{15} = 15$

Sum of squares of differences = 25 + 16 + 9 + 4 + 4+ 4 + 1 + 0+ 1+ 1 + 4 + 9 + 9+ 16 + 25 = 128

$S.D = \sqrt{\dfrac{128}{14}} = 3.02$

Empirical rule:

According to this rule almost all the data lies within three standard deviation of the mean for a normal distribution.
About 68% of data lies within one standard deviation of the mean.
About 95% of data lies within two standard deviations of mean.
Arround 99.7% of data lies within three standard deviation of mean.

Thus, by empirical rule,

$\mu \pm 1\sigma = 15\pm (3.02) = (11.98,18.02)$

According to the Empirical Rule, 68% of the data should fall between 11.98 and 18.02

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