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3 years ago

What is one third of these? 1 3/4 2 1 1/2 2 1/4 1/2

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

5 0

Answer:

1/3

1/4

2/3

1/2

3/4

1/6

Step-by-step explanation:

Simply multiply each number by one-third.

1 * 1/3 = 1/3

3/4 * 1/3 = 3/12 = 1/4

2 * 1/3 = 2/3

1 1/2 = 3/2 * 1/3 - 3/6 = 1/2

2 1/4 = 9/4 * 1/3 = 9/12 = 3/4

1/2 * 1/3 = 1/6

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if you horizontally strech the quadratic parent function, f(x)=x^2, by a factor of 4, what is the equation of the new function?

max2010maxim [7]

Answer:

g(x) = x^2/16

Step-by-step explanation:

To stretch a function horizontally by a factor of k, replace x with x/k.

You want a stretch factor of 4, so your function is ...

g(x) = f(x/4) = (x/4)^2

g(x) = x^2/16

The attached graph shows the horizontal stretch.

8 0

3 years ago

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,

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