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3 years ago

Sum of one-half of a number and 4 is -16. find the number

1 answer:

5 0

X is the number
sum means add

sum of half a number and 4 means
(x/2)+4
result is -16

(x/2)+4=-16
minus 4 both sides
x/2=-20
times 2 both sides
x=-40
the number is -40

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The prices of all college textbooks follow a bell-shaped distribution with a mean of $113 and a standard deviation of $12. Using

Soloha48 [4]

Step-by-step explanation:

In statistics, the empirical rule states that for a normally distributed random variable,

68.27% of the data lies within one standard deviation of the mean.

95.45% of the data lies within two standard deviations of the mean.

99.73% of the data lies within three standard deviations of the mean.

In mathematical notation, as shown in the figure below (for a standard normal distribution), the empirical rule is described as

$\Phi(\mu \ - \ \sigma \ \leq X \ \leq \mu \ + \ \sigma) \ = \ 0.6827 \qquad (4 \ \text{s.f.}) \\ \\ \\ \Phi(\mu \ - \ 2\sigma \ \leq X \ \leq \mu \ + \ 2\sigma) \ = \ 0.9545 \qquad (4 \ \text{s.f.}) \\ \\ \\ \Phi}(\mu \ - \ 3\sigma \ \leq X \ \leq \mu \ + \ 3\sigma) \ = \ 0.9973 \qquad (4 \ \text{s.f.})$

where the symbol $\Phi$ (the uppercase greek alphabet phi) is the cumulative density function of the normal distribution, $\mu$ is the mean and $\sigma$ is the standard deviation of the normal distribution defined as $N(\mu, \ \sigma)$ .

According to the empirical rule stated above, the interval that contains the prices of 99.7% of college textbooks for a normal distribution $N(113, \ 12)$ ,

$\Phi(113 \ - \ 3 \ \times \ 12 \ \leq \ X \ \leq \ 113 \ + \ 3 \ \times \ 12) \ = \ 0.9973 \\ \\ \\ \-\hspace{1.75cm} \Phi(113 \ - \ 36 \ \leq \ X \ \leq \ 113 \ + \ 36) \ = \ 0.9973 \\ \\ \\ \-\hspace{3.95cm} \Phi(77 \ \leq \ X \ \leq \ 149) \ = \ 0.9973$

Therefore, the price of 99.7% of college textbooks falls inclusively between $77 and $149.

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2 years ago

A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to re

d1i1m1o1n [39]

An exponential function is :
f ( x ) = a * b^x,
where x is the number of the years.
a = 240 ( number of the birds at start )
16 % = 0.16
b = 1 + 0.16 = 1.16
f ( x ) = 240 * 1.16^x
Answer:
a = 240, b = 1.16

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3 years ago

Read 2 more answers

Which number is irrational?? Help..!

kakasveta [241]

B is the irrational. C & D are rational as they can be written in a ratio, aka a simple fraction. A is rational as it simplifies to +/-2, a whole number.

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Oxana [17]

Answer:

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lara [203]

Answer:

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