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4 years ago

The sum of twice a number and 18 less than the number is the same as the difference between -30 and the number

Mathematics

2 answers:

maksim [4K]4 years ago

6 0

2x + x - 18 = -30 - x

Monica [59]4 years ago

6 0

Lets say the number is x. The formula would be:
2x + x - 18 = x -30
To find x, you have to get rid of everything els, so minus x from both sides.
2x - 18 = -30
Since -30 is the smallest number, you get rid of that next. Add 30 to both sides
2x + 12 = 0
Now get rid of +12 by doing -12.
2x = -12
divide both sides by 2 to get x by itself
x = -6.

To double check your answer, do the reverse. Substitute -6 iinto the equation wherever it says x.

2x + x - 18 = x -30 becomes (2 x -6) + (-6 - 18) = -6 - 30.
Use BIDMAS (Brackets Indices Division Multiplication Addition Subtraction) to get your answer. Brackets are first
-12 + -24 = -6 - 30
-36 = -6 - 30 which is basically -36 = -36

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3 years ago

Which ratio is equivalent to 4 : 28?

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3 years ago

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The ratio of chicken to vegetables in a soup is 2:3. If there are 9 cups of chicken, how many cups of vegetables are in the soup

zlopas [31]

Answer:

13.5

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3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Anettt [7]

Answer:

Choice C: approximately 121 green beans will be 13 centimeters or shorter.

Step-by-step explanation:

What's the probability that a green bean from this sale is shorter than 13 centimeters?

Let the length of a green bean be $X$ centimeters.

$X$ follows a normal distribution with

mean $\mu = 11.2$ and
standard deviation $\sigma = 2.1$ .

In other words,

$X\sim \text{N}(11.2, 2.1^{2})$ ,

and the probability in question is $X \le 13$ .

Z-score table approach:

Find the z-score of this measurement:

$\displaystyle z= \frac{x-\mu}{\sigma} = \frac{13-11.2}{2.1} = 0.857143$ . Closest to 0.86.

Look up the z-score in a table. Keep in mind that entries on a typical z-score table gives the probability of the left tail, which is the chance that $Z$ will be less than or equal to the z-score in question. (In case the question is asking for the probability that $Z$ is greater than the z-score, subtract the value from table from 1.)

$P(X\le 13) = P(Z \le 0.857143) \approx 0.8051$ .

"Technology" Approach

Depending on the manufacturer, the steps generally include:

Locate the cumulative probability function (cdf) for normal distributions.
Enter the lower and upper bound. The lower bound shall be a very negative number such as $-10^{9}$ . For the upper bound, enter $13$
Enter the mean and standard deviation (or variance if required).
Evaluate.

For example, on a Texas Instruments TI-84, evaluating $\text{normalcdf})(-1\text{E}99,\;13,\;11.2,\;2.1 )$ gives $0.804317$ .

As a result,

$P(X\le 13) = 0.804317$ .

Number of green beans that are shorter than 13 centimeters:

Assume that the length of green beans for sale are independent of each other. The probability that each green bean is shorter than 13 centimeters is constant. As a result, the number of green beans out of 150 that are shorter than 13 centimeters follow a binomial distribution.

Number of trials $n$ : 150.
Probability of success $p$ : 0.804317.

Let $Y$ be the number of green beans out of this 150 that are shorter than 13 centimeters. $Y\sim\text{B}(150,0.804317)$ .

The expected value of a binomial random variable is the product of the number of trials and the probability of success on each trial. In other words,

$E(Y) = n\cdot p = 150 \times 0.804317 = 120.648\approx 121$

The expected number of green beans out of this 150 that are shorter than 13 centimeters will thus be approximately 121.

7 0

3 years ago