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3 years ago

The equation 2x^2+12x=4 is written in the form of 2(x-p)^2+q=0. what is the value of q?

Mathematics

1 answer:

hram777 [196]3 years ago

7 0

1) Factor out the coefficient 2: 2x^2+12x=4 => 2(x^2 + 6x) = 4

2) Complete the square of x^2 + 6x: x^2 + 6x + 9 - 9. Then:

2(x^2 + 6x + 9 - 9) = 4

3) Rewrite the square as the square of a binomial:

2( [x+3]^2 - 9) = 4, or

2([x+3]^2) = 22, or

2( [x+3]^2 ) - 22 = 0

The value of q is -22.

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Twelve identical cylindrical pop cans are placed in a box. If sand fills the space between the pop cans and the cans and the sid

Masteriza [31]

Answer:

Step-by-step explanation:

I don't see any information on dimensions of the cans or box, so I'll assume the question wants a general solution.

Three steps will result in the volume of sand required to fill the remaining space in the box.

1. Calculate the volume of a can using the equation for the volume of a cylinder: Vol = πr²h

2. Multiply the can volume by 12. This will give the total volume of the 12 cans in the box.

3. Calculate the volume of the box: Volume = (Base)(Width)(Height)

[Make sure the units are the same as those used in calculating the can volume. E.g., if the can is calculated with cm as the measue, the box dimensions must also be cm]

4. Subtract the volume of the12 cans (from step 2) from the volume of the box.

The result from 4 will be the volume of sand required to fill the box containing 12 cans.

I'm not clear why filling the box with sand is important, but perhaps it will absorb any soda released from cans broken when the heavy box is dropped by the person shocked that 12 cans of pop could be so heavy.

4 0

2 years ago

Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.173, n = 120$ . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

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

$Z = \frac{34 - 20.76}{4.14}$