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3 years ago

A father is now twice as old as his son. If the sum of their ages ten years ago was fifty two, how old are they today?

Mathematics

2 answers:

Tresset [83]3 years ago

8 0

Answer:

So the son’s age is 24 and the father’s is 48. Ten years ago, they were 14 and 38, which adds up to 52.

Step-by-step explanation:

If the son’s age is x, the father’s age is 2x.

Ten years ago:

(x - 10) + (2x - 10) = 52

3x + 20 = 52

3x = 72

x = 24

2x = 48

Oliga [24]3 years ago

3 0

Answer:

24 and 48

Today, the son is 24 years old, and the father is 48 years old.

Step-by-step explanation:

(x - 10) + (2x - 10) = 52

3x + 20 = 52

3x = 72

x = 24

The father is 2 times his son's age.

= 2(24)

= 48

So, the son is 24 and the father is 48.

10 years ago, son was 14 and father was 38, if added, this adds up to 52, so we know our calculations are correct.

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According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are goin

UkoKoshka [18]

Answer:

21.77% probability that the proportion who are satisfied with the way that things are going in their life exceeds 0.85

Step-by-step explanation:

Problems of normally distributed samples are 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.

For proportions p in a sample of size n, we have that $\mu = p, \sigma = \sqrt{\frac{p(1 - p)}{n}}$

In this problem:

$\mu = 0.82, \sigma = \sqrt{\frac{0.82*0.18}{100}} = 0.0394$

In a sample of 100 Americans, what is the probability that the proportion who are satisfied with the way that things are going in their life exceeds 0.85

This is 1 subtracted by the pvalue of Z when X = 0.85. So

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

$Z = \frac{0.85 - 0.82}{0.0384}$

$Z = 0.78$

$Z = 0.78$ has a pvalue of 0.7823

1 - 0.7823 = 0.2177

21.77% probability that the proportion who are satisfied with the way that things are going in their life exceeds 0.85

5 0

3 years ago

Simplify the expression 4x(2x2 − 7x + 3).<br> This one is killing me..

Papessa [141]

$Use:\\distributive\ property:a(b+c)=ab+ac\\commutative\ property:a\cdot b=b\cdot a\\assiocative\ property:a\cdot(b\cdot c)=(a\cdot b)\cdot c\\and\ a^n\cdot a^m=a^{n+m}\\-----------------------\\\\4x(2x^2-7x+3)=(4x)(2x^2)+(4x)(-7x)+(4x)(3)\\\\=(4\cdot2)(x^1\cdot x^2)-(4\cdot7)(x^1\cdot x^1)+(4\cdot3)(x)\\\\=8x^{1+2}-28x^{1+1}+12x\\\\=\boxed{8x^3-28x^2+12x}$