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3 years ago

Please answer with process

Mathematics

1 answer:

laila [671]3 years ago

6 0

$\mathsf{Given : a - b = 5}$

$\mathsf{Squaring\;on\;both\;sides,\;we\;get :}$

$\mathsf{\implies (a - b)^2 = 5^2}$

$\mathsf{\implies a^2 + b^2 - 2(a.b) = 25}$

$\mathsf{Given : a^2 + b^2 = 29}$

$\mathsf{\implies 29 - 2(a.b) = 25}$

$\mathsf{\implies 2(a.b) = 29 - 25}$

$\mathsf{\implies 2(a.b) = 4}$

$\mathsf{\implies (a.b) = 2}$

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Joseph jumped off of a cliff into the ocean in Miami while vacationing with some friends. His height as a function of time is gi

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Step-by-step explanation:

I think the missing equation in your question is: h(t) = -16 $t^{2}$ + 16t + 480

Here is my answer:

As we know that the vertex form of a parabola, y=a $(x-h)^{2}$ + k where(h,k) is the vertex

h(t) = -16 $t^{2}$ + 16t + 480

= -16 ( $t^{2} -t)$ + 480

= -16 $(t-\frac{1}{2}) ^{2}$ + 484

So the vertex is ( $\frac{1}{2}$ , 484)

a. It take for Joseph $\frac{1}{2}$ second to reach his maximum height

b. The highest point that Joseph reached is the vertex of the function, it is 484 ft

c. Joseph hit the water after how many seconds?

<=> h(t) = 0

<=> -16 $t^{2}$ + 16t + 480 = 0

<=> t = $\frac{192}{32}$ second = 6 sec

Hope it will find you well

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3 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

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

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