Write an expression in expanded form that is equivalent to 3(7d + 4e).

Mathematics

1 answer:

Sergeu [11.5K]3 years ago

8 0

Answer:3*(7*d)+(4e)=3*7d+4e

Step-by-step explanation:

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What is the volume of this cone?

Anna71 [15]

Answer:

1,570 cubic cm

Step-by-step explanation:

Given,

Radius of the cone = 10 cm

Height of the cone = 15 cm

Therefore, volume of the cone

$= \frac{1}{3} \pi {r}^{2} h$

$= \frac{1}{3} \times 3.14 \times 10 \times 10 \times 15$

= 1,570 cubic cm (Ans)

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An article written for a magazine claims that 78% of the magazine's subscribers report eating healthily the previous day. Suppos

Schach [20]

Answer:

89.44% probability that less than 80% of the sample would report eating healthily the previous day

Step-by-step explanation:

We use the binomial approximation 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .