What is the range of the function for the given domain

Mike is driving a boat at 12 mph and is increasing his speed by 0.2 mph each second. Hank is driving a boat at 26.4 mph and is d

VLD [36.1K]

Answer: After 16 seconds the boats will be traveling the same speed.

Step-by-step explanation:

Given: Mike is driving a boat at 12 mph and is increasing his speed by 0.2 mph each second.

Mike's spewed after x seconds = 12 + 0.2x

Hank is driving a boat at 26.4 mph and is decreasing his speed by 0.7 mph each second.

Hank's speed after x seconds = 26.4 -0.7 x

As per given,

12 + 0.2x = 26.4 -0.7 x

Subtract 12 from both sides

0.2x= 26.4-12-0.7x

⇒ 0.2x= 14.4-0.7x

Add 0.7xn on both sides , we get

0.2x+0.7x= 14.4

⇒ 0.9x = 14.4

Multiply 10 on both sides, we get

9x=144

Divide both sides by 9 , we get x= 16

Hence, after 16 seconds the boats will be traveling the same speed.

7 0

3 years ago

For a particular diamond mine, 81% of the diamonds fail to qualify as "gemstone grade". A random sample of 92 diamonds is analyz

Fed [463]

Answer:

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .