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3 years ago

8

Sean is driving to visit his friend in another state. In the first hour, he travels 1/5 of the total distance. Second hour he tr

avels 34miles. If he has 194 more miles to go, how far apart do the friends live?

1 answer:

astra-53 [7]3 years ago

6 0

Answer:

The friends live 285 miles apart.

Step-by-step explanation:

Let total distance in miles Sean needs to cover to visit his friend be = $x$

On first hour distance traveled in miles is = $\frac{1}{5}\ of\ the\ total\ distance = \frac{1}{5}.(x)=\frac{1}{5}x$

Distance left to cover after first hour = $x-\frac{1}{5}x$

On second hour distance traveled = 34 miles

Distance to still left to be covered = 194 miles

Total distance to be covered after first hour will be = $34\ miles+194\ miles$ = 228 miles

Thus, the equation can be given as:

⇒ $x-\frac{1}{5}x=228$

Multiplying each term with 5 to remove fractions.

⇒ $5x-5.\frac{1}{5}x=5\times228$

⇒ $5x-x=5\times228$

⇒ $4x=1140$

Dividing both sides by 4.

⇒ $\frac{4x}{4}=\frac{1140}{4}$

∴ $x=285$

Thus, the friends live 285 miles apart.

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16. A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours

Reika [66]

Answer:

a) 23.11% probability of making exactly four sales.

b) 1.38% probability of making no sales.

c) 16.78% probability of making exactly two sales.

d) The mean number of sales in the two-hour period is 3.6.

Step-by-step explanation:

For each phone call, there are only two possible outcomes. Either a sale is made, or it is not. The probability of a sale being made in a call is independent from other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours, find:

Six calls per hour, 2 hours. So

$n = 2*6 = 12$

Sale on 30% of these calls, so $p = 0.3$

a. The probability of making exactly four sales.

This is P(X = 4).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{12,4}.(0.3)^{4}.(0.7)^{8} = 0.2311$

23.11% probability of making exactly four sales.

b. The probability of making no sales.

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138$

1.38% probability of making no sales.

c. The probability of making exactly two sales.

This is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678$

16.78% probability of making exactly two sales.

d. The mean number of sales in the two-hour period.

The mean of the binomia distribution is

$E(X) = np$

So

$E(X) = 12*0.3 = 3.6$

The mean number of sales in the two-hour period is 3.6.

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Hello there!

Write a compound inequality for this sentence: 'w' is less than 4 and greater than or equal to -8
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If we were to put this together, it would look like:

$4 \ \textgreater \ w \geq -8$

I hope I helped!

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