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Vickie made a recipe for 144 fluid ounces of scented candle wax. How many 1 cup candle molds can she fill with the recipe?

jeka57 [31]

There are 8 fluid ounces in 1 cup. You can solve this problem using these proportions:

$\frac{8}{1} = \frac{144}{x}$

It states that there are 8 fluid ounces in every 1 cup and 144 fluid ounces in every x cups. We have to solve for x using cross-multiplication:

$8x = 144 \\ x=18$

Vickie can fill 18 1 cup candle molds with 144 fluid ounces of scented candle wax.

6 0

3 years ago

In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arre

Veseljchak [2.6K]

Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

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.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that $p = 0.09$

41 people arrested for DUI in Illinois are selected at random.

This means that $n = 41$

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

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

$P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158$

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ .

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791$

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

$E(X) = np = 41*0.09 = 3.69$

d. What is the standard deviation of the number of repeat offenders?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83$

4 0

3 years ago

Combine like terms. What is a simpler form of the expression? -3(-4y + 3) + 7y

sashaice [31]

19y-9. you distribute -3 into (-4y +3) to get 12y -9 and then you combine like terms so 12y +7y to get 19y and you still have the -9 so the simplest form would be 19y-9

4 0

3 years ago

The minimum monthly payment for adeline's credit card is 2.5% of her balance or $30, whichever is higher. if adeline's balance a

madreJ [45]

$1550x.025= 38.75
Answer: 38.75

6 0

3 years ago

Read 2 more answers

Of the 50 fish that Alan caught from the lake,14 were trout.The estimated population of the lake is 7,500 fish. About how many t

Korolek [52]

Relative frequency = event/sample space
50/14 = 0.28

Expected probability = relative frequency*event
0.28*7500 = 2100
About 2100 trout is expected to be in the lake.

6 0

3 years ago