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3 years ago

9

A four-pack of 4242-ounce ink cartridges sells for $85.99$85.99. The expression 42c42c represents the amount of ink in a number

of cartridges. What does the variable cc represent?
A. The amount of ink in a four-pack

B. A number of cartridges

C. The cost of each four-pack

D. A number of four-packs of cartridges

1 answer:

masya89 [10]3 years ago

8 0

The variable cc refers to how much ink is in a certain number of cartridges. If the box says 42cc, that means the amount of ink in those particular cartridges is 42. If a box said 12cc, the amount would be 12. The variable cc just states the amount of ink you can expect from a particular amount of cartridges.

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Nathan brought a pair of boots for $80 and 1 shirt for $20. the sales tax is 5%. how much did Nathan pay for all the items inclu

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3 years ago

Read 2 more answers

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 12

melamori03 [73]

Answer:

98.75% probability that every passenger who shows up can take the flight

Step-by-step explanation:

For each passenger who show up, there are only two possible outcomes. Either they can take the flight, or they do not. The probability of a passenger taking the flight is independent from other passenger. So the binomial probability distribution is used to solve this question.

However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.

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

The probability that a passenger does not show up is 0.10:

This means that the probability of showing up is 1-0.1 = 0.9. So $p = 0.9$

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets

This means that $n = 125$

Using the approximation:

$\mu = E(X) = np = 125*0.9 = 112.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{125*0.9*0.1} = 3.354$

(a) What is the probability that every passenger who shows up can take the flight

This is $P(X \leq 120)$ , so this is the pvalue of Z when X = 120.

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

$Z = \frac{120 - 112.5}{3.354}$

$Z = 2.24$

$Z = 2.24$ has a pvalue of 0.9875

98.75% probability that every passenger who shows up can take the flight

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3 years ago

A pack of cards is numbered 1 to 24. A card is chosen at random. Find the probability that the number on the card is divisible b

serious [3.7K]

Answer:

Step-by-step explanation:

It's simple. So the only cards which are divisible by 2 or 3 are: 2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24. The formula of probability is P= m/n. Where m-Number of ways it can happen and n- Total number of outcomes.

Our answer is P= 16/24=2/3=66,66%

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3 years ago

In a paper bag, 7 of the 15 marbles are yellow. In a cloth bag, 2 of the 15 marbles are yellow. If Tim randomly draws one marble

ddd [48]

Answer :

$\frac{7}{15}$ × $\frac{2}{15}$ = $\frac{14}{225}$

Step-by-step explanation:

P( $Event_{1}$ ) = choosing yellow marble from paper bag = $\frac{favourable outcomes}{possible outcomes}$ = $\frac{7}{15}$

P( $Event_{2}$ ) = choosing yellow marble from cloth bag = $\frac{favourable outcomes}{possible outcomes}$ = $\frac{2}{15}$

∵ Resultant outcome is dependent upon both the events and both events are independent from each other, so we can apply intersection rule [ P(A∩B)=P(A)×P(B) ] here

∴ Probability ( Both marbles are yellow) = P( $Event_{1}$ ) × P( $Event_{2}$ ) = $\frac{7}{15}$ × $\frac{2}{15}$

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3 years ago

Samuel and Christopher go to the movie theater and purchase refreshments for their friends. Samuel spends a total of $34.00 on 6

Llana [10]

Answer:

The system of equations is :

6 p + 4 d = 34

12 p + 7 d = 66.25

The price of a drink is $1.75

Step-by-step explanation:

Assume that the price of one bag of popcorn is $p and the price of a drink is $d

∵ Samuel spends a total of $34 on 6 bags of popcorn and

4 drinks

- Multiply p by 6 and d by 4, then add the products and equate

the sum by 34

∴ 6 p + 4 d = 34 ⇒ (1)

∵ Christopher spends a total of $66.25 on 12 bags of popcorn

and 7 drinks

- Multiply p by 12 and d by 7, then add the products and equate

the sum by 66.25

∴ 12 p + 7 d = 66.25 ⇒ (2)

The system of equations is :

6 p + 4 d = 34

12 p + 7 d = 66.25

Now let us solve it

Multiply equation (1) by -2 to make the coefficients of p in the two equations equal in values and opposite in signs to eliminate it

∵ -12 p - 8 d = - 68 ⇒ (3)

- Add equations (2) and (3)

∴ - d = - 1.75

- Divide both sides by -1

∴ d = 1.75

The price of a drink is $1.75

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3 years ago