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ivanzaharov [21]

3 years ago

11

HELP FAST!!! Ellen wants to purchase a book that is regularly priced at $18. The book is discounted 15%. She also needs to pay a

6% sales tax on the discounted price.
What is the total amount Ellen will pay for the book?
Enter your answer in the box.

1 answer:

vova2212 [387]3 years ago

5 0

The total amount Ellen paid for the book $16.21
Hope this helps!!

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The probability that a student has a Visa card (event V) is .73. The probability that a student has a MasterCard (event M) is .1

snow_lady [41]

We assumed in this answer that the question b is, Are the events V and M independent?

Answer:

(a). The probability that a student has either a Visa card or a MasterCard is<em> </em> $\\ P(V \cup M) = 0.88$ . (b). The events V and M are not independent.

Step-by-step explanation:

The key factor to solve these questions is to know that:

$\\ P(V \cup M) = P(V) + P(M) - P(V \cap M)$

We already know from the question the following probabilities:

$\\ P(V) = 0.73$

$\\ P(M) = 0.18$

The probability that a student has both cards is 0.03. It means that the events V AND M occur at the same time. So

$\\ P(V \cap M) = 0.03$

The probability that a student has either a Visa card or a MasterCard

We can interpret this probability as $\\ P(V \cup M)$ or the sum of both events; that is, the probability that one event occurs OR the other.

Thus, having all this information, we can conclude that

$\\ P(V \cup M) = P(V) + P(M) - P(V \cap M)$

$\\ P(V \cup M) = 0.73 + 0.18 - 0.03$

$\\ P(V \cup M) = 0.88$

Then, <em>the probability that a student has either a Visa card </em><em>or</em><em> a MasterCard is </em> $\\ P(V \cup M) = 0.88$ .<em> </em>

Are the events V and M independent?

A way to solve this question is by using the concept of <em>conditional probabilities</em>.

In Probability, two events are <em>independent</em> when we conclude that

$\\ P(A|B) = P(A)$ [1]

The general formula for a <em>conditional probability</em> or the probability that event A given (or assuming) the event B is as follows:

$\\ P(A|B) = \frac{P(A \cap B)}{P(B)}$

If we use the previous formula to find conditional probabilities of event M given event V or vice-versa, we can conclude that

$\\ P(M|V) = \frac{P(M \cap V)}{P(V)}$

$\\ P(M|V) = \frac{0.03}{0.73}$

$\\ P(M|V) \approx 0.041$

If M were independent from V (according to [1]), we have

$\\ P(M|V) = P(M) = 0.18$

Which is different from we obtained previously;

That is,

$\\ P(M|V) \approx 0.041$

So, the events V and M are not independent.

We can conclude the same if we calculate the probability

$\\ P(V|M)$ , as follows:

$\\ P(V|M) = \frac{P(V \cap M)}{P(M)}$

$\\ P(V|M) = \frac{0.03}{0.18}$

$\\ P(V|M) = 0.1666.....\approx 0.17$

Which is different from

$\\ P(V|M) = P(V) = 0.73$

In the case that both events <em>were independent</em>.

Notice that

$\\ P(V|M)*P(M) = P(M|V)*P(V) = P(V \cap M) = P(M \cap V)$

$\\ \frac{0.03}{0.18}*0.18 = \frac{0.03}{0.73}*0.73 = 0.03 = 0.03$

$\\ 0.03 = 0.03 = 0.03 = 0.03$

3 0

4 years ago

A business has $15,000 to spend on airline tickets to travel to a conference. It wants 27 of its employees to attend. The busine

marusya05 [52]

Answer:

<u>The correct answer is :</u>

<u>D. 700x + 375y = 15,000 </u>

<u>x + y = 27</u>

Step-by-step explanation:

1. Let's review the information given to answer the question correctly:

Budget for airline tickets = US$ 15,000

Number of employees attending the conference = 27

Price of business-class ticket = US$ 700

Price of economy-class ticket = US$ 375

2. Let's create a system of equations that models how many of each type of ticket the business should purchase.

x = Number of employees flying business-class

y = Number of employees flying economy-class

<u>x + y = 27 (Number of employees attending the conference)</u>

<u>700x + 375y = 15,000 (Cost of employees flying business plus cost of employees flying economy equal to budget for buying the airline tickets) </u>

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3 years ago

Explain solving Slope

xeze [42]

ratio of vertical change between 2 points

5 0

3 years ago

Solve x-1/x-4=x+1/x-2 o all real except 2, 4 0 3 no solution

PSYCHO15rus [73]

Solution

Solve

$\frac{x-1}{x-4}=\frac{x+1}{x-2}$

Step 1: Evaluate and cross multiply

$\begin{gathered} \frac{x-1}{x-4}=\frac{x+1}{x-2} \\ x-1(x-2)=x+1(x-4) \\ x^2-2x-x+2=x^2-4x+x-4 \end{gathered}$

Step 2: Collect like terms

$undefined$

6 0

1 year ago

Help this type of work confuses me

Dmitrij [34]

Answer/Step-by-step explanation:

Given:

-x + 3x + 1 + 4(x + 2) = 54

To solve, first open the bracket by applying the distributive property. Multiply every term you have in the bracket by 4

-x + 3x + 1 + 4x + 8 = 54

Add like terms together

6x + 9 = 54

Subtract 9 from each side

6x = 54 - 9

6x = 45

Divide both sides by 6

x = 45/6

x = 7.5

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3 years ago