MATHEMATICS COLLEGE

Algebraic exspression of
15x +8

Answers

Answer 1
Answer:

Answer:

15x-8=0

x=8/15

Step-by-step explanation:

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A group of 12 students is deciding whether to go to the science center or the zoo. Science center tickets are 3 for $36.75 and zoo tickets are 4 for $51.How much will a group of 12 students save by choosing the science center?
Enter your answer in the box.

Answers

The group of 12 students will save$6by visiting the science center instead of the Zoo.

Science center fee :

  • 3 tickets = $36.75

  • Total cost of visiting Science center = (12/3) × 36.75 = $147

Zoo Fee :

  • 4 tickets = $51

  • Total cost of visiting Zoo = (12/4) × 51 = $153

The difference in the total amount spent :

  • Total cost of Zoo - Total cost of Science center

  • $153 - $147 = $6

Therefore, the group will save $6 by visiting the science center.

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ANSWER:

$6

ExPLANATION:

Step 1:

36.75 × 4 = 147

Step 2:

51 × 3 = 153

Step 3:

153 - 147 = 6

Rewrite the expression without using a negative exponent.12x^−4
Simplify your answer as much as possible.

Answers

12x^-4 =
12 * x^-4 =
12 * 1/(x^4) = 
12 / (x^4)
12x^-4
To make the exponent positive you have to bring the term x^-4 down so your answer would be= 12/x^4

Suppose that B1 and B2 are mutually exclusive and complementary events, such that P(B1 ) = .6 and P(B2) = .4. Consider another event A such that P(A | B1) = .2 and P(A | B2) = .5. Find P(A).

Answers

Answer:

So, we get that is P(A)=0.32.

Step-by-step explanation:

We know that:

P(B_1)=0.6\n\nP(B_2)=0.4\n\nP(A|B_1)=0.2\n\nP(A|B_2)=0.5\n

We have the formula for probability:

P(A|B)=(P(A\cap B))/(P(B))\n\n\implies P(A\cap B)=P(A|B)\cdot P(B)

So, we calculate:

P(A\cap B_1)=P(A|B_1)\cdot P(B_1)\n\nP(A\cap B_1)=0.2\cdot 0.6=0.12\n\n\nP(A\cap B_2)=P(A|B_2)\cdot P(B_2)\n\nP(A\cap B_2)=0.5\cdot 0.4=0.2\n

We calculate:

P(A)=P((A\cap B_1)\cup(A\cap B_2))\n\nP(A)=P(A\cap B_1)+P(A\cap B_2)\n\nP(A)=0.12+0.2\n\nP(A)=0.32

So, we get that is P(A)=0.32.

Final answer:

To find P(A), use the law of total probability given that B1 and B2 are mutually exclusive and complementary events. Substituting the provided values, P(A) = 0.32.

Explanation:

The question is asking us to calculate P(A), given the values for P(A | B1) and P(A | B2), and the knowledge that B1 and B2 are mutually exclusive and complementary events. In probability, if events B1 and B2 are mutually exclusive and complementary, this means that one and only one of them can occur, and their occurrence covers all possible outcomes. We can use the law of total probability to find the overall P(A). The law of total probability states that P(A) = P(A | B1) * P(B1) + P(A | B2) * P(B2). Plugging the provided values into this formula, we get P(A) = .2 * .6 + .5 * .4 = .12 + .2 = .32. Therefore, P(A) is .32.

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There are 3 bags each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles. Bag 3 has 45 red and 55 blue marbles. Now a bag is chosen at random and a marble is also picked at random. 1) What is the probability that the marble is blue? 2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each? Make sure to clearly define your probabilistic events and mathematically show how different probability laws and rules that you learned in class could be applied to solve the problems.

Answers

Answer:

0.4 ; 0.6125

Step-by-step explanation:

Given the following :

Bag 1 : 75 red ; 25 blue

Bag 2: 60 red ; 40 blue

Bag 3: 45 red ; 55 blue

Probability = (required outcome / Total possible outcomes)

A) since the probability of choosing each bag is equal :

BAG A:

P(choosing bag A) = 1 / total number of bags = 1/3 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (1/3 × 75/100) = 25/300

BAG B:

P(choosing bag B) = 1/3 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (1/3 × 40/100) = 40/300

BAG C:

P(choosing bag C) = 1/3

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (1/3 × 55/100) = 55/300

= (25/300) × (40/300) × (55/300) = (25 + 40 + 55)/300 = 120/300 = 0.4

2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each?

BAG A:

P(choosing bag A) = 0.5 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (0.5 × 75/100) = (0.5 * 0.75) = 0.375

BAG B:

P(choosing bag B) = (1-0.5) / 2 = 0.25 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (0.25 × 40/100) = (0.25 × 0.4) = 0.1

BAG C:

P(choosing bag C) = (1 - (0.5+0.25)) = 0.25

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (0.25 × 55/100) = 0.25 × 0.55 = 0.1375

= 0.1375 + 0.1 + 0.375 = 0.6125

Please help me with some math im stuck

Answers

y = - 40

- 40 since theres no letters it gonna be -40.

15. In the State of California, there are 25 full-time employees to every 4 part-time employees. If there are 250,000 full-time employees, how many part-time employees are there statewide?

Answers

40,000
I know it's not the mathematical way, but it's the same ratio, so just add the same amount of zeroes.

Final answer:

To find the number of part-time employees in California, set up a proportion and solve for x.

Explanation:

To find the number of part-time employees statewide, we can set up a proportion using the given information. We know that there are 25 full-time employees for every 4 part-time employees. So, we can write the proportion as:

25 full-time employees / 4 part-time employees = 250,000 full-time employees / x part-time employees

Cross-multiplying, we get:

25x = 4 * 250,000

Simplifying, we have:

25x = 1,000,000

Dividing both sides by 25, we find:

x = 40,000

Therefore, there are 40,000 part-time employees statewide in California.

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