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lukranit [14]
3 years ago
5

A flute is on sale for $50 more than half of the regular price. if the sale price is $250, what is the regular price of the flut

e
Mathematics
1 answer:
ololo11 [35]3 years ago
3 0
$250-50=200
200/2=100

regular price=$100
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Tina’s age, y, is 5 years more than her brother Tim’s age, x.
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If you are asking for an equation for this statement, it would be y = x + 5
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Write the equation in slope-intercept form for each line based on the information given.
nexus9112 [7]

Answer:

y = -1x + 6 or y = -x + 6

Step-by-step explanation:

First, let's identify what slope-intercept form is.

y = mx + b

m is the slope. b is the y-intercept.

We know the slope is -1, so m = -1. Plug this into our standard equation.

y = -1x + b

To find b, we want to plug in a value that we know is on this line: (2, 4). Plug in the x and y values into the x and y of the standard equation.

4 = -1(2) + b

To find b, multiply the slope and the input of x(2)

4 = -2 + b

Now, add 2 from both sides to isolate b.

6 = b

Plug this into your standard equation.

y = -1x + 6

This is your equation.

Check this by plugging in the point again.

y = -1x + 6

4 = -1(2) + 6

4 = -2 + 6

4 = 4

Your equation is correct.

Hope this helps!

8 0
3 years ago
Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do ho
oksano4ka [1.4K]

Answer:

a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12

c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.

d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.

Step-by-step explanation:

Let the event that a student does homework regularly be H.

The event that a student passes the course be P.

- 60% of her students do homework regularly

P(H) = 60% = 0.60

- 95% of the students who do their homework regularly generally pass the course

P(P|H) = 95% = 0.95

- She also knows that 85% of her students pass the course.

P(P) = 85% = 0.85

a) The probability that a student will do homework regularly and also pass the course = P(H n P)

The conditional probability of A occurring given that B has occurred, P(A|B), is given as

P(A|B) = P(A n B) ÷ P(B)

And we can write that

P(A n B) = P(A|B) × P(B)

Hence,

P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')

From Sets Theory,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

P(H n P) = 0.57 (from (a))

Note also that

P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)

0.60 = P(H n P') + 0.57

P(H n P') = 0.60 - 0.57

Also

P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)

0.85 = P(H' n P) + 0.57

P(H' n P) = 0.85 - 0.57 = 0.28

So,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

Becomes

0.03 + 0.28 + 0.57 + P(H' n P') = 1

P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12

c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.

Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,

P(A n B) = 0.

But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.

Hence, the two events aren't mutually exclusive.

d. Are the events "pass the course" and "do homework regularly" independent? Explain

Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when

P(A|B) = P(A)

P(B|A) = P(B)

P(A n B) = P(A) × P(B)

To check if the events pass the course and do homework regularly are mutually exclusive now.

P(P|H) = 0.95

P(P) = 0.85

P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671

P(H) = 0.60

P(H n P) = P(P n H)

P(P|H) = 0.95 ≠ 0.85 = P(P)

P(H|P) = 0.671 ≠ 0.60 = P(H)

P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)

None of the conditions is satisfied, hence, we can conclude that the two events are not independent.

Hope this Helps!!!

7 0
3 years ago
Kevin makes several cone-shaped candles. He uses a cone mold that has a height of 15 centimeters and a diameter of 10 centimeter
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Answer:

1,177.5cm^3 of candle wax will be required.

Step-by-step explanation:

The attached files contain further information so please check them.

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The answer is 4 degrees.
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