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balandron [24]
3 years ago
7

A value is in the domain of a function if there is a(n)_____ on the graph at the x-value.

Mathematics
1 answer:
ANEK [815]3 years ago
8 0

Answer:

Point

Step-by-step explanation:

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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
Donny's charge account statement showed a previous balance of $765.98, a finance charge of $7.50, new purchases of $97.50 and $3
nataly862011 [7]
I think the answer is 345.75 

hope this helps
5 0
3 years ago
Read 2 more answers
Pre Algebra
Maslowich

Answer:

A. 36

B. 3.5

Step-by-step explanation:

To solve for the first equation, we could represent the hot dogs as h(1.75-.50), since they are losing .50 cents for each hot dog, <em>h,</em> they make.

Since they want to know how many hot dogs they have to sell to equal the amount of money they spent, we can represent it as an equal sign.

Now all we have to do is add the constants. Add 12 to our overall equation and subtract 57, since the <u>received</u> $12 in donations and <u>lost</u> $57.

Our equation is 12+h1.75=57+.5h We can just put all of the negative numbers on one side and the positive numbers on the other to find out when they will be equal.

First, subtract 12 from 57.

h1.75=45+.5h

Now subtract .5h from both sides.

h1.25=45

Finally, divide both sides by 1.25.

h=36.

They will have to sell 36 hot dogs.

If they want to sell halve the hotdogs for the same price, simply multiply the current price by 2.

The hotdogs will have to cost $3.5.

Hope this helps!

4 0
3 years ago
Ten people at a party decide to compare ages. Five people are 30 years old, three are 32, one is 31, and one is 65.
horrorfan [7]
Given:
Ten People
5 people = 30 years old
3 people = 32 years old
1 person = 31 years old
1 person = 65 years old

We need to arrange the ages in order from least to greatest.

30, 30, 30, 30, 30, 31, 32, 32, 32, 65 
65 is the outlier. 

A.) mean age without the outlier. count of the numbers : 9
5 x 30 =    150
1 x 31 =      31
3 x 32 =<u>      96</u>
total age  277
÷ # of pax<u>    9</u>
mean         30.77 round to the nearest tenth 30.80

b.) Standard deviation:
We need to calculate variance first:
5 pax : 30 - 30.80 = - 0.80 ⇒ -0.80² = 0.64 * 5pax = 3.20
1 pax : 31 - 30.80 =   0.20 ⇒  0.20²  = 0.04 * 1pax = 0.04
3 pax : 32 - 30.80 =   1.20 ⇒  1.20² = 1.44 * 3 pax = 4.32

Variance : (3.20 + 0.04 + 4.32) / 9 pax = 7.56 / 9 = 0.84

Standard deviation is simply the square root of the variance.

Standard deviation = √0.84 = 0.916 

0.916 round to nearest hundredths is 0.92
0.916 round to nearest tenths is 0.90
8 0
3 years ago
Draw a double number line to solve the following problem.
sergeinik [125]
25 minutes
I hope that helped
3 0
3 years ago
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