Translate the sentence into an equation. Use n for the number.

A school employs 30 teachers.how many will there be if there is a 10% reduction

Georgia [21]

Whats the question bro?

8 0

2 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

2 years ago

Consider the vibrating system described by the initial value problem. (A computer algebra system is recommended.) u'' + u = 8 co

krek1111 [17]

Answer:

u(t) = -(3 + w^2 ) cos t /(1- w^2)cos t + 7 sin t + 8 cos wt /(1- w^2)

Step-by-step explanation:

The characteristic equation is k²+1 = 0,⇒k²=−1,⇒ k=±i.

the roots are k = i or -i

the solution has the form u(x)=C₁cosx+C₂sinx.

Using undetermined coefficient method

Uc(t) = Pcos wt + Qsin wt

Uc’(t) = -Pwsin wt + Qwcos wt

Uc’’(t) = -Pw^2cos wt - Qw^2sin wt

U’’ + u = 8cos wt

-Pw^2cos wt - Qw^2sin wt + Pcos wt + Qsin wt = 8cos wt

(-Pw^2 + P) cos wt + (- Qw^2 + Q ) sin wt = 8cos wt

-Pw^2 + P = 8 which implies P= 8 /(1- w^2)

- Qw^2 + Q = 8 which implies Q = 0

Uc(t) = Pcos wt + Qsin wt = 8 cos wt /(1- w^2)

U(t) = uh(t ) + Uc(t)

= C1cos t + c2 sin t + 8 cos wt /(1- w^2)

Initial value problem

U(0) = C1cos(0) + c2 sin (0) + 8 cos (0) /(1- w^2)

C1 + 8 /(1- w^2) = 5

C1 = 5 -8 /(1- w^2) = -(3 + w^2 ) /(1- w^2)

U’(t) = -C1 sin t + c2 cos t - 8 w sin wt /(1- w^2)

U’(0) = -C1 sin (0) + c2 cos (0) - 8 w sin (0) /(1- w^2) = 7

c2 = 7

u(t) = -(3 + w^2 ) cos t /(1- w^2)cos t + 7 sin t + 8 cos wt /(1- w^2)

4 0

2 years ago

Read 2 more answers

Howard has a scale model of the Statue of Liberty. The model is 15 inches tall. The scale of the model to the actual statue is 1

sergiy2304 [10]

Answer:

Required equation $\frac{1}{6.2}=\frac{15}{x}$

The height of statue of liberty is 93 meters.

Step-by-step explanation:

Given : Howard has a scale model of the Statue of Liberty. The model is 15 inches tall. The scale of the model to the actual statue is 1 inch : 6.2 meters.

To find : Which equation can Howard use to determine x, the height in meters, of the Statue of Liberty?

Solution :

The model is 15 inches tall.

The scale of the model to the actual statue is 1 inch : 6.2 meters.

Let x be the height in meters of the Statue of Liberty.

According to question, required equation is

$\frac{1}{6.2}=\frac{15}{x}$

Cross multiply,

$x=15\times 6.2$

$x=93$

Therefore, the height of statue of liberty is 93 meters.

4 0

2 years ago

The Hartman family is saving $400 monthly for Ronald's college education. The family anticipates they will need to

butalik [34]

Answer:

D. The family will likely have enough money. They will have saved $19,200 and have accumulated interest.

Step-by-step explanation:

Got 100% on edge.

3 0

2 years ago