A stadium has 64 sections. Each section has 872 seats. which is the total number of seats in the stadium?

Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t i

Lorico [155]

Answer:

Step-by-step explanation:

We are given the position function and need to find the value of t when h<17.

Create an inequality that represents this situation:

$-16t^2+81$ The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.

The simplest way to solve this is to subtract 81 from both sides:

$-16t^2$ then divide both sides by -16:

$t^2>4$ Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is

t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.

6 0

3 years ago

Read 2 more answers

T object]user: what is the slope of a line that passes through (–4,–13) and (19,11)?

Ray Of Light [21]

<span>Slope is difference in "y" divided by difference in "x"
(–4,–13) (19,11)

slope = (-13 -11) / (-4, -19) = -24 / -23

</span>

8 0

3 years ago

100 Points List all congruent angles and write a proportion that relates the corresponding sides

Reil [10]

Answer:

Angle GHF ~ KHJ

Angle GFH ~ KJH

Angle FGH ~ JKH

Where side:

FH ~ JH

FG ~ JK

GH ~ KH

Step-by-step explanation:

6 0

2 years ago

Solve the compound inequality 6b < 42 or 4b + 12 > 8. (1 point)

Nitella [24]

6b<42
b<7
4b+12>8
4b>-4
b>-1
b>-1 or b<7

8 0

3 years ago

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let

vladimir1956 [14]

Answer:

a) P(X ≤ 2) = 0.87

b) P(X ≥ 5) = 0.01

c) P(1 ≤ X ≤ 4) = 0.71

d) P ( X = 0 ) = 0.28

e) σ(X) = 1.09 , E(X) = 1.25

Step-by-step explanation:

Given:

- Let X = the number of defective boards in a random sample of size n = 25, so X ~ Bin(25, 0.05)

Where, n = 25 and p = 0.05

Find:

(a) Determine P(X ≤ 2).(b) Determine P(X ≥ 5).(c) Determine P(1 ≤ X ≤ 4).(d) What is the probability that none of the 25 boards is defective?(e) Calculate the expected value and standard deviation of X.

Solution:

- The probability mass function for a binomial distribution is given by:

P ( X = x ) = nCr * (p)^r * ( 1 - p )^(n-r)

a) P(X ≤ 2):

P(X ≤ 2) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 )

= (0.95)^25 + 25*0.05*0.95^24 + 25C2*0.05^2*0.95^23

= 0.87

b) P(X ≥ 5):

P(X ≥ 5) = 1 - [P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P(X=4)

= 1 - [ 0.87 + 25C3*0.05^3*0.95^22 + 25C4*0.05^4*0.95^21]

= 1 - 0.98994

= 0.01

c) P(1 ≤ X ≤ 4):

P(1 ≤ X ≤ 4) = P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P(X=4)

= ( 0.87 - 0.95^25) + 0.11994

= 0.71

d) P( X = 0 )

P ( X = 0 ) = 0.95^25 = 0.28

e) E(X) & σ(X):

E(X) = n*p

E(X) = 25*0.05 = 1.25

σ(X) = sqrt ( Var (X) )

σ(X) = sqrt ( n*p*(1-p) ) = sqrt ( 25*0.05*0.95 )

σ(X) = 1.09

4 0

3 years ago