If the probability that Caleb makes a free-throw is 60% what is the probability that Kayla makes two free throws in a row?

determine whether the triangles are similar if so what is the similarity statement and the postulate or theorem used.

zmey [24]

The triangles are similar because of the SAS postulate. The sides are proportional and angle T is equal in both.

6 0

3 years ago

Find the GCF of 27x^2 and 45x^3y^2

Inga [223]

Step-by-step explanation:

27x² = 3*3*3*x*x

45x³y² = 3*3*5*x*x*x*y*y

Now

GCF = 3 * 3 *x * x = 9x²

6 0

3 years ago

$3.98 divided by 100x4

Oliga [24]

$0.00995 is the correct answer.

$3.98/400=0.00995

4 0

3 years ago

Read 2 more answers

Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ti

spayn [35]

Answer:

(a) $D(x)=-2,500x+60,000$

(b) $R(x)=60,000x-2500x^2$

(c) x=12

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

$\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500$

Therefore, we have:

$y=-2500x+b$

At point (12,30000)

$30000=-2500(12)+b\\b=30000+30000\\b=60000$

Therefore:

$D(x)=-2,500x+60,000$

(b)Revenue

$R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2$

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

$R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12$

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

$R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0$

Therefore:

Optimal ticket price:$12
Maximum Revenue:$360,000

3 0

3 years ago

There are 30 balls numbered 1-30 in a bag. One is randomly selected 12 times. What is the probability of getting a prime number

Sliva [168]

Answer: The probability of getting a prime number exactly five times = 0.1908

Step-by-step explanation:

Prime numbers from 1 to 30 are 2,3,5,7,11, 13, 17, 19, 23, 29.

The probability of getting a prime number p= $\dfrac{10}{30}=\dfrac13$

Number of trials n = 12

Binomial probability formula:

$P(X=x) = \ ^nC_x p^x(1-p)^{n-x}$

, where x= number of successes

n= number of trials.

x = Number of successes

p= probability of getting one success.

The probability of getting a prime number exactly five times:

$P(X=5)=\ ^{12}C_5(\frac13)^5(1-\frac13)^{7}$

$=\frac{12!}{5!7!}(\frac1{243})(\frac{128}{2187})\\\\=0.1908$

Hence, the probability of getting a prime number exactly five times = 0.1908

4 0

3 years ago

If the probability that Caleb makes a free-throw is 60% what is the probability that Kayla makes two free throws in a row￼?

If the probability that Caleb makes a free-throw is 60% what is the probability that Kayla makes two free throws in a row?