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A 50 kg pitcher throws a baseball with a mass of 0.15 kg. If the ball is thrown with a positive velocity of 35 m/s and there is no net force on the system, what is the velocity of the pitcher? −0.1 m/s −0.2 m/s −0.7 m/s −1.4 m/s

Answers

Answer 1

Answer:

Answer:

The velocity of the pitcher is −0.1 m/s

Step-by-step explanation:

Given : Mass of pitcher = 50 kg

Mass of Baseball= 0.15kg

Velocity of Ball = 35m/s

To Find : velocity of the pitcher

Solution :

The total momentum of the system is conserved when no external force acts on a system .The total initial momentum of the system is equal to the total final momentum of the system.

Since , the ball and the pitcher are initially at rest, therefore, the total initial momentum of the system is zero.

Since we are given that no external forces act on the system , the total final momentum of the system is also equal to zero.

Let us suppose the mass of the pitcher is $m_(p)$

Speed of pitcher = $v_(p)$

The mass of the ball is $m_(b)$

Speed of ball = $v_(b)$

So, the final momentum of the system of pitcher and the ball is given by:

$momentum =m_(p) v_(p) +m_(b) v_(b) =0$

⇒ $50* v_(p) +0.15*35 =0$

⇒ $50* v_(p) +5.25 =0$

⇒ $v_(p) = (-5.25)/(50)$

⇒ $v_(p) = -0.105$

Thus , The velocity of the pitcher is -0.105m/s≈−0.1 m/s

Negative sign shows the opposite direction.

Hence The velocity of the pitcher is −0.1 m/s

Answer 2

Answer:

the answer is -0.1 m/s if you're looking for the Edgnuity answer. I just took the test. Hope this helps!

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A full 1500 liter water tank springs leaks and is losing 2 liters per minutes

Answers

150 minutes is how long the tanks been leaking

Answer:

I guess you have to know when it will be empty

2L 1500L

1min (1500*1)/2=750min=12h30min

in 12h30min the tank will be empty

Step-by-step explanation:

Write the prime factorization of 20 using exponents

Answers

Prime factorization expresses an integer in terms of multiples of prime numbers. The prime factorization of 20 using exponents can be written as 2²×5¹.

What is prime factorization?

Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.

Prime factorization is when all those factors are prime numbers.

Thus, prime factorization expresses an integer in terms of multiples of prime numbers.

The prime factorization of 20 using exponents can be written as,

20 = 1 × 2 × 2 × 5

= 2² × 5¹

Hence, the prime factorization of 20 using exponents can be written as 2²×5¹.

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Here you go

2 to the second power times 5

You are trying to determine if you should accept a shipment of eggs for a local grocery store. About 4% of all cartons which are shipped have had an egg crack while traveling. You are instructed to accept the shipment if no more than 10 cartons out of the 300 you inspect have cracked eggs. What is the probability that you accept the shipment? (In other words, what is the probability that, at the most, you had 16 cartons with cracked eggs?)a. 1012.
b. 3669.
c. 5319.
d. 4681.
e. 5832.
f. 6331.

Answers

Answer:

0.8809

Step-by-step explanation:

Given that:

The population proportion p = 4% = 4/100 = 0.04

Sample mean x = 16

The sample size n = 300

The sample proportion $\hat p =(x)/(n)$

= 16/300

= 0.0533

∴

$P(\hat p \leq 0.0533) = P\bigg ( \frac{\hat p - p}{\sqrt{(P(1-P))/(n)}}\leq\frac{0.0533 - 0.04}{\sqrt{(0.04(1-0.04))/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{(0.04(0.96))/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{(0.0384)/(300)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\frac{0.0133}{\sqrt{1.28 * 10^(-4)}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq(0.0133)/(0.0113)}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq1.18}\bigg )$

From the z tables;

= 0.8809

Let X be the random variation that follows a normal distribution;

Then;

population mean $\mu$ = n × p

population mean $\mu$ = 300 × 0.04

population mean $\mu$ = 12

The standard deviation $\sigma = √(np(1-p))$

The standard deviation $\sigma = √(300 * 0.04(1-0.04))$

The standard deviation $\sigma = √(11.52)$

The standard deviation $\sigma = 3.39$

The z -score can be computed as:

$z = (x - \mu)/(\sigma)$

$z = (16 -12)/(3.39)$

$z = (4)/(3.39)$

z = 1.18

The required probability is:

P(X ≤ 10) = Pr (z ≤ 1.18)

= 0.8809

Laws have been instituted in Florida to help save the manatee. To establish the number of manatees in Florida, manatees were tagged. A new sample was taken later, and among the manatees in the sample, were tagged. Approximate the number of manatees in Florida. brainly

Answers

Answer:

It think this should be the complete question: Laws have been instituted in Florida to help save the manatee.To establish the number of manatees in Florida, 150 manatees were tagged. A new sample was taken later, and among the 40 manatees in the sample, 3 were tagged. Approximate the number of manatees in Florida.

The approximate number of manatees in Florida is 2,000

Step-by-step explanation:

To solve this problem, we will use the formula

N= (C*R)/M

Where N is the toal estimated population

C is the total first capture

R is the total recapture after the first

M is the total tagged from recapture

Thus, we have:

N = (150*40)/3

N = 6000/3

N= 2,000

So, the approximate manatee is $2000$ .

Ratio and Proportion:

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of $a:b$ , then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are the two important concepts, and it is the foundation to understand the various concepts in mathematics as well as in science. the proportion is represented by,

$(a)/(b)=(c)/(d)$ .

Let us assume $x$ represents the unknown observed manatee, which is actually total manatees so the proportion is, $(40)/(3)=(x)/(150)$ .

Now, cross multiplying the given proportion as,

$3x=40* 150\nx=(40* 150)/(3) \nx=2000$

Learn more about the topic Proportion: brainly.com/question/24320792

An insurance company writes policies for a large number of newly-licensed drivers each year. Suppose 40% of these are low-risk drivers, 40% are moderate risk, and 20% are high risk. The company has no way to know which group any individual driver falls in when it writes the policies. None of the low-risk drivers will have an at-fault accident in the next year, but 10% of the moderate-risk and 20% of the high-risk drivers will have such an accident. If a driver has an at-fault accident in the next year, what is the probability that he or she is high-risk

Answers

Answer:

The probability that he or she is high-risk is 0.50

Step-by-step explanation:

P(Low risk) = 40% = 0.40

P( Moderate risk) = 40% = 0.40

P(High risk) = 20% = 0.20

P(At - fault accident | Low risk) = 0% = 0

P(At-fault accident | Moderate risk) = 10% = 0.10

P(At-fault accident | High risk) = 20% = 0.20

If a driver has an at-fault accident in the next year, what is the probability that he or she is high-risk. Hence, We need to calculate P( High risk | at-fault accident) = ?

Using Bayes' conditional probability theorem

P( High risk | at-fault accident) = ( P( High risk) * P(At-fault accident | High risk) ) / { P( Low risk) * P(At-fault accident | Low risk) +P( Moderate risk) * P(At-fault accident | Moderate risk) + P( High risk) * P(At-fault accident | High risk) }

P( High risk | at-fault accident)= (0.20 * 0.20) / ( 0.40 * 0 + 0.40 * 0.10 + 0.20 * 0.20 )

P( High risk | at-fault accident) = 0.04 / 0 + 0.04 + 0.04

P( High risk | at-fault accident) = 0.04 / 0.08

P( High risk | at-fault accident) = 0.50.

Final answer:

The probability that a driver is high-risk given that they had an at-fault accident can be found using Bayes' theorem. Given the probabilities provided in the question, the probability is approximately 0.3333 or 33.33%.

Explanation:

To find the probability that a driver is high-risk given that they had an at-fault accident, we can use Bayes' theorem. Let's define the events:

A: Driver is high-risk
B: Driver has an at-fault accident

We are given the following probabilities:

P(A) = 0.20 (probability of a driver being high-risk)
P(B|A) = 0.20 (probability of an at-fault accident given that they are high-risk)
P(~A) = 0.80 (probability of a driver not being high-risk)
P(B|~A) = 0.10 (probability of an at-fault accident given that they are not high-risk)

Using Bayes' theorem, the probability of a driver being high-risk given that they had an at-fault accident is:

P(A|B) = (P(A) * P(B|A)) / (P(A) * P(B|A) + P(~A) * P(B|~A))

Substituting the given probabilities:

P(A|B) = (0.20 * 0.20) / (0.20 * 0.20 + 0.80 * 0.10) = 0.04 / (0.04 + 0.08) = 0.04 / 0.12 = 0.3333.

Therefore, the probability that a driver is high-risk given that they had an at-fault accident in the next year is approximately 0.3333 or 33.33%.

Learn more about probability here:

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Find an equation of the sphere with center (-3, 2 , 5) and radius 4. What is the intersection of this sphere with the yz-plane.

Answers

Answer:

The equation of the sphere with center (-3, 2 , 5) and radius 4 is $(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

The intersection of the sphere with the yz- plane gave the equation $(y-2)^(2) + (z-5)^(2) = 7$ which is a 2D- circle with center (0,2,5) and radius $√(7)$ .