The probability that Barry Bonds hits a home run on any given at-bat is 0.16, and each at-bat is independent.

Part A: What is the probability that the next home run will be on his fifth at-bat? (5 points)

Part B: What is the expected number of at-bats until the next home run? (5 points)

Answers

Answer 1

Answer:

a) 0.0797 = 7.97% probability that the next home run will be on his fifth at-bat.

b) The expected number of at-bats until the next home run is 6.25.

Step-by-step explanation:

For each at bat, there are two possible outcomes. Either it is a home run, or it is not. The probability of an at bat resulting in a home run is independent of any other at-bat, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that Barry Bonds hits a home run on any given at-bat is 0.16

This means that [tex]p = 0.16[/tex]

Part A: What is the probability that the next home run will be on his fifth at-bat?

0 on his next 4(P(X = 0) when n = 4)

Home run on his 5th at-bat, with 0.16 probability. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{4,0}.(0.16)^{0}.(0.84)^{4} = 0.49787136 [/tex]

0.49787136 *0.16 = 0.0797.

0.0797 = 7.97% probability that the next home run will be on his fifth at-bat.

Part B: What is the expected number of at-bats until the next home run?

The expected number of trials for n successes is given by:

[tex]E = \frac{n}{p}[/tex]

In this question, [tex]n = 1, p = 0.16[/tex]. So

[tex]E = \frac{1}{0.16} = 6.25[/tex]

The expected number of at-bats until the next home run is 6.25.


Related Questions

HELP PLEASE, Function problem

Answers

Answer:

-2

-1

-2

Step-by-step explanation:

please forgive me, but again, this is the simplest of the simplest things. how is that a problem ?

this costs so much more time to just put it in here and then copy answers than just doing it. this is literally a matter of seconds.

the functional value is -2 for all x that are not equal to 2.

and the functional value is -1, when x = 2

so, what is the problem ?

please see my other answer for more details on the solution.

please help me!!!!!!!!!!!!​

Answers

Step-by-step explanation:

24. = 249030/30

=8,301 rs

Answer:

24. 8301, divide 249030 by 30

25. 9989001, but i dont know the property

Step-by-step explanation:

2) If licorice cost $6.59 a pound, how much would it cost to buy a quarter pound of licoric
(Hint: Convert the mixed fraction to an improper fraction or decimal and multiply by th
quantity required)

Answers

Answer:

$1.65

Step-by-step explanation:

[tex]6.59*.25=1.65[/tex]

or

[tex]6.59*\frac{1}{4} =1.65[/tex]

Find the exact values of the six trigonometric functions at “a” given cos(2a) = - 4/5 and a is
in the 2nd quadrant.

Answers

If a is in the second quadrant, then cos(a) < 0 and sin(a) > 0.

Recall the double angle identity for cosine:

cos(2a) = 2 cos²(a) - 1 = 1 - 2 sin²(a)

It follows that

2 cos²(a) - 1 = -4/5   ==>   cos²(a) = 1/10   ==>   cos(a) = -1/√10

1 - 2 sin²(a) = -4/5   ==>   sin²(a) = 9/10   ==>   sin(a) = 3/√10

Then we find

1/cos(a) = sec(a) = -√10

1/sin(a) = csc(a) = √10/3

sin(a)/cos(a) = tan(a) = -3

1/tan(a) = cot(a) = -1/3

Remember the dataset of alligators which was about the length and weight of several aligators in Florida. The variable X is the length of aligator and the Y variable is the weight of them. A researcher decided to use decision tree and designed two steps: X<4, X>4. What is the name of this method of splitting?A. Multi-way splitting.B. Entropy classification.C. Binary splitting.D. Gini index.

Answers

Answer:

A. multi-way split.

Step-by-step explanation:

Multi way split consists of internal at decision tree branches. Gini index measures probability of impurity in the random variables chosen. Entropy is measure of uncertainty in the sample selected. Binary splitting is used to speed up numerical evaluation.

An alarm clock is slow. It falls behind 4 minutes every 24 hours. If the clock was showing the correct time at 6:00 this morning, how many seconds ahead was the clock at 10:00 last night?

Answers

Answer:

80 Seconds

I dont really want to type the whole thing out, just think about it again, or go to a tutor website, you should be able to get it, you have to use these, multiplication of three numbers, and multiplication and division by factorization of numbers.

Simplify the following expression: (4x2)2 • (3x3)3

Answers

Answer:

432x^13

Step-by-step explanation:

(4x^2)^2 • (3x^3)^3

We know that a^b^c = a^(b*c)

4^2 x^2^2  * 3^3 x^3^3

16 x^4  * 27 x^9

We know that a^b ^ a^c = a^(b+c)

16*27 x^(4+9)

432x^13

Answer:

432x¹³

Step-by-step explanation:

( 4x² ) ² • ( 3x³ ) ²

( 16x²)² • ( 27x³)²

[tex]16 x{}^{2 \times 2} \times 6 {}^{3 \times 3 } \\ 16x {}^{4} \times27 {}^{9} [/tex]

[tex](16 \times 27)x {}^{4 + 9} [/tex]

432x¹³

Test for symmetry and then graph the polar equation.
r=3−5sinθ

Answers

Answer:

Symmetric with respect to the x-axis

Symmetric with respect to the y-axis

Symmetric with respect to the origin

Help with solving this Functions problem

Answers

Answer:

See answers below

Step-by-step explanation:

Given the following functions:

r(x) = x - 6

s(x) = 2x²

r(s(x)) = r(2x²)

Replacing x with 2x² in r(x) will give;

r(2x²) = 2x² - 6

r(s(x)) = 2x² - 6

(r-s)(x) = r(x) - s(x)

(r-s)(x) = x - 6 - 2x²

Rearrange

(r-s)(x) = - 2x²+x-6

(r+s)(x) = r(x) + s(x)

(r-s)(x) = x - 6 + 2x²

Rearrange

(r-s)(x) = 2x²+x-6

PLEASE HELPPP THIS IS DUE ASAPPPP!!!!!!!!!!!!!! WILL GIVE BRAINLIEST

Answers

Answer:

I think the answer is 5/6

Step-by-step explanation:

There are three even numbers and two uneven numbers less than four. Therefore, on a standard die, the.probability of Rollin a number that is even or less than for is 5/6.

Solve the following equation by first writing the equation in the form a x squared = c:
3 a squared minus 21 = 27
A. a = 4
B. a = plus-or-minus 4
C. a = plus-or-minus 16
D. a = 16

Answers

9514 1404 393

Answer:

  B. a = plus-or-minus 4

Step-by-step explanation:

  3a² -21 = 27 . . . . . . . given

  3a² = 48 . . . . . . . . . . add 21 to both sides (desired form)

  a² = 16 . . . . . . . . . . .  divide both sides by 3

  a = ±4 . . . . . . . take the square root

If the total income generated from Gasoline for AER was $408 millions, how much would be the cost for a barrel of gasoline

Answers

Answer:

$20 per gallon

Step-by-step explanation:

Use the figure to find u.

Answers

Answer:

u = 2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj side / hypotenuse

cos 45 = sqrt(2) / u

u cos 45 = sqrt(2)

u = sqrt(2) / cos 45

u = sqrt(2) / 1/ sqrt(2)

u = sqrt(2) * sqrt(2)

u =2

u=2

Answer:

Solution given:

Relationship between base and hypotenuse is given by cos angle.

Cos 45°=base/hypotenuse

[tex]\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{u}[/tex]

doing crisscrossed multiplication

[tex]\sqrt{2}*\sqrt{2}=1*u[/tex]

u=2

A human resources office is working to implement an increase in starting salaries for new
administrative secretaries and faculty at a community college. An administrative secretary
starts at $28,000 and new faculty receive $40,000. The college would like to determine the
percentage increase to allocate to each group, given that the college will be hiring 8
secretaries and 7 faculty in the upcoming academic year. The college has at most $5,000 to
put towards raises. What should the percentage increase be for each group?​

Answers

Answer:

Step-by-step explanation :

Let % increase in administrative secretary be = x

Let % increase in new faculty receive be = y

Administrative secretary salary = 28,000

New faculty receive Salary = 40,000

(8)*(x/100)* (28000) + (7)*(y/100)*(40000) = 5,000

2240x +2800 y = 5,000

224x +280 y = 500

56x +70y = 125

Therefore, x and y should be chosen such that it satisfy the above equation.

Given: Line AC is parallel to DF, Line BE is perpendicular to DF, and angle AEB is congruent to angle CEB, prove angle BAE is congruent to angle BCE. Will give Brainliest if explained thoroughly.

Answers

9514 1404 393

Explanation:

There are several ways you can go at this. Here are a couple. All proofs will start with the given relations being repeated as part of the proof. Here are the next steps.

Angle Sum

∠AED ≅ ∠BAE . . . . alternate interior angles are congruent

∠AED +∠AEB = 90° . . . . angle sum theorem

∠BAE +∠AEB = 90° . . . . substitution property of equality

∠CEF ≅ ∠BCE . . . . alternate interior angles are congruent

∠CEF +∠CEB = 90° . . . . angle sum theorem

∠BCE +∠CEB = 90° . . . . substitution property of equality

∠BAE +∠AEB = ∠BCE +∠CEB . . . . substitution property of equality

∠BAE +∠AEB = ∠BCE +∠AEB . . . . substitution property of equality

∠BAE = ∠BCE . . . . addition property of equality

Congruent Triangles

∠ABE = ∠CBE = 90° . . . . BE ⊥ AC

BE ≅ BE . . . . reflexive property of congruence

ΔBEA ≅ ΔBEC . . . . ASA congruence theorem

∠BAE ≅ ∠BCE . . . . CPCTC

A class contains 18 girls and 14 boys. For all parts of this question, each boy and girl are distinguishable from one another. Answer the following questions:a)In how many ways can a committee of one boy and one girl be chosen

Answers

Answer:

The total number of ways is 252.

Step-by-step explanation:

Number of girls = 18

number of boys = 14

Commitee of one girl and a boy

(18 C 1)(14 C 1)

= 252

Each side of a square is increasing at a rate of 8 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 49 cm2

Answers

Answer:

Step-by-step explanation:

This is nice and simple. I'm going to walk through it like I do when teaching this concept to my class for the first time. This is a good problem for that.

We are given a square and we are looking for the rate at which the area is increasing when a certain set of specifics are given. That means that the main equation for this problem is the area of a square, which is:

[tex]A=s^2[/tex] where s is a side.

Since we are looking for the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], we need to take the derivative of area formula implicitly:

[tex]\frac{dA}{dt}=2s\frac{ds}{dt}[/tex] that means that if [tex]\frac{dA}{dt}[/tex] is our unknown, we need values for everything else. We are given that the initial area for the square is 49. That will help us determine what the "s" in our derivative is. We plug in 49 for A and solve:

[tex]49=s^2[/tex] so

s = 7

We are also given at the start that the sides of this square are increasing at a rate of 8cm/s. That is [tex]\frac{ds}{dt}[/tex]. Filling it all in:

[tex]\frac{dA}{dt}=2(7)(8)[/tex] and

[tex]\frac{dA}{dt}=112\frac{cm^2}{s}[/tex]

The surface area of a square of side L is given by

[tex]A = L^2[/tex]

The rate of change of the area per unit time is

[tex]\dfrac{dA}{dt} = 2L\dfrac{dL}{dt}[/tex]

We can express the length L on the right hand side in terms of the area A [tex](L = \sqrt{A})[/tex]:

[tex]\dfrac{dA}{dt} = 2\sqrt{A}\dfrac{dL}{dt}[/tex]

[tex]\:\:\:\:\:\:\:=2(\sqrt{49\:\text{cm}^2})(8\:\text{cm/s})[/tex]

[tex]\:\:\:\:\:\:\:=112\:\text{cm}^2\text{/s}[/tex]

What is the difference of the two polynomials? (NineX squared plus 8X) minus (twoX squared plus 3X)

Answers

Answer:

[tex]7x {}^{2} + 5x[/tex]

Step-by-step explanation:

[tex]9x {}^{2} + 8x - (2x {}^{2} + 3x) \\ \\ = 9x {}^{2} + 8x - 2x {}^{2} - 3x (remove \: brackets) \\\ \\ = 7x {}^{2} - 5x [/tex]

HELP PLEASE ASAP!!! So for this problem I got the scientific notation however I can not seem to figure out the standard notation. Can someone please help me out here please?

Answers

Answer:

0.000000073

Step-by-step explanation:

Given number is,

7.3E - 8

In scientific notation number will be,

7.3 × 10⁻⁸

In standard form the number will be,

0.000000073

What is 23– 48? Need awnser now

Answers

The answer is -25. Hope this helps!!

Help

The table shows the results of a survey of students in two math classes.
Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Be sure to show and explain your work.

Did You Watch More Than One Hour of TV Last Night?

Answers

Answer:

0.6

Step-by-step explanation:

In this question, the | symbol means "given", so we can phrase the question as "Find the probability that a student watches more than one hour of TV given that they are in the 6th period class"

Next, because there is a 100% chance that the student is in the 6th period class, we can disregard the results of the 3rd period class.

Given that the student is in the 6th period class, there are 15 total students (as 9+6=15 = the sum of the yes and no answers for 6th period) and 9 students that said yes. Therefore, there is a 9/15 = 3/5 = 0.6 probability that a student watches more than 1 hour of TV given that they are in the 6th period class

for every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If each of 35 people bought a $9.75 ticket, how many people bought the more expensive ticket?

Answers

Answer:

21

Step-by-step explanation:

5/3=35/x

3 x 35=105

5 x x= 5x

105=5x

105/5=5x/5

21=x

The number of people who bought the more expensive ticket is 21.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

For every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If every 35 people bought a $9.75 ticket,

Let the number of people be X so we can form the following expression given below:-

5/3=35/x

3 x 35=105

5 x x= 5x

105=5x

105/5=5x/5

21=x

Therefore the number of people who bought the more expensive ticket is 21.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ2

Let $f$ be a linear function for which $f(6)-f(2)=12$. What is $f(12)-f(2)?$ Please explain how you found your answer. Thank you!

Answers

Answer:   30

========================================================

Explanation:

Since f(x) is linear, this means f(x) = mx+b

m = slopeb = y intercept

Let's plug in x = 6

[tex]f(x) = mx+b\\f(6) = m*6+b\\f(6) = 6m+b[/tex]

Repeat for x = 2

[tex]f(x) = mx+b\\f(2) = m*2+b\\f(2) = 2m+b[/tex]

Now subtract the two function outputs

[tex]f(6)-f(2) = (6m+b)-(2m+b)\\f(6)-f(2) = 6m+b-2m-b\\f(6)-f(2) = 4m\\[/tex]

The b terms cancel out which is very handy.

Set this equal to 12, since f(6)-f(2) = 12, and solve for m

[tex]f(6)-f(2) = 12\\4m = 12\\m = 12/4\\m = 3\\[/tex]

So the slope of f(x) is m = 3

-------------------------------------------------------------------------

Next, plug in x = 12

[tex]f(x) = mx+b\\f(12) = m*12+b\\f(12) = 12m+b[/tex]

We can then say:

[tex]f(12)-f(2) = (12m+b)-(2m+b)\\f(12)-f(2) = 12m+b-2m-b\\f(12)-f(2) = 10m\\[/tex]

Lastly, we plug in m = 3

[tex]f(12)-f(2) = 10m\\f(12)-f(2) = 10*3\\f(12)-f(2) = 30\\[/tex]

Please help 20 points an will give Brainiest to who ever is right

Answers

It’s number B I feel like it’s the correct one

Answer:

horizontal expansion factor of 2

2^x =2(2)=4

2^4=2×2×2×2= 16

How many spaces does it move over

Answers

Answer:

The point at the bottom has to move over 2 to the left to be aligned with the point at the top however they will have a 3 space in between the 2 same for the point at the top, the top point moves over 2 to the right to be aligned with the bottom point, then they will have a 3 square space between each other.

Answer:Around 3 spaces between?

Step-by-step explanation:

Kenji simplifies 3^5 x 4^ 5and gets the result 12^10, but Darlene is not sure. Is Kenji correct? Justify your answer.

Answers

That's a question about exponentiation.

Answer:

Kenji is wrong because he does not aply the porperty correctly.

Step-by-step explanation:

A exponetiation has this form:

[tex]\boxed{a^b}[/tex]

a is the base

b is the power or exponent

To understand that situation it's important to know a property about exponentiation. When we have a multiplication with the same exponent and diferent bases, the result is the multiplication of the bases with the same exponent. Let's see this above, in mathematical language:

[tex]\boxed{a^b \cdot c^b = (a\cdot c) ^b}[/tex]

Examples:

[tex]2^3 \cdot 8^3 = (2 \cdot 8) ^3 = 16^3[/tex][tex]10^9 \cdot 23^9 = (10 \cdot 23) ^9 = 230^9[/tex]

Now, we can say why Kenji is wrong. It's easy simplify [tex]3^5 \cdot 4^5[/tex]! We know that the result is [tex](3 \cdot 4) ^5 = 12^5[/tex], but Kenji multiplied the bases and added the exponents, that's why he is wrong.

I hope I've helped. ^^

Enjoy your studies! \o/

what is the length of a rectangular solid with a volume of 180 cu ft, if it is 9 ft high and 4ft wide?

Answers

Answer:

5 ft

Step-by-step explanation:

The formula for Volume is V=lwh, or Volume = length x width x height.

The equation would be:

[tex]180=l(4)(9)[/tex]

or

[tex]180=36l[/tex]

To find the answer, divide by 36.

[tex]\frac{180}{36} =\frac{36l}{36}[/tex]

[tex]5=l[/tex]

By which number should (2/5)^-3 be multiplied to get (1/2)^4 as a product ?​

Answers

Answer:

[tex]\frac{2}{5}^{-3}[/tex]×[tex]x=\frac{1}{2}^{4}[/tex]

[tex]x=\frac{2}{5} ^{3} \\[/tex]×[tex]\frac{1}{2}^{4}[/tex]

(negative in the exponent means reciprocal of the fraction)

x= [tex]\frac{1}{250}[/tex]

Brainliest please

Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x Question 7 options: A) (–4, 0) and (0, 0) B) (0, 0) C) (–4, 0) and (4, 0) D) (0, 0) and (4, 0)

Answers

Answer:

Hello,

Answer A (-4,0) and (0,0)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]

[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]

what is the radius of a circle in it in if the area is 36m²?
A.0.339 m
B.3.39 m
C.78.5 m²
D.339 m

Answers

Answer:

B. 3.39 m

Step-by-step explanation:

r² = A/π

= 36/3.14

= 11.465

r = √11.465 = 3.39

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