Pls help I dont get this

Using Conditional probability,

The probability that after a fair coin is tossed 5 times that the result will contain 3 'heads' given that the first toss was a 'head' is 3/5.

A fair coin is tossed five times .

so, total possible outcomes = 2⁵ = 32

Let A: head observed on first toss

B: 3 heads observed.

Probability that the first toss was head (p) = 1/2

we have to find out probability that on 5 tosses result contain 3 heads given that first toss wss head .

Using Binomial Probability distribution

P (X= x) = ⁿCₓ (p)ˣ (q)⁽ⁿ⁻ˣ⁾

x = 3 , n = 5

we get , P(B) = P(X= 3 ) = ⁵C₃(1/2)³(1/2)²

=> P(B) = 10 ×(1/2)⁵= 5/16

since the first toss is fixed as a head.

P(A ∩ B) =P( X₁ = 1 and X₂+ X₃ + X₄ + X₅) = P(X₁= 1)P(X₂+X₃+X₄+X₅)

= 1/2 × ⁴C₂ (1/2)⁵ = 3 (1/2)⁴

The required probability is , Conditional probability P(B/A) = P(A ∩ B)/P(A)

= 3(1/2)⁴/ 5/16 = 3/5

Hence , the required probability is 3/5.

To learn more about Conditional Probability, refer:

https://brainly.com/question/10567654

#SPJ4

First, the definition of parallel lines is:

Lines on a plane that never meet. They are always the same distance apart.

Considering the definition we draw the parallel line as a line that has all its points at the same distance of the one that passes through A and B.

a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.

b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.

c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.

a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.

b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.

c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.

To learn more about  area Click Here:  brainly.com/question/22469440

#SPJ11

The maximum volume of the prism is 1728 cubic centimeters.

To find the dimensions of the prism with maximum volume, we need to consider the relationship between the volume of the prism and its dimensions.

Let's assume the base of the right triangular prism is an isosceles right triangle with legs of length 'a'. The height of the prism will be 'h'. The prism is inscribed in a hemisphere with a radius of 12 cm.

First, let's determine the relationship between 'a' and 'h'. Since the base of the prism is on the great circle of the hemisphere, the hypotenuse of the triangular base is equal to the diameter of the hemisphere, which is twice the radius. Therefore, the hypotenuse of the base is 2 * 12 = 24 cm.

By using the Pythagorean theorem, we can find 'a':

a^2 + a^2 = 24^2

2a^2 = 576

a^2 = 288

a = √288

Now, let's find the height 'h' of the prism. The height 'h' is equal to the radius of the hemisphere, which is 12 cm.

Therefore, the dimensions of the prism for maximum volume are:

Base length (a) = √288 cm

Height (h) = 12 cm

To find the maximum volume, we can use the formula for the volume of a right triangular prism:

Volume = (1/2) * a^2 * h

Substituting the values, we get:

Volume = (1/2) * (√288)^2 * 12

= (1/2) * 288 * 12

= 1728

Hence, the maximum volume of the prism is 1728 cubic centimeters.

for such more question on volume

https://brainly.com/question/6204273

#SPJ8

No.

x = 9 isn't classified as a function at all. When you graph x instead of y. You will get a vertical line which isn't even a function.

Answer:

Step-by-step explanation:

the two angles are congruent, they are like opposite angles, look at the figure

21x - 6 = 20x

21x - 20x = 6

x = 6°

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

check

21x - 6 = 20x

21 * 6 - 6 = 20 * 6

120  =  120

the answer is good

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

to learn more about probability click on the link below.

https://brainly.com/question/24756209

#SPJ4

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

Answer:

There are two elements arranged in a single row and two columns in the matrix, hence it is an example of a row matrix. Example 3: A Row matrix of the order 1 x 3, is: A = [ 1 3 8 ] 1 × 3. In the above example, there are three elements in the matrix arranged in a single row and three columns.

Step-by-step explanation:

HOPE IT HELPS U BTW HAVE A GOOD DAY :D

7.36 for each cap

$36.80 is the cost for 5 caps. if we divide the cost of the pack to the individual number of idems (caps), the equation (36.80÷5) will come out to $7.36, meaning $7.36 is the cost for each individual cap.

Answer: 720

Step-by-step explanation:

Given

A club has 10 members and needs one president, a vice president, and a secretary

There are 10 positions for president i.e. 10 ways to select a member for it

Similarly, there 9 persons left to choose a position for vice president

likewise 8 persons for secretary

Total no of ways to do it are

\(\Rightarrow 10\times 9\times 8\\\Rightarrow 720\ \text{ways}\)

A quadratic equation x² = 16 has two solutions, x = 4 and x = -4.

A quadratic equation has standard form:

ax² + bx + c = 0

There are several methods to solve a quadratic equation:

- using factorization

- by completing the square

The given quadratic equation is: x² = 16

Method 1: Using factorization

x² = 16

x² - 16 = 0

(x + 4) (x - 4) = 0

Hence, the solution is x = 4 and x = -4

Method 2: By completing the square

x² = 16

This is already a perfect square. Hence,

x = ±√16

x = ±4

Hence, the solution is x = 4 and x = -4

Conclusion: there are two solutions of  x² = 16,  x = 4 and x = -4

There was typos in your question, most likely your question was:

How many solutions does x² = 16 have?

Learn more about quadratic equation here:

https://brainly.com/question/28038123

#SPJ4

1) given

2) definition of midpoint

3) given

4) definition of congruent segments

5) transitive property of equality

6) definition of congruent segments

The probability of getting all tails when flipping a coin three times can be calculated using the multiplication rule of probability. For each flip of the coin, there are two possible outcomes: heads or tails.

Assuming the coin is fair, both outcomes are equally likely, so the probability of getting tails on any one flip is 1/2.

P(all tails) = P(tails on first flip) x P(tails on second flip) x P(tails on third flip)

= (1/2) x (1/2) x (1/2)

= 1/8

Therefore, the probability of getting all tails when flipping a coin three times is 1/8 or 0.125 when expressed as a decimal rounded to four decimal places.

To learn more about “probability” refer to the https://brainly.com/question/13604758

#SPJ11

The linear equation of the graph is y = x - 5

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (1, -4) and (5, 0)

Calculate the slope (m) using

m = (y2 - y1)/(x2 - x1)

So, we have

m = (0 + 4)/(5 - 1)

Evaluate

m = 1

The equation is then calculated as

y = m(x - x1) + y1

So, we have

y = 1 * (x - 5) + 0

Evaluate

y = x - 5

Hence, the linear equation of the graph is y = x - 5

Read more about linear equations at

https://brainly.com/question/14323743

#SPJ1

The probability that exactly 4 students will withdraw is approximately 0.2048.

The problem asks us to calculate the probabilities related to student withdrawals in an introductory statistics course. We are given that 20% of students withdraw from the course and that 20 students registered for the course.

a. To compute the probability that 2 or fewer students will withdraw, we need to calculate the cumulative probability of the binomial distribution. We can use the binomial probability formula:

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

Using the formula, the probability can be calculated as follows:

P(X = 0) = (20 choose 0) * (0.2^0) * (0.8^20) ≈ 0.0115

P(X = 1) = (20 choose 1) * (0.2^1) * (0.8^19) ≈ 0.0729

P(X = 2) = (20 choose 2) * (0.2^2) * (0.8^18) ≈ 0.1948

Therefore, P(X ≤ 2) ≈ 0.0115 + 0.0729 + 0.1948 ≈ 0.2792

b. To compute the probability that exactly 4 students will withdraw, we use the binomial probability formula:

P(X = 4) = (20 choose 4) * (0.2^4) * (0.8^16) ≈ 0.2048

Therefore, the probability that exactly 4 students will withdraw is approximately 0.2048.

Learn more about binomial probability here: https://brainly.com/question/12474772

#SPJ11

We have -2 from the values in the provided solution set, which is the necessary value.

what is solution set?

A solution set is a group of values in mathematics that satisfy a specified set of equations or inequalities. A constrained optimization problem's viable zone is its solution set of constraints.

Given: - 5x - 15 > 10 + 20x

Let's eliminate the variable x in order to solve the inequality.

5 times both sides,

- 5x - 15 + 5x > 10 + 20x + 5x

- 15 > 10 + 25x

Subtracting 10 from both sides

- 15 - 10 > 10 - 10 + 25x

- 25 > 25x

Dividing both sides by - 25

-1 > x

x < - 1

We have -2 from the values in the provided solution set, which is the necessary value.

To learn more about solution set checkout https://brainly.com/question/18119571

#SPJ4

Answer:

B

Step-by-step explanation:

The value of the expression [ -2/3 x (-2/3) ] x ( -9/4) is -1

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

[ -2/3 x (-2/3) ] x ( -9/4)

Evaluate the expression in the bracket

So, we have

[ -2/3 x (-2/3) ] x ( -9/4) = [4/9] x ( -9/4)

Evaluate the product

[ -2/3 x (-2/3) ] x ( -9/4) = -1

Hence, the value of the expression [ -2/3 x (-2/3) ] x ( -9/4) is -1

Read more about expressions at

https://brainly.com/question/723406

#SPJ1

He spent on transport = 20%

spent on breakfast = 60/-

spent on lunch = 15%

remaining amount = 340

rs he spent on transport = 20/100 × 340 =68

rs he spent on lunch = 15/100 × 340 = 51

Therefore, total of his pocket money = 68 + 51 + 60 + 340

= ₹519

P(4, 60°) is not equal to P(4, π/2). The polar coordinate P(4, 60°) has a different angle (measured in radians) compared to P(4, π/2). It is important to convert angles to the same unit (radians or degrees) when comparing polar coordinates.

To determine if P(4, 60°) is equal to P(4, π/2), we need to convert both angles to the same unit and then compare the resulting polar coordinates.

First, let's convert 60° to radians. We know that π radians is equal to 180°, so we can use this conversion factor to find the equivalent radians: 60° * (π/180°) = π/3.

Now, we have P(4, π/3) as the polar coordinate in question.

In polar coordinates, the first value represents the distance from the origin (r) and the second value represents the angle measured counterclockwise from the positive x-axis (θ).

P(4, π/2) represents a point with a distance of 4 units from the origin and an angle of π/2 radians (90°).

Therefore, P(4, 60°) = P(4, π/3) is False, as the angles differ.

Learn more about polar coordinate here:

brainly.com/question/15865602

#SPJ11

The required value of x for the given equation of line is 3.

The equation of straight line is defined as the y = mx +c or ax + by = c, where y is point on y-axis and x is the point n x-axis, m is slope of the line.

According to given data in the question:

we have,

8x-3y=21-----(1)

And 3x+y=10

multiply 3 both sides

9x+3y=30------(2)

To find the value of x,

Add equation 1 and 2, we get

x = 3

Thus required value of x is 3.

To know more about equation of line visit:

brainly.com/question/21511618

#SPJ9

Answer:

Step-by-step explanation:

0 = 0 is the correct equation without any variables.

It means the initial equations will be correct for any value of the variables.

This brings us to the conclusion that the system has infinitely many solutions.

Correct choice is D

Always double-check your graph by entering various x values and ensuring that the associated y values fall along the curve you drew.

A graph is a picture of data that illustrates the connection between two or more factors. A graph in mathematics is typically a two-dimensional coordinate system with a horizontal x-axis and vertical y-axis (vertical). Data points are represented on a graph by points that are drawn with their x- and y-coordinates. The graph can be used to display trends, correlations, and temporal shifts as well as other patterns and connections between the variables. Graphs are used to aid in the interpretation and communication of data in a wide range of disciplines, including mathematics, science, economics, and social studies.

given

Locate the vertex: The vertex of a quadratic function is the lowest or highest spot on the graph. For the x-coordinate of the vertex, use the expression x = -b / (2a), and for the y-coordinate, use y = f(x), where f(x) is the quadratic function.

The places where the graph crosses the x-axis and the y-axis are known as the intercepts. If x = 0, then calculate f to determine the y-intercept (0).

Additional information: Plug a few x values into the function to determine the associated y values. You'll have more data points to display on the graph as a result.

Always double-check your graph by entering various x values and ensuring that the associated y values fall along the curve you drew.

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

The correct answer is c. $100,000.

The required reserve ratio is the percentage of deposits that banks are required to hold as reserves. In this case, Bank A has total deposits of $10 million and the required reserve ratio is 9 percent. Therefore, Bank A is required to hold reserves equal to 9% of its deposits, or:

Reserves required = 0.09 x $10,000,000 = $900,000

However, the bank currently has actual reserves of $1 million, which means it has excess reserves equal to:

Excess reserves = Actual reserves - Reserves required

Excess reserves = $1,000,000 - $900,000 = $100,000

Therefore, the correct answer is c. $100,000.

To know more about  reserve ratio  refer here:

https://brainly.com/question/30076175

#SPJ11

Answer:

he do be running tho

Answer:

He burned a total of 735 calories.

Step-by-step explanation:

4 miles + 3 miles = 7 miles

105 calories/1 mile = 7 miles/ ? calories

105 calories times 7= 735 calories

As per the concept of fraction, we can express 8 feet as 2 ²/₃ yards.

The term fraction refers to the numerical values which are a part of the whole.

8 feet can be expressed in another way.

In order to convert to a yard measurement, we divide the length by the conversion ratio.

Here we know that 1 yard = 3 feet

=> yards = feet ÷ 3

Here we have calculated the measurement of 8 feet.

So, the equivalent yard measurement is expressed as,

=> yards = 8/3

When we convert it into mixed fraction form,  we get,

=> 2 ²/₃ yards.

Read more about fractions:

https://brainly.com/question/78672

#SPJ4

The complete question is:

F) 2*1/3 yards G) 2*1/2 yards H )2*2/3 yards J )2*3/4 yards. A clothesline rope is 8 feet long. Which of these is another way to express 8 feet? answer choices -A/FB/GC/HD/J

Answer:

D. 1 1/2 hours

Step-by-step explanation:

First, we need to find the unit rate to then multiply it by 90. to find the unit rate I did 240 miles divided by 4 hours to get 60 miles per hour. So we know we need at least 1 hour to get the 60 miles and to get 90 miles we need to add 30. Since 30 is half of 60 we can just take half of 1 hour which is 30 minutes. we add it together and get 1 hour and 30 minutes, or 1 hour and a half.

Time taken to cover 90 miles is 1.5 hours

Time taken to cover 240 miles = 4 hours

Time taken to cover 90 miles

Time taken to cover 90 miles = [90 / 240]4

Time taken to cover 90 miles = [360 / 240]

Time taken to cover 90 miles = 1.5 hours

https://brainly.com/question/13326890?referrer=searchResults

To find the indicated function values for the function f(x) = (-x)^3 - x^2 - x + a, let's substitute the given values of x into the function.

a) f(0):

Substituting x = 0 into the function, we have:

f(0) = (-(0))^3 - (0)^2 - (0) + a

f(0) = 0 - 0 - 0 + a

f(0) = a

Therefore, f(0) = a.

b) f(5):

Substituting x = 5 into the function, we have:

f(5) = (-(5))^3 - (5)^2 - (5) + a

f(5) = -125 - 25 - 5 + a

f(5) = -155 + a

Therefore, f(5) = -155 + a.

c) f(-5):

Substituting x = -5 into the function, we have:

f(-5) = (-(-5))^3 - (-5)^2 - (-5) + a

f(-5) = 125 - 25 + 5 + a

f(-5) = 105 + a

Therefore, f(-5) = 105 + a.

d) f(2) + f(-2):

Substituting x = 2 into the function, we have:

f(2) = (-2)^3 - (2)^2 - (2) + a

f(2) = -8 - 4 - 2 + a

f(2) = -14 + a

Substituting x = -2 into the function, we have:

f(-2) = (-(-2))^3 - (-2)^2 - (-2) + a

f(-2) = 8 - 4 + 2 + a

f(-2) = 6 + a

Therefore, f(2) + f(-2) = (-14 + a) + (6 + a) = -8 + 2a.

To summarize:

a) f(0) = a

b) f(5) = -155 + a

c) f(-5) = 105 + a

d) f(2) + f(-2) = -8 + 2a.

Now let's move on to the second part of the question.

Using the provided table for the function h(x):

X | h(x)

6 | 3

0 | 3

6 | ?

a) h(-6):

Looking at the table, we don't have a value for h(-6).

b) h(6):

From the table, h(6) = 3.

c) For what values of x is h(x) = 6?

Looking at the table, there is no x value where h(x) equals 6.

Therefore:

a) h(-6) = N/A

b) h(6) = 3

c) For what values of x is h(x) = 6? None.

Finally, let's analyze the given statement regarding the functions f(x) and g(x):

f(x) | g(x)

-1 | -7

-7 | -1

-8 | -2

-2 | -8

The statement is: f(-1) - f(-2) = -2 - (-8) = -2 + 8 = 6.

The statement f(-1) - f(-2) = 6 is false because the actual result is 10, not 6.

Therefore, the correct choice is:

OB. False; f(-1) - f(-2) = 10.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11