Consider the following balls-and-bin game. We start with one black ball and one white ball in a bin. We repeatedly do the following: choose one ball from the bin uniformly at random, and then put the ball back in the bin with another ball of the same color. We repeat until there are n balls in the bin. Show that the number of white balls is equally likely to be any number between 1 and n − 1.

The value of the equations are a = 10 , b = -5.1 and c = 1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

a + ( -7 ) = 3   be equation (1)

On simplifying the equation , we get

a - 7 = 3

Adding 7 on both sides of the equation , we get

a = 3 + 7

a = 10

Substituting the values in the equation , we get

1.9 + b = -3.2   be equation (2)

Subtracting 1.9 on both sides of the equation , we get

b = -3.2 - 1.9

b = -5.1

Substituting the values in the equation , we get

-1/6 + ( 7/6 ) = c   be equation (3)

c = ( 7 - 1 ) / 6

c = 6/6

c = 1

Hence , the equations are solved

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Answer:

48 liters.

Step-by-step explanation:

Going from 3/4ths full to 1/2 full has a difference of 1/4; that makes 12 liters 1/4 of the tank.

12 times 4 is 48.  

Answer:

48

Step-by-step explanation:

assume holds x litres

1/2 x + 12 = 3/4 x

so 1/4 x =12

x =48

The probability that the dial stops on a red slice is given as follows:

0.

A probability is obtained with the division of the number of desired outcomes by the number of total outcomes in the context of a problem.

The number of total outcomes for this problem is given as follows:

6.

The number of desired outcomes for this problem is given as follows:

0, as there are only blue slices and yellow slices, no red slices.

Then the probability that the dial stops on a red slice is obtained as follows:

p = 0/6

p = 0%.

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The amount of water used in a shower lasting 5 minutes is 3.5 gallons.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, A shower lasting 17 minutes requires 11.9 gallons of water.

Let the amount of water used in a shower lasting 5 minutes be x.

Here, the proportion is

17:11.9 :: 5:x

Now, 17×x=11.9×5

17x=59.5

x=59.5/17

x=3.5 gallons

Therefore, the amount of water used in a shower lasting 5 minutes is 3.5 gallons.

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To obtain the other factor is to take the idea  x² - 6x - 7 /x+ 1. Option A

Algebraic expressions are described as expressions comprising of terms, variables, factors, coefficients, and constants.

They are also made up of arithmetic operations, such as;

Given the expression;

x² - 6x - 7

Factorize the terms

x² - 7x + x - 7

Then, we get

(x+1) (x - 7)

The factors are (x + 1) (x -7)

Hence, the step x² - 6x - 7 divided by x - 1

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Answer:

6155.84

Step-by-step explanation:

23000

6% annual

5 years

23000*(1+6%)^5= 30799.19

so 6155.84 per year

April must pay back her auto loan at a rate of $5980 per year. This is calculated by first determining the total repayment sum (principal + interest), and then dividing this total by the number of repayment years.

In this problem about loan repayment, we are asked to find the rate at which April must pay back her loan of $23000 with an interest rate of 6%, which is to be paid off in 5 years. First, we need to determine the total amount to be paid back which is the principal plus the interest. The interest April will pay is given by the formula: Interest = Principal x Rate x Time. So, Interest = $23000 x 0.06 x 5 = $6900. Thus, the total amount to be repaid is $23000 (the principal) + $6900 (the interest) = $29900.

To find out how much she must pay per year, we divide the total payment by the number of years. Therefore, Annual Payment = $29900 / 5 = $5980 per year. So, April must pay back the loan at a rate of $5980 per year.

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The -value of -2.576 is less than the critical value of 0.05, we can reject the null hypothesis and conclude that the population mean is not less than .

The -value is the probability of observing a test statistic result as extreme or more extreme than the observed result given that the null hypothesis is true. In this hypothesis test, the null hypothesis is that the population mean is less than , and the alternative hypothesis is that the population mean is not less than . With and , the -value can be calculated using the t-distribution as follows:

The t-distribution has degrees of freedom (df) equal to the sample size minus 1. Therefore, the df for this hypothesis test is .

Using the t-distribution with df = , the -value can be calculated as:

-value = P(t≤-2.576)

The -value is the probability of observing a test statistic result as extreme or more extreme than the observed result given that the null hypothesis is true.

Since the -value of -2.576 is less than the critical value of 0.05, we can reject the null hypothesis and conclude that the population mean is not less than .

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The property that justifies the work between Step 3 and Step 4 is the property of real numbers under multiplication and division.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 19 < 4x - 5

By the addition property, add 5 on both sides

19 + 5 < 4x - 5 + 5

24<4x

By Multiplication and division property, divide both sides by 4

(1/4)24<(1/4)4x

6<x

Hence, the property that justifies the work between Step 3 and Step 4 is the property of real numbers under multiplication and division.

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The percent increase in the number of apps Tan has on his phone is 340%

Number of apps downloaded in months 1 = 5 apps

Number of apps downloaded in months 7 = 22 apps

Percentage increase in the number of apps = changes in the number of apps downloaded/ Number of apps downloaded in months × 100

= (22 - 5) / 5 × 100

= 17/5 × 100

= 3.4 × 100

= 340%

In conclusion, Tan downloaded 340% more apps on his phone after 6 months.

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Answer:

Step-by-step explanation:

D

The value of y = 3 and x' = -1, y' = -3/7.

Given the equation y² = xy + 6 and knowing that y = 3 and x' = -1, we can use implicit differentiation to find the derivative of y with respect to t, y'.

       d/dt (y²) = d/dt (xy + 6)

       2y * y' = x' * y + x * y' + 0

       2 * 3 * y' = -1 * 3 + x * y'

       6 * y' = -3 + x * y'

        6 * y' - x * y' = -3

        (6 - x) * y' = -3

       y' = -3 / (6 - x)

        y' = -3 / (6 - -1)

        y' = -3 / 7

So, when y = 3 and x' = -1, y' = -3/7.

The specific case we were discussing is finding the derivative of y with respect to t, given the equation y² = xy + 6, and the values of y and x' at a certain time t. This is a problem in calculus, which is a branch of mathematics that deals with the rate of change and slopes of curves. By differentiating both sides of the equation and substituting in known values, we were able to find the value of y' at a specific time t. This method of finding derivatives is called implicit differentiation and it is used to find the derivative of an implicit equation, where one variable is expressed in terms of another.

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The expression 9/4 is a real number, whereas the expression 9i is a non-real complex number.

Real Numbers:

9/4

The expression 9/4 is a real number. This can be seen by dividing the numerator (9) by the denominator (4) to get the answer 2.25. This is a real number as it can be written with a decimal.

Non-Real Complex Numbers:

9i

The expression 9i is a non-real complex number. This can be seen by taking the coefficient (9) and multiplying it by the imaginary number i. The result is 9i, which is a non-real complex number because it cannot be written with a decimal. The imaginary number i is defined as the square root of -1, which is not a real number.

The expression 9/4 is a real number, whereas the expression 9i is a non-real complex number.

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The value of y when x = 3 is 36.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

y varies directly as x².

This means,

y = kx²

Now,

When x = -1, y = 4

So,

4 = k(-1)²

k = 4/1

k = 4

Now,

y = 4x²

For x = 3,

y = 4 x 3²

y = 4 x 9

y = 36

Thus,

The value of y is 36.

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Answer:

Step-by-step explanation:

You can use conversion to solve for cm

52 km x 1 cm / 4 km = 13 cm

where km cancels out leaving your answer in cm.

the actual distance on the map would be 13 cm

The minimum value of ||v|| is 0, since the vector v can be the zero vector, which points from the origin to the origin.

The equation (10 3) + (-2 1)t describes the line L, where the vector (10 3) is the point on the line L and the vector (-2 1) is the direction vector. The equation can be re-written as v = (10 3) + (-2 1)t, where v is the vector from the origin to a point on L and t is a scalar.

Since t can be any real number, the vector v can be anything from the origin to a point on L. In particular, the vector v can be the zero vector, which points from the origin to the origin. Therefore, the minimum value of ||v|| is 0.

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The two linear inequalities shown in the graph below are y > -2 and

x - y > -1.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this phrase can be replaced by any of the inequality symbols, such as greater than (>), less than (<), more than or equal to (≥), less than (≤), or not equal to (≠).

Given a graph of linear inequalities,

shows a line parallel to the x-axis which means the value of x is zero,

and the shaded portion is on the positive side of x and y,

from the graph, we find that the equation for the line parallel to the x-axis is

y > -2.

The second line passe from (-1, 0)and (0, 1)

linear equation for the line will be,

y = x + 1

y - x = 1

but the shaded portion is below the line,

so the equation of inequality is y - x < 1

multiply -1 on both sides we get,

x - y > -1

Hence options A and H are correct.

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The eigenfunctions of the momentum operator px are wave functions which, when acted upon by px, result in a scalar multiple of the wave function itself, with the scalar being the eigenvalue.

To determine which wave functions are eigenfunctions of the momentum operator px, one can start by solving the eigenvalue equation, px ψ = ħkψ, where ψ is the wave function and ħk is the eigenvalue. In this equation, ħ is Planck's constant divided by 2π and k is the wave number.

To find the eigenvalue, one can multiply both sides of the equation by the complex conjugate of the wave function and integrate over all space. The result is ħk times the normalization constant, which can be used to find the eigenvalue.

The wave functions that satisfy this equation are the eigenfunctions of the momentum operator px, and their corresponding eigenvalues are proportional to their wave numbers.

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Given that cos (0) = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin (0).

sin^2(0) + cos^2(0) = 1

sin^2(0) = 1 - cos^2(0)

sin^2(0) = 1 - 0^2

sin^2(0) = 1

So, sin (0) = sqrt(sin^2(0)) = sqrt (1) = 1.

However, the given value is sin (0) = v3/6. This means that sin (0) = sqrt (3)/2, which is the value of sin (60). Therefore, the correct value of sin (0) is sqrt (3)/2, not 1.

trigonometry, the branch of mathematics deal with specific functions of angles and their application to calculations. There is total six functions of an angle commonly used in trigonometry.

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"the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, the sum of two numbers is twenty-six the difference between five is more than the larger number and twice the smaller number' into a variable expression.

Since x represents the smaller of the two numbers,

Thus the larger number will be 26 - x

The expression asked above will be:

=> 5 + larger number - 2 * smaller number

=> 5 + 26 - x - 2 * x

=> 31 -3x

therefore,  "the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

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Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Zachariah has 9 American stamps out of 15 stamps

Zachariah's ratio is 9 / 15 = 3 / 5=0.6

Khai has 13 American stamps out of 20 stamps.

Khai's ratio is 13 / 20 = 0.65.

0.65>0.6

Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.

Hence, Khai has a higher ratio of American stamps than Zachariah because 9 over 15 is less than 13 over 20.

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Answer:

3.) x=49    4.) x=29

Step-by-step explanation:

3.)

2x+82=180

2x=98

x=49

4.)

3x+3(91)=360

3x+273=360

3x=87

x=29

The best estimate for 38/6 is option C that is equals to  4.

What is division ?

Division is a mathematical operation that involves splitting a number or quantity into equal parts or groups. It is the opposite of multiplication, where we find how many groups of a certain size can fit into a larger number or quantity.

When we divide one number by another, we are finding out how many times one number can be evenly divided by another number. For example, when we divide 12 by 3, we are asking "how many groups of 3 are in 12?" The answer is 4, because we can divide 12 into 4 equal groups of 3.

The best estimate for 38/6 is option C, 4.

We can see that 6 goes into 38 about 6 times (6 x 6 = 36), and there is a remainder of 2. Therefore, the answer is between 6 and 7. Since the options are all whole numbers, the best estimate is 4.

Therefore, The best estimate for 38/6 is option C that is  4.

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The required triangle WYV and XYU are congruent triangles with the SAS postulate.

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

Here,
Consider triangle WYV and XYU

XY = WY                   [Given ]

VY = UY                   [Given ]
∠WYV = ∠UYX         [Alternate interior angles for two intersecting lines are always equal]

ΔWYV ≅ ΔXYU by SAS congruency postulate.

As triangles, WYV and XYU are congruent triangles then,
VW = UX     [sides of a congruent triangle are always equal]

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The condition probability of a given b must be smaller than the intersection of the same two events a and b:

This statement is False.

The condition probability of event "b" given event "a" (P(b|a)) must be less than or equal to the probability of event "b" (P(b)). This is because the occurrence of event "a" restricts the sample space to only those outcomes that belong to event "a", and thus the probability of event "b" given event "a" cannot be greater than the unconditional probability of event "b".

The concept of conditional probability is used to describe the probability of an event given that another event has already occurred.

The formula for conditional probability is

where P(b|a) represents the probability of event "b" given that event "a" has already occurred.

In order for this to be meaningful, it is required that P(b|a) <= P(b). This means that the probability of event "b" given that event "a" has already occurred cannot be greater than the unconditional probability of event "b".

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Answer:

60b + 12b

Step-by-step explanation:

The probability of getting both a dog and a cat image is 0.25.

The probability of getting two dog images with replacement is 0.25. This is because when selecting with replacement, each draw is independent of the previous draw. Thus, the probability of getting one dog image is 0.50 and the probability of getting a second dog image is 0.50. Thus, the probability of getting two dog images is 0.50 x 0.50 = 0.25. Similarly, the probability of getting two cat images with replacement is 0.25.

The probability of getting one dog image and one cat image with replacement is 0.50 x 0.50 = 0.25. Thus the probability of getting both a dog and a cat image is 0.25.

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The continuity equation comes from the conservation of mass.

It can be a mathematical statement of the principle of conservation of mass.

According to this, mass inflow in control volume should be equal to the mass outflow from that region at a particular time and the mass can neither be created nor be destroyed.

A continuity equation is an equation that shows the behavior of a quantity as it moves or is transported from one point or state to another

The general form of the continuity equation:

Where p=density of the fluid,

u,v,w=components of velocity in x,v, and z directions respectively.

The above equation is applicable for steady as well as unsteady, uniform s well as non-uniform, compressible as well as incompressible flow.

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After solving the Algebraic Expression 2(x + 8)= 2x + 8, we will get x∈∅. Variable x is dissolved in itself, making it impossible to find its value.

Before moving to solve the equation , let's learn how to solve any algebraic expression:

Step 1: Determine whether the Distributive is necessary.

Property. If so, spread the word!

Step #2: Group similar terms together on either side of the equals symbol.

(meaning: combine all of the similar factors AND

Add up each and every integer (number).

Step #3: Align the variables so that they are all to one side of the equals symbol.

utilizing the inverse process. REMEMBER: No matter what you do

You MUST do to the other side of the equals sign what you did to the one side.

equals (symbol).

Fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

You MUST do anything you do to one side of the equals sign.

the reverse of the equals symbol).

Step #5: Using the variable's ALONE state, isolate it

the opposite process. DO NOT FORGET: No matter what you do to one

You MUST change the other side of the equals symbol to the equals symbol

Given:

2(x + 8)= 2x + 8

2 × x + 2 × 8= 2x + 8

2x+16= 2x+ 8

16= 8

So, x∈∅.

In this equation , the value of x could not be find because variable x is dissolved in itself.

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Answer:

-3/2

Step-by-step explanation:

Parallel lines have the same slope, but different y-intercepts. We can find the slope by converting to slope-intercept form:

[tex]\displaystyle 3x+2y=8\\\\2y=8-3x\\\\y=4-\frac{3}{2}x\\\\y=-\frac{3}{2}x+4[/tex]

Hence, the slope of the parallel line will also be -3/2

Part a:  Data from Germany are skewed to the left.

Part b) More Germans survey respondents have visited upwards.

Part c) These box plots show that 20-year-old Chinese rarely venture .

For the stated question:

a) Data from Germany, China, as well as the United States are all skewed to the right. Data from Germany are skewed to the left.

b) More Germans survey respondents have visited upwards of eight foreign countries so the box plot for Germany indicates that for at least 50 percent of Germans survey conducted have visited eight or many foreign countries, while a box plot for said United States indicates that less than 25% of US people involved have done so.

c) These box plots show that 20-year-old Chinese rarely venture outside of the country.

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The complete question is-

In a survey of 20-year-olds in China, Germany, and the United States, people were asked the number of foreign countries they had visited in their lifetime. The following box plots display the results.

a. In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected.

b. Have more Americans or more Germans surveyed been to over eight foreign countries?

c. Compare the three box plots. What do they imply about the foreign travel of 20-year-old residents of the three countries when compared to each other