A box contains 3 red marbles, 6 blue marbles, and 1 white marble. the marbles are selected at random, one at a time, and are not replaced. find each compound probability

The inverse function {f⁻¹(x)} for the function f(x) is -

f⁻¹(x) = (3x + 2)/(x - 1)

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is the function f(x) as -

f(x) = (x + 2)/(x - 3)

We can write the function f(x) as -

f(x) = (x + 2)/(x - 3)

We can find the inverse function {f⁻¹(x)} as follows -

y = (x + 2)/(x - 3)

x = (y + 2)/(y - 3)

x(y - 3) = y + 2

xy - 3x = y + 2

xy - y = 3x + 2

y(x - 1) = 3x + 2

y = (3x + 2)/(x - 1)

f⁻¹(x) = (3x + 2)/(x - 1)

Therefore, the inverse function {f⁻¹(x)} for the function f(x) is -

f⁻¹(x) = (3x + 2)/(x - 1)

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{Question in english -

perform the inverse of the following function f(x)=x+2/x-3}

The interest rate that would be required is 5.39%. The solution has been obtained by using concept of compound interest.

What is compound interest?

Both the principal and the interest that has accumulated over the preceding period are taken into account when interest is calculated. In contrast to simple interest, which does not take the principal into account when calculating the interest for the following month, compound interest does. Compound interest is usually represented in algebra by the letter C.I.

We are given that Lamonte is going to invest $48,000 and leave it in an account for 17 years. She wants to end up with $120,000.

So, from this we get the equation as

120,000 = 48000e¹⁷ⁿ     ( n is the interest rate)

Solving this, we get

e¹⁷ⁿ = 2.5

n = 5.39%

Hence, the interest rate that would be required is 5.39%.

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Answer:

when the input t is -7, the output k is -89.

Using the equation k = 10t - 19 and substituting t = -7, we have:

k = 10(-7) - 19

k = -70 - 19

k = -89

Therefore, when the input t is -7, the output k is -89.

Part A: The numerator in the first fraction is closest to 8, so the fraction is nearest to 1.

To see this, we can simplify the fraction 8/10 by dividing both the numerator and denominator by the greatest common factor, which is 2. This gives us:

8/10 = 4/5

Since the numerator of the simplified fraction is closest to 5, we can estimate that the value of the first fraction is nearest to 1.

Part B: The numerator in the second fraction is closest to 2, so the fraction is nearest to 1/3.

To see this, we can simplify the fraction 2/6 by dividing both the numerator and denominator by the greatest common factor, which is 2. This gives us:

2/6 = 1/3

Since the numerator of the simplified fraction is closest to 1, we can estimate that the value of the second fraction is nearest to 1/3.

Part C: The value of the expression can be estimated as 1 + 1/3 = 1 1/3.

To see this, we can add the two estimated fractions from parts A and B:

1 + 1/3 = 3/3 + 1/3 = 4/3

Since 4/3 is closer to 1 1/3 than any other whole number or fraction, we can estimate that the value of the expression is nearest to 1 1/3.

Answer:

it would be -10x-15

Step-by-step explanation:

You're basically using distributive property

5(-2x-3)

5•-2x=-10x

5•-3=-15

-10x-15

It would stop there because you can't combine a number w/ a variable with a number without a variable, I hope that makes enough sense

The decimal equivalent of 0xc9 is 201.

Hexadecimal is a number system with a base of 16, in which we use 16 distinct symbols to represent numbers. The symbols used in hexadecimal are the digits from 0 to 9 and the letters from A to F.  

Hexadecimal notations are commonly used in computer programming and digital electronics because they can represent binary data more compactly than binary notation.

Here we have

0xc9  

By converting each symbol as a number we can calculate as follows

Here 0x represents hexadecimal

And the value of c is 12    

0xc9 =  (12 × 16¹) +  (9 × 16⁰)

= 192 + 9 = 201  

Therefore,  

The decimal equivalent of 0xc9 is 201.

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8 fluid ounces are in one serving is the required fluid ounces in one serving.

Given that,

There are 8 fluid ounces in a cup, how many fluid ounces are in one serving is to be determined.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

There are 8 fluid ounces in 1 cup and in a serving of one cup there will be 8 fluid ounces.

Thus, 8 fluid ounces are in one serving is the required fluid ounces in one serving.

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Answer:

It is called a solution.

The conversion value of pounds to kilogram as per requirement is given by 141 pounds =  ( 63.9576 ) kilograms.

One kilograms is equivalent to 2.20462 pounds.

This implies ,

⇒ 2.20462 pounds = 1 kilograms

Divide both the side by 2.20462 we get,

⇒( 2.20462 / 2.20462 ) pounds = ( 1 / 2.20462 ) kilograms

⇒  1 pounds = ( 0.4536 ) kilograms

Now, Multiply both the side by 141  we get,

⇒ 141 pounds = ( 141 × 0.4536 ) kilograms

⇒ 141 pounds =  ( 63.9576 ) kilograms

Therefore, the conversion factor of kilogram to pounds is 2.20462 this implies 141 pounds =  ( 63.9576 ) kilograms .

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Answer:

14 small floral arrangements

Explanation:

First you subtract 4 from 144

144 - 4 = 140

Second you multiply the cost of a small floral arrangement and how many you have boughten.

7 x 10 = 70

You subtract the cost of 10 medium floral arrangements and how many you have boughten.

140 - 70 = 70

Finally, you divide the cost of the small floral arrangements by the remaining money.

70 / 5 = 14

There are 5 more servings of Uma's cereal than of Cam's cereal.

From the question, we have the following parameters that can be used in our computation:

y = -1.25x + 15

For Uma;s box, we have

Initial = 12.75

Rate = 0.75

This means that

y = -0.75x + 12.75

Set y = 0 and solve for x

y = -1.25x + 15 = 0

1.25x = 15

x = 12

y = -0.75x + 12.75 = 0

0.75x = 12.75

x = 17

By comparison, we have

17 - 12 = 5

Hence, there are 5 more servings of Uma's cereal than of Cam's cereal.

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Answer:

238000

Step-by-step explanation:

hope I did this right!!

Answer:

The total profit the company would make over the course of its first 14 years of operation is approximately $2,562,841.

Step-by-step explanation:

The profit of the company increased at a constant 20% per year. We can use the formula for the future value of an investment to calculate the profit for each year, where:

FV = PV x (1 + r)^n

FV is the future value of the investment

PV is the present value of the investment

r is the annual interest rate

n is the number of years

Using this formula, we can find the profit for each year:

Year 1: $140,000

Year 2: $168,000

Year 3: $201,600

Year 4: $241,920

Year 5: $290,304

Year 6: $348,364

Year 7: $418,037

Year 8: $501,644

Year 9: $601,972

Year 10: $722,367

Year 11: $866,840

Year 12: $1,040,208

Year 13: $1,248,250

Year 14: $1,497,900

To find the total profit over the course of the first 14 years, we can simply add up the profits for each year:

Total profit = $140,000 + $168,000 + $201,600 + $241,920 + $290,304 + $348,364 + $418,037 + $501,644 + $601,972 + $722,367 + $866,840 + $1,040,208 + $1,248,250 + $1,497,900

Total profit = $2,562,841 (rounded to the nearest whole number)

There are 25 boys in the class out of a total of 40 students. The fraction of students who are boys is 5/8 and the fraction of students who are girls is 3/8.

Let's start by using the information given in the problem to determine the fraction of students who are girls in the class:

Fraction of students who are girls = 1 - Fraction of students who are boys

Fraction of students who are girls = 1 - 5/8

Fraction of students who are girls = 3/8

Now we can use the fraction of girls to find the number of boys and girls in the class:

Let the total number of students in the class be x.

Number of boys = 5/8 * x

Number of girls = 3/8 * x

We know that there are 15 girls in the class, so we can set up an equation:

3/8 * x = 15

Solving for x:

x = 15 * 8/3

x = 40

So there are 40 students in the class. Now we can find the number of boys:

Number of boys = 5/8 * x

Number of boys = 5/8 * 40

Number of boys = 25

Therefore, there are 25 boys in the class.

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Infinite Algebra 1 is a software program developed by the company Kuta Software that provides an online resource for teaching and learning algebra 1.

It offers a comprehensive collection of algebra 1 problems and exercises that cover a wide range of topics such as linear equations, systems of equations, inequalities, polynomials, factoring, and graphing.

The program includes features such as an interactive equation editor, step-by-step solutions, and the ability to generate customized worksheets and assessments.

It is designed to provide students with a self-paced and adaptive learning experience that allows them to practice and reinforce their understanding of algebraic concepts. Infinite Algebra 1 is widely used in schools and educational institutions as a tool for teaching and practicing algebra 1.

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50 milliliters (ml) is equivalent to 1.69 fluid ounces (oz). To convert milliliters to fluid ounces, you need to use the conversion factor of 0.03381402 fluid ounces per milliliter.

This means that you can multiply the number of milliliters by this conversion factor to get the equivalent volume in fluid ounces. The conversion between milliliters and fluid ounces is commonly used in the measurement of liquids, especially in cooking and baking recipes.

Some recipes may use milliliters as the standard unit of measurement, while others may use fluid ounces or other units. Being able to convert between different units of measurement is important to ensure accurate measurement and a successful outcome in the recipe.

It's worth noting that fluid ounces are a measure of volume, while ounces can also be a measure of weight. In the United States, fluid ounces are commonly used to measure the volume of liquids, while ounces are used to measure the weight of both solids and liquids.

In summary, 50 milliliters is equal to 1.69 fluid ounces, and understanding how to convert between different units of measurement is important in cooking, baking, and other applications that involve measuring liquids.

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The value of x to one decimal place in the given question is 30.33 and 14.76.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot. Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse. These are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).

We are given that;

In triangle 1

Hypotenuse= x

Perpendicular=27

Angle between base and hypotenuse= 63

In triangle 2

Hypotenuse= 18

Base= x

Angle between hypotenuse and base=35

Now in triangle 1

sin63= 27/x

0.89=27/x

x=27/0.89

x=30.33

In triangle 2

cos35=x/18

0.82=x/18

x=14.76

Therefore by trigonometric identities the answer will be 30.33 and 14.76.

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By using the long division method, the result of 19 divided by 20 is 0.95

Long division is a method of dividing two numbers using a step-by-step process of repeatedly dividing the dividend (the number being divided) by the divisor (the number you are dividing by), writing down the results of each step, and subtracting the remainder from the next dividend.

Here, 19 divided by 20

The picture shows the division process

To divide 19 by 20 using long division, you start by dividing 20 into the first digit of 19, which is 1. The result is 0 with a remainder of 1.

Then bring down the next digit, which is 9, and place it next to the remainder to make 19. You then divide 20 into 19, which gives you 0 with a remainder of 19.

Therefore, 19 divided by 20 is 0.95

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In order to create a 40% alcohol solution, we must combine 280 mL of 55% alcohol combination with 120 mL of the 5% alcohol mixture.

Alcohol can change how the brain functions and appears by interfering with the body's communication networks. In addition to altering attitude and behaviour, these disturbances can also make it more difficult to think effectively and move to coordination.

Let's designate the quantity of a mixture of 55% booze that needs to be added "x" (in mL).

We know that the finished solution must contain 40% pure alcohol by volume in order to achieve our goal of a 40% alcohol solution.

The amount of pure alcohol in the 120 mL of 5% alcohol mixture is:

0.05 * 120 = 6 mL

When we add "x" mL of the 55% alcohol mixture, we will add:

0.55x mL of pure alcohol

In the end, we want the total amount of pure alcohol in the final solution to be:

0.40 * (120 + x) mL

Now we can set up an equation:

0.55x + 6 = 0.40(120 + x)

Simplifying and solving for "x", we get:

0.55x + 6 = 48 + 0.40x

0.15x = 42

x = 280

So we need to add 280 mL of the 55% alcohol mixture to the 120 mL of 5% alcohol mixture to obtain a 40% alcohol solution.

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Answer:

Common Ratio = 5

Step-by-step explanation:

See picture below :)

Option a) Never. A correlation coefficient based on an observational study cannot be used to support a claim of cause and effect, regardless of its value or the characteristics of the scatterplot.

Correlation does not imply causation, which means that even if two variables are strongly correlated, it does not necessarily mean that one causes the other. There may be other variables or factors that are responsible for the observed correlation, and a causal relationship cannot be established from observational data alone. To establish causality, experimental studies are typically needed, where the potential cause is manipulated and the effect is measured.

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The measure of ∠8 is also 118º because angles opposite the vertex are equal.

To explain further, when two lines intersect, they create four angles. The angles that are directly across from each other are called angles opposite the vertex. These angles are always equal. So, if one angle measures 118 degrees, the angle opposite the vertex will also measure 118 degrees.

In this case, ∠11 and ∠8 are angles opposite the vertex. Therefore, if m∠11 = 118, then m∠8 = 118 as well.

So, the measure of ∠8 is 118.

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With the stated cooling rate of k = 0.012, it follows that the puddle of water would ice in the arctic cold front in roughly 97.8 minutes

The oscillation of a substance's components is measured by its temperature. When something is hot, it indicates that its components move relatively quickly on average. Despite having a high temperature, a substance's heat capacity is very low because it has a small number of light elements.

We can use the Newton's law of cooling formula to solve this problem.

[tex]T = R + ( To - R ) \times e ^{(-kt )}[/tex]

Let's assume that the initial temperature of the water is 55°F and the temperature of the surroundings is 5°F (due to the arctic cold front).

We are looking for the time it takes for the water to cool down to 32°F (the freezing point of water).

Therefore, we have:

T = 32°F

T0 = 55°F

R = 5°F

k = 0.012

Substituting these values into the formula, we get:

[tex]32 = 5 + (55 - 5) \times e^{(-0.012t)}[/tex]

Simplifying the equation, we get:

[tex]27 = 50 \times e^{(-0.012t)}[/tex]

Dividing both sides by 50, we get:

[tex]0.54 = e^{(-0.012t)}[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.54) = -0.012t

Solving for t, we get:

t = ln(0.54) / (-0.012)

t ≈ 97.8 minutes

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Answer:

The 1st option

Step-by-step explanation:

Piper's orange probability is 4/20 and Kai's pink probability is 4/20, which makes option 1 correct

to find the probability use the equation below:

(the number of favorable outcomes)/(the total number of outcomes).

outcome/total

The expression "e to the pi" refers to the mathematical constant e raised to the power of the mathematical constant pi (approximately 2.71828). (approximately 3.14159).

As, the exact value is an irrational number that cannot be expressed as a finite decimal or fraction, the value of e to the pi is approximately 23.14069.

The combination of e and pi is a well-known mathematical expression that can be seen in a variety of areas of mathematics, including calculus, number theory, and complex analysis.

Mathematicians are particularly interested in e to the pi because it is a transcendental number (a number that is not the root of any non-zero polynomial with rational coefficients).

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Systems of equations solver called Wolfram or Alphas can resolve systems of linear equations or nonlinear equations, and it can look for solutions that are only integers.

Systems of direct equations are a common and applicable subset of systems of equations. In the case of two variables, these systems can be allowed of as lines drawn in two- dimensional space. However, the system is said to be harmonious and has a result at this point of crossroad, If all lines meet to a common point. The system is said to be inconsistent else, having no results. Systems of direct equations involving further than two variables work also, having either one result, no results or horizonless results( the ultimate in the case that all element equations are original).

More general systems involving nonlinear functions are possible as well. These retain more complicated result sets involving one, zero, horizonless or any number of results, but work also to direct systems in that their results are the points satisfying all equations involved. Going further, more general systems of constraints are possible, similar as bones that involve inequalities or have conditions that certain variables be integers.

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The value of angle BAC is 60°

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex. A pyramid is formed by connecting the bases to an apex. Each edge of the base is connected to the apex, and forms the triangular face, called the lateral face.

Since the base of the pyramid is equal, the lateral lines joining the apex have equal length which will form equal triangle at both sides.

This means that if triangle BCD is equilateral, then, triangle ABC is also equilateral.

Therefore angle BAC = 180/3 = 60°

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The probability that Ron gets his first hit-by-pitch of the playoffs in his first 15 plate appearances is 52.34%

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that, in a recent baseball season, Ron was hit by pitches 22 times in 615 plate appearances during the regular season.

We need to find the probability that Ron gets his first hit-by-pitch of the playoffs in his first 15 plate appearances.

The random variable X= number of times Ron is hits by pitches in 22 plate appearances  follows, a binomial distribution.

P(X=x) = n! / (x!(n-x)!)pˣ(1-p)ˣ

where,

n = plate appearances = 22

p = probability of being hit by pitches = 15 / 615 = 3 / 123 = 1/41

x = number of successes = 1

Substitute the values :-

P(X=1) = 22! / (22-1)! × (1/41)(40/41)

= 0.5234

= 52.34%

Hence, the probability that Ron gets his first hit-by-pitch of the playoffs in his first 15 plate appearances is 52.34%

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The height of a randomly selected giraffe, the number of points scored during a basketball game, the gender of college students, the amount of rain in City Upper B during April, and the number of fish caught during a fishing tournament are all examples of discrete or continuous random variables, while the number of bald eagles in a country is not a random variable.

a. Continuous random variable

b. Discrete random variable

c. Discrete random variable

d. Continuous random variable

e. Discrete random variable

f. Not a random variable

a. The height of a randomly selected giraffe is a continuous random variable because it can take on any value within a certain range.

b. The number of points scored during a basketball game is a discrete random variable because it is a countable number.

c. The gender of college students is a discrete random variable because it is a categorical variable with two possible values.

d. The amount of rain in City Upper B during April is a continuous random variable because it can take on any value within a certain range.

e. The number of amount fish caught during a fishing tournament is a discrete random variable because it is a countable number.

f. The number of bald eagles in a country is not a random variable because it is a fixed number and not a random sample.

The height of a randomly selected giraffe, the number of points scored during a basketball game, the gender of college students, the amount of rain in City Upper B during April, and the number of fish caught during a fishing tournament are all examples of discrete or continuous random variables, while the number of bald eagles in a country is not a random variable.

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Answer:

20:00 is 8:00 pm

Step-by-step explanation:

an easy way to remember is subtract 2 from the military timing and the number in the ones value is the time.

Ex.

14:00

14 - 2= 12

So it’s 2: 00 pm

20- 2= 18

So it’s 8:00 pm

Answer:

23

Step-by-step explanation: