An urn contains 11 red balls numbered 1 through 11, 11 yellow balls numbered 1 through 11, 11 green balls numbered 1 through 11, and 11 black balls numbered 1 through 11. If 4 balls are randomly selected, find the probability of getting

(a) a flush (i.e., all balls the same color).
(b) three of a kind. (Three of a kind is 3 balls of one denomination and a fourth ball of a different denomination. e.g., 5,5,5,2)
(c) two pairs. (A pair is two balls of the same denomination. e.g., 3,3. Two pairs is something like 3,3,5,5, i.e., a pair of one denomination and a second pair of a different denomination.)

please write the steps as well!! thank you so much

Answers

Answer 1

(a) Probability of getting a flush is 0.000546.

(b) Probability of getting three of a kind is 0.00451.

(c) Probability of getting two pairs is 0.0150.

We have,

(a)

To calculate the probability of getting a flush, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of balls = 11 (red) + 11 (yellow) + 11 (green) + 11 (black) = 44 balls

The number of ways to choose 4 balls (without replacement)

= 44C4 = 44! / (4! x (44 - 4)!) = 44! / (4! x 40!)

= 44 x 43 x 42 x 41 / (4 x 3 x 2 x 1)

= 7315

The number of favorable outcomes:

There are 4 different colors of balls, so we have 4 possible flushes (all red, all yellow, all green, all black).

Probability of getting a flush = Number of favorable outcomes / Total number of outcomes = 4 / 7315 ≈ 0.000546

(b)

To calculate the probability of getting three of a kind, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).

Number of ways to choose 3 balls of the same denomination: We have 11 denominations, so we can choose 3 balls of the same denomination in 11C1 = 11 ways.

Number of ways to choose the fourth ball of a different denomination: After choosing 3 balls of the same denomination, we have 3 denominations left from which we can choose the fourth ball. So, the number of ways to choose the fourth ball = 3.

Number of favorable outcomes = Number of ways to choose 3 balls of the same denomination x Number of ways to choose the fourth ball of a different denomination

= 11 x 3

= 33

Probability of getting three of a kind = Number of favorable outcomes / Total number of outcomes = 33 / 7315 ≈ 0.00451

(c)

To calculate the probability of getting two pairs, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of ways to choose 4 balls = 44C4 = 7315 (as calculated in part (a)).

Number of ways to choose the first pair: We have 11 denominations, so we can choose the first pair in 11C1 = 11 ways.

Number of ways to choose the second pair: After choosing the first pair, we have 10 denominations left from which we can choose the second pair. So, the number of ways to choose the second pair = 10.

Number of favorable outcomes

= Number of ways to choose the first pair x Number of ways to choose the second pair

= 11 x 10

= 110

Probability of getting two pairs = Number of favorable outcomes / Total number of outcomes = 110 / 7315 ≈ 0.0150

Thus,

(a) Probability of getting a flush = 4/7315 ≈ 0.000546

(b) Probability of getting three of a kind = 33/7315 ≈ 0.00451

(c) Probability of getting two pairs = 110/7315 ≈ 0.0150

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Related Questions

Paula downloaded 16 songs at a total cost of $32.00. What is the unit rate, in dollars, for the songs?

Answers

Answer: Paula spent $2 for each song.

Step-by-step explanation: For this question, we have to find the unit rate that Paula paid per song. As we're already given the amount of songs downloaded and the total cost, all that we really have to do is divide!

Because we want to know the amount of money spent on one song, we divide the amount of money spent by the amount of songs purchased. This gives us 32/16 = 2.

Paula spent $2 (don't forget the units!) for each song. This is out unit rate. Hope this helps!

Please Help!!

Simplify -|-7+4|

Answers

Answer: 7-4

Step-by-step explanation:

So basically multiply (-1) to -7 and 4

-7(-1)=7 4(-1)=-4

then, 7-4

The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?
answer choices
0.03
±
2.326
(
0.03
)
(
0.97
)
500
0.03±2.326 500
(0.03)(0.97)


0.15
±
2.326
(
0.15
)
(
0.85
)
500
0.15±2.326 500
(0.15)(0.85)


0.03
±
2.576
(
0.03
)
(
0.97
)
500
0.03±2.576 500
(0.03)(0.97)


0.15
±
2.576
(
0.15
)
(
0.85
)
500
0.15±2.576 500
(0.15)(0.85)

Answers

The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

You can find the standard mean error and then use that to find the confidence interval limits.

The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by

Lower limit = 0.0104

Upper limit = 0.0496

The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

To find the confidence interval for proportions

Let the sample size be n

Let the interested quantities in the sample be present x times

Let the confidence level be of p%.

Then the level of significance is given by

The standard mean error is calculated by:

Then the confidence interval limits can be found by

Using the above formula for finding the confidence interval

We have n = 500, x = 15 and

Finding the standard mean error:

From the z tables, we get z = 2.5758

Thus, the confidence interval is obtained by

Lower limit = 0.0104

Upper limit = 0.0496

Thus,

The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by

Lower limit = 0.0104

Upper limit = 0.0496

Therefore, The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

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Unit price of 3 scarves totaling 26.25

Answers

Answer:

Step-by-step explanation:

26.25 divided by three = 8.75

HELP ME PLEASE I WILL GIVE BRAINLIEST AND 10 POINTS!! PLS EXPLAIN

Answers

DE and FG have the same slope, so both the sides are parallel. The opposite side of the quadrilateral are equal. Because, the opposite side of the quadrilateral are equal and parallel, DEFG is a parallelogram.

What is a parallelogram?

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

DE and FG have the same slope, so both the sides are parallel.

Since, DE = FG, the opposite side of the quadrilateral are equal.

Because, the opposite side of the quadrilateral are equal and parallel, DEFG is a parallelogram.

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whats the answer with all the work shown?

Answers

The answer to the work shown is x = 8.

The law of indices.

The law of indices are laws that has to be applied to expressions involving powers or fractions. These laws have individual application.

Considering the given question, we have;

16^(3x - 6) = 64^(x + 4)

It can be deduced that, the factors of;

16 = 4 x 4

   = 4^2

and

64 = 4 x 4 x 4

    = 4^3

So that;

4^2(3x - 6) = 4^3(x + 4)

Divide through by 4 to have;

2(3x - 6) = 3(x + 4)

6x - 12 = 3x + 12

collect like terms,

6x - 3x = 12 + 12

6x = 24

x = 24/6

  = 8

The answer to the work shown in the question is: x = 8

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-5(2x+14)=-2(x+63) x=6

Answers

The value of the variable, x is 7

What are algebraic expressions?

Algebraic expressions are defined as expressions that are composed of terms, coefficients, variables, constants and factors.

These mathematical operations are also made up of arithmetic operations. These operations includes;

AdditionSubtractionMultiplicationFloor divisionBracketParenthesesDivision

From the information given, we have;

-5(2x+14)=-2(x+63)

expand the bracket

-10x -70 = -2x - 126

Now, collect like terms

-10x + 2x = -126 + 70

Add or subtract the terms

-8x = -56

Make 'x'' the subject

x = 7

Hence, the value is 7

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yvette buys sandwiches for $22from a restaurant using its online ordering system her bill includes the food purchase price as well as 8.5% sales tax she choose to add an 18%tip for delivery driver to the bill when she completes the online order.to the nearest whole percent what percent did she pay over the price of the sandwiches

Answers

To the nearest whole percent, the percentage Yvette paid over the price of the sandwiches is 27%.

How is the percentage determined?

The percentage represents a proportion of a whole value.

The percentage is determined as the quotient of the difference (increase or decrease) and the initial value, multiplied by 100.

The purchase price of restaurant sandwiches = $22

Sales tax = 8.5%

= $1.87 ($22 x 8.5%)

Additional tip for delivery = 18%

= $3.96 ($22 x 18%)

Total bill = $27.83 ($22 + $1.87 + $3.96)

Difference between the total bill and the purchase price = $5.83 ($27.83 - $22)

Percent difference = 26.5% ($5.83/$22 x 100)

= 27%

Thus, Yvette paid 27% above the price of the sandwiches in form of sales tax and tips.

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Split 500m in the ratio 1:4

Answers

If 500m is split in the ratio of 1:4, then the first part would equal 125m and the second part would equal 375m.

What is the  ratio ?

The ratio is a comparison of two or more related values or amounts. It is expressed as a fraction or a decimal number, and is used to compare the relative size of two or more values. Ratios can be used to compare numbers, objects, people, or other elements in order to study their relative size or relationships.

If 500m is split in the ratio of 1:4, then the first part would equal 125m and the second part would equal 375m. This is because the ratio of 1:4 can be simplified to 1/5 and 1/5 of 500m is 125m. Therefore, the first part is 125m and the second part is 375m.

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The camp director is putting 85 sack lunches

Answers

The meaning of the situation involving the camp director and the sack lunches, is D. The number of lunches left over after packing the boxes.

What does the remainder show ?

The remainder in this instance, shows the number of lunches that the camp director will not be able to fit in boxes and so will be left over after the boxes have been packed.

There are 85 sack lunches and yet only 3 lunches can go into a single box. The number of boxes would be:

= 85 / 10

= 10 boxes remainder 5 lunches

10 boxes will be filled with lunch sacks and 5 lunches will be leftover.

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The full question is:

The camp director is putting 85 sack lunches in boxes for a picnic. She can fit 8 lunches in each box. She does the division problem shown to find out how many boxes she will need. 85 divided 8 = 10 remainder 5

What is the meaning of the remainder in this situation?

A. The number of extra boxes needed.

B. The number of extra lunches needed.

C. The number of boxes left over after packing the lunches.

D. The number of lunches left over after packing the boxes.

Evaluate the expression when x=6. X^2-9x-7

Answers

The value of the expression x² - 9x - 7 when x = 6 is -25.

What is Quadratic Equation?

Quadratic equations are second degree polynomial equations which are of the form ax² + bx + c = 0, where a, b and c are real numbers and x is the variable with the highest degree of 2.

Given the quadratic expression,

x² - 9x - 7

We have to find the value of the expression when x = 6.

Substitute x = 6, we get,

6² - (9 × 6) - 7 = 36 - 54 - 7

                       = -25

Hence the value of the given expression when the value of x = 6 is -25.

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Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy created all the students in your math class for a week, how many meters could the truck drive?

Answers

For a combined energy of 15 students in a week, a truck will drive for 914.24 meters subjective to the number of students.

How to find the meter?

To find the meters a truck will drive when the energy of a class is combined in one week;

1 day per person = 32 kilometers

One week = 7 days

Assuming a math class with 15 students for 7 days = (15 students x 7 days)

= 1/(15 x 7) x 32

= 1/35 x 32 = 0.02857 x 32 = 0.91424 kilometers

Changing 0.91424 kilometers to meter = 0.91424 x 1000 = 914.24 meters. It will take 15 students 914.24 meters truck drive in one week.

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1. A boat is 15 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 65° angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Round your answer to the nearest tenth of a foot. Show your work.

Answers

The person is 16. 55ft from the boat

How to determine the distance

From the information given, we have that;

The boat is 15ft away from the shoreline65° angle is formed between the closest point to the boat

To determine the distance between the boat and the person, let's use the trigonometric identity, sine

sine θ = opposite side/hypotenuse side

Given that;

Opposite side = 15ftHypotenuse side = dθ = 65 degree

Substitute the value

sin 65 = 15/d

cross multiply

d = 15/sin 65

Find the value

d = 15/0.9063

divide the values

d = 16. 56 ft

Hence, the value is 16.56ft

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help …………… me please

Answers

The value of x is 10 the answer being ten is because the smaller triangle is half the size of the bigger one.

What is a formula for a triangle?

To find a triangle's area, use the formula area = 1/2 * base * height. Choose a side to use for the base, and find the height of the triangle from that base. Then, plug in the measurements you have for the base and height into the formulaThe basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h); where 'b' is the base and 'h' is the height of the triangle. However, there are other formulas that are used to find the area of a triangle which depend upon the type of triangle and the known dimensions.The area of a triangle is the space enclosed within the three sides of a triangle. It is calculated with the help of various formulas depending on the type of triangle and is expressed in square units like, cm2, inches2, and so on.

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Given the function f'(x)=x^{5}-5x^{3}, determine all intervals on which f is decreasing.

Answers

The function f'(x) is decreasing on the interval (-√5, 0) and (0, √5)

What is a function?

A function is a mathematical equation that shows the relationship between two variables.

How to find the interval on which the function is increasing?

Givenj the function f'(x) = x⁵ - 5x³, to find the points at which the function is increasing, we find its critical points by equating it to zero.

So, f'(x) = x⁵ - 5x³

x⁵ - 5x³ = 0

x³(x² - 5) = 0

⇒ x³ = 0 and x² - 5 = 0

⇒ x = 0 and x² = 5

⇒ x = 0 and x = ±√5

To determine the points at which f'(x) is decreasing, we differentiate f'(x) with respect to x and substitute the values of x into it.

So, we have

f'(x) = x⁵ - 5x³

df'(x)/dx = d(x⁵ - 5x³)/dx

f"(x) = 5x⁴ - 15x²

So, f'(x) is decreasing when f"(x) > 0.

So, substituting x = 0 into the equation, we have that

f"(x) = 5x⁴ - 15x²

f"(x) = 0⁴ - 15(0)²

= 0 - 0

= 0

Since f"(x) = 0. This is a point of inflection

Substituting x = √5 into the equation, we have that

f"(x) = 5x⁴ - 15x²

f"(x) = 5(√5)⁴ - 15(√5)²

= 5 (25) - 15 (5)

= 125 - 75

= 50

Since f"(x) = 50 > 0, f'(x) is decreasing

Substituting x = -√5 into the equation, we have that

f"(x) = 5x⁴ - 15x²

f"(x) = 5(-√5)⁴ - 15(-√5)²

= 5 (25) - 15 (5)

= 125 - 75

= 50

Since f"(x) = 50 > 0, f'(x) is decreasing

So, f'(x) is decreasing on the interval (-√5, 0) and (0, √5)

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For the following function f(x)=x-3/5 Find f^-1(x)

Answers

Answer:

the having of the record is that

Examine the straight line depreciation O I/so 1 A value 189 art mintiw graph for a car. 9m 10 Doled 1 35,000 a. At what price was the car purchased? b. After how many years does the car totally depreciate? c. Write the equation of the straight line depreciation graph shown.

Answers

a. The y-intercept of the graph is 35,000, which represents the original purchase price of the car. Therefore, the car was purchased for $35,000.

b. We can see from the graph that the car's value becomes 0 after 9 years. Therefore, the car totally depreciates after 9 years.

c. The equation of a straight line can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope of the graph is the rate of depreciation, which is -4000. The y-intercept is the original price of the car, 35000.

So the equation of the straight line depreciation graph is: y = -4000x + 35000

This equation represents the value of the car, where y is the value of the car (in dollars) x is the number of years since the car was purchased and -4000 is the rate of depreciation and 35000 is the original price of the car.

HELPPPP
Which of the following graphs represents a function?
A Th graph showing a circle intercepting the x-axis at 5 and -5 and the y-axis also at 5 and -5.
B The graph shows a parabola open to the top and touching the base at (0, 0).
C The graph shows a s- shaped curved line starting from (10, 2) and taking the curve at points (0, 1), (-1, 0), (0, -1), and (0, -3) and ending at (-10, -4).
D The graph shows a parabola open to the left and touching the base at (0, 0).

Answers

The graph that represents a function is:

The graph shows a parabola open to the top and touching the base at

(0, 0).

The graph shows a parabola open to the left and touching the base at

(0, 0).

Options B and D is the correct answer.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A function can have many-to-one but not one-to-many.

A

The graph shows a circle intercepting the x-axis at 5 and -5 and the y-axis also at 5 and -5.

This means,

If the center of the circle is (h, k).

The coordinates of the circle are:

(5, k), (-5, k), (h, 5), and (h, -5)

(h, 5) and (h, -5) indicate one-to-many.

This is not a function.

B.

The graph shows a parabola open to the top and touching the base at

(0, 0).

The equation of the parabola is y = x².

For x = 1, y = 1

For x= -1, y = 1

This indicates many-to-one only.

This is a function.

C.

The graph shows an s-shaped curved line starting from (10, 2) and taking the curve at points (0, 1), (-1, 0), (0, -1), and (0, -3) and ending at (-10, -4).

The points (0, 1), (0, -1), and (0, -3) indicate one-to-many.

This is not a function.

D

The graph shows a parabola open to the left and touching the base at

(0, 0).

The equation of the parabola is y² = 4px.

This equation is a function.

Thus,

The graph that represents a function is a parabola open to the top and a parabola open to the left.

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The square below represents one whole.
What percent is represented by the shaded area?

Answers

Answer:

Step-by-step explanation:

77/100 or 0.77

Which table shows a proportional relationship between x and y? Responses x 3 9 10 15 y 1 3 4 5x 3 9 10 15 y 1 3 4 5 , x 2 3 5 6 y 3 4 7 9x 2 3 5 6 y 3 4 7 9 , x 1 5 8 10 y 15 75 120 150x 1 5 8 10 y 15 75 120 150 , x 4 6 8 10 y 6 8 10 12 PLEASE I NEED HELP I NEED HELP NOW!!!!!!!!!

Answers

The table that shows a proportional relationship between x and y is:

C. x 1 5 8 10 y 15 75 120 150

What is a proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of that constant.

If every pair of data values is related in the same way, by multiplying by a factor, then the relationship is proportional. A proportional relationship can be identified by looking at data, an equation, or a graph.

In this case, the constant based on the information will be:

= 15 / 1

= 15

Also when x is 5, y will be:

= 5 × 15.

= 75..

The correct option is C.

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1) Rick had to borrow $35,000 to buy a brand new
car. He has to pay 10% interest for 5 years. How
much interest will he have to pay?
80

Answers

On solving the provided question we can say that the total interest he pay in 5 year is = $17500.

How much is interest?

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money. The basic interest formula is as follows: Interest is equal to P, R, and T. P is the principal sum (the beginning balance). Interest rate, R (usually per year, expressed as a decimal). T = Number of intervals of time (generally one-year time periods).

Money required to borrow new car is $35,000.

and Rick pay 10% interest per year

so, interest he pay in one year = $35000 x 10% = $3500

total interest he pay in 5 year is = $17500

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What is t equal to 30+6t=11t

Answers

If 30+6t=11t then the value of  t is: 6

How to solve the given equation?

This is a simple algebraic equation. To solve for t, we can start by isolating t on one side of the equation.

The equation is 30 + 6t = 11t

First we can subtract 11t from both sides:

30 + 6t - 11t = 11t - 11t

This gives:

30 - 5t = 0

Next, we can add 5t to both sides:

30 - 5t + 5t = 0 + 5t

This gives:

30 = 5t

Finally, we can divide both sides by 5:

30 / 5 = 5t / 5

This gives:

t = 6

So, t is equal to 6.

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17. Which expression is a factor of 6x² + 7x-5?
A 3x + 5
B 2x + 1
C 6x +1
D x + 5

Answers

Answer:

A

Step-by-step explanation:

6x² + 7x - 5

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 5 = - 30 and sum = + 7

the factors are - 3 and + 10

use these factors to split the x- term

6x² - 3x + 10x - 5 ( factor the first/second and third/fourth terms )

= 3x(2x - 1) + 5(2x - 1) ← factor out (2x - 1) from each term

= (2x - 1)(3x + 5) ← in factored form

with 3x + 5 being a factor

Convert each rate using dimensional analysis 44yds/s=?mi/h

Answers

Using dimensional analysis we have converted 44 yards/sec = 90 miles/hour.

What is dimensional analysis?

Dimensional analysis is the study of how dimensions and units of measurement affect the relationship between physical quantities.

Dimensional analysis is crucial because it maintains the consistency of the units, which facilitates accurate mathematical computation.

As we use conversion factors to obtain the same units, dimensional analysis is also known as the Factor Label Method or Unit Factor Method.

We know that 1 yards/sec = 2.04545 miles/hour

Here given that 44yds/s = ? miles/hour

Lets solve

1 yards/sec = 2.04545 miles/hour

44 yards/sec = 44 × 2.04545 miles/hour

44 yards/sec = 89.9998 miles/hour

44 yards/sec = 90 miles/hour

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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.

Answers

Answer: There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9). ✅

PLEASEEEE GIVE BRANLIEST

Step-by-step explanation:

There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9). One statement that could be true for g is:

g(x) = 2x + 8

This function has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45. It also satisfies the values of g(0) = -2 and g(-9) = 6.

It's important to note that this is only one possible function that satisfies the given information and there are many other functions that could also work such as:

g(x) = 3x -2

g(x) = -2x +10

g(x) = x+5

So the statement that could be true for g is that "There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9)."

*Keep in mind you didn't specify a specifc statement to verify false or true*

is either x = 6 or x = 4 a solution to 33 - x = 27?
A: x = 6 is a solution, but x = 4 is not.
B: x = 4 is a solution, but x = 6 is not.
C: Neither are solutions
D: they are both solutions

Answers

Answer: A: x=6

Step-by-step explanation: If we plug in 6 for X in the equation we get

33 - 6. 33 - 6 does equal 27.

Now to make sure X = 4 is not an answer, we plug that in too. 33 - 4.

33 - 4 = 29, so this is not the answer.

Answer:

A: x = 6 is a solution, but x = 4 is not.

Step-by-step explanation:

33-x=27

-33    -33

-x=-6

-x/   -x/

x=6

Jason makes 8 gallons of punch he serves 1 pint containers now he has 12 pints of punch how many pints of punch did jason serve

Answers

The pints of punch that Jason served were 52 pints.

How many pints are in a gallon?

The number of pints that make up a gallon is 8 pints. So, in 8 gallons, we can expect that there will be 64 pints. Now, we are told that Jason served 1 pint container and now he has 12 points remaining, what we are to do is to subtract the remaining pints from the original pints that he had.

Since the original was 64 pints, removing 12 pints will amount to 52 pints. This means that 52 pints of punch were served in the 1-pint containers.

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For the function below, write the differential. f(x) = ln(1 + x2) dy = Calculate dy for the given values of x and dx. x = 2 and dx = 0.2 dy = How accurate is dy in approximating ?y (i.e., what is their difference) to the nearest thousandth?

Answers

The dy for the given values of x and dx. x = 2 and dx = 0.2 dy is 0.16

The given function f(x) = ln(1 + x2) dy

In differentiation, we have a formula where f(x) is calculated:

d/dx ln=1/u.du/dx

Apply this formula for the given function:

f(x) = ln(1 + x2) dy

f'(x)= 1/x²+1*2x dx

f'(x)=2x/x²+1 dx

To calculate the dy for the given values of x and dx. x = 2 and dx = 0.2 dy

substitute these values into f'(x) we get:

f'(x)=2x/x²+1 dx

f'(x)=2(2)/2²+1 (0.2)

f'(x)=4/5(0.2)

f'(x)=0.16

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hi can someone please help with this i’m confused by the graph. helpppp

Answers

Therefore ,  solving the provided question, we can say that the, probability P( 24 period hour) = 5/24

What is probability?

The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number from 0 and 1, in which about 0 represents how likely the event should be to occur and 1 represents certainty. A probability is a quantitative illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrence in a whole set all equally likely options that lead to a specific occurrence.

Here,

=> E1 = stops at 5 clock

=>  E2 = start at 24 hours

=> P( 24 period hour) = 5/24

=> the, probability P( 24 period hour) = 5/24

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What is the product of 6\sqrt{8}6 8 ​ and 3\sqrt{24}3 24 ​ in simplest radical form?

Answers

The product of 6√8 and 3√24 in simplest radical form is 144√3

How to determine the product

We can solve this problem by using the distributive property and simplifying the radicals.

6√8 * 3√24 = (6 * 3) * √(8 * 24)

Evaluate the products

6√8 * 3√24 = 18 * √(8 * 24)

Evaluate the products of radicals

6√8 * 3√24 = 18 * √(192)

Simplify the radical

6√8 * 3√24 = 18 * 4 * √12

So, we have

6√8 * 3√24 = 72√12

Now to simplify the radical, we can divide the radicand by the greatest perfect square that is a factor of it.

So, we have

72√12 =  72 * 2 * √3

= 144√3

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