A swimming pool is shaped like a right rectangular prism with length 20 feet, height 8 feet, and width 15 feet. If the pool's water line is one foot below the top of the pool, find the volume of water in the pool.

The probability of drawing two orange balls, given that at least one ball is orange, is 1/5.

There are a total of 6 possible outcomes when selecting 2 balls from the urn without replacement: (O,O), (O,B), (B,O), (B,B), (O,B), (B,O).

The event that at least one of the balls selected is orange corresponds to the outcomes (O,O), (O,B), and (B,O). The probability of this event is the sum of the probabilities of the individual outcomes:

P(at least one orange) = P(O,O) + P(O,B) + P(B,O)

To calculate the individual probabilities, we can use the formula for the number of combinations of n items taken k at a time:

C(n,k) = n! / (k! (n-k)!).

The probability of each outcome is the number of ways it can occur divided by the total number of possible outcomes:

P(O,O) = C(2,2) / C(4,2)

= 2! / (2! (2!)) / (4! / (2! (2!)))

= 1/6

P(O,B) = C(2,1) * C(2,1) / C(4,2)

= 2 * 2! / (1! (2!)) / (4! / (2! (2!)))

= 2/6

P(B,O) = P(O,B) = 2/6

So,

P(at least one orange) = 1/6 + 2/6 + 2/6

=> 5/6

And the probability that both balls are orange is:

P(both orange) = P(O,O) = 1/6.

So, the probability of drawing two orange balls, given that at least one ball is orange, is 1/5.

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The length of AB cannot be determined with only the information given. To find AB, we need additional information such as the length of BC or the angle between AB and AC.

Answer:

This problem is unsolvable because their is no form of "b" so not enough info.

Area of the backyard is 9000 sq.ft. Area of the flower garden is 60 sq.ft. So the area of backyard planted with grass will be 8940 sq.ft.

Here the backyard is in rectangular shape and the flower garden is a parallelogram.

Backyard has a length  of 120ft and a width of 75ft. Area of a rectangle is given by the equation

Area of rectangle = length× width = 120×75 =9000 sq.ft

Area of backyard = 9000 sq.ft

The flower garden is a parallelogram with base 12 ft and height 5 ft.

Area of a parallelogram =  Base× height = 12×5 = 60 sq.ft

Area of flower garden = 60 sq.ft

All the remaining area is planted with grass. So, the area of the portion of backyard planted with grass = Total area of backyard- area of the flower garden.

Area planted with grass = 9000-60 = 8940 sq.ft

So the area of the backyard is 9000 sq.ft, area of the flower garden is 60 sq.ft and area planted with grass is 8940 sq.ft.

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Full question is given as image.

The solution is, 128 combinations.

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

here, we have,

We are told in the question that a frozen yogurt shop has:

8 flavors of frozen yogurt

2 kinds of syrup

8 toppings.

The combinations that can be made with one flavor of frozen yogurt, one syrup, and one topping is calculated as:

8 × 2 × 8

= 128 combinations

Therefore, the combinations that can be made with one flavor of frozen yogurt, one syrup, and one topping is 128 combinations.

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The average skid mark for the car is 91.7 feet. Option D

The average skid mark can be calculated by the formula -

S = ✓30Dfn,

where;

s is speed of car,

D is skid distance,

f is drag factor and

n is braking efficiency.

Using the values in formula to calculate the value of D.

55 = ✓30 × D × 1.1 × 1

Performing multiplication on Right Hand Side of the equation

55 = ✓D × 33

Taking square on both sides of the equation

D = 55² ÷ 33

Taking square on numerator on Right Hand Side of the equation

D = 3025 ÷ 33

Performing division on Right Hand Side of the equation

D = 98.45 feet

Rounding to the nearest tenth of a foot

D = 91.7 feet

Hence, the average skid mark is 91.7 feet.

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Answer:

62 degrees

Step-by-step explanation:

To find the answer simply add both measures of angles 1 and 2 (29 + 33) to get 62 degrees.

To select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys , there are 1260 ways.

To find the number of ways to select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys, you can use the formula for combinations:

C(n, k) = n! / (k! * (n - k)!)

where n is the total number of items (9 girls and 5 boys), k is the number of items to be selected (3 boys and 4 girls), and ! represents the factorial function.

So, the number of ways to select 3 boys out of 5 boys is:

C(5, 3) = 5! / (3! * (5 - 3)!) = 5! / (3! * 2!) = 10

And the number of ways to select 4 girls out of 9 girls is:

C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = 126

Finally, the number of ways to select a team of 7 members consisting of 3 boys and 4 girls is:

C(14, 7) = 10 * 126 = 1260

So, there are 1260 ways to select a 7-member team consisting of 3 boys and 4 girls out of 9 girls and 5 boys.

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This indicates that the population variance is, with 99% confidence, between 8.53 and 9.35.

The chi-square distribution can be used to compute the population variance's 99% confidence interval estimate based on a sample standard deviation of 12 and a sample size of 10.

The confidence interval's formula is:

(s² / X²) * (n - 1) < σ² < (s² / X²) * n

Where X² is the upper percentile of the chi-square distribution with n-1 degrees of freedom, n is the sample size (10), and s² is the sample variance  (12² = 144).

Using a chi-square table with 9 degrees of freedom and a 99% level of confidence, we can determine that  X² = 16.919 As a result,

the population variance's confidence interval is:

(144 / 16.919) * (10 - 1) < σ² < (144 / 16.919) * 10

(8.53 < σ² < 9.35)

This indicates that the population variance is, with 99% confidence, between 8.53 and 9.35.

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On solving the provided question, we can say that the speed of the boat in still water is 11 miles per hour, and equation  the speed of the current is 9 miles per hour.

A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.

distance = rate × time

to set up two equations using the given information:

Equation 1: 140 = (b + c) × 7 (downstream trip)

Equation 2: 140 = (b - c) × 70 (upstream trip)

b + c = 20 (dividing both sides by 7)

b - c = 2 (dividing both sides by 70)

Now we have two equations with two variables. We can solve for "b" and "c" by adding the two equations together:

[tex](b + c) + (b - c) = 20 + 2\\2b = 22\\b = 11\\[/tex]

So the speed of the boat in still water is 11 miles per hour.

We can then use either Equation 1 or Equation 2 to solve for the speed of the current. Let's use Equation 1:

[tex]140 = (11 + c) × 7\\20 = 11 + c\\c = 9[/tex]

So the speed of the current is 9 miles per hour.

Therefore, the speed of the boat in still water is 11 miles per hour, and the speed of the current is 9 miles per hour.

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Answer:

(2) whole numbers

Step-by-step explanation:

Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.

The three ways a linear function (a straight line) and a quadratic function (a parabola) can intersect are:

     /

    /

   /

  /

 /

/

/____________

Two intersections

\          /

\        /

 \      /

  \    /

   \  /

    \/

/____________

No intersection

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The ANOVA for each regression model shows that the overall F-test is significant, which means that at least one of the regression parameters is significant. This indicates that the regression model is useful for predicting the outcome.

The ANOVA for each regression model was conducted to determine whether the overall model is significant. To do this, an F-test was used to compare the sum of squares (SS) of the regression model versus the residual error (RSS). If the F-test is significant, then at least one of the regression parameters is significant and the model is useful for predicting the outcome. In both cases, the F-test was significant which indicates that the regression model is useful for predicting the outcome. The ANOVA also provides information about the individual parameters, such as the p-value associated with each parameter, which can be used to determine which parameters are significant. Overall, this indicates that the regression model is a useful tool for predicting the outcome and can be used to make informed decisions.

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Part 1 is given in the attached image.

Part 2:

The linear equation is y = 3x

The graph of the equation is given in the attached image.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

Randy needs to buy school supplies.

He needs a headset that costs $30.00.

He also needs notebooks that cost $3.00 each.

Part 1 is given in the attached image.

Part 2:

The linear equation is y = 3x

The graph of the equation is given in the attached image.

Hence, all the solution of part 1 and 2 is given above.

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The solution to the equation does not exist

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

2x - 3 = 0

2x - 3 = 3

Also from the question, we understand that the graph is given as

3 = 0

The above equation is false, and cannot be represented on a graph

This is so because 0 and 3 do not have the same value

Similarly, we have 2x - 3 = 0 and 2x - 3 = 3

By substitution, the equations becomes

0 = 3

Hence, the equation has no solution

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Complete question

Graph of 3=0

Solve the equation 2x - 3 = 0 and 2x - 3 = 3 graphically

Answer:

5.76106287

Step-by-step explanation:

Answer: 5.76106287488

Step-by-step explanation:

Based on the information, it can be inferred that the correct fraction is 8/8 - 3/8 (option B).

To select the correct fraction we must perform the following procedure:

Analyze the fraction that we have as reference. Once we know its elements (numerator and denominator) we can identify any fracture that is related to it.

We analyze the options and identify the one that is related to the reference fraction. In this case the correct fraction would be 8/8 - 3/8 because we leave the same denominator and do the subtraction with the numerators.

So it would be 8 - 3 = 5. So the correct fraction is option B.

Note: This question is incomplete. Here is the complete information:

Question: Which expression has a value of 8/8 - 3/8?

Options:

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The order from smallest to largest is 1.5, 4, 13.

To compare numbers using a horizontal number line, simply need to place each number on the line and see which one is farther to the right (greater) or to the left (less).

Here's how to compare 13, 4 and 1.5 on a number line:

So, in this case, 1.5 is to the left of 4, which is to the left of 13. Therefore, the order from smallest to largest is 1.5, 4, 13.

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Algebraic expression that shows the amount Ms. Jackson will pay for the small truck for the week is $340 + 0.30m.

An algebraic expression does not contain an equal sign and cannot be solved like an equation, but it can be simplified or manipulated using algebraic rules. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.

The amount that Ms. Jackson will pay for the small truck for the week can be expressed as the weekly fee plus the cost of driving the truck for the number of miles driven.

Let's call the weekly fee "wf" and the cost per mile driven "cpm". Then, the total amount that Ms. Jackson will pay can be expressed as:

wf + cpm × m

From the table, the weekly fee for a small truck is $340 and the cost per mile driven is $0.30. So, the algebraic expression for the total amount that Ms. Jackson will pay for a small truck for the week can be expressed as:

wf + cpm × m = $340 + $0.30 × m = $340 + 0.30m

where m is the number of miles Ms. Jackson drives during the week.

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The complete question is :

Ms. Jackson wants to rent a small truck for a week. It will cost the weekly fee plus $0.30 per mile driven. Let m = the number of miles Ms. Jackson drives during the week. Use this information and the table to answer 13-15.

Vehicle               Week         Day

Van                     $320           $90

Small Truck         $340           $100

Medium Truck    $360            $110

Large Truck        $385             $120

Oversized Truck $415             $130

13a. Write an algebraic expression that shows the amount Ms. Jackson will pay for the small truck for the week.

The initial value is 20000 and it is a growth function

The rate is 14%

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

v(t) = 20000(1.14)^t

A function represented as

v(t) =ab^t has teh following features

Initial value = a

Growth/Decay factor = b

This means that

Initial value = 20000

Also, we have

Growth factor = 1.14

This means that

Percentage rate = 1.14 - 1

Percentage rate = .14

So, we have

Percentage rate = 14%

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Answer:

62°

Step-by-step explanation:

a = 90° -28° the answer is 62°

Answer:

62 degrees

Step-by-step explanation:

we say 90 degrees-28 degrees=62 degrees

Answer:

see below

Step-by-step explanation:

the figure shows that GF = FH

so 5x+26 = ∠H

because sum of all angles in a triangle =180 (memorize this)

so then you have 2*(5x+26) + 3x+37 =180

solve for x

10x + 52 +3x +37 =180

13x = 91

x=7

so 5x+26 = 35+26 = 61

3x+37 =21+37 =58

Answer: this would be how the numbers should look on the x axis so you can reflect them on the x axis:)

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the values of x that correspond to y-values of -2, 0, 4, 6, given the relation y = -2/3x +2.

One way to find the x-values is to read them from a graph of the equation. That is what we have done in the first attachment. This tells us the table is ...

  [tex]\begin{array}{|c|c|}\cline{1-2}x&y\\\cline{1-2}6&-2\\3&0\\-3&4\\-6&6\\\cline{1-2}\end{array}[/tex]

You can solve the equation for x, then use that with the given y-values.

  y = -2/3x +2

  y -2 = -2/3x . . . . . subtract 2

  -3/2(y -2) = x . . . . . multiply by -3/2

Using the given y-values, we find the corresponding x-values to be ...

  -3/2({-2, 0, 4, 6} -2) = -3/2{-4, -2, 2, 4} = -3{-2, -1, 1, 2} = {6, 3, -3, -6}

These are the values that we obtained from the graph.

  For y = {-2, 0, 4, 6}, x = {6, 3, -3, -6}.

__

Additional comment

A graphing calculator or spreadsheet can process a list of numbers for you, so you don't have to enter the same computation over and over.

The next two terms of the sequence are 16 and 25.

Square root of a number is the value such that the value when multiplied to itself two times gives the original number.

It is denoted by the symbol √.

For example, square root of 16 is 4 since 4 × 4 = 16

Given the sequence 1, 4, 9.

We have to find the next two terms of the sequence.

1 = 1²

4 = 2²

9 = 3²

The next two terms will be the square of 4 and 5.

4² = 16

5² = 25

Hence the two terms next to the sequence are 16 and 25.

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The car's value will exceed $10,000 during the interval of 6.97 years to  12.97 years.

To find the interval during which the car's value exceeds $10,000, we can use the following formula to calculate the value of the car after n years:

Value = $20,000 × [tex](1 - 0.15)^n[/tex]

We want to find the number of years, n, such that Value > $10,000. Rearranging the equation, we get:

n = (log(Value / $20,000)) / (log(1 - 0.15))

Substituting Value = $10,000, we find that n = approximately 6.97 years.

So, the car's value will exceed $10,000 from approximately 6.97 years after it was purchased until about 12.97 years after it was purchased.

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Step-by-step explanation:

let's say x stands for years.

FFR(x) is a function that calculates the number of fast food restaurant after x years.

FFR(x) = 2x + 13

they have 13 fast food restaurants right now (x = 0).

in 4 years (x = 4) they think they will have 21. that is 8 more than now. that means 2 more per year (2×4 = 8). therefore the factor 2 for every year (x).

FFR(4) = 2×4 + 13 = 8 + 13 = 21

If the player wants to emphasize that his team generally scored a lot of points, it might be best to report the median.

The median and the mean are both measures of center in statistics. They help to describe where the center of the data set is located, but they are not the same thing.

The mean is calculated by adding up all the values in the data set and then dividing by the number of values. It gives a good overall picture of the average of the data set, but it is sensitive to outliers or extreme values.

On the other hand, the median is the middle value in a data set when the values are arranged in order.

To find the median, you must first arrange the values in order and then identify the middle value. If there are an even number of values, the median is the average of the two middle values.

The median is not as sensitive to outliers or extreme values as the mean, so it gives a more accurate picture of the center of the data set when there are outliers or extreme values.

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Bashir would need to invest $18,900, to the nearest hundred dollars, for the value of the account to reach $29,000 in 19 years.

Investment refers to the allocation of money or capital to an asset or a project with the expectation of generating a profit or earning an income. Investment can take many forms, including the purchase of stocks, bonds, real estate, or other financial products, as well as the financing of a business or a startup.

Investing involves risk, as the potential return on investment is not guaranteed. Investors must carefully evaluate the potential risks and returns of each investment opportunity before deciding where to allocate their capital.

Investment can be divided into two main categories: short-term and long-term. Short-term investments, such as savings accounts and money market funds, offer relatively low returns but also have lower risk. Long-term investments, such as stocks and real estate, have higher potential returns but also higher risk.

To find the amount that Bashir needs to invest to reach $29,000 in 19 years, we can use the formula for the future value of an investment:

Future Value = Principal * (1 + (Interest Rate ÷ Number of Compounding Periods))^(Number of Compounding Periods x Time in Years)

In this case, the interest rate is 5.7% compounded quarterly, so:

Interest Rate ÷ Number of Compounding Periods = 5.7 ÷ 4 = 1.425%

And the time in years is 19, so the number of compounding periods is 4 * 19 = 76.

Now, we can plug in the values into the formula:

Future Value = Principal * (1 + (1.425 ÷ 100))^(76)

Future Value = Principal * (1.01425)^76

Future Value = 29,000

Solving for Principal, we get:

Principal = 29,000 ÷ (1.01425)^76

Rounding to the nearest hundred dollars, we get:

Principal = $18,900

So, Bashir would need to invest $18,900, to the nearest hundred dollars, for the value of the account to reach $29,000 in 19 years.

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Using a system of equations and assuming neither pizza nor cake has changed in price, the cost of a pizza in dollars is $10.56.

A system of equations is two or more equations solved at the same time or concurrently.

A system of equations is also called simultaneous equations.

                  Pizzas   Cakes    Total Cost

Last week      12          6             $186

Today           29        24            $554

Let the cost per pizza = x

Let the cost per cake = y

12x + 6y = 186 ... Equation 1

29x + 24y = 554 ... Equation 2

Multiply Equation 1 by 4:

48x + 24y = 744 ... Equation 3:

Subtract Equation 2 from Equation 3:

48x + 24y = 744

-

29x + 24y = 554

18x = 190

x = 10.56

= $10.56

Substitute x = $10.56 in Equation 1:

12x + 6y = 186

12(10.56) + 6y = 186

126.72 + 6y = 186

6y = 59.28

y = 9.88

= $9.88

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