Suppose you are going to roll a 10-sided die 50 times and record p, the proportion of times that the roll is 3 orlower. Which of the following describes the sampling distribution of p?A. Mean = 15; Standard deviation = 0.0648; non-Normal.B. Mean = 15; Standard deviation = 3.24; approximately NormalC. Mean = 0.3; Standard deviation = 3.24; approximately NormalD. Mean = 0.3; Standard deviation = 0.0648; non-NormalE. Mean = 0.3; Standard deviation = 0.0648; approximately Normal

An algebraic expression for representing the Nora's income in form of Tonya's income is given by  y = ( x / 4 ) .

Let us consider 'x' represents the Tonya's income.

And variable 'y' represents the Nora's income.

Tonya income is equal to four times of Nora's income.

This implies,

Nora's income is equal to one fourth times of Tonya's income.

⇒ y = ( x / 4 )

Rewrite an algebraic expression to represents Tonya's income in terms of Nora's income we have,

Simplify by multiplying both the sides of the algebraic expression by 4 we get,

⇒ x  = 4y

Therefore, an algebraic expression to represents the Nora's income in terms of Tonya's income is equal to y = ( x / 4 ).

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There are 12 red socks and 18 black socks in a sock drawer. If you randomly choose two socks at once, the probability you get a matching pair is 50%.

The probability of getting a matching pair of socks can be calculated as follows:

First, we can calculate the total number of ways to choose 2 socks out of 30:

C(30, 2) = 30! / (2! * (30-2)!) = 435

Now, we need to calculate the number of ways to choose 2 socks such that they are both black or both red:

Number of ways to choose 2 black socks: C(18, 2) = 153

Number of ways to choose 2 red socks: C(12, 2) = 66

Therefore, the total number of ways to choose a matching pair of socks is 153 + 66 = 219.

Finally, we can calculate the probability of getting a matching pair of socks by dividing the number of ways to choose a matching pair by the total number of ways to choose 2 socks:

P(matching pair) = 219 / 435 ≈ 0.5034

Therefore, the probability of getting a matching pair of socks is approximately 0.5034 or 50.34%.

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1. It will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.

2. An annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.

3 A principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.

a. Using the TVM Solver function in Excel, we can input the following information:

Present value (PV): -$35,000 (since it's an outgoing cash flow)

Future value (FV): $70,000 (since we want the tithe to double in value)

Interest rate per period (Rate): 7.75%/12 (since the APR is compounded monthly)

Number of periods (Nper): unknown (what we're solving for)

Payment (Pmt): 0 (since there are no recurring payments)

Solving for Nper, we get 96.16 months, or approximately 8 years.

Therefore, it will take about 8 years for the tithe to double in value if invested at 7.75% APR compounded monthly.

b. Present value (PV): -$22,500 (since it's an outgoing cash flow)

Future value (FV): $50,000

Interest rate per period (Rate): unknown (what we're solving for)

Number of periods (Nper): 14*2=28 (since the interest is compounded semi-annually, we need to double the number of years)

Payment (Pmt): 0

Solving for Rate, we get 4.84% APR.

Therefore, an annual interest rate of 4.84% compounded semi-annually would be required for $22,500 to accumulate to $50,000 in 14 years.

c. Using the TVM Solver function in Excel, we can input the following information:

Present value (PV): unknown (what we're solving for)

Future value (FV): $40,000

Interest rate per period (Rate): 4%/4 (since the APR is compounded quarterly)

Number of periods (Nper): 9*4=36 (since the interest is compounded quarterly, we need to multiply the number of years by 4)

Payment (Pmt): 0

Solving for PV, we get $26,512.18.

Therefore, a principal of $26,512.18 invested in a GIC at 4% APR compounded quarterly would return $40,000 in 9 years.

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Answer:

x=130°

Step-by-step explanation:

The sum of the angel of the pentagon is equal to 540°

X+90+x+150+x=540

3x+240=540

3x=540-150

3x=390

X=130

The probability of getting at least one 2 given that the sum of the numbers is 7 is 2/6 or 1/3.

To find the probability that the number 2 has appeared at least once given that the sum of the numbers is 7, we need to use the concept of conditional probability.

Let's consider the possible outcomes when two dice are rolled. The total number of outcomes is 36, as each die has six possible outcomes.

Out of these 36 outcomes, there are six outcomes in which the sum of the numbers appearing on the upper faces is 7. These outcomes are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Out of these six outcomes, there are two outcomes in which the number 2 appears at least once: (1,6) and (2,5).

We can use the formula for conditional probability to verify our answer:

P(2 appears at least once | sum is 7) = P(2 appears at least once and sum is 7) / P(sum is 7)

P(2 appears at least once and sum is 7) = 2/36 = 1/18 (as there are two outcomes with a sum of 7 that have a 2 in them)

P(sum is 7) = 6/36 = 1/6

So, P(2 appears at least once | sum is 7) = (1/18) / (1/6) = 1/3, which is consistent with our previous answer.

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Answer:

Step-by-step explanation:

To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.

First, we need to convert 1 1/4 to an improper fraction:

1 1/4 = (4 x 1 + 1)/4 = 5/4

Then, we can multiply the fractions:

5/7 x 5/4 = 25/28

As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.

The trigonometric expression cosAcotA = 8x/(4x² - 1)

A trigonometric expression is an expression that contains trigonometric ratios.

Given that for any acute angle A if sin A = 2x-1/2x+1, we desire to find the value of cos A cot A?

So, we proceed as follows

cosAcotA = cosA × cosA/sinA  (since cotA = cosA/sinA)

= cos²A/sinA

Now using the trigonometric identity

sin²A + cos²A = 1

⇒ cos²A = 1 - sin²A

So, substituting this into the equation, we have that

cosAcotA = cos²A/sinA

=  (1 - sin²A)/sinA

= 1/sinA - sin²A/sinA

= 1/sinA - sinA

Substituting the value of sinA into the equation, we have

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

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

Taking the L.C.M, (2x - 1)(2x + 1), we have

= [(2x + 1)² - (2x - 1)²]/[(2x - 1)(2x+ 1)]

=  [(2x + 1)² - (2x - 1)²]/[(2x)² - 1²)]

=  [(2x + 1 + 2x - 1)(2x + 1 - (2x - 1)]/(2x)² - 1²)

=  [(2x + 1 + 2x - 1)(2x + 1 - 2x + 1)]/4x² - 1)

=  [(4x)(2)]/4x² - 1)

= 8x/(4x² - 1)

So, cosAcotA = 8x/(4x² - 1)

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Therefore , the solution of the given problem of unitary method comes out to be choice B $385 is the correct response.

The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.

Here,

We must first determine how much is deducted from Claire's gross salary annually for the 401(k) plan in order to determine

how much money is deposited into her retirement account by her employer each month.

Since we are aware that Claire contributes 5% of her total income to her 401(k),

we can figure out how much she contributes as follows:

=>  0.05 x $92,400 = $4,620

As a result, Claire's 401(k) plan deducts $4,620 from her total income each year. We can reduce this amount by 12 (the number of months in a year) to determine how much it is per month:

=> $4,620 ÷ 12 = $385

As a result, Claire's employer contributes $385 each month to her 401(k) savings account.

Therefore, choice (B) $385 is the correct response.

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The ratio of SINA and COSA = 48/50 and 14/50

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question,

sina = perpendicular\ hypotenuse

= 48/50

cosa= base\ perpendicular

=

14/50

Hence, The ratio of SINA and COSA = 48/50 and 14/50

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in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

How to calculate the rate?

To answer these questions, we need to calculate the population and food supply at different points in time and compare them.

Let's first calculate the population after t years:

Population after t years = 2,000,000 * (1 + 4%) raise to the power t

And the food supply after t years:

Food supply after t years = 4,000,000 + 0.5 million * t

Now, let's answer the first question:

If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur?

If the country doubles its initial food supply, the new food supply would be 8,000,000, and it would still increase at a rate of 0.5 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%)^t = 8,000,000 + 0.5 million * t

Solving for t, we get t ≈ 17.77 years.

So, in approximately 18 years, the population would exceed the food supply, even if the country doubles its initial food supply and maintains a constant rate of increase in the supply adequate for an additional 0.5 million people per year.

Now, let's answer the second question:

If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?

If the country doubles the rate at which its food supply increases, the new rate would be 1 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%) raise to the power t  = 16,000,000 + 1 million * t

Solving for t, we get t ≈ 21.96 years.

So, in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

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10-hole harmonicas, which can produce a wider range of notes and are more commonly used in professional music settings.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

The terms "6 holes and 1/2" and "10 holes" are often used to refer to harmonicas, which are small wind instruments that produce sounds when air is blown into or drawn out of them.

The main difference between a 6-hole harmonica and a 10-hole harmonica is the number of holes on the instrument. As the name suggests, a 6-hole harmonica has 6 holes, while a 10-hole harmonica has 10 holes.

In addition to the number of holes, the two types of harmonicas may also differ in their size, range, and the specific notes that they can produce. 6-hole harmonicas are typically smaller and produce a more limited range of notes compared

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The magnitude of the force P is 464.77 N.

STEP BY STEP EXPLANATION:

Step 1: Break down each force into components.
F = 320 N at 30°
Fx = F * cos(30°) = 320 * cos(30°) = 277.13 N (horizontal)
Fy = F * sin(30°) = 320 * sin(30°) = 160 N (vertical)

120 N is in the horizontal direction (assume positive x-direction):
Fx2 = 120 N

80 N is in the vertical direction (assume positive y-direction):
Fy2 = 80 N

Step 2: Sum up the components.
Total horizontal force (Fxtotal) = Fx + Fx2

= 277.13 + 120 = 397.13 N

Total vertical force (Fytotal) = Fy + Fy2

= 160 + 80 = 240 N

Step 3: Find the magnitude of the resultant force.
            Resultant force (R) = sqrt(Fxtotal^2 + Fytotal^2)

= sqrt(397.13^2 + 240^2) = 464.77 N

Step 4: Determine the magnitude of the force P.
Since the resultant of the four forces should act on the rim of the plate, it means that the force P should be equal in magnitude and opposite in direction to the resultant force R.

The magnitude of the force P is 464.77 N.

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Neil will be able to receive Olga's weather updates for a distance of 10 miles on the road.

Equation is a mathematical statement that expresses the equality of two expressions. It is usually written using symbols, such as '=', '<', '>', '+', and '-'. Equations can be used to describe, model, and solve real-world problems. They can also be used to predict the behavior of a system or to find unknown values.

To calculate the approximate number of miles Neil will be able to receive Olga's weather updates, a quadratic equation can be used. The equation is as follows:

A = (x - 15)²+ (y - 15)² <= 100

where A is the area of a circle with a radius of 10 miles, centered at the ranger station, and (x,y) is the position of Neil's car on the road. The equation represents the area that is within the range of Olga's walkie-talkie, which is the area where Neil's car can receive Olga's weather updates.

To solve for x and y, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of (x2 - x1)² + (y2 - y1)². Since we know the starting and ending points of Neil's road, we can use this formula to solve for x and y:

x = Square root of [ (10 - 15)² + (20 - 15)² ] = 10
y = Square root of [ (10 - 15)² + (10 - 15)² ] = 5

Substituting these values into the equation above, we get A = (10 - 15)² + (5 - 15)²= 100, which is Olga's walkie-talkie range. Therefore, Neil will be able to receive Olga's weather updates for a distance of 10 miles on the road.

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Dhruv will most probably admit precisely 1 chocolate if the probability is0.2181 or (21.81%).

Probability refers to eventuality. This area of mathematics examines how arbitrary events be.

First, the total number of ways

= C( 11, 3)

= 11!/ 8! 31

= 11 x 10 x 9/ 3x 2

= 165

Now, If Dhruv gets exactly 1 chocolate there are now 7 chocolate and

3- 1 = 2 bars

So, the number of ways for 1 exactly one chocolate

= C( 9, 2)

= 9!/ 7! 21

= 9 x 8/ 2

= 36 ways

The liability that Dhruv receives exactly one chocolate is now.

= 36/ 165

= 12/ 55

Thus, the probability that Dhruv gets exactly 1 chocolate is 12/55 ≈0.2181 or 21.81%.

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The probability that at most one sample is mutated in 10 samples is 0.746.

To calculate this probability, we use the binomial distribution formula.

The binomial distribution formula is used to calculate the probability of a certain number of successes (in this case, samples that are mutated) in a certain number of trials (10 samples). We need to find the probability of 1 success or fewer in 10 trials.

This is equal to P(x<=1) = 1 - P(x>1), where x is the number of successes.

For this calculation, we need the following parameters: n = 10 (number of trials), p = 0.15 (probability of a single sample being mutated), and x = 1 (number of successes). So, P(x<=1) = 1 - P(x>1) = 1 - P(x = 2) - P(x = 3) - P(x = 4) - P(x = 5) - P(x = 6) - P(x = 7) - P(x = 8) - P(x = 9) - P(x = 10).

The probability of at most one sample being mutated in 10 samples is calculated by adding the individual probabilities of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 samples being mutated, which equals 0.746.

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Option A,B,C,D : Elias might have gotten the answer by calculating the percentage discounts of each item and comparing them to see which ones are the same.

To find which items have the same percent discount, we need to calculate the percent discount for each item.

For the sweater, the percent discount is (20/50) x 100% = 40%.

For the shorts, the percent discount is (12/30) x 100% = 40%.

For the shirt, the percent discount is (14/35) x 100% = 40%.

For the jeans, the percent discount is (24/60) x 100% = 40%.

Therefore, all items have the same percent discount of 40%, and option C (jeans and shirt only) is incorrect. The correct answer is A, sweater and shorts only, B, sweater, shorts, and shirt only, and D, sweater, shorts, and jeans only, have the same percent discount. Elias may have chosen C because he overlooked that the percent discount is the same for all items.

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Which items have the same percent discount?

A. sweater and shorts only

B. sweater, shorts, and shirt only

C. jeans and shirt only

D. sweater, shorts, and jeans only

Elias chose C as the correct answer. How might he have gotten that answer?

Answer:

Factor 64h^3+216k^9

Step-by-step explanation:

The given expression is a sum of two terms:

[64h^3+216k^9

Notice that each term has a common factor. For the first term, the greatest common factor (GCF) is 64h^3, and for the second term, the GCF is 216k^9. So we can factor out these GCFs to get:

64h^3+216k^9 = 64h^3(1 + 3k^6)

This expression cannot be factored any further, so the final answer is:

64h^3+216k^9 = 64h^3(1 + 3k^6)

If you can, give me brainliest please!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here is real answer :>

From the given information provided, the expression that need to determine the total amount is Total cost = $2.85/gallon x g gallons + $3.15/can x c cans.

The expression that can be used to determine the total amount Joe spent on gasoline and oil is:

Total cost = Cost of gasoline + Cost of oil

We can represent the cost of gasoline as:

Cost of gasoline = price per gallon x number of gallons

Substituting the given values, we get:

Cost of gasoline = $2.85/gallon x g gallons

Similarly, we can represent the cost of oil as:

Cost of oil = price per can x number of cans

Substituting the given values, we get:

Cost of oil = $3.15/can x c cans

Putting it all together, we get:

Total cost = $2.85/gallon x g gallons + $3.15/can x c cans

Expression that can be used to determine the total amount Joe spent on gasoline and oil is:

Total cost = $2.85/gallon x g gallons + $3.15/can x c cans

Question - Joe bought g  gallons of gasoline for $2.85 per gallon and c  cans of oil for  $3.15 per can. What expression can be used to determine the total amount Joe spent on gasoline and oil?

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The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.

To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:

12x = 336

Addressing for x, we get:

x = 28

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The vertical axis of the graph represents profit, so the x-intercepts represent prices in the produce 0 profit. The maximum value of the graph is the maximum profit that can be obtained for anyprice

The higher or largest number of the chart is the maximum reach

B) We read the value of f(1) from the graph to be about 120, so the average rate of change is about:

(f(4) -f(1))/(4 -1) = (270 -120)/(3) = 50

The average rate of the change from x = 1 to x = 4 is about 50.* This means profit will increase on average $50 for each $1 increase in price in what interval.

If we take the peak profit to be $270 we can write f(x) as:

f(x) 16.875x(x-8)

Then f(1) = 118.15 and average rate of change is 50.625.

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Answer:

answer is 3

Step-by-step explanation:

Answer:

\

Step-by-step explanation:

Given expression: 3x+9

Take 3 outside from the expression, we get,

= 3(x+3), which is called the equivalent expresion

In conclusion, the relation R on the set of all integers satisfies reflexivity and symmetry but not transitivity.

To determine which properties the relation R on the set of all integers satisfy, we need to check for reflexivity, symmetry, and transitivity.

1. Reflexivity: A relation R is reflexive if for every element a in the set, (a, a) ∈ R.
In this case, we need to check if a * a ≥ 1 for all integers a.
Since any integer squared (a * a) is greater than or equal to 1, R is reflexive.

2. Symmetry: A relation R is symmetric if for every pair (a, b) ∈ R, (b, a) also ∈ R.
In this case, we need to check if a * b ≥ 1 implies b * a ≥ 1.
Since multiplication is commutative (a * b = b * a), the condition holds true, and R is symmetric.

3. Transitivity: A relation R is transitive if for every (a, b) ∈ R and (b, c) ∈ R, (a, c) also ∈ R.
In this case, we need to check if a * b ≥ 1 and b * c ≥ 1 imply a * c ≥ 1.
Let's take the counterexample: a = -1, b = 2, and c = -1. We have -1 * 2 ≥ 1 and 2 * -1 ≥ 1, but -1 * -1 ≥ 1 is false.

Therefore, R is not transitive.

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Answer: 5/2


fraction of 2.5 is 5/2

Answer:

2 1/2 or 5/2 as improper fraction

2 is a whole number and you have .5 left over

To convert to fraction .5 is the same as 1/2

So it gives you 2 1/2

By the way thanks for the Brainly points :)

Answer:

d = 3.75

e = 8/3

Step-by-step explanation:

8/6 = 5/d = e/2

4/3 = 5/d

4d = 3 × 5

d = 3.75

4/3 = e/2

3e = 4 × 2

e = 8/3

The two consecutive positive integers are 5 and 6.

Let the two consecutive positive integers be x and x + 1. We are given that the product of these integers is 3 less than three times their sum. This can be expressed as:
[tex]x(x + 1) = 3(x + x + 1) - 3[/tex]
Now we can solve for x:
[tex]x^2 + x = 6x + 3 - 3[/tex]
[tex]x^2 + x = 6x[/tex]
[tex]x^2 - 5x = 0[/tex]
Factoring the left side of the equation, we get:
[tex]x(x - 5) = 0[/tex]
From this equation, x can be 0 or 5.

However, since the question asks for positive integers, we can't use x = 0. Therefore, x = 5.

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Answer:

The theoretical probability of being dealt exactly two 2's in a 5-card hand from a standard 52-card deck is:

[tex]= \dfrac{2162}{32487}\\\\\approx 0.06655 \text{ in decimnal}[/tex]

Step-by-step explanation:

The problem can be solved by using the combinatorics formula. The number of ways of drawing a subset of r items from a population of n items is given by

[tex]^nC_r = \dfrac{n!}{r! (n-r)!}[/tex]

where n! is the factorial of n, r! the factorial of r and (n-r)! = factorial of (n-r)

The general formula for k! = k x (k - 1) x (k - 2) x ..... x 3 x 2 x 1

The number or ways in which you can get two 2's in a deal of 5 cards is given by

[tex]^5C_2 = \dfrac{5!}{ 2! (5 - 2)! } \\\\= = \dfrac{5!}{2! \times 3! }\\\\= 10[/tex]

Once we have been dealt 2 2's we have to compute how many ways we can get the remaining 3 cards. Since we are looking for exactly two 2's we cannot draw another 2

The number of cards left that we can draw the remaining three cards = 52(total cards) -2(two 2's already drawn) - 2(two 2's that cannot be drawn)

= 48 cards

We can draw 3 cards from 48 cards in [tex]^{48}C_3[/tex]  ways
[tex]^{48}C_3 = \dfrac{48!}{ 3! (48 - 3)! }\\\\\\= \dfrac{48!}{3! \times 45! }\\\\= 17296[/tex]

Therefore the total number of ways of drawing exactly two 2's
= 10 x 17296 = 172960

The number of ways in which we can draw 5 cards from 52 cards is given by
[tex]^{52}C_5 = = \dfrac{52!}{5! (52 - 5)! }\\\\= \dfrac{52!}{5! \times 47! }\\\\= 2598960[/tex]

P(exactly two 2's in a 5-card hand)
[tex]= \dfrac{172960}{2598960}\\\\ \\= \dfrac{2162}{32487}\\\\[/tex]

or, in decimal
[tex]\approx 0.06655[/tex]

Answer: $ 46.50

First divided 31 by 2

Which equals...

15.50

Then add 15.50 to 31.

46.50

The answer is $46.50