help pls show ur work

Answer:

--------------------------

Find the scale factor by dividing the corresponding sides of the given figures:

The area is the product of two dimensions therefore the ratio of areas of similar figures is the square of the scale factor. Let the area of the smaller figure be A, then we got the ratio:

Answer: 18 in²

Step-by-step explanation:

Part A:

The required graph of the function is described.

The vertex of the function is (7,0)

The domain is : (-∝ , ∝) and

The range is : [0,∝), {yIy ≥ 0}

Part B:

The transformation which occurs from f(x) to h(x) is a vertical shift up to 2 units.

Expressions separated by an equal sign are functions. Both dependent and independent variables are present.

Given Part A:

given the function is g(x) = I x - 7 I

hence from the function, vertex = (h,k)

h = 7 and k = 0

(h,k) = (7,0)

Find the domain by finding where the function is defined.

therefore, domain =  (-∝ , ∝) , where {xIx ∈ R}

The range is the set of values that corresponds with the domain.

therefore, range =  [0,∝), {yIy ≥ 0}

Part B:

given the parent function is:  f(x) = |x|

which is transformed to h(x) = |x| + 2

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x axis or y axis, and if there is a vertical stretch.

Parent function = f(x) = |x|

Horizontal shift = none

Vertical shift = up 2 units.

Reflection about the x axis = none

hence from the function we can determine the vertex (h,k)

= (0,2)

Find the domain by finding where the function is defined.

therefore, domain =  (-∝ , ∝) , where {xIx ∈ R}

The range is the set of values that corresponds with the domain.

therefore, range = [2,∝) ,  {yIy ≥ 2}

Hence, we get the required answers.

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The calculated probability of a friend being born on a Friday is 1/7

Assuming that people are equally likely to have been born on any of the 7 days of the week, the probability of the first friend being born on a Friday is 1/7 or approximately 0.143.

This is because there is only one day out of the seven days of the week  that is Friday, and each day has an equal chance of being chosen.

Therefore, the probability of the first friend being born on a Friday is 1/7.

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Complete question

Suppose that people are equally likely to have been born on any of the 7 days of the week. You meet two new friends independently, and ask each of them on what day of the week they were born. (Enter your answers as fractions.) What is the probability that the first friend was born on a Friday

the correct answer is option b) 0.11. To find the experimental probability of drawing a K or 6, we need to first determine how many K's and 6's are in a standard deck of cards.

A standard deck of cards contains 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards, including an ace, numbered cards 2-10, and face cards (jack, queen, king).

Out of the 52 cards in the deck, there are four K's and four 6's, for a total of eight cards that satisfy the condition of being a K or 6.

To calculate the experimental probability of drawing a K or 6 from the table, we need to add up the frequency of drawing a K and the frequency of drawing a 6, and then divide by the total number of draws (100).

From the table, we see that the frequency of drawing a K is 4, and the frequency of drawing a 6 is 7. Therefore, the total frequency of drawing a K or 6 is:

4 (K's) + 7 (6's) = 11

So the experimental probability of drawing a K or 6 is:

11/100 = 0.11

Therefore, the correct answer is option b) 0.11.

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Answer:

The graph shows a proportional relationship because it is a line, and the difference between each point is the same.

explanation: The difference between all points are approximately 2.236.

Water output rate for Mitchell family's sprinkler was 20 L per hour and for Garcia family's sprinkler was 15 L per hour. Their sum is 35 L per hour and total water output was 1075L of water.

Let's denote the water output rate of the Mitchell family's sprinkler by x and the water output rate of the Garcia family's sprinkler by y. We know that the sum of the two rates is 35 L per hour, so equation:

x + y = 35

We also know that the Mitchell family's sprinkler was used for 35 hours, so it produced a total of 35x liters of water. Similarly, the Garcia family's sprinkler was used for 25 hours, so it produced a total of 25y liters of water. The combined total output of 1075L of water will be written as:

35x + 25y = 1075

We use first equation to solve for one of variables in terms of the other. For example, we solve for y:

y = 35 - x

Now substitute this expression for y into second equation:

35x + 25(35 - x) = 1075

Simplifying the equation:

10x + 875 = 1075

Solve for x:

x = 20

Substitute x value into expression for y:

y = 35 - 20 = 15

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The distance traveled after t seconds is given by:

[tex]d = |-\frac{(2t^2 + 2t + 1)e^{-2t}}{4}|[/tex]

Here we know that the particle moves along a straight line with the velocity:

[tex]v(t) = t^2*e^{-2t}[/tex]

Remember that the velocity is the rate of change of the position, so if we want to find the distance traveled after t seconds, we need to integrate this between 0 and t, we will get:

[tex]\int\limits^t_0 {t'^2*e^{-2t'}} \, dt' = -\frac{(2t^2 + 2t + 1)e^{-2t}}{4}[/tex]

That is the expression that gives the distance traveled after t seconds, if we want to get it more exactly, we should take the absolute value, then we get:

[tex]d = |-\frac{(2t^2 + 2t + 1)e^{-2t}}{4}|[/tex]

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The function family name of the parent function shown in the graph above is radical.

In Mathematics, a cube root function is sometimes referred to as a cubic root polynomial or radical function and it can be defined as a type of polynomial that is an inverse of a cubic function.

Generally mathematics, a radical function or a cube root function can be represented or modeled by using the following mathematical equation:

f(x) = a∛(x - h) + k

where:

In this context, we can reasonably infer and logically deduce that the function family name of the parent function shown in the graph above is a radical function or a cube root function.

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As a result, x = 2 and x = -5 are the roots of the quadratic function y = (x - 2)(x + 5). They also serve as the function's x-intercepts on the graph.

Typically, it includes one or more variables that stand in for unknowable values and may include exponents, roots, multiplication, division, and other mathematical operations. Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. In algebra, calculus, and other areas of mathematics, equations are frequently employed to model and resolve issues.

given

This is because the values of x are provided by a quadratic function's factored form.

Let's use Corey's equation, y = (x - 2)(x + 5), as an illustration. We solve for x and put y equal to zero to obtain the roots of this function:

0 = (x - 2)(x + 5)

Only when one of the factors on the left side equals zero is this equation true. As a result, we may set each factor to 0 and find x:

In each equation, the result of solving for x is:

x = 2 or x = -5

This is because the values of x are provided by a quadratic function's factored form.

Let's use Corey's equation, y = (x - 2)(x + 5), as an illustration. We solve for x and put y equal to zero to obtain the roots of this function:

0 = (x - 2)(x + 5)

Only when one of the factors on the left side equals zero is this equation true. As a result, we may set each factor to 0 and find x:

x - 2 = 0 or x + 5 = 0

In each equation, the result of solving for x is:

x = 2 or x = -5

As a result, x = 2 and x = -5 are the roots of the quadratic function y = (x - 2)(x + 5). They also serve as the function's x-intercepts on the graph.

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Probability in sandwich choices analysis refers to the likelihood of a particular sandwich being chosen, based on factors such as taste, price, and availability.

1. To calculate the total number of possible sandwiches, we need to consider the number of options for each category: bread, protein, cheese, and vegetables.

Bread: There are 3 options - Italian, white, and wheat.

Protein: There are 4 options - tuna, ham, turkey, and beans.

Cheese: There are 4 options - provolone, Swiss, American, and none.

Vegetables: There are 5 options, and since we need to choose two, we use combinations. Therefore, there are (5 choose 2) = 10 possible combinations of vegetables: lettuce and tomatoes, lettuce and peppers, lettuce and onions, lettuce and pickles, tomatoes and peppers, tomatoes and onions, tomatoes and pickles, peppers and onions, peppers and pickles, and onions and pickles.

To calculate the total number of possible sandwiches, we multiply the number of options for each category:

3 x 4 x 4 x 10 = 480

Therefore, there are 480 different possible sandwiches.

2. Since Andre only cares about the ham, lettuce, and tomatoes, we only need to consider the number of options for vegetables. He needs to choose two vegetables, so we need to count the number of possible combinations of lettuce, tomatoes, and the remaining vegetables. Since we don't care about the bread or cheese, we can ignore those options.

There are (3 choose 2) = 3 possible combinations of vegetables that would make Andre happy: lettuce and tomatoes, lettuce and peppers, or tomatoes and peppers. Since we don't care about the bread or cheese, there are no restrictions on those categories, so there are 4 options for cheese and 3 options for bread, for a total of 12 possible sandwiches that would make Andre happy.

3. To calculate the probability of randomly choosing a sandwich that would make Andre happy, we divide the number of sandwiches that would make him happy by the total number of possible sandwiches:

3/480 = 1/160

Therefore, the probability is 1/160, or approximately 0.00625. This means that if we were to randomly choose a sandwich, there is a 0.625% chance that it would be a sandwich that would make Andre happy.

The complete question is:

1. A submarine sandwich shop makes sandwiches with one kind of bread, one protein, one choice of cheese, and two vegetables. How many different sandwiches are possible? Explain your reasoning. You do not need to write out the sample space.

Breads: Italian, white, wheat

Proteins: Tuna, ham, turkey, beans

Cheese: Provolone, Swiss, American, none

Vegetables: Lettuce, tomatoes, peppers, onions, pickles.

2. Andre knows he wants a sandwich that has ham, lettuce, and tomatoes on it. He doesn’t care about the type of bread or cheese. How many of the different sandwiches would make Andre happy?

3. If a sandwich is made by randomly choosing each of the options, what is the probability it will be a sandwich that Andre would be happy with?

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The solution to the inequality is y < 9

Inequalities are simply described as a relation with the reflection of a non-equal comparison between two numbers, mathematical expressions or even elements.

The comparison of these expressions or numbers is mostly based on their sizes on the number line.

It is used to compare two values such that one is less than, greater than, or simply not equal to another value.

From the information given, we have the inequality;

-3 + y< 6

To solve for y, collect like terms

y < 6 + 3

add the values

y< 9

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the solution to the system of equations is x = 7.14 and y = 13.57.

In mathematics, an equation is a statement that asserts the equality of two mathematical expressions, usually containing one or more variables.

Given equations are:

5 - 0.7x = 0.2y ...........(1)

-y + 0.4x = 4.3 ...........(2)

To solve for x and y, we can use the elimination method, which involves multiplying one or both equations by a constant to eliminate one of the variables. Here's how we can do it:

First, let's multiply equation (1) by 5 and equation (2) by 2 to eliminate the y variable:

25 - 3.5x = y (multiplying equation (1) by 5)

-2y + 0.8x = 8.6 (multiplying equation (2) by 2)

Now we can substitute the expression for y from equation (1) into equation (2) and solve for x:

25 - 3.5x = 0.2(25 - 3.5x) (substituting y from equation (1))

25 - 3.5x = 5 - 0.7x

-2.8x = -20

x = 7.14

Substituting this value of x back into equation (1), we can solve for y:

5 - 0.7(7.14) = 0.2y

y = 13.57

Therefore, the solution to the system of equations is x = 7.14 and y = 13.57.

By using ALEKS graphing calculator, we get the same values of x and y.

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Using fractions, we can find that   [tex]1\frac{1}{16}[/tex] length of material remains.

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

A fraction is a non-integer that consists of a numerator and a denominator. A mixed fraction is made up of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is less than the denominator.

Material left = initial length - length of the first plate - length of the second plate - (2 x 1/16)

= 123/8 - 33/4 - 95/16 - 2/16

= 17/16

=  [tex]1\frac{1}{16}[/tex].

Therefore,  [tex]1\frac{1}{16}[/tex] length of material remains.

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Answer:

An event that is less likely to occur would have a lower probability than 0.45. Therefore, the options that show a probability less than 0.45 are:

A) 0.42

C) 0.29

D) 0.37

So options A, C, and D are the correct answers.

Therefore, the length of z is approximately 2330.0 cm.

Length is a physical quantity that describes the distance between two points. It is typically measured in units such as meters, feet, inches, centimeters, or kilometers. Length can refer to the size of an object or the distance traveled by an object over a period of time. In geometry, length refers to the size of a line segment, which is the distance between two points in a plane. In physics, length is a fundamental concept that is used to describe the size of objects and the distances between them, and is an important factor in many calculations involving motion, energy, and other physical phenomena.

To find the length of side z, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Using this law, we have:

[tex]z/sin(141°) = x/sin(25°)[/tex]

Solving for z, we get:

[tex]z = x*sin(141°)/sin(25°)[/tex]

[tex]z = 830*sin(141°)/sin(25°)[/tex]

z ≈ 2329.9 cm

Rounding to the nearest tenth of a centimeter, we get:

z ≈ 2330.0 cm

Therefore, the length of z is approximately 2330.0 cm.

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The cube's surface area would be 96m².

The surface area of the right rectangular prism is 37.5 ft².

The height of the prism is 4/3 in.

The approximate lengths of the sides of the base is height of 9 cm and a base of 8.2 cm.

To find the surface area, first find the side length of the cube. The volume of a cube is V = s³, where s is the side length. So:

64m³ = s³ => s = (64)^(1/3) = 4m

Now, the surface area (SA) of a cube is given by the formula SA = 6s². Plugging in the side length:

SA = 6(4m)² = 6(16m²) = 96m²

To find the surface area of the right rectangular prism:

First, find the Lateral Area (LA): LA = Perimeter × height

Perimeter = (2 ft + 1 1/2 ft) × 2 = 7 ft

Height = 4 1/2 ft

LA = 7 ft × 4 1/2 ft = 31.5 ft²

Now, find the Surface Area (SA): SA = LA + 2B

SA = 31.5 ft² + 2(3 ft²) = 31.5 ft² + 6 ft² = 37.5 ft²

To find the height h of the prism:

First, find the Base Area (B): B = Length × Width

B = 3 in × 7 in = 21 in²

Now, use the Surface Area (SA) formula to find the Lateral Area (LA):

SA = LA + 2B => LA = SA - 2B

LA = 68 2/3 in² - 2(21 in²) = 68 2/3 in² - 42 in² = 26 2/3 in²

Now, use the Lateral Area (LA) formula to find the height (h):

LA = Ph => h = LA / P

Perimeter (P) = 2(Length + Width) = 2(3 in + 7 in) = 20 in

h = (26 2/3 in²) / 20 in = 4/3 in

The right triangular prism has two equilateral triangular bases and three rectangular sides. Since the distance between the bases is 9 cm, we can use the surface area of the prism to find the total area of the three rectangular sides:

Surface area = 2 * A (triangle bases) + Lateral area (rectangular sides)

319.5 cm² = 2 * 29.1 cm² + Lateral area

Lateral area ≈ 261.3 cm²

Each of the three rectangular sides has a height of 9 cm and a base of 8.2 cm.

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Step-by-step explanation:

your answers for a. are correct.

b.

(f○g)(x) = f(g(x))

that means we are using the expression of g(x) as input to f(x). so, for f(x), x turns into g(x) = 0.9x

(f○g)(x) = f(g(x)) = 0.9x - 220

what it does is it reduces the price by 10% and then gives on to of that an additional absolute value discount if $220.

The team can be expected to score about 15 goals in 10 games based on their relative frequency of scoring 24 goals in 16 games.

The proportion or percentage of times that even an event or category occurs in a dataset is measured by relative frequency. It is derived by dividing the total number of observations in the dataset by the frequency with which the event or category occurs. In statistics, relative frequency is frequently used to compare the occurrence of various events or categories and to characterise the distribution of a dataset. Also, depending on a sample, it is used to calculate the likelihood that an event will occur in a population.

The goals scored in 10 games can be calculated using proportions:

Given that,

24 goals / 16 games = 1.5 goals per game

For 10 games we have:

1.5 goals per game × 10 games = 15 goals

Hence, the team can be expected to score about 15 goals in 10 games based on their relative frequency of scoring 24 goals in 16 games.

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Answer: 7.5

Step-by-step explanation: Because Noah has five dollars, 100% of 5 is 5, and 50% of 5 is 2.5 so Diego has 7.5 dollars.

Answer:

$7.5

Step-by-step explanation:

There are two ways to solve this:

1) First, write the equation:

150% of 5

Then calculate:

[tex]\frac{150}{100} *5[/tex]

Finally, simplify 1 zero with the 0 in 15:

1.5 * 5

= $7.5

2) For the second way, because 150 is more than over 100 (percent), you deduct 150 and 100:

150 - 100 = 50

Then find 50% of 50:

[tex]\frac{50}{100} *5[/tex]

Then cancel 1 zero in 100 with the zero in 50:

0.5 * 5

= 2.5

Finally, add the product with the original amount of Noah:

5 + 2.5

= $7.5

a) The unit rate for cups of milk per muffin is 1/18 cup of milk per muffin.

b) The unit rate for muffins per cup of milk is 18 muffins per cup of milk.

What are the muffins?

(a) To find the unit rate for cups of milk per muffin, we need to divide the total amount of milk by the number of muffins:

2/3 cup of milk / 12 muffins = (2/3) ÷ 12 cup of milk per muffin

We can simplify this fraction by multiplying the numerator and denominator by 3:

(2/3) ÷ 12 = 2 ÷ (3 x 12) = 2 ÷ 36 = 1/18

So the unit rate for cups of milk per muffin is 1/18 cup of milk per muffin.

b) To find the unit rate for muffins per cup of milk, we need to divide the number of muffins by the total amount of milk:

12 muffins / (2/3 cup of milk) = 12 ÷ (2/3) muffins per cup of milk

To divide by a fraction, we can multiply by its reciprocal:

12 ÷ (2/3) = 12 x (3/2) = 36/2 = 18

So the unit rate for muffins per cup of milk is 18 muffins per cup of milk.

A muffin is a type of small, individual-sized baked good that is usually round in shape and has a slightly sweet taste. Muffins can be made with a variety of ingredients, including flour, sugar, eggs, butter, milk, and baking powder. They can also be flavored with various fruits, nuts, spices, or chocolate chips.

Muffins can be eaten for breakfast, as a snack, or as a dessert. They are often served warm and can be eaten plain or with butter, jam, or honey. Muffins are a popular baked good and are commonly found in coffee shops, bakeries, and grocery stores.

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Complete question is:  Hannah is making muffins. The recipe calls for 2/3 cup of milk to make 12 muffins.

a) The unit rate for cups of milk per muffin is 1/18 cup of milk per muffin.

b) The unit rate for muffins per cup of milk is 18 muffins per cup of milk.

the true statements about the circle equation are:

Remember that the equation of a circle whose center is at(a, b) and has a radius of R units is:

(x -a )²+ (y - b)² = R²

Here the equation is:

x² + y² - 2x - 8 = 0

Completing squares in x we will get:

(x² - 2x) + y² - 8 = 0

(x² - 2x + 1) -1 + y² - 8 =

(x - 1)² + (y - 0)² = 9 = 3²

So the center is (1, 0) and the radius is 3, so the true statements are:

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The measure of the angle POB is equal to 46°. Thus, option C is correct.

The cοllectiοn οf all pοints in the plane that make up a circle are all equally spaced frοm a certain pοint knοwn as the "centre," making the fοrm a clοsed twο-dimensiοnal shape. The symmetry line οf reflectiοn is fοrmed by each line that traverses the circle.

Mοreοver, it pοssesses rοtatiοnal symmetry arοund the centre fοr each angle. A circle is a circular shape that can be created by tracing a mοving pοint in a plane sο that its distance frοm a specified pοint remains cοnstant.

Given

Angle AOC = 46°  

Now, ΔAOP ≅ ΔBOP

As SSS criteria is possible

Then

By CPCT

∠AOC = ∠BOC = ∠POB

∠POB = 46°  

Thus, the measure of the angle POB is equal to 46°. Thus, option C is correct.

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The journal entries to record the transactions for the year is showed below.

1. Journal Entries:

a. Raw materials purchased on account:

Raw Materials Inventory   $162,000

Accounts Payable              $162,000

b. Raw materials used in production (direct and indirect):

Work in Process Inventory   $128,000

Manufacturing Overhead   $13,000

Raw Materials Inventory    $141,000

c. Costs for employee services (direct labor, indirect labor, sales commissions, administrative salaries):

Work in Process Inventory   $159,000

Manufacturing Overhead   $225,000

Sales Commissions Expense   $28,000

Administrative Salaries Expense   $50,000

d. Rent for the year (factory operations and selling/administrative activities):

Manufacturing Overhead   $13,100

Selling and Administrative Expenses   $5,500

Rent Payable                        $18,600

e. Utility costs incurred in the factory:

Manufacturing Overhead   $20,000

Cash                                          $20,000

f. Advertising costs incurred:

Selling and Administrative Expenses   $15,000

Cash                                          $15,000

g. Depreciation recorded on equipment (factory operations and selling/administrative activities):

Depreciation Expense (Factory)   $13,100

Depreciation Expense (Selling and Administrative)   $4,900

Accumulated Depreciation                      $18,000

2. T-Accounts:

a. Raw Materials Inventory:

Beginning balance: $10,400

Purchases: $162,000

Direct Materials Used: $128,000

Ending balance: ?

b. Work in Process Inventory:

Beginning balance: $4,800

Direct Labor: $159,000

Manufacturing Overhead: ?

Direct Materials Used: $128,000

Ending balance: ?

c. Finished Goods Inventory:

Beginning balance: $8,100

Cost of Goods Manufactured: $217,000

Ending balance: ?

d. Manufacturing Overhead:

Beginning balance: $0

Rent: $13,100

Utilities: $20,000

Depreciation (Factory): $13,100

Applied to Jobs: ?

Ending balance: ?

e. Cost of Goods Sold:

Beginning balance: $0

Cost of Goods Manufactured: $217,000

Ending balance: ?

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Answer: 20.99

Step-by-step explanation: you multiply by 0.428571 which is 3/7

Answer: A = 3

Step-by-step explanation:

4x-2=10

4x=12

x =12/4

x=3

Answer:the scale factor of dilation from circle P to Q is 2.5

for among us

Step-by-step explanation:

The similar circles P and Q can be made equal by dilation and translation

The horizontal distance between the center of circles P and Q is 11.70 units

The scale factor of dilation from circle P to Q is 2.5

The horizontal distance between their centers?

From the figure, we have the centers to be:

P = (-5,4)

Q = (6,8)

The distance is then calculated using:

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have:

d = √(6 + 5)^2 + (8 - 4)^2

Evaluate the sum

d = √137

Evaluate the root

d = 11.70

Hence, the horizontal distance between the center of circles P and Q is 11.70 units

The scale factor of dilation from circle P to Q

We have their radius to be:

P = 2

Q = 5

Divide the radius of Q by P to determine the scale factor (k)

k = Q/P

k = 5/2

k = 2.5

Hence, the scale factor of dilation from circle P to Q is 2.5

Answer:

To find the average rate of change of a function over an interval, you can use the formula:

average rate of change = [f(b) - f(a)] / (b - a)

where a and b are the endpoints of the interval.

In this case, you have the function g(x) = log2(x + 3) - 4 and the interval [-2, 5]. So, plugging in the values, you get:

average rate of change = [g(5) - g(-2)] / (5 - (-2))

First, let's evaluate g(5) and g(-2).

g(5) = log2(5 + 3) - 4 = log2(8) - 4 = 3 - 4 = -1

g(-2) = log2((-2) + 3) - 4 = log2(1) - 4 = 0 - 4 = -4

Now you can substitute these values into the formula:

average rate of change = (-1 - (-4)) / (5 - (-2))

= 3 / 7

And the average rate of change of g(x) over the interval [-2, 5] is 3/7.

Therefore, the probability of randomly arranging the digits 3, 4, 5, 6, and 7 to form a three-digit number that is even and greater than 700 is 0.1.

Probability refers to the likelihood or chance that a particular event or outcome will occur. It is a mathematical concept that quantifies the degree of uncertainty associated with an event or situation. Probability is typically expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that it is certain to occur.

by the question.

Therefore, the total number of five card hands that have exactly one ace and no picture cards been 4 * (36 choose 4) = 253,440.

The total number of five card hands is (52 choose 5) = 2,598,960.

Therefore, the probability of being dealt exactly one ace and no picture cards in a five-card poker hand is 253,440 / 2,598,960, which simplifies to 0.097%.

2.There are a total of 5! = 120 possible arrangements of the digits 3, 4, 5, 6, and 7. To form a three-digit number, we need to use three of these digits, so there are 5 x 4 x 3 = 60 possible three-digit numbers we can form.

To be greater than 700, the first digit must be either 6 or 7. If we choose 7 as the first digit, there are 4 x 3 = 12 ways to choose the remaining two digits. If we choose 6 as the first digit, there are 4 x 3 = 12 ways to choose the second and third digits, since we can't repeat digits. Therefore, there are 12 + 12 = 24 three-digit numbers greater than 700.

To be even, the last digit must be either 4 or 6. If we choose 6 as the first digit, there are 2 ways to choose the last digit (either 4 or 6), and 3 ways to choose the middle digit (since we can't repeat digits). This gives us a total of 2 x 3 = 6 even numbers starting with 6.

If we choose 7 as the first digit, there are no even numbers we can form, since the last digit can only be 4 or 6 and we've already used the 6 digit. Therefore, the total number of even three-digit numbers greater than 700 is 6.

So, the probability of randomly selecting an even three-digit number greater than 700 is 6/60 = 1/10 or 0.1.

3.There is a total of C (52, 3) = 22,100 possible ways to choose 3 cards from a deck of 52 cards.

To get one queen and two kings, we need to choose one of the four queens and two of the four kings. There are C(4, 1) ways to choose one queen, and C(4, 2) = 6 ways to choose two kings. Therefore, there are 4 x 6 = 24 ways to choose one queen and two kings.

So, the probability of getting one queen and two kings is 24/22,100 or approximately 0.0011 (rounded to four decimal places).

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