A data set has 25 and standard deviation 5 find the z-score of each value , 39,18,125,25,11

To help you with the journal entries and preparation of the stockholders' equity section for Sikie Shoe Manufacturing Co, let's start with the journal entries for the given transactions:

On January 15, the authorization date:

Journal entry:

Common Stock (200,000 shares * $2 par value) $400,000

Preferred Stock (100,000 shares * $25 par value) $2,500,000

Authorized Capital Stock $2,900,000

On January 20, 50,000 preferred stock were sold for cash at $70 per share:

Journal entry:

Cash $3,500,000

Preferred Stock (50,000 shares * $25 par value) $1,250,000

Common Stock $1,250,000

Paid-in Capital in Excess of Par - Preferred Stock $2,250,000

On February 1, 70,000 common shares were issued with a market price of $8:

Journal entry:

Cash $560,000

Common Stock (70,000 shares * $2 par value) $140,000

Paid-in Capital in Excess of Par - Common Stock $420,000

On February 15, 4,000 common shares were issued to Delkab Consulting Co. in settlement of professional services provided at a fee of $100,000:

Journal entry:

Common Stock (4,000 shares * $2 par value) $8,000

Paid-in Capital in Excess of Par - Common Stock $92,000

Accounts Payable/Professional Services $100,000

On March 20, Mr. Park exchanged a piece of land with a fair value of $150,000 for 10,000 common shares:

Journal entry:

Land (fair value) $150,000

Common Stock (10,000 shares * $2 par value) $20,000

Paid-in Capital in Excess of Par - Common Stock $130,000

On July 1, 45,000 common shares were issued for cash at a market price of $25:

Journal entry:

Cash $1,125,000

Common Stock (45,000 shares * $2 par value) $90,000

Paid-in Capital in Excess of Par - Common Stock $1,035,000

Now let's move on to the questions regarding common shares issued and outstanding:

As of July 31, the number of common shares issued is:

Calculation: 70,000 (February 1) + 4,000 (February 15) + 10,000 (March 20) + 45,000 (July 1) = 129,000 common shares

As of July 31, the number of common shares outstanding is the same as the number of common shares issued since there are no repurchases or retirements mentioned.

Moving on to the treasury stock transactions:

On August 1, purchased 5,000 shares of its own $2 par value common stock at $20 per share:

Journal entry:

Treasury Stock $100,000

Cash $100,000

On September 1, sold 1,500 shares of treasury stock purchased on August 1 for $30 per share:

Journal entry:

Cash $45,000

Treasury Stock $30,000

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Step-by-step explanation:

since both spins are independent events (one does not have any impact on the other), the sequence does not matter. the probability of first blue and then gray is the same as first gray and then blue.

it is the probability of getting 1 gray and 1 blue result.

a probability is always the ratio

desired cases / totally possible cases.

since 6/10 of the area of the spine are gray, and 4/10 of the area are blue, the probability for any single spin to result in gray is 6/10 = 3/5 = 0.6.

and the probability to result in blue is 4/10 = 2/5 = 0.4

the probability to get 1 gray and 1 blue is then the product of both probabilities :

0.6 × 0.4 = 0.24

it is like rolling a die twice and asking for e.g. two 6s or any other combination of 2 specific numbers. that probability is

1/6 × 1/6 = 1/36

FYI :

the probability of getting gray twice is then

0.6 × 0.6 = 0.36

the probability of getting blue twice is

0.4 × 0.4 = 0.16

as mentioned to get gray first and blue second is

0.6 × 0.4 = 0.24

to get blue first and gray second

0.4 × 0.6 = 0.24

and these are all the possible results you can get in 2 spins.

therefore, the probability for any of them is

0.36 + 0.16 + 0.24 + 0.24 = 1

The population growth rate for 2019 would be 800 people.

The population size at the start of 2020 would be 149, 800 people.

The formula is:

Growth rate = rmax × Population × ( 1 - ( Population / Carrying Capacity ) )

Growth rate = 0.8 × 149,000 × ( 1 - ( 149, 000 / 150, 000) )

Growth rate = 0.8 × 149, 000 × 0. 0067

Growth rate = 800 people

The population size at the start of 2020 would therefore be:

=  Initial Population + Growth Rate

= 149, 000 + 800

= 149, 800 people

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Sure, I'd be happy to help you with these questions!

a) To calculate the total number of possible 6-digit security numbers, we can use the permutation formula:

nPr = n! / (n-r)!

where n is the total number of digits available (9) and r is the number of digits we are selecting (6).

So, the number of possible 6-digit security numbers without any restrictions is:

9P6 = 9! / (9-6)! = 9! / 3! = 9 x 8 x 7 x 6 x 5 x 4 = 60,480

Therefore, there are 60,480 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits.

b) If the first digit cannot be a one, we are left with 8 choices for the first digit (since we cannot use 1) and 8 choices for the second digit (since we have already used one digit). For the remaining 4 digits, we still have 7 choices for each digit, since we cannot repeat any digits.

Using the permutation formula again, the number of possible 6-digit security numbers with the first digit not being one is:

8 x 8 x 7 x 7 x 7 x 7 = 1,322,496

Therefore, there are 1,322,496 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the first digit is not one.

c) To create an odd number, the last digit must be an odd number, which means we have 5 choices for the last digit (1, 3, 5, 7, or 9). For the first digit, we cannot use 0 or 1, so we have 7 choices. For the remaining 4 digits, we still have 8 choices for each digit (since we can use any digit).

Using the permutation formula again, the number of possible 6-digit security numbers with the last digit being odd is:

7 x 8 x 8 x 8 x 8 x 5 = 7,1680

Therefore, there are 7,1680 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the last digit is odd.

d) To create a number greater than 300,000, the first digit must be 3, 4, 5, 6, 7, 8, or 9. If the first digit is 3, we have 7 choices for the first digit (3, 4, 5, 6, 7, 8, or 9). For the remaining 5 digits, we still have 8 choices for each digit.

If the first digit is not 3, we have 6 choices for the first digit (since we cannot use 1 or 2). For the remaining 5 digits, we still have 8 choices for each digit.

Using the permutation formula again, the number of possible 6-digit security numbers greater than 300,000 is:

7 x 8 x 8 x 8 x 8 x 8 + 6 x 8 x 8 x 8 x 8 x 8 = 2,526,720

Therefore, there are 2,526,720 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the number is greater than 300,000.

e) To create a number greater than 750,000, the first digit must be 8 or 9. If the first digit is 8, we have 2 choices for the first digit (8 or 9). For the remaining 5 digits, we still have 8 choices for each digit.

If the first digit is 9, we only have one choice for the first digit (9). For the remaining 5 digits, we still have 8 choices for each digit.

Using the permutation formula again, the number of possible 6-digit security numbers greater than 750,000 is:

2 x 8 x 8 x 8 x 8 x 8 + 1 x 8 x 8 x 8 x 8 x 8 = 262,144

Therefore, there are 262,144 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the number is greater than 750,000.

As per the given dimension, we need 343 small cubes to completely cover the larger cube.

To determine how many small cubes are needed to cover the larger cube, we need to think about how many of the smaller cubes can fit inside the larger cube.

We can start by looking at the dimensions of the larger cube. Each side is 7cm long, so the volume of the cube can be calculated by multiplying the length, width, and height:

7cm x 7cm x 7cm = 343 cubic centimeters

Now let's consider the dimensions of the smaller cubes. Each cube is 1cm x 1cm x 1cm, so the volume of each cube is:

1cm x 1cm x 1cm = 1 cubic centimeter

To determine how many of these smaller cubes are needed to cover the larger cube, we need to divide the volume of the larger cube by the volume of each small cube:

343 cubic centimeters ÷ 1 cubic centimeter = 343

So we need 343 small cubes to completely cover the larger cube.

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Complete Question:

How many cubes of dimensions 1cm*1cm*1cm are required to cover a cube of dimensions 7cm*7cm*7cm?

If a and b, then c means that if both a and b are true, then c must also be true. This is an example of a conditional statement, where the truth of one proposition (c) is dependent on the truth of the other two propositions (a and b).

Now, given that the reverse of the if-then statement is also correct, we can conclude that if b is true, then a is also true. This means that both a and b are true. Therefore, according to the original statement, c must also be true.

In other words, if a and b are both true, then c must also be true. This is because the conditional statement "if a and b, then c" holds true in this scenario. Therefore, we can conclude that the value of c is true.

Overall, understanding the logic behind conditional statements and their reverses can help us make logical conclusions about the truth of propositions based on the truth of other propositions.

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The dimensions are;

Length = 7 meters

Width = 5 meters

The area of a rectangle is expressed as;

Area = length × width

From the information given, we have that;

Length = 2w - 3

Area = 65

Substitute the values

65 = (2w - 3)w

expand the bracket

65 = 2w² - 3w

solve the quadratic equation;

2w² + 13w - 10w - 65

Factorize the terms

w(2w + 13) - 5(2w + 13)

w = 5

Substitute the value

Length = 2w - 3 = 2(5) - 3 = 7

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The correct option is (2) triangle, because the slice intersects the cube face at three non-collinear points.

When a cube is cut by a single slice passing through three non-collinear points on a face, the shape of the cross section will be the intersection of the slice with the cube face. In this case, the slice passes through points A, B, and C, which are non-collinear, and thus the shape of the cross section will be a triangle.

This is because a triangle is the only shape that can be formed by the intersection of a plane with three non-collinear points on a flat surface, such as the face of a cube. The other options of rectangle, square, and trapezoid are not possible since they cannot be formed by the intersection of a plane with three non-collinear points on a flat surface.

A rectangle can only be formed by the intersection of a plane with four points that form a right angle, a square can only be formed by the intersection of a plane with four points that form a right angle and are equidistant from each other, and a trapezoid can only be formed by the intersection of a plane with four points that are not collinear, but only two of which are parallel.

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The correct variations of the formula for speed are:

m = 6d

d = m/6

6d = m

The formula for speed is distance divided by time. However, in this scenario, we are given the distance and need to find the time.

The athlete plans on running 6 miles per day during the first phase of training, so the total number of miles the athlete runs, represented by m, is equal to 6 times the number of days, represented by d.

Therefore, the correct equation that represents the relationship is:

m = 6d

This equation shows that the total number of miles, m, is directly proportional to the number of days, d, that the athlete runs.

Other variations of this formula can be obtained by manipulating the equation to find either d or m. For example, if we want to find the number of days, we can divide both sides of the equation by 6:

d = m/6

This equation shows that the number of days is equal to the total number of miles divided by 6.

Alternatively, if we want to find the total number of miles, we can multiply both sides of the equation by 6:

6d = m

This equation shows that the total number of miles is equal to 6 times the number of days.

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The volume of a hemisphere with a radius of 8. 8 cm, rounded to the nearest tenth of a cubic centimeter, is approximately 1436.8 cubic centimeters.

To find the volume of a hemisphere with a radius of 8.8 cm, you can use the formula:

Volume = (2/3)πr³

where r is the radius of the hemisphere. Plugging in the given radius:

Volume = (2/3)π(8.8)³ ≈ 1436.8 cubic centimeters

So, the volume of the hemisphere is approximately 1436.8 cubic centimeters, rounded to the nearest tenth of a cubic centimeter.

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Answer:

when it's maintain supplimentary , it means that the sum of the angles given is 180° , In this case let one of the angle be x and the other is given as 125° .

therefore

125° + x = 180°

x = 180° - 125° = 55°

the compliment of x is the angle which when added to x givens 90° , Let the angle be y.

therefore

x + y = 90°

y = 90° - x = 90° - 55° = 35°

35° is the answer

Using the straight-line method, we can find the depreciation expense per year by dividing the depreciable value (cost - residual value) by the estimated life:

Depreciable Value = Cost - Residual Value

Depreciable Value = $40000 - $10000

Depreciable Value = $30000

Annual Depreciation Expense = Depreciable Value / Estimated Life

Annual Depreciation Expense = $30000 / 6

Annual Depreciation Expense = $5000

To create a depreciation schedule, we can subtract the annual depreciation expense from the cost each year until we reach the residual value:

| Year | Cost |   Depreciation | Accumulated Depreciation | Book Value |

|------|---------------|-----------------  |----------------------------------------|------------|

| 1     | $40000  | $5000                | $5000                             | $35000     |

| 2    | $35000  | $5000                 | $10000                           | $30000     |

| 3    | $30000  | $5000                  | $15000                           | $25000     |

| 4    | $25000  | $5000                  | $20000                          | $20000     |

| 5    | $20000  | $5000                  | $25000                         | $15000     |

| 6    | $15000  | $5000                    | $30000                        | $10000     |

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The linear function representing relation of the number of tickets sold and number of hours since tickets have been on sale is given by y = 32x.

Let us consider the two points of the linear function are,

(x₁, y₁) = (2, 64) and (x₂, y₂) = (6, 192).

Use the two-point form of the equation of a line .

Equation of linear function shows relationship between number of tickets sold y and the number of hours since tickets have been on sale x

Slope of the line is,

slope = (y₂ - y₁) / (x₂ - x₁)

         = (192 - 64) / (6 - 2)

         = 128 / 4

         = 32

Apply the point-slope form of the equation of a line with the point (2, 64),

y - y₁= m(x - x₁)

⇒ y - 64 = 32(x - 2)

⇒ y - 64 = 32x - 64

⇒ y = 32x

Check if the equation of the line passes through the third point (18, 576),

y = 32x

⇒576 = 32(18)

⇒576 = 576

Since the equation of the line passes through all three points,

Therefore, linear function between the number of tickets sold and number of hours since tickets have been on sale is y = 32x.

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The above question is incomplete, the complete question is:

A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale.

Number of Hours (x) 2 6 18

Number of Tickets Sold (y) 64 192 576

Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale. Enter your answer in the box

∠AOD≅∠COB,∠AOB≅∠COD by vertical angle theorem. ΔAOD≅ΔCOB,ΔAOB≅ΔCOD by SAS. ∠DAC≅∠BCA,∠BAC≅∠DCA by CPCTC. AB║CD,AD║BC by converse alternate interior angles theorem

Vertical angles theorem states that perpendicular angles, angles that are contrary each other and formed by two cutting straight lines, are harmonious.

Alternate angle theorem states that when two resemblant lines are cut by a transversal, also the performing alternate interior angles or alternate surface angles are harmonious.

SAS Side angle side

CPCTC Corresponding corridor of harmonious triangles are harmonious.

discourse of alternate interior angle theorem If two alternate interior angles are harmonious also the two lines are resemblant.

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Answer:

22.86 centimeters

Step-by-step explanation:

How many centimeters are in 9 inches?

1 inch = 2.54 centimeters

9 inches = 2.54 x 9 = 22.86 centimeters

So, there are 22.86 centimeters in 9 inches.

Answer:

22.86 centimeters

Step-by-step explanation:

To convert inches to centimeters, multiply the inches by 2.54:

9·2.54=22.86

So, there are 22.86 centimeters in 9 inches.

Hope this helps :)

we first need to find out how many street name boards can be purchased with a budget of R80,000. We can do this by dividing the budget by the cost of each street name board:

R80,000 ÷ R134 = 597.01

Since we cannot purchase a fraction of a street name board, we round down to the nearest whole number. Therefore, the municipality can purchase 597 new street name boards with a budget of R80,000.

To find out how much money will be left in the budget, we can subtract the cost of the street name boards from the initial budget:

R80,000 - (597 x R134) = R1,598

Therefore, the municipality will have R1,598 left in their budget after purchasing 597 new street name boards.

Street name boards are an important part of any municipality as they help residents navigate and locate specific areas. By budgeting for and installing new street name boards, the municipality is taking a proactive approach to improve their community's infrastructure and ensure the safety and well-being of their residents.

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If lea wants to divide the canvas into sections that contain an area of 3 then Lea can create 81 sections on the canvas.

To find the number of sections Lea can create on the painting canvas, given the length is 3^5 mm, the width is 3^7 mm, and each section has an area of 3^8 mm^2 we should follow the steps given below:

Step 1: Calculate the total area of the canvas by multiplying the length and the width.
[tex]Total area = (3^5 mm) * (3^7 mm)[/tex]

Step 2: Use the property of exponents that states a^m * a^n = a^(m+n) to simplify the total area.
Total area = 3^(5+7) mm^2
Total area = 3^12 mm^2

Step 3: Divide the total area of the canvas by the area of each section to find the number of sections.
Number of sections = (3^12 mm^2) / (3^8 mm^2)

Step 4: Use the property of exponents that states a^m / a^n = a^(m-n) to simplify the number of sections.
Number of sections = 3^(12-8)
Number of sections = 3^4

Step 5: Calculate the numerical value of 3^4.
Number of sections = 81

Lea can create 81 sections on the canvas.

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0 represents the surface level of the swimming pool.

The height of the slide in relation to 0 is +10 feet.

Part A: In this situation, 0 represents the surface level of the swimming pool on the number line, acting as a reference point between the depth of the water and the height of the slide.

Part B: The height of the slide in relation to 0 is +10 feet. This means the slide is 10 feet above the surface level of the swimming pool.

Part C: To mark the level of the bottom of the pole on the number line, Kayla should mark it at -3 since the bottom of the pole is at a depth of 3 feet below the surface level of the pool.

This is determined by using the negative value to represent the depth below the surface (0).

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The maximum diameter of the spheres Selim can purchase is approximately 1.78 feet, The correct answer is option (C).

To find the maximum diameter of the concrete spheres Selim can purchase, we need to consider the cost and surface area of the spheres. Given that the spheres cost $2 per square foot and Selim can spend $20 per sphere, we can start by finding the maximum surface area he can afford for each sphere.
1. Calculate the maximum surface area:
$20 ÷ $2 per square foot = 10 square feet
Now that we know the maximum surface area is 10 square feet, we can use the formula for the surface area of a sphere to find the maximum diameter.
2. Use the sphere surface area formula:
Surface area = 4πr², where r is the radius of the sphere.

Since the maximum surface area is 10 square feet, we can plug this value into the formula and solve for the radius.
10 = 4πr²
3. Divide both sides by 4π:
10 ÷ 4π = 0.796
4. Take the square root to find the radius:
r = 0.893 ft
5. Finally, multiply the radius by 2 to get the diameter:
D = 2 * 0.893 = 1.786 ft
Therefore, the maximum diameter of the spheres Selim can purchase is approximately 1.78 feet, which corresponds to option C.

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The 95% confidence interval is (0.56, 0.62). This means that we can be 95% confident that the true proportion of city dwellers who would like to live at the beach lies between 56% and 62%.

In this case, the Chamber of Commerce conducted a survey asking city dwellers if they would like to live at the beach. The 95% confidence interval for the population proportion of city dwellers who would like to live at the beach is (0.56, 0.62).

To break this down:
1. Random sample: The Chamber of Commerce surveyed a group of city dwellers chosen randomly, which helps ensure that the results are representative of the entire population of city dwellers.
2. Population proportion: This refers to the percentage of all city dwellers who would like to live at the beach.
3. 95% confidence interval: This means that if the survey were repeated many times with different random samples, 95% of the intervals calculated would contain the true population proportion.

In this case, the 95% confidence interval is (0.56, 0.62). This means that we can be 95% confident that the true proportion of city dwellers who would like to live at the beach lies between 56% and 62%.

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The critical points of f(x) on the interval 0 < x < 10 are: (2, max), (7.5, min)

To estimate the critical points of f(x) on the interval 0 < x < 10, we need to look for points where the derivative, f'(x), equals zero or is undefined. However, we are given a table of values for f(x) instead of f'(x), so we need to first estimate f'(x) using these values.

One way to do this is to use finite differences. We can calculate the first finite difference for each pair of adjacent values in the table, which gives an estimate of the derivative at the midpoint of the interval:

f'(x) ≈ (f(x+1) - f(x)) / (1)

Using this formula, we can calculate the following table of values for f'(x): 0123456789 23-2.79-8-5

Now we can look for critical points of f(x) by finding where f'(x) equals zero or is undefined: - f'(x) = 0 when x = 2 or x = 7.5 (approximately) - f'(x) is undefined at x = 0 and x = 10 (endpoints of the interval)

To classify each critical point, we need to look at the sign of the derivative near the point. If f'(x) changes sign from positive to negative at a critical point, then it is a local maximum. If it changes from negative to positive, then it is a local minimum. If it does not change sign, then it is neither a maximum nor a minimum.

Using the values in the table for f'(x), we can see that: -

Near x = 2, f'(x) changes sign from positive to negative, so it is a local maximum. - Near x = 7.5, f'(x) changes sign from negative to positive, so it is a local minimum. - At the endpoints x = 0 and x = 10, f'(x) is undefined, so there are no critical points.

Therefore, the critical points of f(x) on the interval 0 < x < 10 are: (2, max), (7.5, min)

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To solve this problem, we first need to understand what "at most 4 of them were successes" means. This includes the cases where there are 0, 1, 2, 3, or 4 successful serves out of the 6 selected.

We can use the table to find the probabilities for each of these cases.

For 0 successful serves, the probability is 0.0002.

For 1 successful serve, the probability is 0.004.

For 2 successful serves, the probability is 0.033.

For 3 successful serves, the probability is 0.132.

For 4 successful serves, the probability is 0.297.

To find the probability of at most 4 successful serves, we add up these probabilities:
[tex]0.0002 + 0.004 + 0.033 + 0.132 + 0.297 = 0.466[/tex]

So the probability of at most 4 successful serves is 0.466.

Therefore, the answer is 0.466 and it is found by adding up the probabilities for the cases where there are 0, 1, 2, 3, or 4 successful serves out of the 6 selected from the table.

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The minimum value of k that satisfies this inequality is k = 9.

To find the value of k for which the area of the triangle is a minimum, we'll use the following terms: vertices, non-degenerate triangle, and area of a triangle. Here's the step-by-step explanation:

1. The vertices of the triangle are $(1, 7), (13, 16),$ and $(5, k)$.
2. A non-degenerate triangle means it has a positive area.
3. The area of a triangle can be calculated using the formula: Area = (1/2) * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Now, let's find the area of the triangle with the given vertices:

Area = (1/2) * |1(16 - k) + 13(k - 7) + 5(7 - 16)|

We want to minimize the area, so let's simplify the expression:

Area = (1/2) * |-9 + 13k - 104|

Since we want a non-degenerate triangle, the area must be greater than 0. Therefore, the expression inside the absolute value must be positive:

-9 + 13k - 104 > 0
13k > 113
k > 113/13
k > 8.69

Since k is an integer, the minimum value of k that satisfies this inequality is k = 9.

The sum of the values of k for which the area of the triangle is a minimum is just the single value we found, which is 9.

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The solution of the system of equations is given by the ordered pair (2, 7).

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

3x - y = -1    ......equation 1.

x - 2y = -12  ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I, and it is given by the ordered pairs (2, 7).

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1. C is the center

2. EF is a secant line

3. AD is the diameter

4. CD is the radius

5. FD is the arc

6. The region bounded by AC, BC and arc AB is a segment

7. The region bounded by FE and arc FE is a sector

8. EF is the chord

9. GF is the tangent line

To match the statements, we need to know the following;

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Of course! Please let me know what you need help with and I'll do my best to assist you within the given time frame.

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The probability of choosing a king or queen from a standard 52-card deck is 2/13 or approximately 15.4%.

The probability of choosing a king or a queen from a standard 52-card deck can be calculated by first determining the number of kings and queens in the deck. There are four kings (hearts, diamonds, clubs, and spades) and four queens (hearts, diamonds, clubs, and spades) in the deck, for a total of eight cards.

To find the probability of choosing a king or a queen, you need to divide the number of desired outcomes (eight) by the total number of possible outcomes (52).

Probability = Number of desired outcomes / Total number of possible outcomes

Probability = 8 / 52

This simplifies to:

Probability = 2 / 13

Therefore, the probability of choosing a king or a queen from a standard 52-card deck is approximately 0.154 or 15.4%.

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24 cm  is the height of cone .

What is known as a cone?

A cone is a three-dimensional geometric object with a smooth transition from a flat, generally circular base to the apex, also known as the vertex.

                                      A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex. Cone. a right circular cone having the following measurements: height, slant height, angle, base radius, and height.

V=1/3hπr²

V = 1/3 * h * 12π

96π = 1/3 * h * 12π

96π * 3/12π  = h

 8 * 3   = h

  h = 24 cm

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I must have left home at 4:54 PM in order to arrive at the park at 4:30 PM after 24 minutes of travel time.

Given the parameters in the question: if i went to park at 4:30 and it took me 24 minutes

Arrival time = 4 : 30PM

Travel time = 24 minutes

I can determine when i left home by simply subtracting the travel time from the time I arrived.

Hence,

Add the travel time to the time you arrived at the park.

4:30 PM (arrival time) + 24 minutes (travel time) = 4:54 PM

Therefore, I must have left home at 4:54 PM.

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The value of the variables are;

x = 52

y = 30

from the information given, we have simultaneous equations ;

−7y−4x=1

7y−2x=53

Make 'y' the subject from equation 1 , we have;

y = 1 + 4x/-7

Substitute the value into equation 2, we get;

7(1 + 4x/-7) - 2x = 53

expand the bracket

7 + 28x/-7 - 2x= 53

7 + 28x + 14x = 53(-7)

then, we have;

7 + 42x =,-371

collect the like terms

42x = 364

x = 52

Substitute the value

y =  1 + 4x/-7

y = 1+ 4(52)/-7

y = 30

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