If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values Σx = 2769 and Σx2 = 132,179 to compute the sample mean and sample standard deviation. (Round s to four decimal places.)

The expression is factored to give;

(x + 4) = 0 , (x + 10) = 0. Step 2

From the information given, we have that the quadratic equation is expressed as;

x² + 14x + 40 =0

Now, find the product of 40 and the coefficient of x squared

The product is 40

Find the pair factors of 40 that adds up to 14, we have;

x² + 10x + 4x + 40 = 0

Group the expression in pairs, we get;

(x² + 10x) + (4x + 10)

factor the common terms, we have;

x(x + 10) + 4(x + 10)

Then, we have;

(x + 4) = 0

(x + 10) = 0

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Answer:

Step-by-step explanation:

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer:

30 paperclips were still on the floor.

Step-by-step explanation:

First, we need to make sure that both of the fractions have the same denominator so that they will be measured on the same scale. 2/5 -> will be 4/10 when multiplied by 2. Now we calculate how many paperclips were picked up. 4/10 + 3/10 = 7/10 which means that 70 paperclips were picked up because 7/10's of a 100 is 70. Next we find the paperclips on the floor 10/10-7/10 = 3/10 or 30 paperclips.

The matrix representing the profit from the sales of book A for each store is:

[  $4  ]

[  $4  ]

[  $4  ]

To represent the profit from the sales of book A for each store, we can use a matrix where the rows correspond to the stores (X, Y, Z) and the columns correspond to the book A.

The matrix representing the profit from the sales of book A for each store is as follows:

Store Book A

X $4

Y $4

Z $4

Therefore, the matrix representing the profit from the sales of book A for each store is:

[  $4  ]

[  $4  ]

[  $4  ]

Each element in the matrix represents the profit from the sales of book A in a specific store, which is $4 for all stores (X, Y, Z).

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The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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(x² + 4)(x² - 4) = x⁴ - 16 and the product is placed in the grid.

Given expression is: (x² + 4)(x² - 4) To multiply two polynomials, we use the distributive property.

We will multiply x² with both x² and -4 and 4 with both x² and -4 as shown below.x² * x² + x² * (-4) + 4 * x² + 4 * (-4)x⁴ - 4x² + 4x² - 16.

The above expression can be simplified further by combining like terms. 4x² gets canceled on adding -4x² and 4x².

Simplified expression is: x⁴ - 16

Hence, (x² + 4)(x² - 4) = x⁴ - 16 and the product is placed in the grid below:   

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A utility approach should be applied when making decisions under conditions of uncertainty or risk.

It is a mathematical framework that quantifies preferences and assigns utilities (values representing desirability) to different outcomes.

By evaluating the expected utilities of various options, decision-makers can make rational choices that maximize their overall well-being or utility.

This approach is particularly useful when there are multiple possible outcomes with associated probabilities, allowing for a systematic analysis of the potential benefits and risks of different choices.

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Answer:

Therefore, the constant of proportionality for the given proportional relationship is 5.

Step-by-step explanation:

To determine the constant of proportionality in the given proportional relationship, we can use the formula:

Constant of Proportionality = Tickets / Games

Let's plug in the values from the table:

For the first set of values (4 games and 20 tickets):

Constant of Proportionality = 20 / 4 = 5

For the second set of values (7 games and 35 tickets):

Constant of Proportionality = 35 / 7 = 5

For the third set of values (10 games and 50 tickets):

Constant of Proportionality = 50 / 10 = 5

In all three cases, the constant of proportionality is equal to 5.

Therefore, the constant of proportionality for the given proportional relationship is 5.

After analyzing various transactions and discrepancies, the adjusted bank balance can be obtained by adding or subtracting the corresponding amounts from the ledger balance of Br. 4,173.83 as of July 31.

The given information describes various transactions and discrepancies between the bank statement balance and the ledger balance of ABC Company as of July 31. To determine the adjusted balance, we need to analyze each item:

The deposit of Br. 410.90 made after banking hours will not appear in the bank statement until the next statement is issued. Therefore, it does not affect the July 31 balance.

The check drawn for Br. 79 was erroneously charged by the bank for Br. 973. This means the bank deducted an incorrect amount from ABC's account. The adjustment will increase the bank balance by Br. 894.

The outstanding checks, totaling Br. 610.75, have not been paid by the bank yet. These checks need to be subtracted from the bank balance.

The check written for Br. 210 was incorrectly charged as Br. 120 by the bank. This error results in an adjustment of Br. 90, increasing the bank balance.

The proceeds from the collection of the interest-bearing note receivable from David, amounting to Br. 500, should be added to the bank balance.

The interest earned on the average account balance during July, Br. 24.75, should be added to the bank balance.

The check for Br. 10, returned with the statement, had been recorded as Br. 100 in the check register. This discrepancy results in an adjustment of Br. 90, decreasing the bank balance.

The bank charged a fee of Br. 5.00 for handling the collection of the note receivable. This fee should be subtracted from the bank balance.

The check from customer John, amounting to Br. 50.25, was charged as Non-Sufficient Funds (NSF) by the bank. This adjustment decreases the bank balance.

The bank service charge for the month of July, Br. 12.70, should be subtracted from the bank balance.

The incorrect recording of check number 875, which was issued for Br. 85 but recorded as Br. 58, results in an adjustment of Br. 27, decreasing the bank balance.

By considering all these adjustments, we can calculate the adjusted bank balance by adding or subtracting the respective amounts from the ledger balance of Br. 4,173.83

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Answer:

14 is an integer

-32.62 is not

-13/4 is not

15/3 = 5 is an integer

51 is an integer

The functions for this problem are defined as follows:

The functions for this problem are given as follows:

The addition and subtraction functions for this problem are given as follows:

At x = -2, the numeric value of the subtraction function is given as follows:

(t - s)(-2) = -2³ - 5(-2)²

(t - s)(-2) = -28.

The product function for this problem is given as follows:

(ts)(x) = [tex]5x^5[/tex]

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The utility can be used to quantify and compare preferences in decision-making scenarios where performance is not measured by monetary value.

The utility can be used as a measure of preference or satisfaction in decision-making situations where performance is not directly measured by monetary value. Utility refers to the subjective value or desirability that an individual assigns to different outcomes or options.

In such cases, utility can be quantified using a utility function, which maps the outcomes or attributes of the decision problem to a numerical representation of the individual's preferences. This function allows for the comparison and evaluation of different options based on their utility values.

For example, consider a decision involving healthcare treatments. The performance of different treatments may not be easily measured in monetary terms, but individuals may have preferences based on factors such as effectiveness, side effects, or quality of life impact.

Utility can be used to capture these preferences and make a decision that maximizes the overall satisfaction or well-being of the individual.

To use utility in decision-making, it is necessary to understand and quantify individual preferences through techniques like surveys, interviews, or experimental methods. By assigning utility values to different outcomes or attributes, decision-makers can then compare options and select the one that maximizes utility.

However, it's important to note that utility is subjective and varies among individuals. Different people may have different utility functions and weigh attributes differently. Therefore, utility-based decision-making requires taking into account the preferences of the specific individual or group involved.

In summary, utility can be employed in decision-making scenarios where performance is not directly measured in monetary terms. It quantifies subjective preferences and allows for the comparison and selection of options based on the utility values assigned to different outcomes or attributes.

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The height of the stone projected upward is given by h(t) = -16t² + 122t + 15

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of the stone above the ground after t seconds. Given that:

h(t) = -16t² + v₀t + h₀

Given that the platform is 15 ft high, hence h₀ = 15 ft. Also, the rate is 122 ft/s, hence, v₀ = 122 ft/sec.

The equation becomes:

h(t) = -16t² + 122t + 15

The height of the stone is h(t) = -16t² + 122t + 15

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Answer:

d = 8 cm

Step-by-step explanation:

We want to find the length of segment d.

We are given a circle, with two segments that intersect the circle. We also know that a = 4 cm, b = 12 cm, c = 6 cm.

We are also given that if two segments intersect inside or outside a circle, ab = cd. Because the two segments do intersect the circle, we can use the equation that was given.

We can plug the values that we know into the equation.

ab = cd

4 * 12 = 6 * d

Now, divide both sides by 6.

[tex]\frac{4 * 12}{6} = d[/tex]

8 = d

So, d is 8 cm.

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

False

Step-by-step explanation:

Since a triangle must contain 3 interior angles all adding to 180°, then there can't be more than one right angle since 2 right angles would add up to 180°.

Solving a system of equations, we can see that the grocer should mix approximately 2.88 pounds of the first kind of candy and 12.12 pounds of the second kind of candy to obtain a 15-pound mix selling for $2.05 per pound.

Let's assume the grocer mixes x pounds of the first kind of candy, which sells for $1.00 per pound, and y pounds of the second kind of candy, which sells for $2.30 per pound.

The total weight of the mix is 15 pounds, so we have the equation:

x + y = 15

The price of the mix is $2.05 per pound, so we have the equation:

(1.00x + 2.30y) / 15 = 2.05

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method:

From equation (1), we can solve for x in terms of y:

x = 15 - y

Substituting this value of x in equation (2), we have:

(1.00(15 - y) + 2.30y) / 15 = 2.05

Simplifying and solving for y:

(15 - y + 2.30y) / 15 = 2.05

(15 + 1.30y) / 15 = 2.05

15 + 1.30y = 30.75

1.30y = 30.75 - 15

1.30y = 15.75

y = 15.75 / 1.30

y ≈ 12.12

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

x + 12.12 = 15

x ≈ 2.88

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The population of the city was 3450 in the year 2000 and it is decreasing by 80 people every year since then.

Given equation: `y = -80x + 3450`Here, `x` represents the number of years after 2000 and `y` represents the city's population.Let's put the value of `x = 0` in the above equation to find out the population in the year 2000.`y = -80x + 3450``y = -80(0) + 3450``y = 3450`Therefore, the population of the city in the year 2000 was 3450.

Let's put the value of `x = 1` in the above equation to find out the population after one year of 2000.`y = -80x + 3450``y = -80(1) + 3450``y = 3370`Therefore, the population of the city after one year of 2000 was 3370.As we know that the coefficient of `x` in the equation `y = -80x + 3450` is negative. This means that the population of the city is decreasing by 80 people every year since 2000.Therefore, based on the given equation `y = -80x + 3450`

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The solutions to the given exponential inequalities are provided below.

To solve exponential inequalities in R, we need to follow certain steps. Let's solve each of the given exponential inequalities one by one:

[tex]25^(5x) = 3^(-s):[/tex]

First, let's take the logarithm on both sides to eliminate the exponentials:

[tex]log(25^(5x)) = log(3^(-s))[/tex]

Using the logarithmic property, we can bring down the exponents:

(5x)log(25) = (-s)log(3)

Since log(25) = 2 and log(3) is a constant, we can simplify the equation:

10x = -slog(3)

Dividing both sides by 10, we get:

x = (-slog(3))/10

[tex]9^(x+3) - 3^(*-440):[/tex]

We can rewrite [tex]3^(-440) as 1/(3^440):\\9^(x+3) - 1/(3^440)[/tex]

Combining the terms with a common base:

[tex](3^2)^(x+3) - 1/(3^440)[/tex]

Using the exponent rule, (a^m)^n = a^(mn):

[tex]3^(2x+6) - 1/(3^440)\\3^(x-3) - 9x - 1 = 1/27:[/tex]

We can rewrite 1/27 as [tex]3^(-3):[/tex]

[tex]3^(x-3) - 9x - 1 = 3^(-3)[/tex]

Moving the terms to one side:

[tex]3^(x-3) - 9x - 1 - 3^(-3) = 0[/tex]

4^(37·2x+8):

Using the exponent rule[tex], (a^m)^n = a^(mn):[/tex]

4^((37·2)x+8)

Simplifying the exponent:

[tex]4^(74x+8)[/tex]

Note that without specific values for variables or more specific instructions, it is not possible to provide numerical solutions.

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The input value that produces the same output value for the two functions on the graph is x = 0.

To determine the input value that produces the same output value for the two functions, we need to find the x-coordinate at which the lines f(x) and g(x) intersect on the graph.

The line labeled f(x) passes through the points (-3, 3), (0, 3), and (4, 3). Since all these points have the same y-coordinate of 3, we can conclude that f(x) is a horizontal line.

The line labeled g(x) passes through the points (-4, -3), (0, 0), and (4, 3). By connecting these points, we can observe that g(x) is not a horizontal line and has a positive slope.

Since the lines f(x) and g(x) intersect at a single point, we need to determine the x-coordinate of this point to find the input value that produces the same output value for both functions.

By examining the graph, we can see that the lines f(x) and g(x) intersect at the point (0, 3).

This means that when x = 0, both f(x) and g(x) have an output value of 3.

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Please find attached the drawing showing the two prisms that make up the composite figures, created with MS Word

Composite figures are geometric figures that comprises of two or more regular figures.

a) The geometric figure in figure a indicates that the figure is a composite figure consisting of two geometric figures which are cuboids, with dimensions;

Cuboid on the left; Width = 4 cm, breadth = 2 cm, height = 7 cm

Cuboid on the right; Width = 5 cm, breadth = 2 cm, height = 3 cm

b) The figure is a composite figure, which consist of a cuboid and a hollow triangular prism opening at its center.

The dimensions of the cuboid are; Width = 10 cm, thickness = 14 cm, height = 10 cm

The dimensions of the hollow triangular prism are; Base length = 6 cm, height = 4 cm

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Answer:

$0.21 per marble

Step-by-step explanation:

Answer:

$0.21 per marble

Step-by-step explanation:

The vertex of f(x) = -5 - x² - 3x is (-3/2, -17/4).

Here's how to find it:First, we need to know that the vertex of a parabola is (-b/2a, f(-b/2a)), where f(x) is the function in standard form, ax² + bx + c.So, in this case, a = -1, b = -3, and c = -5. Thus,-b/2a = -(-3)/2(-1) = 3/2f(-b/2a) = -5 - (3/2)² - 3(3/2) = -5 - 9/4 - 9/2 = -17/4.

Therefore, the vertex of f(x) = -5 - x² - 3x is (-3/2, -17/4). Note that the minus sign in front of x² means the parabola opens downwards, so the vertex is the highest point of the graph.

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Answer:

To find the rectangular coordinates of the polar coordinates (3, -2), we can use the following formulas:

x = r cos(theta)

y = r sin(theta)

where r is the distance from the origin to the point, and theta is the angle between the positive x-axis and the line connecting the origin and the point, measured in radians.

In this case, r = 3 and theta = -2. To convert the angle to radians, we can add 2 pi to it, since negative angles represent angles measured clockwise from the positive x-axis in polar coordinates. So, theta = -2 + 2 pi = 4.283 radians.

Using the formulas, we get:

x = 3 cos(4.283) ≈ -1.008

y = 3 sin(4.283) ≈ -2.573

Therefore, the rectangular coordinates of the polar coordinates (3, -2) are approximately (-1.008, -2.573).

To find the polar coordinates of the rectangular coordinates (2, 5pi/4), we can use the following formulas:

r = sqrt(x^2 + y^2)

theta = atan2(y, x)

where x and y are the rectangular coordinates of the point.

In this case, x = 2 and y = 0. To find the angle, we can use the fact that the point is in the fourth quadrant, where x is positive and y is negative. Therefore, the angle is pi + 5pi/4 = 9pi/4 radians.

Using the formulas, we get:

r = sqrt(2^2 + 0^2) = 2

theta = atan2(0, 2) = 0

Therefore, the polar coordinates of the rectangular coordinates (2, 5pi/4) are (2, 9pi/4).

Answer:

S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:

(3,p): The first element is 3 and the second element is p.

(3,0): The first element is 3 and the second element is 0.

(4,q): The first element is 4 and the second element is q.

(1,4): The first element is 1 and the second element is 4.

An expression which the model represent include the following: A. [tex]\frac{7}{8} \div \frac{1}{8}[/tex].

In Mathematics and Geometry, an expression simply refers to a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

By critically observing the model shown in the image attached below, we can reasonably infer and logically deduce that each interval represents the numerical value, 1/8.

Since the arrow increased from 0 to 7/8, it implies that an expression which the model represent can be written as follows;

[tex]\frac{7}{8} \div \frac{1}{8}[/tex]

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer

the question is not correct

After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.

To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:

Starting with the bank statement balance: Br. 4,964.47

Add the deposit made after banking hours: + Br. 410.90

New bank balance: Br. 5,375.37

Now let's make adjustments for the outstanding checks and other transactions:

Deduct the erroneously charged check: - Br. 973

New bank balance: Br. 4,402.37

Deduct the outstanding checks:

Check No. 801: Br. 100.00

Check No. 888: Br. 10.25

Check No. 890: Br. 294.50

Check No. 891: Br. 205.00

Total deduction: Br. 609.75

New bank balance: Br. 3,792.62

Correct the incorrectly charged check: + Br. 90

New bank balance: Br. 3,882.62

Add the proceeds from the collection of the interest-bearing note: + Br. 500.00

New bank balance: Br. 4,382.62

Add the interest earned on the average account balance: + Br. 24.75

New bank balance: Br. 4,407.37

Deduct the incorrectly recorded check: - Br. 90

New bank balance: Br. 4,317.37

Deduct the fee charged for handling the collection of the note: - Br. 5.00

New bank balance: Br. 4,312.37

Deduct the check returned due to insufficient funds: - Br. 50.25

New bank balance: Br. 4,262.12

Deduct the service charge for the month of July: - Br. 12.70

New bank balance: Br. 4,249.42

Deduct the erroneously recorded check: - Br. 85.00

New bank balance: Br. 4,164.42

Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).

Adjusted bank balance: Br. 4,164.42

Ledger balance: Br. 4,173.83

The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.

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