- Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.

Number of Garments

5

10

15

Company 1

$55.25

$75.50

$95.75

Company 2

$31.25

$57.50

$83.75

The sum of the mixed fractions given is 9 [tex]\frac{4}{3}[/tex].

Mixed fractions are type of fractions which consist of a whole number part and a fractional part.

Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.

Here the two numbers are 7 [tex]\frac{2}{3}[/tex] and 2 [tex]\frac{2}{3}[/tex].

Here 7 [tex]\frac{2}{3}[/tex] is actually 7 + [tex]\frac{2}{3}[/tex] and 2 [tex]\frac{2}{3}[/tex] is actually 2 + [tex]\frac{2}{3}[/tex].

Addition of mixed numbers can be done as following.

First add the whole numbers. Here, add 7 + 2.

Then add the fractional parts together. Fractional parts can be added as normal addition of fractions by making the denominators equal and adding the numerators.

7 [tex]\frac{2}{3}[/tex] + 2 [tex]\frac{2}{3}[/tex] = (7 + [tex]\frac{2}{3}[/tex]) + (2 + [tex]\frac{2}{3}[/tex])

             = (7 + 2) + ([tex]\frac{2}{3}[/tex] + [tex]\frac{2}{3}[/tex])

             = 9 + [tex]\frac{2+2}{3}[/tex]

             = 9 + [tex]\frac{4}{3}[/tex]

             = 9 [tex]\frac{4}{3}[/tex]

The flaw in Jonathan's reasoning is that while he was adding the fractional part, he adds the denominators also instead of keeping it as such.

Hence the sum is 9 [tex]\frac{4}{3}[/tex].

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Answer:

შეგვიძლია ამოვიღოთ რომ CuO და HNO3 რეაგირებენ და ქებისყარის შედეგად Cu(NO3)2 იქნება წარმოდგენისათვის.

სახელში მოცემული მასალების მიხედვით, შეგვიძლია ამოვიღოთ რომ 1 მოლი CuO რეაგირებულია 4 მოლი HNO3-თი, ანუ შესაბამისად, მასალების მიხედვით:

m(CuO) / M(CuO) = n(CuO) = n(HNO3) = m(HNO3) / M(HNO3)

10 გ / 79,55 გ/მოლი = 0,1256 მოლი CuO = 0,1256 მოლი HNO3 = 12,6 გ / 63,01 გ/მოლი

რეაქციის შემდეგ მივიღებთ, რომ 1 მოლი CuO-სთვის გამოვიყენებთ 4 მოლი HNO3-ს, რაც შემდეგ მანამდე გადავაკეთებთ მათ მიერ რეაქციას, ანუ:

n(Cu(NO3)2) = n(CuO) = 0,1256

Step-by-step explanation:

The sample size for the confidence interval is given as follows:

n = 185.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The parameters for this problem are given as follows:

[tex]M = 0.071, \pi = 0.41[/tex]

Hence the sample size is obtained as follows:

[tex]0.071 = 1.96\sqrt{\frac{0.41(0.59)}{n}}[/tex]

[tex]0.071\sqrt{n} = 1.96\sqrt{0.41 \times 0.59}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.41 \times 0.59}}{0.071}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.41 \times 0.59}}{0.071}\right)^2[/tex]

n = 185.

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Answer: The expected value of each warranty sold can be calculated as the sum of the product of the probability of a product failing after the original warranty period and the replacement cost, and the cost of the extended warranty:

Expected value = (0.8% of $300) + ($47)

Expected value = (0.008)($300) + ($47)

Expected value = $2.40 + $47

Expected value = $49.40

Therefore, the company's expected value of each warranty sold is $49.40.

Step-by-step explanation:

Answer:

no

Step-by-step explanation

The probability of selecting a marble at random is 10/21, or 5/10.

Probability is the likelihood or chance of something happening. It is a mathematical measure of how likely an event is to occur, expressed as a number between 0 and 1. Probability can be used to make predictions and decisions about the future and to explain the likelihood of various outcomes. Probability is an important concept in many fields, including mathematics, finance, statistics, and science.

This is because there are 10 marbles out of a total of 21 total objects (3 golf balls, 8 tennis balls, and 10 metal marbles).

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Answer:

Step-by-step explanation:

[tex]2(3x-2) = 2\times3x-2\times2[/tex]     (multiply each term in the parenthesis by 2)

               [tex]=6x-4[/tex]

Answer:

6x - 4

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 2(3x - 2)

Let's simplify the expression,

→ 2(3x - 2)

→ 2(3x) + 2(-2)

→ 6x + (-4)

→ 6x - 4

Hence, the answer is 6x - 4.

Answer:

it is impossible to know

Answer:

The smallest insect is at 1  1/8 inches.

Step-by-step explanation:

Determining measurements:

There are 8 lines between 1 and 2  so each line is 1/8 inch.

The first x is at 1 1/8 inches.

The smallest insect is at 1  1/8 inches.

The expression "The sum of a number and -3 is equal" can be written as: x - 3 =

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

The sum of a number and -3 is equal

As a general rule:

An equivalent expression is a different expression that has the same value or meaning as the original expression.

Express the operators properly

a number + -3 =

Express the numbers properly using x

So, we have

x - 3 =

Hence, the algebraic expression of the statement is x - 3 =

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Complete question

Express the statement as an algebraic expression

The sum of a number and -3 is equal

The answer of the given expression  is -4.

What is expression ?

An expression is a combination of numbers, symbols, and operators that represents a mathematical quantity or relationship. It can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be simple or complex and can be evaluated or simplified to a single value or another expression. Examples of expressions include 2x + 3, 4y - 7, (x + 5) / 2, and √(x² + y²).

We can solve the equation as follows:

|7x+4|/8 = 3

|7x+4| = 3*8

|7x+4| = 24

Now we have two cases to consider:

Case 1: 7x+4 is positive

|7x+4| = 7x+4

7x+4 = 24

7x = 20

x = 20/7

Case 2: 7x+4 is negative

|7x+4| = -(7x+4)

-7x-4 = 24

-7x = 28

x = -4

Therefore, the solutions are x = -4 and x = 20/7. However, we need to check if they satisfy the original equation:

For x = -4:

|7(-4)+4|/8 = 3

|-24|/8 = 3

3 = 3 (satisfied)

For x = 20/7:

|7(20/7)+4|/8 = 3

|24+4|/8 = 3

28/8 = 3.5 ≠ 3 (not satisfied)

So the only solution that satisfies the original equation is x = -4.

Therefore, the answer of the given expression  is -4.

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Answer:

$22.49

Step-by-step explanation:

5 pounds of nectarines costs $8.65

8.65/5 = 1.73

1 pound of nectarines costs $1.73

1.73 times 13 = 22.49

Answer:2249/100

Step-by-step explanation:

13 x 8.65/5

calculate : 13 x 8.65/5

2249/100

Answer:

Step-by-step explanation:

Let's call the distance from the tower's base to the end of the wire "d". According to the problem, the height of the tower is 8 feet greater than "d". We can write this as:

height of tower = d + 8

We also know that the wire is 40 feet long. The wire stretches from the ground to the top of the tower, so we can use the Pythagorean theorem to relate the distance "d", the height of the tower, and the length of the wire:

d^2 + (d + 8)^2 = 40^2

Expanding and simplifying this equation gives:

2d^2 + 16d - 960 = 0

Dividing both sides by 2 gives:

d^2 + 8d - 480 = 0

We can solve this quadratic equation using the quadratic formula:

d = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 8, and c = -480. Substituting these values and simplifying, we get:

d = (-8 ± sqrt(8^2 + 4(480))) / 2

d = (-8 ± sqrt(2080)) / 2

d ≈ -25.73 or d ≈ 17.73

Since "d" represents a distance, it cannot be negative. Therefore, we choose the positive solution:

d ≈ 17.73

Now we can use the equation we derived earlier to find the height of the tower:

height of tower = d + 8

height of tower ≈ 17.73 + 8

height of tower ≈ 25.73

So the distance from the tower's base to the end of the wire is approximately 17.73 feet, and the height of the tower is approximately 25.73 feet.

The equation of circles that have a diameter of 12 units and a center that lies on the y-axis is  (x + 6)² + y² = 144

The equation of a circle with center (h, k) and radius r is given by

(x - h)² + (y - k)² = r²

To determine which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis, we must have that

for the circle to lie on the y - axis, k = 0 and r² = 144

So, comparing the equations that meet this criteria, we have

(x + 6)² + y² = 144

We cannot select the circle  (x – 4)² + y² = 36. Although it lies on the y - axis, its radius is not equal to 12.

So, the circle is (x + 6)² + y² = 144

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Answer:

consonance

Step-by-step explanation:

consonance are words that end the same

spins and veins

The 20% percentage of bill $169.86 is $33.9.

A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Here the total bill amount= $169.86

The percentage for tip is 20%.

Then the tip amount = 20% of bill

=> 20% of 169.86

=> 20% × 169.86

=> [tex]\frac{20}{100}\times 169.86[/tex]

=> $33.9

Hence the bill amount is $33.9.

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As k increases, the graph of f(x) will shift upwards by k units which means Option (2) is the correct answer.

Define the term "graph" ?

In mathematics, a graph is a visual representation of a set of points, often called vertices, that are connected by lines or curves, often called edges or arcs.

The function [tex]f(x) = (x - 5)^3 + k[/tex]  is a cubic function with a vertical shift of k units upwards. The graph of a cubic function is a curve that can have a variety of shapes, including a "hump" shape or a "S" shape, depending on the values of its coefficients.

As k increases, the graph of f(x) will shift upwards by k units. This means that the minimum point of the graph will move higher and higher, while the shape of the curve remains the same. Specifically, the graph will be shifted vertically upwards by k units, and the y-intercept of the curve will be (0,k), instead of (0,0).

If k is very large, the graph of f(x) will approach a vertical line, as the upward shift will dominate the shape of the curve. Conversely, if k is very small, the upward shift will be negligible, and the graph of f(x) will resemble the graph of the basic cubic function y = x^3, with its minimum point at (5, 0).

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If Molly bought a watch in Singapore for 58 Singapore dollars.  the difference between the amounts that Molly and Louis paid for their watches, in pounds, is £1.06.

To compare the prices paid by Molly and Louis in the same currency, we need to convert their respective amounts to pounds.

First, we convert Molly's purchase of 58 Singapore dollars to pounds:

58 Singapore dollars x £0.57/1 Singapore dollar = £33.06

Next, we convert Louis's purchase of 336 Hong Kong dollars to pounds:

336 Hong Kong dollars x £1/10.50 Hong Kong dollars = £32.00

Molly paid £33.06 for the watch, while Louis paid £32.00. The difference in the amounts paid is:

£33.06 - £32.00 = £1.06

So, the difference between the amounts that Molly and Louis paid for their watches, in pounds, is £1.06.

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Answer: 10.5 - 5.4n

Step-by-step explanation:

   To simplify, we will combine like terms.

Given:

   2.5 - 3.4n - 2n + 8

Add 2.5 + 8 and subtract -3.4n - 2n:

   10.5 - 5.4n

Answer:

[tex]-5.4n + 10.5[/tex]

Step-by-step explanation:

[tex]2.5 + 3.4n -2n + 8\\(-3.4n - 2n) + (2.5 + 8)\\-5.4n + 10.5[/tex]

The value of each variable in the triangle are:

x = 28 units

y = 7√6 units

z = 14√3 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Considering the upper triangle:

cos 45° = (14√2)/x

x = (14√2)/cos 45°

x = 28 units

hypotenuse =√((14√2)² + 28²) = 14√6 units

Considering the lower triangle:

The two triangles share the same hypotenuse.

Thus, hypotenuse = 14√6 units

sin 30° = y/hypotenuse

sin 30° = y/(14√6)

y = (14√6) * sin 30°

y = 7√6 units

cos 30° = z/hypotenuse

cos 30° = z/(14√6)

z = (14√6) * cos 45°

z = 14√3 units

Therefore, the value of each variable are x = 28 units, y = 7√6 units and z = 14√3 units.

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Answer:

She got $21.70 an hour

Step-by-step explanation:

130.20/6= 21.7

The solution to 5.650 - 2.913 when regrouped is 2.737

What is regrouping of numbers?

Making groups of ten while doing math operations like addition or subtraction is known as regrouping. This frequently occurs while dealing with double digits.

This process is called regrouping because you’re rearranging numbers into place value to carry out the process. Regrouping is a great way to make larger calculations easier to do, especially for children. When you’re using regrouping with subtraction it can also be known as ‘borrowing’.

This helpful method is taught in schools to make addition and subtraction easier for students. If you’re not sure how it’ll work and if it’ll be as easy as it sounds, don’t worry because we’re going to take you through the process.

When regrouped, 5.650 - 2.913 can be written as:

Therefore, the solution to 5.650 - 2.913 when regrouped is 2.737.

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ABC is an important tool for companies to utilize when they need to accurately assess their product costs and make decisions based on that information. ABC can also be used to create external reports that show customers and other stakeholders the cost of a product.

External reports are documents that are created by outside organizations or individuals and contain information that is relevant to a particular company or industry. They are used to provide insight and data that can help an organization make informed decisions.

Activity-based costing (ABC) is a method of product costing that assigns costs to products based on the activities that go into producing them. It is used to decide how much it costs a company to make a product, and then the company can use this information to set prices and make pricing decisions. With ABC, companies track the costs associated with activities and assign those costs to the products that use the activities. This is different from traditional costing methods that allocate costs to products based on a single cost driver, such as machine hours or direct labor hours. ABC is a more accurate way of determining the cost of a product because it takes into account all of the activities that go into making it. ABC can also be used to create external reports that show customers and other stakeholders the cost of a product. These reports can help a company make decisions about pricing and production efficiency, and can also be used to compare products and services to competitors. ABC is an important tool for companies to utilize when they need to accurately assess their product costs and make decisions based on that information.

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ABC is an impοrtant tοοl fοr cοmpanies tο utilize when they need tο accurately assess their prοduct cοsts and make decisiοns based οn that infοrmatiοn. ABC can alsο be used tο create external repοrts that shοw custοmers and οther stakehοlders the cοst οf a prοduct.

External repοrts are dοcuments that are created by οutside οrganizatiοns οr individuals and cοntain infοrmatiοn that is relevant tο a particular cοmpany οr industry. They are used tο prοvide insight and data that can help an οrganizatiοn make infοrmed decisiοns.

Activity-based cοsting (ABC) is a methοd οf prοduct cοsting that assigns cοsts tο prοducts based οn the activities that gο intο prοducing them. It is used tο decide hοw much it cοsts a cοmpany tο make a prοduct, and then the cοmpany can use this infοrmatiοn tο set prices and make pricing decisiοns. With ABC, cοmpanies track the cοsts assοciated with activities and assign thοse cοsts tο the prοducts that use the activities. This is different frοm traditiοnal cοsting methοds that allοcate cοsts tο prοducts based οn a single cοst driver, such as machine hοurs οr direct labοr hοurs.

ABC is a mοre accurate way οf determining the cοst οf a prοduct because it takes intο accοunt all οf the activities that gο intο making it. ABC can alsο be used tο create external repοrts that shοw custοmers and οther stakehοlders the prοduct cοst . These repοrts can help a cοmpany make decisiοns abοut pricing and prοductiοn efficiency, and can alsο be used tο cοmpare prοducts and services tο cοmpetitοrs. ABC is an impοrtant tοοl fοr cοmpanies tο utilize when they need tο accurately assess their prοduct cοsts and make decisiοns based οn that infοrmatiοn.

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Complete question:

What Activity-Based Costing in Product Costs for External Reports?

Answer:

10000 meters

Step-by-step explanation:

1 kilometer=1000 meters

therefore 10 kilometers = 10×1000 = 10000meters

(a) The number of students who took none of the three subjects is 169.

(b) The number of students who took PE but not BIO or ENG is 19.

(c) The number of students who took BIO and PE but not ENG is 8.

To find the number of students who took none of the three subjects, we can add up the numbers in the "none" region of the diagram.

From the given information, we know that 45 students took PE, 45 took BIO, and 45 took ENG, so the total number of students who took at least one subject is:

45 + 45 + 45 = 135

We also know that 4 students took all three subjects, so we need to subtract them from the total to avoid double-counting:

135 - 4 = 131

Therefore, the number of students who took none of the three subjects is:

300 - 131 = 169

(b) To find the number of students who took PE but not BIO or ENG, we need to look at the region of the diagram that only includes PE.

This includes the 12 students who took both PE and BIO, the 10 students who took both PE and ENG, and the 4 students who took all three subjects.

Therefore, the number of students who took PE but not BIO or ENG is:

45 - 12 - 10 - 4 = 19

(c) To find the number of students who took BIO and PE but not ENG, we need to look at the region of the diagram where BIO and PE overlap, but ENG does not.

This includes the 12 students who took both PE and BIO, as well as the 4 students who took all three subjects.

Therefore, the number of students who took BIO and PE but not ENG is:

12 - 4 = 8

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The scale factor of the dilation is (d) 1 : 5 reduction

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

The larger rectangle is dilated to form the smaller rectangle

Using the above as a guide, we have the following:

Larger rectangle = 5

Smaller rectangle = 1

So, we have

Scale factor = Smaller rectangle : Larger rectangle

Substitute the known values in the above equation, so, we have the following representation

Scale factor = 1 : 5

Hence, the scale factor is 1 : 5 reduction

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The longest distance between vertices on an 3- dimensional, 4-dimensional, 5-dimensional, and n-dimensional cube is the square root of 1.723, 2, square root 2.236, and square root of n respectively.

The ability to execute numerous tasks or calculations concurrently may greatly enhance a system's overall performance, which makes parallel processing important in computer science. A system can perform processes in parallel by employing many processors or cores, which cuts down on the time needed to do complicated calculations or activities.

The longest distance between vertices on an n-dimensional cube, is given by:

d = sqrt(n)

where d is the distance between vertices.

n is the number of dimensions.

For a 3-dimensional cube, we have:

d = sqrt(3) ≈ 1.732

For a 4-dimensional cube, we have:

d = sqrt(4) = 2

For a 5-dimensional cube, we have:

d = sqrt(5) ≈ 2.236

In general, for an n-dimensional cube, we have:

d = sqrt(n)

So the longest distance between vertices on an n-dimensional cube is the square root of n.

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The two measures of these data that best describe the typical number of minutes Addison spent reading each day are mean and median.

Mean is the average value of a set of numbers, found by adding up all the numbers and dividing by the total count of numbers. Median is the middle value in a set of numbers when they are listed in order.

To find the mean of the data set, we add up all the values and divide by the total count:

(90 + 60 + 89 + 94 + 60 + 93) / 6 = 85.33

To find the median of the data set, we first put the values in order:

60, 60, 89, 90, 93, 94

Since there are an even number of values, we take the average of the two middle values:

(89 + 90) / 2 = 89.5

Therefore, the mean is 85.33 minutes and the median is 89.5 minutes, which are the two measures that best describe the typical number of minutes Addison spent reading each day.

In response to the aforementioned query, we may say that The slate roof has a total area of 0.26 square metres.

An area can be used to describe a surface's area. Surface area, also known as planar region, refers to the area of a form or planar layer, whereas planar region refers to the area of an open surface or the border of a three-dimensional object. An object's area is the entire amount of space occupied by its planar (2-D) surface or form. Use a pencil to mark a square on the paper. an individual having two dimensions. A shape's area on paper is the amount of space it occupies. Think of the square as being made up of smaller unit squares.

Height, breadth, and depth together make up volume.

Volume: 4.3 x 3.5 x 2.2 metres

33.77 cubic metres is the volume (rounded to 2 decimal places)

The stone outbuilding has a volume of 33.77 cubic metres.

Area = base x height x half

Height: 2.5 to 2.6 metres

Height = 0.10 metres

Height = (-0.1 m) | (0.1 m)

determine the size of each triangle's face:

Area = base x height x half

Area: 0.6 x 2.6 x 0.1 metres

0.13 square metres is the area.

Total area Equals twice the area

= 2 x 0.13 square metres total area

0.26 square metres is the total area (rounded to 2 decimal places)

The slate roof has a total area of 0.26 square metres.

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