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Three possible rectangles of area 24 square inches are:

A rectangle with width 6 inches and length 4 inches

A rectangle with width 8 inches and length 3 inches

A rectangle with width 4 inches and length 6 inches

It should be noted that W and L are variables because their values can change, whereas A is a constant because it is fixed at 24 square inches. W and L can be any values as long as the product of their values is equal to 24.

In this case, W and L are variables and A is a constant.

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In set builder notation, the set of all numbers larger than or equal to -8 and less than 17 can be written as:

{x | -8 <= x < 17}

An explanation of set builder notation?

A set of items can be mathematically expressed using the set builder notation. The set builder notation's syntax is {x | },  where x stands for one of the set's elements and the condition outlines the requirements that an element must meet in order to be included in the set.

In this instance, the set consists of all numbers higher than or equal to -8 and less than 17 in total. The set must satisfy the constraint

-8 <= x < 17,where x is a real value. This implies that x must exceed or equal to -8 and must be less than 17 to be a part of the set.

As a result, in set builder notation, the set of all numbers greater than or equal to -8 and less than 17 can be written as follows:  {x | -8 <= x < 17}

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 17160\\ P=\textit{original amount deposited}\dotfill & \pounds 11000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &16 \end{cases}[/tex]

[tex]17160 = 11000[1+(\frac{r}{100})(16)] \implies \cfrac{17160}{11000}=1+\cfrac{16r}{100}\implies \cfrac{39}{25}=1+\cfrac{4r}{25} \\\\\\ \cfrac{39}{25}=\cfrac{25+4r}{25}\implies 39=25+4r\implies 14=4r\implies \cfrac{14}{4}=r\implies \stackrel{\%\qquad }{\boxed{3.5=r}}[/tex]

To make the concentration of 50% syrup,

she needs to add 0.5 lb of sugar.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

Emma has half a pound of sugar.

To make the concentration of 50% syrup:

Let n be the required amount.

In decimals, 50% is 0.5.

Applying the percentage formula;

we get,

[tex]\frac{0.5}{n + 0.5} \cdot 100 = 50[/tex]

Applying cross multiplication,

we get,

[tex]\frac{0.5}{n + 0.5} = 0.5[/tex]

0.5 = 0.5(n + 0.5)

1 = n + 0.5

n = 1 - 0.5

n = 0.5 lb.

Therefore, she would have 0.5 + 0.5 = 1 pound of sugar.

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Answer:

The service tax paid was:

0.06 * RM180 = RM10.80

Step-by-step explanation:

To calculate the service tax paid by Mr. Lim, we need to first find the amount of the bill before the service tax was added.

Let's call the original bill amount "x".

After the 6% service tax was added, the total bill became x + (0.06 * x) = RM190.80.

So we can set up the equation:

x + (0.06 * x) = RM190.80

Expanding the right side of the equation:

x + (0.06 * x) = 190.80

Combining like terms:

1.06x = 190.80

Solving for x:

x = 180

So the original bill amount before the service tax was added was RM180.

The service tax paid was:

0.06 * RM180 = RM10.80

The angles x and 3x - 12 are two vertical angles and the measure of the vertical angle x is equal to 48°.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

We shall evaluate for the measure of x as follows:

x + x + 3x - 12 + 3x - 12 = 360° {sum of angles at a point}

2x + 6x - 24 = 360°

8x - 24 = 360°

8x = 360° + 24 {add 24 to both sides}

8x = 384°

x = 384°/8 {divide through by 8}

x = 48°

Therefore, since the angles x and 3x - 12 are two vertical angles we have derived the measure of the vertical angle x to be equal to 48°.

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Answer:

x = 42°

Step-by-step explanation:

Please here it is.

Answer:

(-8 + 35x) / 5x or -8 / 5x + 7 (same)

Step-by-step explanation:

(-32x^8 + 140x^9) / 20x^9 =

= -32x^8 / 20x^9 + 140x^9 / 20x^9 =

= -8 / 5x + 7 =

= (-8 + 7 * 5x) =

= (-8 + 35x) / 5x

A parent function is the most fundamental function that still satisfies the criteria for a specific type of function. When considering the linear functions that make up a family of functions, for instance, the parent function would be y = x. The simplest function is this linear one.

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Answer:

96 stamps

Step-by-step explanation:

We know

Connor collected 80 stamps last year. This year he increased his collection by 20%.

80 stamps = 100%

100% + 20% = 120%

So, this year he collected 120% of the number of stamps from last year.

120% = 1.2

How many stamps are in his collection?

We take

80 times 1.2 = 96 stamps

So, there are 96 stamps in his collection.

The amount invested in the account that earns 10% interest is $4,000 and the amount invested in the account that earns 11% interest is $3,000.

The system of equations that represent the information in the question is:

a + b = 7000 equation 1

0.1a + 0.11b = 730 equation 2

Where:

a = amount invested in the account that earns 10% interest

b = amount invested in the account that earns 11% interest

The elimination method would be used to solve the equations.

Multiply equation 1 by 0.1

0.1a + 0.1b = 700 equation 3

Subtract equation 3 from equation 2

0.01b = 30

Divide both sides of the equation by 0.01

b = 30 / 0.01

b = 3000

Substitute for b in equation 1:

a + 3000 = 7000

a = 7,000 - 3000

a = 4000

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Answer:

45

Step-by-step explanation:

The sample variance and the standard deviation are 52.8 and 7.26

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

23, 16, 5, 7, 11

Calculate the mean

Mean = (23 + 16 + 5 + 7 + 11)/5

Mean = 12.4

The standard deviation is

SD = √[Sum of (1 - Mean)²]/[N - 1]

So, we have

SD = √[(23 - 12.4)² + (16 - 12.4)² + (5 - 12.4)² + (7 - 12.4)² + (11 - 12.4)²]/[5 - 1]

This gives

SD = √211.2/4

So, we have

SD = √52.8

SD = 7.26

Hence, the standard deviation is 7.26

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1. The Venn diagrams are attached

2. When the statistics students number = 10·x + 3, we have;

The number of students that study

When the statistics students number = 2·x + 3, we have;

The number of students that study

The parameters given are;

Total number of students = 30

Therefore;

The number of students that study either algebra or statistics = n(A∪B)

From set theory we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

The number of students that study

a. Algebra

n(A) = 18/11 + 10 = 128/11

b. Statistic

n(B) = 213/11

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11

However, assuming n(B) = (2·x + 3), we have;

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 30 - 3 = 27

Therefore, we have;

n(A∪B) = x + 10 + 2·x + 3 - 4 = 27

2·x+3 + x + 10= 27 + 4 = 31

3·x = 18

x = 6

Therefore, the number of students that study

a. Algebra

n(A) = 16

b. Statistics

n(B) = 15

Hence, we have;

n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12

Similarly, we have;

n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11

The Venn diagrams can be presented as follows;

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Using the proportions of the side lengths of the pair of similar triangles, we have:

1. x = 35

2. x = 20; y = 23.3

3. x = 11

4. x = 9

5. x = 10

Triangles that are similar to each other, will have side lengths that are proportional to each other.

Therefore, using proportions, we would have:

1. x/14 = 40/16

Cross multiply:

16x = 40 * 14

16x = 560

x = 560/16

x = 35

2. x/12 = 15/9

9x = 12 * 15

9x = 180

x = 20

y/14 = 15/9

9y = 210

y = 23.3

3. (x + 5)/24 = 36/54

Cross multiply:

54(x + 5) = 36 * 24

54x + 270 = 864

54x = 864 - 270

54x = 594

x = 11

4. 20/28 = 15/(2x + 3)

Cross multiply:

20(2x + 3) = 28 * 15

40x + 60 = 420

40x = 420 - 60

40x = 360

x = 9

5. 24/28 = x + 8 / 3x - 9

Cross multiply:

24(3x - 9) = 28(x + 8)

72x - 216 = 28x + 224

72x - 28x = 216 + 224

44x = 440

x = 10

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The number that is most likely an irrational number is given as follows:

D. 4.279458105...

Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.

Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.

For this problem, the option D gives the irrational number, as it is the lone non-repeating decimal. For the others, we have that:

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Answer:

324

Step-by-step explanation:

To evaluate (a) f(f(2)), we first evaluate f(2) which is 52-4 = 6. Then, we evaluate f(6) which is 56-4 = 26. So, f(f(2)) = 26.

To evaluate (b) g(g(3)), we first evaluate g(3) which is 23^2 = 18. Then, we evaluate g(18) which is 218^2 = 324. So, g(g(3)) = 324

Here are the steps to complete the budget, as described in the instructions:

Calculate totals for each type of expense and for each month:

Calculate net income for each month:

Add another column to calculate the percentage of total expenses for each category:

Create two different unique charts:

Label each page tab according to the chart:

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A and C are equivalent expressions for a given expression.

What does an expression mean?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is -4y+8.

Given options are:

A. -4(y-2)

By simplifying it we will get -4(y-2) = -4y+8

So, both are equivalent.

B. -4(-2+4y)

By simplifying it we will get -4(-2+4y) = 8-16y

So, both are not equivalent.

C. (2-y)4

By simplifying it we will get (2-y)4 = 8-4y

So, both are equivalent.

D. 4(-y+8)

By simplifying it we will get 4(y-8) = 4y-32.

So, both are not equivalent.

A, and C are equivalent expressions for a given expression.

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Answer:5.5

Step-by-step explanation:

Answer:

$105

Step-by-step explanation:

Let x be the amount of money Carolina has in her checking account. Then, her savings account has x + $30. The total amount of money in both accounts is $180, so we can write the equation:

x + (x + $30) = $180

Expanding the left-hand side:

2x + $30 = $180

Subtracting $30 from both sides:

2x = $150

Dividing both sides by 2:

x = $75

Therefore, Carolina has $75 in her checking account and $75 + $30 = $105 in her savings account.

Example: Add 1/4 + 2/4

Solution: Let us add these fractions using the following steps.

Step 1: Check if the denominators are the same. (Here, the denominators are the same, so we move to the next step)

Step 2: Add the numerators and place the sum over the common denominator. This means (1 + 2)/4 = 3/4

Step 3: Simplify the fraction to its lowest form, if needed. Here, it is not needed. So, the sum of the given fractions is, 1/4 + 2/4 = 3/4

Answer:

yjgdy

hgjg

hhjj

hggh

hhj

Since the triangles are congruent. Then The size of angle Q is 47°

Congruent Angle:

Congruent angles are often used in architecture, construction, design, and art. Isometrics have the same angular measurements. For example, a regular pentagon has 5 sides and 5 angles, each measuring 108 degrees. Regardless of the size or scale of a regular polygon, the angles are always congruent.

Here is a list of rules for the congruence of angles.

1. The only condition for two angles to be congruent is if the measurements of the angles agree.

2. The lengths and orientations of the two sides of this congruent angle are not important.

According to the Question:

It is given that :

B = 6 cm, 12 cm and 9 cm

A = 47°

R' = 29°

If the triangle is congruent, then all the three sides and angles will be same.

Therefore,

Angle Q = Angle A

Therefore, Angle Q = 47°

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The angle AED of arc AD of the circle is calculated to be equal to 8100/πr

We shall use the formula:

arc length = (arc angle/360) × 2 × π × radius

where arc angle is measured in degrees and radius is the distance from the center of the circle to the point on the circle where the arc begins.

If AD = 45 and r the radius, we evaluate the arc angle m ∠AED as follows:

(arc angle/360°) × 2 × π × r

by cross multiplication;

arc angle AED = (360 × 45)/2πr

2 can divide 360° to give;

arc angle AED = (180 × 45)/πr

arc angle AED = 8100/πr

Therefore, the angle AED of arc AD of the circle is calculated to be equal to 8100/πr

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Answer:

x(f)- this is the correct answer

The solution is Option D.

The difference in shopping from store and online is given by the equation D = $ 0.46

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of shopping in physical store be A

Let the total cost of shopping online be B

Now , the equations will be

The number of batteries = 2

The number of stereo = 1

The number of CDs = 3

The cost of buying 2 packs of batteries from store = 2 x ( 5.99 ) = $ 11.98

The cost of buying 1 stereo from store = 1 x ( 100 ) = $ 100.00

The cost of buying 3 CDs from store = 3 x ( 7.95 ) = $ 23.85

The total purchase cost without discount and sales tax = $ 135.83

The cost with 10 % discount = $ 122.247

The cost after 5 % sales tax = $ 128.35935

So , the total cost of shopping in store A = $ 128.35935

And ,

The cost of buying 2 packs of batteries online = 2 x ( 4.99 ) = $ 9.98

The cost of buying 1 stereo from online = 1 x ( 90 ) = $ 90.00

The cost of buying 3 CDs from online = 3 x ( 8.95 ) = $ 26.85

The total purchase cost without discount and sales tax = $ 126.83

The cost with $ 5 discount = $ 121.83

The shipping cost in online store = $ 121.83 + $ 6.99 =

So , the total cost of shopping in online store A = $ 128.82

Now , the difference in shopping from store and online is

D = $ 128.82 - $ 128.35935

On simplifying the equation , we get

D = $ 0.46

Hence , the equation is D = $ 0.46

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Answer:

option (A).

Step-by-step explanation:

The equivalent expression to the given radical expression, when the denominator has been rationalized and x > 5, is 2(√x + √x - 5), or option (A).