-6y-18
factored expression

The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20

When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.

If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.

In 20 years therefore, the value of $100 would be:

Value in 20 years = Value today x (1 - inflation rate) ^ number of years

= 100 x (1 - 4%) ²⁰

= $44.20

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The solution to the given equation is 5.630.

What is a logarithmic equation?

An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

Here, we have

2^(x+1) = 3^(2x-5)

Taking logarithms on both sides, we get

(x+1)log2 = (2x - 5)log3

xlog2 + log2 = 2xlog3 - 5log3

log2 + log3⁵ = 2xlog3 - xlog2

log 2* 243 = x(log6 - log2)

log486 = x(log6/2)

log486 = xlog3

x = log486/log3

x = 5.630

Hence, the solution to the given logarithmic equation is 5.630.

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A summation, also known as a sum, is the result of arithmetic addition of numbers or quantities.

The value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.

Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left and all the remaining values to the right to find the value of x.

From the given information, we get

x - y = 6 ...............(1)

"if five times the smaller number is two times the larger number"

from the above information, we get

5y = 4x + 2

5) To simplify the value of y:

y = (4x +2) / 5 ...............(2)

Substitute  y = (4x +2) / 5 in (1), then we get

x - (4x + 2) / 5 = 6

5x / 5 - (4x + 2) / 5 = 6

simplifying the above equation, we get

(5x - 4x - 2) / 5 = 6

x - 2 = 5 x 6

x -2 = 30

x = 32

Substitute the value of x in (2)

y = 4(32) + 2 / 5

simplifying the above equation, we get

y = 130 / 5

y = 26

From (1), we get

x - y = 6

substitute the value of x and y in the above equation,

32 - 26 = 6

6 = 6

6) T is the 10s digit

X is the one's digit

The two digit number is 10T + X

It is 7 times the sum of the digits, so the 2 digit number is 7 times as large as the sum of the digits

10T + X = 7(T+X)

By using distributive law

10T + X = 7T + 7X

10T + X - 7T - 7X = 0

simplifying the above equation, we get

3T - 6X = 0

3(T - 2X) = 0

T - 2X = 0

T = 2X

The tens digit is 3 more than the one's digits, so

T = X + 3

Then we have  

T = 2X = X  + 3

Subtracting X from both sides,

T - 3 = X  + 3 - 3

X = 3

The Tens digit is 6.

The number is 63.

The sum of the digits is 9.

9 × 7 = 63.

Therefore, the value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.

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Answer:

Strings packs cost $14 each

Step-by-step explanation:

Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?

Lenny: 2s

Lashae: 2s + b

when b = $16 then these equations are:

Lenny: 2s

Lashae: 2s + 16

together they spent $72 so:

lenny + Lashae = $72 or:

2s + 2s + 16 = 72

subtract 26 from both sides:

2s + 2s + 16 - 16 = 72 - 16

2s + 2s = 56

combine s terms:

4s = 56

divide both sides by 4:

4s/4 = 56/4

s = $14

The rate at which the tip of the woman's shadow is moving, found by making use of the relationships between similar triangle and differentiation is 10 ft/s

Similar triangles are triangle in which all three sides of one proportional to three sides of the other triangle

Height of the woman = 6 ft.

The speed with which the woman walks towards the streetlight = 8 ft/s
The length of the shadow of the woman

Height of the street light = 30 ft.

Let a represent the horizontal distance from the woman to the street light, and let b represent the horizontal distance from the woman to the tip of her shadow, from the similar triangles formed by the shadow, we have;

[tex]\dfrac{30}{x+y} =\dfrac{6}{y}[/tex]
Which gives;

[tex]y = \dfrac{x}{4}[/tex]

The length of the tip of the woman's shadow to the street light, l, in terms of x is therefore;

[tex]l =x + y = x + \dfrac{x}{4} = \dfrac{5\cdot x}{4}[/tex]

[tex]\dfrac{dx}{dt} = 8[/tex]

Therefore, dx = 8·dt

x(t) = 8·t

Writing the function for the l in terms of time t gives;

[tex]l = \dfrac{5\cdot x}{4}[/tex]

[tex]l = \dfrac{5\times 8\cdot t}{4} = \dfrac{40\cdot t}{4} = 10\cdot t[/tex]

The speed at which the tip of the shadow is moving,

[tex]\dfrac{dl}{dt} = \dfrac{d}{dt} \left (10\cdot t ) = 10[/tex]

The speed of the shadow dl/dx = 10 ft./s

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The other names of AB in the given figure are

Collinear points refers to points that lies on the same plane and on the same straight line.

The figure shows two planes and point A, B and C are collinear points, while points Q and R are collinear

Points A, B and C are non colinear to points Q and R

Points AB are still part of line AC hence can be noted as part of line segment BC.

The line has arrow head and may also be called rays. In this case the are part of an arrow

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After simplifying an equation the value of x is x = 3.

What is solving an equation?

Unifying Principle for Equation Solving

By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.

The variable term on one side of the equation can be separated using addition or subtraction.

To find the variable, use multiplication or division.

Consider, the given equation

     5(2x - 4) = 10

      10x - 20 = 10                                  Removing parenthesis

10x -20 + 20 = 10 + 20                         Adding 20 on both sides

              10x = 30                                 Simplifying

                  x = 3                                    Dividing both sides by 10

Hence, the value of x is, x = 3.

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The number is 0.75.

From the question, we have

The store was offering a 25% discount.

number = 1-0.25

=0.75

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The minus sign stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above figure) are then moved to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, or equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.

Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:

A = l²

Where l is the side length of the square.

First, substitute the side length of the square in the area formula:

A = (√8)²

Second, use algebraic properties to simplify the expression and find the corresponding result:

A = ([tex]8^{\frac{1}{2} }[/tex])²

A = 8

This number represents a rational number as 8 is equivalent to the rational number 8 / 1.

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Using the corresponding angle theorem, the value of x is 15 and y is 12.

In the given question we have to find the value of x and y.

From the graph we can see that

From the corresponding angle theorem

4x+2=62

Subtract 2 on both side, we get

4x=60

Divide by 4 on both side, we get

x=15

So the value of x is 15.

Similarly from the corresponding angle theorem

12y=144

Divide by 12 on both side, we get

y=12

So the value of y is 12.

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Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

According to the map, North America makes up [tex]\frac{16}{100}[/tex] of the world's land surface area, while Europe makes up [tex]\frac{7}{100}[/tex]. Since both fractions already have a common denominator ( [tex]\frac{n}{100}[/tex] ), we can simply subtract the two to find how much greater the fractional part of North America is than the fractional part of Europe:

[tex]\frac{16}{100}-\frac{7}{100}=\frac{9}{100}[/tex]

The single fraction in its lowest terms will be;

⇒ - 7(2x - 1)/2

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Or, A number which is expressed as a quotient is called fraction.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2

Now,

Solve the fraction as;

The fraction is,

⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2

⇒ 3 (2x - 1)/5 - (4x - 2)

⇒ 3 (2x - 1)/5 - 2 (2x - 1)

⇒ (2x - 1) (3/5 - 2)

⇒ (2x - 1) (3 - 10)/2

⇒ (2x - 1) (- 7/2)

⇒ - 7(2x - 1)/2

Thus, The single fraction in its lowest terms will be;

⇒ - 7(2x - 1)/2

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If the company wants to keep the cost of operation under $14,000 per month, The maximum number of units they can produce is: D. 349.

Given function:

C = $3,173 + $31u

Hence,

Let u represent number of  units

Let c represent the operation cost

Where c = $14,000 per month

$14,000 = $3,173 + $31u

Combine like terms

$14,000 - $3,173 = $31u

$10,827 = $31u

Divide both side by $31u

u = $10,827 / 31

u = 349 units

Therefore the correct option is D.

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Answer:

£27839

Step-by-step explanation:

O×M=N (original x multiplier = original value)

£28000×0.97%=£27160< 1st year decrease

£27160x1.025=£27839<2nd year increase

The integer in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false is 32

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, based on the information we will replace m with 32. This will be illustrated thus:

1/4(32 - 4) ≤ 1/8 (32 - 16)

= 1/4(28) ≤ 1/8(16)

= 7 ≤ 2

In this case, 7 isn't less than or equal to 2. Therefore, 32 is the correct integer.

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If Sebastian filled 10 gallons of gas, the total amount he spent at the gas station was C. $40.50.

Using the mathematical operations of multiplication and addition, we can compute the total amount that Sebastian spent at the gas station.

We first determine the total cost of gas that Sebastian bought by multiplying the unit cost by the quantity.

Secondly, we add the above total cost to the total cost of other items he bought at the station to arrive at the total amount spent.

The cost of gas per gallon = $2.91

The number of gallons of gas bought = 10

The total cost of gas = $29.10 ($2.91 x 10)

The total cost of granola bars and tissues = $11.40

The total amount spent = $40.50 ($29.10 + $11.40)

Thus, mathematically, Sebastian spent C. $40.50 at the gas station.

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The actual weekly labor cost compared to the target is 240 hours

What are Time and Work?

According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.

The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.

Target costing is a system under which a company plans in advance for the price points, product costs, and margins that it wants to achieve for a new product.

Given

Regular Rate $15.00/hr

Overtime Rate $22.50/hr

Targeted Labour Cost $12,000/wk

Labour Hours Needed 800/wk

According to the question:

Overtime means each employee can work beyond the input of 40 hrs. Per week.

Labor requirement = 800 hrs.

14 men labor capacity = 14× 40 = 560 hrs.

So overtime hours required = 800-560=240 hrs

Hence,

The actual weekly labor cost compared to the target is 240

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The equation in slope intercept form of the line that passes through the graph is y = 2/3x + 2

From the graph, we have the points to be given as

(-3,0) and (0,2)

Start by calculating the slope of the points using the following slope equation

m = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3,0) and (0,2)

So, we have

m = (2 - 0)/(0 + 3)

Evaluate

m = 2/3

The equation is then calculated as

y = m(x - x₁) + y₁

Where

(x, y) = (0, 2) and m = 2/3

So, we have

y = 2/3(x - 0) + 2

Expand

y = 2/3x + 2

Hence, the equation in slope intercept form of the line is y = 2/3x + 2

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The 10 forms 1/8 can be written is as follows;

A fraction refers to a number which consists of a numerator and a denominator.

A numerator is the upper value of a fraction.

A denominator is the lower value of a fraction.

1 over 8 can be written in the following ways;

1/8

1 ÷ 8

1/2³

= 1 / 2×2×2

= 1/8

1/√64

= 1/8

[tex]{8}^{ - 1} [/tex]

= 1/8

1 : 8

= 1/8

[tex]{√64}^{ - 1} [/tex]

= 1/√64

= 1/8

[tex]{2}^{ - 3} [/tex]

= 1/2³

= 1/8

2/16

= 1/8

4 : 32

= 4/32

= 1/8

In conclusion, 1/8 can be written in different forms including using square root and ratios.

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The true statement when the frozen yogurt stand charges per ounce of frozen yogurt purchased is B. Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.

In the scenario, the total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.

In this case, it is important to note that Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.

For example, for 2 ounces, this will be:

= 0.45f + 1

= 0.45(2) + 1

= 0.9 + 1

= $1.9

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Answer: Yes, Probably

The orthocenter of the triangle with vertices  P(-1,2), Q(5,2), R(2,1) is

Orthocenter is calculated by

formula for slope is

m = (y₂ - y₁) / (x₂ - x₁)

slope of the perpendicular = -1/m

Using side PR  P(-1,2)  R(2,1) ,

m = (1 - 2) / (2 - -1)

m = 1 / 3

slope of the perpendicular = -1/m = - 1 / (1/3) = -3

using point-slope formula for equation of line passing through Q (5, 2)

point slope formula

(y - y₁) = m (x - x₁)

(y - 5) = -3 (x - 2)

y - 5 = -3x + 6

y = -3x + 6 + 5

y = 11 - 3x

Using side PQ  P(-1, 2), Q(5, 2)

m = (2 - 2) / (5 - -1)

m = 0

slope of horizontal line is zero for horizontal line the perpendicular is a vertical line

using point-slope formula for vertical line passing through R (2, 1)

point slope formula

(y - y₁) = m (x - x₁)

0 = (x - 2)

x =  2

The two equations are

y = 11 - 3x

x = 2

solving both equations with x already known

y = 11 - 3 * 2

y = 11 - 6

y = 5

Therefore the orthocenter is (2, 5)

The triangle is attached

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64x³+125y³

= (4x+5y)( 16x²-20xy+25y²)

a³ + b³ = ( a + b )( a² - ab + b² )

64x³ + 125y³

= ( 4x )³ + ( 5y )³

= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]

= (4x+5y)( 16x²-20xy+25y² )

When a person from this group is selected at random, the probability that this person has type AB blood is 3/40

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

It should be noted that in this case, the number of people with AB blood is 15 and there are 200 people. The probability will be:

= Number of AB blood type / Total number of people

= 15 / 200

= 3/40

The probability is 3/40.

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It could be said that the normal probability plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.

If the data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.975., on analysing

The normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.

Therefore,  It could be said that the normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.

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Answer: [tex]5^{2} + 4[/tex]

Step-by-step explanation:

[tex]2 + 3^3[/tex] =?

2 + 27 = 29

10 * 2 - 9 = 20 - 9 = 11

[tex]5^2 + 4[/tex] = 25 + 4 = 29

[tex]5^3\\[/tex] = 5 * 5*5 = 125

3+ 4 * 3 = 3 + 12 = 15

Answer:

  78°

Step-by-step explanation:

You want the measure of base angle x in an isosceles triangle with a.pex angle 24°.

The two base angles of an isosceles triangle are congruent. The sum of all angles is 180°, so we have ...

  24° +2x = 180°

  12° +x = 90° . . . . . . divide by 2

  x = 78° . . . . . . . subtract 12°

The measure of angle x is 78°.

Answer:

[tex]2,8,14,20[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]2[/tex] and the common difference is [tex]6[/tex], then each successive term in the sequence is [tex]6[/tex] more than the previous term:

[tex]a_n=6n-4[/tex]

Therefore, the first term is [tex]2[/tex], followed by [tex]8[/tex], [tex]14[/tex], and [tex]20[/tex].

The probability that the sample proportion surviving for at least 3 years will be less than 67% is of:

0.1131 = 11.31%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion and the sample size are given as follows:

p = 0.73, n = 80.

Hence the mean and the standard error are given as follows:

The probability that the sample proportion surviving for at least 3 years will be less than 67% is the p-value of Z when X = 0.67, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (0.67 - 0.73)/0.0496

Z = -1.21

Z = -1.21 has a p-value of 0.1131.

Hence the probability is:

0.1131 = 11.31%.

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By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.

In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.

Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.

For this exercise, the elements of the given data set would be listed in ascending order as follows:

Set = {-4, -3, -3, -1, 0, 1, 2, 2}

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