The formula for calculating commission is

A c=x-y

B c=y-x

C c=mx+b

D c=prn

Answer:

width = 6 ft

length = 21 ft

Step-by-step explanation:

Forming algebraic expressions and finding the dimensions of a rectangle:

 Width = w ft

 length =  3*w + 3 = (3w + 3) ft

              2l +2w = P

 2(3w + 3) + 2w = 54

Use distributive property to open the brackets,

 2*3w + 2*3 + 2w = 54

        6w + 6 + 2w = 54

Combine like terms,

          6w + 2w + 6 = 54

               8w   + 6   = 54

Subtract 6 from both sides,

                      8w    = 54 - 6

                         8w = 48

Divide both sides by 8

                           w = 48 ÷ 8

                           [tex]\sf \boxed{\bf w = 6 \ ft}[/tex]

l = 3w + 3

 = 3*6 + 3

 = 18 + 3

l = 21 ft

The simplified rational number that represents this scenario is 1/4

The given parameters are:

14 programming errors for every 56 programmers

The above means:

Error : Actual = 14 : 56

Express as fraction

Error/Actual = 14/56

Simplify the ratio

Error/Actual = 1/4

Hence, the simplified rational number that represents this scenario is 1/4

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Answer:

use a calculator

Step-by-step explanation: the calculator doesn't lie I used a calculator

Answer:

1,000,000

Step-by-step explanation:

Answer:

See the answer below

Step-by-step explanation:

Answer:

Option D: [tex]y=-2[/tex]

Step-by-step explanation:

The line is horizontal, which means the slope is 0. The line also crosses the y-axis at (0,-2). Thus y at 0 is equal to 2.

The function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

We are given the function:

f ( x ) = 2 x² + 5

We need to find the value of f ( -3 ).

We will do this by substituting the value of x = - 3 in the function and then evaluating the expression.

Putting x = -3 in the function, we get that:

f ( x = - 3 ) = 2 (- 3)² + 5

Solving the square, we get that:

f (- 3) = 2 ( 9 ) + 5

Simplifying the expression, we get that:

f (- 3) = 18 + 5

f (- 3) = 23

Therefore, we get that, the function f ( x ) = 2 x² + 5 will have the value 23 for f (- 3).

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The value of d is 18.

Given, the slope of the line is 3.

Slope equals a height change (Change in width) You may also say that a slope is a climb or a run. This formula changes if the graph's horizontal axis is represented by x and the vertical axis by y: Slope is equal to (y-change)/ (Change in x)

Two points which lie are N(₋2 , 3) and D(3,d)

slope of the line = y₂ ₋ y₁/x₂ ₋ x₁

let the points N(₋2 , 3) be (x₁ , y₁)

and D(3,d) be (x₂ , y₂)

therefore, 3 = d ₋ 3/3 ₋ (₋2)

3 = d ₋ 3/3 ₊ 2

3 = d ₋ 3 / 5

15 = d ₋ 3

d = 15₊3

d = 18

Hence we get the value of d as 18.

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The equation representing the product of theirs fractions is -

(- 2/7) x (- 3/4)  and on solving this expression, we get 3/14.

In mathematics, fractions are represented as a numerical value, which defines a part of a whole.

Given that Cassie and Amy are playing a card flash game such that Cassie has a card with the fraction - 2/7 and Amy has a card with fraction - 3/7.

The equation that represent the product of their fractions is -

(- 2/7) x (- 3/4)

Now, solving the above expression, we get -

(- 2/7) x (- 3/4)

(1/7) x (3/2)

3/14

Therefore, the equation representing the product of theirs fractions is -

(- 2/7) x (- 3/4)  and on solving this expression, we get 3/14.

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Using translation concepts, the vertices of the triangle after the rotation are given as follows:

G'(2,-2), E'(5,-4), F'(5,-1).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The rule for a 90º counterclockwise rotation around the origin is:

(x,y) -> (-y,x).

Hence the vertices should be given by:

The correct translation is graphed at the end of the question. You are doing a good job, just there was two small mistakes on the rule :).

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Answer:

6.7

Step-by-step explanation:

√45 = 6.7

.................

Answer: 32604

Step-by-step explanation:

Answer:

1.3 is the correct answer

Step-by-step explanation:

The value of the number is 15.

Let the first number be represented by x.

The second number will be:

(2 × x) - 2 = 2x - 2

Therefore, the addition of the numbers will be:

= x + 2x - 2 = 43

3x - 2 = 43

3x = 43 + 2

3x = 45

Divide

x = 45/3

x = 15.

Therefore, the number is 15

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The first integer is 16 and the next two integers are 17 and 18. The largest one is 18

What in math is an integer?

The first integer will be called x. Consequently, the second integer is x+1 and the third is x+2 (this is because they are consecutive integers). The total of these three numbers is 51, so build up the following equation and answer it.

x+(x+1)+(x+2)=51

3x+3=51

3x=48

x=16

Therefore, the first integer is 16 and the next two integers are 17 and 18. The largest one is 18 and this is the answer.

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58, 62 and 74 are the numbers between 50 and 80 that has exactly 4 factors with 2 being one of them 4.

As per the question statement, we are required to find out the numbers between 50 and 80 that has exactly 4 factors with 2 being one of the factors.

To solve this question, we need to know that every or any number in the number system as has at least 2 factors: 1 and the number itself.

Since we are to find numbers with exactly 4 factors, 2 being one of the factors and as per the above mentioned concept, two of the remaining three factors will be 1 and the number itself, the fourth factor has to be a prime number as prime numbers have no other factors than 1 and itself.

That is, we will have to find prime numbers (say "n") which when multiplied by 2 lies within the range of 50 and 80,

[tex]or, 50\leq (n*2) \leq 80\\or, \frac{50}{2}\leq n\leq \frac{80}{2}\\ or, 25\leq n\leq 40[/tex]

That is, we will need to find the prime numbers between 25 and 40; They are 29, 31 and 37.

Hence, our required numbers are [(29 * 2) = 58], [(31 * 2) = 62] and

[(37 * 2) = 74]. They lie between 50 and 80 that has exactly 4 factors with 2 being one of them.

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The angle in degrees between the two planes is approximately 159.460°.

The equation of the plane, whose form is a · x + b · y + c · z = d is equivalent to this vectorial form (a, b, c) • (x, y, z) = d, where (a, b, c) is the vector of coefficients. The angle between the two planes:

θ = cos⁻¹ [[(a₁, b₁, c₁) • (a₂, b₂, c₂)] / [||(a₁, b₁, c₁)|| · ||(a₁, b₁, c₁)||]]

If we know that (a₁, b₁, c₁) = (1, - 10, - 8) and (a₂, b₂, c₂) = (2, 5, 8), then the angle between the two planes is:

θ = cos⁻¹ [[(1, - 10, - 8) • (2, 5, 8)] / [√165 · √93]]

θ = cos⁻¹ [(-2 - 50 - 64) / √15345]

θ = cos⁻¹ (- 116 / √15345)

θ ≈ 159.460°

The angle in degrees between the two planes is approximately 159.460°.

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Answer:

800,000

Step-by-step explanation:

To do this, simply divide the number by 10. 8000000/10 = 800,000.

For the system of equations y = 2 x + 3 and 2 y - x = 12, the solution will be x = 2 and y = 7.

We are given the system of equations:

y = 2 x + 3   … (1)

2 y - x = 12     …. (2)

We need to solve it to find the values of x and y.

Putting the value of y from equation (1) in equation (2), we get that:

2 y - x = 12

2 (2 x + 3) - x = 12

Multiplying the brackets, we get that:

4 x + 6 - x = 12

3 x + 6 = 12

Subtract 6 from both the sides, we get that:

3 x + 6 - 6 = 12 - 6

3 x = 6

Divide both sides by 3. we get that:

3 x / 3 = 6 / 3

x = 2

y = 2 x + 3

y = 2 (2) + 3

y = 4 + 3

y = 7

Therefore, we get that, for the system of equations y = 2 x + 3 and 2 y - x = 12, the solution will be x = 2 and y = 7.

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The angles of rotation will map the figure onto itself are 60, 120, 180....

In geometry, transformation involves changing the angle, position and/or size of a shape.

The figure that completes the question is added as an attachment

The given parameter is the shape in the figure

From the figure, we can see that the shape has 6 congruent sides

This means that the shape is a regular hexagon

The angle of rotation will map the figure onto itself is calculated as

Angle = 360/Number of sides

So, we have

Angle = 360/6

Evaluate

Angle = 60

The other angles must be a multiple of 60

i.e. 60, 120, 180....

Hence, the angles of rotation will map the figure onto itself are 60, 120, 180....

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Using proportions, it is found that the cost per ounce is of $0.8.

The missing information is the number of ounces in the balm, that is of 20.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The cost per ounce is given by the proportion of the cost by the number of ounces, hence:

Then:

$16/20 = $0.8.

The cost per ounce is of $0.8.

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The raw score from the given table that corresponds with the 20th and 30th percentiles are;

First distribution;

Second distribution;

The Z–Score percentile normal distribution table can be used to find the Z–Score that gives the percentile value of a raw score.

The Z–Score, also known as the standard score, gives the number of standard deviations, a raw score is far from the mean.

The mathematical equation for the Z–Score is as following; [tex]Z = \frac{x - \mu}{ \sigma} [/tex]

Therefore, a positive value of Z is obtained when the raw score, x, is larger than the mean, [tex] \mu[/tex]

and negative Z value is given by raw scores lower than the mean.

Using the standard normal distribution table, raw score corresponds to the 1th percentile when the Z–Score = -2.326, while the Z–Score for the 99th percentile is 2.326.

The Z–Score of the 20th percentile is -0.842, while for the 30th percentile it is -0.524

Comparing the standard values with the values in the given table, we have;

First distribution;

-0.91960-(-0.842) = -0.0776

-0.71082 -(-0.842) = 0.13118

The smaller difference is given by -0.91960.

Similarly;

Second distribution;

While;

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The interval(s) for which f(x) ≥ 0. is x ≥ 2

The function is given as:

f(x) = x - 2

Also, we have:

f(x) ≥ 0

This means that

x − 2 ≥ 0

Add 2 to both sides of the inequality

x ≥ 2

Hence, the interval(s) for which f(x) ≥ 0. is x ≥ 2

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Answer:

  5 + 10 + 15 = 30

Step-by-step explanation:

You want a sum of three multiples of 5 that does not end in 5.

Any odd multiple of 5 will end in 5. An even multiple will not.

In order for the sum to not end in 5, the total of the multipliers must be even:

  1×5 +2×5 +3×5 = 6×5 = 30

  5 +10 +15 = 30 . . . . . . three multiples of 5 whose sum does not end in 5

The true statement about the angles of the triangle OPQ  is the third statement that is  m∠P < m∠O < m∠Q.

It is given that:-

In triangle OPQ,

PQ = 19

QO = 11

OP = 20

We have to find which one of the six statements given in the question is correct.

We know that, in a triangle, if one side of the triangle is longer than the other side, then the angle opposite to the longer side will be larger than the angle opposite the shorter side.

Hence,

In triangle OPQ,

Angle opposite to side OP = ∠Q

Angle opposite to side PQ = ∠O

Angle opposite to side QO = ∠P

As,

QO < PQ < OP , Hence,

m∠P <  m∠ O < m∠Q

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Answer:

x=

Step-by-step explanation:

Answer:

5

Step-by-step explanation: