1) A sales representative earns a 2.5% commission on sales. Find the commission earned when the total sales are $80,500.

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The value of  tan(45°+Θ) after using trigonometric ratio is  

1+tanΘ/ 1-tanΘ.

What is trigonometric ratios?

   There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given,

=> tan(45°+Θ)

Now using formula ,

=> tan(a+b) = [tex]\frac{tan a+tan b}{1-tan a*tanb}[/tex]

=> tan(45°+Θ)= (tan 45°+tanΘ)/(1-tan45°*tanΘ)

We know that tan 45°=1 then ,

=> tan (45°+Θ)= 1+tanΘ/ 1-tanΘ

Hence the formula for  tan (45°+Θ) is  1+tanΘ/ 1-tanΘ.

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Answer:

y=1,-4,-9,-14

Step-by-step explanation:

just replace x with the given value and find what it equals to

y=-5(0)+1

y=1

y=-5(1)+1

y=-5+1

y=-4

y=-5(2)+1

y=-10+1

y=-9

y=-5(3)+1

y=-15+1

y=-14

Hopes this helps please mark brainliest

Answer:

Please mark as brainiest

Step-by-step explanation:

when x = 0:

y= -5(0)+1

y=0+1

y=1

when x = 1:

y= -5(1)+1

y= -5+1

y= -4

when x = 2:

y= -5(2)+1

y= -10+1

y= -9

when x = 3:

y= -5(3)+1

y= -15+1

y= -14

The mean of the previous four tasks was 77%.

What is Mean?

The mean is just the average of the given set of values. It represents a data set's values being distributed evenly.

Solution:

Mean = Sum of Observation / Total Number of Observation

Let, the sum of previous four values be x

According to the question,

78 = x + 82 / 5

here, 5 is the total number of observations

so,

x can be calculated by cross multiplication

390 - 82 = x

x = 308

Since, we have the sum of the four values and the numer of observations is 4, then mean would be

Mean = 308/4

Mean = 77%

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The fraction that 1 4/5 is of 1 2/3 is 1 2/25.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Let the fraction be illustrated as x

Therefore, 1 2/3 of x = 1 4/5

5x/3 = 9/5

Cross multiply

5x × 5 = 3 × 9

25x = 27

Divide

x = 27 / 25

x = 1 2/25.

The fraction is 1 2/25.

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From the given condition of number of tote bags ordered and there costs represents linear equation then cost of ordering 110 tote bags is equal to $915.

As given in the question,

Let us consider y be the cost of ordering a bag.

And x represents the number of bags to be ordered as per the cost.

It is given that Cost of ordering bags and number of tote bags represents the linear equation,

Standard form of Equation is :

y = mx + c

For order of x = 75 tote bags cost is y = $635.

635 = 75m + c   __(1)

For order of x = 125 tote bags cost is y = $1035.

1035 = 125m + c ____(2)

Subtract (1) from (2) we get,

1035 = 125m + c

635 = 75m  + c

400 = 50m

⇒m = 8

Substitute value of m in (1) we get,

635 = 75(8) + c

⇒c = 35

Equation is:

y = 8x + 35

When number of ordering bags x = 110 then,

y = 8(110) + 35

⇒ y = $915

Therefore, from the given condition of number of tote bags ordered and there costs represents linear equation then cost of ordering 110 tote bags is equal to $915.

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The estimated total audited value of the population using the difference method  is $201,000.

The difference method works as follows :

A difference method is a mathematical expression of the form

f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient.

Given that,

A population of 1,000 accounts .  

The sample items have a mean book of $200 and

A mean audited value of $203  

Therefore, the difference of $203 - $200 = $3  

Now, Apply the difference to the population of accounts and we get,

(1000 account × $3) = $3000

As Given in the question,

The book value in the population is $198,000 and we add the difference previously calculated of $3,000  

So, we have = $198,000 + $3,000

                     = $201,000  

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A system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased include the following:

s + l = 15

12s + 18l = 240.

In order to write a system of linear equations could be used to model and determine the number of small boxes purchased and the number of large boxes purchased, we would assign variables to the number of small boxes that were purchased, the number of large boxes that were purchased, and the total number of boxes respectively as follows:

Translating the word problem into an algebraic equation, we have the following;

Since each small box has 12 granola bars and each large box has 18 granola bars, we have:

12s + 18l = 240.

For a total of 15 boxes altogether, we have:

s + l = 15

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A 95% confidence interval is a set of data that contains the real mean of the population 95% of the time. This is not the same as a range that includes 95% of the possible values.

What is Confidence Interval?

In statistics, a confidence interval defines the possibility that a population parameter will fall between a set of values for a certain proportion of the time.

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The line of equation that passes through (5,2) and (6,4) is 4x+y=22.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given points are (5,2) and (6,4)

The equation that passes from two points (x₁,y₁) and (x₂,y₂) is,

y-y₁=m.(x-x₁)

Where m=(y₂-y₁)/(x₂-x₁)

Then linear equation,

y-y₁=(y₂-y₁)/(x₂-x₁)×(x-x₁)

Substitute the values here,

y-2=(6-2)/(4-5) ×(x-5)

y-2=4/(-1)(x-5)

y-2=20-4x

4x+y=22

So the required linear Equation is 4x+y=22.

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The correct coefficient is 147

In scientific notation, a number is represented by an exponent, or the power of 10, multiplied by the coefficient, which appears before the times sign. For instance, 4.3 is the coefficient and 6 is the exponent in the equation 4.3 x 10^6, which is equivalent to 4,300,000 (four million three hundred thousand).

From the question, we have

147,000 = 147 *10^3

The correct coefficient is 147

Multiplication:

Mathematicians multiply two or more numbers to determine the sum of the parts. It is a fundamental mathematical procedure that is commonly used in real-world situations. Multiplication is used when groups of like sizes need to be combined. Multiplication is a mathematical operation that illustrates the fundamental idea of adding the same number again. The product of two or more numbers is what occurs from multiplying them, while the components are the quantities that are multiplied. Multiplying the numbers makes it simpler to repeatedly add the same quantity.

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Answer: No they are not equivalent.

Step-by-step explanation: 8(9x-2) = 72x-2

= 8(9x-2) = 72x - 16

= 72x -16 is not equivalent to 72x -2.

The cost for a passenger going to a distance that is 3/2 times more distant than the average is; 15 pesos

We are given that;

Average distance covered per passenger = x² + 5 Km.

Cost per average distance = 10 pesos

Cost per km = 10/(x² + 5) pesos per km

We are told that a passenger now goes a distance that is 3/2 times more distant than the average. Thus, this distance is;

(3/2)(x² + 5) Km

The cost for this given distance will be;

10/(x² + 5) * (3/2)(x² + 5)

= 10 * (3/2)

= 15 pesos

Thus, we conclude that the travelling cost in pesos is 15 pesos

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The area of the triangle is 43.81 square units

The side a = 8 units

The side b = 11 units

The perimeter of the triangle = 32 units

First we have to find the third side of the triangle

a + b + c = 32

Substitute the values in the equation

8 + 11  + c = 32

19 + c = 32

c = 32 - 19

c = 13 units

Then the area of the triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

The value of s = (a + b + c) / 2

= (8 + 11 + 13) / 2

= 32/2

= 16

Substitute the values in the equation

The area of the triangle = [tex]\sqrt{16(16-8)(16-11)(16-13)}[/tex]

Subtract the terms

= [tex]\sqrt{(16)(8)(5)(3)}[/tex]

= [tex]\sqrt{1920}[/tex]

= 43.81 square units

Hence, the area of the triangle is 43.81 square units

The complete question is:

Find the area of a triangle , two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.

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Answer:

15/16

Step-by-step explanation:

75/80

15/16

Option D, the function is graphed. And the condition is y = {x² +4,x<2

                                                                                            -x+4, x >2

In a mathematical function from a set X to a set Y, exactly one element of Y is assigned to each element of X. The function's codomain and domain are respectively referred to as the sets X and Y as a whole.

Functions were initially thought of as the relationship between varying quantities and other variables. The impact of time on a planet's position serves as an example of this. The concept was historically developed with the development of infinitesimal calculus at the end of the 17th century, and up until the 19th century, the functions taken into consideration were differentiable.

Let us check option A first

y={x² +4, x≤ 2

    -x+4, x<2

For, x² +4, x≤ 2

x   2     1     0     -1      -2

y   3     5    4      5       8

Here, the condition is satisfied

Now, we have to check the condition

-x+4, x<2

The condition is not satisfied.

Similarly, we have to check all the options.

And finally by checking all the conditions,

Option D is correct and the conditions are

y = {x² +4,x<2

      -x+4, x >2

Therefore, the option D function is graphed.

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Answer:

30

Step-by-step explanation:

in index form the nth if a root number is X and that is X to the power so the seventh root of 30 is 30 to the power of 1/7

Answer: The question is a bit unclear but the value of -9 is -9, the absolute value of -9 is 9. Does that answer your question?

Step-by-step explanation:

The probability of more than 3 of the flips turn up tails is 0.0528 i.e 5.28%.

The binomial distribution in contains n independent Bernoulli trials. A Bernoulli trial is a trial that happens to succeed (probability p) or fail (probability 1- p = q )

Suppose we have a variable X for a Bernoulli distribution with parameters n and p, which is written as The probability of x successes in n trials is P(X = x)

= ⁿCₓ pˣ(q)ⁿ ⁻ ˣ

Toss a fair coin 12 times.

Next is the probability that 3 or more flips will be a number.

The probability of success is (P) = 1/2 = 0.5

total number of tosses (n) = 12

we have x = 3

P(X = 3) = ¹²C₃(0.5)³x (1 - 0.5)¹²⁻³

= 220 (0.5)³ (1 - 0.5)⁹

P(X = 3) = 0.0528

P(X = 3) = 5.28%

Hence, the probability that more than 3 of flips turn up tails is 0.0528.

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Answer: The slope is undefined because the line is vertical

Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

Slope = (-3 - 4) / (2 - 2) = -7/0 =undefined

This is a vertical line.  

The probability of getting either 1 or 2 on first and second toss is 1/9

How to calculate the probability?

Probability is numerical description for how likely something is to happen. To know probability something event we just divide no the outcome by total possible of the outcome.

The probability of either 1 or 2 side on first toss is

= no the outcome / total possible the outcome

= 2/6

= 1/3

For second toss is same as first toss

= 2/6

= 1/3

Since the second toss is independent, it is called an independent event. So, we just need to multiply the probability on the first toss by the probability on the second toss,

= 1/3 * 1/3

= 1/9

Thus, the probability of getting either 1 or 2 on first and second toss is 1/9

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Answer:

the answer is 45/100=9/50 according to my solution

The actual measurements of bedroom are 4.8 feet and 13.8 feet. Therefore, option A is the correct answer.

Given that, on a given blueprint, 1 in. :6 ft.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

The dimensions of the bedroom on the blueprint are 0.8 inches × 2.3 inches

Here, 0.8 × 6

= 4.8 feet

2.3 × 6

= 13.8 feet

The actual measurements of bedroom are 4.8 feet and 13.8 feet. Therefore, option A is the correct answer.

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35x + 65y = 815 and x + 7 = y are the system of equations that can be used to find the number of boxes.

What is an algebra?

One of the many different mathematical disciplines is algebra. Algebra is, broadly stated, the study of mathematical symbols and the guidelines for applying those symbols to formulas.

Given,

The weight of each small box = 35 pounds
The weight of each large box = 65pounds
The total weight of the boxes = 815pounds
There were7 times as many small boxes shipped as large boxes
Let 'x' be the number of small boxes and 'y' be the number of large boxes
The weight of 'x' small boxes = 35x pounds
The weight of 'y' large boxes = 65y pounds
The total weight of the two types of  boxes together = 35x+65y

Since the total weight of the boxes is 815 pounds, we have
35x+65y = 815---------------------(1)

Since 7 more small boxes =   large boxes, hence we have,
x + 7 = y ------------------------(2)
Solving both the equations we get,

x = 3.95 or 4
and, y = 10.95 or 11

The number of large boxes shipped = 11

The number of small boxes shipped  = 4

∴ The number of small boxes shipped = 4 and the number of large boxes shipped = 11.

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Answer:

this equal to -13.55 hopefully this helps

Cubic millimeter volume unit is smaller.

You would multiply a measurement in cubic centimeters by 1,000 to translate it to cubic millimeters. This makes sense because you would anticipate needing a lot more cubic millimeters to fill the same space because a cubic centimeter is greater than a cubic millimeter.

Volume:

The total number of cubic units that a cube occupies in three dimensions is its volume. Six faces, twelve edges, and eight vertices make up the three-dimensional shape of a cube. Therefore, the area encircled by a cube's six faces is considered to equal its volume. It differs from 2D shapes in that it adds a third dimension, known as height or thickness, in addition to length and breadth. Since the product of a cube's length, width, and height determines its volume. Cubic units are used to measure it. The volume of a cube increases as the value of its dimensions increases.

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The coordinates of A is (0,2)

How can a image be reflected?

Behind a mirror's glass, people can see a reflection of themselves. The shiny surface creates that image when light rays strike it and reflect or bounce back, creating a "mirror image." Contrary to popular belief, the reflection is not mirrored from left to right as many people believe.

The coordinates of the point A is (-3,-2)

The rule of reflection over x-axis is

(x,y)→(x,-y)

So the point A after reflecting over the x-axis becomes

A(-3,-2)→ A(-3,2)

To move the point P(x,y), a units right and b units up we use

P(x+a,y+b)

As per the question as it moves 3 units right

∴ A(-3.2)

⇒A(-3+3,2)

The point A now is A(0,2)

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The vertical axis of symmetry is x =  -1

the domain is {-2 2}

the range is {-6, 0}

The domain refers to all possible value in the input of a graph. The input is the x coordinate and the possible values here is within the interval

The range refers to all possible value in the out put of a graph. The out put is the y coordinate and the possible values here is within the interval

Axis of symmetry refers to where the graph is bisected, the problem asked of vertical axis of symmetry. Therefore the line will be between the y coordinates

The vertical axis of symmetry and this x = -1

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The parametric equations of the curve are x = -10 + 1t and y = -20 - 4t

A parametric equation is defined as a type of equation that employs an independent variable called a parameter (often denoted by t)

Given: The line with slope -4, passing through (-10, -20)

We can use the given properties of the curve to describe it parametrically as follows

The slope of -4 implies that if y decreases by 4, x increases by 1  i.e slope = Δy/Δx = -4/1. Thus, we have

x = -10 + 1t

y = -20 - 4t

Therefore, the parametric equations are x = -10 + 1t and y = -20 - 4t. So (x(t) , y(t)) = (-10 + 1t,  -20 - 4t)

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