A saleswoman earns 30% commission on all the merchandise that she sells. Last month she sold $800 worth of merchandise. How much commission (in dollars) did she earn last month?

The forecast for the next period when the actual demand turned out to be 278 will be 294 units.

The method of forecasting entails creating assumptions based on historical and current data. These might then be contrasted with what transpires.

Ft = 290, Tt = 8, α = 0.40, δ = 0.50, At = 278. Then the forecast for the next period will be

FITt = Ft + Tt

       = 290 + 8

       = 298 units

Ft + 1 = FITt + α(At − FITt)

        = 298 + 0.40(278 − 298)

        = 298 − 8

        = 290 units

Tt + 1 = Tt + δ(Ft + 1 − FITt)

         = 8 + 0.50(290 − 298)

         = 8 − 4

         = 4 units

FITt + 1 = Ft + 1 + Tt + 1

            = 290 + 4

            = 294 units

The forecast for the next period will be 294 units.

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The point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).

A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).

given that

the coordinates points are (1, 10) and (5,42)

(x1,y1) = (1,10)

(x2, y2) = (5,42)

The formula of point-slope is

(y - y1) = m(x - x1)

Here,

x1 = 1 and y1 = 10 but we don't know the value of m.

now,find the value of m using the following formula

[tex]m = \frac{(y2 - y1)}{(x2 - x1)} [/tex]

now, substitute the values, we get

[tex]m = \frac{(42 - 10)}{(5 - 1)} [/tex]

[tex]m = \frac{30}{4} [/tex]

m = 8

so, the value of m is 8.

substitute these values into the point-slope formula

(y - 10) = 8(x - 1)

Hence, the point slope form of (1,10) and (5,42) is (y - 10) = 8(x - 1).

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Subtraction Property of Equality and Addition Property of Equality are two different approaches to resolving a real-world problem that can be depicted by an equation.

When the identical quantity is added to the both sides of an equation, it generates an equivalent equation, according to the addition property of equality.

To maintain equality, if we deduct a number from one side of the equality, we must subtract the very same number from the opposite side of the equality.

Thus, Subtraction Property of Equality as well as Addition Property of Equality are two different ways of solving a real-world problem that may be represented by an equation.

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Answer:

3x+6

Step-by-step explanation:

Let's simplify step-by-step.

−2x−13+19+5x

=−2x+−13+19+5x

Combine Like Terms:

=−2x+−13+19+5x

=(−2x+5x)+(−13+19)

=3x+6

The perimeter of the triangle is 37.86

Given,

The ratio of the measure of the angles of triangle = 1:2:3

Let the angles be taken as x, 2x, 3x.

Total angle of a triangle is 180°.

We can now find x.

x + 2x + 3x = 180°

6x = 180°

x = 180°/6 = 30°

x = 30°

2x = 2 × 30° = 60°

3x = 3 × 30° = 90°

Let the sides of the triangle be a, b, c.

The length of the shortest side is given = 8

Lets take a as 8.

We can use Trignometric Formulas here:

Trignometric Formulas:

sin θ = [tex]\frac{opposite side}{hypotenuse}[/tex]

cos θ = [tex]\frac{adjacent side}{hypotenuse}[/tex]

tan θ = [tex]\frac{opposite side}{adjacent side}[/tex]

By using sin rule we can find other sides.

That is,

sin 30° = opposite side / hypotenuse

sin 30° = a/b

sin 30° = 8/b

b = 8 × sin 30°

b = 16

Next,

sin 60° = opposite side / hypotenuse

sin 60° = c/16

c = sin 60° × 16

c = 13.86

Now we can find the perimeter of the triangle = a + b + c

= 8 + 16 + 13.86

= 37.86

The perimeter of the triangle is 37.86

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Meter, liter, and gram are all basic units of measure in the metric system.

The U.S. customary system and the metric system are the two major systems of measurement. The  system of measurement that uses the meter, liter, and gram as the base units of length (distance), capacity (volume), and weight (mass) is referred as Metric system.

Most of the countries use the metric system but in the United States, the US Customary system is used where the things are measured in  feet, inches, and pounds. Meter, liter, and gram are all basic units of measure in the metric system.

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Answer:

It is D

Step-by-step explanation: I am verifying the persons answer. You're welcome.

The equation of the circle that passes through the point (√3 , 0) and has a center at the origin is x^2 + y^2 = 3.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (√3 , 0).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(√3 - 0)^2 + (0 - 0)^2

radius= √3

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = √3

(x - 0)^2 + (y - 0)^2 = (√3)^2

x^2 + y^2 = 3

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The arithmetic mean a n of the given terms a n₋₁ = 4, a₊₁ = -3 is [tex]a_{n}[/tex] = 1/2.

an=a1+d(n−1)   by using this formula the arithmetic mean a n of the given terms are

[tex]a_{n}[/tex] = (-3 + 4)/2

[tex]a_{n}[/tex] = 1/2

The sum of a set of numbers divided by the total number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.

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Answer:

43.57

Step-by-step explanation:

subtract 6.43 from 50

Answer: 43.57

Step-by-step explanation:  50 dollars minus 6 dollars and 43 cents and it gives you 43.57

Answer:

Step-by-step explanation:

4.

do A squared plus B squared equal C squared, you should get [squared root[ of 306 then simplify it to 3 squared root 34 by using the family tree

The solution of the system of equations involving 3x + 5y = 13 and 2x + y = 4 is (1 , 2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in x and y,

3x + 5y = 13     (equation 1)

2x + y = 4     (equation 2)

Using the second equation, find the value of one variable, lets say y, in terms of the other.

2x + y = 4     (equation 2)

y = 4 - 2x

Substitute the equation of y to the first equation.

3x + 5y = 13     (equation 1)

3x + 5(4 - 2x) = 13

3x + 20 - 10x = 13

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.

3x + 20 - 10x = 13

3x - 10x = 13 - 20

-7x = -7

x = 1

Substitute the value of x in the equation of y.

y = 4 - 2x

y = 4 - 2(1)

y = 4 - 2

y = 2

Hence, the solution of the given system of equations is (1 , 2).

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We have given the expression -13y + 7 -11 - 4y to write as sum which is

-13y + 7 +(-11) + (-4y).

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. (Number/variable, Math Operator, Number/variable) is the order in which an expression is composed.

Arithmetic operators and numbers make up a mathematical numerical expression. No equality or inequality symbols, or unidentified variables, are present.

Indeterminate variables, integers, and arithmetic operators make up an algebraic expression. Neither equality nor inequality symbols can be found in it.

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Answer:26

Step-by-step explanation:it's 26

Answer:

26

Step-by-step explanation:

You add 24 + 2 = 26 ( SUM means to ADD )

From the situation described, it is found that:

a) The linear function that represents the amount of miles that Bobby & Jack will run together is T(x) = 2(4x + 5).

b) They will have run 74 miles after 8 days.

A linear function is modeled by:

y = mx + b

In which:

For both Bobby's and Jack's function, we have that:

Hence the functions for the number of miles they will have run after x days are given by:

The total amount is:

T(x) = B(x) + J(x)

T(x) = 4 + 3x + 6 + 5x

T(x) = 8x + 10.

T(x) = 2(4x + 5).

After 8 days, the number of miles they will have run is:

T(8) = 2(4 x 8 + 5) = 2 x 37 = 74.

They will have run 74 miles after 8 days.

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In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

WE have been given graph that titled U S population has year on the x-axis, and millions of people on the y-axis. A line increases from 0 in 1800 to 300 in 2000.

The line graph showed that:

The U.S. population was under 50 million in 1800

It increased exponentially after 1880

It reached around 300 million in 2000

The U.S. has seen its population rise exponentially over the last century such that; over 300 million and it was around the year 2000 that this milestone was reached.

Therefore U.S. population in 2000 was around 300 million.

In the line graph it represents us to infer that the U.S. population in 2000 was about 300 million.

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Answer:

300 million is ur answer:)

Step-by-step explanation:

1. The number of cups of orange drink that ASB would need to sell to reach their goal of raising $240 after selling 60 cups of lemonade is 40 cups.

2. To raise $2,500, the equation representing the scenario is 2L + 3D = 2,500.

3. Rewriting the equation from part 2 above to express the number of orange drinks as a function of the number of lemonade drinks is F(D) = (2,500 - 2L)/3.

A mathematical function is a mathematical expression, rule, or law, defining the value relationship between the independent variable and the dependent variable.

For instance, when we state that the number of orange drinks is a function of the number of lemonade drinks, it means that the number of orange drinks to be sold depends on the number of lemonade drinks sold.

                                       Lemonade     Orange Drink

Selling price per cup             $2                    $3

Expected total revenue = $240

Number of cups sold            60

Total revenue                    $120 ($2 x 60)   $120 ($240 - $120)

Number of cups to be sold                           40 ($120/$3)

2. The equation is:

2L + 3D = 2,500

Where:

L is the number of Lemonade

D is the number of Orange drinks sold.

3. The rewritten equation is:

F(D) = (2,500 - 2L)/3

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If x is doubled then the value of y is also doubled.

A sort of proportionality known as "direct variation" occurs when one quantity immediately changes in response to a change in another variable. This suggests that if one number increases, the other quantity will also rise proportionately. Similar to the last example, if one quantity declines, the other amount likewise declines. The link between direct variation and the graph will be linear, resulting in a straight line.

As y varies directly with x,

Using direct variation,

which implies y = kx

if x is doubled,

y = 2kx,

This implies that if x is doubled then the value of y is also doubled.

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Answer:

C. z + 4

Hope this helps :)

Step-by-step explanation:

When it says "sum," it means the answer to 2 number that you add. The first number will be unknow which z will stand for, and the second number is 4 since it was stated in the statement, "the sum of a number and 4."

The surveyor can find AB if he finds CD as CD = AB.

So,

First, connect B and D and make a square ACDB with BC as a diagonal.

So,  ACB ≅ DCB under SAS condition.

Therefore, the surveyor can find AB if he finds CD as CD = AB.

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The sum of the infinite geometric series 6+5+ 25/6 + . .  is S = 36

The given geometric series is:

  6 + 5 +  25/6 + . . .

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 6

a(2) = 5

a(3) = 25/6

Hence, the common ratio is

   r = a(2) / a(1) = 5/6

Since 0 < r < 1, the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) 6 and r = 5/6 into the formula:

S = 6 / (1 - 5/6)

   = 6 / (1/6)

   = 36

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Answer: 49

Step-by-step explanation:

A=πr^2

A=π(7)^2

A=49π in^2

Answer: 49

Answer:

154 Inches square.

r=7

area= πr^2

= 22/7* 49

= 154

A unit rate is represented by the second pair. The graph is also displayed.

A pair made consisting of two sections written inside parantheses and separated by commas is referred to as an ordered pair. For instance, an ordered pair with "x" as the first component and "y" as the second element is shown by the symbol (x, y). These items have unique names and, depending on the situation, can either be variables or constants.

The element order in an ordered pair has some bearing. It suggests that (x, y) could not always equal (y, x).

A coordinate geometry ordered pair is used to specify where a point is on the coordinate plane in relation to the origin.

Therefore, the graph is attached and the second pair represents the unit rate.

Graph is attached at end.

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The table shows the number of Calories José and Natalie

burned after 1, 2, and 3 minutes of running. Graph the

relationship between the number of minutes running and

the number of Calories burned for each person. By which

ordered pair is a unit rate represented?

Calories Burned

X

Time (min) 0 1 2 3

Calories Burned

José 0 8 15 23

Natalie 0 5 10 15

​

Number of Calories

40 30 20 10 0 Calories Burned

Answer: 78 pounds

Step-by-step explanation:

10.4/4 = 2.6

2.6 * 30 = 78

Answer:43

Step-by-step explanation:

(9+17)x2

The entrance fee in the water park for the adult $37 and for the child are $24.

The maximum power of a variable in a linear equation of two variables is one.

Now, for the question's given condition;

Let the cost for the adult is 'x'.

Let the cost for the child is 'y'.

The total cost for entrance fee is $220.

The group of 4 adults and 3 children costs 220.

4x + 3y = 220     ........equation 1

The group of 2 adults and 1 child costs $98.

2x + y = 98           .........equation 2

Use elimination method to solve the equations;

x = 37 and y = 24.

Therefore, the entrance fee in the water park for the adults is $37 and for the child us $24.

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Simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.

As given in the question,

Given equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex]

Simplify the given equation,

x/ 3(x+3) - 8/x(x+3)

= (x² - 24) / 3x(x+3)

Restriction on the variables for the above equation is,

x≠ 0 , x≠ -3

Therefore, simplification of the equation [tex]\frac{x}{3x+9}- \frac{8}{x^{2} +3x}[/tex] is equal to (x² -24)/ 3x(x+3), restriction on the variables are x ≠0 , x≠ -3.

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Answer:

(5+10)u

= 15u

is the solution

Using the concept of the or operation, the solution of the given inequality in the number line is given at the graph in the end of the answer.

The or operation between sets has as a result all the elements that belong to at least one of the sets.

For this problem, we have two inequalities:

Then we solve the inequality then apply the or operation between them.

The solutions to the inequalities are given as follows:

The or operation will involve both the numbers to the left of k = -7 and the numbers to the right of k = 3 being plotted on the number line, as shown in the graph at the end of the answer.

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Answer:

6.34960 correct to 5 decimal places.

Step-by-step explanation

16 ^ 2/3

= cube root of 16^2

∛(16^2)

= ∛(256)

= 6.349604208.

The 2 in the 2/3 means the square of 16, and the 3 in 2/3 mean 16^1/3

which is the same as the cube root.

The evaluation of mixed fractions   [tex]16\dfrac{2}{3}[/tex]  in improper fractions using the simplification rule is [tex]\dfrac{50}{3}[/tex].

The combination of a proper fraction and a whole number is called a mixed fraction.

When the numerator is greater than the denominator, such type of fraction is called an improper fraction.

To evaluate [tex]16 \dfrac{2}{3}[/tex] ,  convert the mixed number to an improper fraction and then simplify it.

Multiply the whole number [tex](16)[/tex]  by the denominator [tex](3)[/tex]  and add the numerator [tex](2)[/tex].

[tex](16 \times 3 )+ 2 \\= 48 + 2\\ = 50[/tex]

The sum is written with the denominator [tex]3[/tex]  as [tex]\dfrac{50}{3}[/tex] .

The evaluation of mixed fractions [tex]16\dfrac{2}{3}[/tex]  in improper fractions is [tex]\dfrac{50}{3}[/tex].

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