Mrs. Parker earns a 8.5% commission on her total sales. Last month, she had sales of $53,910. How much commission did Mrs. Parker earn last month

The point (x, y) where the lines intersect is (0, 0).

What is lines intersect?

The empty set, a point, or another line can cross another line in Euclidean geometry. Examples of applications for identifying these circumstances and locating the intersection include computer graphics, motion planning, and collision detection.

We have the linear system:

y = r[tex]\times[/tex]x

y = s[tex]\times[/tex]x

We want to find the point where the lines intersect,

We know that

r[tex]\times[/tex]x = y = s[tex]\times[/tex]x

r[tex]\times[/tex]x = s[tex]\times[/tex]x

if r and s are different numbers (if r = s, this means that the two lines are the same line)

Then we have that the equality is only true when x = 0.

this means that the value of y is.

y = s[tex]\times[/tex]0 = r[tex]\times[/tex]0 = 0

So the point (x, y) where the lines intersect is (0, 0).

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Answer:

hush Nikki

nnnnmm

nnnnn

Answer:

99 inches

Step-by-step explanation:

1 foot=12 inches

8x12=96

96+3=99

Answer:

[tex]\left(-\frac{1}{3},\:\frac{130}{27}\right) \:\mathrm{Maximum}\left(1,\:6\right)\\\\\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \: < x < \infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\\Not sure if I did it right[/tex]

Answer:

C

Step-by-step explanation:

A rational number can be written as a ratio of two integers. In decimal form, a rational number will either terminate or repeat a pattern.

Answer:

  x ≥ 0

Step-by-step explanation:

You want to know an appropriate limit on the domain of f(x) = 3 -x² so the function is one-to-one.

A function is one-to-one if it passes the "horizontal line test." That is, a horizontal line can intersect its graph in at most one place.

The function f(x) = 3-x² has a turning point at x=0 and is symmetrical about that line. In order to make the function be one-to-one, the domain must be restricted to one of ...

or any subset of either of those domains.

callback restricted is a function that is passed as an argument to another function

It tests whether the condition returned by the callback function holds for at least one item in array.

What is an array?

It should be noted that an array means a data structure that can store a fixed size collection of elements.

In this case, the true statement of the array is that it tests whether the condition returned by the callback function holds for at least one item in array.

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The x - intercept is 40 ,which represents the number of monthly payments needed to repay the loan .

Given :

The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.

From the graph :

Two points are ( 6 , 25500 ) and ( 25 , 11250 )

x - intercept = 40

The x - intercept gives information about the variable represented on the x - axis of a graph which is the number of monthly repayments needed to cover the loan.

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a. P = [tex]\left[\begin{array}{ccc}\frac{2}{3} &\frac{1}{3} &0 \\\\\frac{2}{9} &\frac{5}{9} &\frac{2}{9}\\ \\0&\frac{2}{3} &\frac{1}{3} \end{array}\right][/tex]

b. P[[tex]x_{3} = 2[/tex]] = 0.18

c. p = 0.8353

d   [tex]\pi _{1} = \frac{1}{2} \\\\\pi _{2} = \frac{1}{6} \\\\\pi _{0} = \frac{2}{6}[/tex]

Given that:

{[tex]x_{n}[/tex] ; n > 0} is a Markov chain

[tex]x_{n}[/tex] denotes no of black balls in Urn A after [tex]n^{th}[/tex] round of exchange.

Clearly know that no of black balls in Urn A cannot exceed.

Hence, state space is {0, 1,2}

Transition probabilities can be

(a) [tex]P_{00}[/tex] = P [white ball is selected from A & white ball is selected from B]

          = P [white ball from A] × P [white ball from B]

           = [tex]\frac{2}{3}[/tex]

   [tex]P_{01}[/tex] = P [white ball from A & black ball from B ]

         = [tex]\frac{1}{3}[/tex]

   [tex]P_{10}[/tex] = P [black ball from A & white ball from B]

         = [tex]\frac{2}{9}[/tex]

   [tex]P_{11}[/tex] = P [black ball from A &  black ball from B]

              or P [white from A & white from B]

          [tex]= \frac{1}{3} * \frac{1}{3} + \frac{2}{3} *\frac{2}{3}\\ \\ = \frac{1}{9} + \frac{4}{9}\\ \\= \frac{5}{9}[/tex]

    [tex]P_{12}[/tex] =  P [white from A & white from B]

          = [tex]\frac{2}{9}[/tex]

    [tex]P_{21}[/tex] =  P [black ball from A & white ball from B]

          = [tex]\frac{2}{3}[/tex]

     [tex]P_{22}[/tex] =   P [white from A & white from B]

           = [tex]\frac{1}{3}[/tex]

Transition probability matrix P = [tex]\left[\begin{array}{ccc}\frac{2}{3} &\frac{1}{3} &0 \\\\\frac{2}{9} &\frac{5}{9} &\frac{2}{9}\\ \\0&\frac{2}{3} &\frac{1}{3} \end{array}\right][/tex]

(b) The probability that after 3 exchanges, there are exactly 2 black balls in Urn A.

P[[tex]x_{3} = 2[/tex]]

given initial distribution

[tex]p [x_{0} = 0] = 0 , p [x_{0} = 1] = 1 , p [x_{0} = 2] = 0[/tex]

p[tex][x_{3} = 2] =[/tex] ∑ i = 0 to 2 P [tex][x_{3} = 2 , x_{0} =i ][/tex]

              = ∑ i = 0 to 2 P [tex][x_{3} = 2 , x_{0} =i ][/tex]  . P[tex][ x_{0} = i][/tex]

              =  ∑ i = 0 to 2 P [tex]i^{2^3}[/tex] P[tex][ x_{0} = i][/tex]

Transition probability matrix can be calculated by increasing power of P matrix to 3 i.e [tex]P^{3}[/tex]

P[[tex]x_{3} = 2[/tex]] = 0.18

(c) The probability that by the time we have done 3 exchanges, there has never been 2 black balls in Urn A.

[tex]P[x_{3} \neq 2 , x_{2} \neq 2, x_{1} \neq 2 | x_{0} = 1 ][/tex]

p = 0.8353

(d) Long run proportions of state 0,1,2.

[tex]\pi _{0} = \frac{2}{3} \pi _{0} + \frac{2}{3} \pi _{1}[/tex]

[tex]\pi _{1} = \frac{1}{3} \pi _{0} + \frac{5}{9} \pi _{1} + \frac{2}{3} \pi _{2}[/tex]

[tex]\pi _{2} = \frac{2}{9} \pi _{1} + \frac{1}{3} \pi _{2}[/tex]

[tex]\pi _{0} + \pi _{1} + \pi _{2} = 1[/tex]

[tex]\pi _{0} = \frac{2}{3} \pi _{1} \\[/tex]

[tex]\pi _{2} = \frac{1}{3} \pi _{1}[/tex]

[tex]\pi _{1} [\frac{1}{3} + \frac{2}{3} + 1 ] = 1[/tex]

[tex]\pi _{1} = \frac{1}{2} \\\\\pi _{2} = \frac{1}{6} \\\\\pi _{0} = \frac{2}{6}[/tex]

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The solution is Option D.

The value of x from the triangle is x = 31

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ABC

The measure of side AB = 14.5

The measure of side BC = 15.5

Let the second triangle be XYZ

The measure of side XY = 29

The measure of side YZ = x

Now , if the triangle ABC is similar to triangle XYZ , then the corresponding sides of the triangles will be equal in ratio

So , the equation will be

XY / AB = YZ / BC

Substituting the values in the equation , we get

29 / 14.5 = x / 15.5

On simplifying the equation , we get

x/15.5 = 2

Multiply by 15.5 on both sides of the equation , we get

x = 2 x 15.5

x = 31

Therefore , the value of x is 31

Hence , the value of x of side YZ is 31

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The image's distance from the mirror is -1.87, by using the mirror equation.

Note:-  Although the question is missing, I believe the issue is asking where the image is located.

To find the solution to the problem, the mirror equation can be used:

Mirror equation =  [tex]\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }[/tex]

Where,

f = mirror's focal length

[tex]d_{o}[/tex] = object's distance from the mirror

[tex]d_{i}[/tex] =  image's distance from the mirror

The focal length is assumed to be negative for a convex mirror in our problem.

f = -2.8 m

The object's distance (do) = 5.6m

By using the mirror equation, the image's distance from the mirror can be determined

[tex]\frac{1}{f}+\frac{1}{d_{o} }+\frac{1}{d_{i} }[/tex]

i.e, [tex]\frac{1}{d_{i} } = \frac{1}{f} -\frac{1}{d_{o} }[/tex]

= [tex]-\frac{1}{2.8} -\frac{1}{5.6}[/tex] =  [tex]-\frac{3}{5.6}[/tex]

= - 0.5357

[tex]d_{i} =[/tex] [tex]-\frac{5.6}{3}[/tex]

= -1.87 m

The virtual nature of the image is indicated by the negative sign (located behind the mirror)

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From the given pairs of ordered pairs {(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)} it is a function.

The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

As per the set of ordered pairs given in the question,

1.

{(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)}

It is a function because every input has a single output.

2.

{(-7, 3), (-7, 6), (-7, 12), (-7, 18)}

It is not a function because 7 corresponds to two different images like 3, 6, 12, and 18.

3.

{(9, -3), (4, -2), (1, -1), (0, 0), (1, -3)}

It is not a function because 1 corresponds to two different images, like -1 and 3.

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Answer:

18

Step-by-step explanation:

The name of this man's "small" and "final" theorems are Pierre de Fermat

He was a French mathematician who is recognized for his work on inequality and other early advances that helped pave the way for infinitesimal calculus. He is praised in particular for his work on number theory and his original invention of a technique for determining the largest and smallest ordinates of curved lines that is comparable to differential calculus, which was previously unheard of. He made important advances in probability, optics, and analytical geometry.

The Taniyama-Shimura Conjecture, commonly known as the modularity conjecture, was employed in another theorem that bears this man's name.  

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When you add one-digit number to a decade number, you will notice that the ones place digit sum is interchanged in their positions

You should know the word decade means ten. so a decade number is a number with ten digits. The digits of the decade number are

1,2,3,4,5,6,7,8,9

So write the number as

12345679

A digit number is  say 9

123456789+9

= 123456798

Therefore when a digit number is added to a decade number, the last digits interchange their positions

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The value of f(g(2)) from the given functions f(x) and g(x) is 3.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=2x²+1 and g(x)=3x-5.

We need to find f(g(2)).

Put x=2 in the function g(x)=3x-5, we get

g(2)=3×2-5

= 6-5

= 1

So, g(2)=1

Put x=1 in the function f(x)=2x²+1, we get

f(g(2))=2(1)²+1

= 2+1

=3

Therefore, the value of f(g(2)) is 3.

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Answer:

  see the attachment for the Venn diagram

Step-by-step explanation:

Given the numbers of students in various combinations of three courses, you want the associated Venn diagram and some numbers associated with additional combinations of courses.

It is often easiest to populate the numbers in a Venn diagram by starting with the center one: 286 are taking all three courses. (V. = 286)

Working outwards from there, the numbers taking two courses can be filled in: (II. = History & Dance - V. = 343; IV. = History & Math - V. = 319; VI. = Dance & Math - V. = 318.)

Finally, the number taking a single course can be found. (I. = History -II. -IV. -V.; III. = Dance -II. -V. -VI.; VII. = Math -IV. -V. -VI.)

Adding all the numbers found so far gives the total in History, Dance, or Math (question 4). The difference between the number surveyed and the number in courses is VIII, the number taking none of the courses (question 5).

The least arithmetic may be involved if you rewrite this expression to ...

  H ∪ D' = (H'∩D)' = 2401 -(III +VI) = 2401 -(289 +318) = 1794

This will be the sum of numbers I, IV, VII.

  226 +319 +372 = 917

This is VI alone: 318

This is all but VIIII: 2401 -248 = 2153

This is VIII alone: 248

Answer:

t = 48 litres when full

Step-by-step explanation:

The water tank at the institution is full. A water truck begin to full the tank with water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate the number of litres of water that the tank can hold.

8(15) = 5/2t

120 = 5/2t

240 = 5t

t = 48 litres when full

Answer:

4 11/12

Step-by-step explanation:

2 1/4 + 8/3

9/4 + 8/3

23/12 + 32/12

59/12

4 11/12

The amount allowed for housing and expenses is $2023.73.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Gross pay = $2759

Deduction:

7.65%

= 7.65/100 x 2759

= $211.06

12%

= 12/100 x 2759

= $331.08

7%

= 7/100 x 2759

= $193.13

The remaining amount.

= 2759 - 211.06 - 331.08 - 193.13

= $2023.73

Thus,

The amount allowed is $2023.73.

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Answer:

now

Step-by-step explanation:

d= √(X2 _ X1) +(Y2 - Y1). = (5 -2 )+ (-4- 1)=

Answer:

x ≤ 14

Step-by-step explanation:

x = age of Sis

x - 6 = Martin's age

x + (x-6) ≤ 22

2x - 6 ≤ 22

2x ≤ 28

x ≤ 28/2

x ≤ 14

Option B  [tex]n_{1} = 27 ,n_{2} = 29[/tex]  are the two sample sizes cannot be true.

HYPOTHESIS TEST

Given that:

The degree of freedom for the test of two independent population means is 56.

Degrees of freedom for two independent populations are well known.

[tex]n_{1} + n_{2} - 2[/tex]

[tex]n_{1} + n_{2} - 2[/tex] = 56

[tex]n_{1} + n_{2}[/tex] = 54

Total sample sizes = 54

Option B (   [tex]n_{1} = 27 ,n_{2} = 29[/tex] ) cannot be true.

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Step-by-step explanation:

remember the priorities of doing the calculation operations :

1. brackets

2. exponents

3. multiplications and division

4. addition and subtraction

so,

(22 + 5) / (12 - 9) × 6

(27) / (3) × 6

and to write it without any doubt :

(27 / 3) × 6

9 × 6 = 54

why is

(27 / 3) × 6

better than

(27) / (3) × 6 ?

because if you are really taking it literally, you could understand

27 / 3 × 6

as

27 / (3 × 6)

and then the result is different.

so, many greetings to your teacher ! if what your write here was really what your teacher gave you, he/she was sloppy. in real math documentation people would write that as

((22 + 5) / (12 - 9)) × 6

our leave extra space like

(22 + 5) / (12 - 9) × 6

Answer:

0.875

Step-by-step explanation:

7/8 in decimal form is 0.875.

On solving the provided question, Since rate multiplied by time gives output, 1/5+1/7 (t-1)=1

A formula is a statement that the values ​​of two expressions are equal. The formula essentially says that two things are equal. An equals sign or '=' indicates that. 8+2=12-2 is an example equation. According to the above formula, the left side of the formula is equal to the right side. So the equation is the statement "this is equal to that".

Doug can paint 1/5 of a room per hour, Dave can paint 1/7 of a room per hour, and the time they spend working together is t-1.

Since rate multiplied by time gives output, 1/5+1/7 (t-1)=1

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Answer:

b and c

Step-by-step explanation:

It is said that the rural landscape has been replaced by the urban landscape because rural landscapes have been transformed into urban ones.

We have to:

At present, more and more rural spaces become urban, which is why it is indicated that the urban landscape is replacing the rural one.

¡Hope this helped!

Let us answer the individual questions as per the given conditions:

1. Since the area of the bulletin board is meant to be exactly 12 square feet, the 2 pairs for length and width would be 4feet and 3feet(first pair), 6 feet and 2 feet(second pair) respectively.

2. The possible length and width of the board were determined using trial and error method to find two numbers whose product equal to 12.

3. If width of the board were to be x , and the length be 1 greater than width, we can represent the length as x+1.

4. Given the area of illustration board as 12 sq ft. the equation that represents the given situation is :  

5. The equation can be described as quadratic equation.

6. Yes, I think we can use the equation formulated to find the length and width of the bulletin board.

What is rectangle?

A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. Two dimensions, the length and breadth, define any rectangle form.

What is the formula for calculating area of rectangle?

The formula for calculating the area of rectangle is given by:

A = L * B

where A - area of rectangle

          L - Length of the rectangle

          B - Width of the rectangle

According to the given question:

1. Using the formula for area of rectangle(length * width) , the two pairs of length and breadth can be found by finding two real positive numbers whose product equals to 12. Hence , we get 4 feet and 3 feet as first pair and 6 feet and 2 feet as second pair for length and width respectively.

2. The possible length and width pairs were determined by using the equation of area, A = L*B which is equal to 12 sq ft.

3. Since the width is given to be x by the question and x is mentioned to be    1  greater than width, hence length will be equal to x+1.

4. Using the equation for area of rectangle:

A = L * B

substituting the values as per the given conditions,

12 = x(x+1)

or, x2 + x = 12

or, x2+x-12 =0

Which is the required equation.

5. Since the highest power in the equation is 2. Hence the equation is described as quadratic equation.

6. Yes , we can use the equation formulated to find the length and width of the bulletin word, Simply solving the quadratic equation given above.

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