4-5: MathXL for School: Practice & Problem Solving
4.5.PS-15
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Reasoning Kareem cannot decide which of two washing machines to buy. The selling price of each is $520. The first is
marked down by 40%. The second is marked down by 10% with an additional 30% off. Find the sale price of each
washing machine. Use pencil and paper. Explain why Kareem should buy the first washing machine rather than the
second if the machines are the same except for the selling price.
The sale price of the first washing machine is $
(Round to the nearest dollar as needed.)
Enter your answer in the answer box and then click Check Answer.
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Answer: The common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.

Step-by-step explanation: The common ratio r of a geometric sequence is found by dividing the second term by the first term, and the nth term of the geometric sequence is given by a1 * r^(n-1), where a1 is the first term.

To find the common ratio r of this geometric sequence, we can use the fact that the 3rd term is -18 and the 6th term is 9216:

-18 = a1 * r^2

9216 = a1 * r^5

Dividing these two equations, we get:

-18/9216 = (a1 * r^2) / (a1 * r^5)

-18/9216 = r^-3

r = (-18/9216)^(-1/3)

Since r is the common ratio, it must be positive. Since (-18/9216)^(-1/3) is negative, we must take the positive root:

r = ((-18/9216)^(-1/3))^(1/3)

r = ((-18/9216)^(1/9))

r = (9216/-18)^(1/9)

r = (-512)^(1/9)

r = (-8)^(1/9)

r = (-2)^(2/9)

r = (-2)^(2/3)

r = (1/4)^(2/3)

r = 1/2

To find the first term a1, we can use the fact that the 3rd term is -18 and the common ratio is 1/2:

-18 = a1 * (1/2)^2

-18 = a1/4

a1 = -72

To find the 4th term a4, we can use the fact that the first term is -72 and the common ratio is 1/2:

a4 = (-72) * (1/2)^3

a4 = -9

Therefore, the common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.

For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.

The state of not being equal, particularly in terms of status, rights, and opportunities, is a fundamental concept in social justice theories. It can be perplexing in public conversation since it typically has distinct meanings to different individuals. However, some variations are common. An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is unfair. Various notations are used to denote different kinds of inequality, including:

A less than sign, such as a, denotes that an is greater than b.

Given inequality is:

|2x+7|+9 >18.

First we have to rearrange all the variables to the left side of the given equation:

Then,

|2x+7|>18-9

|2x+7|>9

2x+7>9 or 2x+7< -9

S0, x>1 or x< -8

Therefore, x< -8 or x>1

Hence, For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.

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The 1 dollars found near the table by your friend is likely the money for the tickets.

You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets.

let

x = number of individual ticket

y = number of couple tickets = 2x

Therefore, using equation,

2x(10) + 6x = 1075

2x + x = 195

Hence,

20x + 6x  = 1075

3x = 195

x = 195 / 3

x = 65

Hence,

26x = 1075

26(65) = 1690

Therefore, the money on the table is the ticket money because the money is short of the amount of the tickets in dollars.

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Answer:

Step-by-step explanation:

(2, 0), (3, 4)

(4 - 0)/(3 - 2)= 4/1 = 4

Answer:

27.3

Step-by-step explanation:

21 times 1.3 = 27.3 = original price

She paid 70% of the regular price of $30.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Eliza bought a hat for $21. The regular price is $30. The percentage will be calculated as,

Percentage = 21 / 30

Percentage = 0.7 x 100

Percentage = 70%

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Answer:

1/4

Step-by-step explanation:

1/2 divided by 2 would be 0.25, and since that's a quarter it would be 1/4.

In linear equation,  162 is his new weight .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Mr. Miller weigh =  180pound

10% decrease =  180 * 10/100

                        = 18

new weight = 180 - 18

                   =   162

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Answer:

∠AFB

Step-by-step explanation:

Vertical angles are opposite to one another and share the same vertex or endpoint. ∠DFE is ∠AFE both share the point F, and they are opposite to each other, so they are also vertical to each other.

The required angles  ∠TBS and ∠TCV are 48° and 22° respectively.

A right-angled triangle is a kind of triangle that has one of its points equivalent to 90 degrees. The other two points summarize to 90 degrees. The sides that incorporate the right point are opposite and the foundation of the triangle. The third side is known as the hypotenuse, which is the longest side of each of the three sides

∠TBV = 24°

∠VBS = 24°

So, ∠TBS = (24° ) = 48°

And,

∠SAU = 92°,

So,

∠VAU = 46°

In ΔTAC

∠TAC + ∠TCA = 90°

∠TCA = 90° - 46° = 44°

This angle is bisect by CV

Then,

∠TCV = 44/2 = 22°

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∠TBS = 48°

SV = 17

∠TCV = 20°

What is a angle bisector?

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

As given in question:

AV , BV and CV are the angle bisector of ΔABC

UV = 17, BV = 18

∠SAU =92° and ∠TBV = 24°

Now,

∠TBV = ∠SBV = 24° ( BV is angle bisector)

So, ∠TBS = ∠TBV + ∠SBV

      ∠TBS = 24° + 24° = 48°

SV = UV = 17 (V is the incenter of ΔABC.)

∠SAU + ∠TBS + ∠TCU = 180° (Sum of angles of a triangle)

92° + 48° + ∠TCU = 180°

∠TCU = 180° - 140°

∠TCU = 40°

So, [tex]\angle TCV = \frac{40\degree}{2}[/tex]

       ∠TCV = 20°

∴ ∠TBS = 48°

SV = 17

∠TCV = 20°

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200 rides does it take to break even.

What are the many sorts of cost?

Fixed and variable costs are the two main categories of expenses incurred by enterprises. While variable costs fluctuate with output, fixed costs do not.

                 Sometimes, fixed costs are referred to as overhead costs. They must be paid whether a company produces 100 or 1,000 widgets.

The cost function is given by

C(x ) = 15x + 1000

It is also given that it costs $25 per ride.

so,

Revenue function for x number of rides be

 R(x) = 20x

For break even:-

The cost must be equal to the Revenue i.,e

       C(x) = R(x)

  15x + 1000 = 20x

     1000 = 20x - 15x

     1000 =  5x

        x = 1000/5

        x = 200

Therefore, 200 rides does it take to break even.

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Answer:

-2.25x = 30

Step-by-step explanation:

I hope this helps!

The given statement " in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables. " is false.

In math chi square test means the process of determine if there is a significant relationship between two nominal (categorical) variables.

Here we have the statement, in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables.

And we need to find the statement is true or not.

According to the definition of chi square test, we know that it checks whether two variables are likely to be related or not.

Here we have counts for two categorical or nominal variables.

So, there is no large value comparision take palce.

Therefore, the statement is false.

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Answer:

-1.8x^2

Step-by-step explanation:

Answer:1.44

Step-by-step explanation:

Let X be the number of hours it takes Paige to sort the toys alone.

It takes Madison X + 6 hours to sort the toys alone.

Together, it takes them X + (X + 6) = 4 hours to sort the toys.

Combining like terms, we get 2X = 4

Dividing both sides by 2, we get X = 2

Therefore, it takes Paige 2 hours to sort the toys alone.

It takes Madison 2 + 6 = 8 hours to sort the toys alone.

Answer: I believe 140

Step-by-step explanation: This is how I found my answer:

420 / 3

= 140

420-140

=  280

420= number of all tickets sold.

140= number of adult tickets sold

280= number of student tickets sold

You might wonder how I know why it's 140. I know it's 140, because using my context clues, it stated:

"the number of student tickets sold was three times the number of adult tickets."

So, the one that was the bigger amount must be the student's tickets sold, while the lower amount has to be the adult's tickets sold. I hope this helped!

Answer:

m angle B = 27.54 degree

m angle C = 60.85 degree

Step-by-step explanation:

angle A is 90º so the other two angles must sum to 90º

2x+5x-8=90

7x-6=90

7x=96

x=13.77

therefore,

m angle B = 27.54 degree

m angle C = 60.85 degree

The independent variable in the given function is h.

The Independent variables are those variable whose value does not depend on any other variable. And it causes the change in other variables.

The dependent variable is those variables whose value is not independent and change in this variable is dependent on the change of the independent variable.

Given the function p(h)=20h−50, which represents Lamont works for a company that pays him $20 per hour(h), but $50 each week is deducted from his pay for insurance.

Now, in the given function since the amount that Lamont will get depends upon the number of hours for which he is working.
Therefore, the h is the independent variable and p is the dependent variable.

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Answer:D

beacuse it is correct  just trust me i have done this class and its correct

Answer:

[tex]x=59[/tex]

Step-by-step explanation:

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]\implies x=180-48-73=59[/tex]

Therefore the solution of this question is  the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

Here,

The perimeter of the square drawn on the grid

The vertices given in the question are (3,3) & (7,7)

The length of the vertices given=[tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2}- y_{1})^{2} }[/tex]

Thus at vertices  (3,3) & (7,7)

=>[tex]\sqrt{(7 -3)^{2} +(7-3)^{2} }[/tex]

=>4[tex]\sqrt{2}[/tex]

Therefore the perimeter of the square = 4a

thus,

=>4*4[tex]\sqrt{2}[/tex]

=>16[tex]\sqrt{2}[/tex] units

Therefore the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units

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Answer:

$172,984.44 (nearest cent)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies A=25000\left(1+\dfrac{0.065}{4}\right)^{4 \cdot 30}[/tex]

[tex]\implies A=25000\left(1.01625\right)^{120}[/tex]

[tex]\implies A=25000\left(6.9193776...\right)[/tex]

[tex]\implies A=172984.4404[/tex]

Therefore, if you deposit $25,000 now at 6.5% compounded quarterly,  you will have $172,984.44 (nearest cent) in 30 years.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of x is 1.

The value of y is 4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 = 5 is an equation.

We have,

-4.5x - 2y = -12.5 ____(1)

3.25x - y = -0.75 _____(2)

From (1) we get,

-4.5x + 12.5 = 2y

y = (-4.5x + 12.5) / 2 _____(3)

Now,

3.25x - y = -0.75

Putting (3) in (2) we get,

3.25x - (-4.5x + 12.5) / 2 = -0.75

6.5x + 4.5x - 12.5 = 2 x -0.75

11x - 12.5 = -1.5

11x = -1.5 + 12.5

11x = 11

x = 1

Now,

From (3) we get,

y = (-4.5x + 12.5) / 2

y = (-4.5 x 1 + 12.5) / 2

y = (-4.5 + 12.5) / 2

y = 8/2

y = 4

Thus,

The value of x is 1.

The value of y is 4.

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In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

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Answer: 2x+y=5

Step-by-step explanation:

The standard form of a linear equation is

ax+by=c

Move all terms containing variables to the left side of the equation.

2x+y=5

Answer:

2x + y = 5

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]

Given equation:

[tex]y=-2x+5[/tex]

To write the given equation in standard form, collect the terms with variables on one side of the equation, ensuring the term in x is positive.

Add 2x to both sides:

[tex]\implies y+2x=-2x+5+2x[/tex]

[tex]\implies y+2x=5[/tex]

[tex]\implies 2x+y=5[/tex]

Th length of the enclosed area of the scale model in inches is 32 inches.

Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet.

The enclosed area of the Alamo Mission was 480 feet long and 160 feet wide.

The length of the enclosed area of the scale model in inches can be calculated as follows:

30 feet = 2 inches

480 feet = ?

cross multiply

length of the enclosed area = 480 × 2 / 30

length of  the enclosed area = 960 / 30

length of the enclosed area = 32 inches

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Answer:

Below

Step-by-step explanation:

k = 4-a

a (4-a) = 3

-a^2 +4a -3 = 0   ====> Quadratic Formula ===>  a =  1   and k = 3

1^3 + 3^3 = 28