After a 20% reduction, you purchase a new love seat for $396. What was the price of the love seat before the reduction?

A) First write an equation you can use to answer this question. Use
as your variable and express any percents in decimal form in the equation.

The equation is


B) Solve your equation in part [A] to find the original price of the love seat.

Answer: The original price of the love seat was
dollars.

Part A:

Complete table becomes:
Age (x)               Probability (p)                (x × p)

15                          9/40 = 0.225              3.375

16                         12/40=0.30                     4.8

17                         8/40=0.20                      3.4

18                         11/40=0.275                   4.95

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

Total                     1.00                    16.525

Part B:

Mean becomes: 16.525

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Fundamentally, probability is a discipline of mathematics that uses computations to foretell the potential outcomes of a certain occurrence. It provides you the power to forecast the outcomes of future occurrences, which makes it seem cool.

Part A:

Age (x)               Probability (p)                (x × p)

15                          9/40 = 0.225              3.375

16                         12/40=0.30                     4.8

17                         8/40=0.20                      3.4

18                         11/40=0.275                   4.95

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

Total                     1.00                    16.525

Part B:

mean (μ) = ∑⁴(i = 1) xi pi

mean (μ) = 16.525

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Answer:

Step-by-step explanation:

Quadratic X €

Evaluate -20

Answer:

[tex]x=\frac{1}{2} \pm \frac{i\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Lets solve for [tex]x[/tex] in

[tex]-2^2-2x^2+2x+1=0[/tex]

Evaluate [tex]2^2[/tex]

[tex]-4-2x^2+2x+1=0[/tex]

Add [tex]-4[/tex] and [tex]1[/tex].

[tex]-2x^2+2x-3=0[/tex]

Divide both sides of the equation by [tex]-2[/tex].

[tex]x^2-x+\frac{3}{2}=0[/tex]

Now the equation is in standard form.

[tex]ax^2+bx+c=0[/tex]

We can solve this quadratic by completing the square.

Subtract [tex]\frac{3}{2}[/tex] from both sides of the equation.

[tex]x^2-x=-\frac{3}{2}[/tex]

Take one half of the coefficient of [tex]x[/tex] and square it, then add it to both sides.

Add [tex]\frac{1}{4}[/tex] to both sides.

[tex]x^2-x+\frac{1}{4} =-\frac{3}{2}+\frac{1}{4}[/tex]

[tex]x^2-x+\frac{1}{4} =-\frac{5}{4}[/tex]

The left hand side is a perfect trinomial square.

Factor the left hand side by writing it as a square.

[tex]\left(x-\frac{1}{2}\right)^2 =-\frac{5}{4}[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]x-\frac{1}{2} =\pm\sqrt{-\frac{5}{4}}[/tex]

Rewrite [tex]\frac{5}{4}[/tex] as [tex]\left(\frac{i}{2} \right)^2 *5[/tex]

[tex]x-\frac{1}{2} =\pm\sqrt{\left(\frac{i}{2} \right)^2 *5}[/tex]

Pull terms out from under the radical.

[tex]x-\frac{1}{2} =\pm \frac{i}{2} \sqrt{5}[/tex]

Combine [tex]\frac{i}{2}[/tex] and [tex]\sqrt5[/tex].

[tex]x-\frac{1}{2} =\pm \frac{i\sqrt{5}}{2}[/tex]

Add [tex]\frac{1}{2}[/tex] to both sides of the equation.

[tex]x=\frac{1}{2} \pm \frac{i\sqrt{5}}{2}[/tex]

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After the 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit is at 20 on number line.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.

A rabbit started at point 0 and made 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit we do not know the direction of either jump where on the line could the rabbit be.

Now, Rabbit is at 10 on number line

If rabbit made same jumps, rabbit will be at

10+3+4+2+1

= 20

Therefore, after the 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit is at 20 on number line.

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Below is a function which takes some number of degrees, positive or negative, and returns the reduced equivalent in the interval [0 , 360 )

Below is a Python function that takes an angle in degrees and returns its equivalent in the interval [0, 360):

def deg_reduce(degrees):

   return degrees % 360

The % operator in Python is the modulo operator, which returns the remainder of a division. By using degrees % 360, the function returns the reduced equivalent of degrees in the interval [0, 360).

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Answer:

       For the first picture:

[tex]\frac{1}{3} < \frac{2}{6}[/tex] is false because [tex]\frac{1}{3} x 2 = \frac{2}{6}[/tex]

[tex]\frac{1}{3} > \frac{2}{6}[/tex] is also false because [tex]\frac{1}{3} x 2 = \frac{2}{6}[/tex]

[tex]\frac{1}{3} =\frac{2}{6}[/tex] is true, so the 3rd is the correct option.

       For the second picture:

[tex]\frac{3}{6} ?\frac{1}{4}[/tex] using the LCM method, of 6 and 4 = 12

then it will be [tex]\frac{6}{12} > \frac{3}{12}[/tex] so the symbol will be > (1st option)

      For the third picture:

[tex]\frac{2}{5} =\frac{1}{2}[/tex] is false

[tex]\frac{2}{5} < \frac{1}{2}[/tex] is true, so the 2nd is the correct option.

[tex]\frac{2}{5} > \frac{1}{2}[/tex] is false

      For the forth picture:

The correct answer is the 3rd option ([tex]\frac{5}{8} > \frac{1}{2}[/tex])

Have a wonderful day! :-)

Answer: Let's call the number of cookies Trey has "x".

Gerald has 8 less cookies than Trey, so he has x - 8 cookies.

Trey bought five times the number of cookies as Gerald, so he has 5 * (x - 8) = 5x - 40 cookies.

Combining these two equations, we have:

x + (x - 8) = 5x - 40

Simplifying, we get:

2x - 8 = 5x - 40

Solving for x, we find:

3x = 32

And finally, x = 10.

So Trey has 10 cookies and Gerald has 2 cookies.

Step-by-step explanation:

There are 0.0496 Gg/hr in 8.34 x 10^6 tons/week

To convert from tons/week to Gg/hr:

you need to divide the number of tons by the number of hours in a week and then multiply by 1 Gg/ton.

There are 168 hours in a week, so:

8.34 x 10^6 ton/wk / 168 hrs/week = 49642.85 ton/hr

And 1 Gg = 1,000,000 ton, so:

49642.85 ton/hr * 1 Gg/1,000,000 ton = 0.0496 Gg/hr

So, 8.34 x 10^6 tons/week is equivalent to 0.0496 Gg/hr.

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a. Her AGI is under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock. is $34500.

b. The computation under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock is $21000.

All of the shares used to divide ownership of a corporation or company constitute stock in the financial world. A single share of stock represents a fractional ownership interest in the company based on the total number of shares.

Compute her AGI under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock.

This will be the addition of the taxable pension, half of the social security benefits, stock gain, and the dividend received. This will be:

= $10000 + ($7000 × 50%) + $20000 + $1000

= $10000 + $3500 + $20000 + $1000.

= $34500

The computation is under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock.

= $10000 + $10000 + $1000

= $21000

The correct question is given below.

Lucia is a 69-year-old single individual who receives a taxable pension of $10,000 per year and Social Security benefits of $7,000. Lucia is considering the possibility of selling stock she has owned for years and using the funds to purchase a summer home. She will realize a gain of $20,000 when she sells the stock, which has been paying $1,000 of dividends each year. Lucia says her brother recommended that she sell half the stock this year and half next year because selling all of the stock at once would affect the tax treatment of her Social Security benefits.

a) Computer her AGI under the assumption she sells all of the stock now after receiving $1,000 dividends from the stock.

b) Repeat the computation under the assumption she sells only half of the stock this year and also receives $1,000 in dividends from the stock.

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The expression for the time of the number of games remaining for shoes will be T = 225 - 2W.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jacob just bought a new pair of basketball shoes. He expects the shoes to last for two hundred twenty-five games. He plays two games a week.

The expression for the life of the shoes will be written as:-

T = 225 - 2W

Here, T is the time and W is the number of weeks.

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The statement that the probability of obtaining a sample mean greater than 46 is: p = 0.8413.

The parameters given are;

Sample size; n = 9

Population mean; μ = 50

Population standard deviation; σ = 12

Sample mean; x' = 46

Formula for the z-score here is;

z = (x' - μ)/(σ/√n)

z = (46 - 50)/(12/√9)

z = -4/4

z = -1

From p-value from z-score calculator, we have;

p-value = 0.8413

Thus, the statement is true

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The capacity required for a kitchen size, given the additional BTU recommended, is A. 10, 000 BTUs.

The area of the kitchen would be:

= Length x Width

= 16 x 10

= 160 ft ²

At this capacity, it means that the recommended capacity would be over 5, 000 BTUs which is for 150 ft² kitchens.

The next recommended capacity is 6, 000 BTUs and with a kitchen requiring 4, 000 BTUs over the capacity, the BTUs is :

= 6, 000 + 4, 000

= 10, 000 BTUs

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Answer:

Step-by-step explanation:

Assuming the sides are equal:

-3x - 6 = 4x + 15

-3x - 6 -15 = 4x + 15 - 15

-3x - 21 = 4x

-3x + 3x - 21 = 4x + 3x

-21 = 7x

-21/7 = 7x /7

-3 = x

Answer:

25people =90days

? =15days

cross multiply

25×15÷90

=375÷90

=4.16666666

approximately =4.2

150 people needed to complete the work in 15 days.

Given that 25 people take 90 days to do a job.

Relation between number of people and number of days needed to complete a work when work quantity is fixed is inversely proportional.

That is, if number of people is less then the work needs more time and vice versa.

To complete a job in 90 days the number of people required is = 25

To complete that same job in 1 days the number of people needed is = 25 * 90 = 2250

To complete the same job in 15 days the number of people needed is = 2250/15 = 150.

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Answer:

35280 blinks

Step-by-step explanation:

1 day = 24 hours

24 - 8 = 16 hours

1 hour = 3600 seconds

16 hours = 50400 seconds

Now we have to find how many blink in 1 second

14 divided by 20 = 0.7 blink in 1 second

Now we take

0.7 times 50400 = 35280 blinks

So, Sam blink 35280 times a day

The number of acres that will be pollinated by the bees in 18 beehives is given as follows:

D. 48.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

From the table, the constant is obtained as follows:

3k = 8

k = 8/3.

Hence the equation is of:

y = 8x/3.

The number of acres that will be pollinated by 18 beehives is then given as follows:

y = 8(18)/3

y = 48 acres.

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Answer: D. 48.

Step-by-step explanation:

because the table shows 3k = 8k = 8/3. y = 8x/3. So then it turns into y = 8(18)/3 = y = 48 acres.

Answer:

[tex]x=16\sqrt{30}; \ y=16\sqrt{10}.[/tex]

Step-by-step explanation:

1. if the angles in the given triangle are 30°-60°-90°, then

[tex]2. \ x=32\sqrt{10} *cos[30 к]; \ = > \ x=32\sqrt{10} *\frac{\sqrt{3}}{2} =16\sqrt{30};[/tex]

[tex]3. \ y=0.5*32\sqrt{10}=16\sqrt{10};[/tex]

4. finally, x=16√[30]; y=16√[10].

Each side of the given figure measures 2yd and the area of the polygon is A = 8 + 8√2 square units, and apothem is 8 + 8√2 units.

A polygon is a closed, two-dimensional (2-D) figure formed of segments of straight lines. The octagon is an 8-sided polygon in geometry. An octagon is referred to as a regular octagon if all of its sides and angles have equal lengths. In other words, an ordinary octagon has congruent sides. In a standard octagon, the inside angle is 135 degrees, and the outer angle is 45 degrees. A preset set of formulas known as the "octagon formula" can be used to calculate the area and perimeter of a regular octagon.

Given that the perimeter of the octagon is 16yd.

The perimeter is the sum of all the segments or boundaries. So, the perimeter of the octagon is:

P = 8s

16 = 8s

s= 2yd.

The area of a regular octagon is given as:

A = 2a²(1 + √2)

A = 2(2)²(1 + √2)

A = 8 + 8√2

The apothem is given by:

A = 1/2 (s)(a)

8 + 8√2 = 1/2 (2)(a)

a = 8 + 8√2

Hence, each side of the given figure measures 2yd and the area of the polygon is A = 8 + 8√2 square units, and apothem is 8 + 8√2 units.

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Answer: 8

Step-by-step explanation:

Answer:

triangle ABC ~ triangle GHJ

Step-by-step explanation:

The similarity statement compares the two triangles based on their corresponding sides. If two triangles have proportional corresponding sides, then they are similar.

In this case, triangle ABC and triangle GHJ have corresponding sides that are proportional. Specifically, side AB is half the length of side GH, side BC is three-fifths the length of side HJ, and side AC is two-fifths the length of side GJ. Therefore, by the definition of similarity, triangle ABC is similar to triangle GHJ.

Answer:

Below

Step-by-step explanation:

y - y1   = m ( x - x1 )     is point slope form of a line  m = slope

For point ( -1,3) :

y-3 = 3 (x- -1)

y -3 = 3x + 3        add 3 to both sides

y = 3x + 6         The underlined equations are the same line just different forms....you'll need to pick the one you need

Answer:

The ratio of ozone used to the total amount of water treated per day can be calculated as follows:

Ozone used = 25,000 mg

Amount of water treated = 16,000,000 liters = 16,000,000 x 1000 ml = 16,000,000 x 1000 x 1000 mg = 16,000,000,000,000 mg

Ratio of ozone used to water treated = 25,000 / 16,000,000,000,000 = 1.5625 x 10^-11

So, the ratio of ozone used to the total amount of water treated per day is approximately 1.5625 x 10^-11.

[tex]15.625*10^{-4}[/tex] miligrams of ozone / liter of water.

16,000,000 liters of water

25,000 milligrams of ozone

A ratio is basically telling how much of one thing corresponds to a unit of another thing. Hence, let's express this as a division in the following fashion:

[tex]\frac{25,000}{16,000,000} =\\ \\\frac{0.0015625}{1} =\\ \\\frac{15.625*10^{-4} }{1}[/tex]

[tex]15.625*10^{-4}[/tex] miligrams of ozone / liter of water.

Answer:

[tex]r = \sqrt{\frac{24}{h}}[/tex] inches

Step-by-step explanation:

Volume of a cone = [tex]\frac{1}{3} \pi r^{3}h[/tex]

 where: r = radius of cone

             h = perpendicular height of the cone

Provided volume of cone = 8π cubic inches

[tex]8\pi = \frac{1}{3}\pi r^{2} h[/tex]

Cross multiplication is applied and 'r' is isolated:

[tex]3(8\pi ) = \pi r^{2} h[/tex]

[tex]24\pi =\pi r^{2} h[/tex]

[tex]r^{2} h = \frac{24\pi}{\pi}[/tex]

[tex]\pi[/tex] in the numerator and denominator cancel each other out completely:

[tex]r^{2} h = 24[/tex]

[tex]r^{2} = \frac{24}{h}[/tex]

Taking the square root on both sides of the equation in order to get rid of the square:

[tex]r = \sqrt{\frac{24}{h}}[/tex] inches

Answer:

D=5=14 I hope this helps

Step-by-step explanation:

When h is very small, then the slope would be equal to 6

We have

m = y2 - y1 / x2 - x1

where 2.97² - 3² / 2.97 - 3

we would have

-0.1791 / -0.03

m = 5.97

We have to do the same for   x = 3.001

3.001² - 3² / 3.001 - 3

m = 6.001

finally we have to solve for x = 3 + h

m = [tex]\frac{(3 + h)^2-(3)^2}{3+h-3}[/tex]

m = [tex]\frac{9+h^2+6h-9}{h}[/tex]

m = [tex](\frac{h}{h})*(\frac{h+6}{1} )[/tex]

m = h + 6

if h is close to 0 then m = 6

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Answer:

No, the equations are not balanced.

Step-by-step explanation:

Let's solve 50² - 40 × 6 + 19 - 2.

The equation is now 2500 - 40 × 6 + 19 - 2.

    2. 40 × 6 = 240.

The equation is now 2500 - 240 + 19 - 2.

    3. 240  + 19 = 259.

The equation is now 2500 - 259 - 2.

    4. 2500 - 259 = 2241.

The equation is now 2241 - 2.

    5. 2241 - 2 = 2.

50² - 40 × 6 + 19 - 2 = 2241.

Now, lets solve 2279 - 2.

2241 ≠ 2277. In addition, 2241 is not equal to 2277, meaning that the equations are not balanced.

The partition and shade to show 5/7 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

partition and shade to show 5/7

To do this, we can make use of a tape diagram

Such that the size of each partition is equal

Using the above as a guide, we have the following:

5/7 implies that we create 7 partitions and shade 5 sections

Next, we make the tape diagram (see attachment)

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Answer:

Step-by-step explanation:

Total marbles = 0
Number of green marbles = 6
so,
Probability of getting 2 green marbles = 2/20 = 1/10

The probability that Jerod selects two green marbles at random from the bag is 1/10

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Jerod has a bag of 20 marbles containing 12 red, 6 green, and 2 blue marbles.

Total marbles = 0

Number of green marbles = 6

Therefore,

Probability of getting 2 green marbles ;

= 2/20 = 1/10

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