A furniture store pays a certain amount for a mattress, called the wholesale price.

Then, the store marks up the amount they paid to 225% of their cost (wholesale price) to sell it (retail price).

The mattresses didn't sell, so later they put the mattress on sale for 50% off of the retail price. A customer just bought the mattress on sale and paid $800.

What was the retail price (selling price) of the mattress, before the discount? #

Answer:

Step-by-step explanation:

The Mega Clean mixture with 3 1/2 per gallon has more cleaner in it. The first mixture has .75 oz per quart. The second mixture has .875 oz per qt.

HOPE THAT HELP YOU

Answer:

3/2

Step-by-step explanation:

Answer:

Dad, is that you?

Step-by-step explanation:

The axiom of regularity is a set theory principle which states that every non-empty set C contains an element that is disjoint from C.

The set theory concept rules that for every non-empty set C there is an element x of C such that x does not intersect C. The regularity axiom aims to establish that no non-empty set will have itself as an element.

The principle which is also called the axiom of foundation is a fundamental concept in set theory and credited to Zermelo–Fraenkel.

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The forecast high represents the day's highest temperature, which is normally reached in late afternoon. It is anticipated that this heat will at minimum during night, probably around daybreak following morning.

The measurement of an entity's sexiness or coolness in relation to a reference value is called its temperature. The thermometer is the name of the device that monitors body temperature.

A little cup of water, for instance, possesses the same temperatures as a tank of water, but still the tub or water is hotter because it contains more moisture and hence has less heat energy overall. Joule is the SI unit for heat. Kelvin is the SI unit of temperature.

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Answer:

45.5

Step-by-step explanation:

You do the linear length multiplied by the longitudinal length

The distance across the lake is 320 ft.

Given is a scenario of a lake, a survey crew has laid out the concept of similar triangles to find the distance across the lake.

The figure shows the base of the larger triangles is the distance across the lake. [please refer to the figure attached]

The dimensions of the imaginary triangles are 30 ft, 30 ft, 40 ft and 240 ft, 240 ft, x ft.

Here, x is the distance across the lake which we are asked to find.

Using the definition of the similar triangles,

Two triangles are considered similar if their corresponding angles are equal, and the ratios of the lengths of their corresponding sides are equal.

So,

\(\frac{240}{30} = \frac{x}{40}\)

\(x = \frac{240 \times 40}{30}\)

x = 320

Hence the distance across the lake is 320 ft.

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Answer:

she participated in 4 tournaments

Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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The value of Quotient from the given terms is 9.6* 10^8

According to the statement

we have given that the two terms and we have to find the quotient of the these terms.

So, we know that the

Quotient is a the number resulting from the division of one number by another.

And for find the quotient we have to divide the terms with each other.

So, The given terms are \(7.536*10^7\)and \(7.85*10^2\)

divide both terms with each other.

Quotient = \(\frac{7.536*10^7}{7.85*10^2}\)

Then

The value of quotient becomes

Quotient = \(0.96 * 10^9\)

After removing the decimal from the answer it will become

Quotient = \(9.6* 10^8\).

So, The value of Quotient from the given terms is 9.6* 10^8

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Answer: its 7.85x10^-9

Step-by-step explanation:

Answer:

g(-3x) = -9x - 3

Step-by-step explanation:

Step 1: Define function

g(x) = 3x - 3

g(-3x) = x = -3x

Step 2: Substitute

g(-3x) = 3(-3x) - 3

g(-3x) = -9x - 3

Answer:

See Explanation

Step-by-step explanation:

\(m\angle 1 = m\angle 4\\...(corresponding \: \angle 's) \\

\because m\angle 4 = 45\degree \\

\huge \red {\therefore m\angle 1 = 45\degree} \\\\

\because m\angle 1 + m\angle 2 = 90\degree \\

\therefore 45\degree+m\angle 2 = 90\degree \\

\therefore m\angle 2 = 90\degree-45\degree\\

\huge \purple {\therefore m\angle 2 = 45\degree} \\\\

m\angle 3 = 35\degree... (given) \\\\

\because m\angle 3 + m\angle 5 = 90\degree \\

\therefore 35\degree + m\angle 5 = 90\degree \\

m\angle 5 = 90\degree-35\degree \\

\huge \orange {m\angle 5 = 55\degree} \\\\

\because m\angle 4 =m\angle 5...(vertical \: \angle 's) \\

\huge \pink{\therefore m\angle 4 = 55\degree} \\ \\

\because m\angle 6 =m\angle 5...(alternate \: \angle 's) \\

\huge \blue{\therefore m\angle 6 = 55\degree} \\

\)

Answer:

Answer:

11+ 9 = 20

Step-by-step explanation:

=> 21-9=11

21 - 9 equals to 11 is actually a wrong answer

So in order to find the subtraction problem that will help us truly know whether the equation is wrong

=> 11+ 9 = 20

OR THE SECOND EQUATION IS

=> 21 - 11 = 10

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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Part a: Probability Americans drink coffee or drink tea = 0.50.

Part b: Conditional probability: 2/3.

Part a: Probability, Americans drink coffee or drink tea.

P(C∪T) = P(C) + P(T) - P(C∩T)

P(C∪T) = 0.40 + 0.30 - 0.20

P(C∪T) = 0.50

Part b: They are more likely to consume coffee if they also drink tea.

P(C | T) = P(C∩T)/P(T)

P(C | T) = 0.20/0.30

P(C | T) = 0.20/0.30

P(C | T) = 2/3

Thus, the conditional probability they drink coffee given that they drink tea is 2/3.

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4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

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Answer:

\(\frac{-4}{3}\)

Step-by-step explanation:

a rational number is expressed as

\(\frac{a}{b}\) where a and b are integers , then

- 1 \(\frac{1}{3}\) = \(\frac{-4}{3}\)

The service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

a. Service charge rate

Service charge rate=Budgeted cost/ Budgeted activity base quantity

Help desks:

Service charge rate=$160,000/3,200 calls

Service charge rate=$50 per call

Network center:

Service charge rate=$735,000/9,800 devices

Service charge rate=$75 per device monitored

Electronic mail:

Service charge rate=$100,000/10,000 accounts

Service charge rate=$10 per user or per e-mail account

Local voice support:

Service charge rate=$124,600/8,900 phone extensions

Service charge rate=$14 per phone extension

b.  Help desk charge

Help desk charge =(Number of employees times × Percentage of office employees× Percentage with a computer ×Number of calls)× Service charge rate

Help desk charge:

(5,200 employee×25%×96%×1.5)× $50 per call

=$93,600

Network center charge:

[(5,200 employee×25%×96%)+ 600]× $75 per device

=$138,600

Electronic mail:

(5,200 employee×25%×96%×100)×$10 per user or per e-mail account

=$12,480

Local voice support:

(5,200 employee×25%)× $14 per phone extension

=$18,200

Therefore the service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

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Using linear function concepts, it is found that the slopes and intercepts of the functions are given as follows:

a) -4.

b) P = 25.

c) 2.

d) P = 5.

A linear function is modeled by: y = mx + b

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The demand is given by:

D = 100 - 4P.

Hence the slope is -4. The demand is equals to zero when:

100 - 4P = 0 -> P = 25.

The supply is given by:

QS = -10 + 2P.

Hence the slope is 2. The supply is equal to zero when:

-10 + 2P = 0 -> P = 5.

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Answer:

Step-by-step explanation:

a. 5/2 ÷ 1/2  =

b. 6/9 ÷ 5/6

c. 3/6 ÷ 2/5

d. 7 1/2 ÷ 6 =

e. 1 1/3 ÷ 1 2/3=

Answer:

Trick answer none of them do.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

side BC = side AB

so their base angles that is ∠A = ∠C = (3x+20)°

now, total measure of the angles of a triangle is 180° & ∠B = x°

Now,

m∠A + m∠B + m∠C = 180

⇒ 3x + 20 + x + 3x + 20 = 180

⇒ 7x + 40 = 180

⇒ 7x = 140

⇒x = 20

Answer:  

5x+3y=-6  

Step-by step explanation:  

(-3,3) (3,-7)  

Slope=(-7-3)/(3-(-3))=-10/6=-5/3  

y=mx+c  

y=-5/3*x-2[from graph]  

y=-5x-6/3  

3y=-5x-6  

3y+5y=-6  

5x+3y=-6

Answer:

Step-by-step explanation:

y = mx + b

slope m = Δy/Δx =  (-7 - 3) / (3 - (-3)) = -10/6 = -5/3  

y intercept is read directly from the chart at x = 0

b = -2

y = (-5/3)x - 2

Answer:

The last option is the correct choice 33.5

Step-by-step explanation:

\(V=\pi r^2\frac{h}{3} \\=\pi 2^2\frac{8}{3} \\=33.51\\=33.5\)

Answer:

D

Step-by-step explanation:

In the attached file

Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

The completed word problem based on the inequality is: Jessica's goal is to read at least 11 books this year. She has read 18 books already (7 fewer than 25), and she plans to read at most 3 books every month.

To solve the inequality 3x + 7 > 25, we first subtract 7 from both sides, which gives us 3x > 18. Then, we divide both sides by 3 to get x > 6. This means that any number greater than 6 will satisfy the inequality.

Now, let's use this information to solve the word problem.

We know that Jessica has already read 7 fewer than more than 25 books, which means she has read 18 books (25 - 7).

We also know that she plans to read at most 3 books every month. If we multiply 3 books by 12 months, we get 36 books, which is the maximum number of books Jessica can read in a year.

To find the minimum number of books Jessica needs to read to meet her goal of at least 11 books, we subtract the number of books she has already read (18) from her goal (11), which gives us 11 - 18 = -7.

Since we can't read a negative number of books, we know that Jessica needs to read at least 11 books this year to meet her goal.

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Answer:

y = - \(\frac{1}{3}\) x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 3 ← is in slope- intercept form

with slope m = 3

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{3}\) , then

y = - \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 6, 9 ) into the partial equation

9 = - \(\frac{1}{3}\) (-6) + c = 2 + c ( subtract 2 from both sides )

7 = c

y = - \(\frac{1}{3}\) x + 7 ← equation of perpendicular line

The Equation of line is 3x - y + 24 =0.

Given:

The table is given by:

X: 0 1 2 3 4 5 6 7

Y:-8 -5 -2 -1 -1 2 5 8

To find the equation of line by using the above data.

Now, According to the question:

From the table, We have

We know that,

Slope (m) = \(\frac{y_{2}-y_{1} }{x_{2} - x_{1} }\)

and, slope (m) = \(\frac{-5-(-8)}{1-0}\)

m = (-5 + 8)/ 1 = 3

So, \(y - y_{1} = m (x - x_{1} )\)

y - 0 = 3 (x - (-8))

y = 3(x + 8)

y = 3x + 24

Hence, The Equation of line is 3x - y + 24 =0.

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Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)