The wholesale price for a chair is $108. A certain furniture store marks of the wholesale price by 27%. Find the price of the chair in the furniture store. Round your answer to the nearest cent as necessary.

x²+9x+8

Rewrite

(x+1)(x+8)

Distribute

x²+8x+1x+8

Simplify

x²+9x+8

Answer:

[tex]x^{2}[/tex] + 9x + 8    i hope this helps!   :)

Step-by-step explanation:

distribute the x to the x and 8   [tex]x^{2}[/tex] + 8x

distribute the 1 to the x and 8   x + 8

put the two together   [tex]x^{2}[/tex] + x + 8x + 8

combine like terms   [tex]x^{2}[/tex] + 9x + 8

Answer:

x > 5

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

(4x + 2) - (2x - 4 • (x - 8)) > 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

6x - 30 = 6 • (x - 5)

Equation at the end of step 3 :

6 • (x - 5) > 0

Step 4 :

4.1 Divide both sides by 6

Solve Basic Inequality :

4.2 Add 5 to both sides

x > 5

Answer:

12a cm2

2b cm2

(6a + b) cm2

Step-by-step explanation:

The complete question is

The figure consists of 12 congruent equilateral triangles. The area of one equilateral triangle is a cm2. The area of the hexagon, shaded slightly darker, is b cm2.

Which expressions represent the area of the entire shaded region, including the light and dark shading? Check all that apply.

12a cm2

2b cm2

(6a - b) cm2

(12a + 2b) cm2

(6a + b) cm2

The picture of the question in the attached figure

we know that

The area of the entire shaded  region is equal to the area of the the light and dark shading

so

step 1

Find the area of the light shading

The area is equal to the area of six congruent equilateral triangles

[tex]A_1=6a\ cm^2[/tex]

step 2

Find the area of the dark shading

The area is equal to the area of the regular hexagon

[tex]A_2=b\ cm^2[/tex]

step 3

1) Find the total area

[tex]A=A_1+A_2=(6a+b)\ cm^2[/tex]

2) Remember that the figure consists of 12 congruent equilateral triangles

so

[tex]A=12a\ cm^2[/tex]

3) The area of the light shading is the same that the area of the dark shading

so

6a=b

therefore

[tex]A=2b\ cm^2[/tex]

Answer: 1 2 5

Step-by-step explanation:

The amount of revenue Sandy's Beauty Salon will earn in one day for x haircuts is represented by a linear graph.

The graph that represents the amount of revenue Sandy's Beauty Salon will earn in one day for x haircuts is a linear graph. This is because the revenue is directly proportional to the number of haircuts. The equation that represents this relationship is y = 15x, where y is the revenue and x is the number of haircuts.

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Answer: Andy should invest RS. 2784.19 for 12 years .

Step-by-step explanation:

Since we have given that

Amount = Rs. 5000

Time = 12 years

Rate of interest = 5%

So, We need to find the sum:

Using "Compound interest" , we get :

[tex]A=P(1+r)^t\\\\5000=P(1+0.05)^{12}\\\\5000=P(1.05)^{12}\\\\\dfrac{5000}{1.05^{12}}=P\\\\2784.19=P[/tex]

Hence, Andy should invest RS. 2784.19 for 12 years .

Final answer:

To find out how much Andy needs to invest today to fulfill his promise to Opie in 12 years with a 5% interest rate, we use the present value formula. Andy needs to invest approximately $2475.64 today to ensure he can fulfill his promise to Opie.

Explanation:

To calculate how much Andy must invest today to fulfill his promise to Opie, we can use the concept of present value.

Answer:

I believe its 15

Step-by-step explanation:

Answer for 12+7+(-4)= 15

Answer for -1.75+(-6.25)+6= -2

I hope this helps

Answer:

If the coin is fair, then the odds of getting heads or tails should be equal, 12. Then 3 tosses of tails will have a chance of 12⋅12⋅12=18. Tossing of the coin is an independent event. The probablility of each event is 12.

Answer:

Step-by-step explanation:

opposite= 8 : the length opposite angle c

adjacent=15 : the length next to angle c, not the hypotenuse

hypotenuse= 17 : the hypotenuse will always be opposite the right angle

[tex]sinC=\frac{opposite}{hypotenuse}\\ \\sinC=\frac{8}{17}[/tex]

[tex]cosC=\frac{adjacent}{hypotenuse}\\\\cosC=\frac{15}{17}[/tex]

[tex]tanC=\frac{opposite}{adjacent} \\\\tanC=\frac{8}{15}[/tex]

Answer:

2.5 mg

Step-by-step explanation:

We are given that

A=Initial amount=10 mg

Half life,h=8 days

We have to find the mass of radioactive isotope remains after 16 days.

t=16 days

We know that the amount of radioactive isotope after t days is given by

[tex]P(t)=A(1\frac{1}{2}^{\frac{t}{h})[/tex]

Using the formula

[tex]P(t)=10(\frac{1}{2}^{\frac{16}{8}})[/tex]

[tex]P(t)=10\times (\frac{1}{2})^2[/tex]

[tex]P(t)=2.5 mg[/tex]

Answer:

its b on edg

Step-by-step explanation:

its B I answered the question on my test and got it correct

Step-by-step explanation:

Take a look at this graph (sorry, it's small).  The graph shows three data points, (0, 1), (2, 6), and (4, 8).  The line is called the "line of best fit" or "regression line."

The equation for the line is y = 1.75x + 1.5 .

The data did not include a point for x = 3, but it can be predicted by finding the y-coordinate on the line that corresponds to x = 3.

Substituting x = 3 into the line's equation gives

y = 1.75(3) + 1.5 = 6.75

That's the predicted value of y for x = 3 given the linear relationship shown.

Answer:

x=-1.67 or x=-4

Step-by-step explanation:

3x+5=0          and 2x+8=0

3x=0-5               2x=-8,,,divide both sides by 2, the two's cancel then x=-4

3x=5 Divide by 3 to hve x on one side,,, thus the answer is -5÷3=1.666...

Answer:

-5/3 and -4

Step-by-step explanation:

I got it correct.

Answer:

d

Step-by-step explanation:

answer:

it's the second one -7^2-x+2

explanation:

in order to be a quadratic function it has to meet this criteria: ax² + bx + c

The quadratic function is -7x²-x+2. Therefore, option B is the correct answer.

The standard form of a quadratic equation is given as:

ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.

Here, the quadratic function is -7x²-x+2

Therefore, option B is the correct answer.

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Answer:

distance travelled first day is 542 miles while that travelled on second day = 271 miles.

Step-by-step explanation:

please kindly see the attached files for details

Richard and Linda travel 542 miles on the first day and 271 miles on the second day to reach Hilton Head Island, with the total distance being 813 miles.

The student's question pertains to splitting a total distance into two parts, with a given ratio between the two parts. Since Richard and Linda travel twice as far on the first day as the second day, we can let the distance traveled on the second day be x miles. Therefore, the distance they travel on the first day would be 2x miles.

The total distance traveled to Hilton Head is 813 miles, so we can write an equation based on the sum of the distances traveled on both days: 2x (first day) + x (second day) = 813 miles. Simplifying this equation, we have 3x = 813 miles. Dividing both sides of the equation by 3 yields x = 271 miles.

This means that Richard and Linda travel 271 miles on the second day and 2 * 271 miles, which is 542 miles, on the first day. So, the distances Richard and Linda travel to Hilton Head Island on the first and second days are 542 miles and 271 miles, respectively.

Answer:

a= 35°

b=70

c=70

Step-by-step explanation:

if u need explanation comment and I'll explain

Answer:

18

Step-by-step explanation:

Mean is the average of the data.

There is one 7.

Three 9's.

Two 10's

7+9+9+9+10+10=54

There are only 3 numbers with actual data so 6 and 8 don't matter.

54÷3=18

Answer:

$73.60

Step-by-step explanation:

take 460 times .032 witch is 14.72 then times that by 5

Answer:

The correct answer is two designs are used 12 times each and other four designs are used for 13 times each.

Step-by-step explanation:

Width of the quilt Lu is making is 18 rows of 20 squares each.

Thus the perimeter of the quilt is 20 + 20 + 18 + 18 = 76.

We can also say there are 76 square as the boundary which are to be bordered with toy designs.

Each square can hold 1 design of toy and there are 6 different designs of toys.

Thus number of times each design is used [tex]\frac{76}{6}[/tex] = 12 [tex]\frac{4}{6}[/tex].

Thus there are two designs used 12 times each and other four designs are used for 13 times each.

Given:

Given that each vertex of the polygon forms a right angle.

The measurements of the sides of the polygon were given.

We need to determine the area of the polygon.

Let us divide the polygon into 3 rectangles.

Area of the rectangle can be determined using the formula, [tex]A=length \times width[/tex]

Area of rectangle 1:

The length of rectangle 1 is 17 inches.

The width of rectangle 1 is 8.5 inches.

The area of rectangle 1 is given by

[tex]17 \times 8.5 =144.5 \ in^2[/tex]

Area of rectangle 2:

The length of rectangle 2 is 16.5 inches.

The width of rectangle 2 is (17 - 9) = 8 inches.

The area of rectangle 2 is given by

[tex]16.5 \times 8 =132 \ in^2[/tex]

Area of rectangle 3:

The length of rectangle 3 is 13 inches.

The width of rectangle 3 is 11 inches.

The area of rectangle 3 is given by

[tex]13 \times 11=143 \ in^2[/tex]

Area of the polygon:

The area of the polygon can be determined by adding the areas of the three rectangles.

Thus, we have;

[tex]Area=144.5+132+143[/tex]

[tex]Area=419.5 \ in^2[/tex]

Thus, the area of the figure is 419.5 square inches.

Hence, Option B is the correct answer.

Answer:

acute scalene

Step-by-step explanation:

Answer:

A university wants to estimate the average distance that commuter students travel to get to class with an error of ±3 miles and 90 percent confidence. What sample size would be needed, assuming that travel distances are normally distributed with a range of X = 0 to X = 50 miles, using the Empirical Rule μ ± 3σ to estimate σ.

The required sample size, n=(zσ/E)² = 21.0

Step-by-step explanation:

The estimated σ here  = (range)/6 = (50/6) = 8.33

In the case of  90 % , CI value of z = 1.64

standard deviation, σ=  8.33

margin of error E = 3

The required sample size, n=(zσ/E)² = 21.0

Answer:

n = 21

Step-by-step explanation:

Solution:-

- Let denote a random variable "X" : average distance that commuter students travel to get to class.

- The population is given to be normally distributed, such that:

                    Range X: [ 0 , 50 ] miles

- We will use the given range coupled with the empirical rule for normal distribution to determine the mean (u) and standard deviation of population (σ):

                   P ( μ - 3σ < X < μ + 3σ) = 0.997  ..... (Empirical Rule)

- According to the standardized results for Z-table:

                   P ( -3 < Z < 3 ) = 0.997

So,               P ( Z ≤ 3 ) = 1 - (1 - 0.997) / 2 = 0.9985

                   P ( Z ≥ -3 ) = 1 - (1 - 0.997) / 2 = 0.9985

- The standardized values for the given data can now be determined:

                   P ( X ≥ μ - 3σ ) = P ( Z ≥ -3 ) = 0.9985

                   X ≥ μ - 3σ  = Upper limit - 0.9985*( Range )

                   X ≥ μ - 3σ  = 50 - 0.9985*( 50 )

                  μ - 3σ = 0.075   ..... Eq1

                   P ( X ≤ μ + 3σ ) = P ( Z ≤ 3 ) = 0.9985

                   X ≤ μ + 3σ  = Lower limit + 0.9985*( Range )

                   X ≤ μ + 3σ  = 0 + 0.9985*( 50 )

                  μ + 3σ = 49.925   ..... Eq2

- Solve the Eq1 and Eq2 simultaneously:

                   2μ = 50 , μ = 25 miles                  

                    3σ = 24.925

                    σ = 8.30833

- Hence, the normal distribution parameters are:

                    X ~ N ( μ , σ^2 )

                    X ~ N ( 25 , 8.308^2 )

- The standard error in estimation of average distance that commuter students travel to get to class is E = ±3 miles for the confidence level of 90%.

- The Z-critical value for confidence level of 90%, Z-critical = 1.645  

- The standard error estimation statistics is given by the following relation with "n" sample size.

                     E = Z-critical*σ /√n    

                     n = [ Z-critical*σ /E ]^2

- Plug in the values:

                     n = [ 1.645*8.308/3]^2    

                     n = 20.75306 ≈ 21  

Answer: The sample size needed to estimate average distance that commuter students travel to get to class with error of ±3 miles and 90 percent confidence, is n = 21.      

Answer: We do not sufficient evidence that mean is greater than 0.

Step-by-step explanation:

Since we have given that

n = 36

mean = 0.9

Standard deviation = 15.8

at 0.01 level of significance,

Hypothesis would be:

[tex]H_0:\mu =0\\\\H_1=\mu\neq 0[/tex]

Standard error of mean would be :

[tex]\dfrac{\sigma}{\sqrt{n}}=\dfrac{15.8}{\sqrt{36}}=\dfrac{15.8}{6}=2.63[/tex]

statistic value would be :

[tex]t=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{0.9-0}{2.63}\\\\t=\dfrac{0.9}{2.63}\\\\t=0.342[/tex]

Degree of freedom = df = 36-1=35

So, p value = 2.4377

Since 2.4377 > 0.342, we will not reject null hypothesis.

Hence, We do not sufficient evidence that mean is greater than 0.

Answer:

The distance as product of 38 and a power of 10 is [tex]38*10^{6}[/tex]

Step-by-step explanation:

In math when we're dealing with big numbers like this we express them in power of 10, since it'll be easyer to read that way. We take the parts of the number to the left that are not equal to "0", in this case 38, and multiply it by a power of 10. The expoent to this power of 10 will be the number of "0" after the 38 and before the ",". In this case the closest distance from Earth to Venus is 38,000,000 (there's a typo in the question). So we take the 38 and multiply it by [tex]10^{6}[/tex], since there are 6 zeros.

The distance as product of 38 and a power of 10 is [tex]38*10^{6}[/tex]

Answer:

n = 12, she has played 12 games

Step-by-step explanation:

40 = 16 + 2n

24 = 2n

24/2 = n

n = 12

The division is one of the four fundamental arithmetic operations. The number of games that Hannah has played is 12.

Division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that Hannah is at an arcade where each game requires her to use 2 tokens. Also, the total number of tokens Hannah has is 40.

Therefore, the number of tokens that Hannah has used is,

Number of tokens Hanna used

= Total number of toke - Number of tokens left

= 40 - 16

= 24

Now, the number of games that Hannah has played is,

Number of games Hannah has played = Number of tokens used / Number of token per game

n = 24 / 2

n = 12 game

Hence, the number of games that Hannah has played is 12.

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Answer:

plane parallel to the circular base, not passing through the tip of the cone: circle

plane parallel to the circular base, passing through the tip of the cone: A point

plane not parallel to the base, not passing through the base, and making an angle with the horizontal that is less than that made by the slant height of the cone: an oval that becomes more elongated as the angle with the horizontal increases

plane making an angle with the horizontal that is greater than that made by the slant height, passing through the tip of the cone : an isosceles triangle

Step-by-step explanation:

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Answer:

a. 39.55%

b. 44.02%

Step-by-step explanation:

We have the following data:

n = 5

x = 1

p = 5/20 = 0.25

to. If the sampling is done with replacement.

We apply the binomial distribution formula, which is as follows:

P = nCx * (p ^ x) * ((1-p) ^ (n-x))

Where nCx, is a combination, and is equal to:

nCx = n! / x! * (n-x)!

replacing we have:

5C1 = 5! / 1! * 4! = 5

replacing in the main formula:

P = 5 * (0.25 ^ 1) * ((1- 0.25) ^ (5-1))

P = 0.3955

that is, without replacing the probability is 39.55%

b. if the sampling is done without replacement.

Here it is a little different from the previous one, but what you should do is calculate three cases,

the first was the one at point a, when n = 5 and x = 1

5C1 = 5! / 1! * 4! = 5

the second is when n = 20 and x = 5, this is all possible scenarios.

20C5 = 20! / 5! * 15! = 15504

and the third is when n = 15 (20-5) and x = 4 (5-1), which corresponds to the cases when none were damaged

15C4 = 15! / 4! * 11! = 1365

In the end, it would be:

P = (5C1 * 15C4) / 20C5

Replacing:

P = 5 * 1365/15504

P = 0.4402

Which means that without replacing the probability is 44.02%

Answer:

Assets: $231,775

Liabilities: $180,275

Net worth: $51,500

Step-by-step explanation:

- Assest is something of value. ex. house, barns, tractors. To find this take...

215,000+12,500+1,875+2,400=$231,775

(All these numbers are good things he has, not debt.)

- Liability is debt you will need to repay. ex. loans or accounts payable. To find this take...

175,000+4,000+1,275=$180,275

- Net worth is the difference between your total assests and total liabilities. Knowing difference is subtraction, we should subtract assests minus liablities. To find this take...

$231,775-$180,275=$51,500

- Hope this helps! If you have any further questions or other problems you need help on please let me know as I would be glad to help.

Answer:

The correct answer is 2.912 cm.

Step-by-step explanation:

A company is designing a new cylindrical water bottle.

Volume of a cylinder is given by π × [tex]r^{2}[/tex] × h, where h is the height of the cylinder and r is the radius of the cylinder.

The volume of each bottle will be 211 [tex]cm^{3}[/tex].

The height (h) of the water bottle be 7.9 cm.

Let the radius of the bottle be r cm.

∴ π × [tex]r^{2}[/tex] × h = 211 ; (π = 3.15)

⇒ [tex]r^{2}[/tex] × 24.885 = 211

⇒ r = 2.912

The radius of the water bottle is 2.912 cm.

Answer:

I would just guess, but if i were to actually think about it, i would think C. I hope it helps, and blame it on me if you fail.

Step-by-step explanation:

Step-by-step explanation:

The coin roll revolution = 4 rev / sec

Angle = 180° which is 1/2 of a revolution(360°).

The circumference of a circle is 2πr.

Radius of the circle, r = 10 mm

The circumference of this coin = 20π mm.

Again 180° is half of a roll,

the circumference = [tex]\frac{20\pi }{2}[/tex] = 10π

The coin travels 31.42 mm.