Mathematics High School

Darrin lives in Washington, D.C., which has a sales tax of 6%. He just bought a video camera whose full price was $620, but after sending in a rebate form, he later received a check in the mail for $95. What was the total amount that Darrin ended up paying after receiving the rebate? A.$562.20 B.$556.50 C.$525.00 D.$657.20

Answers

Answer 1

562.20 So the answer is A.

Answer 2

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Cost of video camera = $620

Rate of sales tax = 6%

Amount of sales tax is given by

[tex]\dfrac{6}{100}\times 620\\\\=\$37.2[/tex]

Total amount after sales tax is given by

[tex]\$620+\$37.2\\\\=\$657.20[/tex]

Amount of rebate = $95

So, final amount that Darrin ended up paying after receiving the rebate is given by

[tex]\$657.20-\$95\\\\=\$562.20[/tex]

Hence, option 'A' is correct.

Related Questions

In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots as shown. Explain why the ropes forms a right angle

Answers

The Egyptians used a rope with 13 equally spaced knots in it, which gave them 12 equal sections of rope. These would be the units. One of the most recognized Pythagorean triples is 3, 4, 5. This comes from the Pythagorean theorem:
3²+4²=5²
9+16=25

With the sides of the triangle being 3, 4 and 5, the perimeter would be 3+4+5=12.

Final answer:

In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots. The tensions in the rope on either side of the right angle were equal, resulting in the formation of a right angle.

Explanation:

In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots. The ropes formed a right angle because the angles on either side of the rope were equal. When the rope was stretched taut, the tensions in the rope on either side of the right angle were equal. This resulted in the formation of a right angle.

1. is not consided a high risk investment

A- investing in stocks
B- inversting in cds
C- investing in start up ventures
D-investing in entrepreneurial activities

2. the dow is where are exchanged

A-certificates of deposit
B-bonds
C-stocks
D-companies,

Answers

Of the options listed for 1, only investing in CDs is considered to not be a high-risk investment. The others are equity investments that contain no guarantee of security, whereas CDs are held with FDIC-insured banks. With respect to question 2, the Dow Jones Industrial Average is a measure of aggregate performance of C, stocks. However, as a matter of clarification, it is not an exchange, but rather simply a collective performance measure.

Divide.

refer to the picture

Answers

The quotient is 10x +16.
The remainder is 28x^2 +10x +22.

Given f(x)=4x2−5 and g(x)=x+3 .

What is (fg)(x) ?

Answers

I just took the test, it was A. 4x^3+12x^2-5x-15 :)

Answer:

[tex](fg)(x)=4x^3+12x^2-5x-15[/tex]

First option is correct.

Step-by-step explanation:

We have been given that

[tex]f(x)=4x^2-5[/tex]

[tex]g(x)=x+3[/tex]

We know that [tex](fg)(x)=f(x)g(x)[/tex]

Hence, we have to find the product of f(x) and g(x)

[tex](fg)(x)=(4x^2-5)(x+3)[/tex]

Apply distributive property

[tex](fg)(x)=4x^2\cdot x+4x^2\cdot3-5x-5\cdot3[/tex]

Simplifying, we get

[tex](fg)(x)=4x^3+12x^2-5x-15[/tex]

First option is correct.

Write the percent as a decimal and as a fraction.

215% (1 point)
2.15; 2 1/20
2.15; 2 3/20
21.5; 21,1/2
21.5; 21, 3/10
Just tell me what one what it is..

I'LL GIVE A MEDAL (:,

Answers

To write 215% as a decimal you can approach the problem two ways. You can divide 215 by 100. 215/100 = 2.15 You can also move the decimal two places to the left 215.0 = 2.15 To write 2.15 as a fraction you will place 215 over 100. {215/100}. You will then want to write this fraction in it’s simplest form. The greatest common denominator is 5 so you will then divide the numerator and denominator by 5. 215/5 = 43 100/5 = 20 215/100 = 43/20 To write this fraction as a mixed fraction you would divide 43 by 20. 43 ÷ 20 = 2 with a remainder of 3 This is written as: 2 3/20

How do I find X in this math problem?

Answers

You can use the fact that an exterior angle of a triangle is equal to the sum of the opposite interior angles.

97 +x = 64 +27 . . . . the relevant geometric relationship
x = 64 +27 -97 . . . . subtract 97
x = -6 . . . . . . . . . . . do the arithmetic

The figure below shows a right triangle:

What is r ÷ q equal to? (6 points)

sin y°
sin x°
tan x°
tan y°

Answers

r/q= sin y
I got sin y,
or option one

Hope this helps ;3

The value based on the information given about the right angle will be such that r ÷ y is sin y°.

It should be noted that the sine of an angle is calculated as:

Sine = Opposite / Hypotenuse

Based on the information given, it can be seen that r is the angle that's facing y° while q units is hypotenuse. Therefore, the value based on the information given that r ÷ y will be sin y°.

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Use Pascal's triangle to expand the binomial (d-5)^6

please solve step by step

Answers

check the picture below.

Answer:

what that guy said

Step-by-step explanation:

Could someone please help me with this?

Answers

Answer:
The exact answer is sqrt(170)
The approximate answer is roughly 13.0384

=======================================

Explanation:

We have a right triangle with two known sides. Use the pythagorean theorem to find the third side

Known sides:
a = 7
b = 11

Unknown side is c which is the hypotenuse (longest side)

a^2 + b^2 = c^2
7^2 + 11^2 = c^2
49 + 121 = c^2
170 = c^2
c^2 = 170
c = sqrt(170)
c = 13.0384
Note: the last value is approximate

Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin. Naturally, she wants to place the roof beams in such an angle that each pair of opposite beams would meet exactly in the middle. What is the angle of elevation, in degrees, of the roof beams?

Answers

Answer: The angle of elevation should be 38.9 degrees.

To find this answer, it is always best to draw a picture of the building. The point of the roof, will be directly over the middle of the cabin. Therefore, we could draw an altitude down from the top to the cabin and create a right triangle.

This would form a triangle with an adjacent side and hypotenuse with our needed angle.

We could write and solve the following cosine equation:

cos(x) = 21/27
x = 38.9

The angle of elevation is 38.9° if Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

Width of the cabin = 42 meters

Wooden beam length = 27 meters

Since opposite beams would meet exactly in the middle.

The half of the beam width = 42/2 ⇒ 21 meters

As we can see in the right angle triangle:

[tex]\rm cosx = \frac{21}{27}[/tex]

[tex]\rm x = cos^{-1}(\frac{21}{27} )[/tex]

x = 38.9°

Thus, the angle of elevation is 38.9° if Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin.

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A pizza place is offering 20% discount off all it's pizzas Ali orders a pizza for the reduced price of £5.60 Work out the original price

Answers

The original price was 7.

You can get this by dividing the new price by .8, which is the 80% that is left from the original price.

At a local store you find the following prices listed:
Tape 2 rolls for $1.28
Notepads 3 pads for .87
Highlighters 1 for 1.59
Pens 2 for 1.98

How much would you pay for one roll of tape, two note pads, two highlighters, and two pens?

A. $4.50
B. $6.38
C. $8.07
D. $5.72

Answers

Hello!

Find the cost of each individual item.

1.28 / 2 = 0.64

Each roll of tape costs $0.64.

0.87 / 3 = 0.29

Each notebook costs $0.29.

Each highlighter costs $1.59.

1.98 / 2 = 0.99

Each pen costs $0.99.

One roll of tape is $0.64, two notepads are $0.58 two highlighters cost $3.18, two pens are 1.98.

Add them up: .

0.64 + 0.58 + 3.18 + 1.98 = 6.38

ANSWER:

You would pay B. $6.38.

We have to determine what it costs for one single item and then divide or multiply by the quantity needed.

1 roll Tape= $1.28÷2= $0.64

2 rolls Notepads= 0.87÷3= 0.29x2= $0.58

2 Highlighters= $1.59x2= $3.18

2 Pens= $1.98

Add these totals:
+0.64
+0.58
+3.18
+1.98
=$6.38

ANSWER: B) $6.38

Hope this helps! :)

Una was asked to write about predicting population means by taking the means of samples. She recorded a list of some statements generated from her classmates. Which statements are true? Check all that apply. The best prediction of the population mean is the value that falls between the least and greatest sample means. It is unlikely that the population mean will be the least or greatest mean from the samples. If the means of different samples are close in number, or have small variation, then they cannot be used to make predictions for the actual population. A more accurate prediction of the population mean can be made by decreasing the number of random samples. Samples are a random selection of data values from a population. To find the range of the sample means, subtract the least value from the greatest value.

Answers

Answer:

1, 2, and 5.

Step-by-step explanation:

The best prediction of the population mean is the value that falls between the least and greatest sample means.

It is unlikely that the population mean will be the least or greatest mean from the samples.

To find the range of the sample means, subtract the least value from the greatest value.

Hope that is helpful ¯\_(ツ)_/¯

The correct statements for the population mean are 1, 2, and 5.

What is the population mean?

The population mean formula basically calculates the group's arithmetic mean by adding up all the data points and dividing the result by the total number of items in the sample.

The correct statements are given below:-

The best prediction of the population mean is the value that falls between the least and greatest sample means.It is unlikely that the population mean will be the least or greatest mean from the samples.To find the range of the sample means, subtract the least value from the greatest value.

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Find the radius of a circle with the equation 2x2+y2-6x+2y-45=0

Answers

2x²+y²-6x+2y-45=0
center:(3/2,-1)
vertex1:(3/2,-1+√202/2)
vertex2:(3/2,-1-√202/2)
focus1:(3/2,-1+√101/2)
focus2:(3/2,-1-√101/2)

I hope this helps!!!!!!!!!!

Julia and Maya are walking towards each other. When they started, the distance between them was 1600 feet. What will be the distance between them in 2.5 minutes, if they walk with the same speed: 80 feet per minute?

Answers

The distance between them after 2.5 minutes would be 1200 ft.

Walking 2.5 minutes at 80 ft/min is walking a distance of 200 ft. Each person walks 200 ft towards the other; 200*2 = 400 ft off of the distance; 1600-400 = 1200 ft.

To determine the distance between them after walking for 2.5 minutes, you will need to calculate how far they will walk in that time.

You can use the distance formula: d = rt, where d is the distance, r is the rate, and t is the time.

d = 80 ft/min x 2.5 min
d = 200 ft for each of them

1600 - 200 - 200 = 1200 feet

They are 1200 feet away from each other.

Find the 7th term of the arithmetic sequence -5x-8,-x-14,3x-20,...

Answers

a₁ = -5x-8; a₂ = -x-14; a₇=?

d = a₂ - a₁
= x-14 - (-5x-8)
= -x - 14 + 5x + 8
= 4x-6

a(n) = a₁ + (n-1)d

a₇ = -5x-8 + (7-1)(4x-6)
= -5x-8 + 6(4x-6)
= -5x - 8 + 24x - 36
= 19x - 44

(Sin3 theta + cos 3 theta / sintheta + cos theta) + sin theta cos theta

Answers

that comes to sin 3 theta + cos 3 theta + 2 sin theta cos theta + 1
-----------------------------------------------------------------
sin theta + cos theta

[tex]\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\\\ \textit{also recall that }sin^2(\theta)+cos^2(\theta)=1\\\\ -------------------------------\\\\ \cfrac{sin^3(\theta )+cos^3(\theta )}{sin(\theta )+cos(\theta )}+sin(\theta )cos(\theta )[/tex]

[tex]\bf \cfrac{\underline{[sin(\theta )+cos(\theta )]}~~[sin^2(\theta )-sin(\theta )cos(\theta )+cos^2(\theta )]}{\underline{sin(\theta )+cos(\theta )}}+sin(\theta )cos(\theta ) \\\\\\ \cfrac{sin^2(\theta )-sin(\theta )cos(\theta )+cos^2(\theta )}{1}+sin(\theta )cos(\theta ) \\\\\\ sin^2(\theta )\underline{-sin(\theta )cos(\theta )}+cos^2(\theta )\underline{+sin(\theta )cos(\theta )} \\\\\\ sin^2(\theta )+cos^2(\theta )\implies 1[/tex]

If f(x) = 9x – 7 and g(x) = 2x2 – 3x + 1, what is (f + g)(4)?
a. -8
b. 8
c. 34
d. 50

Answers

Answer:

D. 50

Step-by-step explanation:

[tex]f(x) = 9x - 7 \\ g(x) = 2x {}^{2} - 3x + 1 \\( f + g)(x) = 9x - 7 + (2x {}^{2} - 3x + 1) \\ (f + g)(x) = 2x {}^{2} + 6x - 6 \\ (f + g)(4) = 2(4 ){}^{2} + 6(4) - 6 \\ (f + g)(4) = 32 + 24 - 6 \\ (f + g)(4) = 56 - 6 \\ (f + g)(4) = 50[/tex]

10,11, and 12 please and show work

Answers

10). 5 x 10^6 5.3 x 10^-4
5 x 1,000,000 5.3 x 0.0001
5,000,0000 x 0.00053 = 2,650

2,650

F(x) = 2x2 – 4x – 3

0 = 2x2 – 4x – 3

3 = 2(x2 – 2x)

3 + 1 = 2(x2 – 2x + 1)

4 = 2(x – 1)2

2 = (x – 1)2

± = x – 1

1 ± = x

Mica is solving for the zeros of a quadratic function by completing the square. Her work is shown. What error did Mica make?

ANSWER CHOICES
Mica should have set each x = 0 instead of f(x).
Mica should have added 2 to 3 instead of 1.
Mica should have multiplied both sides by 2 instead of dividing.
Mica should have subtracted 1 from both sides instead of adding.

Answers

Mica should have added 2 to 3 instead of 1 to 3.

She factored out a 2 on the righthand side, so adding 1 within the parentheses is equivalent to adding 2 outside the parentheses. Since this is an equation, what we do to one side, we must do to the other, so Mica should've added 2 to the lefthand side.

Mica should have added 2 to 3 instead of 1.

What is the perimeter of this equilateral triangle?

Answers

It is equilateral so all sides are same.

18+18+18 = 54

the perimeter is 54 cm

please help I don't understand this
Solve for x
2/(9x) = 4/7

18/7
I don't know
- 18/7
7/18
- 7/18

Answers

The correct answer is: [C]:  " [tex] \frac{7}{18} [/tex]" .
____________________________________________________
Explanation:
____________________________________________________
Given:
____________________________________________________

2 / (9x) = 4 / 7 ; solve for "x" ;
____________________________________________________

Cross-multiply:

→ (9x)*4 = 2 * 7 ;

  → 36x = 14 ;

Divide each side of the equation by "36" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ 36x / 36 = 14 / 36 ;

x = 14/ 36 ;

  → x = 14/36 = (14÷2) / (36÷2) = 7/18 ;
______________________________________________________

The answer is: " [tex] \frac{7}{18} [/tex]" ;

→ which is: Answer choice: [C]: " [tex] \frac{7}{18} [/tex]" .
______________________________________________________

Bluesky air has the best on-time arrival rate with 80% of its flights arriving on time. a test is conducted by randomly selecting 16 bluesky air flights and observing whether they arrive on time. what is the probability that 2 flights of bluesky air arrive late? (please carry answers to at least six decimal places in intermediate steps. give your final answer to the nearest four decimal places).

Answers

This is a binomial distribution where 80% of flights arrive on time (p = 0.8) and 20% do not (q = 1 - 0.8 = 0.2). Then the probability that exactly 2 flights arrive late follows the formula:
(nCr)(p^r)(q^(n-r)), where n = 16 (total # of flights), r = 14 (flights that arrive on time)
(16C14)(0.8^14)(0.2^2) = 0.2111

Final answer:

The problem can be solved by using the binomial probability formula. We know that the binomial model deals with the probability of success of an event in a series of experiments. Plug the values into the binomial formula to find the probability that 2 flights out of 16 selected flights will arrive late.

Explanation:

This problem can be solved using the binomial probability formula. The binomial distribution model deals with finding the probability of success of an event that has only two possible outcomes in a series of experiments, such as a coin toss.

Given that the probability of a flight arriving on time is 80%, the probability (p) for a flight arriving late is 20% or 0.2. We are looking for the probability that 2 out of 16 flights arrive late. This is a binomial problem where n=16 (the number of trials), k=2 (the number of successes), and p=0.2 (probability of success).

The binomial formula is P(X=k) = C(n, k) * (p^k) * (1-p)^(n-k)

where C(n, k) is a combination that calculates the number of possible combinations of n items taken k at a time, without regard to the order of selection.

So, to solve this problem:

First, calculate C(16, 2).Second, calculate (0.2^2).Third, calculate ((1-0.2)^(16-2)).Lastly, multiply those three results together to get the final probability.

The probability that 2 flights out of 16 selected flights will arrive late can be computed by plugging these values into the binomial formula.

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The length of a rectangle is 5 more than 3 times its width. Find the length and width of the rectangle with an area of 182 square units.

PLEASE EXPLAIN.

Answers

Let
x------------> the length of rectangle
y-----------> the width of rectangle
A----------> area of rectangle

we know that
A= 182 units²
A=x*y ------------> x*y=182 --------> equation 1
and
the length of a rectangle is 5 more than 3 times its width
then
x=5+3*y-------------> equation 2
substitute 2 in 1
(5+3y)*y=182--------> 5y+3y²=182------------> 3y²+5y-182=0

using a graph tool------------> I solve the quadratic equation
see the attached figure
the solution is
y=7
x*y=182-----------> x=182/7----------> x=26

the answer is
the length of rectangle is 26 units
the width of rectangle is 7 units

The length and width of the given rectangle with area of 182 square units is; Length = 26 units and width = 7 units

Area of a Rectangle

Let the length of the rectangle be x

Let the width of rectangle be y

Let the area of rectangle be A

Formula for area of rectangle is;

A = length * width

Thus;

A = xy

We are told that area is 182 square units. Thus;

xy = 182 sq.units -----(eq 1)

Also the length of the rectangle is 5 more than 3 times its width. Thus;

x = 3y + 5 ------(eq 2)

Put 3y + 5 for x in eq 1 to get;

y(5 + 3y) = 182

3y² + 5y = 182

3y² + 5y - 182 = 0

Using online quadratic equation calculator gives; y = 7

Thus; x = 182/7

x = 26

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PLEASE HELP ME QUICKLY!!!!!!!!!!!!!!

Answers

First answer because you had to do the elimination method

Hello,

ANSWER: The first choice

To get to the second equation, you have to multiply the first equation by 4. Then, add the 2 equations. Doing this will eliminate the y variable from the equations.

This is called the elimination method. When you use this method, your goal is to eliminate 1 variable, so you can solve for the other variable.

Best of luck,
MrEQ

helpppppppppppppppppppppppppppppppppppp

Answers

Hello there! The lines between the a are absolute value symbols, and absolute value symbols are always positive. They are the distance a number is away from 0. We are looking at the values less than 3, so this is definitely not an or statement. C and D are eliminated. The compound inequality would be -3 ≤ x ≤ 3. A is the answer choice that fits this. The answer is A.

Hello again!

|a| ≤ 3

Solve for the absolute value

We know either a ≤ 3 and a ≥ -3

So we have a ≤ 3 and a ≥ -3

Thus,

The correct answer is option A

A cube with side length 2f is stacked on another cube with side length 3g2. Choose the expression that represents the total volume of the cubes.

Answers

The expression that represents the total volume of both cubes is [tex]8f^3+27g^6[/tex].

The volume of a cube is found by multiplying its length, width, and height; for the first cube, this is
V=(2f)(2f)(2f)=8f³.

For the second cube, this is
V=(3g²)(3g²)(3g²)=27g⁶.

The total area is their sum, so 8f³+27g⁶.

Answer:

the answer is c

Step-by-step explanation:

helpppppppppppppppppppppp

Answers

Answer:
-1

Explanation:
3π / 4 = (3*180) / 4 = 135 degrees
Since 135 is in the 2nd quadrant, therefore:
tan (135) = - tan (45) = -1

cot θ = 1/tanθ
Therefore:
cot (3π / 4) = 1/tan(3π / 4)
cot(3π / 4) = -1

Hope this helps :)

in one u.s city, the taxi cost is $2 plus 0.08 per mile. if you are traveling from the airport, there is and additional charge of $4.50 fir tolls. How far can yoh travel from the airport by taxi for 34.50?

Answers

First we define variables.
x = number of miles.
y = total cost in $
We write the equation that adapts to the problem:
y = 2.08x + 4.50
For y = 34.50 we have:
34.50 = 2.08x + 4.50
We clear x:
x = (34.50-4.50) / (2.08)
x = 14.4 miles
Answer:
You can travel from the airport by taxi for 34.50 about 14.4 miles.

Anita says CD can also be called DC. Do you agree?Explain
I'm talking about line segments

Answers

CD can be called DC, since each letter represents a point on the line. If the line segment has two points, it may be referenced with the points in any order. In the same way, a segment with points A and B could be called AB or BA.

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