The Hu family goes out for lunch, and the price of the meal is $52. The sales tax on the meal is 6%, and the family also leaves a 20% tip on the pre-tax amount. What is the total cost of the meal?

Answer:

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Explanation:

The letter O looks very similar to the number zero, so I'm going to use other letters to avoid confusion. For the smaller circle on the left, it'll have center P. The circle on the right will have center Q. See the diagram below.

Based on that, we can say that PQ = 20 cm.

Let x = length of PK

PK + KQ = PQ

KQ = PQ - PK

KQ = 20 - x

We'll keep this in mind for later. I'll refer to this as "Fact 1" when it does come up later.

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We're given this equation

3AK=2BK

Let's get the numbers to one side and the letters to the other side like so:

3AK=2BK

3AK/BK = 2

AK/BK = 2/3

We'll use this later as well.  I'll refer to this as "Fact 2" when it does come up later.

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Next, draw a segment from P to A to form triangle PAK (also shown in the diagram below). Do the same for points Q and B to form triangle QBK.

The segments PA and PK are radii of the smaller circle, so PA = PK which leads to triangle PAK being isosceles. Triangle QBK is also isosceles for similar reasoning.

The angles AKP and QKB are vertical angles, so they are congruent.

The facts mentioned so far boil down to the two triangles being similar triangles (use the angle angle method to prove).

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Now that we know the triangles are similar, we can use a proportion to solve for x.

PK/KQ = AK/KB

PK/KQ = 2/3  .... use fact 2

x/(20-x) = 2/3 .... use fact 1

3x = 2(20-x) .... cross multiply

3x = 40 - 2x

3x+2x = 40

5x = 40

x = 40/5

x = 8

So,

The radius of the smaller circle on the left is 8 cm.

The radius of the larger circle on the right is 12 cm.

Answer:

32/9

Step-by-step explanation:

2*(2)(8/9) = 4*8/9 = 32/9

Answer:

50%

Step-by-step explanation:

75/150 = x/100

x = 50

Answer:

50%

explanation

half of 150 is 75(75x2)

Answer:

open the brackets

mx+mn=n

mx=n-mn

since we want to know the value of x , then we divide both sides with m ,thus giving us

x=n/m - n

Answer:

x = [tex]\frac{n-mn}{m}[/tex]

Step-by-step explanation:

m(x + n) = n ← distribute parenthesis on left side by m

mx + mn = n ( subtract mn from both sides )

mx = n - mn ( isolate x by dividing both sides by m )

x = [tex]\frac{n-mn}{m}[/tex]

Answer:

79

over

2000 or 79/2000 or 3.95%

Step-by-step explanation:

The probability that one of this​ manufacturer's cars was manufactured at plant A and has a defective emissions control​ device is 6.33%.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Given, An automobile manufacturer produces 79​% of its cars at plant A and 5​% of the cars manufactured at plant A have defective emissions control​ devices.

∴ The probability that one of this​ manufacturer's cars was manufactured at plant A and has a defective emissions control​ device is,

= (5/79)×100%.

= 6.33%.

learn more about conditional probability here :

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Answer:

151 meters

Step-by-step explanation:

6946/46=151 meters

Answer:

Step-by-step explanation:

If you want to be formal, let the shorter bridge = x

46x = 6946                  Divide by 46

x = 6946/46

x = 151

So the shorter bridge is 151 meters long.

Answer:

x = 3

Step-by-step explanation:

2x+6=x+9 subtract x in both sides

x +6 =9 subtract 6 in both sides

x = 3

Answer:

8/15

Step-by-step explanation:

not sure but I think you just multiply them

Answer:

It is reported as an equation but it has no equal sign.

Care to explain?

Step-by-step explanation:

Answer:

  (4, -3) is the center

Step-by-step explanation:

The equation ...

  16x^2 +25y^2 -128x +150y +81 = 0

can be rearranged by completing the square(s) to ...

  (4x -16)^2 +(5y +15)^2 = 400

Dividing by 400 gives ...

  (x -4)^2/5^2 +(y +3)^2/4^2 = 1

This is the equation of an ellipse centered at (4, -3) with major axis 10 and minor axis 8.

Answer: -3 + n >= 5

Step-by-step explanation: I got it wrong on the test but got the correct answer from test review on K12

Answer:

Step-by-step explanation:

parrallel line = gongruent angles

16x - 7 = 15x

16x - 15x = 7

x = 7

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7 * 15 = 105° your answer

--------------------------------

16 * 7 - 7 = 15 * 7

105 = 105

the answer is good

Answer:

- 7% of 3.98...

... is equivalent to multiplying them:

- 7% × 3.98 ≈ - 0.28

(Rounded to a maximum of 2 decimals)

Step-by-step explanation:

Answer:

  9.89×10^-9

Step-by-step explanation:

  0.000 000 009 89 = 9.89×10^-9

__

We have introduced spaces in the number to make the digits easier to count. (Some technical publications will write the number with thin spaces for just that reason.) The most-significant digit is in the 9th place to the right of the decimal point, so has a place value of 10^-9.

well, the numeric difference will be 136 - 80 = 56, now, if we take 80 (original price) to be the 100%, what is 56 (the increase) in percentage off of it?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 80&100\\ 56&x \end{array}\implies \cfrac{80}{56}=\cfrac{100}{x}\implies \cfrac{10}{7}=\cfrac{100}{x} \\\\\\ 10x=700\implies x = \cfrac{700}{10}\implies x = \stackrel{\%}{70}[/tex]

Answer:

Step-by-step explanation:

Answer:

(10,8)

Step-by-step explanation:

Answer:

158

Step-by-step explanation:

We know the supplement of angle 6 is 22, due to the fact that they are corresponding angles. Simply subtract 22 from 180 to get the answer. 180-22=158

Answer:

158 degrees

Step-by-step explanation:

Angle 6 has a same side interior relationship with the 22 degrees, so the sum of these angles are equal to 180 degrees.

To find the missing angle, subtract 180 by 22 degrees.

180-22= 158

Answer: B

Step-by-step explanation: I beilieve it's B but, don't take my word.

Who's Joe? I am in dire need of therapy.

Answer:

Infinitely many solutions

Step-by-step explanation:

6(2x + 4) = 3(4x + 8)

Distribute the 6

6 * 2x = 12x and 6 * 4 = 24

12x + 24 = 3(4x+8)

Distribute the 3

3 * 4x = 12x and 3 * 4 = 24

12x + 24 = 12x + 24

On both sides of the equal sign we have 12x + 24.

When both sides are equal there are infinitely many solutions.

Answer:

D

Step-by-step explanation:

n = 5

an = 176

an = a1*x^(n -1)

a5 = a1 * x^4 = 176

a7 = a1 * x^6 = 704

a7/a6 = a1 * x^6 / a1*x^4 = 704 / 176

Cancel out a1

x^6/x^4 = 704/176      Divide numerator and denominator by 176

x^2 = 4                        Take the square root of both sides

x = 2 or - 2

176 = a1 * x^4

176 = a1 * 16

a1 = 11

a1 is going to be 11 whether x is 2 or minus 2.

hi mallllll. hehehe

once again its [tex]a_{1} = -11[/tex]

Answer:

No

Step-by-step explanation:

There is no formula

There is no formula

Check the picture below.

Answer: HIs income was  $6744.04

Step-by-step explanation: 8798.04 + 3650 - 5700 = 6744.04 Hope this helps!

The taxable income last year is $552.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It from simdiffers ple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

We have,

Last year, a part-time housekeeper earned $8798.

He claimed he was exempt, costing $365.

$570.00 is the standard deduction.

Gross income less the standard deduction and all exemptions equals taxable income.

= 8798 - 3650 - 5700

= $-552

The negative sign indicates that he owes no taxes.

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Answer:

-2x + 2

Step-by-step explanation:

Answer:

I think it is 50 because 75-25=50

Answer:

d! 35 ......!!!!!!!!!!!!

Answer:

multiply 5 times 3 that is equal to 15.

15 plus 8 is equal to 23 and add the x.