Unit 4, Lesson 8: Tax and Tip newste
8.1: Notice and Wonder: The Price of Sunglasses
You are on vacation and want to buy a pair of sunglasses for $10 or less. You
find a pair with a price tag of $10. The cashier says the total cost will be
$10.45.
1. The tax is what percent of the original price?
2. An item that costs $20 would have a tax of how much?
3. Ray Bans cost $852.00, how much would the total be after tax?

Answer:

128 dollars

Step-by-step explanation:

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Proved  that the line L and M are parallel lines

Here we have to prove that L and M are parallel

One angle at the point at F is given that 139 degrees

We know sum of angles on a straight line is 180 degrees

Then the other angle will be

139 + a = 180

a = 180 - 139

a = 41 degrees

Now consider the triangle and find the value of x

The sum of interior angles of a triangle is 180 degrees

then

(3x+8) + (3x) + (9x+7) = 180

3x+8 +3x +9x + 7 = 180

15x + 15 = 180

15x = 180 - 15

15x = 165

x = 165/15

x  = 11

Then the value of angle 3x +  8 = 3 × 11 + 8

= 33 + 8

= 41 degrees

Before that we have solved the angle at f = 41 degrees, therefore both are equal angles  which is called corresponding angles

Therefore, the line L and M are parallel

Hence, proved  that the line L and M are parallel lines

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The equation of line is y = 3x - 6

Define Equation of line.

          y - y₁ = m (x - x₁)  

We have the given points,

(1, -3) and (3, 3)

Let, (x₁ , y₁) = (1, -3)     and,

(x₂, y₂) = (3, 3)

Formula for equation of line is,

y - y₁ = m (x - x₁)

Where m is slope and for that we have formula for slope is

m =  (y₂ - y₁) / (x₂ - x₁)

plug in the values,

m = (3 - (-3) ) / (3 - 1)

m = 6 / 2

m = 3

Now, we get the slope. Now, just put the values in equation of line formula

y - y₁ = m (x - x₁)

y - (-3) = 3 (x - 1)

y + 3 = 3x - 3

y = 3x - 6

Hence, the equation of line is y = 3x - 6

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If the brake can hold the wheel stationary when the force applied to the lever i

(a) P = 30 N     -> No

(b) P = 70 N     -> Yes

To hold lever,

x + Σ[tex]M_{O} = 0[/tex]             [tex]F_{B}(0.15) - 5 = 0[/tex]            [tex]F_{B} = 33.333 N[/tex]

Require

[tex]N_{B} = \frac{33.333}{0.3}[/tex]

      = 111.1 N

Lever,

x + Σ[tex]M_{A} = 0[/tex]            [tex]P_{Reqd.}[/tex](0.6) - 111.1(0.2) - 33.333(0.5) = 0

[tex]P_{Reqd.}[/tex] = 39.8 N

(a) P = 30 N < 39.8 N           No

(b) P = 70 N > 39.8 N           Yes  

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The solution for the system of equations shown in this graph is (-2, 1)

In this question, we need to determine the solution for the system of equations shown in this graph.

From given graph of system of equations we can observe that the  system of equations represent lines intersected at point.

This means that the system of equations has a solution.

The point of intersection of given line is (-2, 1)

Therefore, the solution for the system of equations shown in this graph is (-2, 1)

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The Recursive formula for the given explicit formula is u(1) = 1 and u(n+1) = u(n) + 4 , for n = 1 , 2 , 3 ....  , the correct option is (b) .

In the question ,

it is given that ,

the explicit formula is u(n) = 4n - 1 .

and u(n) = 1 ,

we need to find the recursive formula ,

We substitute n + 1 in place of n , in the equation u(n) = 4n - 1

after substitution , we get

u(n+1) = 4(n + 1) - 1

u(n+1) = 4n + 4 - 1

u(n+1) = 4n + 3

Subtracting u(n) = 4n - 1 from u(n+1) = 4n + 3  ,

we get

u(n+1) - u(n) = 4n + 3 - (4n - 1)

u(n+1) - u(n) = 4n + 3 - 4n + 1

u(n+1) - u(n) = 3 + 1

u(n+1) - u(n) = 4

u(n+1) = u(n) + 4

Therefore , The Recursive formula for the given explicit formula is u(1) = 1 and u(n+1) = u(n) + 4 , for n = 1 , 2 , 3 ....

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x = 8

Step-by-step -e-x-p-l-a-n-a-t-i-o-n- below

The angles shown are vertical angles

Vertical angles are congruent (equal to each other)

This means that 8x + 36 = 5x + 60

Using this equation we can solve for x

8x + 36 = 5x + 60  

==> subtract 36 from both sides

8x = 5x + 24

==> subtract 5x from both sides

3x = 24

==> divide both sides by 3

x = 8

Answer:

[tex]\huge\boxed{\sf x = 8}[/tex]

Step-by-step explanation:

8x + 36 = 5x + 60 (Vertically opposite angles are equal)

Subtract 5x to both sides

8x - 5x + 36 = 60

3x + 36 = 60

Subtract 36 to both sides

3x = 60 - 36

3x = 24

Divide 3 to both sides

x = 24/3

[tex]\rule[225]{225}{2}[/tex]

Answer:

4x²

Step-by-step explanation:

2x × 3x - 2x²

= 6x² - 2x²

= 4x²

Answer:

below

Step-by-step explanation:

Simple interest =  20 000 * .1 * 5               (.1   is 10% in decimal)

at 1/2 the 10% interest it will take twice as long = 10 years

The precise value of p is 4/18. Jae Hee's expected score in the game is 1.833. Jae Hee has a 1/162 chance of receiving a total score of -3. The likelihood that something will happen is defined as probability.

Therefore,

Value of p is,

∈p = 1

1/18 + p + 3/18 + 1/18 + 2/18 + 7/18 = 1

14/18 + p = 1

p = 4 / 18

So the exact value of p is 4/18

Expected score of the game :

∈(x) = ∈xi pi

= -3 (1/18) - 1 (4/18) + 0 (3/18) + 1 (1/18) + 2 (2/18) + 5 (7/18)

= 33/18

= 1.833

Expected score of the game Jae Hee plays is 1.833

Calculate Probability of Jae Hee getting total score of -3

p (total score -3 )

= p(x= -3) and p(x=0) + p(x=0) and p (x=3)

= 1/18 × 1/18 + 1/18 × 1/18

=1/162

Probability of Jae Hee getting total score of -3 is 1/162

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Answer:

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

[tex] \frac{1}{2} ( \frac{1}{10} + \frac{2}{5} )[/tex]

[tex] \frac{1}{2} ( \frac{1}{10} + \frac{4}{10} ) = \frac{1}{2} ( \frac{5}{10} ) = \frac{1}{2} ( \frac{1}{2} ) = \frac{1}{4} [/tex]

Answer:

2

Step-by-step explanation:

Degree is the largest exponent        = 2   (as written)

The probability of a student playing a sport but not playing an instrument is around 0.4286.

The likelihood of a student not playing an instrument, provided they play a sport, is:
[tex]Probability=\dfrac{Number\ of\ students\ who\ play\ a\ sport\ but\ do\ not\ play\ an\ instrument​}{Number of \students\ who\ play\ a\ sport}[/tex]

It is known that 14 students participate in a sport, while 8 students do not engage in either a musical instrument or a sport. Thus, the number of students who play a sport but do not play an instrument is:

Number of students who play a sport but do not play an instrument = 14- 6
                                                                                                                 = 6
Now, let's calculate the probability:

Probability = 6/14
                  = 0.4286

Rounded to four decimal places, the likelihood of a student playing a sport but not playing an instrument is approximately 0.4286.

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​

Answer:

A x<-3

y ≤-x+1

Step-by-step explanation:

x<-3

y ≤-x+1

The probability that the sample mean falls between 4800 psi and 5200 psi is 0. 0.9973.

Probability refers to the numerical descriptions of how likely an event is to occur. For the given information, the mean µ = 5000 psi and standard deviation σ = 400 psi.

For a random sample, n = 36, in order to determine the probability that the sample mean falls between 4800 psi and 5200 psi, the z test statistics for the range must be calculated.

z = (x - µ)/ (σ/√n) = (4800 - 5000)/ (400/√36) = -3

z = (x - µ)/ (σ/√n) = (5200 - 5000)/ (400/√36) = 3

Hence, the probability that the sample mean falls between 4800 psi and 5200 psi would be p ( -3< z < 3).

From the table,

p ( -2.4 < z < 2.4) = 0.9973

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Answer: 20

Step-by-step explanation:

i got 100

The total student increases by 10.85% from last year.

A relative value indicating hundredth parts of any quantity is called percentage.

Given that, last there were 125 boys and 50 girls, and it increased by 12% and 8% next year,

Total students last year = 125+50 = 175

Boys increased = 125x112/100 = 140

Girls increased = 50x108/100 = 54

Total students current year = 140+54 = 194

Percentage increase = (194-175)/175x100 = 10.85%

Hence, The total student increases by 10.85% from last year.

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Answer:

5.  (6 hours)/(1 day)

6.  (8 quarts)/(1 container)

Step-by-step explanation:

5.  The number line shows both hours and days.  It does not indicate why the relationship exists.  Perhaps the hours are the ones worked in a day.  What’s important is whether the relationship between the two is the same for all data pairs.  E.g., 12/2 = 6; 36/6 = 6; 60/6 - 5, and so forth.  They are all the same ratio, or rate: (6 hours)/(1 day)

6.  The number line shows both quarts and containers.  The  relationship between the two is the same for all data pairs.  E.g., 8/5,  16/10 or 8/5; 24/15 or 8/5; 32/20 or 8/5, and 40/25 or 8/5.   They are all the same ratio, or rate: (8 quarts)/(1 container).

We can use proportional reasoning to describe that when the two quantities multiplied equal a constant.

Hence, Option (C) is correct.

What is a proportion?

A proportion is a type of ratio in which the denominator also contains the numerator. For example, the proportion of male deaths would be deaths to males divided by deaths to males plus deaths to females (i.e. the total population).

Let 'x' be the numerator and 'y' be denominator,

then one ratio is 'x/y' and its reciprocal by using the proportion would be 'y/x'

and then their multiplication will be

                               [tex]=\frac{x}{y}*\frac{y}{x} \\\\\=1[/tex]

Multiplication gave us '1', which is a constant.

Hence option (C) is the correct answer.

We can use proportional reasoning to describe that when the two quantities multiplied equal a constant.

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Answer:

The answer would be 52 if you rounded by the nearest whole number.

Step-by-step explanation:

Find your place

Look next door (to the minor digit)

Four or less just ignore

Five or more let it sore.

Answer:

8 chickens, and 28 sheep.

Step-by-step explanation:

The chickens have the ratio of 4. Chickens have 2 legs, so 4 x 2 = 8 chickens.

The sheep have the ratio of 7. Sheep have 4 legs, so 7 x 4 = 28 sheep.

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Answer:

3 cups

Step-by-step explanation:

let's assume that sari made pancake batter in a jar.

1 jar is equivalent to 4 cups

so if 1 cup of batter is left, it can be concluded that Sari uses 3 cups of batter in making pancakes.

The perimeter of the triangle is 64 when the triangle is ZTW.

Given that,

In the picture we have a triangle ZWT.

The U and V are mid points of WT and Y and X are midpoints of ZW.

We have to find the perimeter of the triangle.

We get the sides

ZT=22

We have,

TU/ZY= UV/YX= VW/XW  (Thales theorem)

6/8= a/12= 3/b

3/4=a/12= 3/b

Take,

3/4=a/12

a=3/4×12

a=3×3

a=9

Take,

3/4=3/b

b=3×4/3

b=4

The side TW=6+9+3=18

The side ZW=8+12+4=24

The perimeter of the triangle is sum of the sides.

The perimeter of the triangle=ZT+ZW+TW

The perimeter of the triangle= 22+24+18

The perimeter of the triangle= 64

Therefore, The perimeter of the triangle is 64 when the triangle is ZTW.

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The completed table of coordinates for the exponential function can be  presented as follows;

x; -2,       -1,  0, 1,       2

y ; 16/9, 4/3, 1, 3/4, 9/16

Please find attached the graph of the function created with MS Excel

The correct graph is therefore, option D

An exponential function is one that has the argumant as an exponent

The values in the table can be found as follows;

[tex]f(x) = \left(\frac{3}{4} \right)^x[/tex]

[tex]f(x) = \left(\frac{3}{4} \right)^{-2} = \dfrac{16}{9}[/tex]

[tex]f(x) = \left(\frac{3}{4} \right)^{-1} = \dfrac{4}{3}[/tex]

[tex]f(x) = \left(\frac{3}{4} \right)^{0} = 1[/tex] The y-intercept

[tex]f(x) = \left(\frac{3}{4} \right)^{1} = \dfrac{3}{4}[/tex]

[tex]f(x) = \left(\frac{3}{4} \right)^{2} = \dfrac{9}{16}[/tex]

The completed table is therefore;

x; -2,       -1,  0, 1,       2

y ; 16/9, 4/3, 1, 3/4, 9/16

The graph of the function ,  [tex]f(x) = \left(\frac{3}{4} \right)^x[/tex], therefore, has a y-intercept of 1, and a maximum value of 16/9 at x  = -2

The best cprect option  for the graph is therefore option  D

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The volume of the balloon after the addition of the extra gas is 11.87 liters

The initial volume of the balloon = 5.29 liters

Initial quantity of argon in the balloon = 2.51 mole

Here we have to use the unitary method

The volume of the 1 mole of argon = The initial weight  of the balloon / Initial quantity of argon in the balloon

Substitute the values in the equation

The volume of the 1 mole of argon = 5.29 / 2.51

= 2.11 liters

Additional argon added = 2.51 mole

Total quantity of argon = 2.51 + 3.13

= 5.64 mole

The volume of the 5.64 mole of argon = 5.64 × 2.11

= 11.87 liters

Hence, the volume of the balloon after the addition of the extra gas is 11.87 liters

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The domain of this function c(x) = 14x + 13 using interval notation is (0, ∞).

The range of this function c(x) = 14x + 13 using interval notation is (13, ∞).

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

Additionally, the vertical extent of any graph represents all its range values and they are always read and written from smaller to larger numerical values, and from the bottom of a graph to the top.

By critically observing the graph of this function shown in the image attached below, we can reasonably infer and logically deduce the following:

Domain = (0, ∞).

Range = (13, ∞).

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The amount owed at the end of the 6 years duration is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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The slope of the line is 1/3

First we have to choose two points from the graph

The first point = (1, -5)

The second point = (7, -3)

The slope of the line is the change is y coordinate with respect to the change in x coordinate of the function

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinate of the first point

[tex](x_2,y_2)[/tex] is the coordinate of the second point

Substitute the values in the equation

The slope of the line = (-3 - (-5) / (7 - 1)

= (-3+5) / 6

= 2 / 6

= 1/3

Hence, the slope of the line is 1/3

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Answer:

Ann’s work is correct

Step-by-step explanation:

Answer:

(1,3)

Step-by-step explanation:

The solution to a system of equations graph is the point of intersection of the two lines.

In this case the point where both lines meet is at x = 1 and y = 3

hence the answer being (1,3)