A store is having a sale in which all items
are discounted 20%. Including tax, Colin paid $21 for a picture. If the
sales tax rate is 5%, what was the original price of the picture?

Answer: -2 1/2 or -2.5

Step-by-step explanation:

Yes, it can be simplified.

-5/2 can be simplified to -2 1/2 which can be as a decimal as -2.5

Answer is y=1/2x+2 because the slope is 1/2 and the starting point is +2

The absolute value equation to represent the definition of betweenness is

AB + BC = AC ↔ B ∈ A,C  

Absolute value equation:

An absolute value equation is a function that contains an algebraic expression within absolute value symbols.

Given,

Here we have the statement "If three points a, b, and c lie on the same line, then b is between a and c if and only if the distance from a to c is equal to the sum of the distances from a to b and from b to c.".

Here we need to find the absolute value function for this statement.

In order to find the absolute value equation,

First we have to identify the symbols for the terms mentioned in the statement they are,

between = ∈

if and only if = ↔

sum = +

Now, we have to divide the statement as two parts.

First one is, "c lie on the same line, then b is between a and c"

It can be written as,

B ∈ A,C

Then the second part is, "the distance from a to c is equal to the sum of the distances from a to b and from b to c."

Which can be written as

AB + BC = AC

When we combine it, the we get the absolute value equation as,

B ∈ A,C ↔  AB +BC = AC

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If the remaining balance for 48 months with an APR of 4.5%. the monthly payment that Jenna pays is: $595.17.

Using this formula to determine the monthly payment

P = A ×r × ( 1 +r)^n  ÷( 1+ r)^n -1

Where:

P = Principal = ?

A = Amount = $29,000 × ( 1- .10) = 26,100

r = Interest rate = 4.5% / 12 = 0.00375

n = number of months = 48 months

Let plug in the formula

P = 26,100 × 0.00375 × ( 1+ 0.00375)^ 48 ÷ ( 1+ 0.00375)^ 48 -1

P = 26,100 × 0.00375 × ( 1.00375)^ 48 ÷ ( 1.00375)^ 48 -1

P = 26,100 × 0.00375 × 1.196814377  ÷  1.196814377 -1

P = 26,100 × 0.00375 × 1.196814377  ÷  0.196814377

P = $117.1382456  ÷  0.196814377

P = $595.17

Therefore $595.17 is the monthly payment.

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a) The price (amount) of the house after 1 month = $9540

b) The price (amount) of the house after 3 months  = $10719.14

c) The price (amount) of the house after 10 months = $16117.629

a ) How to find the rental price of the house after 1 month ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 1

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100}) \\\\= 9000(\frac{106}{100})\\\\= 90*106\\\\= 9540[/tex]

The rental price of the house after 1 month = $9540

b ) How to find the rental price of the house after 3 months ?

The rental price of a dacha = Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 3

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^3 \\\\= 9000(\frac{106}{100})^3\\\\= 9000*(1.06)^3\\\\= 10719.14[/tex]

The rental price of the house after 3 months = $10719.14

c ) How to find the rental price of the house after 10 months ?

The rental price of a dacha =Principle =  $9000

Percentage increase in price = r = 6%

Number of months = n = 10

Amount of a compound interest is given by,

 [tex]Amount = P(1 +\frac{r}{100} )^n\\\\=9000( 1 +\frac{6}{100})^{10} \\\\= 9000(\frac{106}{100})^{10}\\\\= 9000*(1.06)^{10}\\\\= 9000*1.790\\\\= 16117.629[/tex]

The rental price of the house after 10 months = $16117.629

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Answer: A.

Step-by-step explanation:

1. The function is even (symmetric about the y-axis)

2. The function F(x) is positive

[tex]\displaystyle\\Hence,\\F(x)=\frac{1}{x^2}[/tex]

The probability of getting a green of a yellow marble can be determined like this:

Probability = (yellow marbles + green marbles) / total number of marbles

Probability = (1 + 4) / 10

Probability = 5 / 10

Probability = 1/2

By multiplying the given probability by the number of times a marble will be drawn, we get how many times we can predict that a green or a yellow marble will be picked, then we get:

Number of predictions = 150 × 1/2

Number of predictions = 75

Then, the answer is 75 times

Answer:

75 times.

Step-by-step explanation:

There are a total of 10 marbles in the bag.

Probability a green marble is drawn (in 1 draw) = 4/10 = 2/5.

In 150 draws you can expect to draw 150* 2/5 = 60 green marbles.

Probability a yellow marble is drawn (in 1 draw) = 1/10.

In 150 draws you can expect to draw 150* 1/10 = 15 yellow marbles.

So, the number of times for a green or yellow marble

= 60+15= 75.

[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]

without given any restriction x is all the numbers greater than 0.

NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.

A family taking a road trip vacation travels 126 miles in 3 hours.

We can calculate the constant of proportionality as:

Then, in 5 hours they would travel:

In 5 hours they would travel 210 miles.

Each child will receive the 1.1 cup of milk.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that a container of milk contains 8 cups of milk. if paul sets aside [tex]1\dfrac{2}{5}[/tex] cups of milk for use in a recipe , then we get the leftover;

8  -  [tex]1\frac{2}{5}[/tex] = 8 -  7/5

= 40- 7/5

= 33/5

= 6.6

The the rest cups of milk = 6.6

Then the rest evenly among his three children 6.6/3 = 1.1

Hence, Each child will receive the 1.1 cup of milk.

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The rate of change of angle of elevation between the radar station and airplane is

                       [tex]\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]

The airplane is flying at the speed of 200 mph

The airplane is at an altitude of 3 miles over the radar station

The distance travelled by the airplane after 3 mins

      distance = speed x time

                     = 200 mi/hr x 3 min

Since the speed is hour let us convert it to mins

                     = 200 x 3 x 1/60

                     = 600 / 60

                    = 10 miles

So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles

Then the elevation angle of the between radar station and airplane can be find by

                              tan θ = O / A
where O is the opposite side to the angle of elevation

          A is the adjacent side to the angle of elevation.

But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time

                                [tex]\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}[/tex]

                                        [tex]\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}[/tex]

                                       [tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}[/tex]

The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.

                                   [tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}[/tex]

We had found the value of sec²θ = (hyp/adj)²

                                    [tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}[/tex]

Now , let us convert in terms of rad/min

                                   [tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)[/tex]

                                  [tex]\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]    

Therefore , the rate of change of angle of elevation is -10/109 (rad/min)    

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Answer:

1000000

Step-by-step explanation:

100000000:    2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5

100000:    2 2 2 2 2       5 5 5 5 5      

GCF:    2 2 2 2 2       5 5 5 5 5      

The Greates Common Factor (GCF) is:   2 x 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 5 = 100000

Answer:

x = 3 and y = 5

Step-by-step explanation:

1st: The sum of the same side interior angles equal 180°. Use this to solve for x.

45x - 5 + 16x + 2 = 180

61x - 3 = 180

61x - 3 + 3 = 180 + 3

61x/61 = 183/61

x = 3

2nd: find the measure of angle 16x + 2

16x + 2

16(3) + 2

48 + 2

50°

3rd: the sum of the 50° angle and the angle 26y° is 180 since they make a straight angle. Make an equation and solve for y.

50 + 26y = 180

50 - 50 + 26y = 180 - 50

26y = 130

26y/26 =130/26

y = 5

Answer:

76 child tickets were sold

Step-by-step explanation:

let a represent number of adults and c number of child tickets sold, then

a + c = 165 → (1)

5.8a + 8.9c = 1192.6 → (2)

multiplying (1) by - 5.8 and adding to (2) will eliminate a

- 5.8a - 5.8c = - 957 → (3)

add (2) and (3) term by term to eliminate a

0 + 3.1c = 235.6

3.1c = 235.6 ( divide both sides by 3.1 )

c = 76

that is 76 child tickets were sold that day

Answer:

F (false)

Step-by-step explanation:

i hope this helps! Have a good day! c:

The rate of the slowest car is 86 km/hr using the concept of relative velocity.

Relative speed is the rate at which one moving body moves in relation to another. The differential between two moving bodies determines their relative speed while they are traveling in the same direction. However, when two bodies are traveling in opposition to one another, the relative speed is determined by averaging their respective speed.

Let the speed of 1st car is v₁.

Let the speed of 2nd car is v₂.

v₁- v₂ = 18 km/hr --- (1)

And using the concept of relativity.

S(rel) = D(rel)/time

S(rel) = 360 / 2

S(rel) = 190

v₁ + v₂ = 190 --- (2)

Adding equations 1 and 2 we get

v₁ = 104 km/hr

v₂ = 86 km/hr

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Answer: Yes

Step-by-step explanation:

because their overall shape it the same, their size is the only thing that sets them apart, so they're not identical

Answer:

[tex]-2\sqrt{} 6x^{8}[/tex]

Step-by-step explanation:

From the given values, we know there are 2 defective resistors and 9 not defective. then, we have

where

denote the combinations of 9 elements taking in 3, that is 3 good resistor from the 9 which are not defective. Similarly,

denotes the combinations of 2 elements taking in 1, that is, 1 defective resistor form the 2 defective resistors.

Then, we have

then, the answer is

Answer:

8 out of 10.

Step-by-step explanation:

if you flip a coin independent then it doesn't matter what the other outcomes are. So if it's a one out of two chance every time then it's 8 /10.

Solution:

From the given diagram;

The statements that are correct about the given diagram are

b)

d) The sum of exterior angles of a polygon is 360°,

Hence, the sum of the exterior angles of polygon ABCDE and the sum of exterior angles of polygon DEHGF is 720°

e)

Answer: 19

Step-by-step explanation:

[tex]g(5)=5-2=3\\\\\impies f(g(5))=f(3)\\\\=3(3)+10=19[/tex]

Vector a = (3, 2), then;

Also, vector b = (-5, 6), then;

Then, -3a + 2b = (-9, -6) + (-10, 12)

The answer is (-19,6)

In the system of equations, the value of the variable 'b' will be 3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of the equations is given below.

Equations 1: - 4 = 9a - 3b + c

Equation 2: 14 = 9a + 3b + c

Equation 3: - 4 = c

Put the value of c in equations 1 and 2, then we have

- 4 = 9a - 3b - 4

9a - 3b = 0                 ...4

14 = 9a + 3b - 4

9a + 3b = 18               ...5

Subtract equation 4 from 5,

9a + 3b - 9a + 3b = 18 - 0

6b = 18

b = 3

In the system of equations, the value of the variable 'b' will be 3.

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Answer: 1/5

Step-by-step explanation: It might be first easier to put it in decimal form so 8/10 is 0.8 and 0.8 divided by 4 is 0.2. 0.2 as a fraction is 1/5.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

convert element to fraction: 4 = [tex]\frac{4}{1}[/tex]

= [tex]\frac{8}{12}[/tex] ÷[tex]\frac{4}{1}[/tex]

The fraction rule: a/b ÷ c/d = a/b x d/c

= [tex]\frac{8}{12}[/tex] × [tex]\frac{1}{4}[/tex]

Cross - cancel common  factor: 4

= [tex]\frac{2}{12}[/tex]

Cancel the common factor: 2

= [tex]\frac{1}{6}[/tex]

The greatest possible integer of the inequality is 19.902.

What is the inequality?

In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, as to if it is less than or greater than. The different inequality symbols, properties, and methods for resolving linear inequalities inside one variable and two variables will all be covered in this article along with examples.

Given that,

3.806< 19.902

In which, less than inequality is used.

The given numbers are in decimal form.

comparison be between the given numbers and check which one is greater.

3.806< 19.902

19.902 is the greater than 3.806

Hence, the greatest possible integer is 19.902.
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EXPLANATION:

We are given the original price of a laptop computer at $1,700.

Now the price has been increased to $1,800.

Note that there is a $100 increase over the original price.

For us to calculate the percent increase we shall use the ratio of the increase over the original price and calculate as a percentage.

We can now set up the following equation;

We now cross multiply;

Rounded to one decimal place, the percent increase is;

ANSWER:

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Answer:B

Step-by-step explanation:

Answer:

Let's break down the given information.

Car A

Speed - 30 mph

Hence the distance traveled per minute would 30/60 mph which is 0.5 Miles every minute.

Car B

Speed - 36 mph

The distance traveled per minute would 36/60 mph which is 0.6 Miles every minute.

Initial distance between the cars is 10 Miles

Car A travels 1 miles in 2 minutes and Car B travels 1.2 miles in 2 minutes.

Hence to calculate the distance between the 2 cars we need to calculate

Initial distance - Distance travelled by Car A - Distance traveled by Car B

Which is

10 - 1 - 1.2

7.8 Miles distance between the 2 cars