You are debating whether to buy a new computer for $1,360.00 with a discount of 10% and sales tax of
6.5% or a refurbished computer with the same equipment for $1,095.00 and sales tax of 5.75%. If a
savings account earns a 3.75% APR, how much do you really save with a refurbished computer if you put
the difference into the savings account for a year and calculate using the simple interest formula?
Be sure to include in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning

Answer:

  268,000

Step-by-step explanation:

You want to know the population of bacteria an hour ago if it was 1 million 20 hours ago and 1/2 million 10 hours ago, and decreasing exponentially.

The population can be described by a function of the form ...

  P = p0·(1/2)^(t/h)

where p0 is the initial population, and h is the half-life.

Here, we have p0 = 1 million, h = 10 hours, and we want to evaluate this function at t=19.

The population is ...

  P = 1·(1/2)^(19/10) ≈ 0.2679 . . . . million

The population an hour ago was about 268 thousand.

__

Additional comment

The population figures are given to 1 significant figure, so we cannot legitimately report population down to the units. Even the number 268,000 probably has more precision than is justified.

Answer:

m∠2 = 35° and m∠3 = 55°

Step-by-step explanation:

∠3 + ∠4 = 90° as shown with the square marking on the other side.

∠3 + 35° = 90°, 90°- 35° = ∠3

∠3 = 55°

∠1 = 90°, ∠3 = 55°, ∠2 = ?

A triangle's interior angles always add up to 180°.

90° + 55° + ? = 180°

145° + ? = 180°

? = 180° - 145°

? = 35°

The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

Answer: The final speed of the bicyclist is 6.60m/s.

Step-by-step explanation:

To find the final speed of the bicyclist, we need to use the formula:

Speed = Distance / Time

We know that the distance covered by the bicyclist is 31.0m and the time taken to cover that distance is 4.70s. So, we can substitute these values into the formula:

Speed = 31.0m / 4.70s

Solving this equation, we get:

Speed = 6.60m/s

So, the final speed of the bicyclist is 6.60m/s.

By solving a system of equations, we can see that renting a video game costs $1.50 and a movie costs $5.50

First, let's define the variables:

We know that renting 5 movies and 3 video games costs $32, then:

5*m + 3*v = 32

And renting 2 movies and 12 video games will costs $29.

2*m + 12*v = 29

Then we have a system of equations at:

5*m + 3*v = 32

2*m + 12*v = 29

Using the second equation, we can find the value of m.

2m = 29 - 12v

m = (29 - 12v)/2

m = 14.5 - 6v

Now we can replace that in the other equation:

5*m + 3*v = 32

And replace the equation for m:

5*(14.5 - 6v) + 3v = 32

72.5 - 30*v + 3v = 32

72.5 - 27v = 32

72.5 - 32 = 27v

40.5 = 27v

40.5/27 = v

1.5 = v

So the cost of renting a videogame is $1.5

And for a movie it is:

m = 14.5 - 6*1.5

m = 5.5

The cost of renting a movie is $5.5

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The probability of the event that all three are blue is 1/455 or 0.0022

In probability theory, the probability of an event is a measure of the likelihood that the event will occur. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be expressed as a decimal, a fraction, or a percentage.

Probability is used to quantify the uncertainty associated with a random event. It is based on the idea that if an experiment is repeated many times under the same conditions, the proportion of times the event of interest occurs will be close to the probability of that event.

The probability of an event can be calculated using the following formula:

Probability of an event = Number of favorable outcomes / Total number of possible outcomes

In this problem, we can define our variables.

Total number of possible outcomes = 15

P(All three are blue) = (3/15) * (2/14) * (1/13)

P(All three are blue) = 1/455

P(all three are blue) = 0.0022

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The expression 4^[-2] × 8^[0] × 5^[6] can be written with positive exponents as follows 4^[2] × 8^[0] × 5^[6].

Exponent is the term used to describe a way to represent huge numbers using powers. In other words, the exponent describes how many times a number has been multiplied by itself. Law of Multiples: Exponents should be added while maintaining the same base when multiplying similar bases.

When bases are raised by a power of two or more, multiply the exponents while maintaining the original base.

Division Rule: When dividing like bases, take the exponent of the denominator and divide it by the exponent of the numerator, keeping the base constant.

The expression 4^[-2] × 8^[0] × 5^[6] can be written with positive exponents as follows:

4^[2] × 8^[0] × 5^[6]

The negative sign in the value 2 can be ignored because squaring a number yields a positive value irrespective of the sign of the value.

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Answer: 5^6/ 4^2 Question : Rewrite the expression 4^-2 x 8^0 x5^6 using only positive exponents.

A function which could be the function graphed above "On a coordinate plane, a curve starts in quadrant 2 and crosses the y-axis and goes into quadrant 1. The curve opens down and to the right" is: D. f(x) = √(x + 4).

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

This ultimately implies that, there are four (4) major types of quadrants in any graph and these include the following:

In this scenario, we would use an online graphing calculator to plot all of the given functions in order to determine the function that was graphed, which we can logically deduce that it is function f(x) = √(x + 4).

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Complete Question:

Which could be the function graphed below?

On a coordinate plane, a curve starts in quadrant 2 and crosses the y-axis and goes into quadrant 1. The curve opens down and to the right.

f(x) = √(x - 5) + 1

f(x) = √(x - 2)

f(x) = √x

f(x) = √(x + 4)

Answer:

the mistake is from the 5th line

from the 3rd line,

2x+8=30

therefore,

2x=30-8

2x=24

x=24/2

x=12

Answer:I don’t understand it I would help

Step-by-step explanation:

Answer:

$ 140.00.

Step-by-step explanation:

I = $ 140.00

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year,

then, solving our equation

I = 1000 × 0.07 × 2 = 140

I = $ 140.00

The simple interest accumulated

on a principal of $ 1,000.00

at a rate of 7% per year

for 2 years is $ 140.00.

The amount of exemption on annual state 2.5% is 807.5.

What are amount of exemptions ?

Income liable to income tax is decreased by an exemption. The Internal Revenue Service permits many different exemptions (IRS). Personal and dependent exemptions used to be the two most popular forms. However, the personal exemption has been eliminated through the end of 2025 as a result of the changes made by the 2017 Tax Cuts and Jobs Act (TCJA).

There are still additional types of exemptions besides dependent ones.

Step by step Explaination:

Julie earns 32,300 annually.

she pays State tax rate 2.5%

So, first we should calculate tax rat for 1%

32300*1%

=32300/100

=323.

For state tax rate 2.5%

32300*2.5%

=32300*2.5/100

=807.5

Exemption amount on 2.5% is 807.5.

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Answer:

In the explanation:

Hope this helps!

Step-by-step explanation:

Because of the vertical angle theorem, ∠1 is also 20°, which means 16, 14, 11, 9, 5, and 7 all equal 20° as well. Because ∠2 & ∠3 and ∠4 & ∠3 are supplementary ( angles adding up to 180° ), 15, 13, 10, 12, 6, and 8 all equal 160°.

1, 16, 14, 11, 9, 5, 7  = 20°

2, 4, 15, 13, 10, 12, 6, 8 = 160°

An expression that is equivalent to 6 + 5x - 4 - 3x is 2 + 2x.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Here, we have

Given: 6 + 5x - 4 - 3x

We have to find an expression that is equivalent to the given equation.

We solve the given equation by simplification and we get

= 6 + 5x - 4 - 3x

= 6 - 4 + 5x - 3x

= 2 + 2x

Hence, an expression that is equivalent to 6 + 5x - 4 - 3x is 2 + 2x.

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Answer:

D

Step-by-step explanation:

Graph D has a y intercept of 3 and a slope of 6.25

The probability that a car selected at chance is moving at more than 70mi/hr is 0.02

Normal usually refers to the word "normal" in a normal distribution.

The word normal is used when something occurs that has occurred frequently. The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.

Since the speeds of cars are normally distributed, is expressed as

z = (x - µ)/σ

Where x = speeds of cars

µ = mean speed

σ = standard deviation

From the information given,

µ = 60 mi/hr

σ = 5 mi/hr

P(x < 70 )

For x = 70

z = (70 - 60)/5 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02

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Let the equation be 3 over 54 plus 4 over 6 then we get 0.72222222222.

A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

There are three main fraction kinds in mathematics. They come in three varieties: proper fractions, incorrect fractions, and mixed fractions. Numerator and denominator terms are known as fractions. We define its types in light of these two words. The phrases used to describe a whole object's components are called fractions.

[tex]$(3 / 54)+(4 / 6)=$[/tex] 0.72222222222

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Answer:

please see the details below

Step-by-step explanation:

x< 2

y > = -3

62.38% is the necessary discount. Basic discount calculations include multiplying the original price by the given percentage rate in decimal notation.

Suppose MP is 100. later Net SP

[tex]$=(100-10) \%$[/tex] of [tex]$(100-24) \%$[/tex] of [tex]$(100-45) \%$[/tex] of [tex]100 $=90 \%$[/tex] of [tex]$76\%$[/tex] of [tex]$55\%$[/tex] of 100

[tex]$$=\left(\frac{90}{100} \times \frac{76}{100} \times \frac{55}{100} \times 100\right)=37.62$$[/tex]

Required discount [tex]=(100-68.40) \%=31.6 \%$[/tex][tex]=(100-37.62) \%=62.38 \%$[/tex]

The simplest method for figuring out a discount is to multiply the original cost by the percentage rate in decimal notation. Any item's selling price is determined by deducting the discount from the purchase price.

An enormous, red percentage symbol with a black outline. If you multiply two percentages that are fractions of 100 or decimals, you can find the percentage of another percentage. Calculating, for instance, 50% of 40% results in (50/100) x (40/100) = 0.50 x 0.40 = 0.20 = 20/100 = 20%.

Therefore the correct answer is option D ) 62.38%

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Answer:

the answer for 2 examples is in the picture

Answer:2x34=344343

Step-by-step explanation:32323=23=232

Therefore , the solution of the given problem of speed comes out to be

K travels at a speed of 10 mph and W =15mph.

The speed seen from a distance tells us how fast something is moving. An object's speed determines how far it travels in a predetermined amount of time. Velocity is determined as velocity = distance * time. Meters / sec (m/s), kilometres per hourly (km/h), and kilometers / second (mph) are the three units of speed that are most frequently used (mph).

Here,

Let's say Wendy completes a 30-mile bicycle ride in the same amount of time that Kim completes a 20-mile ride.

Find the speed of each if Wendy bikes 5 mph faster than Kim.

When s Equals K's speed, (s+5) becomes W's speed.

They inform us that the 2 and half are equivalent, thus we can use this information to create a straightforward time equation: Time = Speed/Distance

K's time equals W's time, therefore

=> 20/s= 30/(s+5).

=>30s = 20(s+5)

=>30s = 20s + 100

=>30s - 20s = 100

=>10s = 100

=> s = 10

K travels at a speed of 10 mph, while W travels at 15 mph.

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The required equation of the line is y = -3x +11 which passes through the points (2, 5) and (5, -4)

The slope is simply expressed as an inclination of the line in the coordinate system.

Slope m = (y₂ - y₁) / (x₂ - x₁)

Given that the line that passes through two points (2, 5) and (5, -4)

Let x₁ = 2, y₁ = 5 and x₂ = 5, y₂ = -4

The required equation of the line is

y - y₁  = {(y₂ - y₁ )/( x₂ - x₁ )}( x - x₁ )

Substitute the values in the formula to get the slope of the line,

y - 5 = {(-4 - 5 )/( 5 - 2)}(x - 2)

y = {( -9 )/( 3 )}(x - 2) + 5

y = -3x + 6 + 5

y = -3x +11

Therefore, the required equation of the line is y = -3x +11

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Kims team won 31 games and lost 2 games.

Two or more expressions with an Equal sign is called as Equation.

Kim’s soccer team played in 33 games.

The number of games won are w and number of games lost is w

W+L=33

They won 1 more than 15 times of the number of games they lost.

W=15L+1

Now substitute W in first equation

15L+1+L=33

16L=32

Divide both sides by 16

L=2

Now substitute L in first equation

W+2=33

W=31

Hence, Kims team won 31 games and lost 2 games.

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The value of a is 34.

Value is a subjective concept that is based on personal preferences. It is a measure of how much something is worth to an individual. Value can be assigned to physical objects, experiences, services, relationships or even intangible qualities such as time. It can be determined by comparing a thing to similar things or by assessing the usefulness or pleasure it provides.


To solve this equation, we can use algebra. We start by isolating a on one side of the equation. We can do this by subtracting b from both sides of the equation. This leaves us with a+b-b-13=17-b. Simplifying this equation, we get a-13=17-b. We can then add 13 to both sides to get a=17-b+13. We know from the equation that ab=40, so we can substitute b with 40/a. Plugging this into the equation, we get a=17-(40/a)+13. Simplifying this equation, we get a=34. Therefore, the value of a is 34.
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Complete questions as follows-
If ab=40, and a+b-13=17, what is the value of a?

The total amount of money Walter paid for the book after the removal of discount and addition of sales tax is $21.726

Percentage discount = 20%

Original price = $25.50

Sales tax = 6.5%

New price after discount = $25.50 - (20% × $25.50)

= 25.50 - (5.1)

= $20.4

Actual amount paid with sales tax = $20.4 + (6.5% × $20.4)

= 20.4 + 1.326

= $21.726

Therefore, Walter paid $21.726 for the book after discount and sales tax have been applied.

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