The country has approximately 3 cellular phones per person.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
In other words it compares 1 unit of some quantity with different amount of another quantity.
Given that a country has approximately 2,900 cellular phones per 1,000 people.
Number of cell phones for 1000 people = 2900
Number of cell phones for 1 person = 2900 / 1000 = 2.9 ≈ 3
Hence there are approximately 3 cellular phones per person.
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Lucas earns R875,00 in five working days how much would he earn in 12 working days,at the same rate
Answer:
Below
Step-by-step explanation:
12/5 * 875 = R 2 100 000
to see how this works, set up a ratio
5 is to 875 000 as 12 is to x
5 / 875 000 = 12/x
x = 12/5 * 875 000
Answer:
R210,000
Step-by-step explanation:
875,00 : 5 days
x :12 days
cross multiply:
87500*12 = 1050000
5*x = 5x
divide:
1050000/5 = 210000
HELPP PLS FAST MATH MATH MATH
The answer to each part is given above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the functions as follows -
p(x) = - 5x + 5
q(x) = - 4x - 2
We can write -
(p о q)(5) = (- 5x + 5)(- 4x - 2)
(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2)
(p о q)(5) = 20x² + 10 - 20x - 10
(p о q)(5) = 20x² - 20x
(p о q)(5) = 20 x 25 - 20 x 5
(p о q)(5) = 500 - 100
(p о q)(5) = 400
(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2) = (q о p)(5) = 400
(q о p)(5) = 400
Therefore, the answer to each part is given above.
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Writing vectors v1,…,v4 that are parallel to the boundaries of the feasible set, computing z.vi for each boundary, and using the information to put arrows on each boundary indicating the direction in which the objective function z increases. Name Find max z(x,y) = "-3x" - 6y +8 Subject to g,(x,y) = "-3x" - 2y = "-6" = b, g2(x,y) = 5x – 2y = 40=b2 gz(x,y) = 2x + 4y - 8 = b; g4(x,y) = x + y = 5 = 54
The final result would be a feasible set with arrows indicating the direction of increase of the objective function z.
The feasible set can be found by solving the system of equations g1, g2, g3 and g4.
g1: -3x - 2y = -6
g2: 5x - 2y = 40
g3: 2x + 4y - 8 = 0
g4: x + y = 5
Solving for x and y,
We will get the coordinates of the feasible set: (2,2), (5,0), (0,5).
Next, we find the vectors that are parallel to each boundary:
g1: (-3, -2),
g2: (5, -2),
g3: (2, 4),
g4: (1,1)
To determine the direction in which the objective function z increases, we compute z.v1 for each boundary:
z.v1 = (-3, -2) * (-3, -6) = 18 + 12 = 30
z.v2 = (5, -2) * (-3, -6) = -15 - 12 = -27
z.v3 = (2, 4) * (-3, -6) = -6 - 24 = -30
z.v4 = (1,1) * (-3, -6) = -3 - 6 = -9
Based on the results, we can see that the objective function z increases in the direction of vector v2 and decreases in the directions of vectors v1, v3, and v4.
To put arrows on each boundary indicating the direction in which the objective function z increases, we would place arrows pointing towards the direction of vector v2 on g2 and away from the direction of vector v2 on g1, g3 and g4.
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A Vending machine at Canada's Wonderland dispenses candies for children in a park. The machine only accepts a quarter (Q: 25 cents), a dime (D: 10 cents) and/or a nickel (N: 5 cents). You cannot put two coins of the same value though. You can choose a different type of candies from the machine: Gummies-5 cents, Licorice-10 cents, Lollipops-15 cents, Caramels-35 cents, Chocolate-40 cents. The machine dispenses a candy only if the exact amount is entered. I You are asked to design the simplest circuit that will control the situation and dispense a candy. 1. Create the truth table for the above requirements
The truth table for the above requirements is shown as the relationship between the coins inserted (N/D/Q) and the candies dispensed (Gummies/Licorice/Lollipops/Caramels/Chocolate).
What is Truth table?
A truth table is a mathematical table used in logic that spells forth the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables.
The truth table for the vending machine scenario is represented in following figure.
The table shows the relationship between the coins inserted (N/D/Q) and the candies dispensed (Gummies/Licorice/Lollipops/Caramels/Chocolate). A 1 in the table indicates that the candy is dispensed, while a 0 indicates that it is not.
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The following adjusted trial balance was drawn from the records of the Dakota Company. Account Title Dr Cr Cash 500 Equipment 2,000 Accounts Payable 1,000 Common Stock 700 Retained Earnings 600 Service Revenue 900 Operating Expenses 600 Dividends 100 Totals 3,200 3,200 Based on the information in the trial balance, the total amount of the debit column is
The total amount of the debit column in the adjusted trial balance is $5,400.
To find the total amount of the debit column in the adjusted trial balance, we need to sum up all the debit amounts listed in the accounts of teh given question.
Debits represent money being paid out of a particular account;
Looking at the trial balance provided, we can identify the following accounts with debit balances:
1. Cash: $500
2. Equipment: $2,000
3. Accounts Payable: $1,000
4. Common Stock: $700
5. Retained Earnings: $600
6. Service Revenue: $900
7. Operating Expenses: $600
8. Dividends: $100
In order to find the total amount of the debit column, we add up all these amounts,
Which gives us:
$500 + $2,000 + $1,000 + $700 + $600 + $900 + $600 + $100 = $5,400
Therefore, the total amount of the debit column in the adjusted trial balance is $5,400
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Rahul is 1.45 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
If Rahul is 1.45 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. the height of the tree is 9.43m.
How to find the height?Let x represent the height
x /1.45 = 31.55 -26.7
Cross multiply
x = 31.55 × 1.45 / 4.85
x = 45.7475 /4.85
x = 9.43
Therefore the height is 9.43.
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The numeral preceding 100000 base 2
One less than the given number is known as preceding number whereas one more than the given number is the succeeding number.
The logics followed in order to find them:
Base numbers work exactly the same as base 10 numbers (the ones we use on a daily basis).
Take for example, in a decimal system, we have 10 digits available:
0,1,2,3,4,5,6,7,8,9.
When counting, when we get to the 9, we start over again, but writing a 1 to the left.
0,1,2,3,4,5,6,7,8,9,10,11,12....20,21,22,23....,90,91,92,93,94,95,96,97,98,99,10
When reaching 99, we have no more digits to use, so we start the count again and go from 99 to 100.
The same works with any other base number, take for example the base 7 number.
When counting in base 7, we only have 7 digits available: (0,1,2,3,4,5,6) So when 0_{7},each the digit 6, we go immediately to 10, like this:
It went from 6 to 10 and from 16 to 20. This is because in base 7, there is no digits from 7 to 9, so we have directly to 20.
So, if working with decimal numbers, the previous value for 640 would be 639, but notice that in base 7,
There is no such thing as the digit 9, so the greatest digit we can use there 6,
Therefore, the previous value for the number would be. The next number would be because the 1 does exist for a base 7 system.
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Complete question :-
What is the numeral preceding and succeeding each of the following.
A) 640 base 7
B) 100000 base 2
C) 555 base 6
D) 100 base 5
E) 10000 base 4
F) 405 base 6
1.)Which of the following statements about time-series forecasting is true? A. It makes extensive use of the data collected in the qualitative approach. B. It is based on expert’s subjective opinion. C. It is based on the assumption that future demand will be the same as past demand. D. The analysis of past demand helps predict future demand. 2.)A researcher wants to test if elementary school children spend less than 30 minutes per day on homework. The alternative hypothesis for this example will be that the population mean is: A. less than 30 minutes B. equal to 30 minutes C. not equal to 30 minutes D. less than or equal to 30 minutes 3.) Normal probability distribution is applied to: A. a subjective random variable B. a discrete random variable C. any random variable D. a continuous random variable
1) "The analysis of past demand helps predict future demand" is true about Time series forecasting.
2) A researcher wants to test if elementary school children spend less than 30 minutes per day on homework. The alternative hypothesis for this example will be that the population mean is: less than 30 minutes.
Hence, option (A) is the correct choice.
3) Normal probability distribution is applied to: a continuous random variable
Hence, option (d) is the correct choice.
A time series is a sequence of data points indexed in time order in mathematics. A time series is most frequently defined as a succession of photos taken at evenly spaced moments in time. As a result, it is a series of discrete-time data.
Time series forecasting is the process of making scientific forecasts based on time stamped data from the past. It entails developing models based on previous data and utilizing them to make observations and drive future strategic decisions.
The straight-line approach, moving averages, simple linear regression, and multiple linear regression are the four basic forecast methodologies. The straight-line and moving average techniques both presume that the company's past results will be broadly consistent with future results.
We are provided the following details:
- Average mu in the population: 30
The following is an alternate theory.
[tex]$$H_1: \mu < 30 \text { ( Claim ) }$$[/tex]
For this case, the alternative hypothesis is that the population mean is less than 30 minutes.
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two-thirds times g times 10.
The mathematical expression, for the given statement is 20g/3
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is a statement, two-thirds times g times 10.
Converting into mathematical expression,
2/3 of g = 2g/3
And,
2/3 of g of 10
= 2g/3 × 10
= 20g / 3
Hence, the mathematical expression, for the given statement is 20g/3
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36÷9643 what is the solution and answer
Answer:
0.0037
Step-by-step explanation:
Because 36/9643 cannot be simplified down any further, the only other way to describe it is as a decimal which is ~0.0037.
let a denote the event thsat moe than 1000 wells are formed, let b donate the event that that the well failed, let c denote that less than 500 wells are formed. what so the probabilyt of b given a g
(a) The probability of a failure given there are more than 1,000 wells in a geological formation is 0.1001.
(b) The probability of a failure given there are fewer than 500 wells in a geological formation is 0.0852.
(a) We have to determine the probability of a failure given there are more than 1,000 wells in a geological formation.
P(B∣A) = Total number of failed wells more than 1000 wells/Total number of wells with 1000 failed wells
P(B∣A) = (180 + 443 + 60)/(1685 + 3733 + 1403)
P(B∣A) = 683/6821
P(B∣A) = 0.1001
(b) We have to determine the probability of a failure given there are fewer than 500 wells in a geological formation.
P(B∣C) = Number of failed well/Number of failed wells with total less that 500 wells
P(B∣C) = (2 + 14 + 44 + 3)/(28 + 363 + 309 + 39)
P(B∣C) = 63/739
P(B∣C) = 0.0852
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The complete question is:
Consider the well failure data in the table below. Let A denote the event that the geological formation of a well has more than 1000 wells, let B denote the event that a well failed, and let C denote the event that the geological formation of a well has fewer than 500 wells.
(a) What is the probability of a failure given there are more than 1,000 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣A)=
(b) What is the probability of a failure given there are fewer than 500 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣C)=
King Arthur had 30 3030 gold coins and 43 4343 silver coins in his pocket. How many coins did he have in all?
Answer:
737373
Step-by-step explanation:
You just add them together? Am I missing something?
What is the value of x in 2(5^x) =14?
A. log 7 - log 5
B. log 5/log 7
C. log 2
D. log 7/log 5
Help pls I’m in the test rn..
Answer: it would be B:log 5/log 7
Step-by-step explanation:
Elimination method
7) 2x + 2y = 8
x + y = -2
Answer:No solution because 0≠12, so it like a trick question.
Step-by-step explanation: There is no solution because if you multiply the bottom equation by -2 everything will cancel making 0≠12.
One-fourth of the animals at the shelter are cats. If there are 660 animals at the shelter how many are cats?
Answer:
165 of the animals at the shelter are cats.
Step-by-step explanation:
If one-fourth of the animals at the shelter are cats and there are 660 animals at the shelter, to get the number of cats you divide the total number of animals by the percentage of cats.
660 / 4 = 165
Students’ GPAs and scores on standardized tests (SATs and ACTs) are entered into a formula that calculates an “admissions index” score. The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state. In this context, what percentile does the top 12% represent?
The percentile of the top students will be 88%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state.
The percentile of the top student is given as,
⇒ 100% - 12%
⇒ 88%
The percentile of the top students will be 88%.
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In ΔTUV, t = 820 inches, mm∠U=132° and mm∠V=25°. Find the length of u, to the nearest inch.
The measure of the length of u for the condition is 1560 inches (approx).
What are the laws of sines?The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle.
Given ΔTUV
t = 820 inches
∠U = 132°
∠V = 25°
and ∠T = 180 - 132 - 25
∠T = 23°
so according to the law of sines
[tex]\frac{SinT}{t} = \frac{SinU}{u}= \frac{SinV}{v}[/tex]
so u = t*(SinU/SinT)
u = 820(Sin132/sin23)
u = 820(1.9019)
u = 1559.58 inches = 1560 inches (approx)
Hence the value of u is 1560 inches (approx).
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Find the most important variable in the problem.
A bag of marbles is full with 20 marbles, 12 of which are yellow. How many
are not yellow?
• A. the number of marbles that are not yellow
B: the number of yellow marbles
• C. the total number of marbles
There are 20 marbles, and 12 of them are yellow; therefore, the number of yellow marbles does not equal the number of marbles, nor does the number of yellow marbles equal the number of yellow marbles because they are yellow.
What might possibly be the smallest amount of marbles in the bag *?I There can only be 31 marbles in the bag, since 30 marbles is the most number that each person can have equitably, plus one extra marble. As a result, the first response is A. Since 60 is divisible by 2, 3, and 5, plus 1 (leaving 1 remaining), 61 might also be a conceivable number of marbles in the bag.
How do you calculate the likelihood of a ball?The likelihood of selecting a ball from a bag is calculated by dividing the total number of balls by the quantity of that color. As a result, the likelihood of a red ball in the first case is 3/9, or 1/3. The likelihood of selecting a second ball if that ball is now eliminated is 2/8 or 1/4.
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seven less than the product of 3 and a number is equal to 8 use the variable y for the unknown number
Answer:
y = 5
Step-by-step explanation:
3y - 7 = 8 Add 7 to both sides
3y - 7 + 7 = 8 + 7
3y = 15 Divide both sides by 3
y = 5
a glass jar containing five red 7 green 9 blue an 11 yellow marbles if a single marble is picked at random from the jar what is the probabilty of it beign a blue marble?
If a single marble is picked at random from the jar then the probability of it begin a blue marble is 9/32.
A glass jar containing five red 7 green 9 blue an 11 yellow marbles.
If a single marble is picked at random from the jar then we have to determine the probability of it begin a blue marble.
Red Marble = 5
Green Marble = 7
Blue Marble = 9
Yellow Marble = 11
Total Marble = Red Marble + Green Marble + Blue Marble + Yellow Marble
Total Marble = 5 + 7 + 9 + 11
Total Marble = 32
The probability of it begin a blue marble = Blue Marble/Total Marble
The probability of it begin a blue marble = 9/32
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Solve ◇ABC if A - 90º, B = 44°, and c = 17. 12pt v Paragraph
The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .
What is a Triangle ?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The properties of a Triangle are :
Three sides and three angles make up a triangle.A triangle's total angles are always 180 degrees.A triangle's outside angles are always a sum of 360 degrees.The total of the parallel interior and exterior angles is additional.The six types of triangles are: isosceles, equilateral, scalene, obtuse, acute, and right.
In triangle ΔABC
∠B = 44° and ∠C = 17°
So, The sum of angles of a triangle is 180°
Therefore,
∠A + ∠B + ∠C = 180°
⇒∠A + 44° + 17° = 180°
⇒∠A = 180° - 61°
⇒∠A = 119°
The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .
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A box contains orange balls and green balls. The number of green balls is seven more than 2 times the number of orange balls. If there are 73 balls altogether, then how many green balls and orange balls are there in the box?
Answer:
52-green
15-orange
Step-by-step explanation:
g + o = 67
g = green, o = orange, x = total = 3o + 7
use substitution: (3o + 7) + o = 67
solve for o:4o + 7 = 67
4o = 60o
= 60/4 = 15
solve for g:
g + 15 = 67
g = 52
Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible
quarterly. The interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest
he earns during t = 0 to t = 1. Find the exact value of R.
Answer:
8%
Step-by-step explanation:
We can start solving the problem by using the formula for compound interest:
A =[tex]P(1+\frac{R}{n})^{nt}[/tex]
Where A is the final amount, P is the initial principal, R is the interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.
Given that the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. We can use this information to set up an equation as follows:
[tex]P(1+\frac{R}{4})^{2}[/tex] = [tex]1.0816*P(1+\frac{R}{4})[/tex]
We can simplify this equation by canceling out the P and the (1+R/4) on the right side:
[tex](1+\frac{R}{4})[/tex] = 1.0816
We can then solve for R:
[tex]\frac{R}{4}[/tex]=[tex]\sqrt{(1.0816)-1}[/tex]
R = [tex]4(\sqrt{(1.0816)-1)}[/tex]
R ≈ 0.08, is the exact value of R.
So, Mr. Saver's nominal interest rate is 8%.
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f(x) has been horizontally compressed by a factor of 3, translated left 2, up 4 and reflected across the x-axis. Which equation represents the transformed
equation?
O g(x)=√√(x + 2) + 4
O g(x) = -√√(x+2)+4
O g(x) = -√3 (2+2)+4
g(x) = -√3 (2+2)+4
O g(x) = -√2-2 +4
O g(x)=√(-2) + 4
Answer:
g(x) = -√3 (x/3 + 2) + 4.
Step-by-step explanation:
Interpret the slope.
f(x)=4+x
The slope is
Therefore , the solution of the given problem of slope comes out to be
line's equation is y =.1333 x + 1.55.
What is meant by slope?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).If you look at the line from left to right, a line that is moving up will have a positive slope and a line that is moving down will have a negative slope.
Here,
Given : f(x) =4 +x
The line's "intercept" of the y-axis marks the location of the y-intercept. It also makes sense because a player with a 25 cm heel to toe measurement is about 1.55 metres tall. This is most likely.
Any line has the equation y=mx+b (m=slope, b=y-intercept).
Finding two spots on this line where it crosses will reveal the slope of the line. I'll use the numbers (25.5, 1.6) and (26.25,1.7).
=> (y(2)-y(1)) / (x(2)-x(1))
=> m 1.7 - 1.6 / 26.25 - 25.5
=>.1/.75 =.13333 is the formula to calculate the slope.
At roughly 1.55m, this line crosses the y-intercept.
This line's equation is y =.1333 x + 1.55.
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find f(g(1)) if f(x)=4x and g(x)=2x+5
Evaluating the composition of functions in x = 1 gives:
f(g(1)) = 28
How to find the composition of functions?Here we have the two functions:
f(x) = 4x
g(x) = 2x + 5
And we want to find to find the composition f(g(x)), we will get:
f(g(x)) = 4*g(x)
Replacing g(x) there we will get:
f(g(x)) = 4*(2x + 5)
= 8x + 20
Now we can evaluate that in x = 1, then we will get:
f(g(1)) = 8*1 + 20 = 28
That is what we wanted to find.
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In art class students are mixing black and white paint to make gray paint. Hai mixes 6 cups of black and 5 cups of white.Arianna mixes 6 cups of black and 1 cup of white paint. Whose gray will be darker?
Christine received a $1500 bonus. She decided to invest it in a 5-year certificate of deposit (CD) with an annual interest rate of 1.44% compounded annually. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) (b) Assuming no withdrawals are made, how much money is in Christine's account after 5 years? How much interest is earned on Christine's investment after 5 years? X S
a) Assuming Christine makes no withdrawals, her $1,500 investment in a 5-year certificate of deposit with an annual interest rate of 1.44% compounded annually, will be worth (future value of) $1,611.16 after 5 years.
b) The total interest earned on Christine's investment after 5 years is $111.16.
What is the future value?The future value represents the compounded present value.
The future value can be computed using an online finance calculator.
N (# of periods) = 5 years
I/Y (Interest per year) = 1.44%
PV (Present Value) = $1,500
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $1,611.16
Total Interest = $111.16
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From a point within a triangle, Segments are drawn to the vertices. A necessary.and sufficient condition that the three triangles formed have equal areas, is that the point be:
(A) such that the three angles formed each have a
measure of 120°
(B) the centre of the inscribed circle
(C) the centre of the circumscribed circle
(D) the intersection of the medians
Option D is the correct Answer. A necessary and sufficient condition that the three triangles formed have equal areas, is that the point be the intersection of the medians.
To divide a triangle into three triangles of equal area is to find the centroid the point where the medians intersect. After determining the centroid point G below, construct the segments connecting the vertices to the centroid. The three triangles created are of equal area.
So from a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be the intersection of the medians of the triangle.
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Pete's Plumbing charges 25x + 50 dollars for x hours of work. Plugged Pipes charges 50x + 75
dollars for the same number of hours.
a. Write an expression in simplest form to represent how much more Plugged Pipes costs
than Pete's Plumbing for x hours of work.
b. If they each work for 2 hours, how much more expensive is Plugged Pipes?
Answer:
a. To find out how much more expensive Plugged Pipes is than Pete's Plumbing, we need to subtract Pete's Plumbing's cost from Plugged Pipes' cost. The expression for the difference in cost is:
(50x + 75) - (25x + 50) = 25x + 25
This is the simplified form of the expression that represents the difference in cost.
b. If they each work for 2 hours, we can substitute x = 2 into the expressions for their costs and compare the results:
Plugged Pipes: 50(2) + 75 = 125 dollars
Pete's Plumbing: 25(2) + 50 = 100 dollars
So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.
Step-by-step explanation:
Sure, here is a step-by-step explanation of how to find the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work:
Start with the expression for the cost of Plugged Pipes: 50x + 75Subtract the expression for the cost of Pete's Plumbing: 25x + 50To do this, we need to distribute the subtraction (-) sign to the x and the constant terms: (50x + 75) - (25x + 50)Next, we'll combine like terms: 50x - 25x + 75 - 50 = 25x + 25The final expression, 25x + 25, represents the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work.To find out how much more expensive Plugged Pipes is for 2 hours of work we can substitute x = 2 into the expression for their costs and compare the results:
Plugged Pipes: 50(2) + 75 = 125 dollars
Pete's Plumbing: 25(2) + 50 = 100 dollars
So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.
