Answer:
16x - 2y
Step-by-step explanation:
12x+4(x+y)-6y
Distributive property
= 12x + 4x + 4y -6y
Combine like terms
= 16x - 2y
Expand
12x + 4x + 4y - 6y
Collect like terms
(12x + 4x) + (4y - 6y)
Simplify
16x - 2y
A van travels 240 miles on 20 gallons of gas. How far does it travel per gallon? Carlos installed 24 wooden cabinets in 8 days. On the average, how many cabinets did he install each day? Which is a better buy—100 sheets of binder paper at $2.50, or 150 sheets at $3.50? Julie is trying to choose between two packs of cookies. Pack A has 36 cookies for $5.90. Pack B has 24 cookies for $4.10. Which pack has cheaper cookies? Anita is offered two summer jobs. One is in retail and pays $500 for a 40-hour work week. The other job is at a restaurant and pays $12 an hour. Which job has a higher hourly rate?
Answer:
van : 12 miles per gallon
cabinets: 3 cabinets a day
retail job for $500
Step-by-step explanation:
van: 240 miles/20 gallons = 12 miles per gallon
cabinets: 24/8= 3
jobs: $500 for 40 hours and $12 times 40 hours gets you $480
first job pays $20 bucks more
Ques 1)
A van travels 240 miles on 20 gallons of gas.
This means that 20 gallons of gas is used to travel 240 miles.
This means that:
1 gallon of gas is used to travel :
[tex]\dfrac{240}{20}=12\ miles[/tex]
Hence, it travels 12 miles per gallon.
Ques 2)
Carlos installed 24 wooden cabinets in 8 days.
i.e. in 8 days he install 24 cabinets
This means in 1 day he will install
[tex]\dfrac{24}{8}=3\ cabinets[/tex]
On the average, he will install 3 cabinets each day.
Ques 3)
100 sheets cost $ 2.50
This means that cost of 1 sheet is: $ 0.0250
( since, [tex]\dfrac{2.50}{100}=0.0250[/tex] )
150 sheets at $3.50
This means that cost of 1 sheet is: $ 0.0233
( since, [tex]\dfrac{3.50}{150}=0.02333[/tex] )
This means that the cost per sheet is cheaper in the buy:
150 sheets at $3.50.
Ques 4)
Pack A has 36 cookies for $5.90.
This means that cost of 1 cookie is: $ 0.16388 )
( since, [tex]\dfrac{5.90}{36}=0.16388[/tex] )
and Pack B has 24 cookies for $4.10.
This means that cost of 1 cookie is: $ 0.170833
( since, [tex]\dfrac{4.10}{24}=0.170833[/tex] )
The cost per cookie is cheaper in Pack A.
Hence, the pack which has cheaper cookies is: Pack A.
Ques 5)
One is in retail and pays $500 for a 40-hour work week.
This means that the payment for 1 hour is: $ 12.5
( since, [tex]\dfrac{500}{40}=12.5[/tex] )
The other job is at a restaurant and pays $12 an hour.
This means that the job which has a higher hourly rate is:
In retail which pays $500 for a 40-hour work week.
( since 12.5>12 )
Grant is planting one large tree and several smaller trees. He has a budget of $1400. A large tree coast $200. Each smaller tree is $150. How many total trees can grant purchase on his budget
He is buying one large tree, so subtract the cost of a large tree from the total:
1400 - 200 = 1200
He can spend 1200 on small trees.
Divide 1200 by the cost of a small tree to find how many small trees can be bought:
1200 / 150 = 8
He can buy 8 small trees.
Total number of trees = 8 small + 1 large = 9 total
What is the probability of getting a head on the coin and an odd number on the die?
Answer:
1/4
Step-by-step explanation:
The probability of getting a heads is 1/2
The probability of getting an odd number
1,3,5
----------- = 3/6 = 1/2
1,2,3,4,5,6
Since they are independent events, we multiply the probabilities
1/2 * 1/2 = 1/4
Maria is in the state park riding her bike on the new bike trail. She starts at the beginning of the trail and rides for 4 miles. After the first 4 miles, her friend Aiden joins her and they ride the rest of the trail. By the end of the trail, Maria has been riding for two and half hours, while Aiden has been riding for two hours. Assuming they are both riding their bikes at a constant speed the entire time, how long is the bike trail?
Answer:
10 miles
Step-by-step explanation:
Thinking process:
The distance that Maria rides: 4 miles
Total time by Maria = 2.5 hrs
The friend = 2hrs
Hector went shopping for a computer. At RST store, a computer originally prices at $955 had a price reduction of 40%. What was the reduced price?
x 40
------ = --------
955 100
Cross multiply
955x40=38200
38200÷100=382
u get 382
955 -382= 573
$573
So here are the rules with change by percentage (m = percentage in decimal form, n = original, and r = new):
If increase: (1 + m)n = rIf decrease: (1 - m)n = rSince this is a price reduction, we will be following the second rule. In this case:
[tex]40\%=0.4\\\\(1-0.4)*955=r\\0.6*955=r\\573=r[/tex]
Answer:In short, the reduced price of the computer is $573.
A restraint has one type of lemonade that is 12% sugar and another that is 7% sugar. How many gallons of each type does the restaurant need to make 20 gallons of a lemonade mixture that is 10% sugar?
Answer:
D
Step-by-step explanation:
I have answers to whole packet:
1.D
2.A
3.C
4.D
5.C
6.D
7.A
8.C
9.A
10.B
11.A
12.A
13.A
14.B
15.A
16.B
17.A
18.A
19.B
20.C
21.A
22.A
23.D
24.B
using a scale, or rate, of 1/4 inch per foot, calculate the rooms dimensions for your drawing
Answer: 81 in. (6.75 ft.) by 60 in. (5 ft.)
First, convert 27 ft. and 20 ft. to inches to make it easier to work with. This would convert like this:
27 ft. x 12 in. = 324 in.
20 ft. x 12 in. = 240 in.
This also means that the scale converts to 1/4 in. = 12 in.
Now, take your 324 in. and 240 in. and apply them to the scale.
For every 12 in. (1 ft.) in the non-scale room dimensions, there will be one 1/4 in. on the scale. That would apply like this:
324 in. (27 ft.) x
1/4 in. =81 in. [or 6.75 ft.]
240 in. (20 ft.) x
1/4 in. = 60 in. [or 5 ft.]
Step-by-step explanation: If incorrect sorry, Hope this helps!!
the intial value is also known as?
Answer:
Cauchy problem
Step-by-step explanation:
If you are talking about 'initial value problem', it is when talking about differential equations, an initial value problem is called a Cauchy problem by some authors as well. This is an ordinary differential equation together with a specified value which is called the initial condition. I really hope this helps!
The initial value is also known as the y intercept
What is the initial valueThe initial value, also known as the y-intercept or constant term, is a fundamental concept in mathematics, particularly in linear equations or functions. It represents the starting point or baseline on a graph, indicating the value of x is zero.
The y-intercept is where a line intersects the y-axis and serves as a reference for the function's behavior, influencing its direction and movement on the coordinate plane.
Hence we can say that The initial value is also known as the y intercept
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samantha has a stick that is one foot long. she cuts off 5 inches with saw. what is the length of the piece is left?
46×.029 how can I show my steps
Answer:
For 46•.029
First you would show how you multiply 9 times six then 9 times 4 then you put it on the bottom
After that you would do 2 times six then 2 four then you put it one space down from the other aanswer and add them
Sorry ignore this if it’s complicated
Step-by-step explanation:
x/ 2 = 7
A) x = 5
B) x = 7
C) x = 9
D) x = 14
Answer:
D) x = 14
Step-by-step explanation:
x/2 = 7
We want to isolate x
We can multiply by 2 on each side.
2 * x/2 = 7*2
x = 14
Answer:
14
Step-by-step explanation:
Well if you simplify or divide how ever you want to say it, it will be simplified to 7.
Please help me out with this problem
Answer:
1) Given
2) if lines are parallel, then corresponding angles are equal
3) Substitution
4) if altenate interior angles are equal, then the lines are parallel
parentheses 3 squared - 2 cubed parentheses 66
[tex]( {3}^{2} - {2}^{3} ) ^{66} [/tex]
Answer:
1
Step-by-step explanation:
evaluate the parenthesis before raising to power 66
3² = 9 and 2³ = 8, hence
(3² - 2³)= (9 - 8) = 1
[tex](3^2-2^3)^{66}[/tex] = [tex]1^{66}[/tex] = 1
Which expression is equivalent to (jk)l? (j + k) + l j(kl) (2jk)l (j + k)l
Answer: j(kl) I hope I helped the reason this correct is because it the expression but then the parenthesis are in a different placement.
your question is incomplete. please read below to find the missing content.
A. (j + k)
B. l j(kl)
C. (2jk)l
D. (j + k)l
(jk)l is equivalent to l j(kl)
Which describes the solutions of the equation?
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.
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find the difference 5/6 - 2/5
Answer:
13/30
Step-by-step explanation:
5/6 -2/5
We need to get a common denominator of 30
5/6 *5/5 = 25/30
2/5 * 6/6 = 12/30
5/6 - 2/5
25/30 - 12/30
13/30
Answer:
13/30
Step-by-step explanation:
First find their least common multiple. ( you can list it out)
6= 6,12,18,24,30
5=5,10,15,20,25,30
LCM= 30
5/6= 25/30
2/5=12/30
25/30 - 12/30= 13/30
find the exact value of x please help
ΔABC and ΔACD are similar. Therefore the sides are in proportion:
[tex]\dfrac{x}{4}=\dfrac{4}{2}[/tex]
[tex]\dfrac{x}{4}=2[/tex] multiply both sides by 4
[tex]\boxed{x=8}[/tex]
Mable’s cookie recipe calls for 3/4 of a cup of flour. Her mother’s recipe calls for 2/3 as much as Mable’s. How many cups of flour does her mother’s recipe require?
HELPP!!! PLEASE IM TIMED
Answer:
ITS 1/2
Step-by-step explanation:
Marble's mother requires 1/2 cup of flour .
What is proportion?Proportion is the number which is considered in comparative relation to a whole.
What is fraction?Fraction is a number expressed as a quotient, in which a numerator is divided by a denominator
How to find how many cups of flour does her mother’s recipe require?According to the problem,
Mable’s cookie recipe calls for 3/4 of a cup of flour.Her mother’s recipe calls for 2/3 as much as Mable’s cup.∴ Number of cup of flour that Marble's mother require is 2/3 part of 3/4
= (2/3 x 3/4) = 1/2
∴ Marble's mother requires 1/2 cup of flour .
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Tom want to buy a sweater for $30.in which city will it be the most expensive
Answer:
Long Beach, California, tax = 10.25%
a weekly salary of $325 plus a 6.5% commission on sales at a store. How much would she make in a work week if she sold $4800 worth of merchandise?
Answer:
Income = 637
Step-by-step explanation:
Income = weekly salary + commission
commission = 6.5% * sales
commission = .065* 4800
= 312
Income = weekly salary + commission
Income = 325+312
Income = 637
Help me with this question please.
Answer:
Essence is 140 flyers per hour
Raizon is 80 flyers per hour
Step-by-step explanation:
In essence (if you see what I did there) a unit rate (strictly in this context) is how much work is done for 1 hour of time. To find this, we simply divide the number of flyers by the number of hours of worked.
So, for Essence:
[tex]\frac{420}{3} = 140[/tex]
The units for this problem will be flyers per hour. So, Essence has a unit rate of 140 flyers per hour.
For Raizon:
[tex]\frac{640}{8} = 80[/tex]
Raizon has a unit rate of 80 flyers per hour.
HELP!! ANSWER IF YOU KNOW!!!
Solve:
7 = x + 12
A) -19
B) -5
C) 4
D) 5
how much of the circle is shaded? Write your answer as a fraction in simplest form.
1/4 & 2/7
Based on the information given, it can be concluded that 35% of the circle is shaded, which is equivalent to the fraction 7/20.
What area of the circle is shaded?To understand what area of the circle is shaded, let's first calculate how much is not shaded:
First area: 1/4 = 0.25
Second area: 2/5 = 0.4
Total of the area that is not shaded: 0.65
The total area shaded: 1 -0.65 = 0.35
This means that the total shaded is 0.35. Now, let's convert 0.35 to a fraction:
[tex]\frac{35}{100} = \frac{7}{20}[/tex]
Based on this, the shaded area is 7/20
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Please HELP on geometry I need this answer quick. At a high school, the probability that a student is a senior is 0.20. The probability that a student plays a sport is 0.15. The probability that a student is a senior and plays a sport is 0.05. What is the probability that a randomly selected student plays a sport, given that the student is a senior. A: 0.15 B: 0.05 C: 0.25 D: 0.33
Answer:
C: 0.25
Step-by-step explanation:
We will use conditional probability formula to solve our given problem.
[tex]P(B|A)=\frac{P(\text{A and B})}{P(A)}[/tex], where,
[tex]P(B|A)[/tex]= Probability of event B, given probability of event A.
[tex]P(\text{A and B})[/tex]= Probability of event A and event B.
[tex]P(A)[/tex]= Probability of event A.
Let us substitute our given values in conditional probability formula.
[tex]P(B|A)[/tex]= Probability that a student plays a sport given that student is a senior.
[tex]P(\text{A and B})[/tex]=The probability that a student is a senior and plays a sport = 0.05.
[tex]P(A)[/tex]= Probability that a student is a senior = 0.20.
[tex]P(B|A)=\frac{0.05}{0.20}[/tex]
[tex]P(B|A)=\frac{1}{4}[/tex]
[tex]P(B|A)=0.25[/tex]
Therefore, the probability that a randomly selected student plays a sport, given that the student is a senior will be 0.25 and option C is the correct choice.
Answer:
probability that a randomly selected student plays a sport, given that the student is a senior is 0.25
Step-by-step explanation:
Let, A be an event that a student is senior.
Probability can be given as , p(A) = 0.20
B be the event where student plays a sport
Probability can be given as , p(B) = 0.15
We have given that the probability of a student is a senior and plays a sport is 0.05.
i.e p(A∩B) = 0.05
We need to find the probability that a randomly selected student plays a sport, given that the student is a senior i.e p(B/A) .
Use the formula: p(B/A) = p(A∩B) / p(A)
Plug corresponding values to get p(B/A).
p(B/A) = p(A∩B) / p(A) = 0.05 /0.20
p(B/A) = 0.25 , this is the answer
-7(k-8)+2k
Please help. My mom doesnt think my answer is right :( my answer is 3k+(-1) and she thinks its -5k +56
Step-by-step explanation:
-7(k-8)+2k Use distributive property.
-7k+56+2k Combine like terms.
-5k+56
Mother knows best :)
distibutive property
Answer:
Everything should simplify down to -9a-3 (your answer)
Step-by-step explanation:
Distributive property is basically multiplying the outside number into the inside parenthesis (). Basically #(a)--->#a or #(a+b)---> #a+#b
Since you're not ask to solve for anything but simplify, just multiply 3 to -3a and -1.....
so 3*-3a is -9a and 3*-1 is -3 and you have 3(-3a-1)= -9a-3
Final answer:
The distributive property is a mathematical property that allows us to distribute multiplication over addition or subtraction. It helps simplify expressions and perform calculations more efficiently in algebra and arithmetic.
Explanation:
The distributive property is a mathematical property that allows us to distribute multiplication over addition or subtraction. It states that for any numbers a, b, and c, the expression a * (b + c) is equal to a * b + a * c. This property helps us simplify expressions and perform calculations more efficiently.
For example, if we have the expression 3 * (2 + x), we can use the distributive property to simplify it to 3 * 2 + 3 * x, which becomes 6 + 3x. This allows us to break down the calculations into smaller steps and avoid errors.
The distributive property is one of the fundamental properties of multiplication and is widely used in algebra and arithmetic.
A pizza delivery worker purchased a used motor scooter that had been driven 12,100 miles. He drives the motor scooter only on days he is working, during which he drives an average of 50 miles per day. After d days of pizza delivery, the motor scooter has been driven a total of 25,000 miles. Which of the following equations best models this situation?
Final answer:
The equation that best models the situation of the pizza delivery worker's scooter mileage is 50d = 12,900, where d represents the number of days worked.
Explanation:
The question asks us to find out which equation best models the situation where a pizza delivery worker drives a certain number of miles after d days of pizza delivery. To start, the worker bought a scooter with 12,100 miles on it. Each day of work he adds 50 miles to the total. After d days of delivery, the total miles driven on the scooter equals 25,000. We are looking for an equation that represents this scenario.
The total mileage on the motor scooter after d days can be calculated by the initial mileage plus the product of the number of days and the average miles driven per day. Mathematically, this is represented by:
12,100 miles + 50 miles/day × d days = 25,000 miles
To find the equation that models this situation, we subtract 12,100 from both sides to isolate the term with d on one side:
50d = 25,000 - 12,100
So, the equation that models this situation is:
50d = 12,900
Collin needs 300 tickets to win a coloring book at the arcade.He already has 124 tickets.How many more tickets does he need?
Answer:
300-124=176
I think this is corroct
Simplify. 18−−√
36√
23√
32√
29√
Answer:
Option C.
Step-by-step explanation:
The given expression is
[tex]\sqrt{18}[/tex]
We need to find the most simplified form of the given expression.
The given expression can be rewritten as
[tex]\sqrt{2\times 3\times 3}[/tex]
[tex]\sqrt{2\times 3^2}[/tex]
Using the properties of radical expression, we get
[tex]\sqrt{2}\times \sqrt{3^2}[/tex] [tex][\because \sqrt{mn}=\sqrt{m}\sqrt{n}][/tex]
[tex]\sqrt{2}\times 3[/tex]
[tex]3\sqrt{2}[/tex]
Therefore, the correct option is C.
What is One fourth the difference of 16 and a number? Which expression represents the phrase:
1/4 (16-x)
1/4 (x+16)
1/4 (x-16)
4 (x-16)
Answer:
[tex]\frac{1}{4} (16-x)[/tex]
Step-by-step explanation:
Let the number be x
difference of 16 and a number =[tex]16-x[/tex]
one fourth the difference of 16 and a number =[tex]\frac{1}{4} (16-x)[/tex]
Answer:
The expression represents the phrase is [tex]\frac{1}{4}[/tex] (16-x)
Step-by-step explanation:
Let the number is 'x'
The difference of 16 and a number is
16-x
The one fourth the difference of 16 and a number is
[tex]\frac{1}{4}[/tex] (16-x)
Hence, the expression which represent the phrase is
[tex]\frac{1}{4}[/tex] (16-x)
6 + 5|2x -3| ≥ 4 pls pls pls help
Answer:
x is all real numbers
Step-by-step explanation:
6 + 5|2x -3| ≥ 4
The first step is to subtract 6 from each side
6 -6+ 5|2x -3| ≥ 4-6
5|2x -3| ≥ -2
Now divide each side by 5
5/5|2x -3| ≥ -2/5
|2x -3| ≥ -2/5
Absolute values are always positive. Our absolute value is greater than a negative number. It is always true. X can be any number and our absolute value will still be greater than -2/5.
x is all real numbers