Least common denominator of 9/4 and 5/6
Answer:
12
Step-by-step explanation:
We want the smallest possible number that can be divided by both 4 and 6 with no remainders.
12 is the least common multiple (LCM) of both 4 and 6, meaning it's the smallest number that 4 and 6 both divide into evenly.
24 could be used as a common denominator, but it isn't the least common denominator. It has more prime factors than is necessary to be the LCD.
12, when its prime factorization is written out, is 2² • 3.
24, when its prime factorization is written out, is 2³ • 3.
9/4 → (9•3)/(4•3) → 27/12
5/6 → (5•2)/(6•2) → 10/12
Howard bought 3/5 pound of granola. He divided the
granola evenly among 4 friends. How much granola did
each friend get?
Answer:
Step-by-step explanation:
So because Howard wants to divide the granola evenly among all of his friends, we have to divide the amount of pounds he has by the number of friends he has.
(3/5) / 4
Dividing by four is the same as multiplying by the reciprocal of 4 which is 1/4.
So (3/5) * (1/4) is 3/20 which is .15 pounds
Bridgette has $1,000 to invest. She has two different investment options, shown in the table below. Each option would give her a different value over three years.
Number of Years 1 2 3
Option A (amount in dollars) 1100 1200 1300
Option B (amount in dollars) 1100 1210 1331
Part A: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option A? Explain your answer.
Part B: Write a function, a(t), to describe the value of the investment, in dollars, of Option A after t years.
Part C: What type of function, linear or exponential, would be best to describe the value of the investment over a fixed number of years using Option B? Explain your answer.
Part D: Write a function, b(t), to describe the value of the investment, in dollars, of Option B after t years.
Part E: Bridgette wants to invest in whichever option would increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Bridgette's investment after 20 years if she uses Option A over Option B? Explain your answer, and show the investment value after 20 years for each option.
Answer:
Part A:
Option A is a linear function
Part B:
a(t) = t × 100 + 1000
Part C:
Option B is an exponential function
Part D
[tex]b(t) = 1000 \times (1 + 0.1)^t[/tex]
Part E:
There will be a significant difference in the value of Bridget's investment after 20 yeas if she uses Option A over Option B
Step-by-step explanation:
The given parameters are;
The amount Bridgette has to invest = $1,000
The value of each investment option is given as follows;
Number of years [tex]{}[/tex] Option A [tex]{}[/tex] Option B
1 [tex]{}[/tex] 1100 1100
2 [tex]{}[/tex] 1200 1210
3 [tex]{}[/tex] 1300 1331
Part A:
Given that the first difference between subsequent data values are 2 - 1 = 1 and 1200 - 1100 = 100, 3 - 2 = 1 and 1300 - 1200 = 100 both of which are constant, the type of function that would be best to describe option A is a linear function
Part B:
The function a(t) for Option A is given as follows;
The rate of change of the function amount with time is (1300 - 1200)/(3 - 2) = 100
Therefore, comparing with the general form of a linear function, y = m·x + c, we have;
m = The rate of change of the function = 100
The y-intercept, the value of the amount a 0 time (the start of the investment) = c = 1000
The function in terms of t, a(t) = t × 100 + 1000
Part C:
The first difference of Option B are different but the first ratio given as follows;
1210/1100 = 1331/1210 = 1.1 = Constant which is the characteristics of an exponential variable
Therefore, the equation to describe the value of the investment in dollars, of Option B is an exponential function
Part D
We, have for an exponential function;
[tex]b(t) = 1000 \times (1 + r)^t[/tex]
When t = 1, we have;
[tex]b(1) = 1000 \times (1 + r)^1 = 1100[/tex]
∴ 1 + r = 1100/1000 = 1.1
r = 1.1 - 1 = 0.1
We check for t = 2, to get;
[tex]a(2) = 1000 \times (1 + 0.1)^2 = 1210[/tex]
We check for t = 3, to get;
[tex]b(3) = 1000 \times (1 + 0.1)^3 = 1331[/tex]
The function b(t) to describe the value of the investment in dollars, of Option B after t years is [tex]b(t) = 1000 \times (1 + 0.1)^t[/tex]
Part E:
The investment value after 20 years is given as follows;
For Option A, we have;
a(20) = 20 × 100 + 1000 = 3000
For Option B, we have;
[tex]b(20) = 1000 \times (1 + 0.1)^{20} \approx 6727.5[/tex]
Therefore, the difference in the investment value after 20 years for Option B and Option A is approximately $6727.5 - $3000 = $3727.5 which is significant.
Farah's brother is 7 years less than twice Farah's age, f. The sum of Farah's age and
her brother's age is 41. Which equation represents this relationship?
Answer:
f+(2f-7)=41
Step-by-step explanation:
Farah's age is represented by the first f and her brother's age is represented by the (2f-7) and the sum of their ages is 41, therefore this is the correct answer
Given the figure above, determine
Answer:
Step-by-step explanation:
since A and W are complementary, use 180 - 117 to find A. You get 63
since C and X are complementary, use 180 - 82 to find A. You get 98
all interior angles of a triangle add up to 180 so you can use what you have now to find B. B is 19
subtract B from 180 to find Y. Y is 161.
Solve for x.
y=4x
y=20
Simplify your answer as much as possible.
PLEASE HELP ME
Answer:
x = 5
Step-by-step explanation:
y = 20; y = 4x
20 = y = 4x
20 = 4x
5 = x
x = 5
Answer:
Step-by-step explanation:
Y=2x........ equation 1
Y=20....... equation 2
If y=20 then let's substitute y=20 into equation 1
20=2x
Solve for x by dividing both sides by 2.
20/2=2x/2
x=10.
You find an object made of pure metal. What could you do to identify what type of metal the object is made of?How do you find density?
Answer:
by the texture and will need volume and mass to find density
Step-by-step explanation:
Consider the division expression LaTeX: 7\frac{1}{2}\div27 1 2 ÷ 2. Select all multiplication equations that correspond to this division expression.
Answer:
2 x ? = 7 1/2 and ? x 2 = 7 1/2
Step-by-step explanation:
This is the answer because it didn't show the answer so all you have to figure out is the multiplication problem that goes with the division problem. So 2 x ? = 7 1/2 and ? x 2 = 7 1/2 you don't have to include the answer all you have to include is where the answer will do if you DID have the answer. These two are correct because the multiplication number can go in any order.
I know this might not be the best step-by-step explanation ever but I truly tried but the answer is correct.
What is the average of 37, 82, 63, and 58?
Answer:
60
Step-by-step explanation:
Add 37 82 63 and 58 to get 240 and divide by 4 to get the average.
pls help i will mark you as brainliest
Answer:
2.25x+2.50=9.25
3 games
Step-by-step explanation:
Answer:
The first one is 2.50+2.25x=9.25
The second one is 3 games
Genghis Motors wants to build cars and motorbikes on a budget. The company plans to spend at most $75000
and use at least 320 workers to build cars and motorbikes.
8000C + 5500M < 75000 represents the number of cars C and motorbikes M the company can build by
spending at most $ 75000.
52C + 38M > 320 represents the number of cars and motorbikes the company can build by using at least
320 workers.
Can the company meet both of its expectations by building 4 cars and 6 motorbikes?
Answer:
52 + 38,000,000 = 38000052- 75000= 37999977
Step-by-step explanation:
52 + 38M The 320 Is Just A Distraction Don't worry about that then subtract 75000 and that is how you do it
Tell whether the triangle with the given side lengths is a right triangle.
1. 32 m, 56 m, 64 m
1. Add file
2,875,784,527 rounded to the nearest million
Answer:
2,876,000,000
Step-by-step explanation:
round the 5 up to 6.
Your parents gave you $20 to spend at the book fair. You are getting the new Diary of the Wimpy kid book that costs $8.99/ If pencils and erasers cost $0.79 each, what is the maximum you can buy with the money provided?
Answer:
You can buy a maximum of 13 erasers/pencils.
Step-by-step explanation:
Your total is 20 dollars. The book cost 8.99, so you take away that amount from 20, getting you 11.01. You have $11.01 left. Then you divide your total (11.01) by the price of each eraser (0.79). This gets you 13.9367088608. Since thats not an even number, you have to round down because you don't want a broken pencil?eraser.
Suppose you have $10 and your brother has $54. If you decide to save $10 of your allowance each week and your brother decides to save $6 of his allowance each week, in how many weeks will you have the same amount of money?
Set up the problem in steps please
Answer: 11 weeks
Step-by-step explanation: 11 x 10 + 10 = $120 and 11 x 6 +54 = $120
I WILL MARK BRAINLIEST IF HELP!!
Answer:
a 20 X 40 X x
b just a guess but 2 centimeters
c 1600 or 800 depending on what x is
I only need help with number 1 and 2
Answer:
1. 12
2. 8
Step-by-step explanation:
\PLEASE MARK BRAINLIEST IT WILL HELP SM
Graph the line that passes through the points ( 0 , − 4) and (−5,2) and determine the equation of the line.
i am highly sorry but there is no graph for me to help you with on this site :(
but to help you the X line always comes first for example the (-5,2) the -5 would be on the X line. I really hope that this help. :)
How can it be done? Fill in the blank.
3,400 is______3,409*
Answer:
< or less than
Which is a simplified form of the expression 6(2t – 3) + 3(t + 5)?
A. 11t – 2
B. 12t – 8
C. 9t – 2
D. 15t – 3
Answer:
The answer is d I just got that one:)
Answer:
D
Step-by-step explanation:
I need help right away
Answer:
(0.3)
Go step by step and you will get it. I know that you can do it. Adios!
Write 8 1/3 as a proper fraction
Answer:
divde 81/3 to find 27
Step-by-step explanation:
The mixed fraction 8( 1/3 ) in the form of the proper fraction will be ( 25 / 3 ).
What is a fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction can also be an ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.
A mixed fraction is one that has both a quotient and a remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.
Given mixed fraction is 8 ( 1 / 3 ). The fraction will be solved by multiplying the whole number with the denominator and adding the numerator.
8 ( 1/3 ) = ( 24 + 1 ) / 3
8 ( 1/3 ) = ( 25 ) / 3
Therefore, the mixed fraction 8( 1/3 ) in the form of the proper fraction will be ( 25 / 3 ).
To know more about fractions follow
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Please help!
A.
B.
C.
D.
Answer: its b
Step-by-step explanation:
Hailey wants to brighten up her front yard by adding some flowers. She decides on zinnias and marigolds. She wants more than 3 trays of marigolds, which cost $12.00 each, and at least 5 trays of zinnias, which cost $10.00 each. How many of each can she buy if she has a budget of $150.00? Let the number of zinnias = and the number of marigolds = .
Answer:
5 Marigolds and 9 Zinnias
Step-by-step explanation:
5x12=60
9×10=90
90+60=150
So that is your answer
Hailey can buy at least 5 trays of marigolds and 9 trays of zinnias with a budget of $150.00.
Let's solve the problem step by step. Let the number of trays of zinnias that Hailey buys be represented by the variable 'Z', and the number of trays of marigolds be represented by the variable 'M'.
Each tray of marigolds costs $12.00, so the total cost of the marigolds would be 12M. Hailey wants more than 3 trays of marigolds, so M > 3.
Similarly, each tray of zinnias costs $10.00, so the total cost of the zinnias would be 10Z. Hailey wants at least 5 trays of zinnias, so Z ≥ 5.
Hailey has a budget of $150.00, so the total cost of the flowers cannot exceed $150.00. Therefore, we can write the following inequality:
12M + 10Z ≤ 150
To find the possible values of M and Z that satisfy the given conditions, we can use trial and error or a systematic approach. Let's check a few values that satisfy the given conditions:
For M = 4 and Z = 5:
12(4) + 10(5) = 48 + 50 = 98, which is less than $150.00, so this is a valid solution.
For M = 5 and Z = 9:
12(5) + 10(9) = 60 + 90 = 150, which is equal to $150.00, so this is also a valid solution.
Other possible combinations could be M = 6 and Z = 5, M = 6 and Z = 6, and so on.
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what is the number that have 6 odd factors?
Answer:
840 has 6 odd factors
Step-by-step explanation:
A local television station runs 2.5 minutes of commercials during every 30 minutes of programming. At this rate, how many minutes of commercials will run from 7:00 a.m. until 9:30 a.m.?
Answer:
12.5 minutes of commercials
Step-by-step explanation:
9:30 - 7:00 = 2 and a half hours on air = 150 minutes.
150 / 30 = 5
5 x 2.5 = 12.5
Answer:
92 minutes or 1 hour and 42 minutes
Step-by-step explanation:
i need help right aways plz help
In the student council election, Davina received 50 votes, Binh received 40 votes and Eden received 80 votes. What is the ratio of Binh’s votes to Davina’s votes in simplest form?
A
5 to 4
B
4 to 5
C
1 to 2
D
4 to 17
Answer:
4:5
Step-by-step explanation:
Binh's = 40
Davina's = 50
40:50 = 4:5
find the missing length the triangles are similar
Answer:
13
Step-by-step explanation:
The triangle we need to find out one of the measurements for has one length of 11, the similar triangle has a length of 22.
22 divided by 2 is 11 there for 26 divided by 2 is 13.
Convert the given amount to the given unit
4. 63 yd; feet
5. 168h; days
6. 2.5lb; ounces
7. 200 cm; meters
8. 4 min; seconds
9. 5kg; pounds
Answer:
4- 189 feet
5- 7 days
6- 40 ounces
7- 2 meters
8- 240 seconds
9- 11 lbs
Step-by-step explanation: