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katrin [286]
3 years ago
12

Why do you think rates are usually written as unit rates?

Mathematics
2 answers:
stellarik [79]3 years ago
6 0
Coooooooooooooooooooooool
Elden [556K]3 years ago
6 0
It's so you can compare two rates

For example, 
person A walks 10 miles in 2 hours
person B walks 40 miles in 4 hours

If you want to know who is the faster walker, then you divide the distance over the time
person A's speed = distance/time = 10/2 = 5 miles per hour
person B's speed = distance/time = 40/4 = 10 miles per hour

So we can see that person B is faster as 10 is larger than 5. This is only possible by comparing the unit rates of 5 mph (for person A) and 10 mph (for person B)
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PLEASE HELPPP
MAXImum [283]
The complete question is

Khianna is trying to help her neighbor Mrs. Johnson design and estimate the cost of a new square patio to be made from 16 inch square pavers. The pavers are sold in boxes of 12 and cost $99.99

 Part I: Scale Drawing

Decide on a scale factor to represent the distance covered by the patio. Then, use the space below to design Mrs. Johnson’s patio to be a square that is at least 8 feet on each side.

 a) Scale Factor: ____________________________

 b) Use a straightedge and a ruler to draw to scale a design for Mrs. Johnson’s patio:

c) What are the dimensions of Mrs. Johnson’s patio?

<span>d) Calculate the area of Mrs. Johnson’s patio.  Show all work. 

</span> <span>e) How many pavers will be needed?  Show all work.

</span> <span>f) What will it cost to build the patio?  Show all work. 

</span>

Part II: Bigger Design

There is a saying that bigger is better, so why not double the dimensions of Mrs. Johnson’s patio to make the side measurement twice as big? Mrs. Johnson and I think that it would better meet her needs.  After seeing the original estimation, she thinks that she could afford to double the size. I explained that making the patio twice as big would mean twice the cost. Mrs. Johnson says, “Let’s do it!”

<span>a) What would be the new dimensions of Mrs. Johnson’s patio?

</span> <span>b) Calculate the new area of Mrs. Johnson’s patio.  Show all work. 

</span> <span>c) How many pavers will be needed for the new design?  Show all work.

</span> <span>d) What will it cost to build the bigger patio?  Show all work. 

</span> <span>e) Is Khianna right?  Will doubling the size of the patio, double the cost?
</span>

ANSWERS 

Part I: Scale Drawing
Decide on a scale factor to represent the distance covered by the patio. Then, use the space below to design Mrs. Johnson’s patio to be a square that is at least 8 feet on each side.
 a) Scale Factor: 1 in/ 2 ft 
Use a straightedge and a ruler to draw to scale a design for Mrs. Johnson’s patio
b) see the picture attached
Mrs. Johnson’s patio to be a square that is 10 ft x 10 ft
c) What are the dimensions of Mrs. Johnson’s patio? the dimensions of Mrs. Johnson’s patio are 10 ft x 10 ft
d) Calculate the area of Mrs. Johnson’s patio.  Show all work.  

area of the square=b²
where
 b is the length side of the square
b=10 ft
so
 Area=10²-----> area of Mrs. Johnson’s patio=100 ft²

e) How many pavers will be needed?  Show all work. 

we know that
1 paver is 16 in x 16 in dimensions
convert in to ft
1 ft----------->12 in
x ft-----------> 16 in
x=16/12-----> x=4/3 ft
so
1 paver is (4/3) ft x (4/3) ft dimensions
area of one paver=(4/3)²----> 16/9 ft²

if one paver has an area of----------------> 16/9 ft²
x pavers----------------------->  100 ft²
x=100/(16/9)------> x=100*9/16-----> x=56.25 pavers

if one box --------------> 12 pavers
x box---------> 56.25 pavers
x=56.25/12-----> x=4.68 box-------> x=5 boxes
5 boxes of pavers will be needed 

f) What will it cost to build the patio?  Show all work. 
 the cost of one box is--------> $99.99
5 boxes-----------> x
x=5*$99.99------>x=$499.95
the cost to build the patio is $499.95

Part II: Bigger Design
There is a saying that bigger is better, so why not double the dimensions of Mrs. Johnson’s patio to make the side measurement twice as big? Mrs. Johnson and I think that it would better meet her needs.  After seeing the original estimation, she thinks that she could afford to double the size. I explained that making the patio twice as big would mean twice the cost. Mrs. Johnson says, “Let’s do it!”
 
a) What would be the new dimensions of Mrs. Johnson’s patio?
 the new  dimensions of Mrs. Johnson’s patio are 20 ft x 20 ft

b) Calculate the new area of Mrs. Johnson’s patio.  Show all work.
area of the square=b²
where
 b is the length side of the square
b=20 ft
so 
Area=20²-----> new area of Mrs. Johnson’s patio=400 ft² 
 
c) How many pavers will be needed for the new design?  Show all work. 
1 paver is (4/3) ft x (4/3) ft dimensions
area of one paver=(4/3)²----> 16/9 ft²
if one paver has an area of----------------> 16/9 ft²
x pavers----------------------->  400 ft²
x=400/(16/9)------> x=400*9/16-----> x=225 pavers

if one box --------------> 12 pavers
x box---------> 225 pavers
x=225/12-----> x=18.75 box-------> x=19 boxes
19 boxes of pavers will be needed 

d) What will it cost to build the bigger patio?  Show all work.
  the cost of one box is--------> $99.99
19 boxes-----------> x
x=19*$99.99------>x=$1899.81
the cost to build the bigger patio is $1899.81

e) Is Khianna right?  Will doubling the size of the patio, double the cost?
Khianna is wrong, <span>doubling the dimensions, the area quadruples, therefore also costs quadruple</span>

6 0
3 years ago
Read 2 more answers
Set Q contains 20 positive integer values. The smallest value in Set Q is a single digit value and the largest value in Set Q is
Lerok [7]

Answer: possible values of Range will be values that are >=91 or <=998

Step-by-step explanation:

Given that :

Set Q contains 20 positive integer values. The smallest value in Set Q is a single digit value and the largest value in Set Q is a three digit value.

Therefore,

given that the smallest value in set Q is a one digit number :

Then lower unit = 1, upper unit = 9( this represents the lowest and highest one digit number)

Also, the largest value in Set Q is a three digit value:

Then lower unit = 100, upper unit = 999 ( this represents the lowest and highest 3 digit numbers).

Therefore, the possible values of the range in SET Q:

The maximum possible range of the values in set Q = (Highest possible three digit value - lowest possible one digit) = (999 - 1) = 998

The least possible range of values in set Q = (lowest possible three digit value - highest possible one digit value) = (100 - 9) = 91

5 0
3 years ago
(5/7) to the power of 4 i need to know as a fraaction
yuradex [85]

Answer:

625/2401

Step-by-step explanation:

5/7 ^ 4 = 5 * 5 * 5 * 5 / 7*7*7*7 = 625/2401

8 0
3 years ago
Read 2 more answers
Is the sequence {4, 7, 10, 13, 16, ...} a function? Explain.
jek_recluse [69]

Step-by-step explanation:

tricky, as the sequence does not define the input values.

by we can assume that the corresponding input values are 1, 2, 3, 4, 5, ... as it is usual for a sequence.

in that sense, b is the correct answer.

3 0
2 years ago
What is the least common denominator of the fraction 2 over x plus the fraction x over x plus 1 plus the fraction x plus 1 over
Anna71 [15]
3x is the least common denominators because you need to be able to make sure all other denominators can go multiple into it.  Since the rest are just x, the largest number of 3x would be the denominator you want. 
5 0
3 years ago
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