1/3bag = 1 day
1/3bag x ? days = 1 1/3 bags
1/3d = 1 1/3 or 4/3
divide each side by 1/3 or multiply each side by its inverse 3/1
1/3 * 3/1 d = 4/3 * 3/1
the 1’s and 3’s cancel each other out on the left and the 3’s cancel each other out on the right.
You are left with d = 4
The food will last 4 days.
Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:
- Set up a proportion using the corresponding parts
- Solve the proportion to find the missing measure
<h3>What is Reduction?</h3>
Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.
Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:
Set up a proportion using the corresponding parts
10/8 = 4/x
Solve the proportion using cross products to find x:
10x = (8)(4)
10x = 32
x = 32/10
x = 3.2 cm
The missing length is 3.2 cm.
Learn more about reduction on:
brainly.com/question/10362588
#SPJ1
Answer:
Step-by-step explanation:
We'll use rule of exponents to simplify expression.
Now, use the commutative property of multiplication.
In order to multiply power of the same base, we add their exponents.
→ Add exponents:
→ Multiply 3* -8
__________________________________________
The number of trays that contain both a cup and a plate = 11.
<h3>What are sets?</h3>
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind
To find the elements in the sets A and B, we refer to the formula:
n(A) + n(B) - n(A∪B) = n(A∩B),
where,
- n(A) = number of elements in set A,
- n(B) = number of elements in set B,
- n(A∪B) = number of elements that are either in set A or B,
- n(A∩B) = number of elements that are in both the sets A and B.
Given:
- Number of trays on a table: 25
- Each tray has either:
- only a cup
- only a plate
- both cup and plate
- Trays containing cups = 15
- Trays containing plates = 21
To find: number of trays containing both cup and plate.
Finding:
Let the number of trays containing cups be C and those containing plate be P.
Then, n(C) = number of tray containing only cups = 15
n(P) = number of tray containing only plates = 21
n(C∩P) = ?
Since, each plate contains at least a cup or a plate, n(U) = total number of trays = n(C∪P) = number of trays containing either a cup or a plate
=> n(C∪P) = 25
By the formula of sets: n(A) + n(B) - n(A∪B) = n(A∩B),
We get: n(C∩P) = 15 + 21 - 25 = 15 - 4 = 11
Hence, the number of trays that contain both a cup and a plate = 11.
To learn more about sets, refer to the link: brainly.com/question/13458417
#SPJ4