Step-by-step explanation:
According to PEMDAS parentheses are first.
2(6+1) can be simplified to 12+2.
5(3+2) can be simplified to 15+10
Add these two together.
12+2+15+10
14+15+10
29+10
y=39
Note - when you have something like this in math 2(6+1) it means you need to do 2 x 6 and 2 x 1
Answer: There are 35 spellers participated in the spelling bee.
Step-by-step explanation:
Since we have given that
Rank of Anish's placement at the highest = 11 th
Rank of Anish's placement at the lowest = 25 th
We need to find the number of spellers participated in the spelling bee.
So, Number of spellers participated in the spelling bee is given by
Highest + Lowest - 1
= 11 + 25 - 1
= 36 - 1
= 35
Hence, there are 35 spellers participated in the spelling bee.
<span>1,
During a 1-hr television program, there were 22 commercials, Some
commercials were 15 sec and some were 30 sec long. Find the number of
15- sec commercials and the number of 30 sec commercial if the total
playing time for commercial was 9.5 minutes.
</span>a) <span>show how to formulate your system of equations for your problem,
Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language
b) state the two equations:
- translate the word statement into algebraic equations:
</span><span>* there were 22 commercials => x + y = 22
* the total playing
time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>
Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y = 570
c) state which method you will use to solve either addition or substitution
Answer:
adition: multiply the first equation times - 15 and add the two equations.
d) solve your system showing and explaining each step of the process
Answer:
- muliply eq (1) times - 15
-15x - 15y = - 330
- add that to the eq (2):
-15x + 15x - 15y + 30y = -330 + 570
- add like terms: 15y = 240
- divide both members by 15: 15y/15 = 240 / 15 => y = 16
- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6
Solution: x = 6, y = 16
e) Be sure to check your solution!
x + y = 22
6 + 16 = 22
22 = 22 --> check
15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check
f) Once a solution is found explain what this solution means in the context
of the problem, write the answer to the word problem in words</span><span>
The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.
2, How many quarts of water should be mixed with a 30% vinegar solution
to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>
a) variables:
- state the variables
x: number of quarters of water
y: number of quarters of vinegar
- translate the words into mathematical language
12 qt 25% vinegar solution
=> total number of quarts = 12 = x + y
balance in vinegar:
vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution
0 + 0.3y = 0.25 (x + y)
c) Equations
Eq (1) x + y = 12
Eq (2): 0.3y = 0.25x + 0.25y
=> 0.25x - 0.05y = 0
d) solve
- multiply eq (1) times 0.05 and add to eq (2)
0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6
x = 0.6 / 0.3 = 2
x + y = 12 => y = 12 - y = 12 - 2 = 10
Solution: x = 2, y = 10
e) check:
x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check
vinegar:
10*0.3 = 12*0.25
3 = 3 -> check
f) Explanation of the solution
The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.
Answer:
242.52 cubic inches
Step-by-step explanation:
Volume of the cake pan = Length × Width × Height
From the about question, we have the following dimensions for the cake pan
8 inches wide = Width
11 inches long = Length
7 cm deep = Height
We are asked to find the maximum volume in inches. Hence all the dimensions have to be in inches.
Converting Height in cm to inches
From the question,
2.54 cm = 1 inch
7cm = x inch
Cross Multiply
2.54 × x = 7 × 1
x = 7/2.54
x = 2.7559055118 inches
Volume of the cake pan =
8 × 11 × 2.7559055118
= 242.51968504 cubic inches
Approximately, the volume of the cake pan = 242.52 cubic inches
What is the maximum volume, in cubic
inches, the cake pan can hold is 242.52 cubic inches
Answer:
Because it only has one answer and there are no variety of answers.
hope this helps
