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Tanya [424]
2 years ago
10

Let an optimus prime be a prime number whose digit sum is also a prime number. How

Mathematics
1 answer:
kodGreya [7K]2 years ago
4 0

Answer:

7

Step-by-step explanation:

2 = 2 ✓

3 = 3 ✓

5 = 5 ✓

7 = 7 ✓

11 = 1 + 1 = 2 ✓

13 = 1 + 3 = 4 ×

17 = 1 + 7 = 8 ×

19 = 1 + 9 = 10 ×

23 = 2 + 3 = 5 ✓

29 = 2 + 9 = 11 ✓

I hope this helps you :)

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Greg builds a new pond which has a volume of 7.35 m3. It is 4.2 m long and 50 cm deep. What is the width of the pond?
Morgarella [4.7K]

volume = length x width x depth

50cm = 0.5 m

7.35 = 4.2 x 0.5 x X

7.35 = 2.1 x  X

x = 7.35 / 2.1

x = 3.5

width = 3.5 meters


3 0
3 years ago
Read 2 more answers
A linear equation in two variables has infinitely many solution the set of all solutions to a linear equation in two variables f
Greeley [361]
<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.

5 0
3 years ago
Helen's house is located on a rectangular lot that is1 1-8 miles by 9/10 mile.Estimate the distance around the lot
klemol [59]

Answer: The distance around the lot is given by

4\frac{1}{20}\ miles

Step-by-step explanation:

Since we have given that

Length of rectangular lot is given by

1\frac{1}{8}\\\\=\frac{9}{8}\ miles

Width of rectangular lot is given by

\frac{9}{10}\ mile

We need to find the distance around the lot.

As we know the formula for "Perimeter of rectangle":

Perimeter=2(Length+Width)\\\\Perimeter=2(\frac{9}{8}+\frac{9}{10})\\\\Perimeter=2(\frac{45+36}{40})\\\\Perimeter=2\times \frac{81}{40}\\\\Perimeter=\frac{81}{20}\\\\Perimeter=4\frac{1}{20}\ miles

Hence, the distance around the lot is given by

4\frac{1}{20}\ miles


3 0
3 years ago
Read 2 more answers
James is participating in a 5-mile walk to raise money for a charity. he has received $200 in fixed pledgesand raises $20 extra
xxMikexx [17]
5x20=100 100+200=300 or atlas what i think if this is wrong i am sry but if isn't I'm glad I'm able to help ^u^

7 0
2 years ago
The population of a town increased from 10,550 to 16,275. What was the approximate percent of increase?
ss7ja [257]
I got 35% of an increase
6 0
3 years ago
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