It was found that an unknown solid had a density of 20 g/cm3 and a volume of 30 cm3. Determine the mass of the solid.

You have 64 coins, consisting of pennies, nickels, and quarters. The value of

Romashka-Z-Leto [24]

Answer:

There are 20 pennies, 33 nickels and 11 quarters

Step-by-step explanation:

- You have 64 coins, consisting of pennies, nickels, and quarters

- The value of the coins is $4.60

- Assume that there are p pennies, n nickles, and q quarters

∴ p + n + q = 64 ⇒ (1)

- Lets find the value of each types of coins

∵ 1 penny = 1 cent ⇒ p = p cents

∵ 1 nickel = 5 cents ⇒ n = 5n cents

∵ 1 quarter = 25 cents ⇒ q = 25q cents

∵ 1 dollar = 100 cents ⇒ $4.60 = 4.60 × 100 = 460 cents

∴ p + 5n + 25q = 460 ⇒ (2)

- You also know that you have three times as many nickels as quarters

∴ n = 3q ⇒ (3) ⇒ the number of nickles by quarters

∵ 5n = 5(3q)

∴ 5n = 15q ⇒ (4) ⇒ the values of nickles by quarters

- Substitute (3) in equation (1) and (4) in equation (2)

∴ p + 3q + q = 64

∴ p + 4q = 64 ⇒ (5)

∴ p + 15q + 25q = 460

∴ p + 40q = 460 ⇒ (6)

- Subtract equation (5) from equation(6) to eliminate p

∴ 36q = 396

- Divide both sides by 36

∴ q = 11

- Substitute the value of q in equation (5)

∴ p + 4(11) = 64

∴ p + 44 = 64

- Subtract 44 from both sides

∴ p = 20

- Substitute the value of q in (3)

∴ n = 3(11) = 33

∴ n = 33

<em>There are 20 pennies, 33 nickels and 11 quarters</em>

6 0

3 years ago

Read 2 more answers

Sergio plans to drive 150 miles at a rate of 60 miles per hour. He figures that it will take 25 hours. Which is NOT a reason why

Tanzania [10]

Answer:

B

Step-by-step explanation:

This is a distance-rate-time problem, so we need to use the equation: $d=rt$ , where d is the distance, r is the rate, and t is the time.

Here, we know that the total distance is 150, so d = 150. Also, we are given that Sergio's rate is 60 mph, so r = 60. Put these in:

d = rt

150 = 60t

To solve for t, we divide both sides by 60. Because we are dividing and not multiplying, we know that B is the only one that is incorrect.

Hope this helps!

7 0

4 years ago

Read 2 more answers

Nancy is making cookies for a bake sale. She needs a total of 4 pounds of chocolate chips. She has a 28-ounce bag of chocolate c

Westkost [7]

How many ounces are in a pound? 16! SO 16 times 4 = 64. So Nancy needs 64 ounces in all. So 28 plus 10 = 38 that's still not enough, so lets add some more 38 plus 10 = 48 still not enough, add some more 48 plus 10 plus 10 = 68. So lets add up how many bags we need. So in all with her 28 that she already has, we need 4 bags.

4 0

3 years ago

100 POINTS!!! PLEAAASSEEE HELP ME!!!!

DIA [1.3K]

Answer:

2/3 = 5/8

Step-by-step explanation:

If two figures are similar, then the ratio of its corresponding sides is equal and is called the scale factor

In this problem

2/3 = 5/8 -----> is not true

therefore

The figures are not similar

8 0

3 years ago

Read 2 more answers

Angelica colored in 0.60 of the squares on her grid. What is the expression 0.60 as tenth in fraction

xz_007 [3.2K]

If I understand the question correctly, 6/10.

8 0

4 years ago