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3 years ago

If 1/2 gallon of paint covers 1/5 of a wall, then how much paint is needed for the entire wall

1 answer:

6 0

2 1/2 gallons of paint.

If 1/2 gallon covers 1/5 of the wall, multiply 1/2 gallon by 5 to find how much is needed to cover 5/5, or the entire wall. You get 5/2. Now, simplify. 5/2 = 2 1/2 gallons of paint.

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Noel and Casey both start at the same place. Noel walks due south and Casey walks due east. After some time has passed, Noel is

Dovator [93]

Answer:

2.04 miles per hour

Step-by-step explanation:

Given

Noel

$n_1 =6miles$

$r_1 = 2mph$

Casey

$c_1 = 8miles$

$r_2 =1mph$

Required

The rate at which the distance increases

Their movement forms a right triangle and the distance between them is the hypotenuse.

At $n_1 =6miles$ and $c_1 = 8miles$

The distance between them is:

$d_1 = \sqrt{n_1^2 + c_1^2}$

$d_1 = \sqrt{6^2 + 8^2}$

$d_1 = \sqrt{100}$

$d_1 = 10miles$

After 1 hour, their new position is:

New = Old + Rate * Time

$n_2 = n_1 + r_1 * 1$

$n_2 = 6 + 2 * 1 = 8$

And:

$c_2 = c_1 + r_2 * 1$

$c_2 = 8 + 1 * 1 = 9$

So, the distance between them is now:

$d_2 = \sqrt{n_2^2 + c_2^2}$

$d_2 = \sqrt{8^2 + 9^2}$

$d_2 = \sqrt{145}$

$d_2 = 12.04$

The rate of change is:

$\triangle d = d_2 -d_1$

$\triangle d = 12.04 -10$

$\triangle d = 2.04$

5 0

2 years ago

4 square feet is equivalent to how many square yards?

s2008m [1.1K]

Answer:

4 square feet = 0.444444444 square yards

Step-by-step explanation:

5 0

3 years ago

A machine at a bottling company fills water bottles. the number of bottles filled is proportional to the amount of time the mach

Whitepunk [10]

In the table shown below:

Let N be the number of bottles filled,

Let T be the time in hours.

Given that the number of bottles filled is proportional to the amount of time the machine runs, we have

$\begin{gathered} N\propto T \\ \text{Introducing a proportionality constant, we have } \\ N\text{ = kT} \\ \Rightarrow k\text{ = }\frac{N}{T} \\ \end{gathered}$

Let's evaluate the value of k for each day.

Thus, on monday,

$\begin{gathered} N\text{ = 9900} \\ T\text{ = 5.5} \\ \text{thus,} \\ k\text{ = }\frac{9900}{5.5} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Tuesday:

$\begin{gathered} N\text{ = }11160 \\ T\text{ = }6.2 \\ \text{thus,} \\ k\text{ = }\frac{11160}{6.2} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Wednesday:

$\begin{gathered} N\text{ = }12330 \\ T\text{ = }6.25 \\ \text{thus,} \\ k\text{ = }\frac{12330}{6.25} \\ \Rightarrow k\text{ = 1972.8} \end{gathered}$

Thursday:

$\begin{gathered} N\text{ = }10440 \\ T\text{ = }5.80 \\ \text{thus,} \\ k\text{ = }\frac{10440}{5.8} \\ \Rightarrow k=1800 \end{gathered}$

It is observed that all exept wednesday have the same value of k.

Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as

$\begin{gathered} N\text{ = }12330 \\ k\text{ = 1800} \\ T\text{ = ?} \\ \text{but} \\ k\text{ = }\frac{N}{T} \\ 1800\text{ = }\frac{12330}{T} \\ \Rightarrow T\text{ = }\frac{\text{12330}}{1800} \\ T\text{ = 6.85} \end{gathered}$

Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.