405 is what percent of 6750

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.

3 0

1 year ago

What is the Volume if the Mass = 35g and Density = 5g/cm^3 ?

VLD [36.1K]

density = mass / volume

4 = 35 / v

v = 35/4 = 8.75 cm^3

6 0

3 years ago

Determine the unknown side of the similar triangle. A) 8 B) 12 C) 18 D) 24

blsea [12.9K]

Answer:

B-12

Step-by-step explanation:

Since 24÷12=2 you have to do 6×2 to find the ? and 6×2=12

8 0

3 years ago

Write down the exact value of: a) cos 30° b) sin 45° c) tan 30°

Alexus [3.1K]

Answer:

a) 0.86602540378

b) 0.70710678118

c) 0.57735026919

Step-by-step explanation:

4 0

3 years ago

What is the probability that a student eye color would be blue if their grade in physics is A? A two way table is presented belo

Zarrin [17]

The correct answer is:

16/45.

Explanation:

We want the probability that a student's eye color is blue if they made an A in physics. This means we look at the column for students with an A.

There are 32 students with blue eyes in the A column.

This is out of 32+58=90 students that made an A.

This makes the probability 32/90, which simplifies to 16/45.

8 0

2 years ago