1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
QveST [7]
1 year ago
14

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

ine runs. A worker records how many bottles are filled on four consecutive days and how many hours the machine runs on those days. The worker's data are shown in the table.

Mathematics
1 answer:
Whitepunk [10]1 year ago
3 0

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.

You might be interested in
A golfer keeps track of his score for playing nine holes of golf​ (half a normal golf​ round). His mean score is 8080 with a sta
solniwko [45]

Answer:

Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and 11\sqrt2 respectively.

Step-by-step explanation:

Given that,

For the first 9 holes X:

E(X) = 80

SD(X)=13

For the second 9 holes Y:

E(Y) = 80

SD(Y)=13

For the sum W=X+Y, the following properties holds for means , variance and standard deviation :

E(W)=E(X)+E(Y)

     and

V(W)=V(X)+V(Y)

⇒SD²(W)=SD²(X)+SD²(Y)        [ Variance = (standard deviation)²]

\Rightarrow SD(W)=\sqrt{SD^2(X)+SD^2(Y)}

∴E(W)=E(X)+E(Y) = 80 +80=160

            and

∴SD(W)=\sqrt{SD^2(X)+SD^2(Y)}

              =\sqrt{11^2+11^2}

               =\sqrt{2.11^2}

               =11\sqrt2

Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and 11\sqrt2 respectively.

                                               

4 0
3 years ago
I NEED IMMEDIATE HELP!!
DENIUS [597]

It A because the two mirror each other so you can simplify them to (3x−5)^2.

7 0
3 years ago
Read 2 more answers
Consider the function: f(x) = 2x^2 - 1.5x - 5 and its graph.
Dominik [7]

Answer:

f(x) = -4x² + 19x - 18

Step-by-step explanation:

f(x) = 2x^2 - 1.5x - 5

i) If it is translated 2 units in the positive x direction, therefore we use f(x-2)

y=f(x-2) = 2(x-2)^2 - 1.5(x-2) - 5\\y = 2(x^2-4x+4) - 1.5x+3 - 5\\y=2x^2-8x+8-1.5x+3-5\\y=2x^2-9.5x+6

f(x) = 2x² - 9.5x + 6

If it is then translated 3 units in the positive y, we add 3 to the input function to get:

y=f(x)+3=2x^2-9.5x+6+3\\y = 2x^2-9.5x+9

ii) stretched vertically by a factor of 2, we multiply the function by 2 to get:

y =2( 2x^2-9.5x+9) = 4x^2-19x+18\\y= 4x^2-19x+18

iii) reflected across the x-axis

we multiply the parent function by –1, to get a reflection about the x-axis.

y= -1(4x^2-19x+18)=-4x^2+19x-18\\y=f(x)=-4x^2+19x-18

5 0
3 years ago
There are 54 people at the party, 18 of them are wearing red. What percent of people are not wearing red?
forsale [732]
Number of person not wearing red: 54 - 18 = 36

Then percentage: 36/54 = 66.7%
7 0
3 years ago
Read 2 more answers
Which expression is equivalent to 2.3 x 2.3 x 2.3 x 2.3 x 2.3?
aev [14]

The expression (2.3)⁵ is equivalent to 2.3 x 2.3 x 2.3 x 2.3 x 2.3

4 0
2 years ago
Read 2 more answers
Other questions:
  • An envelope is 3 inches wide, and it measures 7 inches along the diagonal. What is the envelope’s length? If necessary, round to
    9·1 answer
  • X and y-intercept of y=X-5
    15·1 answer
  • If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.
    11·2 answers
  • How many zeros does this equation have?
    6·2 answers
  • Round 132874015 to the nearest hundreds-thousands.
    7·2 answers
  • 22. The measures of the angles of ADEF are in the ratio 2:4:4. What are the
    5·1 answer
  • How do you multiply polynomials by using the distributive property?
    13·1 answer
  • Two statements are given-one labeled Assertion (A) and the other labeled Reason(R). Select the correct answer to these questions
    8·1 answer
  • The volume of a cone is represented by the formula V = 1 T?n. If the volume of a cone is 30rt and the height is 2.5, what is the
    5·1 answer
  • A trapezoid has a height of 10 centimeters. One parallel base has a length of 7 centimeters, and the other parallel base has a l
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!