During a recent test in his Business Skills class, Lionel typed 207 words in 5 minutes .

9. Water is added to two containers for 16 minutes. The equations below model the ounces of

Vladimir [108]

The two containers hold 328 ounces at the they hold same amount of water.

<u>Step-by-step explanation:</u>

The equations below model the ounces of water, y, in each container after x minutes.

$y = 16x + 104$

$y = -2x^{2} +40x+160$

At the time after the start when the containers hold the same amount of water, the two equations must be equal.

⇒ $16 x + 104 = -2x^{2} + 40 x + 160$

The first step is to divide everything by 2 to make it simplified.

⇒ $8 x + 52 = - x^2 +20 x + 80$

Now put everything on the left .

$x^2 + 8 x - 20 x + 52 - 80 = 0$

Add the like terms together to further reduce the equation

$x^2 - 12 x - 28 = 0$

Factorizing the equation to find the roots of the equation.

Here, b = -12 and c = -28

where,

b is the sum of the roots ⇒ -14 + 2 = -12
c is the product of the roots ⇒ -14 × 2 = -28

Therefore, (x-14) (x+2) = 0
The solution is x = -2 or x = 14

Take x = 14 and substitute in any of the given two equations,

⇒ $y = 16(14) + 104$

⇒ $y =224+104$

⇒ 328 ounces

∴ The two containers hold 328 ounces at the they hold same amount of water.

5 0

3 years ago

Dwayne plays five games of rock-paper-scissors. In order to seem unpredictable, he never chooses the same move (rock, paper, or

Andreyy89

Answer:

48

Step-by-step explanation:

First, in this problem, you would assume that there are five numbers to multiply since Dwayne played 5 games.

In the first blank, he could choose any move, and there are three, rock, paper, and scissors. In the first blank, you would put 3. Then, since you already picked one, you can't repeat it, so you would end up with 2 for the second blank. Continuing with the next blanks, the third, fourth, and fifth spaces would be 2 choices because you cannot have the one choice you chose previously. In the end, the blanks would look somewhat like this:

3 2 2 2 2

And you would multiply all the numbers.

3 x 2 x 2 x 2 x 2

= 6 x 8

= 48

6 0

3 years ago

In one year, a school uses 13,170 pieces of white paper, 6,570 fewer pieces of blue paper than white paper, and 3,300 fewer piec

SIZIF [17.4K]

Answer:

23,070

Step-by-step explanation:

13,170-6570=6600

6600-3300=3300

13,170+6600+3300=23,070

The school uses 23,070 pieces of paper

3 0

3 years ago

Read 2 more answers

The following table shows the number of hours some teachers in two schools expect students to spend on homework each week: Schoo

Lerok [7]

Answer:

For school A: Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17, IQR=9.5

For school B: Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19, IQR=7.5

No, the box plots are not symmetric.

Step-by-step explanation:

Part A

The given data sets are

School A : 9,14,15,17,17,7,15,6,6

School B : 12,8,13,11,19,15,16,5,8

Arrange the data in ascending order.

School A : 6,6,7,9,14,15,15,17,17

School B : 5,8,8,11,12,13,15,16,19

Divide each data set in four equal parts.

School A : (6,6),(7,9),14,(15,15),(17,17)

School B : (5,8),(8,11),12,(13,15),(16,19)

For school A:

Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17

Interquartile range of the data is

$IQR=Q_3-Q_1=16-6.5=9.5$

For school B:

Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19

Interquartile range of the data is

$IQR=Q_3-Q_1=15.5-8=7.5$

Part B:

The box plots are not symmetric because the data values are different. Five number summary and IQR of both the data set are different.

4 0

3 years ago

In a Harris Interactive survey of 2276 adults in the United States, it was found that 33% of those surveyed never travel using c

S_A_V [24]

Answer:

Population: Adults in the United States

Sample: 2276 adults in the United States

33% is a statistic.

Step-by-step explanation:

The population consists of adults in the United States because that is the wider range, and the sample is 2276 of those adults.

The value 33% is an statistic due to the definitions of both words. A statistic is defined as a fact or piece of data obtained from a study of a large quantity of numerical data. While a parameter is a numerical or other measurable factor forming one of a set that defines a system or sets the conditions of its operation.

5 0

3 years ago