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Jet001 [13]
3 years ago
10

The function below shows the number of car owners f(t), in thousands, in a city in different years t: f(t) = 0.25t2 − 0.5t + 3.5

The average rate of change of f(t) from t = 2 to t = 6 is ______ thousand owners per year. Answer for Blank 1:
Mathematics
1 answer:
N76 [4]3 years ago
5 0
We solve this by the definition of slope in analytical geometry. The definition of slope is the rise over run. In equation, that would be

m = Δy/Δx = (y₂-y₁)/(x₂-x₁)

The x-coordinates here are the t values, while the y-coordinates are the f(t) values. So, let's find the y values of the boundaries.

At t=2: f(t)= 0.25(2)²<span> − 0.5(2) + 3.5 = 3.5
Point 1 is (2, 3.5)
At t=6: </span>f(t)= 0.25(6)² − 0.5(6) + 3.5 = 9.5
Point 2 is (6, 9.5)

The slope would then be

m = (9.5-3.5)/(6-2)
m = 1.5

Hence, the slope is 1.5. Interpreting the data, the rate of change between t=2 and t=6 is 1.5 thousands per year.
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Answer:

c .3.3

Step-by-step explanation:

pH is the negative log of the molar hydrogen ion concentration.The equation to calculate pH is;

pH = -log10[H+]

pH = -log10(5.0 x 10-4)

pH = 3.30

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3 years ago
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An airplane takes off from an airport and travels 1100 miles east and then travels 600 miles north. This trip can be plotted on
IgorLugansk [536]

Answer:

The plane is now at (1100, 600) in unit mile

Step-by-step explanation:

The airport is the point (0 ,0) and the plane travels from there 1100 miles east and thereafter 600 miles north. If the unit is in mile then we may say that the planes co -ordinates are now (1100 , 600)

Since,

positive x -axis points towards east and positive y-axis points towards north.

4 0
3 years ago
What number have the absolute value of 8
Agata [3.3K]

Answer:

4

Step-by-step explanation:

half of 8 is 4 . a absolute value you halfing the number

4 0
3 years ago
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Which of the following are equivalent to the statement “the price decreased by 1/3”?
Fittoniya [83]

Therefore, the only statement that is equivalent to <em>"the </em><em>price decreased</em><em> by </em>\frac{1}{3}<em>"</em> is:

<u>F. The price is now </u><u>66, 2/3% </u><u>of what it was before</u>

<u />

<u />

Given that the original price of something decreased by 1/3, it means:

the original price is reduced by one-third.

  • One-third is not equal to half of the price.

  • 1/3 is less than 1/2.

  • 1/3 of the original price would be \frac{1}{3} \times 100 = 33.3% less of the original price.

  • This means that the new price would be: <em><u>100 - 33 = 66% of the </u></em><em><u>original price.</u></em> This shows a reduction in price. The price would drop.

  • 1/3 is more than a quarter (1/4).

<em>Any option showing or suggesting an increase is definitely the wrong answer.</em>

Therefore, the only statement that is equivalent to <em>"the </em><em>price decreased</em><em> by </em>\frac{1}{3}<em>" </em>are:

<u><em>F. The price is now </em></u><u><em>66, 2/3% </em></u><u><em>of what it was before</em></u>

Learn more here:

brainly.com/question/11293133

7 0
2 years ago
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Polly stacked the tins from five boxes of cat food onto an empty shelf in a supermarket. There were 15 tins of cat food in each
Alexandra [31]

Answer:

(a) 3\frac{2}{3} boxes of cat food had been sold.

(b) \frac{11}{3} boxes of cat food had been sold.

Step-by-step explanation:

From the question,

Polly stacked the tins from five boxes of cat food onto an empty shelf and there were 15 tins of cat food in each box. That is,

5 × 15 tins of cat food were stacked onto the empty shelf.

5 × 15 = 75

Hence, 75 tins of cat food were stacked onto the empty shelf.

Also, from the question,

At the end of the week there were 20 tins left on the shelf and the rest of the tins had been sold, that is

75 - 20 tins had been sold

75 - 20 = 55

Hence, 55 tins of cat food had been sold.

To determine the number of boxes of cat food that had been sold,

Since there are 15 tins of cat food per box, then

we will divide 55 tins of cat food that had been sold by 15 tins of cat food per box

55 ÷ 15 = \frac{55}{15}

Hence, \frac{55}{15} boxes of cat food had been sold

(a) As a mixed number

\frac{55}{15}  = 3\frac{2}{3}

Hence, 3\frac{2}{3} boxes of cat food had been sold.

(b) As an improper fraction

\frac{55}{15}  = \frac{11}{3}

Hence, \frac{11}{3} boxes of cat food had been sold.

7 0
3 years ago
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