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3 years ago

The average price of a certain type of coffee worldwide was $0.51 per pound in 2008. The

Mathematics

2 answers:

Vilka [71]3 years ago

5 0

Answer:

b. graph

Step-by-step explanation:

y axis is at 0.5 and it increase more horizontal- not the steep one

zaharov [31]3 years ago

3 0

Answer:

The graph is attached

Step-by-step explanation:

The graph that will represent the relationship between t years after 2008, and the price P per pound will have some characteristics that we can identify.

In 2008, i.e at t= 0, P = 0.51; this means the y-intercept is 0.51.

The coffee price is increasing by 0.18 every year; the slope is 0.18.

Thus we have the equation

$P =0.18t+0.51$

the graph of which is attached.

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Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

2 years ago

James is selecting a marble. James chooses a marble at random and then replaces it. He then selects a second marble at random. W

tresset_1 [31]

Answer:

The probability of selecting a solid black marbles both times;

P = 9/100

Attached is the completed question;

Step-by-step explanation:

Number of solid black marbles = 3

Total number of marbles = 10

The probability of selecting a solid black marble;

P1 = 3/10

With the assumption that the marbles are replaced before next selection.

The probability of selecting a solid black marbles both times;

P = P1 × P1 = 3/10 × 3/10 = 9/100

P = 9/100

7 0

2 years ago

The product of two consecutive even integers is 360360. find the integers.

professor190 [17]

There are no 2 consecutive integers which give a product 360360

5 0

3 years ago

A cube has a volume of 729 cubic inches. What is the length of each edge? Explain

Kipish [7]

Answer:

$The\:length\:of\:each\:edge\:is\:9$

Step-by-step explanation:

$Volume\:of\:cube:V=a^{3} \:(a\:is\:the\:length\:of\:each\:edge)\\\Leftrightarrow a=\sqrt[3]{V} \Leftrightarrow a=\sqrt[3]{729} =9$

7 0

3 years ago

A high school spends approximately $9,000 hosting a football games (e.G. The hourly pay for staff, the electricity, water usage,

Yanka [14]

Answer:

$4800

Step-by-step explanation:

The expected net income is the probability when rains multiplied by net income (profit) summed with the probability of not raining with that days net income multiplied.

First, Chance of rain = 12% = 12/100 = 0.12

Profit/Loss = Income - Cost

Income is 5000

Cost = 9000

So,

Loss = 5000 - 9000 = 4000

Or, Net Income (profit) = - 4000

Now, Change of not raining = 100 - 12 = 88% = 88/100 = 0.88

Profit = Income - Cost

Income = 15,000

Cost = 9000

Net Income (profit) = 15000 - 9000 = 6000

So, we can write the expected net income as:

Expected NI = (0.12)(-4000) + (0.88)(6000) = $4800

8 0

2 years ago