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2 years ago

Find the equation of the line shown

Mathematics

2 answers:

Mariana [72]2 years ago

4 0

Answer:

From the graph, the y-intercept is 9 and the slope is -1 so the equation is y = -x + 9. We know the slope is -1 because when x goes up by 1, y decreases by 1.

tigry1 [53]2 years ago

4 0

Step-by-step explanation:

When we know both the x- and y-intercepts of a line, we can conveniently use the intercept form.

Let

A=x-intercept=9

B=y-intercept=9

the intercept form of the equation is therefore

x/A + y/B =1

substituting numerical values,

x/9 + y/9 =1 ..........................(1)

Factoring the identical denominators

(x+y)/9 = 1

Cross multiply

x+y = 9 ...............................(2)

Both (1) and (2) are valid forms of equation of the given line.

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2 years ago

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

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"a pollster wishes to estimate the number of left-handed scientists. how large of a sample is needed in order to be 98% confiden

nadezda [96]

The sample size should be 250.

Our margin of error is 4%, or 0.04. We use the formula

$\text{ME}=z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

To find the z-score:
Convert 98% to a decimal: 0.98
Subtract from 1: 1-0.98 = 0.02
Divide both sides by 2: 0.02/2 = 0.01
Subtract from 1: 1-0.01 = 0.99

Using a z-table (http://www.z-table.com) we see that this value has a z-score of approximately 2.33. Using this, our margin of error and our proportion, we have:

$0.04=2.33\sqrt{\frac{0.08(1-0.08)}{n}}
\\
\\0.04=2.33\sqrt{\frac{0.08(0.92)}{n}}$

Divide both sides by 2.33:
$\frac{0.04}{2.33}=\sqrt{\frac{0.08(0.92)}{n}}$

Square both sides:
$(\frac{0.04}{2.33})^2=\frac{0.08(0.92)}{n}$

Multiply both sides by n:
$(\frac{0.04}{2.33})^2n=0.08(0.92)$

Divide both sides to isolate n:
$\frac{0.08(0.92)}{(\frac{0.04}{2.33})^2}=n
\\
\\249.73=n
\\n\approx 250$

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2 years ago