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2 years ago

What is f(–3) for the function f(a) = –2a2 – 5a + 4?

Mathematics

2 answers:

Dmitriy789 [7]2 years ago

9 0

F(−3)=−18+15+4
And the result is:
f(−3)=1
This is the answer.

tino4ka555 [31]2 years ago

4 1

Follow the order of operation (PEMDAS) giving you 31

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Example 4.5 introduced the concept of time headway in traffic flow and proposed a particular distribution for X 5 the headway be

exis [7]

Answer:

a. k = 3

b. Cumulative distribution function X, $F(x)=\left \{ {0} , x\leq 1 \atop {1-x^{-3}, x>1}} \right.$

c. Probability when headway exceeds 2 seconds = 0.125

Probability when headway is between 2 and 3 seconds = 0.088

d. Mean value of headway = 1.5

Standard deviation of headway = 0.866

e. Probability that headway is within 1 standard deviation of the mean value = 0.9245

Step-by-step explanation:

From the information provided,

Let X be the time headway between two randomly selected consecutive cars (sec).

The known distribution of time headway is,

$f(x) = \left \{ {\frac{k}{x^4} , x > 1} \atop {0} , x \leq 1 } \right.$

a. Value of k.

Since the distribution of X is a valid density function, the total area for density function is unity. That is,

$\int\limits^{\infty}_{-\infty} f(x)dx=1$

So, the equation becomes,

$\int\limits^{1}_{-\infty} f(x)dx + \int\limits^{\infty}_{1} f(x)dx=1\\0 + \int\limits^{\infty}_{1} {\frac{k}{x^4}}.dx=1\\0 + k \int\limits^{\infty}_{1} {\frac{1}{x^4}}.dx=1\\k[\frac{x^{-3}}{-3}]^{\infty}_1=1\\k[0-(\frac{1}{-3})]=1\\\frac{k}{3}=1\\k=3$

b. For this problem, the cumulative distribution function is defined as :

$F(x) = \int\limits^1_{\infty} f(x)dx + \int\limits^x_1 f(x)dx$

Now,

$F(x) = 0 + \int\limits^x_1 {\frac{k}{x^4}}.dx\\= 0 + \int\limits^x_1 3x^{-4}.dx\\= 3 \int\limits^x_1 x^{-4}dx\\= 3[\frac{x^{-4+1}}{-4+1}]^3_1\\= 3[\frac{x^{-3}}{-3}]^3_1\\=(\frac{-1}{x^3})|^x_1\\=(-\frac{1}{x^3}-(\frac{-1}{1}))=1- \frac{1}{x^3}=1-x^{-3}$

Therefore the cumulative distribution function X is,

$F(x)=\left \{ {0} , x\leq 1 \atop {1-x^{-3}, x>1}} \right.$

c. Probability when the headway exceeds 2 secs.

Using cdf in part b, the required probability is,

$P(X>2)=1-P(X\leq 2)\\=1-F(2)\\=1-[1-2^{-3}]\\=1-(1- \frac{1}{8})\\=\frac{1}{8} = 0.125$

Probability when headway is between 2 seconds and 3 seconds

Using the cdf in part b, the required probability is,

$P(2$

≅ 0.088

d. Mean value of headway,

$E(X)=\int\limits x * f(x)dx\\=\int\limits^{\infty}_1 x(3x^{-4})dx\\=3 \int\limits^{\infty}_1 x(x^{-4})dx\\=3 \int\limits^{\infty}_1 x^{-3}dx\\=3[\frac{x^{-3+1}}{-3+1}]^{\infty}_1\\=3[\frac{x^{-2}}{-2}]^{\infty}_1\\=3[\frac{1}{-2x^2}]^{\infty}_1\\=3[- \frac{1}{2x^2}]^{\infty}_1\\=3[- \frac{1}{2(\infty)^2}- (- \frac{1}{2(1)^2})]\\=3(\frac{1}{2})=1.5$

And,

$E(X^2)= \int\limits^{\infty}_1 x^2(3x^{-4})dx\\=3 \int\limits^{\infty}_1 x^{-2} dx\\=3[- \frac{1}{x}]^{\infty}_1\\=3(- \frac{1}{\infty}+1)=3$

The standard deviation of headway is,

$= \sqrt{V(X)}\\ =\sqrt{E(X^2)-[E(X)]^2} \\=\sqrt{3-(1.5)^2} \\=0.8660254$

≅ 0.866

e. Probability that headway is within 1 standard deviation of the mean value

$P(\alpha - \beta < X < \alpha + \beta) = P(1.5-0.866 < X < 1.5 +0.866)\\=P(0.634 < X < 2.366)\\=P(X$

From part b, F(x) = 0, if x ≤ 1

$=1-(2.366)^{-3}\\=0.9245$

8 0

2 years ago

Rob is a geologist. He is surveying a conical crater that was created by a meteor impact. From one end to another, the crater fo

skelet666 [1.2K]

Answer:

equation: d(h) = 0.25|h -1600| -400
depth is 250 ft at 1000 ft and 2200 ft from the west edge

Step-by-step explanation:

The crater shape can be modeled by an absolute value function with a slope of 0.25. The vertex of the function will not be at (0, 0) but will be at (1600, -400). The usual methods of translating functions apply. Horizontal displacement of the vertex is subtracted from the independent variable; vertical displacement is added to the function value.

d(h) = 0.25×|h -1600| -400

We know the horizontal displacement is 1600 ft, because the depth changes at a rate of 1/4 foot for each horizontal foot. A depth change of 400 feet will require 1600 horizontal feet to accomplish.

At a depth of 250 ft, the distance from the west edge can be found from ...

-250 = 0.25|h -1600| -400

150 = 0.25|h -1600| . . . . . . . . add 400

600 = |h -1600| . . . . . . . . . . . multiply by 4

This resolves to two equations:

-600 = h -1600 ⇒ h = 1000
600 = h -1600 ⇒ h = 2200

The depth is 250 ft at distances of 1000 ft and 2200 ft from the west edge.

_____

<em>Comment on the equation</em>

We have chosen to make depths be negative numbers. If you want the equation to give positive numbers for depth, multiply it by -1:

d = 400 -0.25×|h -1600|

7 0

2 years ago

The manager at Gabriela's Furniture Store is trying to figure out how much to charge for a book shelf that just arrived. The boo

maria [59]

The shelf should sell for $235.20.

Marking the price up by 60% means taking 160% of the cost:
160% = 160/100 = 1.6; 1.6(147) = 235.20

5 0

2 years ago

Read 2 more answers

Bernard solved the equation 5x+(-4)=6x+4 using algebra tiles. Which explains why Bernard added 5 negative x-tiles to both sides

densk [106]

A) He wanted to create zero pairs on the left side of the equation to get a positive coefficient of x on the right side

7 0

2 years ago

Read 2 more answers

a car travels 30 1/2 miles in 2/3 of an hour. what is the average speed, in miles per hour, of the car ?

Contact [7]

Answer:

speed=225.75 miles per hour

Step-by-step explanation:

given:

s=301/2

t=2/3

we have,

v=s/t

v=(301/2)/(2/3)

=(301/2)×3/2

=903/4

v=225.75

therefore, speed of car will be 225.75 miles per hour

6 0

1 year ago