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3 years ago

Given: f(x) = 3x² - 2x +1 and g(x) =x -4

Mathematics

1 answer:

Alja [10]3 years ago

3 0

Answer:

For finding f(g(x)) ~ (x - 4) = 3x^2 - 26x + 57

For finding g(f(x)) ~ g (3x^2 - 2x + 1) = 3x^2 - 2x - 3

Step-by-step explanation:

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What is the compound interest on investing $600 for 3 years at 7% per annum?

Marysya12 [62]

Answer:

About $735.03

Step-by-step explanation:

The compound interest formula is A=P(1+r/n)^nt

P is the original amount (principal)

r is the rate

n is the number of times compounded (1 for this one since it is annual)

and t is the time compounded

5 0

3 years ago

Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1

alexandr1967 [171]

Answer:

$a) \simeq 0.3012$ $b) \simeq 0.0494$ c) $\simeq 0.2438$

Step-by-step explanation:

Rate of collision,

1.2 collisions every 4 months

or, $\frac{1.2}{4}$

= 0.3 collisions per month

So, the Poisson distribution for the random variable no. of collisions per month (X) is given by,

P(X =x) = $\frac{e^{-\lambda}\times {\lambda}^{x}}}{x!}
$

for x ∈ N ∪ {0}

= 0 otherwise --------------------------------------(1)

here, $\lambda = 0.3$ collision / month

No collision over a 4 month period means no collision per month or X =0

Putting X = 0 in (1) we get,

P(X = 0) = $\frac{e^{-0.3}\times {\0.3}^{0}}{0!}
$

$\simeq 0.7408182207$ ------------------------------------(2)

Now, since we are calculating this for 4 months,

so, P(No collision in 4 month period)

= $0.7408182207^{4}$

$\simeq 0.3012$ -----------------------------------------------------------(3)

2 collision in 2 month period means 1 collision per month or X =1

Putting X =1 in (1) we get,

P(X =1) = $\frac{e^{-0.3}\times {\0.3}^{1}}{1!}
$

$\simeq 0.2222454662$ ------------------------------------(4)

Now, since we are calculating this for 2 months, so ,

P(2 collisions in 2 month period)

= $0.2222454662^{2}$

$\simeq 0.0494$ -----------------------------------------(5)

1 collision in 6 months period means

$\frac{1}{6}$ collision per month

Now, P(1 collision in 6 months period)

= P( X = 1/6] (which is to be estimated)

= $\frac {P(X=0)\times 5 + P(X =1)\times 1}{6}$

= \frac {0.7408182207 \times 5 + 0.2222454662 \times 1}{6}[/tex]

$\simeq 0.6543894283$ -------------------------------------------(6)

So,

P(1 collision in 6 month period)

= $0.6543894283^{6}$

$\simeq 0.0785267444$ ------------------------------------------------(7)

So,

P(No collision in 6 months period)

= $(P(X =0)^{6}$

$\simeq 0.1652988882$ ---------------------------------(8)

so,

P(1 or fewer collision in 6 months period)

= (8) + (7 ) = 0.0785267444 +0.1652988882

$\simeq 0.2438$ ---------------------------------------------(9)

7 0

3 years ago

Directions: Directions: Identify x1, x2, y1, and y2. Solve for the of the line passing through the given points. Identify if the

Arlecino [84]

Answer:

Remember you are just a normal account

8 0

3 years ago

Read 2 more answers

The volume of a pyramid that fits exactly inside a cube is 10 cubic feet. What is the volume of the cube?

Tatiana [17]

Answer:

the cubic feet will be 1000

6 0

3 years ago

What times 4/5 equals 3/4

bagirrra123 [75]

Answer:

15/16

Step-by-step explanation:

4/5 x=3/4

x=(3/4)/(4/5)

x=15/16

6 0

3 years ago