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3 years ago

Let f(x)=3x^2+x-3 and g(x)=x^2-5x+1. Find f(x)-g(x)

Mathematics

2 answers:

serg [7]3 years ago

7 0

Answer:

$2x^{2} + 6x - 4$

Step-by-step explanation:

$(3x^{2} + x - 3) - (x^{2} - 5x + 1) \\ 3x^{2} + x - 3 - x^{2} + 5x - 1 \\ combine\: like \: terms \\ 2x^{2} + 6x - 4$

notsponge [240]3 years ago

5 0

Subtract each term of g(x) from each corresponding term of f(x)

3x^2 - x^2 = 2x^2

X—5x = x +5x = 6x

-3 -1 =-4

Now combine them to get final answer:

2x^2 + 6x -4

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A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that t

Alina [70]

Answer:

75.76% probability that there will be 10 or more customers at this bank in one hour.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

A bank gets an average of 12 customers per hour.

This means that $\mu = 12$

Find the probability that there will be 10 or more customers at this bank in one hour.

Either there are less than 10 customers, or there are 10 or more. The sum of the probabilities of these events is 1. Then

$P(X < 10) + P(X \geq 10) = 1$

We want $P(X \geq 10)$

Then

$P(X \geq 10) = 1 - P(X < 10)$

In which

$P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-12}*12^{0}}{(0)!} \approx 0$

$P(X = 1) = \frac{e^{-12}*12^{1}}{(1)!} = 0.0001$

$P(X = 2) = \frac{e^{-12}*12^{2}}{(2)!} = 0.0004$

$P(X = 3) = \frac{e^{-12}*12^{3}}{(3)!} = 0.0018$

$P(X = 4) = \frac{e^{-12}*12^{4}}{(4)!} = 0.0053$

$P(X = 5) = \frac{e^{-12}*12^{5}}{(5)!} = 0.0127$

$P(X = 6) = \frac{e^{-12}*12^{6}}{(6)!} = 0.0255$

$P(X = 7) = \frac{e^{-12}*12^{7}}{(7)!} = 0.0437$

$P(X = 8) = \frac{e^{-12}*12^{8}}{(8)!} = 0.0655$

$P(X = 9) = \frac{e^{-12}*12^{9}}{(9)!} = 0.0874$

$P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0 + 0.0001 + 0.0004 + 0.0018 + 0.0053 + 0.0127 + 0.0255 + 0.0437 + 0.0655 + 0.0874 = 0.2424$

Then

$P(X \geq 10) = 1 - P(X < 10) = 1 - 0.2424 = 0.7576$

75.76% probability that there will be 10 or more customers at this bank in one hour.

3 0

4 years ago

Which is the axis of symmetry of a parabola with equation x^2=-4y?

Effectus [21]

Y=a(x-h)²+k

x=h is the axis of symmetry
so
-4y=x²
times both sides by -1/4
y=(-1/4)x²
y=(-1/4)(x-0)²+0
axis of symmetry is x=0

3rd option

7 0

3 years ago

Read 2 more answers

Castel and Chelsea are selling pies for a school fundraiser. Customers can buy cherry pies and lemon meringue pies. Castel sold

tiny-mole [99]

Answer:

the cost each of one cherry pie and one lemon meringue pie is 9 and $12 respectively

Step-by-step explanation:

The computation of the cost of one cherry pie and the lemon meringue pie is shown below:

Let us assume the cherry pie be x

And, the lemon meringue pie be y

So according to the question

x + 5y = $69

5x + 7y = $129

Now multiply by 5 in the equation 1

5x + 25y = $345

5x + 7y = $129

18y = $216

y = $12

And, x would be

x + 5($12) = $69

x = $9

Hence, the cost each of one cherry pie and one lemon meringue pie is 9 and $12 respectively

4 0

3 years ago

PLEASE HELP WITH MATH

lesantik [10]

Volume is length x width x height.

Calculate the volume of each rectangle and add them together.

7.5 x 7.5 x 3.55 = 199.6875

7.5 x 3.55 x 3.55 = 94.51875

Volume = 94.51875 + 199.6875 = 294.21 cubic meters

6 0

3 years ago

Read 2 more answers

17 − 2v = 41 solve v

anastassius [24]

17-2V=41

subtract 17 from both sides

-2v =24

v = 24 / -2 = -12

v=-12

3 0

3 years ago