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stiv31 [10]
3 years ago
9

Which is one of the transformations applied to the graph of f(x)=x^2 to change it into the graph of g(x)=4x^2+24x*30?

Mathematics
1 answer:
AfilCa [17]3 years ago
5 0

Answer:

Changing g(x) to this form: a(x-h) + k, we have:

g(x) = 4 (x+3)^2 - 6

Comparing this to the original equation, f(x) = x^2, we have the following transformations:

The graph is widened.

The graph is shifted left 3 units.

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Verify that the functions are probability mass functions, and determine the requested probabilities.
Free_Kalibri [48]

Answer:

a) 3/64 = 0.046 (4.6%)

b) 63/64 = 0.9843 (98.43%)

c) 1/64 = 0.015 (1.5%)

d) 1/4 = 0.25 (25%)

Step-by-step explanation:

in order to verify that the f(x) is a probability mass function , then it should comply the requirement that the sum of probabilities over the entire space of x is equal to 1. Then

∑f(x)*Δx = 1

if f(x)=(3/4)(1/4)^x , x = 0, 1, 2, ...

then Δx=1 and

∑f(x) = (3/4)∑(1/4)^x = (3/4)* [ 1/(1-1/4)] = (3/4)*(4/3) = 1

then f represents a probability mass function

a) P(X = 2)= f(x=2) = (3/4)(1/4)^2 = 3/64 = 0.046 (4.6%)

b) P(X ≤ 2) = ∑f(x) =  f(x=0)+ f(x=1) + f(x=2) = (3/4) + (3/4)(1/4) +  3/64 = 63/64 = 0.9843 (98.43%)

c) P(X > 2)= 1- P(X ≤ 2) = 1 - 63/64 = 1/64 = 0.015 (1.5%)

d) P(X ≥ 1) = 1 - P(X < 1) = 1 - f(x=0) = 1- 3/4 = 1/4 = 0.25 (25%)

4 0
3 years ago
Given the relationship x2 + 3y2 =12, with y &gt; 0 and dx, dt = 2 units/min., find the value of dy, dt at the instant y = 1 unit
matrenka [14]
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\bf \textit{now, when y = 1, what is \underline{x}?}\qquad x^2+3y^2=12\implies x^2+3(1)^2=12&#10;\\\\\\&#10;x^2=9\implies x=\sqrt{9}\implies x=3\\\\&#10;-------------------------------\\\\&#10;\begin{cases}&#10;y=1\\&#10;x=3\\&#10;\frac{dx}{dt}=2&#10;\end{cases}\implies \cfrac{dy}{dt}=-\cfrac{3\cdot 2}{3\cdot 1}\implies \cfrac{dy}{dt}=-2
7 0
2 years ago
A board game has a spinner divided into sections of equal size. Each section is labeled with a number between 1 and 5. Which num
Valentin [98]

Answer:

75

Step-by-step explanation:

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3 0
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Fedex typically deleviers 2,400 packages per day and uses 75 trucks for delivery. If the number of trucks used per day is propor
irina1246 [14]

Answer:

A

Step-by-step explanation:

8 0
2 years ago
I need some help with geometry?​
kramer
39=9x+7-3x+20

Subtract 27 from each side

12=6x
2=x

Now plug in 2 for x to find AB and BC

9x+7= AB
9(2)+7=AB
18+7= AB
25= AB

-3x+20= BC
-3(2)+20= BC
-6+20= BC
14= BC
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2 years ago
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