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2 years ago

Given f(x)=2x^2-3 and g(x) = x+4 What is (fg)(x)?

Mathematics

1 answer:

Ira Lisetskai [31]2 years ago

4 0

Answer: $f(g(x))=2x^2+16x+29$

Step-by-step explanation:

$f(x)=2x^2-3\\g(x)=x+4$

f of g of x means "function f, replace x by the value of g of x"

$f(g(x))=2x^2-3\\f(g(x))=2(x+4)^2-3\\f(g(x))=2(x^2+8x+16)-3\\f(g(x))=2x^2+16x+32-3\\f(g(x))=2x^2+16x+29$

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Which event has exactly 12 possible outcomes?

lara [203]

Answer:

rolling a number cube with sides labeled 1 through 6 and tossing a coin.

Step-by-step explanation:

We will resolve each statement to determine the events that has exactly 12 possible outcomes.

N = number of possible outcomes for a cube

Nc = number of possible outcomes for a coin

Nca = number of possible outcomes for the cards

i. rolling a number cube with sides labeled 1 through 6 and then rolling the number cube again

Nt = N × N

N = 6 ( cube has 6 possible outcomes and its rolled twice)

Nt = 6 × 6 = 36

ii. tossing a coin and randomly choosing one of 4 different cards.

Nt = Nc × Nca

Nc = 2 ( coin has two outcomes)

Nca = 4 ( 4 possible cards )

B = 2 × 4 = 8

iii. rolling a number cube with sides labeled 1 through 6 and tossing a coin.

N = N × Nc

N = 6 ( cube has 6 possible outcomes)

Nc = 2 (coin has two faces)

N = 6 × 2 = 12 (correct)

Iv. tossing a coin 6 times.

N = Nc^6

Nc = 2

N = 2^6 = 64

Therefore, the correct answer is iii.

rolling a number cube with sides labeled 1 through 6 and tossing a coin.

3 0

3 years ago

Instructions: Match each equations with correct type of event.

Mazyrski [523]

The question is incomplete. Below you will find the missing contents.

The correct match of events with order are,

P(A)P(B|A) - Dependent event
P(A)+P(B) - Mutually exclusive events
P(A and B)/P(A) - Conditional events
P(A) . P(B) - Independent Events
P(A)+P(B) -P(A and B) - not Mutually exclusive events.

When two events A and B are independent then,

P(A and B)=P(A).P(B)

when A and B are dependent events then,

P(A and B) = P(A) . P(B|A)

When two events A and B are mutually exclusive events then,

P(A and B)=0

So, P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B)

P(A) + P(B) = P(A or B)

When events are not mutually exclusive then the general relation is,

P(A or B) = P(A) + P(B) - P(A and B)

If the probability of the event B conditioned by A is given by,

$\mathrm{P(B|A)=\frac{P(A~and~B)}{P(A)}}$

Hence the correct match are -

$\mathrm{P(A)P(B|A)\rightarrow}$ Dependent event
$\mathrm{P(A)+P(B)}\rightarrow$ Mutually exclusive events
$\mathrm{\frac{P(A ~and ~B)}{P(A)}\rightarrow}$ Conditional events
$\mathrm{P(A) . P(B)\rightarrow}$ Independent Events
$\mathrm{P(A)+P(B) -P(A ~and ~B)\rightarrow}$ not Mutually exclusive events.

Learn more about Probability of Events here -

brainly.com/question/79654680

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1 year ago

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2 years ago

If a rectangle has a length of 4 square root of 2 and a width of 7 square root of 18 what

Orlov [11]

Answer:8^4 + 14^36 is the perimeter because they are for sides in a rectangle so you have to double the amount.

7 0

2 years ago

Is 12.54 greater than 12.539?

Damm [24]

Answer:

yes

Step-by-step explanation:

12.54

12.53

reason why is because of the 4>5

8 0

2 years ago

Read 2 more answers