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3 years ago

Consider these functions

Mathematics

1 answer:

vitfil [10]3 years ago

5 0

9514 1404 393

Answer:

C. 3x² +24

Step-by-step explanation:

Use the given function definitions and simplify.

$g(f(x))=g\left(\dfrac{1}{3}x^2+4\right)\\\\=9\left(\dfrac{1}{3}x^2+4\right)-12\\\\=3x^2+36-12\\\\\boxed{g(f(x))=3x^2+24}\qquad\textbf{matches C}$

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The radius of the dinner table is 12.5mm calculate the area of the dinner table by using 3.14 to two decimal places

Makovka662 [10]

Answer:

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Step-by-step explanation:

7 0

3 years ago

400 Suppose a particular surveillance system has a 99% chance of correctly identifying a future terrorist and a 99.8% chance of

alexgriva [62]

Answer:

1.236 × 10^(-3)

Step-by-step explanation:

Let A be the event that the person is a future terrorist

Let B the event that the person is identified as a terrorist

We are told that there are 1,000 future terrorists in a population of 400 million. Thus, the Probability that the person is a terrorist is;

P(A) = 1000/400000000

P(A) = 0.0000025

P(A') = 1 - P(A)

P(A') = 1 - 0.0000025

P(A') = 0.9999975

We are told that the system has a 99% chance of correctly identifying a future terrorist. Thus; P(B|A) = 0.99

Thus, P(B'|A) = 1 - P(B|A)

P(B'|A) = 1 - 0.99

P(B'|A) = 0.01

We are told that there is a 99.8% chance of correctly identifying someone who is not a future terrorist. Thus; P(B'|A') = 0.998

Hence: P(B|A') = 1 - P(B'|A')

P(B|A') = 1 - 0.998

P(B|A') = 0.002

We want to find the probability that someone who is identified as a terrorist, is actually a future terrorist. This is represented by: P(A|B)

We can find it from bayes theorem as follows;

P(A|B) = [P(B|A) × P(A)]/[(P(B|A) × P(A)) + (P(B|A') × P(A')]

Plugging in the relevant values;

P(A|B) = [0.99 × 0.0000025]/[(0.99 × 0.0000025) + (0.002 × 0.9999975)]

P(A|B) = 0.00123597357 = 1.236 × 10^(-3)

8 0

3 years ago

What is the solution of the system? Use substitution.<br><br> y = 6x + 2<br> 3y - 18x = 12

kicyunya [14]

3(6x+2)-18x=12 (y=6x+2, so you plug in 6x+2 into the y in 3y-18x=12)
18x+6-18x=12 (Then you distribute the 3 to the 6x and to the 2)
6=12 (Combine like terms 18x-18x)

There is no solution. Hope this helps and makes sense.

5 0

3 years ago

Read 2 more answers

Please help me with this. It needs to be done soon, so I’d appreciate anyone who answers this.

creativ13 [48]

Answer:

A. 4 1/2 ==+ 3

B. 2 + 4

C. 1/2 + 1/2

D. 2 1/2 + 1

E. 4 1/2 + 2

Step-by-step explanation:

Read the coordinates and just like figure out the order which it's like 1 through 5 but wit fractions. hope this helps.

8 0

3 years ago

You roll a 4-sided die repeatedly. On your odd-numbered rolls (1st,3rd,5th, etc.) you are victorious if you get a 4. On your eve

Sunny_sXe [5.5K]

Answer:

E (Y) = 3

Step-by-step explanation:

If a 4-sided die is being rolled repeatedly; and the odd-numbered rolls (1st 3rd,5th, etc.)

The probability of odd number roll will be, p(T) = $\frac{1}{2}$

However, on your even-numbered rolls, you are victorious if you get a 3 or 4. Also, the probability of even number roll, p(U) = $\frac{1}{2}$

In order to calculate: E (Y); We can say Y to be the number of times you roll.

We know that;

E (Y) = E ( Y|T ) p(T) + E ( Y|U ) p(U)

Let us calculate E ( Y|T ) and E ( Y|U )

Y|T ≅ geometric = $\frac{1}{4}$

Y|U ≅ geometric = $\frac{1}{2}$

also; x ≅ geometric (p)

∴ E (x) = $\frac{1}{p}$

⇒ $\frac{Y}{T}$ = 4 ; also $\frac{Y}{U}$ = 2

E (Y) = 4 × $\frac{1}{2}$ + 2 ×

= 2+1

E (Y) = 3

7 0

3 years ago