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seropon [69]
2 years ago
15

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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Two types of defects are observed in the production of integrated circuit boards. It is estimated that 6% of the boards have sol
aalyn [17]

Answer:

(a) 0.09

(b) 0.06

(c) 0.0018

(d) 0.9118

(e) 0.03

Step-by-step explanation:

Let <em>A</em> = boards have solder defects and <em>B</em> = boards have surface defects.

The proportion of boards having solder defects is, P (A) = 0.06.

The proportion of boards having surface-finish defects is, P (B) = 0.03.

It is provided that the events A and B are independent, i.e.

P(A\cap B)=P(A)\times P(B)

(a)

Compute the probability that either a solder defect or a surface-finish defect or both are found as follows:

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

=P(A)+P(B)-P(A\cap B)+P(A\cap B)\\=P(A)+P(B)\\=0.06+0.03\\=0.09

Thus, the probability that either a solder defect or a surface-finish defect or both are found is 0.09.

(b)

The probability that a solder defect is found is 0.06.

(c)

The probability that both defect are found is:

P(A\cap B)=P(A)\times P(B)\\=0.06\times0.03\\=0.0018

Thus, the probability that both defect are found is 0.0018.

(d)

The probability that none of the defect is found is:

P(A^{c}\cup B^{c})=1-P(A\cup B)\\=1-P(A)-P(B)+P(A\cap B)\\=1-P(A)-P(B)+[P(A)\times P(B)]\\=1-0.06-0.03+(0.06\times0.03)\\=0.9118

Thus, the probability that none of the defect is found is 0.9118.

(e)

The probability that the defect found is a surface finish is 0.03.

6 0
3 years ago
Your favorite video game just went on sale for 33% off.
abruzzese [7]

Answer:

$40.20

Step-by-step explanation:

60 / 100 = 0.6

0.6 x 33 = 29.8

60 - 29.8 = 40.2

Thus he price after the discount would be $40.20

3 0
2 years ago
A european business has offered to donate to the Salvation Army, but they are requiring a detailed report on expenditures. Chase
dedylja [7]

Answer:

Both processes are correct.

Step-by-step explanation:

Let the mile taken by Chase be 10miles .

He doubles it so it will be 20 and

20% of 20 will be 4

20-4 = 16km

Now Alex operations

(10/5 )*8 = 2*8= 16 km

In both cases the answer will be the same

1 mile = 1.60034 km

Now 10 miles = 16.00 34 km

which is the same as above.

Both the processes are correct.

7 0
3 years ago
Solve the equation. y + 6 = –3y + 26
stiks02 [169]

Answer:

Step-by-step explanation:

3y+y = 26-6

4y = 20

4y/4 = 20/4

y = 5

4 0
3 years ago
Read 2 more answers
How do you round 25.691 to the greatest place explain
spayn [35]

In order to round 25.691 to the greatest place or the nearest whole number, first start at the last digit behind the decimal, in the case, being the 1. When it comes to things like this, if the digit is 4&under meaning its the number 4,3,2,1 or 0. If it is 5&up, that means it could be 5-9, making the digit go up (but if its 2, then the digit just goes away, you wont have to worry about that one specific number).

Next step is to round the 9 which makes the 6 go up one digit (meaning it turns into a 7). Now, when you round the seven, it will make the whole number go up one digit, but if you want to round that as well, to start, it's first rounding equaled up to 26. If you're rounding it to a whole tens number, it would be 30. I hope that this helps you understand this subject or topic much better! :3

7 0
3 years ago
Read 2 more answers
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