6 times $0.97 plus $2.64 minus 20 equals $11.54 remaining on the gift card.
Answer:
<h2>
B. 9</h2>
Step-by-step explanation:
|<-------------- 27 ------------>|
L--------------M----------------N
18 MN
LN = LM + MN
27 = 18 + MN
MN = 27 - 18
<h2>
MN = 9</h2>
The question regards composite functions. A composite function is a function composed of more than one function. Sorry for saying the word function so many times there, it's just what it is...
The phrase f(g(x)) means 'perform g on an input x, then perform f on the result'. You can then see that there are many options for f(x) and g(x) here, in fact an infinite number of one were to be ridiculous about it.
However a sensible choice might be g(x) = x^2, and f(x) = 2/x + 9. Checking:
g(x) = x^2
f(g(x)) = 2/(x^2) + 9
That is the first question dealt with. Next up is Q2. It is relatively simple to show that these functions are inverses. If you start with a value x, apply a function and then apply the function's inverse, you should return to the same starting value x. To take a common example, within a certain domain, sin^-1(sin(x)) = x.
f(g(x)) = (sqrt(3+x))^2 - 3 = 3 + x - 3 = x
g(f(x)) = sqrt(x^2 - 3 + 3) = sqrt(x^2) = x
A final note is that this is only true for a certain domain, that is x <= 0. This is because y = x^2 is a many-to-one function, so unrestricted it does not have an inverse. Take the example to illustrate this:
If x = -2, f(x) = (-2)^2 - 3 = 4 - 3 = 1
Then g(f(x)) =sqrt(1 + 3) = sqrt(4) = 2 (principal value).
However the question isn't testing knowledge of that.
I hope this helps you :)
Step-by-step explanation:
The area of triangle given as 120 cm2
Area of Triangle = 1/2 x b x h = 120
therefore bxh = 240
240 can be factorized as 10 x 24
The perimeter of the triangle is given as 60
so the other side has to be 26 cm
As this is a right angle triangle it should satisfy pythagoras theorem
(10)2 + (24)2 = (26)2
100+576 =676
Hence the sides of the triangle are 10 cm, 24 cm and 26 cm
Total number of people in ward = 16
Number of nurses = 10
Number of male nurses = 4
Number of female nurses = 6
Number of doctors = 6
Number of male doctors = 3
Number of female doctors = 3
We are to find the probability of selecting a female or a doctor.
Probability of selecting a female or a doctor = Probability of selecting a female + probability of selecting a doctor - probability of selecting a female doctor
Probability of selecting a female or a doctor = 9/16 + 6/16 - 3/16 = 3/4
Thus, the probability of selecting a female or a doctor is 3/4