The fraction of boys to total students would be 5/8
The fraction of boys to girls would be 5/3
Answer:
=−12x+4
Step-by-step explanation:
−6(
−2
/3
+2x)
=(−6)(
−2
/3
+2x)
=(−6)(
−2
/3
)+(−6)(2x)
=4−12x
=−12x+4
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
<h3>What is the composite function of f(x) and g(x)?</h3>
The composite function of f(x) and g(x) is given as follows:
![(f \circ g)(x) = f(g(x))](https://tex.z-dn.net/?f=%28f%20%5Ccirc%20g%29%28x%29%20%3D%20f%28g%28x%29%29)
In this problem, the functions are:
.
The composite function is of the given functions f(x) and g(x) is:
![f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}](https://tex.z-dn.net/?f=f%28g%28x%29%29%20%3D%20f%28%5Csqrt%7Bx%20%2B%203%7D%29%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%20%2B%203%7D%20-%203%7D)
The square root has to be non-negative, hence the restriction relative to the square root is found as follows:
![x + 3 \geq 0](https://tex.z-dn.net/?f=x%20%2B%203%20%5Cgeq%200)
![x \geq -3](https://tex.z-dn.net/?f=x%20%5Cgeq%20-3)
The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:
![\sqrt{x + 3} - 3 \neq 0](https://tex.z-dn.net/?f=%5Csqrt%7Bx%20%2B%203%7D%20-%203%20%5Cneq%200)
![\sqrt{x + 3} \neq 3](https://tex.z-dn.net/?f=%5Csqrt%7Bx%20%2B%203%7D%20%5Cneq%203)
![(\sqrt{x + 3})^2 \neq 3^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bx%20%2B%203%7D%29%5E2%20%5Cneq%203%5E2)
![x + 3 \neq 9](https://tex.z-dn.net/?f=x%20%2B%203%20%5Cneq%209)
![x \neq 6](https://tex.z-dn.net/?f=x%20%5Cneq%206)
Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:
[–3, 6) ∪ (6, ∞)
More can be learned about composite functions at brainly.com/question/13502804
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Answer:
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Step-by-step explanation:
Answer:
The number of tiles the rug will cover is 54 tiles
Step-by-step explanation:
Here we have,
Total area covered by the rug = 18 ft²
Size of one tile = 1/3 ft²
Therefore the number of tiles that can fit into the the area is given by;
Total area of the rug ÷ Area of one tile
= 18 ft² ÷ 1/3 ft²
Here we note that we are dividing a number by a fraction which is the same as multiplying the number by the inverse of the fraction as follows
= 18 × 3/1 ft²/ft² = 54 tiles
The number of tiles the rug will cover = 54 tiles.