Let A be the cars that have Air conditioning, B the cars that have Automatic transmission and C the cars that have pwoer Steering. Lets denote |D| the cardinality of a set D.

Remember that for 2 sets E and F, we have that

$|E \cup F| = |E| + |F| - |E \cap F|$

Also,

|E| = |E ∩F| + |E∩F^c|

We now alredy the following:

|A| = 89

|B| = 99

|C| = 74

$|A \cap B \cap C| = 5$

|(A \cup B \cup C)^c| = 24

|A \ (B U C)| = 24 (This is A minus B and C, in other words, cars that only have Air conditioning).

|B \ (AUC)| = 65

|C \ (AUB)| = 26

$|B \cap C| = 11$

We want to know |(A∩B) \ C|. Lets calculate it by taking the information given and deducting more things

For example:

99 = |B| = |B ∩ C| + |B∩C^c| = 11 + |B∩C^c|

Therefore, |B∩C^c| = 99-11 = 88

And |A ∩ B ∩ C^c| = |B∩C^c| - |B∩C^c∩A^c| = |B∩C^c| - |B \ (AUC)| = 88-65 = 23.

This means that the amount of cars that have both transmission and air conditioning but now power steering is 23.

3 0

3 years ago

The function f(x)= square root of x is translated using the rule (x, y) → (x – 6, y + 9) to create A(x). Which expression descri

Alex73 [517]

The function $f(x)=\sqrt{x}$ is translated according to the rule

$(x,y)\rightarrow (x-6,y+9).$

This translation is translation 6 units to the left and 9 units up.

1. Translation of the function $f(x)=\sqrt{x}$ 6 units to the left gives you the function $g(x)=\sqrt{x+6}.$

2. Translation of the function $g(x)=\sqrt{x+6}$ 9 units up gives you the function $A(x)=\sqrt{x+6}+9.$

The domain of the function $A(x)$ is $[-6,\infty),$ then the range of the function $A(x)$ is $[9,\infty).$

Answer: $[9,\infty).$

4 0

3 years ago