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Vlad [161]
3 years ago
6

Which expression is equal to 5^4 x 5^8 ? A: 5^12 B: 5^4 C: 5^2 D: 5^−4

Mathematics
2 answers:
galben [10]3 years ago
6 0

Something to remember is how to multiply terms with same bases, but different exponents:

a^b \cdot a^c = a^{(b+c)}


Essentially, we add the exponents.


Using the information above, we can find our answer:

5^4 \cdot 5^8 = 5^{(4+8)} = \boxed{5^{12}}


Our answer is \boxed{5^{12}}, or A.

podryga [215]3 years ago
6 0

It equals 5^12

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Of the cars sold during the month of July, 89 had air conditioning, 99 had an automatic transmission, and 74 had power steering.
DedPeter [7]

Answer:

There are a total of 23 cars with air conditioning and automatic transmission but not power steering

Step-by-step explanation:

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
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