77) How many 3-digit numbers can be made from the set (3,4,5,6) if no digit can appear more than once in the same number?
(I got 24)
78) Under the current tax law, tax payers calculate the amount be which their yearly medical expenses exceed 2% of their yearly income. Last year, Veronica had an income of $115,000 and medical expenses of $32,000. By what amount did her yearly medical expenses exceed 2% of her yearly income?
(I got $900)
81) Light travels about 186,000 miles per second. About how many miles does light travel in one hour? Answer in scientific notation.
(I got 6.70 x 10^8)
77) is correct
78) does not match my answer. 32000 is way more than 2% of 115,000 A good bench mark number would be 10%. 10% of 115000 is 11000. And she paid 32000$
81) is rounded correctly : )
OH WAIT . ITS $3,200! I'm sorry! If this is the medical expense would it be $900
YES, now it is a much better answer : )
It is mathematically correct : )
Haha okay thank you!
77) To solve this question, we need to determine how many 3-digit numbers can be formed using the set (3, 4, 5, 6) without repeating any digits.
First, let's consider the hundreds place. Since a 3-digit number cannot start with zero, we have three options for the hundreds digit (3, 4, and 5).
Then, for the tens place, we can choose any of the remaining three digits (since we cannot repeat the digit in the hundreds place).
Finally, for the units place, we have two remaining digits to choose from.
Multiplying the number of options for each place value, we get: 3 x 3 x 2 = 18.
Therefore, there are 18 different 3-digit numbers that can be formed using the set (3, 4, 5, 6) without repeating any digits.
78) To find the amount by which Veronica's yearly medical expenses exceed 2% of her yearly income, we can use the following steps:
1. Calculate 2% of Veronica's yearly income: 2% of $115,000 = ($115,000 x 2) / 100 = $2,300.
2. Subtract this amount from her actual medical expenses: $32,000 - $2,300 = $29,700.
Therefore, Veronica's yearly medical expenses exceed 2% of her yearly income by $29,700.
81) To determine how many miles light travels in one hour, we can use the following calculation:
Light travels at a speed of approximately 186,000 miles per second.
To find how many miles it travels in one hour, we need to multiply this speed by the number of seconds in an hour.
There are 60 seconds in a minute, and 60 minutes in an hour, so there are 60 x 60 = 3,600 seconds in an hour.
Therefore, light travels 186,000 miles per second x 3,600 seconds per hour = 669,600,000 miles per hour.
To express this in scientific notation, we move the decimal point to the left until there is only one digit to its left. In this case, we move the decimal point seven places to the left, giving us 6.70.
Since we moved the decimal point seven places to the left, the exponent of 10 is 7. Therefore, the answer is 6.70 x 10^7 (not 6.70 x 10^8 as you mentioned).