Bill must choose a number between 49 and 95 that is a multiple of 2, 8, and 12. Write all the numbers that he could choose. If there is more than one number, separate them with commas.
To find the numbers that are multiples of 2, 8, and 12 between 49 and 95, we need to first find the least common multiple (LCM) of the given numbers.
The prime factorization of 2 is $2 = 2^1$.
The prime factorization of 8 is $8 = 2^3$.
The prime factorization of 12 is $12 = 2^2\cdot 3^1$.
To find the LCM, we take the highest exponent of each prime factor that appears in any of the numbers:
$2^3\cdot 3^1 = 24$.
Therefore, the LCM of 2, 8, and 12 is 24.
The multiples of 24 between 49 and 95 are: 48, 72, 96.
However, since we are looking for numbers between 49 and 95, the only number that satisfies this condition is 72.
Therefore, the only number Bill can choose is $\boxed{72}$.
At a sale this week, a suit is being sold for $403. This is a 38% discount from the original price.
What is the original price?
Let's denote the original price as $x$.
We know that $38\%$ of the original price is equal to the discount.
This can be written as: $0.38x = x - 403$
To solve for the original price, we can isolate $x$ on one side of the equation:
Subtracting $0.38x$ from both sides yields: $0.62x = 403$
Finally, dividing both sides by $0.62$ gives us the original price:
$x = \dfrac{403}{0.62} \approx 651.61$
Therefore, the original price of the suit is approximately $\$651.61$.
write 9 and 3 over 4 as a decimal
To write the fraction 9 and 3/4 as a decimal, we first need to convert the mixed number to an improper fraction.
The whole number 9 can be rewritten as 9/1.
Thus, we have 9 and 3/4 as (9 × 4 + 3) / 4 = 39 / 4.
To turn this fraction into a decimal, we divide the numerator (39) by the denominator (4):
39 ÷ 4 = 9.75
Therefore, the decimal representation of 9 and 3/4 is 9.75.
write 42.5% as a fraction in simplest form.
To write 42.5% as a fraction in simplest form, we must divide the percentage by 100 and simplify if possible.
42.5% divided by 100 is equal to 0.425.
Now, to write 0.425 as a fraction, we can put the decimal value over 1:
0.425/1
To simplify this fraction, we can multiply both the numerator and denominator by 1000 to remove the decimal point:
(0.425 × 1000) / (1 × 1000) = 425 / 1000
Both the numerator and denominator can be divided by 25:
(425 ÷ 25) / (1000 ÷ 25) = 17/40
Therefore, 42.5% as a fraction in simplest form is 17/40.
Diane deposits $400 into an account that pays simple interest at a rate of 2% per year. How much interest will she be paid in the first 5 years?
To calculate the interest earned by Diane in the first 5 years, we need to multiply her initial deposit ($400) by the interest rate (2%) over the time period (5 years).
The formula for calculating simple interest is:
Interest = Principal × Rate × Time
In this case, the principal is $400, the rate is 2% (or 0.02 as a decimal), and the time is 5 years.
Interest = $400 × 0.02 × 5
Calculating this expression:
Interest = $40
Therefore, Diane will be paid $40 in interest in the first 5 years.