Answer:
The statement "There is an integer that is divisible by 6 and is also divisible by 8, but is not divisible by 48." is true.
Step-by-step explanation:
Consider the provided information.
We need to prove that there exist an integer that is divisible by 6 and is also divisible by 8, but is not divisible by 48 with the help of an example.
The prime factors of the number 6 is:
6 = 2 × 3
The prime factors of the number 8 is:
8 = 2 × 2 × 2
Now the Least Common Multiple of the number 6 and 8 is:
2 × 2 × 2 × 3 = 24
Since, it is clear that the number 24 is divisible by 6 and 8 but the number is not divisible by 48.
There exist infinite numbers which can be divisible by 6 and 8 but not divisible by 48.
All the odd multiples of 24 are divisible by 6 and 8 but all the odd multiples of 24 are not divisible by 48.
For example:
24 × 3 = 72 (The number is divisible by 6 and 8 but not divisible by 48.)
24 × 5 = 120 (The number is divisible by 6 and 8 but not divisible by 48.)
Hence, the statement "There is an integer that is divisible by 6 and is also divisible by 8, but is not divisible by 48." is true.
<u>The </u><u>profit </u><u>made is </u><u>$4,460.</u>
What is a profit in business?
- In its simplest form, it's the amount left after subtracting your total expenses from your total revenue.
- The money remaining, your profits, can either be kept in the business and re-invested to finance future growth, or distributed as a draw or dividends to stakeholders.
The profit model, P(x) = -10x² + 498x - 1,500
Where, x = price per sign sold
If the price per sign sold is $20. Hence, x = $20
The profit made can be calculated thus :
Put x = 20 in the profit function :
P(20) = -10(20)² + 498(20) - 1,500
P(20) = - 10(400) + 9960 - 1500
P(20) = - 4000 + 9960 - 1500
P(20) = $4,460
The profit made is $4,460
Learn more about profit
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For this case we have the following function that models the problem is:
The time for which the maximum height occurs is obtained by deriving the equation:
We equal zero and clear x:
The maximum height is obtained by evaluating the time obtained in the given equation:
Then, by the time it reaches the ground we have:
From here, we clear x solving the quadratic equation:
We discard the negative root, and obtain as a result:
Answer:<span>
2.The pumpkin's maximum height is 151.02 feet and it hits the ground after 6.04 seconds </span>
Hypotenuse Leg.
You have vertical angles so you have a hypotenuse, a leg, and an angle that is congruent.
We know that it’s not SAS because the angle is not between the two sides.
Additionally, we only have one congruent angle so it cannot be ASA.
The only theorem that meets the description is HL.
Answer:
$180
Step-by-step explanation:
Since the discount is 40 percent and is also $72, We will cross multiply. 72 x 100 = 40 x what?
7200/40 = 180
The mirror was originally $180.