Find the least common multiples of 4, 10, 12, 15
multiples of 4:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80
multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120
multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150
The least common multiple of 4, 10, 12, and 15 is 60.
4 x 15 = 60
10 x 6 = 60
12 x 5 = 60
15 x 4 = 60
Answer:
Step-by-step explanation:
This is an Annuity question. It is asking for recurring monthly payment(PMT). <em>You can use a financial calculator to solve it. I am using (Texas Instruments BA II plus)</em>
Since the payments occur monthly , adjust the interest rate to monthly rate and multiply 40 years by 12 since we have 12 months in a year<em>.</em>
Total duration of investment ; N = 40*12 = 480
Interest rate; I/Y = 5.75% /12 = 0.4792%
Future value; FV = 6,000,000
Present value ; PV = 0
then CPT PMT = 3,222.912
Therefore $3,222.91 should be deposited each month to achieve the goal.
Answer:
P(1) = 0.2857
P(2) = 0.1428
P(3) = 0.1428
P(4) = 0.1428
P(5) = 0.1428
P(6) = 0.1428
Step-by-step explanation:
From the question, we know that Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers, so we can write the following equation:
P(1) = 2X
Where X is the probability of rolling each of the other five numbers or:
P(2) = P(3) = P(4) = P(5) = P(6) = X
Additionally, the sum of all the probabilities is 1, so:
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
Now, we can replace P(1) by 2X and P(2), P(3), P(4), P(5) and P(6) by X, as:
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
2X + X + X + X + X + X = 1
Finally, solving for X, we get:
7X = 1
X = 1/7
X = 0.1428
So, the probability of rolling a 1 is equal to:
P(1) = 2X = 2*(0.1428) = 0.2857
And the probability of rolling each of the other five numbers is:
P(2) = P(3) = P(4) = P(5) = P(6) = X
P(2) = P(3) = P(4) = P(5) = P(6) = 0.1428
Answer: E
Step-by-step explanation: In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. ... Many mathematical theorems are conditional statements.
Answer:
11 feet (Option C)
Step-by-step explanation:
Let the longer side be l and the shorter side be b.
We know that,
→ Perimeter of rectangle = 2 ( longer side + shorter side )
Here,
- Perimeter of rectangle is 32 feet.
→ 32 = 2 (l + b)
→ 32 = 2l + 2(5)
→ 32 = 2l + 10
→ 32 - 10 = 2l
→ 22 = 2l
→ 
= l
→ 11 = l
→<u> 11 feet = longer side</u>
<u>Length</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>longer</u><u> </u><u>side</u><u> </u><u>is</u><u> </u><u>1</u><u>1</u><u> </u><u>feet</u><u>.</u>
