Answer:
10 years and 10 months.
Step-by-step explanation:
The annually interest rate (ia) can be converted by monthly (im) by the equation:
(1 + im)¹² = 1 + ia
(1 + im)¹² = 1 +0.01
(1 + im)¹² = 1.001 (putting ln in both sides)
ln(1 + im)¹² = ln1.001
12*ln(1 + im) = 1.0x10⁻³
ln(1 + im) = 8.33x10⁻⁵(applying "e in both sides)
1 + im = 1.00083
im = 0.00083 = 0.083%
For a investimenting, the final amount (A) can be calculated by:
Where R is the amount invested per month, i is the interest, and n the number of months:
160000 = 400 *
= 400
1.00083ⁿ - 1 = 0.332
1.00083ⁿ = 1.332 (applying ln in both sides)
n*ln1.00083 = ln1.332
8.3x10⁻⁴n = 0.2867
n = 345.4 months
345.4 months *1 yea12 months = 10 years and 10 months.
We conclude that the measure of that angle is 150 degrees.
<h3>
How to get the measure of angle BFE?</h3>
Notice that the measure of angle ∠BFE will be equal to:
∠BFE = ∠BFC + ∠CFD + ∠DFE
Where:
∠CFD = 90°
∠DFE = 30°
And we will have that:
∠AFC = 180° - 90° - 30° = 60°
And we know that BF bisects that angle, then:
∠BFC = 30°
So we conclude that:
∠BFE = ∠BFC + ∠CFD + ∠DFE = 30° + 90° + 30° = 150°
We conclude that the measure of that angle is 150 degrees.
If you want to learn more about angles:
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Answer:
2:55 P.M.
Step-by-step explanation:
First, add the amount of time Jim played outside; 45+55=100
100 minutes is equal to 1 hour 40 minutes.
If he left the playground at 4:35 P.M., then you have to subtract in order to find out when he arrived there.
Subtract 1 hour 40 minutes from 4:35 P.M. to then get 2:55 P.M.
To confirm your answer, you can add back the 1 hour and 40 minutes to 2:55 P.M. and you'll get 4:35 P.M.; back with what you started with.
Hope this helped !!!
Answer:
202.3 ounces of real silver
Step-by-step explanation:
Another example would be like pizza. If there are 6 slices of pizza in each box, then 2 boxes of pizza would have 6 + 6 slices = 12 slices. It is 6 slices each * 2 boxes = 12 slices total. The same applies to the coin situation, for every additional coin, multiply 0.85 by the number of coins to get the total weight of real silver.
If there are 238 silver coins, then you have 238 0.85 ounces of real silver. Multiplying 238 by 0.85 to simplify gives you 202.3 ounces of real silver.
The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)
The distance between both lighthouses is 5783.96 m
I've added an attachment that represents the scenario.
From the attachment, we have:
Convert to degrees
Convert to degrees
So, the measure of angle S is:
---- Sum of angles in a triangle
The required distance is distance AB
This is calculated using the following sine formula:
Where:
So, we have:
Make AB the subject
Hence, the distance between both lighthouses is 5783.96 m
Read more about bearing and distance at:
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