Answer:
13 is Prime
Step-by-step explanation:
The amount invested in the account that yields 7% interest is $4000.
The amount invested in the account that yields 12% interest is $1000.
<h3>What are the linear equations that represent the question?</h3>
a + b = 5000 equation 1
0.07a + 0.12b = 400 equation 2
Where:
a = amount invested in the account that yields 7% interest.
b = amount invested in the account that yields 12% interest.
<h3>How much is invested at each rate?</h3>
Multiply equation 1 by 0.07
0.07a + 0.07b = 350 equation 3
Subtract equation 3 from equation 2
0.05b = 50
b = 50 / 0.05
b = 1000
Subtract 1000 from 5000: 5000 - 1000 = 4000
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Answer:
a) 13, 10, 16
Step-by-step explanation:
The usual form of the triangle inequality requires the sum of the two shortest sides exceed the longest side (a+b>c). The only choice for which this is true is ...
10 + 13 > 16 . . . . choice A
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<em>Comment on the triangle inequality</em>
Some authors also allow the sum to equal the longest side (a+b≥c). In that case, choice B (1+2=3) is also an answer. This "triangle" would look like a line segment of length 3. It has zero area.
cos(37°15') = cos(37.25°) ≈ 0.7960
15' means 15/60 of a degree, or 0.25 degrees.
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Note: the calculator mode is set to <em>Degrees</em>.
Answer:
x is any integer not a multiple of 3
Step-by-step explanation:
This is equivalent to ...
(x mod 3)² = 1
x mod 3 = ±1 . . . . . . taking the square root
Possible values of x mod 3 are 0, 1, 2 (≅-1), so the only value excluded is 0.
x mod 3 ≠ 0 . . . . . . for any integer x