Answer:
F. 5:4
Step-by-step explanation:
Solve for a and c to find the ratio of a to c:
- 2a = 3b
- a = 3/2(b)
- 6b = 5c
- c = 6/5(b)
Now, we can use the value of a and c to find the ratio of a to c:
- (3/2(b))/(6/5(b))
- 3b/2 × 5/6b
- 15b/12b
- 5/4
F. 5:4 is the correct answer
Answer:
$1,179
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
<em>P = initial balance</em>
<em>r = interest rate (decimal)</em>
<em>n = number of times compounded annually</em>
<em>t = time</em>
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First, lets change 2.6% into a decimal:
2.6% -> -> 0.026
Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:
The account balance after 10 years will be $1,179
Pick a number: 5
Add 7: 5+7=12
Triple the result: 12*12*12=1728
Add 9= 1728+9=1737
Divide by 3 = 1737/3=579
Subtract original number = 579-5=574
Now pick a different number a do the same process
Hope that helps
Answer:
the solution set consists of {x < -2 ∪ x > 10/3}
Step-by-step explanation:
|3x - 2| > 8 is equivalent to the following set of inequalities:
1) 3x - 2 > 8
and
2) -(3x - 2) > 8
In case 1, above, add 2 to both sides, obtaining 3x > 10, or x > 10/3.
In case 2, above, carry out the indicated multiplication first:
-3x + 2 > 8. Next, subtract 2 from both sides: -3x > 6.
Next, divide both sides by -3, remembering to reverse the direction of the inequality sign: x < -2.
Thus, the solution set consists of {x < -2 ∪ x > 10/3}
Note that
108° = 90° + 18°
so
sin(108°) = sin(90° + 18°) = sin(90°) cos(18°) + cos(90°) sin(18°) = cos(18°)
Then
sin²(108°) + sin²(18°) = cos²(18°) + sin²(18°) = 1
by the Pythagorean identity.