Find the exact volume of the cylinder.
2 answers:
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Answer:
x = 4
y = -3
Step-by-step explanation:
We can use substitution, elimination, or graphically.
Step 1: Rearrange first equation
2x + 4y = -4
2x = -4 - 4y
x = -2 - 2y
Step 2: Rewrite systems of equations
x = -2 - 2y
3x + 5y = -3
Step 3: Substitution
3(-2 - 2y) + 5y = -3
-6 - 6y + 5y = -3
-6 - y = -3
-y = 3
y = -3
Step 4: Find <em>x</em> using <em>y</em>
2x + 4(-3) = -4
2x - 12 = -4
2x = 8
x = 4
Graphically:
Use a graphing calc and analyze where the 2 lines intersect.
(1)
Mean length of all fish in the sample -
<u>Mean</u> = (Sum of observations)/(Number of observations)
= (12 + 5 + 3 + 5 + 8 + 2 + 10 + 9 + 4 + 4)/(10)
= 62/10
=<em> 6.2</em>
(2)
Mean length of adult fish in the sample -
<u>Mean</u> = (Sum of observations)/(Number of observations)
= (12 + 5 + 8 + 10)/(4)
= 35/4
=<em> 8.75</em>
(3)
Mean length of juvenile fish in the sample -
<u>Mean</u> = (Sum of observations)/(Number of observations)
= (5 + 3 + 2 + 9 + 4 + 4)/(6)
= 27/6
<em>= 4.5</em>
(4)
Percentage of sample that were adult fish -
<u>Percentage</u> = (No. of adult fishes)/(Total no. of fishes) × 100
% = (4/10) × 100
<em>% = 40</em>
(5)
Percentage of sample that were juvenile fish -
<u>Percentage</u> = (No. of juvenile fishes)/(Total no. of fishes) × 100
% = (6/10) × 100
<em>% = </em><em>6</em><em>0</em>
(6)
Percentage of sample that were juveniles over 8 inches long -
<u>Percentage</u> = (No. of juveniles over 8 inches)/(Total no. of fishes) × 100
% = (1/10) × 100
<em>% = </em><em>1</em><em>0</em>