Answer:
Total laps = 10d
Step-by-step explanation:
Let c = Carl's laps
d = Daria's laps
e = Erin's laps
c = 3d
c = e/2
c + d + e = totals laps
We can insert 3d in place of c in the third equation
3d + d + e = total laps
Also, e/2 equals 3d
e/2 = 3d
Multiply both sides by 2
(e/2 = 3d)2
e = 6d
Insert the new e
3d + d + 6d = 10d = totals laps
I guess the chef is making the mixture for the sheriff... Let <em>x</em> be the amount of dressing with 5% vinegar that is required, and <em>y</em> the amount of 15% vinegar dressing (both amounts in mL).
The sheriff wants 390 mL of the mixed dressing, so that
<em>x</em> + <em>y</em> = 390
<em>x</em> mL of the 5% dressing contains 0.05<em>x</em> mL of vinegar, while <em>y</em> mL of the 15% dressing contains 0.15<em>y</em> mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means
0.05<em>x</em> + 0.15<em>y</em> = 35.1
Solve for <em>x</em> and <em>y</em> :
<em>y</em> = 390 - <em>x</em>
0.05<em>x</em> + 0.15 (390 - <em>x</em>) = 35.1
0.05<em>x</em> + 58.5 - 0.15<em>x</em> = 35.1
23.4 = 0.10<em>x</em>
<em>x</em> = 234
<em>y</em> = 156
Answer:
27.8°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relationship between the angle and the relevant sides of the triangle is ...
Cos = Adjacent/Hypotenuse
In this case, the hypotenuse of the triangle is the length along the road; the distance parallel to the ground is the side adjacent to the angle of depression. So, you have ...
cos(angle) = (23 mi)/(26 mi)
angle = arccos(23/26) ≈ 27.8°
The angle of depression is about 27.8°.
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<em>Comment on the road</em>
The grade on such a road is about 53%. A road with an 8% grade for any distance is considered marginally safe for trucks. A 53% grade for 26 miles would wear out the brakes in no time.
The elevation drop on this road is about 12 miles, or more than 64,000 feet. The highest mountain on Earth is less than half that height, so this must be on a different planet.
Answer:
98
Step-by-step explanation:
2 (x + y) ²
= 2 (3 + 4 ) ²
= 2 x 7²
= 2 x 49
= 98
Answer:
0.22
Step-by-step explanation:
Add all the probabilities together then subtract it from 1