Answer:
$7 for the first question
$6.50 for the last one
factoring
Step-by-step explanation:
although all methods work, since it's x^2 it's easier to factor the x variable.
Angles LNM and MNI are supplementary, so their measures sum to 180°. This means
∡ LNM + ∡ MNI = 180°
∡ LNM = 180° - (19<em>x</em> + 2)°
The sum of the interior angles of any triangle is also 180°, so
∡ LNM + ∡ NML + ∡ MLN = 180°
(180° - (19<em>x</em> + 2))° + (15<em>x</em> - 2)° + (6<em>x</em>)° = 180°
Solve for <em>x</em> (I'll omit the degree symbol):
180 - 19<em>x</em> - 2 + 15<em>x</em> - 2 + 6<em>x</em> = 180
2<em>x</em> - 4 = 0
2<em>x</em> = 4
<em>x</em> = 2
Then ∡ MNI = (15•2 - 12)° = (30 - 12)° = 18°.
The best firm for the Appliance manufacturer for the repair work is Firm 2 .
In the question ,
it is given that ,
An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis .
The acceptable range of the repair time is 50 minutes to 90 minutes.
the mean repair time for firm 1 = 74 minutes and standard deviation of 4 minutes .
the mean repair time for firm 2 = 72 minutes and standard deviation of 5.1 minutes .
the range is calculated using the formula
Range = Mean ± Standard Deviation
So , for firm 1 ,
the Range = 74 ± 4
= 74
4 and 74 - 4
= 78 and 70
the range for firm 2 is
= 72 ± 5.1
= 72
5.1 and 72 - 5.1
= 7.1 and 66.9
The second company has a lower range and it should be preferred .
Therefore , The best firm for the Appliance manufacturer for the repair work is Firm 2 .
Learn more about Standard Deviation here
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