Answer: 43.1 degrees (choice B)
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Work Shown:
Use the law of sines
sin(A)/a = sin(C)/c
sin(A)/20 = sin(82)/29
sin(A) = 20*sin(82)/29
sin(A) = 0.68294349
A = arcsin(0.68294349)
A = 43.074088
A = 43.1 degrees
To multiply 9x475 using expanded form and the distributive property, you will break 475 into three numbers, multiply each of them by 9, and add the products together:
475 = 400 + 70 + 5
400x9 = 3600
70x9 = 630
5x9 = 45
3600 + 630 + 45 = 4,275
You divided in the wrong order. The resulting image always goes first then the preimage is afterward.
scale factor = (new)/(old) = 10/8 = 1.25
<h3>Answer is choice B</h3>
The scale factor is larger than 1, so this means we have an enlargement going on.
Answer: 80
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Explanation:
x = number of defective drives in the shipment of 20,000 total
We are told that 2 defective drives are in the shipment of 500. So the first fraction to set up is 2/500
The second fraction is x/20000 as we divide in the same order as before (number of defective over the total)
Set those two fractions together to get this proportion
2/500 = x/20000
Now cross multiply
2/500 = x/20000
2*20000 = 500*x
40000 = 500*x
500x = 40000
The last step is to divide both sides by 500 to isolate x
500x = 40000
500x/500 = 40000/500
x = 80 which is the answer we want
Note: This is an expected/estimated amount and not entirely guaranteed to be reality. It's based on the previous ratio of 2/500, assuming the same ratio is held in check.