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Dahasolnce [82]
2 years ago
10

A foreman for an injection-molding firm admits that on 55% of his shifts, he forgets to shut off the injection machine on his li

ne. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 3% to 15%. The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night?
Mathematics
1 answer:
motikmotik2 years ago
5 0

Answer:

0.8594

Step-by-step explanation:

Let a denote the event of forgetting to shut off machine and b be the event of being defective.

-A foreman forgets to shut off machine 55% of the time.

-If he forgets, 15% of molds are defective.

-If he does not, 3% of molds are defective.

#The probability that he forgot to shut off the machine is calculated as:

P(a \ and \ b)=0.55\times 0.15\\\\=0.0825\\\\

P(a and ~b)=0.55(1-0.15)=0.4675

P(~a and b) = (1-0.55)*0.03=0.0135

P(~a and ~b) = (1-0.55)*(1-0.03)=0.4365

#Conditional probability is defined as:

P(a|b)=\frac{P(a \ and\  b)}{P(a)}\\\\=\frac{P(a \ and \ b)}{[(P(a \ and \ b)+P(\~a \ and \ b)}\\\\\\=\frac{0.0825}{0.0825+0.0135}\\\\\\=0.8594

Hence,  the probability that the foreman forgot to shut off the machine the previous night is 0.8594

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a ladder leaning against a house makes an angle of 39 with the ground the foot of the ladder is 10 feet From the foot of the hou
dsp73

Answer:

39+10=49

Step-by-step explanation:

I hope this helps you.

4 0
3 years ago
What are the square roots of; (note: i think there are supposed to be 2 each) 36 12 1.96 0.64 400 25/36
Goryan [66]

Answer:

36 : 6 and -6

12 = 2\sqrt{3} ,  -2\sqrt{3}

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = 2^2*\sqrt{3} *\sqrt{3}

\sqrt{12} = 2\sqrt{3}

also

12 = -2\sqrt{3} *-2\sqrt{3}

\sqrt{12} = -2\sqrt{3}

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

\sqrt{1.96}  = 14/10  \ or -14/10

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

\sqrt{400}  = 20\\\sqrt{400}  = -20\\

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6

7 0
2 years ago
Use the distributive property to write an expression that is equivalent to: 3(x + 5)
lana [24]

Answer:

3x=15

Step-by-step explanation:

Here's what I found on google about the distributive property-

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Now for the math-

3(x+5)

distribute the numbers-  3(x)+3(5)

solve-  3*5=15

3x+15

3 0
2 years ago
Explain why 2a+3b=5ab
Ahat [919]

That's not correct. The terms 2a and 3b are not like terms, so we cannot combine them to get 5ab. We simply leave it as 2a+3b.

If you had 2a+3a, then it would simplify to 5a

Similarly, 2b+3b = 5b

Or you could have 2ab+3ab = 5ab

The key is that the variable portions must match up to be able to add them.

8 0
3 years ago
Read 2 more answers
3/38-3/7<br> 2+1/35<br> 3/56+3/2
prohojiy [21]

Answer:

87/56

Step-by-step explanation:

Simplify the following:

3/56 + 3/2

Put 3/56 + 3/2 over the common denominator 56. 3/56 + 3/2 = 3/56 + (28×3)/56:

3/56 + (28×3)/56

28×3 = 84:

3/56 + 84/56

3/56 + 84/56 = (3 + 84)/56:

(3 + 84)/56

3 + 84 = 87:

Answer:  87/56

4 0
3 years ago
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