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Semenov [28]
3 years ago
7

Explain why the function is discontinuous at the given number

Mathematics
1 answer:
Blizzard [7]3 years ago
5 0
For f to be continuous at x=5, we need to have

\displaystyle\lim_{x\to5}f(x)=f(5)

Note that x\to5 means that x\neq5, but that x is *approaching* 5. We're told that for x\neq5, we have

f(x)=\dfrac{x^2-5x}{x^2-25}

We can write

\dfrac{x^2-5x}{x^2-25}=\dfrac{x(x-5)}{(x+5)(x-5)}=\dfrac x{x+5}

and the limit would be

\displaystyle\lim_{x\to5}\frac x{x+5}=\dfrac5{5+5}=\dfrac5{10}=\dfrac12\neq1=f(5)

and so f is discontinuous.
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See below

Step-by-step explanation:

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75 * 50.3 = ~3800 cm^2

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1. Which diagram(s) show adjacent angles?
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9). Four friends earned $4.20 for washing a car. They decided to split the money equally. How much money did each friend get?​
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2 years ago
Read 2 more answers
A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the
forsale [732]
<h3>The probability of  student passing the quiz with  at least 50% of the questions correct is 0.05457.</h3>

Step-by-step explanation:

Here, the total number of T/F question = 10

The minimum answers needed correctly answered = 8

So, student needs to answer at least 8 questions correctly.

Here, the possibility of answering a question correctly  = (\frac{1}{2})   = p = 0.5

Also, the possibility of answering a question wrong  = (\frac{1}{2})  = q = 0.5

Now, to pass he needs to answer 8 or more (  8 , 9 or 10) answers correctly.

P(answering 8 correct answer)  = ^{10}C_8(p)^8(q)^2 = ^{10}C_8(0.5)^8(0.5)^2  = 0.0439

P(answering 9 correct answer)  =  ^{10}C_9(p)^9(q)^1 = ^{10}C_9(0.5)^9(0.5)^1  = 0.0097

P(answering 10 correct answer)  = ^{10}C_{10}(p)^{10}(q)^0 = ^{10}C_{10}(0.5)^{10}(0.5)^0  = 0.00097

So, the total Probability   = P(8) + P(9) + P(10)

= (0.0439) + (0.0097) + (0.00097)

= 0.05457

Hence, the probability that the student passes the quiz  with  at least 8 of the questions correct is 0.05457.

6 0
3 years ago
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