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3 years ago

Find the derivative of f(x) = 9x + 5 at x = 7.

Mathematics

1 answer:

mafiozo [28]3 years ago

5 0

$f(x)=9x+5\implies f'(x)=9\implies f'(7)=9$

Or, using the definition of the derivative,

$f'(7)=\displaystyle\lim_{x\to7}\frac{f(x)-f(7)}{x-7}$

$\displaystyle=\lim_{x\to7}\frac{(9x+5)-(63+5)}{x-7}$

$\displaystyle=\lim_{x\to7}\frac{9(x-7)}{x-7}$

$\displaystyle=\lim_{x\to7}9=9$

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3 years ago

Read 2 more answers

You are running a race. The probability that you win is 3/5. What is the probability that you lose at most 2 out of your 6 races

Veronika [31]

Answer:

The probability that you lose at most 2 out of your 6 races is 0.54432.

Step-by-step explanation:

We are given that you are running a race. The probability that you win is 3/5.

There are total of 6 races.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 6 races

r = number of success = at most 2 lost

p = probability of success which in our question is probability that

you lose a race = 1 - (3/5) = 2/5 or 0.4

Let X = Number of races lost

So, X ~ Binom(n = 6, p = 0.40)

Now, the probability that you lose at most 2 out of your 6 races is given by = P(X $\leq$ 2)

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{6}{0} \times 0.40^{0} \times (1-0.40)^{6-0} + \binom{6}{1} \times 0.40^{1} \times (1-0.40)^{6-1} + \binom{6}{2} \times 0.40^{2} \times (1-0.40)^{6-2}$

= $1 \times1 \times 0.60^{6} + 6 \times 0.40^{1} \times 0.60^{5} +15\times 0.40^{2} \times 0.60^{4}$

= 0.54432

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3 years ago

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Sorry, I can't draw a picture, but I can help answer the question...

The way to determine the area of a square or rectangle is to multiply the base and the height, which in this case, is 24 and 18. So 24 times 18 is 432. Therefore, the amount of glass needed to repair the window is 432 inches squared.

Hope that helps!

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4 years ago

The Daily Focus newspaper has a circulation of 382 198. Round this number to the nearest 100 000.

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4 years ago

If $10,500 is borrowed for 5 years at an annual simple interest rate of 1.73%, how much interest will be paid if the entire loan

AlekseyPX

So, yearly $2100 is paid, plus the 1.73% interest, so 1.73% interest is $2136.33every year interest stacks on itself so youll take 1.73% of the year 1 total with interest.

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3 years ago