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e-lub [12.9K]
2 years ago
10

Please help. Have a good day

Mathematics
1 answer:
Verizon [17]2 years ago
7 0
It will take her 9 days to run 4 miles. She will not be able to run in whole week.
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Differentiate f and find the domain of f. (enter the domain in interval notation.)f(x) = ln(x2 − 12x)derivative f '(x) = 2x−12x2
guajiro [1.7K]
F(x) = ln(x² - 12x)
The derivative is
f'(x)= \frac{2x-12}{x^{2}-12x}

f(x) is undefined when x² - 12x = x(x - 12) = 0
That is, when x = 0 or x = 12.
Therefore the domain is (-∞, 0)∪(0,12)∪(12, ∞)

Answer:
The derivative is
f'(x) =  \frac{2x-12}{x^{2}-12x}
The domain is
(-∞, 0)∪(0, 12)∪(12,∞)



3 0
3 years ago
A five​-digit number starts with a number between 4​-9 in the first​ position, with no restrictions on the remaining 4 digits. a
Maurinko [17]

Answer:

(a) Pr = 0.3024

(b) Pr = 0.6976

(c) Pr = \frac{^9P_{n-1}}{10^{n-1}}

Step-by-step explanation:

Given

Start = \{5,6,7,8\} i.e. between 4 and 9

n(Start) =4

Digits = 5

Solving (a): Probability that each of the 5 digit are different

Since there is no restriction;

The total possible selection is as follows:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 10\\ (i.e. any of the 10 digits 0 - 9)

Third\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fourth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

Fifth\ digit = 10 (i.e. any of the 10 digits 0 - 9)

So, the total is:

Total = 4 * 10 * 10 * 10 * 10

Total = 40000

For selection that all digits are different, the selection is:

First\ digit = 4 (i.e. any of the 4 start digits)

Second\ digit = 9 (i.e. any of the remaining 9)

Third\ digit = 8 (i.e. any of the remaining 8)

Fourth\ digit = 7 (i.e. any of the remaining 7)

Fifth\ digit = 6 (i.e. any of the remaining 6)

So:

Selection =4 * 9 * 8 * 7 * 6

Selection =12096

So, the probability is:

Pr = \frac{Selection}{Total}

Pr = \frac{12096}{40000}

Pr = 0.3024

Solving (b): At least 1 repeated digit

The probability calculated in (a) is the all digits are different i.e. P(None)

So, using laws of complement

We have:

P(At\ least\ 1) = 1 - P(None)

So, we have:

Pr= 1 - 0.3024

Pr = 0.6976

Solving (c): An expression to model the probability.

<em>Using (a) as a point of reference, we have;</em>

Pr = \frac{Selection}{Total}

Where

Selection =4 * 9 * 8 * 7 * 6 ---- for selection of 5 i.e. n = 5

Total = 4 * 10 * 10 * 10 * 10

Selection =4 * 9 * 8 * 7 * 6

This can be rewritten as:

Selection = 4 * ^9P_4

4 can be expressed as: 5 - 1

So, we have:

Selection = (5-1) *^9P_{5-1}

Substitute n for 5

Selection = (n-1) *^9P_{n-1}

Selection = (n-1)^9P_{n-1}

Total = 4 * 10 * 10 * 10 * 10

This can be rewritten as:

Total = 4 * 10^4

Total = (5-1) * 10^{5-1}

Total = (n-1) * 10^{n-1}

Total = (n-1) 10^{n-1}

So, the expression is:

Pr = \frac{(n-1)^9P_{n-1}}{(n-1)10^{n-1}}

Pr = \frac{^9P_{n-1}}{10^{n-1}}

<em>Where n represents the digit number</em>

5 0
3 years ago
Need help asap...........
Vesna [10]
All there is, is a picture. Is there a question?
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Last year the robotics club had 30 members. This year the club has 24 members. Find the percent change in the number of members.
Naddika [18.5K]

Answer:

the answer is .6

Step-by-step explanation:

so 30 minus 24 is 6 turn 6 into percentage which is 0.6

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3 years ago
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3 Which of the following represents a function? A {(-2, 1), (-2, 0), (-2, 1), (-2, 2)} B {(-1,0), (0, 1), (1, 2), (2, 3)} C {(1,
solong [7]

Answer:

A

Step-by-step explanation:

because they want you to look for the number who repeat in the right like A (

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3 years ago
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