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Elena L [17]
3 years ago
6

Need Help on Pre Cal

Mathematics
1 answer:
makvit [3.9K]3 years ago
6 0
<h3>Answer: 17</h3>

======================================================

Explanation:

This is a piecewise function. It's composed of 3 pieces of other functions. A piecewise function is a function that changes its identity based on what the input is.

We have three different situations here

  • If t = 17, then h(t) = sqrt(17t) based on what the first row says
  • If t = 19, then h(t) = -34/t which is the second row of the piecewise function.
  • If t does not equal either 17 or 19 (ie t is anything but those values), then h(t) = 23-t

The notation h(17) means we want to evaluate h(t) when t = 17. So we'll use the first case mentioned above. Plug t = 17 into h(t) = sqrt(17t) to get...

h(t) = sqrt(17t)

h(17) = sqrt(17*17)

h(17) = sqrt(17^2)

h(17) = 17

In the last step, I used the rule that sqrt(x^2) = x when x is nonnegative.

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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
2 years ago
What number can go into 21 and 27
astra-53 [7]

3 only

Hope this helps

4 0
2 years ago
Read 2 more answers
Please need help asap!!
vagabundo [1.1K]

a+b+c=180,  \text{ }c+e=180 \implies \\ a+b+c=c+e \implies \\ a+b=e\\

This result is actually true for any exterior angle. The exterior angle of a triangle is equal to the sum of the two remote angles, and above is a short proof of it.

6 0
3 years ago
Two numbers total 63 and have a difference of 31. Find the two numbers
Anastaziya [24]

Answer: 47 and 16

Step-by-step explanation:

- Make Two Equations

x + y = 63

x - y = 31

- Set one of the equations equal to one of the variables

x + y = 63

x = 31 + y

- Substitute the equation back into the other one

(31 + y) + y = 63

31 + 2y = 63

2y = 32

y = 16

- Substitute the answer back into the equation

x + y = 63

x + 16 = 63

x = 47

5 0
3 years ago
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How many duckling were swimming at the pond?
EleoNora [17]

Answer:

There are 20 ducklings.

Step-by-step explanation:

For every group of 6 ducks, 5 would be ducklings.

24 / 6 = 4

There are 4 groups of ducks.

5 * 4 = 20

4 0
3 years ago
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