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MA_775_DIABLO [31]
3 years ago
11

caleb throws a ball three times for his dog leo. for each throw. leo either catches the ball of misses it. identify the sample s

pace​
Mathematics
1 answer:
Tpy6a [65]3 years ago
3 0

Answer: {MMM ,MCC ,CMC, CCM ,CMM ,MCM ,MMC ,CCC }

Step-by-step explanation:

  • The sample space of an random experiment is the set of all possible results of that particular experiment.

Let C denotes the event when dog catches the throw and M denotes the event when dog misses the throw.

Given: Caleb throws a ball three times for his dog leo.

Then the sample space for the situation is given by :-

{MMM ,MCC ,CMC, CCM ,CMM ,MCM ,MMC ,CCC }

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How to solve these 3 problems
Bingel [31]

Answer:

  1. a. decay; b. growth; c. decay; d. neither
  2. r = 4; a = 1; y = 1·4^x
  3. a. an = 3(5^(n-1)); b. f(x) = (3/5)(5^x); c. exponential growth; d. y-intercept: 3/5; first term: 3.

Step-by-step explanation:

There are two kinds of exponential problems here.

  1. exponential functions of the form f(x) = a·b^x
  2. exponential sequences of the explicit form an = a1·r^(n-1)

The second problem gives you a table that suggests the sequence form, but it asks for the exponential function form. The third problem does something similar.

__

<h3>1.</h3>

In an exponential function of the form f(x) = a·b^x, the function grows if b>1 and decays if b<1. Using this check, we can easily answer ...

  a. 0.4 < 1 . . . decay

  b. 1.3 > 1 . . . growth

  c. 1/2 < 1 . . . decay

  d. 1 = 1 . . . neither growth nor decay; the function is constant: j(x) = 1.

__

<h3>2.</h3>

The value of x is given starting at 1, so we can consider this a geometric sequence. The common ratio is r = 16/4 = 4. The first term is a1 = 4, so the explicit formula for the sequence is ...

  an = 4·4^(n-1)

When this is expanded to get rid of the constant in the exponent, we have ...

  an = 4·(4^n)·(4^-1) = 1·4^n

We recognize this form as matching the functional form f(x) = a·r^x. The multiplier of the exponential factor is a=1. In summary, ...

  r = 4; a = 1; f(x) = 1·4^x

__

<h3>3.</h3>

The first term of this geometric sequence is a1 = 3. The common ratio is r = 15/3 = 5. Using the explicit formula, we have ...

 a. explicit form: an = 3·5^(n-1)

Using the method of question 2 to write the functional form, we find ...

  an = 3(5^n)(5^-1) = (3/5)(5^n)

  b. functional form: f(x) = (3/5)(5^x)

  c. function family: exponential growth functions

 d. y-intercept: (3/5) . . . . read this from the f(x) form

     1st term: the first term listed in the given sequence is 3

_____

<em>Additional comment</em>

The "y-intercept" of a sequence is irrelevant (undefined), as the sequence term numbering starts with 1, not 0. The domain of the explicit formula is <em>natural numbers</em>, which does not include 0.

Similarly, the "first term" of a function f(x) needs further definition. Here, we've answered the question by saying the first term is f(1). There is no conventional definition of a "first term" for a continuous function.

3 0
2 years ago
Factor completely 2x2 − 2x − 40
Montano1993 [528]

Answer:

2(x-5)(x+4)

Step-by-step explanation:

2x^2 − 2x − 40

Factor out a 2

2(x^2 -x -20)

What 2 numbers multiply to -20 and add to -1

-5*4 = -20

-5+4 = -1

2(x-5)(x+4)

4 0
3 years ago
Write the slope-intercept form of the equation for the line given the slope and y-intercept (equation: y=mx+b) Slope = 5, y-inte
Dima020 [189]

Answer:

The answer is y = 5x +2

Step-by-step explanation:

4 0
2 years ago
Ruben decides to leave a 24% tip after eating dinner at Sun Bistro. If the bill is $23.35, how much should he pay? Round to the
Igoryamba

Answer:

$3.50

Step-by-step explanation:

3 0
3 years ago
Six times the sum of a number and twelve is forty. Which equation represents this?
Anton [14]

Step-by-step explanation:

40=6x+12

we know the total of everything is 40, so out that on one side.

1. Let the number be X

Therefore, six times the sum=6x

and twelve

so, 6x+12

put that together,

6x+12=40

7 0
3 years ago
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