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Brrunno [24]
2 years ago
9

The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 12 B, and 48 C. Show th

e frequency and relative frequency distributions.
Mathematics
1 answer:
zimovet [89]2 years ago
5 0

Answer:

CLASS     FREQUENCIES     RELATIVE FREQUENCIES

A                        60                                 0.5

B                        12                                  0.1

C                        48                                 0.4

TOTAL              120                                  1

Step-by-step explanation:

Given that;

the frequencies of there alternatives are;

Frequency A = 60

Frequency B = 12

Frequency C = 48

Total = 60 + 12 + 48 = 120

Now to determine our relative frequency, we divide each frequency by the total sum of the given frequencies;

Relative Frequency A = Frequency A / total = 60 / 120 = 0.5

Relative Frequency B = Frequency B / total = 12 / 120 = 0.1

Relative Frequency C = Frequency C / total = 48 / 120 = 0.4

therefore;

CLASS     FREQUENCIES     RELATIVE FREQUENCIES

A                        60                                 0.5

B                        12                                  0.1

C                        48                                 0.4

TOTAL              120                                  1

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musickatia [10]
Let us model this problem with a polynomial function.

Let x =  day number (1,2,3,4, ...)
Let y = number of creatures colled on day x.

Because we have 5 data points, we shall use a 4th order polynomial of the form
y = a₁x⁴ + a₂x³ + a₃x² + a₄x + a₅

Substitute x=1,2, ..., 5 into y(x) to obtain the matrix equation
|   1     1    1    1    1  |  | a₁ |      | 42 |
| 2⁴  2³  2²  2¹  2⁰  |  | a₂ |      | 26 |
| 3⁴  3³  3²  3¹  3⁰   |  | a₃ |  =  | 61 |
| 4⁴  4³  4²  4¹  4⁰   |  | a₄ |      | 65 |
| 5⁴  5³  5²  5¹  5⁰  |  | a₅ |      | 56 |

When this matrix equation is solved in the calculator, we obtain
a₁ =      4.1667
a₂ =  -55.3333
a₃ =  253.3333
a₄ =  -451.1667
a₅ =   291.0000

Test the solution.
y(1) = 42  
y(2) = 26
y(3) = 61
y(4) = 65
y(5) = 56

The average for 5 days is (42+26+61+65+56)/5 = 50.
If Kathy collected 53 creatures instead of 56 on day 5, the average becomes
(42+26+61+65+53)/5 = 49.4.

Now predict values for days 5,7,8.
y(6) = 152
y(7) = 571
y(8) = 1631


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3 years ago
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Mashcka [7]
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3 years ago
Find f(−1) given that f(x)=x3+2x2+3x+4. <br>A. 10 <br>B. -2 <br>C. 2 <br>D. -10
Finger [1]

Answer:

The answer is option C

Step-by-step explanation:

f(x) = x³ + 2x² + 3x + 4

To find f(-1) substitute the value of x that's

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<h3>f( - 1) =  ({ - 1})^{3}  + 2 ({ - 1})^{2}  + 3( - 1) + 4 \\  =  - 1 + 2(1)  - 3 + 4 \\  =  - 1 + 2 - 3 + 4 \\  = 1 - 3 + 4</h3>

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