Drake rolls two fair number cubes.
1 answer:
Answer:
The probability that the product of 2 numbers that Drake rolls is less than =
Step-by-step explanation:
Drake rolls two fair number cubes i.e. 6 sided die. He then multiplies the numbers shown on each die. The result of the all possible products are shown in the given table. The given table is missing a 1 in the first row. The complete first row will be:
1 2 3 4 5 6
The total number of possible outcomes are 36. We have to find the probability that product of two numbers that Drake rolled is less than 10. For this, first we need to count the number of outcomes that are less than 10. From the table we can see that the number of possible outcomes that are less than 10 are = 17
Probability is defined as the ratio of favorable outcomes to the total number of outcomes. Here, total outcomes are 36 and favorable outcomes are 17.
So,
The probability that the product of 2 numbers that Drake rolls is less than =
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Answer:
(a) a = 43.25 , b = 41 and c = 1547
(b) The number of craft-beer breweries in 2016 = 4643
Step-by-step explanation:
Given that the number of small craft-beer breweries from 2008 to 2012 is modeled by using a quadratic function of the form f(t) = at² + bt + c where a, b, and c are constants and t is measured in years, with t = 0 corresponding to 2008.
(a) Now we have to find these constants given f(0) = 1547, f(2) = 1802, and f(4) = 2403.
So, <em>f(0) = </em><em> which implies that </em><em>c = 1547</em><em>.</em>
<em>f(2) = </em><em> = 4a + 2b + c</em>
4a + 2b + c = 1802 ----------- [Equation 1]
<em>f(4) = </em><em> = 16a + 4b + c </em>
16a + 4b + c = 2403 ----------- [Equation 2]
Further solving Equation 1 we get; 4a + 2b + 1547 = 1802
4a + 2b = 1802 - 1547 ; 4a + 2b = 255 ----------- [Equation 3]
Further solving Equation 2 we get; 16a + 4b + 1547 = 2403
16a + 4b = 2403 - 1547 ; 16a + 4b = 856 ----------- [Equation 4]
Now, Solving Equation 3 and 4 we get ;
a = 43.25 and b = 41 .
Therefore, values of constants a, b and c are 43.25, 41 and 1547 respectively.
(b) So, model we obtained in part (a) is represented as :
f(t) =
Now to estimate the number of craft-beer breweries in 2016, assuming that the trend continued we know that t would be 8 as 2016 - 2008 = 8 years.
<em>So, f(8) = </em><em> = 4643.</em>