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Paul [167]
3 years ago
11

After having been on the air for more than a decade, Fox's American Idol seemed to be suffering from viewer fatigue. The average

number of viewers from the 2011 season through the 2013 season is approximated by f(t) = 32.744e−0.252t (1 ≤ t ≤ 4) where f(t) is measured in millions, with t = 1 corresponding to the 2011 season.(a) What was the average number of viewers in the 2011 season? million viewers (b) What was the average number of viewers in the 2014 season, assuming that the trend continued into that season? million viewers
Mathematics
1 answer:
mixas84 [53]3 years ago
5 0

Answer:

(a)25.45 million viewers

(b) 11.95 million viewers

Step-by-step explanation:

The average number of viewers from the 2011 season through the 2013 season is approximated by the function:

f(t) = 32.744*e^{-0.252t} (1 ≤ t ≤ 4) where f(t) is measured in millions.

t = 1 corresponds to the 2011 season.

(a) In 2011, t=1

Average number of viewers in the 2011 season,

f(1) = 32.744*e^{-0.252*1}

=25.45 million viewers

(b) In the 2014 season, when =4

f(4) = 32.744*e^{-0.252*4}

=11.95 million viewers

assuming that the trend continued into that season

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Consider the graph with four lines below. On a coordinate plane, line a has a positive slope and goes through points (negative 1
yan [13]

Answer:

The correct option is;

line a and line b

Step-by-step explanation:

Lina a passes through (-1, 0) and (1, 2)

Line b passes through (2, 2) and (-1, -1)

Line c passes through (0, 3) and (1, 0)

Line d passes through y = 1

An equation that has no solution

By examination, from the plot of the coordinates using an online tool, the system that would have no solution is the system of line a and line b because they are parallel lines and cannot meet or have a point where there is a common solution, therefore, there are no solutions when the equations of the two lines are combined in one equation

Slope of line a = -2/-2 = 1

Slope of line b = 3/3 = 1

The slopes of lines a and b are equal, therefore, line a and line b are parallel.

5 0
3 years ago
A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado l
lisov135 [29]

Answer:

The null and alternative hypothesis are:

H_0:\mu =2.6\\H_a:\mu >2.6

There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles

Step-by-step explanation:

Consider the provided information.

The claim that the mean tornado length is greater than 2.6 miles.

If there is no statistical significance in the test then it is know as the null which is denoted by H_0, otherwise it is known as alternative hypothesis which denoted by H_a.

Therefore, the required null and alternative hypothesis are:

H_0:\mu =2.6\\H_a:\mu >2.6

significance level α =0.05

From the given table the test statistic T=2.230166

P-value is 0.0131

0.0131<0.05

P value is less than the significance level, so reject the null hypothesis.

There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles

6 0
3 years ago
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Romashka-Z-Leto [24]
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7 0
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REY [17]

Answer:

A

-2 < x ≤ 3 (All x values between -2 and 3; excluding -2 and including 3)

Step-by-step explanation:

I feel the answer is A because from what we know, domain is the x-intercept or x. So both C and D are not the answer because the y-intercept is not the domain, the y-intercept is the range. Next I looked at both A and B, well, if you look closely answer choice A says "excluding -2 and including 3" and choice B says "including -2 and excluding 3". I also seen on the graph that the point of (3,3) has a filled in dot and the point at (-2,-1) has an opened dot. A filled in dot always means you either have a ≥ (greater than or equal to sign) or a ≤ (less than or equal to sign). While an opened dot always means you just have < (greater than) or a > (less than) sign. So the correct answer is A!! Hope you have a fantastic rest of your day! :)))

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