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const2013 [10]
3 years ago
5

WILL GIVE BRAINIEST ANSWER IF ANSWER IS CORRECT

Mathematics
2 answers:
IRISSAK [1]3 years ago
4 0
F(x) = x+4
f(4) = 8, f(5) = 9
Change = 1

f(x) = 3x-7
f(-3) = -16, f(5) = 8
Change = 24/8 = 3

f(x) = 9x+1
f(-5) = -44, f(-2) = -17
Change = 27/3 = 9

f(x) = 2x+9
f(1) = 11, f(2) = 13
Change = 2

In order: f(x) = 9x+1, f(x) = 3x-7, f(x) = 2x+9, f(x) = x+4
ipn [44]3 years ago
4 0

Answer::

Average rate of change(A(x)) of f(x) over the interval [a, b] is given by:

A(x) = \frac{f(b)-f(a)}{b-a}

As per the statement:

Given :

f(x) = x+4 over the interval [4, 5]

At x = 4

f(4) = 8

at x = 5

f(5) = 9

Using the above formula: we have;

A_1(x) = \frac{f(5)-f(4)}{5-4} = \frac{9-8}{1} = \frac{1}{1} = 1

Similarly for :

f(x) = 3x-7 over the interval [-3, 7]

at x = -3

f(-3) = -16

At x = 7:

f(7) = 14

then;

A_2(x) = \frac{f(7)-f(-3)}{7-(-3)} = \frac{14+16}{10} = \frac{30}{10} = 3

For:

f(x) = 9x + 1 over the interval [-5, -2]

At x = -5

f(-5) = -44

At x = -2

f(-2) = -17

then;

A_3(x) = \frac{f(-2)-f(-5)}{-2-(-5)} = \frac{-17+44}{3} = \frac{27}{3} =9

For:

f(x) = 2x + 9 over the interval [1, 2]

At x = 1

f(1) = 11

At x =2

f(2)= 13

then;

A_4(x) = \frac{f(2)-f(1)}{2-1} = \frac{13-11}{1} = \frac{2}{1} =2

We have to Arrange these functions from the least to the greatest value based on the average rate of change in the specified interval.

A_1 < A_4< A_2

⇒1< 2< 3< 9

⇒x+4 < 2x + 9 <  3x-7 < 9x + 1

Therefore, the least to the greatest value based on the average rate of change in the specified interval is:

f(x) = x+4, f(x) = 2x+9, f(x) = 3x-7, f(x) = 9x+1,

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satela [25.4K]

Answer:

(1) (4.82, 4.98)

(2) Large sample size

(3) Yes, the temperature is within the confidence interval of (37.40, 37.60)

(4) (15.083, 15.117)

Step-by-step explanation:

Confidence Interval (CI) = mean + or - (t×sd)/√n

(1) mean = 4.9, sd = 0.35, n = 68, degree of freedom = n-1 = 68 - 1 = 67

t-value corresponding to 67 degrees of freedom and 95% confidence level is 1.9958

CI = 4.9 + (1.9958×0.35)/√68 = 4.98

CI = 4.9 - (1.9958×0.35)/√68 = 4.82

CI is (4.82, 4.98)

(2) Error margin = (t-value × standard deviation)/√sample size

From the formula above, error margin varies inversely as the square root of the sample size. Since the relationship between the error margin and sample size is inverse, increase in one (sample size) will conversely lead to a decrease in the other (error margin)

(3) mean = 37.5, sd = 0.6, n= 100, degree of freedom = n-1 = 100-1 = 99

t-value corresponding to 99 degrees of freedom and 90% confidence level is 1.6602

CI = 37.5 + (1.6602×0.6)/√100 = 37.5 + 0.10 = 37.60

CI = 37.5 - (1.6602×0.6)/√100 = 37.5 - 0.10 = 37.40

37.53 is within the confidence interval (37.40, 37.60)

(4) mean = 15.10, sd =0.08, n = 104, degree of freedom = n-1 = 104-1 = 103

t-value corresponding to 103 degrees of freedom and 97% confidence interval is 2.2006

CI = 15.10 + (2.2006×0.08)/√104 = 15.10 + 0.017 = 15.117

CI = 15.10 - (2.2006×0.08)/√104 = 15.10 - 0.017 = 15.083

CI is (15.083, 15.117)

4 0
3 years ago
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andrey2020 [161]

Answer:

The answer is J

Step-by-step explanation:

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hope this helped! :)

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