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Doss [256]
2 years ago
9

What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?

Mathematics
1 answer:
Mila [183]2 years ago
5 0
Average rate of change refers to the slope of a function/equation. 
To solve this, plug in for both x values and calculate the average, or mean. 

x = 1 
f(1) = 5(2)^1 
      = 5(2) 
      = 10

x = 5 
f(5) = 5(2)^5
      = 5(32) 
      = 160

Now, you calculate the average: 
10 + 160 = 170 
Divide by 2 and you get 85.



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Are the marks one receives in a course related to the amount of time spent studying the subject? To analyze this mysterious poss
sertanlavr [38]

Answer:

a) 98.522

b) 0.881

c) The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time.

Step-by-step explanation:

a.

As the mentioned in the given instruction the co-variance is first computed in excel by using only add/Sum, subtract, multiply, divide functions.

Marks y Time spent x y-ybar x-xbar (y-ybar)(x-xbar)

77                    40 5.1         1.3 6.63

63                     42 -8.9            3.3 -29.37

79                     37 7.1            -1.7 -12.07

86                     47 14.1            8.3 117.03

51                    25 -20.9  -13.7 286.33

78                     44 6.1            5.3 32.33

83                      41 11.1            2.3 25.53

90                     48 18.1            9.3 168.33

65                     35 -6.9           -3.7 25.53

47                    28 -24.9 -10.7 266.43

Covariance=\frac{sum[(y-ybar)(x-xbar)]}{n-1}

Co-variance=886.7/(10-1)

Co-variance=886.7/9

Co-variance=98.5222

The co-variance computed using excel function COVARIANCE.S(B1:B11,A1:A11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted co-variance is 98.52222.

b)

The correlation coefficient is computed as

Correlation coefficient=r=\frac{sum[(y-ybar)(x-xbar)]}{\sqrt{sum[(x-xbar)]^2sum[(y-ybar)]^2} }

(y-ybar)^2 (x-xbar)^2

26.01        1.69

79.21       10.89

50.41             2.89

198.81       68.89

436.81       187.69

37.21       28.09

123.21        5.29

327.61        86.49

47.61         13.69

620.01         114.49

sum(y-ybar)^2=1946.9

sum(x-xbar)^2=520.1

Correlation coefficient=r=\frac{886.7}{\sqrt{520.1(1946.9)} }

Correlation coefficient=r=\frac{886.7}{\sqrt{1012582.69} }

Correlation coefficient=r=\frac{886.7}{1006.2717 }

Correlation coefficient=r=0.881

The correlation coefficient computed using excel function CORREL(A1:A11,B1:B11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted correlation coefficient is 0.881.

c)

The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time. It means that as the study time increases the marks of student also increases and if the study time decreases the marks of student also decreases.

The excel file is attached on which all the related work is done.

Download xlsx
7 0
2 years ago
(t,-3) and (2,6); Slope = -1
tangare [24]
-1=\frac{Δy}{Δx}
-1=\frac{6-(-3)}{2-t}
t-2=9
t=11
4 0
3 years ago
If cos(x) = 0.5, then what is x?
Anestetic [448]

Answer:

=60 the second option.

Step-by-step explanation:

Given the trigonometric ratio, we can find the value of the angle by simply finding the inverse of the given ratio.

If for example Cos ∅= a, then ∅=Cos⁻¹a

If Cos (x)= 0.5, then x= Cos⁻¹ 0.5

Cos⁻1 0.5=60°

The angle whose sine is 0.5 is ∅=60°

5 0
3 years ago
Read 2 more answers
Additive inverse of -0.5
Veseljchak [2.6K]

Answer:

0.5

Step-by-step explanation:

If you add 0.5 to -0.5, it will equal 0.

4 0
2 years ago
Helppp PLS
Alik [6]
The answer to 1. Is c

The answer to 2. Is 176
8 0
2 years ago
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