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vladimir2022 [97]
3 years ago
15

A standard die (a six-sided cube with the numbers 1‚ 2‚ 3‚ 4‚ 5‚ and 6 on the sides) is rolled 150 times. Which of the following

is the most likely number of times that a 1 or a 4 would appear? A 2 B 25 C 50 D 100
Mathematics
1 answer:
Mama L [17]3 years ago
7 0

Answer:

50

Step-by-step explanation:

1÷6×150=25

1÷6×150=25

ans:25+25

=50

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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
3 years ago
The area of a square dollhouse is 289 square inches. How long is each side of the dollhouse?
EastWind [94]

Answer:

17

Step-by-step explanation:

8 0
3 years ago
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What is an equation of the line that passes through the points (6, 4) and (4,1)?
netineya [11]

Answer:

3/2 x-5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The sum of two numbers it 226. their differences is 200. what are the numbers?
jekas [21]
<span>To get the bigger number, divide by 2 the sum of the given sum of the numbers and their difference. In this case-
(226 + 200)/2 = 426/2 = 213.
To get the smaller number, divide by 2 the difference of the given sum of the numbers and their difference. In this case -
(226 - 200)/2 = 26/2 =13.
The two numbers are 213 and 13.
The bigger number is 213</span>
7 0
3 years ago
Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (3, 0), and (0, 3). Cro
Reil [10]

Answer:

27/2

Step-by-step explanation:

Given

Vertices (0, 0), (3, 0), and (0, 3)

Since the base of the equilateral in the plane perpendicular to the x-axis goes from the x-axis to the line y = 3 - x.

So, the length of each side of the triangle is (3-x)

Calculating the area;

Area = ½bh

Where b = base = 3 - x

height is calculated as;

h² = (3-x)² + (½(3-x))² --- from Pythagoras

h² = 9 - 6x + x² + (3/2 - ½x)²

Let h² = 0

0 = 9 - 6x + x² + (9/4 - 6/4x + ¼x²)

0 = 9 + 9/4 - 6x - 6/4 + x² + ¼x²

0 = 45/4 - 30x/4 + 5x²/4

0. = 5x²/4 - 30x/4 + 45/4

0 = 5x² - 15x/4 - 15x/4 + 45/4

0 = 5x(x/4-¾) - 15(x/4 - ¾)

0 = (5x - 15)(x/4 - ¾)

5x = 15 or x/4 = 3/4

x = 3 or x = 3

So, h = 3

Area = ½bh

Area = ½ * (3-x) * 3

Area = ½(9-3x)

Volume= Integral of ½(9-3x) {3,0}

V = 9/2 - 3x/2 {3,0}

V = 9x/2 - 3x²/4 {3,0}

V = 9(3)/2 - 3(3)²/4

V = 27/2 - 27/4

V = 27/2

4 0
3 years ago
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