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taurus [48]
3 years ago
5

In order to estimate the average time spent on the computer terminals per student at a local university, data were collected fro

m a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. The standard error of the mean is_______.
a. 7.5
b. 0.014
c. 0.160
d. 0.133
Mathematics
1 answer:
Ksju [112]3 years ago
7 0

Answer:

d. 0.133

Step-by-step explanation:

-Standard error is  calculated using the formula:

E=\frac{\sigma}{\sqrt{n}}\\\\\sigma-=standard \ deviation\\n=sample \ size

#We substitute the given values in the formula to solve for E:

E=\frac{\sigma}{\sqrt{n}}\\\\=\frac{1.2}{\sqrt{81}}\\\\=0.133

Hence, the standard error is 0.133 and the correct option is d

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Step-by-step explanation:

a_1=6\\a_2=a_1+1\to a_2=6+1=7\\a_3=a_2+1\to a_3=7+1=8\\a_4=a_3+1\to a_4=8+1=9\\\vdots\\\\\text{The recursive formula}\\a_n=\left\{\begin{array}{ccc}a_1=6\\a_n=a_{n-1}+1\end{array}\right\\\\\text{It's an arithmetic sequence with}\ a_1=6\ \text{and difference}\ d=1\\\\\text{The explicit formula of an arithmetic sequence:}\\\\a_n=a_1+(n-1)d\\\\\text{Substitute:}\\\\a_n=6+(n-1)(1)\\a_n=6+n-1\\a_n=5+n\\\\a_n=n+5

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3 years ago
Serena has attached a 10 inch ribbon to the corners of a frame to hang it on the wall. The frame 9 inches wide. How far above th
kherson [118]

Answer: The hook would be 2.2 inches (approximately) above the top of the frame

Step-by-step explanation: Please refer to the picture attached for further details.

The top of the picture frame has been given as 9 inches and a 10 inch ribbon has been attached in order to hang it on a wall. The ribbon at the point of being hung up would be divided into 5 inches on either side (as shown in the picture). The line from the tip/hook down to the frame would divide the length of the frame into two equal lengths, that is 4.5 inches on either side of the hook. This would effectively give us two similar right angled triangles with sides 5 inches, 4.5 inches and a third side yet unknown. That third side is the distance from the hook to the top of the frame. The distance is calculated by using the Pythagoras theorem which states as follows;

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse (longest side) and AB and BC are the other two sides

5^2 = 4.5^2 + BC^2

25 = 20.25 + BC^2

Subtract 20.25 from both sides of the equation

4.75 = BC^2

Add the square root sign to both sides of the equation

2.1794 = BC

Rounded up to the nearest tenth, the distance from the hook to the top of the frame will be 2.2 inches

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3 years ago
In an examination 80% students passed. if 15 less have appeared and 10 less have passed, the ratio of passers to failures would
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Answer:

60 students passed, and 75 appeared in examination.

Step-by-step explanation:

Let's say s is the total number of students and p is the number of students who passed.

80% of the students passed, so:

0.8 s = p

If there were 10 less passers, and 15 less students (5 less failures), then the ratio of passers to failures would be 5/1.

(p − 10) / (s − p − 5) = 5 / 1

Simplify the second equation:

p − 10 = 5 (s − p − 5)

p − 10 = 5s − 5p − 25

6p = 5s − 15

Substitute the first equation.

6 (0.8 s) = 5s − 15

4.8 s = 5s − 15

0.2 s = 15

s = 75

p = 0.8 s

p = 60

60 students passed, and 75 appeared in examination.

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