Answer:
Option c.
Step-by-step explanation:
Using the normal curve to approximate a sampling distribution:
For a sample size n and a proportion n, the normal curve can be used if:
and 
Option a:


So option a cannot be used.
Option b:


So option b cannot be used.
Option c:


So option c can be used, and is the answer
Option d:


So option d cannot be used.
The answer is given by option c.
Answer:Please see answer in explanation column
Step-by-step explanation:
A
The sum of a number and 7 is not more than 10
Given answer: x + 7 < 10 , This is false
Reason :Not more than 10 means at most 10, less than or equal to 10 , " or " not greater than 10 "and therefore the correct inequality is written as
x + 7 ≤ 10
B
The product of a number and 4 is at least 20
Given answer: 4X > 20 ---- False
Reason :At least 20 means at no less than 20 " or " greater than or equal to 20 therefore the correct inequality is written as
4X ≥ 20
C
The difference between a 15 and a number is at most 12
Given answer: 15-x>12----False
Reason :At most 12 means " no more than 12 , " " less than or equal to 12 , " or " not greater than 12"therefore the correct inequality is written as
15-x ≤ 12
D
The quotient of a number and 8 is greater than or equal to
Given answer 8x <3 --False
Reason : It clearly stated greater than or equal to 3. Therefore the correct inequality is 8x ≥ 3
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Answer:
See below ~
Step-by-step explanation:
<u>Given</u>
- Maitri and Aabhas do a work in 12 hours
- Aabhas and Kavya do the work in 15 hours
- Kavya and Maitri do the work in 20 hours
<u>Solving</u>
- Take Maitri, Aabhas, and Kavya to be x, y, z respectively
- <u>x + y = 12</u> (1)
- <u>y + z = 15</u> (2)
- <u>x + z = 20</u> (3)
<u>Take Equation 1 and rewrite it so that it is equal to x.</u>
<u>Take Equation 2 and rewrite it so that it is equal to z.</u>
<u>Now, substitute these values in Equation 3.</u>
- x + z = 20
- 12 - y + 15 - y = 20
- -2y + 27 = 20
- 2y = 7
- y = 7/2 = <u>3.5 hours [Aabhas]</u>
<u></u>
<u>Substitute the value of y in Equation 1.</u>
- x + 3.5 = 12
- x = <u>8.5 hours [Maitri]</u>
<u>Substitute the value of y in Equation 2.</u>
- 3.5 + z = 15
- z = <u>11.5 hours [Kavya]</u>
<u></u>
<u>Add the values of x, y, and z together.</u>
- x + y + z
- 8.5 + 3.5 + 11.5
- 12 + 11.5
- <u>23.5 hours [together]</u>
These are two separate problems: in the first we will have to substitute in a new value for x into the original equation and in the second we will manipulate the preexisting equation for f(x).
To begin, we will sub in f(x/3). To do this, we will substitute each variable x in the equation (in this case there is only one) with x/3, and then simplify the resulting equation.
f(x) = 6x - 18
f(x/3) = 6(x/3) - 18
To simplify, we should distribute the 6 on the right side of the equation.
f(x/3) = 6x/3 - 18
Now, we can divide the first term on the right side to finalize our simplification.
f(x/3) = 2x -18
Secondly, we are asked to find f(x)/3. To do this, we will take our original value for f(x), and then simplify divide that entire function by 3.
f(x) = 6x - 18
f(x)/3 = (6x-18)/3
This means that we must divide each term of the binomial by 3, so we are really computing
f(x)/3 = 6x/3 - 18/3
We can simplify by dividing both of the terms.
f(x)/3 = 2x - 6
Therefore, your answer is that f(x/3) = 2x - 18, but f(x)/3 = 2x - 6. It is important to recognize that these are two similar, yet different, answers.
Hope this helps!