Step-by-step explanation:
Let's look at A(x) and see how it is different from f(x)
- it is shifted downwards by 8 units
- it is not shifted to the left or the right
Therefore A(x) = f(x) - 8
Let's look at B(x) and see how it is different from f(x)
- it is not shifted downwards or upwards
- it is shifted to the left 7 units
Therefore B(x) = f(x + 7)
Let's look at C(x) and see how it is different from f(x)
- it is shifted upwards by 4 units
- it is shifted to right by 5 units
Therefore C(x) = f(x - 5) + 4
Let's look at D(x) and see how it is different from f(x)
- it is not shifted downwards or upwards
- it is not shifted to right by 12 units
Therefore D(x) = f(x - 12)
Answer:
3d - 4f
Step-by-step explanation:
(12d + 28f) - 5f - (27f + 9d)
12d + 28f - 5f - 27f - 9d
(12-9)d + (28-5-27)f
3d - 4f
don't forget to put bracket, it is fundamental
To find the highest common factor (HCF) between two numbers , first to take HCF of both the numbers.
- Take every common prime factor between 12 and 40
- Finally, identify the factors common to each number and multiply those common factors together.
Answer:
The confidence interval for the mean is given by the following formula:
Step-by-step explanation:
1) Notation and definitions
number of people or things with a specific characteristic.
random sample taken
estimated proportion of people or things with a specific characteristic.
true population proportion of people or things with a specific characteristic.
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The population proportion have the following distribution
If we have all the conditions required in order to construct the confidence interval:
1) Random sample selected
2) np >10
3) n(1-p)>10
Then the confidence interval for the mean is given by the following formula: