Answer:
C), D) and E)
Step-by-step explanation:
First let's see what an arithmetic sequence is.
A arithmetic sequence is series of numbers where the difference between the successive terms must be a constant.
For example,
2, 4, 6, 8, 10.....
If you find the difference between the successive terms, it will be the same constant.
4 -2 = 2
6 -4 = 2
8 -6 = 2
This is called arithmetic sequence.
A and B are not the arithmetic sequence. The different is not the same constant.
C) 345, 346, 347, 348, 349....
Difference = 1 between the two successive terms.
So it is an arithmetic sequence.
D) 54, 71, 88, 105, 122...
Difference = 71 - 54 = 17
88 - 71 = 17
So it is an arithmetic sequence.
E) -3, -10, -17, -24, -31...
Difference = -10 -(-3) = -10 + 3 = -7
Difference of -10 and -17 is -17 -(-10) = -17 +10 = -7
So it is an arithmetic sequence.
Answer: C), D) and E)
Answer:
Step-by-step explanation:
From your last step, divide by 3 throughout.
You cannot divide by 6x throughout because 3 cannot be divided by 6x.
Another way to do it is:
However, if the question requires you to leave your answer in a single fraction in its simplest form, only the first answer is accepted.
This problem can be solved through simple arithmetic progression
Let
a1 = the first term of the sequence
a(n) = the nth term of the sequence
n = number of terms
d = common difference
Sn = sum of all terms
given
a1 = 12
a2 = 16
n = 10
d = 16 -12 = 4
@n = 10
a(n) = a1 + (n-1)d
a(10) = 12 + (9)4
a(10) = 48 seats
Sn = (n/2) * (a1 + a(10))
Sn = 5* (12 + 48)
Sn = 300 seats
Therefore the total number of seats is 300.
Answer: 0.9996
Step-by-step explanation:
Given : The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F.
Sample size : n=25
Let x be the random variable that represents the body temperatures of adults.
z-score :
For x= 99° F
Now, the probability that their mean body temperature is less than 99° F will be :-
Hence, the probability that their mean body temperature is less than 99° F = 0.9996
To find the probability that the mean body temperature of 25 randomly selected adults is less than 99°F, we can use the Central Limit Theorem and calculate the Z-score. The mean body temperature of adults is 98.6°F with a standard deviation of 0.60°F. The sample size is 25.
To find the probability that the mean body temperature of 25 randomly selected adults is less than 99°F, we can use the Central Limit Theorem. According to the Central Limit Theorem, the sampling distribution of the sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the mean body temperature of adults is 98.6°F with a standard deviation of 0.60°F. The sample size is 25. So, the mean of the sampling distribution would still be 98.6°F, but the standard deviation would be 0.60°F divided by the square root of 25, which is 0.12°F.
Now, we can use the Z-score formula to find the probability that the mean body temperature is less than 99°F. The Z-score is calculated by subtracting the population mean from the desired value (99) and dividing it by the standard deviation of the sampling distribution (0.12). We can then use a Z-table or calculator to find the probability associated with the Z-score.
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