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3 years ago

Which of the sequences is an arithmetic sequence?

Mathematics

2 answers:

Dennis_Churaev [7]3 years ago

7 0

Answer:

B. -3, -10, -17, -24, -31

Step-by-step explanation:

An Arithmetic sequence is defined as a set of numbers with a common difference. In answer choice B, it is seen that the difference between each number is seven.

A is incorrect as one to eight has a difference of seven, while the other numbers have a difference of eight.

C is incorrect as it skips the number 12 between 9 and 15, thus breaking the sequence.

D is incorrect as the numbers jump from positive to negative, thus not having a common difference.

Hope this helps!

11111nata11111 [884]3 years ago

7 0

Answer: “B”

Step-by-step explanation: An arithmetic sequence is a pattern where the same number is repeatedly added or subtracted. “B” would be the correct answer because each time, we have a common difference of -7 because we subtract 7 each time to get to our next term. We could also write this in recursive description as followed.

Starting at -3, subtract 7 to get to the next term.

You might be interested in

The surface area of a cylinder is 602.88. If the dimensions of the cylinder are

lana66690 [7]

Answer:

you all have to divide by 2

Step-by-step explanation:

602.88÷2= 301.44

3 0

2 years ago

In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%

lions [1.4K]

Answer:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

Step-by-step explanation:

Previous concepts

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".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

6 0

2 years ago

37 pumpkins each weighs 48 ounces

KiRa [710]

37 * 48 = 3 * (c - 140 )+ 2 *(c - 140 ) + ( c - 140 ) =>
37 * 48 = 6 * ( c - 140 ) =>
37 * 48 / 6 = c - 140 =>
37 * 8 = c - 140 =>
296 = c - 140 =>
c = 296 + 140 =>
c = 436 ounces.

5 0

3 years ago

Isabella save 2 nickels today, if she doubles the number of Nicole, she saves every day, how many days, including today, will it

Elden [556K]

Answer:

8 days

Step-by-step explanation:

On day 8, Isabella will save 256 nickels, bringing her total to 510.

_____

The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.

_____

The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.

The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...

an = a1·r^(n-1) = 2·2^(n-1) = 2^n

The sum of n terms of the sequence is ...

S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)

S = 2^(n+1) -2

We want S > 500, so ...

500 < 2^(n+1) -2

502 < 2^(n+1)

251 < 2^n

log(251) < n·log(2)

n > log(251)/log(2)

n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels

3 0

3 years ago

There are 3 3/4 pounds of bricks in a bag. Each brick weighs 5/8 of a pound. How many bricks are in the bag.

Bess [88]

Answer: There are 6 bricks in the bag.

Step-by-step explanation:

Convert from mixed number to decimal number. To do it, divide the numerator of the fraction by the denominator and add the result to the whole number part. Then:

$3\frac{3}{4}\ lb=(3+0.75)\ lb=3.75\ lb$

Convert from fraction to decimal number. To do it you need to divide the numerator by the denominator. Then, you get:

$\frac{5}{8}lb=0.625\ lb$

Let be "x" the number of bricks in the bag<em>.</em>

<em> </em>Based on the information given in the exercise, you can set up the following proportion:

$\frac{1}{0.625}=\frac{x}{3.75}$

Finally, you must solve for "x" in order to find its value. This is:

$(3.75)(\frac{1}{0.625})=x\\\\x=6$

8 0

3 years ago