All categories

3 years ago

An arithmetic sequence with a third term of 8 and a constant difference of 5.

1 answer:

8 0

An arithmetic sequence (a_n) is as follows:

$a_1\\a_2=a_1+d\\a_3= a_1+2d\\a_4=a_1+3d,...$ where $a_1$ is the first term and d is the constant difference,

thus, we see that the n'th term of an arithmetic sequence is $a_n=a_1+(n-1)d$

in our particular case d=5, the third term is 8, so we have:

$a_3=8=a_1+2\cdot5\\\\8=a_1+10\\\\a_1=-2$

and the general term is $a_n=-2+5(n-1)$ ,

Answer: first term is -2, n'th term is -2+5(n-1)

You might be interested in

What is a 25% markup on $27.00?

kipiarov [429]

the value of 25% marked up on $6.75

8 0

3 years ago

To estimate the mean height μ of male students on your campus,you will measure an SRS of students. You know from government data

nexus9112 [7]

Answer:

a) $\sigma = 0.167$

b) We need a sample of at least 282 young men.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

This Zscore is how many standard deviations the value of the measure X is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

(a) What standard deviation must x have so that 99.7% of allsamples give an x within one-half inch of μ?

To solve this problem, we use the 68-95-99.7 rule. This rule states that:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we want 99.7% of all samples give X within one-half inch of $\mu$ . So $X - \mu = 0.5$ must have $Z = 3$ and $X - \mu = -0.5$ must have $Z = -3$ .

$Z = \frac{X - \mu}{\sigma}$

$3 = \frac{0.5}{\sigma}$

$3\sigma = 0.5$

$\sigma = \frac{0.5}{3}$

$\sigma = 0.167$

(b) How large an SRS do you need to reduce the standard deviationof x to the value you found in part (a)?

You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. This means that $\sigma = 2.8$

The standard deviation of a sample of n young man is given by the following formula

$s = \frac{\sigma}{\sqrt{n}}$

We want to have $s = 0.167$

$0.167 = \frac{2.8}{\sqrt{n}}$

$0.167\sqrt{n} = 2.8$

$\sqrt{n} = \frac{2.8}{0.167}$

$\sqrt{n} = 16.77$

$\sqrt{n}^{2} = 16.77^{2}$

$n = 281.23$

We need a sample of at least 282 young men.

6 0

4 years ago

Y intercepts of 3x^2-12x+6

Inessa05 [86]

Y=3x^2. -12x+6

If x= 0 then y= 3•0^2 -12•0+6=6
X=0, y=6

y intercept is the place where the curve touches the y-axis and is at point (0, 6)

6 0

3 years ago

PLEASE ANSWER ASAP! 15 POINTS ! NO SCAM LINKS OR REPORTED :)

mixas84 [53]

Answer: C

Step-by-step explanation: You have to plug in the values to see if it matches the values on the table of values

5 0

3 years ago

Can you help me fill in the missing blanks thank you!!

Natasha_Volkova [10]

You just have to find what number times 9 equals your original equation so 9 and -2 are -18 and 9 and 3 are 27 so your distributed equation would be:

9(-2x+3)

5 0

3 years ago