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Anika [276]
3 years ago
7

The mean of 3 consecutive terms in an arithmetic sequence is 10, and the mean of their squares is 394. What is the largest of th

e 3 terms?
Mathematics
1 answer:
poizon [28]3 years ago
5 0
Let the numbers be:
a, a+b, a+2b
mean of the numbers is:
(a+a+b+a+2b)/3=10
(3a+3b)/3=10
a+b=10
thus second term is 10

The sum of square will be:
((10 - b)² + 10² + (10 + b)²<span>) / 3 = 394 
</span>(100 - 20b + b² + 100 + 100 + 20b + b²<span>) / 3 = 394
</span><span>(300 + 2b</span>²<span>) / 3 = 394
</span>(150+b²)=591
b²=441
b=-21,21

thus the numbers will be:
10-21, 10, 10+21
=-11,10,31
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horrorfan [7]

Answer:

AOE = 138, EOD = 48

Step-by-step explanation:

Since AD is the diameter of the circle and goes through the middle

angle AOE + angle EOD  = 180

Solving the equation (x + 138) + ( x+ 48) = 180

We get x = 0.

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2 years ago
4 and 1 over 4 divided by 1 and 7 over 8
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3 and 23 Over 32

Step-by-step explanation:

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2 years ago
A sociologist was investigating the ages of grandparents of high school students. From a random sample of 10 high school student
umka2103 [35]

Answer:

(69.8-71.6) -2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= -8.908  

(69.8-71.6) +2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= 5.308  

So then the confidence interval for the difference of means is given by:

-8.908 \leq \mu_M -\mu_F \leq 5.308

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".

\bar X_{M}= 69.8 represent the mean for the age of grandmother

\bar X_{F}= 71.6 represent the mean for the age of grandfather

s_{M}= 8.38 represent the sample deviation for the age of grandmother

s_{F}= 6.65 represent the sample deviation for the age of grandfather

n_M = n_F= 10

Solution to the problem

For this case the confidence interval is given by:

(\bar X_{M} -\bar X_F) \pm t_{\alpha/2} \sqrt{\frac{s^2_M}{n_M} +\frac{s^2_F}{n_F}}

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n_M +n_F-2=10+10-2=18

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that t_{\alpha/2}=2.101

And replacing we got:

(69.8-71.6) -2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= -8.908  

(69.8-71.6) +2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= 5.308  

So then the confidence interval for the difference of means is given by:

-8.908 \leq \mu_M -\mu_F \leq 5.308

5 0
3 years ago
Please need help on this
SashulF [63]

We can Notice that ∠ABC = ∠ACB

We know that if Two Angles are Equal then Angles Corresponding to those Sides are also Equal.

⇒ AB = AC

⇒ 4x + 4 = 6x - 14

⇒ 6x - 4x = 4 + 14

⇒ 2x = 18

⇒ x = 9

⇒ Length of BC = 2x + 7 = 2(9) + 7 = 18 + 7 = 25 units

4 0
3 years ago
A plane travels at a constant speed. It take 5 hours to travel 6,250 miles. What is the plane's speed in miles per hour?
crimeas [40]

Answer:

1,250 miles/hour

Step-by-step explanation:

To find miles per hour - \frac{6250 miles}{5 hours}.

4 0
3 years ago
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