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Nikolay [14]
3 years ago
15

(A) If the 13th and 38th terms of an arithmetic sequence are -53 and -128,

Mathematics
1 answer:
grigory [225]3 years ago
7 0

9514 1404 393

Answer:

  (A) -2018

  (B) 5/36

Step-by-step explanation:

(A) The rate of change between any pair of terms in an arithmetic sequence is the same:

  (a668 -a38)/(668 -38) = (a38 -a13)/(38 -13)

  a668/630 = a38/630 +(a38 -a13)/25 . . . . add a38/630 to both sides

  a668 = a38 +630/25(a38 -a13) = -128 +25.2(-128 -(-53)) = -128 -1890

  a668 = -2018

__

(B) The sum of an infinite geometric series is ...

  S = a1/(1 -r) . . . . . . for first term a1 and common ratio r

We are given S = 6, a1 = 5, so we can find r to be ...

  6 = 5/(1 -r)

  1 -r = 5/6

  1 -5/6 = r = 1/6

Then the 3rd term is ...

  a3 = 5×(1/6)^(3 -1) = 5/36

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Answer:

2 hours or less depending on how skilled or how they're felling that day

Step-by-step explanation:

4 0
3 years ago
a major metroplitan newspaper selected a simple random sample of 1,600 readers from their list of 100,000 subscribers. they aske
Arisa [49]

Answer:

The 99% confidence interval for the proportion of readers who would like more coverage of local news is (0.3685, 0.4315).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 1600, \pi = 0.4

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 2.575\sqrt{\frac{0.4*0.6}{1600}} = 0.3685

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 2.575\sqrt{\frac{0.4*0.6}{1600}} = 0.4315

The 99% confidence interval for the proportion of readers who would like more coverage of local news is (0.3685, 0.4315).

7 0
3 years ago
Solve the equation:<br><br> a) -3 = 7+2t/3<br><br> b) 4(5x-2) = 7(2x+3) <br><br> c) 2x-6 = 30-2.5x
Umnica [9.8K]
Let's start by solving the first equation.

a) -3 = 7 + 2t/3 
To begin simplifying this equation, we should multiply both sides by 3 to get rid of the denominator on the right side of the equation.
-9 = 7 + 2t
Next, we should subtract 7 from both sides to cancel out the 7 on the right side.
-16 = 2t
Finally, we should divide both sides by 2.
t= -8


Now let's move on to the next equation.

b) 4(5x-2) = 7(2x+3)
Let's use the distributive property to get rid of the parentheses and their coefficients.
20x-8 = 14x + 21

Now, lets subtract 14x from both sides of the equation.

6x - 8 = 21

Next, let's add 8 to both sides of the equation.

6x = 29

And divide both sides by the coefficient of x, which is 6.

x = 29/6 or 4 5/6

Now for the last equation.

C) 2x - 6 = 20 - 2.5x
First, we should add 2.5x to both sides to cancel out the -2.5x on the right side of the equation.
4.5x - 6 = 20
Now, let's add 6 to both sides to get the variable term alone.
4.5x = 26
Finally, we should divide both sides by 4.5 to get x by itself.
x = 5 7/9

Hope this helps! :)
7 0
3 years ago
PLSSSSSSSSSSASS HELPPPPPPPPPPP MEEEEEEEE OUTTTTT
allochka39001 [22]
The answer is f

jowokandnrjeosozmd gnal
8 0
3 years ago
PLEASE HELP I BEG CLICK ON THIS!! It’s not that hard<br> :(((( sorry if blurry
mash [69]

Answer:

b hope i helped you have a good day

8 0
3 years ago
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