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Sloan [31]
3 years ago
8

ABC is translated 6 units up and 3 units left to create ∆A'B'C'.

Mathematics
1 answer:
aivan3 [116]3 years ago
6 0
B is the right answer for  this 

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Find the sum of the first 8 terms of the series. 1/2 + 1 + 2 + 4
Roman55 [17]

\bf \cfrac{1}{2}~~,~~\stackrel{2\cdot \frac{1}{2}}{1}~~,~~\stackrel{2\cdot 1}{2}~~,~~\stackrel{2\cdot 2}{4}~~,...

so as you can see the common ratio is 2, and the first term is 1/2,

\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad  \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1=\frac{1}{2}\\ n=8 \end{cases} \\\\\\ S_8=\cfrac{1}{2}\left( \cfrac{1-2^8}{1-2} \right)\implies S_8=\cfrac{1}{2}\left( \cfrac{-255}{-1} \right)\implies S_8=\cfrac{255}{2}

4 0
3 years ago
Read 2 more answers
67% as a fraction in simplest form
CaHeK987 [17]
It's 67/100 because a percent is out of 100 which is already simplified
6 0
3 years ago
Read 2 more answers
19. What is the 6th term in the sequence below? 1, 3, 7, 15, 31, _, 127​
bearhunter [10]
The 6th term in the sequence should be 63
6 0
2 years ago
The square of a number is equal to two less than three times the number. What are two possible values of the number?
ycow [4]

Answer:

A, 1,2

Step-by-step explanation:

we translate it first into language of math

we use n for the number

n² = 3n - 2

then, do some algebra things

n² - 3n + 2 = 0

then factorize it

(n - 2)(n - 1) = 0

first n

n - 2 = 0

n = 2

2nd n

n - 1 = 0

n = 1

so n can be 1 or 2

4 0
3 years ago
An accounting firm is planning for the next tax preparation season. From last years returns, the firm collects a systematic rand
Elena L [17]

Answer:

a)From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the standard error for the mean would be:

\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14

b) We want this probability:

P(\bar X >120)

And we can use the z score formula given by:

z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

P( z>2.143) = 1-P(Z

Step-by-step explanation:

Previous concepts

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".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

Part a

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the standard error for the mean would be:

\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14

Part b

We want this probability:

P(\bar X >120)

And we can use the z score formula given by:

z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

P( z>2.143) = 1-P(Z

4 0
3 years ago
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