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3 years ago

1

Mathematics

2 answers:

Sindrei [870]3 years ago

7 0

Answer:

Step-by-step explanation:

88+100+90+87=365

365 divided by 4=91.25

the answer is 88

alina1380 [7]3 years ago

4 0

The answer is 88 if you take the average as the mean.
100 + 90 + 88 + 87 = 365 / 4 is 91.25 which rounds down to 91 percent. If you want to get exactly 91% the answer would be 87 as you do 100+ 90+ 87 + 87 which is 364 / 4 which is 91...
Hope this helps!

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Consider the arithmetic sequence 13, 24, 35, ....

Nostrana [21]

Answer: 27

Step-by-step explanation:

The given sequence : 13, 24, 35, ....

Here, first term : a= 13

Common difference: d=24-13 =11

The nth term of arithmetic sequence is given by :-

$a_n=a+(n-1)d$

It is given that the nth term is 299, so put $a_n=299, a=13 ; d=11$

$299=13+(n-1)11$

Subtract 13 from both sides , we get

$286=(n-1)11$

Divide both sides by 11, we get

$26=n-1$

Add 1 on both sides , we get

$n=27$

Hence, the value of n= 27

4 0

3 years ago

Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample

fomenos

Answer:

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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

The Z-score measures how many standard deviations the measure 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

37% of the company's orders come from first-time customers.

This means that $p = 0.37$

A random sample of 225 orders will be used to estimate the proportion of first-time-customers.

This means that $n = 225$

Mean and standard deviation:

$\mu = p = 0.37$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.37*0.63}{225}} = 0.0322$

What is the probability that the sample proportion is between 0.26 and 0.38?

This is the pvalue of Z when X = 0.38 subtracted by the pvalue of Z when X = 0.26.

X = 0.38

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

By the Central Limit Theorem

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

$Z = \frac{0.38 - 0.37}{0.0322}$

$Z = 0.31$

$Z = 0.31$ has a pvalue of 0.6217

X = 0.26

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

$Z = \frac{0.26 - 0.37}{0.0322}$

$Z = -3.42$

$Z = -3.42$ has a pvalue of 0.0003

0.6217 - 0.0003 = 0.6214

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

5 0

3 years ago

Please help with the following

Neporo4naja [7]

Answer:

a: start at n=1 end at infinity equation = 4^n

b: start at n=3 end at 5 equation = n/(n+1)

c: start at n=1 end at 100 equation = (-1)^n*(1/n)

d: start at n=1 end at n=9 equation = -2

e: starts at n = 0, ends at infinity equation = 5 + 2n

f: starts at n = 0 ends at 4 equation = (7+n)*m^(6+n)

Let me know if you don't see how this works.

Step-by-step explanation:

So sigma notation has three parts, the start, the end and the equation, the start is below the sigma, the end is above and the equation of course is to the side. i will tell you the parts, but let me know if you need further explanation

4 + 16 + 64 + 256

I always start with checking if it is arithmetic which would mean something is added Well, you add 12 to 4 to get 16 and way more than 12 to get to 64, so that's not right.

Next I check geometric. 4*4 = 16 then 16*64, so we're good there. Geometric sequences have the form ab^x where a is the starting number and b is the number that is multiplied by. well both are 4 so we can just use 4^x, though with sigma notation n s usually used instead of x.

so, the equation is 4^n, the starting point is n=1 becaus the starting number is 4 and for 4^n to be 4 n has to be 1. Now, where does it end? Well it doesn't have one, which is shown by the ... at the end. so you should put infinity.

b. 3/4 + 4/5 + 5/6

Not arithmetic or geometric, you can't add anything to each or multiply anything 3/4 gets .05 added to it but 4/5 doesn't and 3/4 is mltiplied by 16/15 but 4/5 is not. So now we look for more special sequences..

Well for 3/4 4 is one more than 3, and the same in 4/5 and 5/6. Also, 4 is the denominator in the first then the numerator in the second, so we have a pattern. the equation is n/(n+1) then it starts at 3 and ends at 5 since there is no ...

c. -1 + 1/2 - 1/3 + 1/4 - ... + 1/100

Again, not arithmetic of geometric. First thing to notice is that it alternates from - to +, now how can a number do that? well what is a negative number to different exponents? let's take (-1)^1, (-1)^2, (-1)^3 and so on. ou'll notice this alternates between -1 and 1, so let's use that. also note the first number is negative, so we want to make sure that's the case for us.

Now for the numbers themselves. I think the pattern is pretty obvious 1/1, 1/2, 1/3 and so on, so the equation is 1/n up to 100. So this one does have an end, even though there's that ..., there is also a number after that though. So let's set this up with a start at 1 and end at 100

(-1)^n*(1/n) and it keeps the negative as the first number too

d. -2 - 2 - 2 - 2 - 2 - 2 - 2 - 2

This one's pretty easy, there are eight 2s. since the 2s have nothng to do with any variable the equation is just 2, and we can start at any n as long as we end at an n 8 away. let's do it normally and start at n=1 so we end at n=9

e. 5 + 10 + 17 + 26 + ...

... means no end again. No obvious pattern so let's check arithmetic and geometric. Well we add 5 to 5, 7 to 10 then 9. Now, those aren't the same numbers, but they are increasing 5 has 2 added to it to get to 7, then 7 gets 2 added to get to 9. so the equation is 5 + (2n) as long as it starts at n=0. So all together that's starts at n = 0, ends at infinity equation = 5 + 2n

f. 49m^6 + 64m^7 + 81m^8 + 100m^9 + 121m^10

Little bit tricky, hope you know your square numbers. more obviously though the exponents are increasing y 1, so we have that. m^(6+n) where n starts at 0 and then ends at 4 to get to m^(6+4) at the end. The numbers of the terms meanwhile are increasing as well. Hopefully you can tell they are square numbers. 49 = 7^2 64 = 8^2 and so on. so it starts at 7^2so now we know the equation is (7+n)m^(6+n). You could also play with the start and ending points to make it look simpler, but I would just go with that.

5 0

3 years ago

Samples of laboratory glass are in small, light packaging or heavy, large packaging. Suppose that 2% and 1%, respectively, of th

mixer [17]

Answer:

The solution is attached below:

6 0

4 years ago

Please help it is easy. i just dont get it. you get extra points for this question

Igoryamba

2,3,7,and 5 are the factors

7 0

3 years ago