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2 years ago

11

Here are the first five terms of a number sequenceS . 10 16 22 28 34 Find an expression, in terms of n , for the nth term of thi

s sequence.

1 answer:

andrew11 [14]2 years ago

8 0

Answer:

t = 4 + 6n

Step-by-step explanation:

a = 10

d = 6

in general

tn = a + (n-1)*d

tn = 10 + (n-1)*6

tn = 10 + 6n - 6

tn = 4 + 6n

So if n = 5 then

t5 = 4 + 6*5

t5 = 4 + 30

t5 = 34 which agrees with your givens.

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Prove the following using a proof by contradiction:The average of four real numbers is greater than or equal to at least one of

skelet666 [1.2K]

Answer:

By contradiction it can be proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

Step-by-step explanation:

Method of contradiction means we assume opposite to the facts to be proved and then we contradict our assumption.

As a result, we prove the fact.

Here, let the four number be:

$p, q, r, s$

The average will be Sum of all numbers divided by count of numbers.

$\dfrac{p+ q+ r+ s}4$

Now, let us assume the opposite that the average is less than all the numbers.

i.e.

$\dfrac{p+ q+ r+ s}4$

$\dfrac{p+ q+ r+ s}4$

Now, let us add all of them:

$\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 < p+q+r+s\\\Rightarrow \dfrac{4(p+q+r+s)}4$

Which can never be possible hence, our assumption is contradicted.

our assumption is wrong.

Therefore, by contradiction it is proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

8 0

2 years ago

The radius of circle G is 4 cm. What is the tangent

qaws [65]

The tangent of a given circle is perpendicular to the radius a the point called point if tangency. The radius of the circle is perpendicular to the tangent at the point of tangency. This property is especially useful in cases where the radius that connects to the point of tangency forms a part of right angle because the pythagorean theorem and trigonometry apply to right angles.

4 0

2 years ago

A web page design firm has two designs for an online hardware store. To determine which is the more effective design, the firm u

tatyana61 [14]

Answer:

Explanatory variable : web page design

Response variables : Visitor's rating and amount of time visiting the site.

Kindly check explanation for the rest.

Step-by-step explanation:

The explanatory variable simply means the independent or predictor variable which is used to bring about a change in the dependent or predicted variable. The explanatory variable in the scenario above is the web page design which is used to measure the behavior and changes in the response variable which are the rating given by visitors and the number of visits on each of the two different web page designs available (explanatory variable).

The confounding factor which may affect the study is the different area assigned to test the effectiveness of each page ; designating one page for the Oakland area and the other for Miami. User preferences for each area may itself mask the actual outcome of the experiment.

4 0

2 years ago

p.s 15 points Which best describes the solution to 4 minus 7? Because Negative 4 + (negative 7) is an equivalent expression, the

luda_lava [24]

Answer:

because 4 + (negative 7) is an equivalent expression, the answer is -3.

Step-by-step explanation:

4 + (-7) = -3

4 0

1 year ago

According to a Pew Research survey, about 27% of American adults are pessimistic about the future of marriage and the family. Th

IgorLugansk [536]

Answer:

P(X≤5)=0.5357

Step-by-step explanation:

Using the binomial model, the probability that x adults from the sample, are pessimistic about the future is calculated as:

$P(x)=\frac{n!}{x!(n-x)!} *p^{x}*(1-p)^{n-x}$

Where n is the size of the sample and p is the probability that an adult is pessimistic about the future of marriage and family. So, replacing n by 20 and p by 0.27, we get:

$P(x)=\frac{20!}{x!(20-x)!}*0.27^{x}*(1-0.27)^{20-x}$

Now, 25% of 20 people is equal to 5 people, so the probability that, in a sample of 20 American adults, 25% or fewer of the people are pessimistic about the future of marriage and family is equal to calculated the probability that in the sample of 20 adults, 5 people of fewer are pessimistic about the future of marriage and family.

Then, that probability is calculated as:

P(X≤5)= P(1) + P(2) + P(3) + P(4) + P(5)

Where:

$P(0)=\frac{20!}{0!(20-0)!}*0.27^{0}*(1-0.27)^{20-0}=0.0018$

$P(1)=\frac{20!}{1!(20-1)!}*0.27^{1}*(1-0.27)^{20-1}=0.0137$

$P(2)=\frac{20!}{2!(20-2)!}*0.27^{2}*(1-0.27)^{20-2}=0.0480\\P(3)=\frac{20!}{3!(20-3)!}*0.27^{3}*(1-0.27)^{20-3}=0.1065\\P(4)=\frac{20!}{4!(20-4)!}*0.27^{4}*(1-0.27)^{20-4}=0.1675\\P(5)=\frac{20!}{5!(20-5)!}*0.27^{5}*(1-0.27)^{20-5}=0.1982$

Finally, P(X≤5) is equal to:

P(X≤5) = 0.0018+0.0137 + 0.0480 + 0.1065 + 0.1675 + 0.1982

P(X≤5) = 0.5357

3 0

2 years ago