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3 years ago

Enter the first four terms.

Mathematics

1 answer:

Inga [223]3 years ago

8 0

Answer:

1/2, 2, 9/2, and 8.

Step-by-step explanation:

In this case, we have an explicit rule.

So, to find the nth term, we can simply substitute a value into our function and evaluate.

For the first term, n=1. Thus:

$f(1)=\frac{(1)^2}{2}$

Evaluate:

$f(1)=\frac{1}{2}$

Hence, our first term is 1/2.

For the second term, n=2. Thus:

$f(2)=\frac{(2)^2}{2}$

Evaluate:

$f(2)=\frac{4}{2}=2$

Hence, the second term is 2.

For the third term, n=3. Thus:

$f(3)=\frac{3^2}{2}=\frac{9}{2}$

So, the third term is 9/2.

And for the fourth term, n=4. Thus:

$f(4)=\frac{4^2}{2}=\frac{16}{2}=8$

Therefore, the fourth term is 8.

Hence, our first four terms are: 1/2, 2, 9/2, and 8.

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Answer these series of events

Alchen [17]

Answer: A= 34

B= 25

C= -30

D= -25

E= -1.3

F= 0.6 repeating or rounded to the nearest tenth place 0.7

Hope this helps!

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Caroline has a movie card worth $75 that her grandfather gave to her for her birthday. After seeing her first movie, the card’s

faust18 [17]

Answer:

f(m) = 75-8m

Step-by-step explanation:

She began with $75. After the first movie, she had $67 remaining; this means she spent

75-67 = $8

After the second movie, she had $59 remaining; she spent

67-59 = $8

After the third movie, she had $51 remaining; she spent

59-51 = $8

Each movie costs $8. Letting m represent the number of movies, this gives us 8m.

Since she is spending money, we subtract this from the original amount, $75; this gives us

f(m) = 75-8m

3 0

3 years ago

In a recent year, a poll asked 2362 random adult citizens of a large country how they rated economic conditions. In the poll,

Harman [31]

Answer:

a) The 99% confidence interval is given by (0.198;0.242).

b) Based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

c) $\alpha=0.01$

Step-by-step explanation:

Data given and notation

n=2362 represent the random sample taken

X represent the people who says that they would watch one of the television shows.

$\hat p=\frac{X}{n}=0.22$ estimated proportion of people rated as Excellent/Good economic conditions.

$p_o=0.24$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that 24% of people are rated with good economic conditions:

Null hypothesis: $p=0.24$

Alternative hypothesis: $p \neq 0.24$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Part a: Test the hypothesis

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np = 2362x0.22=519.64>10 and n(1-p)=2364*(1-0.22)=1843.92>10

Condition satisfied.

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.22 -0.24}{\sqrt{\frac{0.24(1-0.24)}{2362}}}=-2.28$

The confidence interval would be given by:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The critical value using $\alpha=0.01$ and $\alpha/2 =0.005$ would be $z_{\alpha/2}=2.58$ . Replacing the values given we have:

$0.22 - (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.198$

$0.22 + (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.242$

So the 99% confidence interval is given by (0.198;0.242).

Part b

Statistical decision 

P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided is $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

So based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

Part c

The confidence level assumed was 99%, so then the signficance is given by $\alpha=1-confidence=1-0.99=0.01$

6 0

3 years ago

Sixty dash fivesixty-five percent of households say they would feel secure if they had? $50,000 in savings. you randomly select

Effectus [21]

To solve the following problems, we use the binomial probability equation:

P (r) = [n!/(n-r)! r!] p^r q^(n-r)

where,

n = total number of households = 8

r = number of sample

p = probability of success = 65% = 0.65

q = probability of failure = 0.35

A. r = 5

P (r=5) = [8! / 3! 5!] 0.65^5 0.35^3

P (r=5) = 0.28

B. r >5

P (r=6) = [8! / 2! 6!] 0.65^6 0.35^2

P (r=6) = 0.26

P (r=7) = [8! / 1! 7!] 0.65^7 0.35^1

P (r=7) = 0.14

P (r=8) = [8! / 0! 8!] 0.65^8 0.35^0

P (r=8) = 0.03

Therefore total is:

P (r>5) = 0.26 + 0.14 + 0.03 = 0.43

C. r ≤ 5

P (r ≤ 5) = 1 - P (r>5)

P (r ≤ 5) = 1 – 0.43

P (r ≤ 5) = 0.57

3 0

3 years ago

Find the value of x. Round your answer to the nearest tenth.

skad [1K]

Answer:

x = 9.7

Step-by-step explanation:

Reference angle (θ) = 68°

Opposite = 24

Adjacent = x

Apply, the trigonometric function, TOA which is:

$tan (/theta) = \frac{Opp}{Adj}$

Plug in the values

$tan 68 = \frac{24}{x}$

Multiply both sides by x

$x*tan 68 = 24$

Divide both sides by tan 68

$x = \frac{24}{tan 68}$

x = 9.69662942

x = 9.7 (nearest tenth)

8 0

3 years ago