All categories

3 years ago

Given a sequence is defined by the explicit definition t_n= n^2+nt n = n 2 + n, find the 4th term of the sequence. (i.e. t_4t 4)

Mathematics

2 answers:

Ne4ueva [31]3 years ago

7 0

<em>*100% CORRECT ANSWERS</em>

kykrilka [37]3 years ago

5 0

Answer:

Question 1: 20

Question 2: 27

Step-by-step explanation:

Question 1:

Given a sequence is defined by the explicit definition $t_{n} = n^{2} + n$

Therefore, the 4th term i.e. $t_{4} = 4^{2} + 4 = 20$ (Answer)

So, the third option is correct.

Question 2:

Given a sequence is defined by the explicit definition $t_{n} = 2^{n} - n$

Therefore, the 5th term i.e. $t_{5} = 2^{5} - 5 = 27$ (Answer)

So, the third option is correct.

You might be interested in

The chart gives three different international calling plans. Jamie has budgeted $20 per month for international calls. Round ans

oksano4ka [1.4K]

A. 200.625 minutes B. 184.166 minutes C. 200 minutes (round these answers like the question asked) 4. Plan A is the best because you get the most minutes for your money. I will explain my work for A, but if you need to explain the rest just ask. So, if you have to pay $3.95 every month no matter what and $0.08 for every minute you talk you can write the equation as, Cost = 3.95 + 0.08m (m stands for minutes), and the cost is 20$ then the equation is 20 = 3.95 + 0.08m, subtract 3.95 from the right side to make it 16.05 = 0.08m, then divide everything by 0.08 to get m, which gives you m= 200.625

4 0

3 years ago

The ratio of boys to girls in a class is 3:1. There are 36 students in the class. How many more boys than girls are there?

Ainat [17]

well, if you add the numbers 3+1 you get 4. from this we know that there are 4 units total. 36÷4=9 so each unit is equal to 9. we can multiply 9•3 to get 27. there are 27 boys. we can multiply 9•1 to get 9 girls. subtracting 9 from 27, we get 18 more boys that girls.

4 0

3 years ago

Read 2 more answers

Iron deficiency anemia is an important nutritional health problem in the U.S. A dietary assessment was performed on 51 boys 9-11

Bond [772]

Answer:

a) Null hypothesis: $\mu = 14.44$

Alternative hypothesis: $\mu \neq 14.44$

b) $t=\frac{12.50-14.44}{\frac{4.75}{\sqrt{51}}}=-2.917$

The degrees of freedom are given by:

$df =n-1= 51-1=50$

Now we can calculate the p value taking in count the alternative hypothesis

$p_v =2*P(t_{50}$

Since the p value is lower than the significance $\alpha=0.05$ we have enough evidence to reject the null hypothesis and the true mean is significantly different from 14.44

c) $12.50 -2.01 \frac{4.75}{\sqrt{51}}= 11.163$

$12.50 +2.01 \frac{4.75}{\sqrt{51}}= 13.837$

Step-by-step explanation:

Information given

$\bar X=12.50$ represent the mean for the daily iron intake

$s=4.75$ represent the sample deviation

$n=51$ sample size

$\mu_o =14.44$ represent the reference value

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

Part a

We want to test if the mean iron intake among the low-income group is different from that of the general population, the system of hypothesis would be:

Null hypothesis: $\mu = 14.44$

Alternative hypothesis: $\mu \neq 14.44$

Part b

Since we don't know the population deviation the statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info we got

$t=\frac{12.50-14.44}{\frac{4.75}{\sqrt{51}}}=-2.917$

The degrees of freedom are given by:

$df =n-1= 51-1=50$

Now we can calculate the p value taking in count the alternative hypothesis

$p_v =2*P(t_{50}$

Since the p value is lower than the significance $\alpha=0.05$ we have enough evidence to reject the null hypothesis and the true mean is significantly different from 14.44

Part c

The confidence interval would be given by:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$

For the 95% confidence interval we can find the critical value in a t distribution with 50 degrees of freedom and we got:

$t_{\alpha/2}= 2.01$

And replacing we got:

$12.50 -2.01 \frac{4.75}{\sqrt{51}}= 11.163$

$12.50 +2.01 \frac{4.75}{\sqrt{51}}= 13.837$

7 0

4 years ago

How do you estimate weight?

nlexa [21]

With lbs(pounds) I think

8 0

3 years ago

Read 2 more answers

Determine whether the integral is convergent or divergent. ∫[infinity] 2 e^−1/x / x^2 dx : O Convergent O divergent If it is con

monitta

Let $f(x)=e^{-1/x}$ . Then $f'(x)=\frac1{x^2}e^{-1/x}>0$ for all $x\ge2$ , so $f$ is strictly increasing. As $x\to\infty$ , $e^{-1/x}\to e^0=1$ , so $f$ is bounded above by 1. This is to say,