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4 years ago

Write the first five terms of the sequence. an=n2 +2

Mathematics

1 answer:

Alla [95]4 years ago

4 0

Answer:

The first five terms of the given sequence

3, 6, 11, 18, 27

Step-by-step explanation:

It is given that,

an=n² +2

<u>To find the first five terms</u>

a₁ = 1² + 2 = 1 + 2 = 3

a₂ = 2² + 2 = 4 + 2 = 6

a₃ = 3² + 2 = 9 + 2 = 11

a₄ = 4² + 2 = 16 + 8 = 18

a₅ = 5² + 2 = 25 + 2 = 27

Therefore the first five terms of the given sequence

3, 6, 11, 18, 27

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New heat lamps are reported to have the mean lifespan of 100 hours with a standard deviation of 15 hours. Before replacing their

Tom [10]

Answer:

The correct option is C

The correct option is A

The correct option is B

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 100$

The standard deviation is $\sigma = 15$

The sample size is $n = 36$

The sample mean is $\= x = 105.1$

Generally

The null hypothesis is $H_o: \mu = 100 \ hours$

The alternative hypothesis is $H_a : \mu \ne 100\ hours$

Given that the null hypothesis is true then the distribution of sample means $\mu_{\= x }$ , from a sample size of 36 is mathematically represented as

$\mu_{\= x } = \mu$

=> $\mu_{\= x } = 100$

According to the Central Limit Theorem the test stated in the question is approximately normally distributed if the sample size is sufficiently large $(n > 30 )$ so given that the sample size is large n = 36

Then the test is normally distributed and hence the standard deviation is 15

Generally the standard error of mean is mathematically represented as

$\sigma_{\= x } = \frac{ \sigma }{\sqrt{n} }$

=> $\sigma_{\= x } = \frac{15}{\sqrt{36} }$

=> $\sigma_{\= x } = 2.5$

Generally the approximate probability of observing a sample mean of 105.1 or more is mathematically represented as

$P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(\frac{\= X - \mu }{\sigma_{\= x }}$

=> $P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(Z$

From the z-table (reference calculator dot net )

$P(Z$

$P( \= X \ge 105.1 )= 1 - P(\= X < 105.1) = 1- 0.97932$

$P( \= X \ge 105.1 ) =0.02$

4 0

4 years ago

Answers to 1,2,or 3 of these 3

vivado [14]

4)
pine tree is most numerous on tree farm which is 40%

5)
if 480 trees total,
pine trees = 480 x 0.40 = 192 trees

6)
if 480 trees total,
spruce trees = 480 x 0.30 = 144 trees
(p.s. also firm trees = 144 (same as spruce trees)

7 0

4 years ago

X-y=10 in the form of y=mx+b

creativ13 [48]

Y = 10+x
(Moving the x)

y = x+10
(Reordering the x so it becomes y=mx+b)

The equation is y = x + 10

Hope this helps! :)

4 0

4 years ago

Find the perimeter??

svp [43]

Answer:

13 in

Step-by-step explanation: