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3 years ago

Write an explicit formula fo the sequence 7,2,-3,-8,-13.... Then find the 14th term

Mathematics

1 answer:

MrRa [10]3 years ago

6 0

Answer:

The 14th term is -58

Step-by-step explanation:

The formula for an arithmetic sequence is

an = a1+d(n-1)

where a1 is the first term

d is the common difference and

n is the term number

a1 = 7

d = 2-7 = -5

Check -3-2 = -5 so d = -5

an = 7 -5(n-1)

We want the 14th term

a14 = 7 -5(14-1)

a14 = 7 -5(13)

a14 = 7 -65

a14 = -58

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The heights of 40 randomly chosen men are measured and found to follow a normal distribution. An average height of 175 cm is obt

AVprozaik [17]

Answer:

95% two-sided confidence interval for the true mean heights of men is [168.8 cm , 181.2 cm].

Step-by-step explanation:

We are given that the heights of 40 randomly chosen men are measured and found to follow a normal distribution.

An average height of 175 cm is obtained. The standard deviation of men's heights is 20 cm.

Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average height = 175 cm

$\sigma$ = population standard deviation = 20 cm

n = sample of men = 40

Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.

So, 95% confidence interval for the true mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times }{\frac{\sigma}{\sqrt{n} } }$ ]

= [ $175-1.96 \times }{\frac{20}{\sqrt{40} } }$ , $175+1.96 \times }{\frac{20}{\sqrt{40} } }$ ]

= [168.8 cm , 181.2 cm]

Therefore, 95% confidence interval for the true mean height of men is [168.8 cm , 181.2 cm].

The interpretation of the above interval is that we are 95% confident that the true mean height of men will be between 168.8 cm and 181.2 cm.

3 0

3 years ago

Question 5 (1 point)

aleksley [76]

Answer:

A = x^2 + 5x - 14

Step-by-step explanation:

A = L × W

A = (x+7) × (x-2)

A = x^2 + 7x - 2x - 14

5 0

4 years ago

Mrs. Burnham has a 1-cup measure that has no other markings. Can she make 6 batches of modeling clay using on the 1-cup measure?

dexar [7]

Something along the lines of multiplying and adding

6 0

4 years ago

Read 2 more answers

The fee to check luggage with a

Vlad [161]

Answer:

$10.71

Step-by-step explanation:

divide 7.14 by 42 to get the price per pound, then multiply that by 63.

8 0

3 years ago

One coin in a collection of 65 has two heads. The rest are fair. If a coin, chosen at random from the lot and then tossed, turns

geniusboy [140]

Answer:

P=1/65.

Step-by-step explanation:

We knaow that one coin in a collection of 65 has two heads. If a coin, chosen at random from the lot and then tossed, turns up heads 6 times in a row. We calculate the probability that it is the two-headed coin.

We calculate the number of possible combinations:

$C_1^{65}=\frac{65!}{1!(65-1)!}=65$

Number of favorable combinations is 1.

Therefore, the probability is

P=1/65.

6 0

3 years ago