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3 years ago

What is the missing term of the arithmetic sequence? 6, ______, 30

Mathematics

1 answer:

Andrei [34K]3 years ago

3 0

Let k = the constant amount added to the sequence since this is an arithmetic sequence

x = missing number

You have to formulate an equation based on the sequence:

6 + k = x or k = x – 6

x + k = 30

Substitute the value of k to the second formula:

x + x – 6 = 30

2x = 36

x = 18

Therefore, the missing number is 18.

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Construct a 99% confidence interval for the population mean, mu. Assume the population has a normal distribution. A group of 1

Zarrin [17]

Answer:

99% confidence interval for the population mean is [19.891 , 24.909].

Step-by-step explanation:

We are given that a group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean age of selected students = 22.4 years

s = sample standard deviation = 3.8 years

n = sample of students = 19

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.878 < $t_1_8$ < 2.878) = 0.99 {As the critical value of t at 18 degree of

freedom are -2.878 & 2.878 with P = 0.5%}

P(-2.878 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.878) = 0.99

P( $-2.878 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.878 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ]

= [ $22.4 -2.878 \times {\frac{3.8}{\sqrt{19} }$ , $22.4 +2.878 \times {\frac{3.8}{\sqrt{19} }$ ]

= [19.891 , 24.909]

Therefore, 99% confidence interval for the population mean is [19.891 , 24.909].

6 0

3 years ago

What is the rate of change in y with respect to x in the function x + 5y = 10?

rosijanka [135]

Answer:

-1/5

Step-by-step explanation:

let's put the function in slope intercept form (y = mx + b).

x + 5y = 10

y = - (1/5)x + 2

when the function is in slope intercept form, (m) is the rate of change or the slope.

therefore, the rate of change -1/5

7 0

2 years ago

As the distance of a sound wave from its source quadruples, how is the intensity changed?

natulia [17]

Answer:

I think its b

Step-by-step explanation:

because 4×4 is 16

5 0

3 years ago

Andrea gets a monthly allowance. She first spends a fourth of her money on Target. Then, she spends $5 on food. She has $12 left

motikmotik

Answer:

Step-by-step explanation:

12 + 5 = 17

17 x 4 = 68

Andrea's monthly allowance is $68.

5 0

2 years ago

Read 2 more answers

Given f(x) = x + 9 and g(x) = x2 find (gºf)(x).

marissa [1.9K]

Answer:

g(f(x)) = (x + 9)^2 or x^2 + 18x + 81

Step-by-step explanation:

(gºf)(x) is the "c .... " of two functions f(x) and g(x): f(x) is the input to g(x).

We start with g(x): g(x) = x^2. We replace the first x with f(x) and the second x with x + 9:

g(f(x)) = (x + 9)^2 or x^2 + 18x + 81

8 0

3 years ago