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3 years ago

Prove that for any natural value of n the value of the expression: c (3n+1)^2–(3n–1)^2 is divisible by 12

Mathematics

1 answer:

Anna11 [10]3 years ago

7 0

Expanding the expression gives

$(3n+1)^2-(3n-1)^2=(9n^2+6n+1)-(9n^2-6n+1)=12n$

and clearly $12\mid12n$ for any natural number $n$ .

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A well known pharmaceutical manufacturer is manufacturing a newly developed vaccine, and is concerned about variability in the i

Lana71 [14]

Answer:

The null hypothesis is $H_o : \ \sigma^2 = 1.9$

The alternative hypothesis is $H_a : \ \sigma^2 \ne 1.9$

$X^2 = 13.74$

The decision rule is

Reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

Step-by-step explanation:

From the question we are are told that

The variance is $\sigma ^2 = 1.9$

The sample size is n = 30

The sample variance is $s^2 = 0.9$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \ \sigma^2 = 1.9$

The alternative hypothesis is $H_a : \ \sigma^2 \ne 1.9$

Generally the test statistics is mathematically represented as

$X^2 = \frac{ (n- 1 ) * s^2 }{ \sigma^2 }$

=> $X^2 = \frac{ (30 - 1 ) * 0.9 }{1.9 }$

=> $X^2 = 13.74$

Generally from the degree of freedom is mathematically represented as

$df = n- 1$

=> $df = 30 - 1$

=> $df = 29$

Generally from the chi distribution table the critical value of $\frac{\alpha}{2} \ and \ 1 - \frac{ \alpha }{2}$ at a degree of freedom of $df = 29$ is

$X^2 _{ \frac{\alpha }{2} , df } = X^2 _{ \frac{0.05 }{2} , 29 } = 45.7$

=> $X^2 _{ 1 - \frac{\alpha }{2} , df } = X^2 _{1 - \frac{0.05 }{2} , 29 } = 16.0 5$

Gnerally from the values obtained we see that

$X^2 < X^2 _{ 1 - \frac{\alpha }{2} , df }$ hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

6 0

2 years ago

Find the area pleaseeee

noname [10]

Answer:

108

Step-by-step explanation:

Divide into smaller shapes. 24 + 84 = 108

3 0

3 years ago

Pls help, I’m kinda in middle of a quiz atm

Basile [38]

x = 40

I hope this helps :))

4 0

3 years ago

Read 2 more answers

She answer 42 of the 60 questions correctly on a test. What methods should she use to find the percent of questions she answered

Allushta [10]

Divide the number of questions she got correct by the total number of questions on the test them multiply the decimal answer by 100 to get the percent.

42/60 = 0.7

0.7 x 100 = 70%

7 0

3 years ago

Mr. Williams is painting only the back of his bar a gallon of paint cover and 70 ft.² how many square feet will Mr. Williams be

bulgar [2K]

Answer:

264/70, or 3.77142857.

Step-by-step explanation:

You can first calculate how much paint is needed for the bottom part.

Do 18*12 to do this, and you'll find that 216 sq ft is needed for that.

You can then calculate the top, or the triangle part.

The formula for area of a triangle is .5b*h.

The base is 12 feet, and the height is 10 feet, as you can find this by doing 28-18.

Putting this in the formula, you'll find that the entire triangle is .5*12*10 = 60.

However, you have to get rid of the window at the top, so do 4*3 (dimensions of the window), and subtract that from 60, which = 48.

Now, with values from the bottom part and the top part, you can add them together to get how much sq ft it is. 216+48= 264.

Now, you will do 264/70 to find how many gallons you need. This = around 3.77.

8 0

3 years ago