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3 years ago

3 12 27 48. what is the rule?

Mathematics

2 answers:

Shkiper50 [21]3 years ago

8 0

Answer:

Step-by-step explanation:

3(1)^2=3, 3(2)^2=12, 3(3)^2=27, 3(4)^2=48

f(n)=3n^2, n≥1

pshichka [43]3 years ago

3 0

Answer:

this rule follow the airthmatics progression.

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3х - 30 = у 7y - 6 = 3х

mars1129 [50]

Answer:

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3x – 30 = y and the second is 7y – 6 = 3x

As I look, I see 3 ways to use substitution to solve this:

substitute 7y – 6 for 3x
substitute 3x – 30 for y
solve 3x – 30 = y for 3x and make it equal to 7y – 6

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

Method 1:

3x – 30 = y

7y – 6 = 3x — initial system of equations

7y – 6 – 30 = y — substitute 7y – 6 for 3x

7y – 6 – 30 = y — marking like terms, bold for constants, underlined for variables

7y – 36 = y — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract y from both sides, divide by 6 OR subtract 7y from both sides and divide by –6 . For the sake of time, I'm subtracting 7y, though I don't like dealing with negatives.

7y – 7y – 36 = y – 7y — subtract 7y from both sides

–36 = –6y — simplify

–36 ÷ –6 = –6y ÷ –6 — divide by –6 on both sides

y = 6 — simplify

Again, we can diverge here: substitute y into 3x – 30 = y or substitute y into 7y – 6 = 3x

I'm going to choose 3x – 30 = y but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3x – 30 = y — initial equation

3x – 30 = 6 — substitute 6 for y

3x – 30 + 30 = 6 + 30 — add 30 to both sides to isolate 3x

3x = 36 — simplify the expression

3x ÷ 3 = 36 ÷ 3 — divide both sides by 3 to isolate x

x = 12 — simplify

So, we have x = 12 and y = 6 . We know they work for 3x – 30 = y but not if they work for 7y – 6 = 3x . Let's substitute those in to see if (12, 6) really is the solution point.

7y – 6 = 3x — original equation

7(6) – 6 ≟ 3(12) — substitute 6 for y and 12 for x

42 – 6 ≟ 36 — simplify by multiplying

36 = 36 ✔ — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

8 0

3 years ago

Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X deno

Roman55 [17]

Answer:

a) P(X>np+3 $\sqrt{np(1-p)}$ =0.017

b) P(x>1)=0.190

c) P(Y>1)=0.651

Step-by-step explanation:

This a binomial experiment where success is denoted by parts that need rework.

X ∼ B(n, p); n = 20; p = 0.01

The expected value of X is: E(X) = np =20×0.01= 0.2

The variance is: Var(X) = np(1 − p) = 0.2 × 0.99 = 0.198,

The standard deviation SD(X)= $\sqrt{0.198}$ ≈ 0.445

a) P(X>np+3 $\sqrt{np(1-p)}$ =P(X>0.2+3×0.445)=P(X>1.535)=P(X≥2)

Probability function is given by:

$\frac{n!}{x!(n-x)!} *p^x*(1-p)^{(n-x)}$

P(X≥2)=1-P(X<2)=1-P(X=1)-P(X=0)= 1 - $\frac{20!}{1!(20-1)!} *(0.01)^{1}*(1-0.01)^{(20-1)}$ - $\frac{20!}{0!(20-0)!} *(0.01)^{0}*(1-0.01)^{(20-0)}$

P(X≥2)=1-0.165-0.818=0.017

b) p=0.04

P(x>1)=P(x≥2)= 1 - P(x=1) - P(x=0)= 1 - $\frac{20!}{0!(20-1)!} *(0.04)^{1}*(1-0.04)^{(20-1)}$ - $\frac{20!}{0!(20-0)!} *(0.04)^{0}*(1-0.04)^{(20-0)}$

P(x>1)= 1 - 0.368 - 0.442=0.190

c) In this case we consider p=0.19 (Probability that X exceeds 1)

In this experiment Y is the number of hours and n= 5 hours.

Then, we check the probability in each hour:

P(Y>1)=1- P(Y=0)

P(Y=0)= $\frac{5!}{0!(5-0)!} *(0.19)^{0}*(1-0.19)^{(5-0)}$ =0.349

P(Y>1)=1-0.349=0.651

3 0

3 years ago

The cable provider's "triple play" package offers a land line, internet service, and cable TV for one fixed price. If you alread

cupoosta [38]

Answer:

$166.16, you would have to subtract 132 by 12% or .12 and would get 166.16 :)

5 0

3 years ago

Read 2 more answers

Find the measure of unlabeled angle in the quadrilateral

Tpy6a [65]

Answer:

x=140

Step-by-step explanation:

A quadralterial interior angles sum up to 360. We are given three angles and need to find the missing angle.

Let x, represent the missing angle.

$60 + 55 + 105 + x = 360$

$220 + x = 360$

$x = 140$

4 0

3 years ago

A cylindrical soup can has a radius of 1.2 in. and is 6 in. tall. What's the volume?

Sergio [31]

Answer:

Volume= 27. 12inches³

Step-by-step explanation:

to solve this question lets write out the parameters given

radius of the cylinder = 1.2 inches

height of the cylinder = 6 inches

volume of the cylinder = ?

solution

the fomular to find the volume of a cylinder is given to be

Volume= πr²h

Volume= 3.14 × ( 1.2)² × 6

Volume= 3.14 × 1.44 × 6

Volume= 27. 12inches³

therefore the volume of the cylinder equals to 27. 12inches³

7 0

3 years ago

3 12 27 48. what is the rule?​

3 12 27 48. what is the rule?