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3 years ago

Find the common ratio of the geometric sequence 6, 48, 384, ...

Mathematics

1 answer:

gregori [183]3 years ago

8 0

Answer:

r = 8

Step-by-step explanation:

The common ratio r of a geometric sequence is

r = $\frac{a_{2} }{a_{1} }$ = $\frac{a_{3} }{a_{2} }$ = ..... = $\frac{a_{n} }{a_{n-1} }$

Then

r = $\frac{48}{6}$ = $\frac{384}{48}$ = 8

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Eduardo is combining two 6-inch pieces of wood with a piece that measures 4 inches. How many total inches of wood does he have?.

beks73 [17]

Answer:

8 inches

Step-by-step explanation:

7 0

3 years ago

Mathew buys a single ticket for $8 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. How much

miss Akunina [59]

Given:

The number of tickets = 1000

Mathew buys a single ticket for $8

Winning price = $800

To find:

The expected earning per ticket.

Solution:

It is given that the total number of tickets is 1000. So, the probability of winning is:

$P(Winning)=\dfrac{1}{1000}$

The probability of losing is:

$P(losing)=\dfrac{999}{1000}$

The expected earning per ticket is:

$E(x)=800\times P(Winning)-8\times P(losing)$

$E(x)=800\times \dfrac{1}{1000}-8\times \dfrac{999}{1000}$

$E(x)=\dfrac{800}{1000}-\dfrac{7992}{1000}$

$E(x)=\dfrac{800-7992}{1000}$

$E(x)=\dfrac{-7192}{1000}$

$E(x)=-7.192$

Therefore, the expected earning per ticket is -7.192. Here, negative sign means loss of $7.192.

5 0

3 years ago

10 – 2x + 3 = 5x – 9 + 4x<br><br> please help me solve this equation

Darina [25.2K]

Answer:

x=2

Step-by-step explanation:

Hi there!

Whenever we're solving an algebraic equation, our goal is always to isolate the variable, which in this case is x. We would do this by performing inverse operations on both sides of the equal sign to cancel values out.

$10-2x + 3 = 5x-9 + 4x$

Combine like terms on both sides of the equal sign

$10+ 3-2x = 5x+ 4x-9 \\13-2x = 9x-9$

Add 2x to both sides to cancel out -2x (addition is the inverse of subtraction)

$13-2x +2x = 9x-9 +2x\\13 = 11x-9$

Add 9 to both sides to cancel out -9 and isolate 11x (addition is the inverse of subtraction)

$13+9 = 11x-9+9\\22=11x$

Divide both sides by 11 to isolate x (division is the inverse of multiplication) $\frac{22}{11} =\frac{11x}{11} \\2=x$

Therefore, x=2.

I hope this helps!

7 0

3 years ago

Anya had 4 pounds of bananas and 3 1/2 pounds of apples. If she have 1/4 of her bananas to James, how many pounds of bananas doe

quester [9]

Answer:

3 3/4 pound of bananas

hope this helps

3 0

3 years ago

A Pew Research study finds that 23% of Americans use only a cell phone, and no land line, for making phone calls (The Wall Stree

azamat

Answer:

We accept H₀ sample does not give evidence to support that the proportion of Americans who solely use cell phone differs from 23 %

Step-by-step explanation:

A pew research finds that 23 % ( μ ) of Americans use only cell phone

Sample Information

sample size n = 200

x₁ = 51 then p₁ = 51/200 p₁ = 0,255

and q₁ = 1 - p ₁ q₁ = 1 - 0,255 q₁ = 0,745

Sample big enough for the approximation of the binomial distribution to the normal distribution

p₁*n = 0,255 * 200 = 51 > 5 and q₁*n = 0,745* 200 = 149 > 5

Test hypothesis

Null hypothesis H₀ p₁ = μ = 0,23

Alternative hypothesis Hₐ p₁ ≠ 0,23

Is a two tail test. We choose CI = 95 % then significance level is α = 0,05 %

α = 0,05 as is a two tail test α/2 = 0,025

from z-table z(c) = 1,96

To calculate z(s) = ( x - μ ) /√p₁*q₁/n

z(s) = ( 0,255 - 0,23 )/√0,255*0,745/200

z(s) = 0,025 / 0,0308

z(s) = 0,81

Comparing z(s) and z(c)

z(s) < z(c) 0,81 < 1,96

Then z(s) is in the acceptance region: we accept H₀

3 0

3 years ago

Find the common ratio of the geometric sequence 6, 48, 384, ...​

Find the common ratio of the geometric sequence 6, 48, 384, ...