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2 years ago

Write an i explicit formula for an, the nth term of the sequence 200, 40, 8, ....

Mathematics

1 answer:

Ugo [173]2 years ago

5 0

Answer:

$T_n = 200 * (\frac{1}{5})^{n-1$

Step-by-step explanation:

Given

$Sequence: 200,40,8$

Required

The nth term

The given sequence is a geometric sequence.

So, first we identify the first term

$a = 200$

Calculate common ration

$r = \frac{40}{200}$ or $r = \frac{8}{40}$

$r = \frac{1}{5}$

So, the nth term is:

$T_n = ar^{n-1$

$T_n = 200 * (\frac{1}{5})^{n-1$

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The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a st

Minchanka [31]

Answer:

0.0323 = 3.23%. Is unusual

Step-by-step explanation:

Using the normal distribution we can find z value with the mean and standard deviation as follows. x is the value we want to know its probability

z = (x - mean)/standard deviation

z = (5-8.54)/1.91

z = -1.85

Using z tables for normal distribution, for z = 1.85, we have an area under the curve of 0.9677. Since we want to know the probability for 5 minutes or less, we have to substract from

p = 1- 0.9677

p = 0.0323

An event with a probability less than 5% is considered unusual.

8 0

3 years ago

A farmer fills his field proportionately with soybeans and corn. Last year he planted 200 acres of corn and 50 acres of soybeans

malfutka [58]

Answer:

Part A) Is a directly proportional

Part B) The constant of proportionality is $k=0.25$

Part C) The equation is $y=0.25x$

Part D) $62.5$ acres of soybeans

Step-by-step explanation:

Part A) Are the number of acres of corn and the number of acres of soybeans directly proportional or inversely proportional?

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$

Let

x-----> the number of acres of corn

y----> the number of acres of soybeans

$y/x=k$

if the number of acres of corn increases then the number of acres of soybeans increases

if the number of acres of corn decreases then the number of acres of soybeans decreases

therefore

The relationship is a directly proportional

Part B) What is the constant of proportionality?

we have that

For x=200, y=50

substitute

$y/x=k$

$k=50/200$

$k=0.25$

Part C) Let x equal the number of acres of corn and y equal the number of acres of soybeans. Write an equation to show this relationship.

The linear equation that represent the direct variation is equal to

$y/x=k$

we have

$k=0.25$

substitute

$y/x=0.25$

$y=0.25x$

Part D) How many acres of soybeans can the farmer plant this year if he plants 250 acres of corn?

For x=250

Find the value of y

substitute in the linear equation the value of x and solve for y

$y=0.25(250)=62.5$ -----> acres of soybeans

7 0

2 years ago

Pls need help fast ._.

yuradex [85]

Answer:

65.75% change

Step-by-step explanation:

Equation for percent change

(|x2-x1| / x1) * 100%

48 million / 73 million * 100% = 65.75% decrease

4 0

2 years ago

Read 2 more answers

How many solutions does the equation 3x − 7 = 4 + 6 + 4x have? (5 points) Two None Infinitely many One

statuscvo [17]

Answer:

There is one solution.

x = -17

Proof and step-by-step explanation:

Step 1: Add the numbers

3x-7 = 4+6+4x

3x-7 = 10+4x

Step 2: Move terms

3x-7 = 10+4x

3x-4x = 10+7

Step 3: Collect the like terms and calculate the sum

3x-4x = 10+7

-x = 17

Step 4: Change the sign by multiplying both sides by -1

-x (×-1) = 17 (×-1)

x = -17

I hope this helped ! :)

7 0

3 years ago

What % of 25 is 15. Please help me

erik [133]

Answer:

15 is 60% (percent) of 25.

Step-by-step explanation:

6 0

2 years ago