What is the remainder when x 3 − 7x + 5 is divided by x + 3 ?

Determine the first four terms of the sequence in which the nth term is a_n=(n+1)!/(n+2)!

Vilka [71]

Answer: Choice B) 1/3, 1/4, 1/5, 1/6

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Plug in n = 1 to find the first term

a_n = ( (n+1)! )/( (n+2)! )

a_1 = ( (1+1)! )/( (1+2)! )

a_1 = ( 2! )/( 3! )

a_1 = ( 2*1 )/( 3*2*1 )

a_1 = 2/6

a_1 = 1/3

The first term is 1/3. Optionally you can stop here because only choice B has 1/3 listed as the first term, so this must be the answer. However, I'm going to keep going to show how to find the three other terms. This will help confirm why choice B is the answer, and it will be handy for those times when you aren't given multiple choice answers.

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Plug in n = 2

a_n = ( (n+1)! )/( (n+2)! )

a_2 = ( (2+1)! )/( (2+2)! )

a_2 = ( 3! )/( 4! )

a_2 = ( 3*2*1 )/( 4*3*2*1 )

a_2 = 6/24

a_2 = 1/4

The second term is 1/4

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Plug in n = 3

a_n = ( (n+1)! )/( (n+2)! )

a_3 = ( (3+1)! )/( (3+2)! )

a_3 = ( 4! )/( 5! )

a_3 = ( 4*3*2*1 )/( 5*4*3*2*1 )

a_3 = 24/120

a_3 = 1/5

The third term is 1/5

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Plug in n = 4

a_n = ( (n+1)! )/( (n+2)! )

a_4 = ( (4+1)! )/( (4+2)! )

a_4 = ( 5! )/( 6! )

a_4 = ( 5*4*3*2*1 )/( 6*5*4*3*2*1 )

a_4 = 120/720

a_4 = 1/6

The fourth term is 1/6

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The first four terms are: 1/3, 1/4, 1/5, 1/6, so that confirms why choice B is the answer.

4 0

3 years ago

Julio is paid 1.4 times his normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 35 hours and

Harman [31]

<span>Julio is paid 1.4 times his normal hourly rate for every excess hour he works in a week.
last week he worked 35 hours and got 436.60 dollars.
We need to find an equation so we can be able to solve Julio’s earnings:
=> Let X be the value of Julio’s rate
=> 30 * X + 5 x 1.4x = 436.6
=> 30x + 7x = 436.6
=> 37x = 436.6
=> 37x / 37 = 436.6 / 37
=> x = 11.8
Thus the original rate of Julio is 11.8 dollars
=> 1.4 x 11.8 = 16.52 dollars, the rate of Julio with added rate
=> 30 x 11.8 + 5 x 16.52
=> 354 + 82.6
=> 436.6

</span>

3 0

3 years ago

Klara has decided to file her tax return electronically. How will she benefit from e-filing?

damaskus [11]

Answer:

C. If she's expecting a tax refund, e-filing can expedite the refund from the IRS.

Step-by-step explanation:

Filing the tax return electronically provides some benefits like doing it in an easy way as the website has a step by step process that guides people through it and it allows to be more accurate as the program checks what you do. Also, it helps to save time and it allows to receive the tax refund faster because e-filing give you the possibility to ask for a deposit on your account instead of waiting for a check to arrive. According to this, the answer is that Kiara will benefit from e-filing because if she's expecting a tax refund, e-filing can expedite the refund from the IRS.

7 0

3 years ago

) Suppose that a subset of five balls will be randomly selected from an urn containing amber, blue, and green balls. (a) If the

vazorg [7]

Answer:

0.0023 = 0.23% probability that all 5 balls selected will be the same color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the balls are selected is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.