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3 years ago

What are the first five terms of the arithmetic sequence

Mathematics

2 answers:

dimulka [17.4K]3 years ago

7 0

Answer: d : 11, 8, 5, 2, -1

nlexa [21]3 years ago

3 0

Answer:

option d : 11, 8, 5, 2, -1

Step-by-step explanation:

Given a=14-3n

To get first term we plug in 1 for n

n=1 , $a_1= 14- 3(1)= 14-3=11$

n=2 , $a_2= 14- 3(2)= 14-6=8$

n=3 , $a_3= 14- 3(3)= 14-9=5$

n=4 , $a_4= 14- 3(4)= 14-12=2$

n=5 , $a_5= 14- 3(5)= 14-15=-1$

So first five terms are 11, 8, 5, 2, -1

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A component is assembled in a four-step process. The probability of making a defect in step 1 is 10%; in step 2, 20%; in step 3,

rjkz [21]

Answer:

0.37072

Step-by-step explanation:

Let A be the event that step 1 is defective (P(A) = 10%), B the event that step 2 is defective(P(B) = 20%), C the event that step 3 is defective (P(C) = 8%), D the event that step 4 is defective(P(D) = 5%). Let us suppose that the occurance of a failure at any step is indepent of the other steps.

Recall the following properties

$P(A) = 1- P(A^c)$

$(A\cup B )^c = A^c \cap B^c)$

And given A, B, C, D independent , then

$P(A\cap B \cap C \cap D) = P(A)P(B)P(C)P(D)$

REcall that if the a set of events A,B,C,D are independent, their complements are also indepent.

Since we are asked for the probability of a defective item, this means that at least one of the steps is defective. Then, we are asked for the following probability:

$P(A\cup B \cup C \cup D) = 1 - P((A\cup B \cup C \cup D)^c) = 1 - P(A^c \cap B^c \cap C^c \cap D^c ) = 1 - P(A^c)P(B^c) P(C^c) P(D^c) = 1-(1-P(A))(1-P(B))(1-P(C))(1-P(D))$

$= 1-(0.9)(0.8)(0.92)(0.95) = 0.37072$

4 0

3 years ago

Read 2 more answers

One year, the population of a city was 354,000. Several years later it was 407,100. Find the percent increase.

tekilochka [14]

Answer:

15%

Step-by-step explanation:

GIven data

Initial population= 354,000

Final population=407,100

%Error= Final- Initial/initia*100

%Error= 407,100- 354,000/ 354,000*100

%Error= 53100/ 354,000*100

%Error=0.15*100

%Error=15%

Hence the error is 15%

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3 years ago

Expression Name Expression

gulaghasi [49]

Answer:

b hope this helps

Step-by-step explanation:

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3 years ago

A woman weighs herself. Her mass is 43.4 kg and she is trying to increase .She successfully increases her mass by 8%. a) Work ou

-Dominant- [34]

Answer:

Increase in her mass = 3.472 kg

Her new mass = 46.872 kg

Step-by-step explanation:

Her original mass = 43.4 kg

Percentage increase in her mass = 8%

Increase in her mass = 8% of 43.4 kg

= 8/100 * 43.4 kg

= 0.08 * 43.4 kg

= 3.472 kg

Increase in her mass = 3.472 kg

b) Work out her new mass

Her new mass = Her original mass + Increase in her mass

= 43.4 kg + 3.472 kg

= 46.872 kg

Her new mass = 46.872 kg

7 0

3 years ago

What is the slope of the line between (-4, 4) and (-1, -2)?<br> 1<br> 2<br> -2<br> -1

zubka84 [21]

Answer: -2, which is choice C

Work Shown:

$(x_1,y_1) = (-4,4) \text{ and } (x_2,y_2) = (-1,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 4}{-1 - (-4)}\\\\m = \frac{-2 - 4}{-1 + 4}\\\\m = \frac{-6}{3}\\\\m = -2\\\\$

The slope is -2

7 0

2 years ago