1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pshichka [43]
2 years ago
10

HELP!!!!!!!!!!!!!!!!!!!

Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
3 0

Answer:

4) a₁₅ = 128

5) B. a_n=a_{n-1}+6

Step-by-step explanation:

4)

This is an arithmetic sequence, where all terms have a common difference:

a_n=a_1+(n-1)d

Here, the common difference is 9.

11-2=9\\20-11=9

Use that to write the equation and solve for a₁₅:

a_n=2+(n-1)9\\\\a_{15}=2+(15-1)9\\a_{15}=2+(14)9\\a_{15}=2+126\\a_{15}=128

5)

This is also an arithmetic sequence, but it is a recursive arithmetic sequence in the form of:

a_n=a_{n-1}+d

This simply states that each term is d more than the term before it.

Here, the common difference is 6:

2--4=6\\8-2=6\\14-8=6

And the equation for this is B. a_n=a_{n-1}+6

You might be interested in
Sixty percent of Company A’s employees are considered top performers. Fifty five percent of Company A’s employees are in a rigor
pickupchik [31]
Not exactly. there are still 40 percent of the employees that are not top performers. for all you know those 40 percent could make up the majority of the employees in the training program<span />
5 0
3 years ago
Read 2 more answers
A coin is biased such that it results in 2 heads out of every 3 coins flips on average
alina1380 [7]

<span>The mathematical theory of probability assumes that we have a well defined repeatable (in principle) experiment, which has as its outcome a set of well defined, mutually exclusive, events.</span>


If we assume that each individual coin is equally likely to come up heads or tails, then each of the above 16 outcomes to 4 flips is equally likely. Each occurs a fraction one out of 16 times, or each has a probability of 1/16.

Alternatively, we could argue that the 1st coin has probability 1/2 to come up heads or tails, the 2nd coin has probability 1/2 to come up heads or tails, and so on for the 3rd and 4th coins, so that the probability for any one particular sequence of heads and tails is just (1/2)x(1/2)x(1/2)x(1/2)=(1/16).

Now lets ask: what is the probability that in 4 flips, one gets N heads, where N=0, 1, 2, 3, or 4. We can get this just by counting the number of outcomes above which have the desired number of heads, and dividing by the total number of possible outcomes, 16. 
  
 

<span>N     # outcomes with N heads     probability to get N heads</span>

0                1                                       1/16 = 0.0625

1                4                                       4/16 = 1/4 = 0.25

2                6                                      6/16 = 3/8 = 0.375

3                4                                      4/16 = 1/4 = 0.25

4                1                                      1/16 = 0.0625

We can plot these results on a graph as shown below.

 
The dashed line is shown just as a guide to the eye. Notice that the curve has a "bell" shape. The most likely outcome is for N=2 heads, where the curve reaches its maximum value. This is just what you would expect: if each coin is equally likely to land heads as tails, in four flips, half should come up heads, that is N = 4x(1/2) = 2 is the most likely outcome. Note however that an occurrence of N = 1 or N = 3 is not so unlikely - they occur 1/4 or 25% of the time. To have an occurrence of only N = 0, or N = 4 (no heads, or all heads) is much less likely - they occur only 1/16 or 6.25% of the time.

The above procedure is in principle the way to solve all problems in probability. Define the experiment, enumerate all possible mutually exclusive outcomes (which are usually assumed to be each equally likely), and then count the number of these outcomes which have the particular property being tested for (here for example, the number of heads). Dividing this number by the total number of possible outcomes then gives the probability of the system to have that particular property.

Often, however, the number of possible outcomes may be so large that an explicit enumeration would become very tedious. In such cases, one can resort to more subtle thinking to arrive at the desired probabilities. For example, we can deduce the probabilities to get N heads in 4 flips as follows:

N=0: There is only one possible outcome that gives 0 heads, namely when each flip results in a tail. The probability is therefore 1/16.

N=4: There is only one possible outcome that gives 4 heads, namely when each flip results in a head. The probability is therefore 1/16.

N=1: There are 4 possible outcomes which will have only one coin heads. It may be that the 1st coin is heads, and all others are tails; or it may be that the 2nd coin is heads, and all others are tails; or it may be that the 3rd (or the 4th) coin is heads, and all others are tails. Since there are 4 possible outcomes with one head only, the probability is 4/16 = 1/4.

N=3: To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin. Thus there are only 4 outcomes which have three heads. The probability is 4/16 = 1/4.

N=2: To enumerate directly all the possible outcomes which have exactly 2 heads only, is a bit trickier than the other cases. We will come to it shortly. But we can get the desired probability for N=2 the following way: We have already enumerated all possible outcomes with either N = 0, 1, 3, or 4 heads. These account for 1 + 4 + 4 + 1 = 10 possible outcomes. The only outcomes not include in these 10 are those with exactly N=2 heads. Since there are 16 possible outcomes, and 10 do not have N=2 heads, there must therefore be exactly 16 - 10 = 6 outcomes which do have exactly N=2 heads. The probability for N=2 is therefore 6/16 = 3/8.

2) Consider the experiment of rolling 3 dice, each of which has 6 sides.

What is the probability that no two dice land with the same number side up, i.e. each of the three dice rolls a different number?

Since each die has 6 possible outcomes, the number of possible outcomes for the roll of three dice is 6x6x6 = 216. We could enumerate all these 216 possibilities, and then count the number of outcomes in which each die has a different number. This is clearly too tedious! Instead we reason as follows:


6 0
2 years ago
Read 2 more answers
For each sequence, find the first 4 terms and the 10th term.<br> A) n+5<br> B)2n-1
snow_tiger [21]

Answer:

see explanation

Step-by-step explanation:

(a)

To find the first 4 terms substitute n = 1, 2, 3, 4 into the n th term formula.

a₁ = 1 + 5 = 6

a₂ = 2 + 5 = 7

a₃ = 3 + 5 = 8

a₄ = 4 + 5 = 9

For the 10 th term substitute n = 10, that is

a₁₀ = 10 + 5 = 15

The first 4 terms are 6, 7, 8, 9 and the 10 th term is 15

(b)

Substitute n = 1, 2, 3, 4 and 10 into the n th term formula

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 = 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

a₁₀ = 2(10) - 1 = 20 - 1 = 19

The first 4 terms are 1, 3, 5, 7 and the 10 th term is 19

5 0
3 years ago
Which pairs of angles in the figure below are verticle angles? Check all that apply.
vazorg [7]

Answer:

correct answer options are ; C and D

Step-by-step explanation:

By definition, vertical angles are those that are opposite each other when two lines cross and are equal.

Observing the given options;

C. ∠LRE and ∠FRA

D.∠TRF and ∠NRL

In the other options given, it could have been correct if stated as;

A. ∠ARS and ∠ERO

B. ∠NRA and ∠TRE

3 0
3 years ago
25. What is the range of the list of numbers 3,22, 16, 8, 34, 7, and 20?
antoniya [11.8K]

Answer:

31

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set.

First arrange all the figures in order from the smallest to the largest value

3,7,8,16,20,22,34

Therefore, finding range would be; 34-3 =31

Hope this helps!

7 0
3 years ago
Other questions:
  • Each month cameron budgets $1040 for fixed expenses $980 for living expenses and $120 for annual expenses his annual net income
    12·2 answers
  • HELP!!!!!!!
    15·2 answers
  • Which planet is an inner planet, and which one is an outer planet? Explain your answer.
    15·1 answer
  • Range is a keyword for what operation in math
    15·1 answer
  • How many 5 person squads can a basketball coach send out on an 11 person team
    5·2 answers
  • Write 5 equivalent fractions for each fraction. 1/2, 1/4, 1/8, 1/3, 1/6
    5·1 answer
  • Need help ASAP!!! Using postulate and/or theorems learned in unit 1, determine whether PQR MRN. Show all your work and explain w
    9·1 answer
  • Heeeeeeeeeelpppppppp meeeeeeee
    6·1 answer
  • ∠A and ∠B are supplementary such that
    8·1 answer
  • How to find the missing side of a triangle
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!