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Ad libitum [116K]
3 years ago
8

Probability help please with questions 1, 2, 3, 4, 5 and 7 please? Thanks in advance! I appreciate your time so much!

Mathematics
1 answer:
Katarina [22]3 years ago
7 0
1. 3/6 = 1/2
2. 5/6
3. 3/6 : 3/6 = 3 : 3
4. 3/6 : 3/6 = 3 : 3
5. 5/6 : 1/6 = 5 : 1
7. 3/6 × 1/2 = 1/4
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Write a recursive formula and an explicit formula for the following arithmetic sequence.
xenn [34]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

11, 13, 15, 17, 19, ...

Determining the Recursive formula:

We know that a recursive formula is termed as a formula that specifies each term of the given sequence using the preceding terms.

From the given sequence it is clear that every term can be obtained by adding two to the previous term.

i.e. 13 = 11+2, 15 = 13+2, 17 = 15+2, 19 = 17+2

so

aₙ₊₁ = aₙ+2, for n ≥1

Therefore, a recursive formula is:

  • aₙ₊₁ = aₙ+2, for n ≥1

Determining the Explicit formula:

Given the sequence

11, 13, 15, 17, 19, ...

An arithmetic sequence has a constant difference 'd' and is defined by  

a_n=a_1+\left(n-1\right)d

computing the differences of all the adjacent terms

3-11=2,\:\quad \:15-13=2,\:\quad \:17-15=2,\:\quad \:19-17=2

The difference between all the adjacent terms is the same and equal to

d=2

also

a_1=11

so substituting d=2, a_1=11 in the nth terms

a_n=a_1+\left(n-1\right)d

a_n=2\left(n-1\right)+11

a_n=2n+9

Therefore, the Explicit formula is:

a_n=2n+9

4 0
3 years ago
-1/286 what is the quotient form
n200080 [17]

-1÷286 is -1/286 in quotient form

8 0
3 years ago
Two airplanes are flying in the air at the same height: airplane A is flying east at 250 mi/h and airplane B is flying north at
just olya [345]

Answer:

  decreasing at 390 miles per hour

Step-by-step explanation:

Airplane A's distance in miles to the airport can be written as ...

  a = 30 -250t . . . . . where t is in hours

Likewise, airplane B's distance to the airport can be written as ...

  b = 40 -300t

The distance (d) between the airplanes can be found using the Pythagorean theorem:

  d^2 = a^2 + b^2

Differentiating with respect to time, we have ...

  2d·d' = 2a·a' +2b·b'

  d' = (a·a' +b·b')/d

__

To find a numerical value of this, we need to find the values of its variables at t=0.

  a = 30 -250·0 = 30

  a' = -250

  b = 40 -300·0 = 40

  b' = -300

  d = √(a²+b²) = √(900+1600) = 50

Then ...

  d' = (30(-250) +40(-300))/50 = -19500/50 = -390

The distance between the airplanes is decreasing at 390 miles per hour.

3 0
3 years ago
What is the equation of this line in slope-intercept form?
Rudik [331]
The answer is (b) y = 3x + 1
4 0
3 years ago
Find the perimeter and area of each figure below.
KonstantinChe [14]
A) Perimeter of Trapezium = 8+5+6+15.5
= 34.5in
Area= 1/2*(a+b)*h
=1/2*(8+15.5)*4
=47in^2

B)Perimeter= 12+6+8.5
=26.5mm

Area=1/2*b*h
=1/2*12*4
=24mm^2
6 0
3 years ago
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