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Andrei [34K]
3 years ago
13

What is the explicit rule for the sequence? −182,−175,−168,−161,...

Mathematics
2 answers:
andreyandreev [35.5K]3 years ago
7 0

an = 7n − 189

Hope this helps :)

UNO [17]3 years ago
4 0

Answer:

a_n = 7n - 189

Step-by-step explanation:

The given sequence is -182, -175, -168, -161, ...

It is an arithmetic sequence, because the difference between the successive term is the same constant.

d = -175 - (-182) = -175 +182 = 7

d = -168 - (-175) = -168 + 175 = 7

So the difference (d) = 7

The first term is a_1 = -182

The explicit formula of an arithmetic sequence is a_n = a_1 + (n -1)d

Now plug in a_1 = -182 and d = 7

a_n = -182 + (n-1)7

a_n = -182 + 7n - 7

Simplify the like terms

a_n = 7n - 189

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Find the surface area of the composite solid.
Westkost [7]

We have:

4 triangles with the base b = 5ft and the height h = 6ft

4 rectangles with the lenght l = 5ft and the width w = 4ft

1 square with side a = 5ft.

The formula of an area of a riangle:

A_T=\dfrac{1}{2}bh

Substitute:

A_T=\dfrac{1}{2}(5)(6)=\dfrac{1}{2}(30)=15\ ft^2

The formula of an area of a rectangle:

A_R=lw

Substitute:

A_R=(5)(4)=20\ ft^2

The formula of an area of a square:

A_S=a^2

Substitute:

A_S=5^2=25\ ft^2

The Surface Area of composite solid:

SA=4A_T+4A_R+A_S

Substitute:

SA=4(15)+4(20)+25=60+80+25=165\ ft^2

<h3>Answer: The Surface Area of the composite solid is 165 ft².</h3>
3 0
3 years ago
Solve the equations help
Leni [432]

Answer:

First equation x=2, Y=9, Second Eq, x=2, y=1

Step-by-step explanation:

X+Y=11

2X-Y=-5 by substitution Y=11-X

So, 2x-(11-x)=-5, 2x-11+x=-5, 3x=6, x=2. Thus, Y=11-2=9

2x+y=5

3x-2y=4

so, y=5-2x

Thus, 3x-2(5-2x)=4

3x-10+4x=4, 7x=14, x=2, Thus, Y=5-2(2)= 1

5 0
3 years ago
Using two normal dice, what is the probability of rolling numbers that add up to 3?
Blizzard [7]
That would be rolling a 1 and a 2 .

so possibilities are 1 on first die and 2 on the second die

OR 2 on first die and 1 on the second.

Both of these have a probability of 1/6 * 1/6 = 1/36

so required probability = 1/36 + 1/36 = 2/36 = 1/18


4 0
3 years ago
The probability that a plane departs on time at a certain airport is .87 The probability that a plane arrives on time given it d
sleet_krkn [62]

Answer:

0.9355

Step-by-step explanation:

What we will use here is conditional probability formula.

let A be the event that the plane departs on time

and B be the event that it arrives on time

P(A) = 0.87

P(B|A) = 0.93

P(B) = ?

P(A n B) = ?

Mathematically;

P(B|A) = P(B nA)/P(A)

0.93 = 0.87/P(A)

P(A) = 0.87/0.93

P(A) = 0.935483870967742

which is 0.9355 to four decimal places

7 0
3 years ago
Question 11
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