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Juli2301 [7.4K]
2 years ago
14

When n=1 there is 1 dot when n=2 there are 3 dots when n=3 there are 6 dots notice that the total number of dots d(n) increases

n by each time use induction to prove that d(n) = n(n+1)/2 prove the statement is true for n equals 1
Mathematics
1 answer:
Maslowich2 years ago
4 0

Answer:

When n=1, there is 1 dot. When n=2, there are 3 dots. When n=3, there are 6 dots.  so when n=1 the eqaution would show as  when sloving this combin the like terms in the parenthesis so 1+1 =2 and 1*2 = 2 when that is divided it equals 1.

Step-by-step explanation:

PLATO answer

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What is 3√243 expressed in simplest radical form?
Volgvan

Answer:

H is correct

Step-by-step explanation:

(243)^1/3

(3^3 × 3^2)^(1/3)

(3^3)^1/3 × (3^2)^1/3

3×(9)^1/3

3 0
2 years ago
While sailing, Jacob is 150 feet from a lighthouse. The angle of elevation from his feet on the boat (at sea level) to the top o
Vlada [557]

Answer:

The height of the lighthouse is approximately 166.6 feet.

Step-by-step explanation:

Let the height of the lighthouse be represented by s, then;

Tan 48° = (opposite) ÷ (adjacent)

Tan 48° = s ÷ 150

⇒ s = 150 × Tan 48°

      = 150 × 1.1106

     = 166.59

s ≅ 166.6 feet

Therefore, the height of the lighthouse is approximately 166.6 feet.

7 0
2 years ago
What pattern do you notice in the numbers below?
Andru [333]

Step-by-step explanation:

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4 0
3 years ago
Read 2 more answers
2(x-3)^2+10=82 solve by isolating x
Leviafan [203]
We have the following equation:
 2 (x-3) ^ 2 + 10 = 82
 We must clear x.
 We pass the constant terms to one side of the equation:
 2 (x-3) ^ 2 = 82 - 10
 2 (x-3) ^ 2 = 72
 (x-3) ^ 2 = 72/2
 (x-3) ^ 2 = 36
 Square root to both members:
 x-3 = +/- root (36)
 x-3 = +/- 6
 The solutions are:
 x1 = 6 + 3 = 9
 x2 = -6 + 3 = -3
 Answer:
 
x1 = 9
 
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7 0
3 years ago
A raffle offers one $8000.00 prize, one $4000.00 prize, and five $1600.00 prizes. There are 5000 tickets sold at $5 each. Find t
Harman [31]

Answer:

The expectation is  E(1 )= -\$ 1

Step-by-step explanation:

From the question we are told that  

     The first offer is  x_1 =  \$ 8000

     The second offer is  x_2 =  \$ 4000

      The third offer is  \$ 1600

      The number of tickets is  n  =  5000

      The  price of each ticket is  p= \$ 5

Generally expectation is mathematically represented as

             E(x)=\sum  x *  P(X = x )

     P(X =  x_1  ) =  \frac{1}{5000}    given that they just offer one

    P(X =  x_1  ) = 0.0002    

 Now  

     P(X =  x_2  ) =  \frac{1}{5000}    given that they just offer one

     P(X =  x_2  ) = 0.0002    

 Now  

      P(X =  x_3  ) =  \frac{5}{5000}    given that they offer five

       P(X =  x_3  ) = 0.001

Hence the  expectation is evaluated as

       E(x)=8000 *  0.0002 + 4000 *  0.0002 + 1600 * 0.001

      E(x)=\$ 4

Now given that the price for a ticket is  \$ 5

The actual expectation when price of ticket has been removed is

      E(1 )= 4- 5

      E(1 )= -\$ 1

4 0
3 years ago
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