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lesya692 [45]
3 years ago
14

In how many different ways can 6 people line up in a luncjlh line

Mathematics
1 answer:
pogonyaev3 years ago
3 0
There a six possible people for the first spot. 5 next, then 4, then 3, 2, 1. Multiply it together and you get 720. Another way to write 6*5*4*3*2*1 is 6!, or 6 factorial.
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The equation of motion for a weight suspended from a particular spring is given by p(t)=2sint3+5cost3p(t)=2sin⁡t3+5cos⁡t3, where
daser333 [38]
The given displacement at time, t, is
p(t) = 2 sin(t³) + 5 cos(t³)

The initial equilibrium position is
p(0) = 5

To determine future equilibrium postions, define
f(t) = p(t) - 5 = 2 sin(t³) + 5 cos(t³ - 5
The derivative of f(t) is
f'(t) = (3t²)[2 cos(t³) - 5sin(t³)]

Equilibrium is established when f(t) = 0.
To solve this equation numerically, we shall use the Newton-Raphson method, given by.
t(n+1) = t(n) - f[t(n)]/f'[(t(n)], n=0,1,2, ...,

As a guess, let (0) = 1.
The iterative solution for t is shown below.

  n         t(n)
 ---   -----------
   0   1.0000
   1    0.9344
   2   0.9147
   3   0.9130
   4   0.9130

The solution converges rapidly to t = 0.913 s.
The graphical solution (shown below) confirms the numerical solution.

Answer:
The weight first reaches the equilibrium position in 0.913 sec.

4 0
3 years ago
The boxes are shaped as right rectangular prisms. The larger box has a length of 24cm a width of 10 cm, and height of 30cm. The
irina1246 [14]

Answer:

900cm^2

Step-by-step explanation:

24, 10, 30 in half= 12, 5, 15 so, 12*5*15=900cm^2

5 0
3 years ago
Which object shown below could we slice perpendicular to its base/face to create a trapezoid cross-section
alekssr [168]

Answer:

B

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Deepak wrote out the steps to his solution of the equation StartFraction 5 Over 2 minus 3 x minus 5 plus 4 x equals negative Sta
Anna35 [415]

Answer:

Step 1 is incorrect.

Step-by-step explanation:

The given expression is :

\dfrac{5}{2}-3x-5+4x=\dfrac{-7}{4}

In step 1, Deepak rearranged the terms in order to simplify like terms together that is followed in step 2.

o, rearranging of the terms of an expression is commutative property and not distributive property.  The distributive property is generally applicable to multiplication and is given as:

x(y+z)=xy+yz

The commutative property is given as:

x+y = y +a

Therefore, adding terms by changing their order is commutative property of addition and not distributive property. Step 1 instruction is wrong.

6 0
3 years ago
Read 2 more answers
In a freshman class of 80 students,22 students take Consumer Education,20 students take French,and 4 students take both.Which eq
MAXImum [283]
<h3>Answer: Choice C</h3>

P = 11/40 + 1/4 - 1/20

=========================================================

Explanation:

The formula we use is

P(A or B) = P(A) + P(B) - P(A and B)

In this case,

  • P(A) = 22/80 = 11/40 = probability of picking someone from consumer education
  • P(B) = 20/80 = 1/4 = probability of picking someone taking French
  • P(A and B) = 4/80 = 1/20 = probability of picking someone taking both classes

So,

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 11/40 + 1/4 - 1/20

which is why choice C is the answer

----------------

Note: P(A and B) = 1/20 which is nonzero, so events A and B are not mutually exclusive.

6 0
3 years ago
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