Answer: 0.3741
Step-by-step explanation:
Poison probability ;
P(x) = [U(^x) e(^-U)] ÷ x!
Where U = mean
Note: e = exponential symbol
Number of checks that year = 171
Number of days in a year = 365
U = 171/365 = 0.468
Average checks per day = 0.4685
Probability that at least one check was written per day is can be calculated by;
P(not 0) = 1 - P(0)
Therefore,
P(x) = [U(^x) e(^-U)] ÷ x!
P(0) = [ 0.4685^0 * e^-0.4685] ÷ 0!
P(0) = [ 1 * 0.6259] ÷ 1
P(0) = 0.6259
Therefore,
P(not 0) = 1 - 0.6259 = 0.3741
You can use the distributive property and multiply this out.
2x(3x² +9x -3) -2(3x² +9x -3)
= 6x³ +18x²-6x -6x² -18x +6
= 6x³ +12x² -24x +6
The coefficient of the x² term is 12.
_____
You can do this in your head using the techniques of Vedic mathematics. Write the coefficients of the two expressions, putting 0 for the x² coefficient in the first factor.
0 2 -2
3 9 -3
The x² term of the product will be the sum of the products of terms whose degrees add to 2. That is, the first term of the first row times the last term of the second row, plus the product of the middle two numbers in each row, plus the product of the first term in the second row times the last term in the first row.
Here's a more visual representation of the products that get added to get the coefficient of the x² term.
0 2 -2
3 9 -3 . . . . product is 0
0 2 -2
3 9 -3 . . . . product is 18
0 2 -2
3 9 -3 . . . . product is -6
The sum, of course, is 0 +18 -6 = 12
Answer:
(-4,1)
Step-by-step explanation:
The answer is (-4,1) because if you reflect any point on the y axis, the y will stay the same, but the x will become the opposite. The opposite of 4 is -4, so the coordinates are (-4,1).
Answer: x = 7 , y = 3
Step-by-step explanation:
Since they are integers , it means they are whole numbers.
Let the first number be x and the second number be y , then ,interpreting the question , we have
x + y = 10 ...................................... equation 1
x - y = 4 ........................................ equation 2
solving the resulting simultaneous linear equation by substitution method.
From equation 2 , make x the subject of the formula, that is
x = 4 + y .............. equation 3
substitute x = 4 + y into equation 1 , equation 1 becomes
4 + y + y = 10
4 + 2y = 10
subtract 4 from both sides
2y = 10 - 4
2y = 6
divide through by 2
y = 3
substitute y = 3 into equation 3 to find the value of x
x = 4 + y
x = 4 + 3
x = 7
Therefore : x= 7 and y = 3
The question is an illustration of right-angled triangles.
- <em>The length of RF is 49.1 m</em>
- <em>The length of SR is 65.5 m</em>
- <em>The elevation from S to T is 30 degrees</em>
See attachment for the sketch
<u>(a) Show that RF = 49.1</u>
Considering 
We have:
---- tangent ratio
This gives:
Make RF the subject
Approximate
<u>(b) Calculate SR</u>
Considering 
We have:
---- Pythagoras theorem
This gives
Take square roots
<u>(c) The elevation from S to T</u>
To do this, we make use of tangent ratio from 
Take arc tan of both sides
Read more about right-angled triangles at:
brainly.com/question/3770177
