Answer: 0.99822
Step-by-step explanation:
Our inter-arrival time follows Poisson distribution with parameter 14 which is in hour so first we have to calculate this in minutes as we have to calculate probability in minutes.
So converting 14 into minutes will give 
=0.233
Let X=inter-arrival time between two customers
and here 
= 0.233
Probability(X is less than or equal to 2 minutes) = P(X=0) + P(X=1) + P(X=2)
Now the Poisson distribution has PDF = 
So P(X = 0) = 
= 0.79215
P(X= 1) = 
= 0.18457
P(X=2) = 
= 0.02150
Now adding all three probability gives = 0.79215 +0.18457 + 0.02150=0.99822
Let's make a system of equations to solve for this:
n + q = 84
0.05n + 0.25q = 12.80
where n = nickels and q = quarters.
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Solve for n in the first equation by subtracting q from both sides.
n = 84 - q
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Plug n into the second equation.
0.05(84 - q) + 0.25q = 12.80
Distribute 0.05 inside the parentheses.
4.2 - 0.05q + 0.25q = 12.80
Combine like terms.
4.2 + 0.2q = 12.80
Subtract 4.2 from both sides.
0.2q = 8.6
Divide both sides by 0.2.
q = 43
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Plug 43 for q in the first equation.
n + (43) = 84
Subtract 43 from both sides.
n = 41
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There are 41 nickels and 43 quarters in the piggy bank. ✅
18 = 2×3×3
30 = 2×3×5
The LCM will have factors of 2, 3², and 5. (Choose the highest power of each prime.)
2×3×3×5 = 90 is the LCM of 18 and 30.
Answer:
The answer would be; 3 5/8
Step-by-step explanation:
Words to the wise: Please express exponentials as x^2, not x2.
x2 + y2 = 81 should be <span>x^2 + y^2 = 81 = 9^2
Comparing this to x^2 + y^2 = r^2, we see that r= radius=9. y-intercepts are where x=0, so purposely set x=0 and solve for y:
0^2 + y^2 = 9^2. Then y = 9 or y = -9.
The graph intersects the y-axis at (0,9) and (0, -9).</span>
