<h2>
Answer: 6 gallons </h2>
First we are told that we initially had 1/3 of the tank and when 10 gallons were added we had 3/4 of the tank:
(1)
(2)
(3)
This means 1 gallon is equivalent to 1/24 tank.
On the other hand if we have 3/4 of a tank and need to reach 1 tank we have to add another fraction of the tank:
(4)
(5)>>>>This is the fraction needed to complete 1 tank
Now we need to know <u>how much that 1/4 tank is equivalent in gallons</u>.
From (3) we know . So, we can write the following relation to transform from fractions of a tank to gallons:
Therefore:
<h2>
6 more gallons are needed to fill the tank</h2>
Answer:
m = -2
Step-by-step explanation:
24 = -6(m + 1) + 18 (Given)
24 = -6(m) + -6(1) + 18 (Distributive Property of Equality)
24 = -6m - 6 + 18 (Simplify)
24 = -6m + 12 (Simplify)
24 - 12 = -6m + 12 - 12 (Subtraction Property of Equality)
12 = -6m (Simplify)
(Division Property of Equality)
-2 = m (Simplify)
m = -2 (Distributive Property of Equality)
Answer:
a) The value of a= 0.59
b) The probability that there are at-least 3 cars passing through the stop sign
P(x>3) = 0.03
c)
The Expected value of X = 0.62
d)
The variance of X is σ² = 0.9556
e)
The standard deviation of X
σ = 0.9775
Step-by-step explanation:
<u><em></em></u>
Given data
X : 0 1 2 3 4 5
P(x) : a 0.30 0.05 0.03 0.02 0.01
a)
∑ 
= 1
a + 0.30+ 0.05+ 0.03+ 0.02+0.01 = 1
a + 0.41 = 1
a = 1 - 0.41
<em> a = 0.59</em>
b)
<em> The probability that there are at-least 3 cars passing through the stop sign</em>
<em>P(x >3) = P( x=4) + P( x=5)</em>
= 0.02 +0.01
= 0.03
c)
X : 0 1 2 3 4 5
P(x) : 0.59 0.30 0.05 0.03 0.02 0.01
The Expected value of X
E(X) = ∑ x P(X= x)
= 0 + 1 ×0.30 + 2×0.05 + 3×0.03 + 4×0.02 + 5×0.01
= 0.30 + 0.1 + 0.09 +0.08 +0.05
= 0.62
<em>The Expected value of X </em>
<em> E(X) = 0.62</em>
<em>d) </em>
The variance of the discrete distribution
σ² = ∑ x²p(x) -μ²
σ² = 0 + 1² ×0.30 + 2² ×0.05 + 3² ×0.03 + 4² ×0.02 + 5²× 0.01 - (0.62)²
= 1.34 - 0.3844
= 0.9556
σ² = √0.9556
<em>e) The standard deviation of the discrete distribution</em>
<em> σ = 0.9775</em>
<em></em>
Answer:
The temperature decreased by 9 °F in <u>6 days.</u>
Step-by-step explanation:
Let the number of days it takes for the temperature to decrease by 9 °F be 
.
Given:
Average daily temperature decreases by 
°F.
Decrease of temperature in 1 day = = 1.5 °F.
∴ Decrease in temperature in x days is 
.
Now, as per question, decrease in temperature in 'x' days is 9 °F.
Therefore, 
Therefore, the temperature decreased by 9 °F in 6 days.
