Answer:
Step-by-step explanation:
You are to make 5 assemblies.
Each assembly requires the use of 1 Type A bolt.
To make the 5 assemblies, you need 5 Type A bolts.
The container of bolts has a total of 60 bolts.
The focus - Type A bolts - is 20 out of this 60.
The probability of obtaining a Type A bolt at all, is 20/60, which is = 1/3
(A) What is the probability of taking the exact number of Type A bolts you need for your 5 assemblies, if you randomly take 10 bolts from the container?
- The exact number of Type A bolts you need for the 5 assemblies is 5
1/3 × 5/10 = 5/30 = 1/6 = 0.167
(B) What is the probability of taking/having less than 5 Type A bolts out of the randomly selected 10 bolts? The solution is to sum up the following:
1/3 × 4/10 = 0.133
1/3 × 3/10 = 0.1
1/3 × 2/10 = 0.067
1/3 × 1/10 = 0.033
1/3 × 0/10 = 0
TOTAL = 0.333
The elevation of Mia's campsite is 5,244 ft. Just add the elevation in which she started in the morning plus the 985 ft and then subtract it by 320.
Answer:
$43.20
Step-by-step explanation:
The price with tax is 100% + 8% = 1.08 times the price before tax. The discount multplies that price by 100% -20% = 0.80. The discount multiplier is the same whether the discount is applied before or after the tax.
The combined effect of the two multipliers is ...
... 1.08 × 0.80 = 0.864
so the discounted price with tax added is 0.864 × $50 = $43.20
_____
Perhaps you're supposed to figure the tax (8% of $50 = $4), add the tax ($50 +4 = $54), then subtract the discount (20% of $54 = $10.80) to get
$54.00 -10.80 = $43.20
Answer:
x = 250
y = 125
u(x,y) = 3125500
Step-by-step explanation:
As given,
The utility function u(x, y) = 100xy + x + 2y
= 2 , 
= 4
Now,
Budget constraint -
x + y = 1000
⇒2x + 4y = 1000
So,
Let v(x, y) = 2x + 4y - 1000
Now,
By Lagrange Multiplier
Δu = Δv
⇒< 100y + 1, 100x + 2 > = < 2, 4 >
By comparing, e get
100y + 1 = 2 ........(1)
100x + 2 = 4 .........(2)
Divide equation (2) to equation (1) , we get
⇒2(100y+1) = 1(100x+2)
⇒200y + 2 = 100x + 2
⇒200y = 100x
⇒2y = x
Now,
As 2x + 4y = 1000
⇒2x + 2(2y) = 1000
⇒2x + 2x = 1000
⇒4x = 1000
⇒x = 250
Now,
As 2y = x
⇒2y = 250
⇒y = 
= 125
∴ we get
x = 250
y = 125
Now,
u(250, 125) = 100(250)(125) + 250 + 2(125)
= 3125000 + 250 + 250
= 3125000 + 500
= 3125500
⇒u(250, 125) = 3125500
First find the volume of the patio by multiplying the three dimensions since it's rectangular. (25)(20)(1.5) = 750
Then take the amount per cubic foot 4.99 and multiply it by the volume 750 to get
$3742.50
