Answer:
- Part a → dv/dt = 24 cm³/per second
- Part b → dv/dt = 1176 cm³/per second
Step-by-step explanation:
As all edges of a cube are expanding at a rate of 2 centimeters per second.
i.e ds/dt = 2 cm/s
The formula of volume of cube: V = s³
Differentiating the volume:
dv/dt = 3s²
Write ds/dt following derivative of volume
dv/dt = 3s² ds/dt
plug in the value: ds/dt = 2 cm/s
dv/dt = (3s²) (2)
dv/dt = 6s²
Given the edge is 2cm.
so plug in the value: s=2
dv/dt = 6s²
= 6(2)²=6(4)=24 cm³/per second
SIMILARLY,
When the edge is 14cm
dv/dt = 6s²
plug in the value: s=14
dv/dt = 6s²
= 6(14)²=6(196)=1176 cm³/per second
Thus,
- Part a → dv/dt = 24 cm³/per second
- Part b → dv/dt = 1176 cm³/per second
3/10 is the probability of them losing.
Answer:
Intital investment= £6,911.57
Step-by-step explanation:
Giving the following information:
Future Value (FV)= £8,001
Number of periods (n)= 3 years
Interest rate (i)= 5% = 0.05 compounded annually
<u>To calculate the initial investment (PV) needed to reach £8,001 (over £8,000) in 3 years, we need to use the following formula:</u>
PV= FV / (1+i)^n
PV= 8,001 / (1.05^3)
PV= £6,911.57
The amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars
<h3>How to solve for the mortgage that is on this house</h3>
The data from the questions says that the cost of the house = $245000
The down payment amount amount is 45000
Given that they already paid 45000 from the cost of the house, the mortgage would be 245000 - 45000
= $200000
The cost of 1.5 points is the same as the cost of 1.5% of the mortgage of this house.
This is calculated as 0.015 x 200000
= $3000
The conclusion is that the amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars
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Answer:
Fail to reject H₀
Step-by-step explanation:
To reject the null hypothesis, the P-value must be less than 0.05.
Since the P-value is 0.15 which is greater than 0.05, we would fail to reject the null hypothesis as there is no sufficient evidence against the null hypothesis.
Thus, the conclusion would be to fail to reject H₀.