Answer:
The edge length of the shipping container is 14 in.
Step-by-step explanation:
The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.
To find the volume of a cube we need to recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. Or as a formula:
![V=s^3](https://tex.z-dn.net/?f=V%3Ds%5E3)
where, <em>s</em> is the length of any edge of the cube.
To find the edge length of the shipping container we use the fact that the volume of a cube shaped shipping container is 2744 in³ and the above formula.
![2744=s^3\\\\s^3=2744\\\\s=\sqrt[3]{2744}\\\\s = 14\:in](https://tex.z-dn.net/?f=2744%3Ds%5E3%5C%5C%5C%5Cs%5E3%3D2744%5C%5C%5C%5Cs%3D%5Csqrt%5B3%5D%7B2744%7D%5C%5C%5C%5Cs%20%3D%2014%5C%3Ain)
Answer:
Step-by-step explanation:
multiply the one to each bracket =
(x +2)+ (x-1) = 3 add the Xs and the numbers
x+X = 2x
2+(-1)= 1
2x+1=3
2x=3-1
2x =2
x =2/2
x =1
:)
Answer:
The probability that an individual has this disease given that the test indicates its presence is 0.1
Step-by-step explanation:
Let A be the event which indicates Having disease
Let B be the event in which test indicates that disease presence
Now we are given that 10% of the individuals in this age group suffer from this form of arthritis
So, P(A)=0.1
We are also given that the proposed test was given to individuals with confirmed arthritics disease, and a correct test result was obtained in 85% of the cases.
P(B|A)=0.85
Now we are given that. When the test was administered to individuals of the same age group who were known to be free of the disease, 4% were reported to have the disease
So,P(B|A')=0.04
We are supposed to find the probability that an individual has this disease given that the test indicates its presence i.e. P(A|B)
So we will use Bayes theorem
![P(A|B)=\frac{P(B|A) P(A)}{\sum P(B|A) P(A)}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cfrac%7BP%28B%7CA%29%20P%28A%29%7D%7B%5Csum%20P%28B%7CA%29%20P%28A%29%7D)
![P(A|B)=\frac{0.85 \times 0.1}{0.85 \times 0.1+0.85 \times 0.9}=0.1](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%5Cfrac%7B0.85%20%5Ctimes%200.1%7D%7B0.85%20%5Ctimes%200.1%2B0.85%20%5Ctimes%200.9%7D%3D0.1)
Hence the probability that an individual has this disease given that the test indicates its presence is 0.1
Answer:
4 ohms
Step-by-step explanation:
The question is "In two minutes a current of 5 amps develops 1,200 heat units in a wire of 8 ohms resistance. What resistance does a similar wire have, which develops 6,000 heat units with a current of 10 amps in 5 minutes?"
Current, I₁ = 5 A
Heat, Q₁ = 1200 units
Resistance, R₁ = 8 ohms
Time, t₁ = 2 min = 120 s
New heat, Q₂ = 6000 units
Current, I₂ = 10 A
New time, t₂ = 5 min = 300 s
We need to find the new resistance.
Heat developed is given by :
![Q=I^2Rt](https://tex.z-dn.net/?f=Q%3DI%5E2Rt)
![\dfrac{Q_1}{I_1^2R_1t_1}=\dfrac{Q_2}{I_2^2R_2t_2}\\\\R_2=\dfrac{Q_2\times I_1^2R_1t_1}{Q_1I_2^2t_2}\\\\R_2=\dfrac{6000\times 5^2\times 8\times 120}{1200\times 10^2\times 300}\\\\=4\ \Omega](https://tex.z-dn.net/?f=%5Cdfrac%7BQ_1%7D%7BI_1%5E2R_1t_1%7D%3D%5Cdfrac%7BQ_2%7D%7BI_2%5E2R_2t_2%7D%5C%5C%5C%5CR_2%3D%5Cdfrac%7BQ_2%5Ctimes%20I_1%5E2R_1t_1%7D%7BQ_1I_2%5E2t_2%7D%5C%5C%5C%5CR_2%3D%5Cdfrac%7B6000%5Ctimes%205%5E2%5Ctimes%208%5Ctimes%20120%7D%7B1200%5Ctimes%2010%5E2%5Ctimes%20300%7D%5C%5C%5C%5C%3D4%5C%20%5COmega)
So, the new resistance is 4 ohms.
Answer:
Step-by-step explanation:
To get the area of the cone we need to find the radius first.
tan 70=r/12
r=12tan 70
area of a circle is given by:
A=πr²
thus the area of the ground covered by the tent will be:
A=π(12tan70)²
The answer is
A] A=π(12tan70°)²