A used boat is is on sale for 2,400. Austin makes an offer equal to 3/4 of his price. How much does Austin offer for the boat
1 answer:
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Answer:
Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.
Step-by-step explanation:
Given that,
A box is being created out of a 15 inches by 10 inches sheet of metal.
The length of the one side of the squares which are cut out of the each corners of the metal sheet be x.
The length of the metal box be = (15-2x) inches.
The width of the metal box be =(10-2x) inches
The height of the metal box be =x inches
Then, the volume of the metal box= length×width×height
=(15-2x)(10-2x)x cubic inches
=(150x-50x²+4x³) cubic inches
∴ V= 4x³-50x²+15x
Differentiating with respect to x
V'=12x²-100x+15
Again differentiating with respect to x
V''=24x-100
For maximum or minimum value, V'=0
12x²-100x+15=0
Apply quadratic formula , here a=12, b= -100 and c=15
For x= 8.18, The value of (15-2x) and (10-2x) will negative.
∴x=0.1528 .
Now,
∴At x=0.1528 inch, the volume of the metal box will be maximum.
Therefore the dimensions of the square should be 0.1528 inch by 0.1528 inch so, the box has largest volume.
Answer:
P (Even number) = 1/2
P(spinner will land on an odd number) = 1/2
P(spinner will not land on 2 or 3) = 3/4
P(spinner will not land on a multiple of 3) = 3/4
Step-by-step explanation:
Here, while spinning the spinner total possible outcomes
are 8 = {1,2,3,4,5,6,7,8}
Now,
a) E: Probability of getting even number
Favorable outcomes are {2,4,6,8}
Hence,
b)E: Probability that the spinner will land on an odd number.
Favorable outcomes are {1,3,5,7}
Hence,
c) E: Probability that the spinner will not land on 2 or 3
Favorable outcomes are {1, 4,5,6,7,8}
Hence,
d) E: Probability that the spinner will not land on a multiple of 3
Favorable outcomes are {1,2,4,5,7,8}
Hence,