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avanturin [10]
3 years ago
11

Help me please 2. You learn from your science teacher that water expands when you freeze it. The next time that you freeze your

water bottle, you leave room for the water to expand so that the bottle does not crack. What kind of reasoning did you use? inductive reasoning deductive reasoning algebraic reasoning direct reasoning I think the answer is b
Mathematics
1 answer:
harkovskaia [24]3 years ago
3 0
You would be correct. Direct reasoning you already have your teacher who told you what would happen you are simply doing a reaction because of her.
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In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun
sveticcg [70]

Answer:

a. f_X(x) = \dfrac{1}{3.5}8.5

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c.  the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e.  86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let  X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability  density function can now be determined as :

f_X(x) = \dfrac{1}{B-A}A

where A and B  are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

f_X(x) = \dfrac{1}{12-8.5}8.5

f_X(x) = \dfrac{1}{3.5}8.5

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The  probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

F(x) = \dfrac{x-A}{B-A}

F(10) = \dfrac{10-8.5}{12-8.5}

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx

P(X\geq11) =  {\dfrac{1}{3.5}} (x)^{12}_{11}

P(X\geq11) =  {\dfrac{1}{3.5}} (12-11)

P(X\geq11) =  {\dfrac{1}{3.5}} (1)

P(X\geq11) = 0.2857

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx

P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}

P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)

P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)

P(9.5 \leq X\leq11.5) =0.2857* (2)

P(9.5 \leq X\leq11.5) =0.5714

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx

P(X \geq 9) =  {\dfrac{1}{3.5}}(x)^{12}_{9}

P(X \geq 9) =  {\dfrac{1}{3.5}}(12-9)

P(X \geq 9) =  {\dfrac{1}{3.5}}(3)

P(X \geq 9) =  0.2857*}(3)

P(X \geq 9) =  0.8571

NOW; The Number of iPad  that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0
3 years ago
What is the result of converting 81 inches to feet remember there are 12 inches in a foot?
AlekseyPX
81 inches converted to feet is 6.75 feet
7 0
3 years ago
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