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4 years ago

Estimate then find product 5,339 times 6

Mathematics

1 answer:

Aneli [31]4 years ago

7 0

The answer is 32,000,because 5,339 times 6 is 32,034.

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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

4 years ago

19. Use Gauss-Jordan elimination to solve the following system of equations. 3x + 5y = 7 6x − y = −8

MrRa [10]

$\left[\begin{array}{cc}3&5\\6&-1\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}7\\-8\end{array}\right]\\\left[\begin{array}{cc|c}3&5 &7\\ 6& -1 & -8\end{array}\right] \rightarrow \left[\begin{array}{cc|c}3&5& 7\\0&-11 & -22\end{array}\right] \rightarrow \left[\begin{array}{cc|c}3&5& 7\\0&1 & 2\end{array}\right]\\3x +5y = 7\\\\y = 2\\\therefore x = -1$

6 0

3 years ago

UseU={1,2,3,4,5,6,7,8,9,10},A={1,3,4},B={4,7,8,9},and C={2,6,10}to find the given set AUB

salantis [7]

Answer:

A ∪ B = { 1,3,4,7,8,9}

Step-by-step explanation:

U = {1,2,3,4,5,6,7,8,9,10}

A={1,3,4} B={4,7,8,9} and C={2,6,10}

UNION OF SETS:

Union of two sets is defined as the set which has all the elements from both the sets.

Also, REPETITION OF THE ELEMENTS in NOT allowed in union of sets.

Now, here:

A={1,3,4} B={4,7,8,9}

So, A ∪ B = { 1,3,4,7,8,9} ( element 4 is written only ONCE here)

3 0

3 years ago

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f (x )equalsStartFraction x

ankoles [38]

Answer:

The rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities are:

a) 0.52

b) 2.63

Step-by-step explanation:

The rate of change of a function at a given point P can be obtained by evaluating the 1st derivative of the function in P. Thus,

$f(x)=\frac{x^2}{2(1-x)}$

$\frac{df(x)}{dx} = \frac{d(\frac{x^2}{2(1-x)})}{dx} \\\frac{df(x)}{dx} =\frac{x}{1-x} + \frac{x^2}{2(1-x)^2} \\\frac{df(x)}{dx} = -\frac{x(x-2)}{2(x-1)^2}$