In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.
Define combination.Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Given,
Ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards:
Through combination:
²⁴C₅
24!/51(24-5)!
Simplifying:
24!/5!(19!)
24 × 23× 22× 21× 20×19!/5! × 19!
24 × 23 × 22 × 21 × 20/ 5× 4 × 3 × 2 × 1
42504
In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.
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lify.
(√-4)(4√-25) help me i dont get how to do this
Answer:
-40
Step-by-step explanation:
The Concept here is Complex Numbers
where [tex]\sqrt{-1}=i \ and \ i^{2} = -1[/tex]
Then [tex]\sqrt{-4}=\sqrt{4i^{2} } =\sqrt{(2i)^{2} } =2i[/tex]
Also [tex]\sqrt{-25}=\sqrt{25i^{2} } =\sqrt{(5i)^{2} } =5i[/tex]
Then [tex](\sqrt{-4} )(4\sqrt{-25} )=(2i)(4*5i)=40i^{2} =40*-1=-40[/tex]
Glad to Help:)
23.45+1.9-5.78-2.6 ?
Answer:
16.97
Step-by-step explanation:
Jeremy has a huge display of holiday decorations outside his home. He used 6 kilowatt hours (KWH) of electricity in November and used a total of 120KWH during the holiday season until he took them down on December 30. Set up and solve an equation that can be used to calculate the amount of electricity Jeremy used per day during the month of December.
The equation that can be used to find the amount of electricity Jeremy used per day during the month of December is 3.8KWH per day and Jeremy used 3.8KWH per day electricity in the month of December.
How to write and solve an equation?Electricity Jeremy used in November = 6 kilowatt hours (KWH)
Total electricity used in the holiday season = 120KWH
He took the decorations down on December 30
Amount of electricity Jeremy used per day during the month of December =
(Total electricity used in the holiday season - Electricity Jeremy used in November) / 30 days
= (120KWH - 6KWH) / 30
= 114KWH / 30
= 3.8KWH per day
In conclusion, the amount of electricity Jeremy used per day in December is 3.8KWH per day.
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Larissa is standing at point L Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain
If LR equals 12 and PR equals 4, then: LP = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.
What is the Segment Addition Postulate?The Segment Addition Postulate states that when there are two endpoints on a line segment (L) and (C), a third point (P) would lie on the line segment (LR), if and only if the magnitude of the distances between the endpoints satisfy the requirements of this equation LP + PR = LR.
This ultimately implies that, the Segment Addition Postulate is only applicable on a line segment that contains three collinear points.
By applying the Segment Addition Postulate to the given endpoints, the value of LP is given by:
LP + PR = LR
LP = LR - PR
Substituting the given parameters into the formula, we have;
LP = 12 - 4
LP = 8.
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Complete Question:
Larissa is standing at point L. Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain
LP = 16 because 12 + 4 = 16 according to the addition property of equality.
LP = 8 because 12 - 4 = 8 according to the subtraction property of equality.
PR = 16 because LR + LP = PR according to the Segment Addition Postulate, and 12 + 4 = 16 using substitution.
PR = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.
Answer: Lp = 8
Step-by-step explanation:
Got it right
A: 10:00 am a truck started traveling from point A with a speed of 40mph. 3 hours
and 10 minutes later a car started to drive from point A in the same direction
with an
average speed of 60mph. At what time will the car catch up with
the truck?
Answer:h
Step-by-step explanation:
ihlug
(y+6) (y+13) find the product
step by step explanation pls
Answer:
(y + 6)(y + 13) = y² + 19y + 78
Step-by-step explanation:
[tex] \rm \implies (y + 6)(y + 13) \\ \\ \rm \implies y(y + 13) + 6(y + 13) \\ \\ \rm \implies {y}^{2} + 13y + 6y + 78 \\ \\ \rm \implies {y}^{2} + 19y + 78[/tex]
Question 10 of 10
Which of the following is the solution to | x | +5 ≤1?
OA. No solution
OB. xs-4
C. All values are solutions *
OD. xs-4 and x ≥ −6
The solution of | x | +5 ≤ 1 is option C, All values are solutions
We need to find the solution of | x | +5 ≤ 1
Upon removing the modulus function, the term presnet within it can be either negative or positive
considering it as postive
| x | +5 ≤ 1
x + 5 ≤ 1
x ≤ 1 - 5
x ≤ -4
considering it as negative
| x | +5 ≤ 1
-x + 5 ≤ 1
-x ≤ 1 - 5
-x ≤ -4
x ≥ -4
Therefore, the solution of | x | +5 ≤ 1 is All values are solutions
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3. One batch of pancakes needs 1½ cups of pancake mix. One box has 9 cups of pancake mix.
How many batches of pancakes can be made with one box of pancake mix?
In linear equation, 27/2 pancakes are in the box .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a " of two variables," where x and y are the variables.Number of b pancake mix to be need = 1½ cups
Number of box has pancake mix = 9 cups
Therefore, in order to get the total number of batches of pancakes needed for the batches will be calculated thus
= 1½ * 9
= 3/2 * 9
= 27/2
therefore 27/2 pancakes are in the box .
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F(x,y) = x^2 + y^2 - 2x, D is the closed triangular region with vertices (0,0), (0,2), and (0,-2). Find the absolute maximum and minimum values of f on the set D. I know the maximum and minimum are f(0,+-2) = 4, minimum f(1,0) = -1. I need a step by step process on how to get to this answer
The absolute maximum value is f(0,±2) = 4 and the absolute minimum value is f(1,0) = -1.
The given function is F(x,y) = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex] → 1
D is the closed triangular region with the vertices (0,0), (0,2) and (0,-2).
Differentiate 1 partially with respect to x:
df/dx = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]
[tex]f^{'}[/tex](x) = 2x - 2
Differentiate 1 partially with respect to y:
df/dy = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]
[tex]f^{'}[/tex](y) = 2y
Consider [tex]f^{'}[/tex](x) = 0 and [tex]f^{'}[/tex](y) = 0 to find the critical points.
[tex]f^{'}[/tex](x) ⇒ 2x -2 =0
x = 1
[tex]f^{'}[/tex](y) ⇒ 2y
y = 0
Thus, the critical point is (x,y) = (1,0).
Calculate the values of f(x,y) at (0,0), (0,2), (0,-2) and (1,0).
At (x,y) = (0,0)
f(0,0) ⇒ 0 + 0 - 0 = 0
At (x,y) = (0,2)
f(0,2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (0,-2)
f(0,-2) ⇒ 0 + 4 - 0 = 4
At (x,y) = (1,0)
f(1,0) ⇒ 1 + 0 - 2 = -1
Therefore, the absolute maximum is f(0,±2) = 4 and the absolute minimum is f(1,0) = -1.
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I NEED HELP!!
Information:
Ryan conducted a 6-day study observing the effects of an organic plant food on the growth of his sprouting bean plant. He tracked these two pieces of information:
1. the amount of plant food remaining in the container after each day’s feeding
2. the height of the plant over time
(There was a total of 72 millimeters of plant food)
Question:
Write a function rule for the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
This relationship is not a function because more than one amount of plant food remains each day.
What is a function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that, Ryan did an experiment by observing the effects of plant food and the growth of the sprouting bean plant. He made a note of the height of the bean plant and the amount of food remaining in the container for the plant after feeding each day.
Thus, he observed that the plant food in the container decreases by an equal amount every day as the bean plant grew. Thus, this states that it is not a function between the two, as there are more than one plant food remaining each day for the plant.
Hence, This relationship is not a function because more than one amount of plant food remains each day.
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Write a rule for g that represents the indicated transformations of the graph of f.
f(x)=2x5−x3+x2+4; reflection in the y-axis and a vertical stretch by a factor of 3, followed by a translation 1 unit down
The rule that represents the transformation is g(x) = -6x⁵ + 3x³ + 3x² + 11
How to determine the transformation of the function?The equation of the function is given as
f(x) = 2x⁵ - x³ + x² + 4
The sequence of transformations is given as follows:
Reflection across the y-axisVertically stretched by a factor of 3Translate down by 1 unitWhen the above transformations are combined, we have:
g(x) = 3f(-x) - 1
So, we have
3f(-x) - 1 = 3[2(-x)⁵ - (-x)³ + (-x)² + 4] - 1
This gives
3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 12 - 1
Expand
3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 11
So, we have
g(x) = -6x⁵ + 3x³ + 3x² + 11
Hence, the function is g(x) = -6x⁵ + 3x³ + 3x² + 11
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700% of what number is 1,540
If 700% of a number is 1540, then the number is 220
The given percentage = 700%
The percentage of a number is defined as the ratio that can be expressed as the fraction of 100.
Consider the number as x
Here the 700% of the number is 1540
Then the equation will become
x × 700% = 1540
Solve the equation and find the value of x
x × (700/100) = 1540
Divide the terms first
x × 7 = 1540
Move the 7 to the right hand side of the equation
x = 1540/7
Divide the terms
x = 220
Hence, if 700% of a number is 1540, then the number is 220
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James knows that he eventually wants to buy a motocycle, and the model he has in mind cost $5000. he has found a bank that will let him open a saving account with 7% interest that is compounded monthly. if he wants to buy his motocycle in 5 years ( he's still nervious) how much money should he invest in the account now
He should invest $86.29 in the account now, which has a 7% interest compounded monthly.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months
Based on the given information, P is the unknown and
B = $5000
t = 5 years = 60 months
r = 7% = 0.07
n = 1
Plug in the values and solve for P or the amount that should be invested today.
B = P(1 + r/n)^t
$5000 = P(1 + 0.07/1)^60
$5000 = P(1.07)^60
P = $5000/(1.07)^60
P = $86.29
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Find the least common denominator. Then express each fraction using the least common denominator. 3/4 and 5/6
I need a answer
Answer:
The least coomon denominator is 12, so
9/12 and 10/12
if the probability of a is 0.45 and the probability of the intersection of a and b is 0.15, then the probability that b will occur given that a has occurred is:
The probability that b will occur given that a has occurred is 2/5 as the probability of a is 0.45 and the probability of the intersection of a and b is 0.15.
What is probability?It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
P(A)=0.45
P(A∩B)=0.15
P(A∪B)=1
P(B)=1-(0.45+0.15)
=1-0.60
=0.4
=2/5
With a probability of 0.45 and a and b's intersection having a 0.15 probability each, the likelihood that b will happen given that a has happened is 2/5.
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Suppose U = {2,3,6,9,10,13,14,17,19) is the universal set and A = {2,9,10). What is A'?
The complement of set A is { 3, 6, 13, 14, 17, 19}
What is the complement of a given set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
U = {2,3,6,9,10,13,14,17,19}, A = {2,9,10}
set A complement are all the elements in the Universal set U not contained in set A. Those elements are in set A' = { 3, 6, 13, 14, 17, 19}
In conclusion the complement of set A is { 3, 6, 13, 14, 17, 19}
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A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side.
The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse.
The length (in cm) of the hypotenuse is 17 cm.
What is Pythagoras' theorem?According to Pythagoras' theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
H² = P² + B²
Let the hypotenuse = H
Shortest side = B
Third side = P
So, according to the question
H = 2B +1 ..... (1)
P = 2B -1 ..... (2)
Use Pythagoras' theorem,
H² = P² + B²
(2B+1)² = (2B-1)² + B²
4B² + 1 + 4B = 4B² + 1 - 4B + B²
4B = - 4B +B²
B² =-8B
B = - 8
But the length cannot be negative, so B = 8 cm
The length of the shortest side = 8 cm
So the hypotenuse will be
H = 2B + 1
= 2(8) + 1
= 17 cm
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One share of kimcos common stock pays an annual dividend of 1. 43. Today kimco closed at 19. 09 with a net cahnge of +0. 72. The stock yield yesterdays closing price is about 8
With a net change of +0.72 yesterday's closing price was 19.81 and stock dividend yield for yesterday's closing price is 7.2%.
How to calculate the Dividend Yield?
To calculate dividend yield, all you have to do is divide the annual dividends paid per share by the price per share.
Dividend Yield = Annual Dividends Paid Per Share / Price Per Share
According to the given question:
Net change = today's price - yesterday's price
0.72 = 19.09 - yesterday's price
∴ Yesterday's price = 19.81
Stock dividend yield
= (1.43/19.81) x 100
= 7.2%
Therefore the stock yield of yesterday's closing price is 7.2%
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Part A: Timothy said that triangle KLM was dilated by a scale factor of 1.5 centered at the origin. Is Timothy correct? Explain your answer or show your work by listing the coordinates of the primage and image and showing the scale factor
Part B: Are the two triangles similar? Explain.
a. Timothy is correct regarding the dilation, considering the vertices of each triangle.
b. The two triangles are similar, as they have congruent angle measures.
What is a dilation?A dilation occurs when each of the vertices of a polygon is multiplied by a constant, which is called scale factor.
The effects of a dilation are given as follows:
Congruence is lost, as the side lengths will be different due to the multiplication by the scale factor.Similarity is kept, as the side lengths are proportional, hence the angles remain constant.The vertices of each triangle in this problem are given as follows:
Triangle KLM: K(-1,3), L(8,4) and M(10,-3).Triangle K'L'M': K'(-1.5, 4.5), L'(12, 6) and M'(15, -4.5).The scale factor is obtained by the division of any of the equivalent factors, hence:
k = 4.5/3 = 1.5.
Confirming that Timothy's statement regarding the scale factor of the dilation is correct.
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assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. the u.s. marine corps requires that the heights of men be between 64 and 78 inches. if 500 men want to enlist in the u.s. marine corps, how many would you not expect to meet the height requirements?
The percentage of men who didn't expect to meet the height requirements be 96.29%
Given, that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.
Find the percentage of men who meet the height requirements.
z(64) = (64-69)/2.8 = 1.7857
z(78) = (78-69)/2.8 = 3.2143
P(64 <= x <= 78) = P(1.78457<= z <=3.2143) = 0.0371 = 3.71%
So, the percentage of men who meet the height requirements be 3.71%
Now, the percentage men who didn't expect to meet the height requirements be
100 - 3.71 = 96.29%
Hence, the percentage of men who didn't expect to meet the height requirements be
96.29%
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equation of the line that passes through the points (1,-4)(1,−4) and (5,-1)(5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The points are given below.
(1, −4) and (5, −1)
The equation of the line that passes through (1, −4) and (5, −1) will be given as,
(y + 4) = [(−1 + 4) / (5 − 1)](x − 1)
y + 4 = (3/4)x − 3/4
y = (3/4)x + 13/4
The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.
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[tex]a(n)=a(n-1)-5[/tex]a(n)=a(n-1)-5
The first five terms of the arithmetic sequence with the formula a(n) = a(n - 1) - 5 is; -5, -10, -15. -20, -25
What is the nth term of the arithmetic sequence?
The general formula for an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
d is common difference
aₙ is the nth term of the sequence
Now we are given the formula for the nth term of a sequence as;
a(n) = a(n - 1) - 5
Thus;
1) First term is when n = 1;
a(1) = a(1 - 1) - 5
a(1) = -5
2) Second term is when n = 2;
a(2) = -5(2 - 1) - 5
a(2) = -5 - 5
a(2) = -10
3) Third term is when n = 3;
a(3) = -5(3 - 1) - 5
a(3) = -15
4) Fourth term is when n = 4;
a(4) = -5(4 - 1) - 5
a(4) = -20
5) Fifth term is when n = 5;
a(5) = -5(5 - 1) - 5
a(5) = -25
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Complete question is;
Write the first five terms sequence defined by a(n) = a(n - 1) - 5
In a wildlife park they were 18 gray wolves after three years they were 27 gray wolves. What is the percent gain?
Answer: 66.66.....% (6 recurring) / 66.67%
Step-by-step explanation: To get the percent form of this, you'll need to turn this into a fraction, which would be 18/27, then you can simplify it to 2/3 and convert it to a percent which would be 66.66..... .
a circle is always sometimes or never similar to the other circle because we can always sometimes or never map one onto the other using dilations and rigid transformations
Answer: always, always
Step-by-step explanation:
Every circle is similar to every other circle.
Write the prime factorization of 27.
Order the factors from least to greatest (for example, 2 × 2 × 3 × 5).
Answer:
3*3*3 or 3^3
Step-by-step explanation:
27/3=9/3=3
so 3*3*3 or 3^3
when x = -2, y = []
when x = 0, y = []
when x = 2, y = []
when x = 4, y = []
The values of y respective to x values are when x = -2 then y = 12 when x = 0 then y = 2 when x = 2 then y = -8, & when x = 4 then y = -18.
What is a function rule?
The equation-based relationship between the dependent and independent variables is known as a function rule. In simple words, a function is an association between inputs in which each input is connected to precisely one output.
Given, y = -5x + 2
when x= -2, y = (-5)* (-2) + 2 = 10 + 2 = 12, y = 12
when x= 0, y = (-5)* (0) + 2 = 0 + 2 = 2, y = 2
when x= 2, y = (-5)* (2) + 2 = -10 + 2 = -8, y = -8
when x= 4, y = (-5)* (4) + 2 = -20 + 2 = -18, y = -18
Hence, these are the required values of y to the respective input value of x.
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aisha wants to buy apples and raspberries to make a fruit tart. apples cost $3 per pound and raspberries cost $2.75 per pound. how many pounds of fruit does she buy if she buys 3 pounds of apples and 2.5 pounds of raspberries? how many pounds of fruit does she buy if she buys xx pounds of apples and yy pounds of raspberries?
Answer:
6.4
Step-by-step explanation:
I guessed and got it right.
a random sample of 42 college graduates revealed that they worked an average of 7.3 years on the job before being promoted. the sample standard deviation was 2.9 years. using the 0.99 degree of confidence, what is the confidence interval for the population mean?
The confidence interval for the population mean with 99% confidence interval is (6.90;8.50).
What is meant by confidence interval?A confidence interval is a set of values that, with a particular level of certainty, includes a population value. When a population mean is between an upper and lower interval, it is frequently stated as a percentage.
The population mean is mean [tex]\bar{x}[/tex]=7.3.
The sample's standard deviation is 2. 9
Number of samples: 42
The range of possibilities for the mean, [tex]\bar{x}[/tex]
The confidence interval for the mean is
[tex]\bar{x}[/tex] ± (σ/√n)
To calculate the critical value, we must first determine the degrees of freedom, which are given by:
df=n-1
df=42-1
df=41.
Since the confidence level is 0.99 or 99%, the values of and can be used to calculate the critical value using Excel, a calculator, or a table is 2.701
7.3-2.701(2.9/√42)=6.9013
7.3+2.701(2.9/√42)=8.5086
The 99% confidence interval in this instance would therefore be provided by (6.90;8.50).
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g in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. calculate the expected value to two decimals.
Using the concepts of probability, we got that 0.4286 is the probability that the battery life for an iPad Mini will be 10 hours or less which is about 42.86%.
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 :
[tex]f_X(x)[/tex] = [tex]\frac{1}{B-A}[/tex] where A<x<B
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 :
[tex]f_X(x)[/tex] = [1 / (12-8.5)]8.5<x<12
[tex]f_X(x)=[/tex](1/3.5)8.5<x<12
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(10)=[tex](x-A)/(B-A)[/tex]
F(10)=(10-8.5)/(12-8.5)
F(10)=1.5/3.5
F(10)=0.4286
Hence, the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286
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(Complete question)
In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
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Answer: Nice
Step-by-step explanation: