The values of x for the given equations are:
1. The value of x = 0
2. The values of x are ±1
3. The values of x are 0 and -7/16
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
To find the values of x in each of the equations, we need to simplify them using algebraic operations:
1. 8x² = 6x² + 5x²
Combining like terms on the right-hand side:
8x² = 11x²
Subtracting 6x² from both sides:
2x² = 0
Dividing both sides by 2:
x² = 0
Taking the square root of both sides:
x = 0
Therefore, the only solution to this equation is x = 0.
2.Similarly, we can calculate values of x for this equation:
-7x² + 6 = x² - 7x²
x² = 1
Taking the square root of both sides:
x = ±1
Therefore, the solutions to this equation are x = 1 and x = -1.
3. 7x² + 9x² = -6x² - 7x
x(16x + 7) = 0
Using the zero product property:
x = 0 or 16x + 7 = 0
Solving for x in the second equation:
16x = -7
Dividing both sides by 16:
x = -7/16
Therefore, the solutions to this equation are x = 0 and x = -7/16.
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Explain how a formula can help solve problems.
Answer:
A formula can help solve problems as it gives the person a step-by-step mini key or guide when needing to actually answer a mathematical or scientific equation or question.
A researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. Her data is expressed in the scatter plot and line of best fit below. Based on the line of best fit, what temperature would it most likely be outside if this same species of cricket were measured to chirp 120 times in one minute?
D=S×T
150×2 1/2
please help
A ringtoss toy is composed of a rectangular prism on top of a cylinder. The rectangular prism is completely filled with water. The dimensions of the rectangular prism are shown in the diagram.
What is the volume of the rectangular prism in cubic centimeters?
The volume of the rectangular prism will be 270 cm³. The correct option is B.
What is volume?The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.
The volume of the rectangular prism will be the multiplication of the three parameters which are Length, Width, and Height of the prism.
The volume will be calculated by the formula:-
Volume = L x W x H
Volume = 2 x 9 x 15
Volume = 270 cubic cm
The volume of the rectangular prism will be 270 cm³.
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The complete question is given below and the missing image is attached with the answer below.
A ringtoss toy is composed of a rectangular prism on top of a cylinder.
The rectangular prism is completely filled with water.
The dimensions of the rectangular prism are shown in the diagram.
What is the volume of the rectangular prism in cubic centimeters?
A) 26 cm3
B) 270 cm3
C) 165 cm3
D) 348 cm3
Question 2: Express each of the following numbers using exponential rotation
a. 343 b. 3145
The total change in the daily high temperature from Monday to Saturday in one week in Columbus was -15° F.
Complete the table to show the possible temperature change for Monday.
Monday
Tuesday: +7
Wednesday: 12
Thursday: +2
Friday: -6
The temperature change for Monday is -30 degrees Fahrenheit,
The completed table is: Monday: -30, Tuesday: +7, Wednesday: +12, Thursday: +2, Friday: -6, to make the total change from Monday to Saturday equal to -15 degrees Fahrenheit.
To complete the table, we need to find the temperature change for Monday that makes the total change from Monday to Saturday equal to -15 degrees Fahrenheit.
Let x be the temperature change for Monday. Then, we can set up the equation:
x + 7 + 12 + 2 - 6 = -15
Simplifying and solving for x, we get:
x = -30
Therefore,
The temperature change for Monday is -30 degrees Fahrenheit, and the completed table is:
Monday: -30
Tuesday: +7
Wednesday: +12
Thursday: +2
Friday: -6
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Use the drop-down menus to complete the statements
to match the information shown
by the graph.
The correct drop down menus from the graph are:
First box: faster than, slower than, at the same rate as.Second box: greatest x-value, line, y-intercept, slope.Third box: greater than, less than, equal to.Fourth box: greatest x-value, x-intercept, y-intercept, slope, origin.Fifth box: minutes per gallon, gallons per minute.What is our observation on the graph?Pool A is filling up slower than Pool B because the slope of the graph of Pool A is less than that of the graph for Pool B.
The slope of the graph tells you the unit rate in gallons per minute. Its means the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
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A passenger train leaves a train depot 1 h after a freight train leaves the same depot. The freight train is traveling 18 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in 2 h.
A. passanger train ___ mph
B. freight train ___ mph
A. passenger train 36mph
B. freight train 18mph
What is meant by speed?
Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.
Given that, A freight train departs from a train depot and let us consider it is travelling at an 'x' mph
and An hour later a passenger train departs the same train depot with a speed 'of x+18 mph.
After 2 hours the passenger train overtakes the freight train.
The total distance travelled by both trains when the passenger train overtakes the freight is equal.
Distance travelled by freight train = x*3
Distance travelled by passenger train = (x+18)*2
Now, 3x = 2x + 36
x = 18
and x + 18 = 36
Therefore, The speed of the passenger train and freight train are 36mph, and 18mph respectively
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A space dome theatre is composed of a cylindrical base and a hemispherical roof. The space dome theatre has a base radius of 20m and a cylindrical height of 20m. what is the total volume of the space dome theatre?
The total volume of the space dome theatre is 41867 m³.
What is a sphere?In geometry, a sphere is a three-dimensional solid figure, which is round in shape.
The surface area is 4πr².
The volume is (4/3)πr³.
The diameter is 2×radius of the sphere.
What is a cylindrical shape?A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, The space dome theatre has a base radius of 20m.
Therefore, The volume of the hemispherical dome is,
= (2/3)π(20)³.
= (2/3)π×8000.
= (16000/3)π m³.
And, As the dome base has a radius of 20 m the cylindrical shape will also have the same.
Therefore, The volume of the cylindrical shape is,
= π(20)²×20.
= 8000π m³.
And, The total volume is the sum of the volumes of two shapes,
= 8000π + (16000/3)π m³.
= [(24000 + 16000)/3]π m³.
= (40000/3)π m³.
= 41867 m³.
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Lina is older than her cousin Sarika. This year the sun or their ages is 31, and the difference between their ages is 5. Which system of equations correctly represents the situations where L represents Linas age and S represents sarikas age
The system of equations that correctly represents the situation of Lina and Sarika's ages are:
L + S = 31L - S = 5.What is a system of equations?A system of equations is two or more equations solved concurrently or at the same time.
A system of equations is called simultaneous equations.
The sum of Lina and Sarika's ages = 31
Lina's age > Sarika's by 5 years
Let Lina's age = L
Let Sarika's age = S
L + S = 31... Equation 1
L - S = 5... Equation 2
2L = 36
L = 18.
Substituting L = 18 into either Equation 1 or 2:
18 + S = 31
S = 31 - 18
S = 13
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HELPP PLSSS
Factor the polynomial.
x²+2x² +14x+7x²
Answer:
2x(5x+7)
Step-by-step explanation:
[tex]x^2+2x^2+14x+7x^2\\=10x^2+14x\\=2x(5x+7)[/tex]
7) The cost, C, in dollars for advertising on a social networking website is proportional to the number n
of clicks on the advertisement. Suppose a business is charged $108.50 for 310 clicks on its
advertisements. What is the slope of the line that represents the relationship between cost and clicks?
The slope of this line is 0.35, which represents the amount that the cost increases for each additional click.
What is equation of straight line ?
Equation of straight line can be as follows, y = mx +b
where m is a slope of line.
Given,
To find , The cost, C, in dollars for advertising on a social networking website is proportional to the number n] of clicks on the advertisement.
When a business is charged $108.50 for 310 clicks on its advertisements.
The cost, C, and number of clicks, n, are related by the equation
C = k * n, where k is the constant of proportionality.
From the given information, we know that C = $108.50 when n = 310. We can use this information to find the value of k:
$108.50 = k * 310
Solving for k:
k = $108.50 / 310
k = $0.35
So, the equation for the relationship between cost and clicks is:
C = $0.35 * n
Therefore, The slope of this line is 0.35, which represents the amount that the cost increases for each additional click.
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Compare the slope and length of segment EF with the slope and length of segment AB. What do you notice? What are you wondering?
The slope of segment EF and AB is same but the length of segment EF is half of the length of segment AB.
What is Line segment ?
An unmoving portion of a line is called a line segment. Two points serve as its ends. By the termination points, it is identified.
Let's assume the length of EF to be "x"
from the figure, we can clearly see that AB is made up of two segments which are of same length as EF.
So, we can say that AB = 2 times of the length of EF
i.e. AB = 2 x
Hence, By comparing, we conclude that AB's length is double of EF.
Now, if we look at slope,
Slope of EF = CE/CF
and, Slope of AB = BC/AC
But, we know that AC = 2 CF and BC = 2 CE
So, Slope of EF = CE/CF
and, Slope of AB = 2 CE / 2 CF
= CE/CF.
Hence, Both segments have same slope direction.
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If the diameter of the pie is ten inchefls, what is the approximate arc length of one slice of pie?
A. 1.67 inches
B. 13.08 inches
C. (c) 3.14 inches
D. D 5.24 inches
The approximate arc length of one slice of pic is 5.24 inches according to the circle circumference.
Let us assume that the pic is equally cut into 6 pieces. Also given that the diameter of the pie is 10 inches.
Diameter (D)=10.
So the radius will be D/2.
Radius (R)=10/2=5.
The pie's circumference is given by:
C=2πR
C=2π*5
C= 10π (in)
Because the pie is divided into six pieces, the circumference of the pie is divided into six equal-length arcs. So,
Length of Arc (L)= 10π/6
L = 5π/3
L= 5(3.14)/3
L=5.234=5.24
Therefore the approximate arc length of one slice of pie is 5.24 inches.
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Wendell purchased a hot dog and 3 orders of french fries for $6.00. If the hot dog cost $2.25, what was the cost of each order of french fries?
The cost of each order of french Fries is $1.75.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Wendell purchased a hot dog and 3 orders of French fries for $6.00.
If the hot dog cost $2.25.
Then the cost of Hot dog
= 6 - 2.25
= 3.75
and, the cost of each order of French Fries
= 3.75 / 3
= $1.25
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CAN SOMEONE HELP FAST!!
In a certain city, E street, W street, C street, and D street are parallel streets that intersect K street and M street. How long is K street between C street and D street?
Answer:
The required measure of Street K between Street C and D is 337.5 ft.
Step-by-step explanation:
have a nice day.
Janie has $180 m. She spends 50% of her money on a new pair of ice skates. How much does she spend on ice skates?
Answer:
$90
Step-by-step explanation:
180 - 50% or 180 x .50 = $90
Question 5(Multiple Choice Worth 2 points) (Linear Functions MC) Which of the following tables represents a linear function? x −2 −1 0 1 2 y 4 1 −2 −5 −8 x −2 −1 0 1 2 y 4 1 0 1 4 x 2 2 0 2 2 y −2 −1 0 1 2 x 0 1 2 3 4 y −2 1 0 1 −2
50 POINTS HURRY UP!!!!
Answer:
The table that represents a linear function is:
x 0 1 2 3 4
y −2 1 0 1 −2
Step-by-step explanation:
Answer:
Step-by-step explanation:
Step-by-step explanation: The linear function is a function that has a straight line when plotted on a
graph.
The correct option;
The table of ordered pairs that represent a linear function is the option; x/y -8/-7 0/0 8/7 16/14
Reasons why the above selection is correct:
Given;
The given data can be presented as follows;
x/y -8/22 0/1 8/22 16/102
x/y -8/-7 0/1 8/9 8/2
x/y -8/-7 0/0 8/7 16/14
x/y -8/-7 0/1 8/5 16/4
Representation of the options in tabular form;
In a tabular format, we have;
Characteristic of linear function;
In a linear function, when the x-values have a constant rate of increase the
the first difference in the y-values is constant.
Selection of the table representing a linear function;
The option that has a constant first difference along with a continuous rate of
increase in the x-value is the option with the following table;
, which is the option x/y -8/-7 0/0 8/7 16/14
Write an inequality.
You need to buy several pencils and an eraser. You can spend no more than $7. The eraser costs $.75 and
pencils cost $.25.
Answer: .75 + .25x ≤ 7
Step-by-step explanation: The x equals the amount that you can buy for each item.
please help idek how to slove this give a step by step too please
Answer:
x = 3/85
Step-by-step explanation:
log2 (6) - log2 (5x) = log2 ( 34)
We can use the properties of logs.
First subtract log2 (6) from each side.
log2 (6) - log2 (5x) - log2 (6) = log2 ( 34)-log2 (6)
- log2 (5x) = log2 ( 34)-log2 (6)
Now we know that log a - log b = log a/b
- log2 (5x) = log2 ( 34/6)
- log2 (5x) = log2 ( 17/3)
Multiply each side by -1
log2 (5x) = -log2 ( 17/3)
We know that -log (a/b) = log ( b/a)
log2 (5x) = log2 ( 3/17)
The terms inside the logs must be the same
5x = 3/17
Divide each side by 5
5x/5 = 3/17 * 1/5
x = 3/85
Jamarie and DJ go bowling. Jamarie knocks a total of 26 pins. DJ knocks down three times as
many. How many did they knock down together?
Show your work
In total they knocked down 104 pins.
I got this by multiplying 26 by 3, which equals 78, then adding 26 to 78 to get the final answer, 104.
Hope this helps!
Jan has a cookie jar that contains five peanut butter cookies, eight chocolate chip cookies, and twelve oatmeal raisin cookies. Jan reaches in and grabs a cookie, what is the probability that she will get a chocolate chip cookie?
Answer:
8/25
Step-by-step explanation:
5+8+12=25
8/25
Answer: 8/25
Step-by-step explanation:
Find probability with item/total.
total is 25
there are 8 chocolate chip cookies
8/25 is your answer
HOPE THIS HELPS _ MM
question 5
pls help me as soon as possible
i'm being timed i only have a hour
Answer:
CD = 36°
Step-by-step explanation:
the measure of secant angle BFE is half the difference of the measures of the intercepted arcs , that is
[tex]\frac{1}{2}[/tex] (BE - CD) = ∠ BFE
[tex]\frac{1}{2}[/tex] (128 - x) = 46 ( multiply both sides by 2 to clear the fraction )
128 - x = 92 ( subtract 128 from both sides )
- x = - 36 ( multiply both sides by - 1 )
x = CD = 36°
if alpha and beta are the roots of the equation 6x2+x-2 find sum of the product, roots of the product
Answer:
-1/3
Step-by-step explanation:
Yhe equation 6x^2 + x - 2 has two roots, alpha and beta, that can be found by using the quadratic formula or by factoring.
The sum of the roots (alpha and beta) can be found by using the formula:
-b/a
where a = 6, b = 1 and c = -2
-1/6
The product of the roots (alpha and beta) can be found by using the formula:
c/a
where a = 6, b = 1 and c = -2
-2/6 = -1/3
So, the sum of the roots is -1/6 and the product of the roots is -1/3.
A computer and printer cost a total of $954. The cost of the computer is two times the cost of the printer. Find the cost of each item.
Solve For n !
[tex] \large \frak{2n + 5 = 6( {n}^{2} - 5) }[/tex]
Thank You!:)
The solution to the equation 2n + 5 = 6( n² - 5 ) is n = ( 1 - √(211 )) / 6 and n = ( 1 + √(211 )) / 6
What is the solution to the quadratic equation?Given the quadratic equation in the question;
2n + 5 = 6( n² - 5 )
First we simplify the given equation;
2n + 5 = 6( n² - 5 )
2n + 5 = 6n² - 30
6n² - 2n - 5 - 30 = 0
6n² - 2n - 35 = 0
To solve for n, we use the quadratic formula.
n = (-b±√(b² - 4ac)) / (2a)
Compare 6n² - 2n - 35 = 0 to the quadratic equation in its standard form an² + bn + c = 0.
a = 6b = -2c = -35Plug the values into the quadratic formula
n = (-b±√(b² - 4ac)) / (2a)
n = ( -(-2) ±√( (-2)² - 4 × 6 × -35 )) / (2 × 6 ))
n = ( 2 ±√( 4 + 840 )) / ( 12 )
n = ( 2 ±√( 844 )) / ( 12 )
n = ( 2 ±2√(211 )) / ( 12 )
n = ( 1 ± √(211 )) / 6
n = ( 1 - √(211 )) / 6 or n = ( 1 + √(211 )) / 6
Therefore, the values of n are ( 1 - √(211 )) / 6 and ( 1 + √(211 )) / 6.
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Use Evcel fo find the probabinty that in 112 trials with probabinty0.42of success that there are 30 or fewer suce ses. Round to 6 decimaiplaces Type your answer hern
The probability that there are 30 or fewer successes in 112 trials with a probability of 0.42 of success is 0.874763 rounding to 6 decimaiplaces.
To use the Excel spreadsheet programme to calculate the likelihood that 30 or fewer successes occur in 112 trials with a success probability of 0.42, follow these steps:
In Excel, create a new spreadsheet with the first column labelled "Number of Successes" and the second column labelled "Probability."
Enter "0" in the first row of the "Number of Successes" column.
Enter "1" in the second row of the "Number of Successes" column.
Continue to input numbers in the "Number of Successes" column in ascending order until you reach 30.
Enter the following formula in the field next to the "0" in the "Probability" column: =BINOM.DIST (0,112,0.42,TRUE)
Enter the following formula: =SUM (B1:B31)
The result in the cell where you input the formula in step 8 will be the chance of 30 or fewer successes in 112 trials with a success rate of 0.42.
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What is x and y equal to?
-10x + 4y = -14
7x + 5y = 2
Answer: x =1, y = -1
Step-by-step explanation:
-10x+4y=-14
7x+5y=2
Let's eliminate y.
5(-10x+4y= -14)
4(7x + 5y=2)
[ I multiplied the first equation by the coefficient of y in the second equation and did the same in the second equation].
=> -50x+20y =-70
28x+20y = 8
Notice how the coefficients of y are the same. We can subtract the 2 equations to eliminate y.
Thus,
-78x = -78 ( y has been eliminated)
∴ x=-78/-78 =1.
Put the value of x in any equation to find y.
7x + 5y =2
=> 7(1) + 5y =2
7+5y=2
5y = 2-7
5y = -5
y = -1.
Hope this helps :)
What is the area of this polygon?
Enter your answer in the box.
units?
Check the picture below.
so the polygon is really just a 5x7 rectangle with a triangle that has a base of 7 units(vertically) and a height of 2 units.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(5)(7)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(2)}}\implies 35~~ + ~~7\implies \text{\LARGE 42}~units^2[/tex]
lights of america claims that the life length of one of its light bulbs, the twister 7 years bulb2, is normally distributed with a mean of 10,000 hours and a standard deviation of 1000 hours. lang selects one of these light bulbs at random and places it on accelerated life test. (i) what is the probability that the bulb that lang selects will last exactly 9950 hours? (ii) what is the probability that the bulb that lang selects will last at most 9950 hours? (iii) what is the probability that the bulb that lang selects will last at least 9950 hours? (iv) what is the probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours? (v) what is the probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively? (vi) what lifelength represents the 95th percentile?
(i) The probability that the bulb that lang selects will last exactly 9950 hours is 0.3085.
(ii) The probability that the bulb that lang selects will last at most 9950 hours is 0.5
(iii) The probability that the bulb that lang selects will last at least 9950 hours is 0.6915.
(iv) The probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours is 0.0668
(v) The probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively is 0.6826.
(vi) The life length represents the 95th percentile is 11,645
The lifespan of the Lights of America light bulb is normally distributed, with a mean of 10,000 hours and a standard deviation of 1000 hours. This means that the majority of bulbs will last around 10,000 hours, but there will be some that last longer or shorter than this.
(i) To find the probability that the bulb selected by Lang will last exactly 9950 hours, we need to use the normal distribution formula. We know that the mean is 10,000 hours and the standard deviation is 1000 hours. Using these values, we can calculate the z-score (standardized value) for 9950 hours.
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. Therefore, the probability that the bulb will last exactly 9950 hours is 0.3085.
(ii) To find the probability that the bulb will last at most 9950 hours, we need to find the area under the normal curve to the left of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at most 9950 hours, we need to add the area under the normal curve to the left of -0.5, which is 0.3085 + 0.1915 = 0.5. Therefore, the probability that the bulb will last at most 9950 hours is 0.5.
(iii) To find the probability that the bulb will last at least 9950 hours, we need to find the area under the normal curve to the right of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at least 9950 hours, we need to add the area under the normal curve to the right of -0.5, which is 1 - 0.3085 = 0.6915. Therefore, the probability that the bulb will last at least 9950 hours is 0.6915.
(iv) To find the probability that the bulb will last less than 9000 hours or more than 11,500 hours, we need to find the areas under the normal curve to the left of 9000 hours and to the right of 11,500 hours, and add them together. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,500 hours.
For 11,500 hours: z = (11,500 - 10,000) / 1000 = 1.5
Then the corresponding probability from Z table is written as,
=> 0.0668
(v) To find the probability that the bulb will last between 9000 hours and 11,000 hours, inclusively, we need to find the area under the normal curve between the z-scores for 9000 hours and 11,000 hours. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,000 hours.
For 9000 hours: z = (9000 - 10,000) / 1000 = -1
For 11,000 hours: z = (11,000 - 10,000) / 1000 = 1
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -1 (for 9000 hours), which is 0.1587, and the probability of a z-score of 1 (for 11,000 hours), which is 0.8413. Subtracting the area under the normal curve to the left of -1 from the area under the normal curve to the left of 1, we get the probability of the bulb lasting between 9000 hours and 11,000 hours inclusively, which is 0.8413 - 0.1587 = 0.6826.
(vi) To find the lifelength that represents the 95th percentile, we need to find the z-score that corresponds to the 95th percentile of the normal distribution. We can use a standard normal distribution table or calculator to find this value, which is approximately 1.645.
Using the z-score formula, we can solve for the life length that corresponds to a z-score of 1.645:
1.645 = (x - 10,000) / 1000
Multiplying both sides by 1000 and adding 10,000, we get:
x = 11,645
Therefore, the life length that represents the 95th percentile is 11,645 hours, which means that only 5% of bulbs will last longer than this value.
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