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Using the exponential distribution, it is found that:
a) There is a 0.0952 = 9.52% probability that a television set fails in less than 10,000 hours.
b) There is a 0.3012 = 30.12% probability that a television set lasts more than 120,000 hours.
c) There is a 0.1809 = 18.09% probability that a television set fails between 60,000 and 100,000 hours of use.
d) The 90th percentile is of 230,259 hours.
In probability theory and records, the exponential distribution is a non-stop possibility distribution that frequently issues the quantity of time till a few specific events happen. It is a method wherein activities show up continuously and independently at a regular common rate.
As an instance, the amount of time (starting now) until an earthquake occurs has an exponential distribution. Different examples consist of the duration, in mins, of long-distance enterprise phone calls, and the quantity of time, in months, a car battery lasts.
The lifetime of LCD TV sets follows an exponential distribution with a mean of 100,000 hours. Compute the probability a television set:
a. Fails in less than 10,000 hours.
b. Lasts more than 120,000 hours.
c. Fails between 60,000 and 100,000 hours of use.
d. Find the 90th percentile. So 10 percent of the TV sets last more than what length of time?
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Solution :
0.9
0.3012
0.1809
230258.
Given that:
μ = 100,000
λ = 1/μ = 1 / 100000 = 0.00001
a. Fails in less than 10,000 hours.
P(X < 10,000) = 1 - e^-λx
x = 10,000
P(X < 10,000) = 1 - e^-(0.00001 * 10000)
= 1 - e^-0.1
= 1 - 0.1
= 0.9
b. Lasts more than 120,000 hours.
X more than 120000
P(X > 120,000) = e^-λx
P(X > 120,000) = e^-(0.00001 * 120000)
P(X > 120,000) = e^-1.2
= 0.3011942 = 0.3012
c. Fails between 60,000 and 100,000 hours of use.
P(X < 60000) = 1 - e^-λx
x = 60000
P(X < 60,000) = 1 - e^-(0.00001 * 60000)
= 1 - e-^-0.6
= 1 - 0.5488116
= 0.4511883
P(X < 100000) = 1 - e^-λx
x = 100000
P(X < 60,000) = 1 - e^-(0.00001 * 100000)
= 1 - e^-1
= 1 - 0.3678794
= 0.6321205
Hence,
0.6321205 - 0.4511883 = 0.1809322
d. Find the 90th percentile. So 10 percent of the TV sets last more than what length of time?
P(x > x) = 10% = 0.1
P(x > x) = e^-λx
0.1 = e^-0.00001 * x
Take the In
−2.302585 = - 0.00001x
2.302585 / 0.00001
= 230258.5
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A rectangular garden plot measures 9 m by 5 m. Chillies are planted in a rectangular area of the garden that measures 4.5 m by 2 m. What percent of the garden is planted in chillies?
Answer:
20% of the garden is in chillies.
Step-by-step explanation:
[tex] \frac{4.5 \times 2}{9 \times 5} = \frac{9}{45} = \frac{1}{5} = 20\%[/tex]
Line segment pq is a directed line segment beginning at p(6,-5) and ending at q(-2,4). find point r on the line segment pr that partitions it into the segments pr and pq in the ratio 3:2.
Using proportions, the coordinates of point R are given as follows: R(1.2, 0.4).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Segments pr and pq are partitioned in the ratio 3:2, hence:
[tex]PR = \frac{3}{5}PQ[/tex]
[tex]R - P = \frac{3}{5}(Q - P)[/tex]
The points are:
R(x,y).P(6,-5).Q(-2,4).For the x-coordinate, we have that:
[tex]R - P = \frac{3}{5}(Q - P)[/tex]
[tex]x - 6 = \frac{3}{5}(-2 - 6)[/tex]
x - 6 = -4.8
x = 1.2.
For the y-coordinate, we have that:
[tex]R - P = \frac{3}{5}(Q - P)[/tex]
[tex]y + 5 = \frac{3}{5}(4 + 5)[/tex]
y + 5 = 5.4.
y = 0.4.
The coordinates are: R(1.2, 0.4).
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the ratio of girl to boys is 6 2, there were 14 boys how many total members were there in the club
Answer:
The club has 56 members
Step-by-step explanation:
We can set up a ratio problem to find the total number of kids in the club. There are two ways to do this, and I will show you both. The first way is to immediately set up a ratio between the number of boys and the number of total members in the club. Since the ratio of girls to boys is 6:2, the ratio of boys to members is 2:8 (add the number of girls and boys in the ratio to get the total number of people). Now, we can set up an equation, letting x equal the number of members total, and solve using cross multiplication:
[tex]\frac{2}{8}=\frac{14}{x}\\\\ 112=2x\\\\ x=56[/tex]
The other way to solve this problem would be to figure out the number of girls in the club if there are 14 boys and then add the two quantities together. If we let y be the number of girls in the club, we get the following solution:
[tex]\frac{6}{2}=\frac{y}{14}\\\\ 2y=84\\\\ y=42\\\\x+y=56[/tex]
Either way, we get that the total number of members is 56
What is the answer to this
Answer: H
Step-by-step explanation:
TY:XY: = 2:5, not 3:5.
Answer:
H H H H H H H
Step-by-step explanation:
TY:XY: =2:5, NOT 3:5.
please help ill give whoever answers the best the brainliest answer
10-2 area about the x axis. 6. Determine the moment of inertia of the composite 150 mm 1150 mm 1 100 mm 100 mm 75 mm 300 mm.
Answer:21
Step-by-step explanation:
I need help fast please
Answer:
4
Step-by-step explanation:
The formula is P = 2(l +w)
w = P/2 - l = 20/2 - 6 = 4m
pleaseeeee help :((!!
Answer:
Option A
Step-by-step explanation:
Hello!
We can find the graph by finding the roots of the equation.
Since the equation is already in factored form, we can use the Zero Product Property to find the roots. The roots of an equation are the value(s) of x when y is 0 (x-axis).
Find the Rootsy = (x - 2)(x - 3)0 = (x - 2)(x - 3)0 = (x - 2)The roots of the equation are 2 and 3. That means the graph intersects the x-axis at points 2 and 3. Looking at the graphs shown, the answer is Option A.
calculate f (x) = 3 - | 2 - 3x| when x = - 5
Answer: fx=−14
Step-by-step explanation:
10. What is the exact equation for the quadratic modeled in the table below?
X
-4
-2
2
4
y
24
12
0
0
0
4
6
4
The quadratic equation is y = 1/2x^2 - 3x + 4
How to determine the equation?A quadratic equation is represented as:
y = ax^2 +bx + c
Using the values on the table, we have:
a(0)^2 + b(0) + c = 4 ---- when x = 0
a(2)^2 + b(2) + c = 0 ---- when x = 2
a(4)^2 + b(4) + c = 0 ---- when x = 4
Evaluate these equations
c = 4
4a + 2b + c = 0
16a + 4b + c = 0
Substitute c = 4
4a + 2b + 4 = 0
16a + 4b + 4 = 0
Divide through by 2 and 4
2a + b + 2 = 0
4a + b + 1 = 0
Subtract both equations
2a -1 = 0
Solve for a
a= 1/2
Substitute a= 1/2 in 4a + b + 1 = 0
4 * 1/2 + b + 1 = 0
Evaluate
2 + b + 1 = 0
Solve for b
b = -3
So, we have:
y = ax^2 +bx + c
This gives
y = 1/2x^2 - 3x + 4
Hence, the quadratic equation is y = 1/2x^2 - 3x + 4
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I need help with question 3, I chose the answers that made the most sense but it keeps telling me I'm wrong?
Answer: DL, PS, SL
Step-by-step explanation:
All sides of a square are congruent.
Todd and his brother robert are going to use 512 square feet of their backyard for skateboard ramps. the shape of the backyard is rectangular, with the length twice as long as the width. what are the dimensions of the backyard? which quadratic equation would be used to solve for the unknown dimensions? 0 = 2w2 512 = w2 512 = 2w2 512 = 2l 2w
The dimensions are 16 ft by 32 ft
The quadratic equation is w^2-256=0
We have given that,
Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. the shape of the backyard is rectangular, with the length twice as long as the width.
What is the area of the rectangle?
The area of a rectangle is equal to
A=WL
Where L is the long side of the rectangle
W is the width side of the rectangle
in this problem we have
A=512ft^2
S0,512=LW -----> equation A
L=2W ------> equation B
substitute equation B in equation A
512=2W(W)
512=2w^2
2w^2-512=0
W^2=512/2
W=\sqrt(256)
W=16
Find the value of L
L=2W
L=2(16)
L=32ft
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Answer:
C)512 = 2w2
Step-by-step explanation:
trust
is 30x^2 - 26x -12 a polynomial
Answer:
Yes.
Step-by-step explanation:
It is a polynomial with degree 2 ( as it has x^2 as its highest power)
help me please i dont understand
Answer:
6/5 or 1.2, they're the same value
Step-by-step explanation:
When it says "rate of change", it's really just asking for the slope. If you don't know what the slope is, essentially how much the y-value increases by whenever x increases by 1. This can be formally defined using the equation: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. The subtraction is finding the difference between the two numbers to see how much it's changed by. Btw the order doesn't matter, I could plug in (-3, -2) as (x2, y2) or I could plug it in as (x1, y1) as long as I make sure to input it in correctly. In this example I'll just say (-3, -2) = (x1, y1) and (2, 4) = (x2, y2). Plugging these values into the equation gives you: [tex]\frac{4- (-2)}{2- (-3)} = \frac{6}{5}[/tex] that's the rate of change
the stem plot shows the number of swimming laps completed by swim team members at a single practice
Which of the following is a correct statement about the distribution?
The correct statement is the distribution is unimodal.
What is the correct statement?A Stem plot is a table where each data value is split into a stem which is the first digit or digits and a leaf which is the last digit.
Mode refers to a value that appears most frequently in a data set. A unimodal data set is a distribution with one clear most frequent values. There are only one set of modes in the data. They are 76.
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If geometry symbol represented as small triangle with three sides. abc geometry congruent symbol represented as two small horizontal parallel lines and a horizontal symbol s. geometry symbol represented as small triangle with three sides. dec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2
Hence, The value of x in the congruent triangles abc and dec is 1
What is geometry?the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.
How to solve?The question implies that the triangles abc and dec are congruent triangles.
The congruent sides are,
ab = de
bc = ce = 4
ac = cd = 5
The congruent side ab = de implies that,
4x - 1 = x + 2
Collect like terms,
4x - x = 2 + 1
Evaluate the like terms,
3x = 3
Divide through by 3
x = 1
Hence, the value of x is 1
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Find x,y They have no other givens. Im not sure how to solve this.
Answer:
Step-by-step explanation:
HELP
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of pulling out a red marble 3 times in a row, assuming you put each marble back into the bag before drawing another?
The probability of pulling out a red marble 3 times in a row will be 1/64.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles.
Then the probability of pulling out a red marble 3 times in a row will be
The total number of events will be
Total events = 3 + 4 + 5 = 12
The favorable event will be
Favorable event = 3
Then the probability will be
P = (3/12)(3/12)(3/12)
P = (1/4)(1/4)(1/4)
P = 1/64
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A system with the same line has an infinite number of solutions.
True or False
Which is bigger, a third of 45 or one-sixth c
138?
Applying the knowledge of fractions, the bigger one is: one-sixth of 138.
What are Fractions?Fractions can be defined as a part of a digit or number, and are not whole numbers. For example, a third is 1/3, one-sixth is 1/6, which are both fractions.
Therefore, let's evaluate each statement:
1/3 of 45 = 1/3 × 45 = 15
1/6 of 138 = 1/6 × 138 = 23
Therefore, the bigger of the two is: one-sixth of 138.
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PLEASE HELP I HAVE 45 min to SUBMIT WILL GIVE ANYTHING
Let's take these problems step-by-step:
To solve these problem, simply plug in the values in parentheses in front of f:
[tex]f(a) = 6a - 8\\\\f(a+h) = 6(a+h)-8=6a + 6h - 8\\\\\frac{f(a+h)-f(a)}{h} =\frac{(6a+6h-8)-(6a-8)}{h} =\frac{6a+6h-8-6a+8}{h} =\frac{6h}{6}=h[/tex]
Hope that helps!
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what one is right? for this
360
Step-by-step explanation:
HELP PLEASE!) Given the circle below, find the measure of angle CDE.
Answer: 33 degrees
Step-by-step explanation:
Angles inscribed in the same arc are congruent, so
[tex]13+4x=-7+8x\\\\20+4x=8x\\\\20=4x\\\\x=5\\\\\implies m\angle CDE=-7+5(8)=33^{\circ}[/tex]
Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether the line rises, falls, is horizontal, or is vertical.
(-5, 2), (-3, 6)
Answer:
Step-by-step explanation:
work out the value of (6.8x10^3)x(1.3x10^-3) give your answer in standard form
The standard form of the expression (6.8x10³)x(1.3x10⁻³) is 8.84 × 10⁰.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have:
Mathematical expression:
= (6.8x10³)x(1.3x10⁻³)
= 6.8x1.3
= 8.84
= 8.84 × 10⁰
Thus, the standard form of the expression (6.8x10³)x(1.3x10⁻³) is 8.84 × 10⁰.
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Area=
Help me please :(
Answer:
A = 18 units²
Step-by-step explanation:
MNOP is a parallelogram whose area ( A) is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 6 and h = 3 , then
A = 6 × 3 = 18 units²
The length of a bridge is 230 m. The length of each of Robert's paces is 75 cm.
What is the minimum number of full paces that it would take Robert to walk the full length of the bridge?
Answer:
307 paces
Step-by-step explanation:
First, lets convert Robert's pace to metres. (cm > m)
75cm = (75/100)m
= 0.75m
Number of Full Paces = Length of Bridge / 1 Full Pace
=
[tex] \frac{230m}{0.75m} \\ = 306 \frac{2}{3} paces[/tex]
See , we must have full paces, and in this case we are finding the minimum number of paces, so we will be looking at the lowest possible whole number, which in this case, is 307 paces.
A number cube is rolled 14 times and the results are recorded in the table. what, in simplest form, is the experimental probability that the number cube shows 4? a. 0 b. 1/6 c.2/7 d.5/14
The experimental probability is 5/14.
What is Experimental Probability?The term "probability" refers to an event's likelihood of happening. A probability has a value between 0 and 1, therefore if an occurrence is impossible, it has a probability of 0, and if it is certain, it has a probability of 1. Experimental probability is the probability that is established based on the outcomes of an experiment. The term "empirical probability" also applies to this. A probability that has been established by a series of tests is called an experimental probability. To ascertain their possibility, a random experiment is conducted and iterated over a number of times; each iteration is referred to as a trial. The goal of the experiment is to determine the likelihood that an event will occur or not.Since, 4 appeared five times over the total, The experimental probability is 5/14.
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help me please i am struggling
Answer:
46 cm²
Step-by-step explanation:
Find the area of the rectangle and the triangle, then subtract. Take a look at the steps to know how.
The area of the rectangle:
10×7=70
Area of triangle:
1/2×6×8=24
Subtract the area of the triangle from the area of the rectangle.
70-24=46.
The area of the new shape is 46 cm².
It is cm² because it is a 2D object.
Hope this helps!
39. For the following exercises, sketch a line with the given features.
39. An x-intercept of (-2,0) and y-intercept of (0,4)
Answer: the attachment i put with this file
Step-by-step explanation:
to graph this linear function, you can use the mantra "rise and run" to plot the points on the graph, and draw a line through the points.