the answer is,
541.42%
I think this is the answer.
Suppose X has an exponential distribution with mean equal to 11. Determine the following: (a) (Round your answer to 3 decimal places.) (b) (Round your answer to 3 decimal places.) (c) (Round your answer to 3 decimal places.) (d) Find the value of x such that . (Round your answer to 2 decimal places.)
Answer:
[tex]P(X > 11) = 0.368[/tex]
[tex]P(X > 22) = 0.135[/tex]
[tex]P(X > 33) = 0.050[/tex]
[tex]x = 33[/tex]
Step-by-step explanation:
Given
[tex]E(x) = 11[/tex] --- Mean
Required (Missing from the question)
[tex](a)\ P(X>11)[/tex]
[tex](b)\ P(X>22)[/tex]
[tex](c)\ P(X>33)[/tex]
(d) x such that [tex]P(X <x)=0.95[/tex]
In an exponential distribution:
[tex]f(x) = \lambda e^{-\lambda x}, x \ge 0[/tex] --- the pdf
[tex]F(x) = 1 - e^{-\lambda x}, x \ge 0[/tex] --- the cdf
[tex]P(X > x) = 1 - F(x)[/tex]
In the above equations:
[tex]\lambda = \frac{1}{E(x)}[/tex]
Substitute 11 for E(x)
[tex]\lambda = \frac{1}{11}[/tex]
Now, we solve (a) to (d) as follows:
Solving (a): P(X>11)
[tex]P(X > 11) = 1 - F(11)[/tex]
Substitute 11 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{1}{11}* 11})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{11}{11}})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-1})[/tex]
Remove bracket
[tex]P(X > 11) = 1 - 1 + e^{-1}[/tex]
[tex]P(X > 11) = e^{-1}[/tex]
[tex]P(X > 11) = 0.368[/tex]
Solving (b): P(X>22)
[tex]P(X > 22) = 1 - F(22)[/tex]
Substitute 22 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{1}{11}* 22})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{22}{11}})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-2})[/tex]
Remove bracket
[tex]P(X > 22) = 1 - 1 + e^{-2}[/tex]
[tex]P(X > 22) = e^{-2}[/tex]
[tex]P(X > 22) = 0.135[/tex]
Solving (c): P(X>33)
[tex]P(X > 33) = 1 - F(33)[/tex]
Substitute 33 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{1}{11}* 33})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{33}{11}})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-3})[/tex]
Remove bracket
[tex]P(X > 33) = 1 - 1 + e^{-3}[/tex]
[tex]P(X > 33) = e^{-3}[/tex]
[tex]P(X > 33) = 0.050[/tex]
Solving (d): x when [tex]P(X <x)=0.95[/tex]
Here, we make use of:
[tex]P(X<x) = F(x)[/tex]
Substitute [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X<x) = 1 - e^{-\lambda x}[/tex]
So, we have:
[tex]0.95 = 1 - e^{-\lambda x}[/tex]
Subtract 1 from both sides
[tex]0.95 -1= 1-1 - e^{-\lambda x}[/tex]
[tex]-0.05=- e^{-\lambda x}[/tex]
Reorder the equation
[tex]e^{-\lambda x} = 0.05[/tex]
Substitute 1/11 for [tex]\lambda[/tex]
[tex]e^{-\frac{1}{11} x} = 0.05[/tex]
Solve for x:
[tex]x = -\frac{1}{1/11}\ ln(0.05)[/tex]
[tex]x = -11\ ln(0.05)[/tex]
[tex]x = 32.9530550091[/tex]
[tex]x = 33[/tex] --- approximated
What is the discriminate of y=x^2-8x+2
Answer:
56
Step-by-step explanation: Use the values of a, b, and c to find the discriminant.
Answer:
[tex]\Delta =56[/tex]
Step-by-step explanation:
We are given:
[tex]y = x^2 - 8x + 2[/tex][tex]y=x^2-8x+2[/tex]
So, a = 1, b = -8, and c = 2.
The discriminant (symbolized by Δ) is given by:
[tex]\Delta =b^2-4ac[/tex]
So, our discriminant in this case will be:
[tex]\Delta=(-8)^2-4(1)(2)=64-8=56[/tex]
Since our discriminant is a positive value, our equation has two real roots.
3/4 x 25 please bro and i need to make this longerrrr
Answer:
18.75
Step-by-step explanation:
18.75
2. Two boxes are being shipped at a facility. One
box weighs 25.09 pounds, and the other box
weighs 25.018. Which box weighs more? Explain
and prove your answer.
Answer:
i think 25.09 weighs more
Step-by-step explanation: well simply 25.018 has more decimal places down therefore making it a smaller number
sorry if you get it wrong :c
I’ll give you 15 points if you know the answers to this question
It would be B)no.
Hope This Helps!
Which statement is true if a is the fourth root of 16, Show your work
a x a x a x a = 16
a = 164
4a = 16
a = 16/4
Given:
The statement is " a is the fourth root of 16".
To find:
The true statement for the given statement.
Solution:
The given statement is
a is the fourth root of 16.
Mathematically, it can be written as
[tex]a=\sqrt[4]{16}[/tex]
Taking power 4 on both sides.
[tex]a^4=(\sqrt[4]{16})^4[/tex]
[tex]a\times a\times a\times a=16[/tex]
Therefore, the correct option is A.
A true statement , if a is the fourth root of 16 is
a x a x a x a = 16
Important Information :
'a' is the fourth root of 16'a' is the fourth root of 16 can be written as
[tex]a=\sqrt[4]{16}[/tex]
To remove fourth root, we take exponent 4 on both sides
[tex]a=\sqrt[4]{16}\\(a)^4=(\sqrt[4]{16})^4[/tex]
Exponent 4 and fourth root will get cancelled
[tex]a^4=16\\a \cdot a\cdot a \cdot a=16[/tex]
a x a x a x a = 16
A true statement , if a is the fourth root of 16 is
a x a x a x a = 16
learn more about the radicals here:
brainly.com/question/1799883
What is the fraction shown above?
Find the difference.
4-(-8)=
Answer:
4
Step-by-step explanation:
subtract negative 4 by negative 8
Help quick plzzzzz Plzzzzzzzzzzzzz
12873t456473892220-209873
what unfortunate mistake did the champion ice skater make with his gold medal
Answer:
He Had It Bronzed
Step-by-step explanation:
Hope this help pls mark as brainlest!!
solve and recieve brain list I took a better picture
Graphing linear equation using a table [ x = - 1 ]
• • • • • • • • • • • • • • • • • • • • • • • • • • • •
(I only need help in filling the table, aswell as the slope and y-intercept, thanks! ^u^)
0
1
2
3
4
5
take x 1 so 1-1
2-1..........
Please help me!!!!!!!!!!
Which graph represents the parametric equations x = 1 – t2 and y = 2t, where 0 ≤ t ≤ 5?
ANSWER: A
After plotting the above equation on the coordinate plane, we can see the graph of the function.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
We have two parametric equations:
x = 1 – t² and
y = 2t
t = y/2 and
0 ≤ t² ≤ 5
1 ≤ 1 - t²≤ 4
1 ≤ x≤ 4
Plug the above value in x = 1 – t²
x = 1- (y/2)²
x = 1 - y²/4
4x = 4 - y²
y² = 4(1 - x)
Thus, after plotting the above equation on the coordinate plane, we can see the graph of the function.
Learn more about the parametric function here:
brainly.com/question/10271163
#SPJ2
The lifetimes of a certain brand of light bulbs are known to be normally dsitributed with a mean of 1700 hours and standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. The probability is 0.20 that the sample mean lifetime is more than how many hours?
A. 1652.
B. 1725.
C. 1752.
D. 1670.
Answer:
1742 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Single light:
Mean of 1700 hours and standard deviation of 400 hours, which means that [tex]\mu = 1700, \sigma = 400[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{400}{\sqrt{64}} = 50[/tex]
The probability is 0.20 that the sample mean lifetime is more than how many hours?
This is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]0.84 = \frac{X - 1700}{50}[/tex]
[tex]X - 1700 = 50*0.84[/tex]
[tex]X = 1700 + 50*0.84[/tex]
[tex]X = 1742[/tex]
Please help me!!!!
Ernest bought some cans of paint and 4/5 of a liter of special paint additive formulated to reduce mildew. Before painting his house, he used all of the additive to put 2/5 of a liter of additive in each can. How many cans of paint did Ernest buy?
Answer:
He bought 2 cans of paint
Step-by-step explanation:
If he put ⅖ in each, and ⅘ total, he would have had 2 cans
Quantity of special paint additive Ernest bought = [tex] \tt \frac{4}{5} \: of \: a \: litre [/tex]
Quantity of additive he put in each can = [tex] \tt \frac{2}{5} \: of \: a \: litre [/tex]
Number of cans of paint he bought :
[tex] =\tt \frac{4}{5} \div \frac{2}{5} [/tex]
[tex] = \tt\frac{4}{5} \times \frac{5}{2} [/tex]
[tex] = \tt\frac{4 \times 5}{5 \times 2} [/tex]
[tex] =\tt \frac{20}{10} [/tex]
[tex]\color{plum} = \tt2 \: paint \: cans[/tex]
▪︎Therefore, Ernest bought 2 paint cans.
Let f(x) = 4x - 1, h(x) = - X-3.
Find (f o h)(-5).
Answer:
(f o h)(-5)=-33
Step-by-step explanation:
Let f(x) = 4x - 1, h(x) = - X-3.
(f o h)=4(-x-3)-1
(f o h)=-4x-12-1
(f o h)=-4x-13
(f o h)(-5)=-4(-(-5))-13
(f o h)(-5)=-20-13
(f o h)(-5)=-33
SOMEONE PLZZ HELP, I HAVE A TEST AND DONT KNOW HOW TO DO THIS!!
At a deli, Joe bought 2.2 pounds of coleslaw for $7.15. What was the unit price?
Answer:
$3.25 for 1 pound of coleslaw
Step-by-step explanation:
i think,.
I'm so confused what is the answer plz?
Answer:
option b .
yes, by SAS.
.............
a classroom is 30 feet wide the ceiling is 10 feet above the floor what is the volume
Answer:
300 sqft
Step-by-step explanation:
30 times ten is 300 and the measure is feet squared
Answer:
9000 ft 3
Step-by-step explanation:
The medical practice you are working at has seen an average of 22.4 patients a day for the past 3 months. 3/4ths of those patients have insurance in one form or another.
Find the radius of the circle. The center of the circle is (2, -3) and a point that lies on the circle is (-1, -2).
Answer:
[tex]\displaystyle r = \sqrt{10}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Geometry
Definition of a radius - the center of a circle to any point to the circumferenceAlgebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Center (2, -3) → x₁ = 2, y₁ = -3
Circumference point (-1, -2) → x₂ = -1, y₂ = -2
In this case, the distance d from the center to the circumference point would be the radius r of the circle.
Step 2: Find Radius r
[Distance Formula] Define equation [Radius]: [tex]\displaystyle r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute in points [Radius]: [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2--3)^2}[/tex][Radius] [√Radical] (Parenthesis) Simplify: [tex]\displaystyle r = \sqrt{(-1-2)^2+(-2+3)^2}[/tex][Radius] [√Radical] (Parenthesis) Subtract/Add: [tex]\displaystyle r = \sqrt{(-3)^2+(1)^2}[/tex][Radius] [√Radical] Evaluate exponents: [tex]\displaystyle r = \sqrt{9+1}[/tex][Radius] [√Radical] Add: [tex]\displaystyle r = \sqrt{10}[/tex]12+22+32+...+102 =?
Answer:
750 is the answer. Hope it helps!
Find c. Round to the nearest tenth.
Answer:
Here,
150+10=180
162-180=18
Answer is 18°
Step-by-step explanation:
So the round of nearest tenth is 18°
Hope it will help have a great day at school. ^_^
sophie uses 18 beads to make a neckalace , 3/6 of the beads are purple
Answer:
9 beads are purple
Step-by-step explanation:
we know that
To find out how many beads are purple, multiply the total beads by the fraction of the beads that are purple
so
therefore
9 beads are purple
Another way to solve the problem is convert the fraction in percentage
we have
so
If the total are 18 beads
50% is 9 beads
therefore
9 beads are purple
4/5 ÷ 1/5 = ?????????
Answer:
4
Step-by-step explanation:keep change flip 4/5 x 5/1 = 20/5= 4
what is the equivalent property of 8(4x - 3)
Answer:
=32x−24
Step-by-step explanation:
What is the factors for x squared plus 5x - 6
Answer:
=[tex](x-1)(x+6)[/tex]
Step-by-step explanation:
Answer:
[tex]x^{2} +5x-6=(x-1)(x+6)[/tex]
Step-by-step explanation:
ILL GIVE BRAINLEST !!!!
Enter an equation for the function that includes the points. Give your answer in the form a(b*). In the
event that a = 1, give your answer in the form b*.
(1, 12) and (2, 144)
The equation is f(x)=