Solution :
P(H) = 0.7 ; P(T) = 0.3
If heads, then Urn H, 1 blue and 4 red marbles.
If tails, then Urn T , 3 blue and 1 red marbles.
a).
P ( choosing a Red marble )
= P (H) x P( Red from Urn H) + P (T) x P( Red from Urn T)
[tex]$=0.7 \times \frac{4}{5} + 0.3 \times \frac{1}{4}$[/tex]
= 0.56 + 0.075
= 0.635
b). If P (B, if coin showed heads)
If heads, then marble is picked from Urn H.
Therefore,
P (Blue) [tex]$=\frac{1}{5}$[/tex]
= 0.2
c). P (Tails, if marble was red)
[tex]$=P (T/R) = \frac{P(R/T)}{P(R)} \ P(T)$[/tex]
Where P (R/T) = P ( red, if coin showed tails)
[tex]$=\frac{1}{4}$[/tex]
= 0.25 (As Urn T is chosen)
P (R) = P (Red) = 0.635 (from part (a) )
P (T) = P (Tails) = 0.3
∴ [tex]$P(T/R) = \frac{0.25 \times 0.3}{0.635}$[/tex]
= 0.118
Hhhhhhhhhhhhhhhhuuiuu
Answer:
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
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What are the first and third quartiles for the following data set?
12, 15, 18, 16, 14, 9, 12, 21
A 9 and 21
C 12 and 17
B 12 and 16
D 15 and 17
Answer:
A
Step-by-step explanation:
I guess that is it may be
Please help please !!!
========================================================
Explanation:
You can use the AAS (angle angle side) theorem to prove that triangle ABD is congruent to triangle CBD.
From there, we can then say that AD and DC are the same length
AD = DC
3y+6 = 5y-18
3y-5y = -18-6
-2y = -24
y = (-24)/(-2)
y = 12
Solve the problem,
289 chocolates are to be packed into boxes, each of which will contain 12
chocolates. How many boxes of chocolates will there be? How many chocolates will
be left over?
Answer:
24 boxes, 1 chocolate remaining
Step-by-step explanation:
289 chocolates total, each box is 12.
just divide it and whatever is left will be your remainder.
289/12 = 24 boxes, 1 chocolate remaining
sub to gauthmath sub reddit for more help like this !
If there was a system where 5 points was equivalent to $1 how many points would $43 be?
Answer:
Step-by-step explanation:
5 pts = $1
$43 × (5 pts)/$1 = 43×5 pts = 215 pts
Find m∠F=....................
.................................
What would it equal??
m∠F= what is it???
Answer:
45°
Step-by-step explanation:
[tex] \sin \: m\angle F = \frac{EG}{FG} \\ \\ \sin \: m\angle F = \frac{2 \sqrt{11} }{2 \sqrt{22} } \\ \\ \sin \: m\angle F = \frac{\sqrt{11} }{ \sqrt{22} } \\ \\ \sin \: m\angle F = \frac{1}{ \sqrt{2} } \\ \\ \sin \: m\angle F = \sin \: 45 \degree \\ \\ \huge \boxed{ \purple{m\angle F = 45 \degree }}[/tex]
Bạn được một cá nhân thuê làm tư vấn tài chính, anh ta nhận được 2 đề nghị hợp ký đồng làm
việc với thời hạn 5 năm theo 2 sự lựa chọn sau:
- Lựa chọn 1: Lương 3 triệu/năm
- Lựa chọn 2: Lương 1.5 triệu/năm và được thưởng 9 triệu khi kết thúc hợp đồng làm việc.
a. Nếu lãi suất 8% bạn sẽ khuyên anh ta nhận lựa chọn nào?
b. Nếu lãi suất tăng 10% theo bạn có cần phải đổi lựa chọn không?
The The Laplace Transform of a function , which is defined for all , is denoted by and is defined by the improper integral , as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of as a fixed constant) 1. Find (hint: remember integration by parts)
Answer:
a. L{t} = 1/s² b. L{1} = 1/s
Step-by-step explanation:
Here is the complete question
The The Laplace Transform of a function ft), which is defined for all t2 0, is denoted by Lf(t)) and is defined by the improper integral Lf))s)J" e-st . f(C)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of s as a fixed constant) 1. Find Lft) (hint: remember integration by parts) A. None of these. B. O C. D. 1 E. F. -s2 2. Find L(1) A. 1 B. None of these. C. 1 D.-s E. 0
Solution
a. L{t}
L{t} = ∫₀⁰⁰[tex]e^{-st}t[/tex]
Integrating by parts ∫udv/dt = uv - ∫vdu/dt where u = t and dv/dt = [tex]e^{-st}[/tex] and v = [tex]\frac{e^{-st}}{-s}[/tex] and du/dt = dt/dt = 1
So, ∫₀⁰⁰udv/dt = uv - ∫₀⁰⁰vdu/dt w
So, ∫₀⁰⁰[tex]e^{-st}t[/tex] = [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ - ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]
∫₀⁰⁰[tex]e^{-st}t[/tex] = [[tex]\frac{te^{-st}}{-s}[/tex]]₀⁰⁰ - ∫₀⁰⁰ [tex]\frac{e^{-st}}{-s}[/tex]
= -1/s(∞exp(-∞s) - 0 × exp(-0s)) + [tex]\frac{1}{s}[/tex] [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰
= -1/s[(∞exp(-∞) - 0 × exp(0)] - 1/s²[exp(-∞s) - exp(-0s)]
= -1/s[(∞ × 0 - 0 × 1] - 1/s²[exp(-∞) - exp(-0)]
= -1/s[(0 - 0] - 1/s²[0 - 1]
= -1/s[(0] - 1/s²[- 1]
= 0 + 1/s²
= 1/s²
L{t} = 1/s²
b. L{1}
L{1} = ∫₀⁰⁰[tex]e^{-st}1[/tex]
= [[tex]\frac{e^{-st} }{-s}[/tex]]₀⁰⁰
= -1/s[exp(-∞s) - exp(-0s)]
= -1/s[exp(-∞) - exp(-0)]
= -1/s[0 - 1]
= -1/s(-1)
= 1/s
L{1} = 1/s
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 10 .
Answer:
The probability of getting two numbers whose sum is 10 is 25%.
Step-by-step explanation:
Given that a single die is rolled twice, and there are 36 equally-likely outcomes, to find the probability of getting two numbers whose sum is 10 the following calculation must be performed:
1 = +9
2 = +8
3 = +7
4 = +6
5 = +5
6 = +4
7 = +3
8 = +2
9 = +1
9/36 = 0.25
Therefore, the probability of getting two numbers whose sum is 10 is 25%.
An electronic switching device occasionally malfunctions, but the device is considered satisfactory if it makes, on average, no more than 0.20 error per hour. A particular 5-hour period is chosen for testing the device. If no more than 1 error occurs during the time period, the device will be considered satisfactory.
(a) What is the probability that a satisfactory device will be considered unsatisfactory on the basis of the test? Assume a Poisson process.
(b) What is the probability that a device will be accepted as satisfactory when, in fact, the mean number of errors is 0.25? Again, assume a Poisson process.
Solution :
It is given that the device works satisfactorily if it makes an average of no more than [tex]0.2[/tex] errors per hour.
The number of errors thus follows the Poisson distribution.
It is given that in [tex]5[/tex] hours test period, the number of the errors follows is
= [tex]0.2 \times 5[/tex]
= 1 error
Let X = the number of the errors in the [tex]5[/tex] hours
[tex]$X \sim \text{Poisson } (\lambda = 0.2 \times 5 =1)$[/tex]
Now that we want to find the [tex]\text{probability}[/tex] that a [tex]\text{satisfactory device}[/tex] will be misdiagnosed as "[tex]\text{unsatisfactory}[/tex]" on the basis of this test. We know that device will be unsatisfactory if it makes more than [tex]1[/tex] error in the test. So we will determine probability that X is greater than [tex]1[/tex] to get required answer.
So the required probability is :
[tex]P(X>1)[/tex]
[tex]$=1-P(X \leq 1)$[/tex]
[tex]$=1-[P(X=0)+P(X=1)]$[/tex]
[tex]$=1- \left( \frac{e^{-1} 1^0}{0!} + \frac{e^{-1} 1^0}{1!} \right) $[/tex]
[tex]$=1-(2 \times e^{-1})$[/tex]
[tex]$=1-( 2 \times 0.367879)$[/tex]
[tex]$=1-0.735759$[/tex]
[tex]=0.264241[/tex]
So the [tex]\text{probability}[/tex] that the [tex]\text{satisfactory device}[/tex] will be misdiagnosed as "[tex]\text{unsatisfactory}[/tex]" on the basis of the test whose result is 0.264241
The graph of the piecewise function f(x) is shown.
What is the range of f(x)?
6
5
O {x1-2 sx<4)
O {x1-2
Oy1-5
O {1-5 sys-1)
3+
2+
1
-7 -6 -5 -4 -3
-
1
3
4
5
8
The range is virtually the answer to the question,
"In which interval can find all y-values of the function".
So you look at the y-axis and see that your function begins with [tex]y=-5[/tex] (including -5 because of the dot on the graph) and ends at including [tex]y=-1[/tex].
So the interval notation is,
[tex]y\in[-5,-1][/tex]
But you are asked to specify the set notation of the interval, to do so first rewrite the interval using inequality operators, say we find some y in between (and including) -5 and -1,
[tex]-5\leq y\leq-1[/tex]
To specify that this is a set use curly bracelets and a bar,
[tex]\{y\mid-5\leq y\leq-1\}[/tex].
The y before bar is a step function and everything followed after the vertical bar is the range of the step function.
Hope this helps.
Using it's concept, it is found that the range of f(x) is given by:
{y|-5 <= -y <= -1}
What is the range of a function?The range of a function is the set that contains all possible output values. In a graph, it is given by the values of y, that is, the values of the vertical axis.
In the function described by this graph, the vertical axis assumes values between -1 and -5, inclusive, hence the range is given by:
{y|-5 <= -y <= -1}
More can be learned about the range of a function at https://brainly.com/question/24374080
An empty freight train traveled 60 miles from an auto assembly plant to an oil refinery. There, its tank cars were filled with petroleum products, and it returned on the same route to the plant. The total travel time for the train was 4 1 2 hours. If the train traveled 20 mph slower with the tank cars full, how fast did the train travel in each direction
Answer:
On the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.
Step-by-step explanation:
Since an empty freight train traveled 60 miles from an auto assembly plant to an oil refinery, and there, its tank cars were filled with petroleum products, and it returned on the same route to the plant, and the total travel time for the train was 4.5 hours, if the train traveled 20 mph slower with the tank cars full, to determine how fast did the train travel in each direction the following calculation must be performed:
60/20 = 3
60/40 = 1.5
60/20 = 3
3 + 1.5 = 4.5
Therefore, on the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.
A line passes through the point (5,6) and is parallel to the line given by the equation y = 2x - 12. Which of these is an equation for the line? O A. y-5=-264-6) B. y - 6 = -2(x - 5) C. y + 6 = 2(x + 5) D. Y- 6 = 2(x - 5)
Answer: D
Step-by-step explanation:
(lines parallel to each other have the same slope)
slope = m = 2
y = mx + b, (5,6)
6 = 2(5) + b
6 = 10 + b
b = -4
y = 2x - 4
y - 6 = 2(x - 5)
y - 6 = 2x - 10
y = 2x -4
bionomial probabilities
Answer:
Binomial probability refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment).
Hope this will help you :)Quy tắc suy luận nào là cơ sở của suy diễn sau: "Biết rằng: 2 đường thẳng d và d' song song hoặc cắt nhau. Ta đã có d không song song với d'. Vậy d cắt d'
Select one:
a. Luật loại trừ
b. Luật rút gọn
c. Luật phản chứng
d. Luật tách rời
Answer: a
Step-by-step explanation:
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.
x = 3 sin^2(t), y = 3 cos^2(t), 0< t<3pi
What is the length of the curve?
The length of the curve (and thus the total distance traveled by the particle along the curve) is
[tex]\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt[/tex]
We have
x(t) = 3 sin²(t ) ==> x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )
y(t) = 3 cos²(t ) ==> y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )
Then
√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|
and the arc length is
[tex]\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt[/tex]
Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.
Now,
• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)
• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)
so we split up the integral as
[tex]\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)[/tex]
which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.
Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.
Please help!! Can’t figure this out for the life of me.
Select the correct answer from each drop-down menu.
If _______, then AABC and ADEF are congruent by the ASA criterion.
If _______, then AABC and ADEF are congruent by the SAS criterion.
AABC and ADEF are congruent if ______
Answer:
Angle b is congruent to angle E
CA=FD
Step-by-step explanation:
If _______, then triangle ABC and triangle DEF are congruent by the ASA criterion. ASA is angle side angle . We know angle C= angle F and side CB = side FE We need to know angle B = angle E
If _______, then triangle ABC and triangle DEF are congruent by the SAS criterion. SAS is side angle side, we know side CB = side FE and then angle C= angle F then we need side CA = side FD
If ∠ABC = ∠DEF, then ΔABC and ΔDEF are congruent by the ASA criterion.
If AC = DF, then ΔABC and ΔDEF are congruent by the SAS criterion.
What are congruent figures?Two figures are said to be congruent of they have the same shape and all the corresponding sides and angles are congruent.
The HL (hypotenuse leg) congruence theorem states that if the hypotenuse and one leg of a triangle is congruent to another triangle, then both triangles are congruent.
In triangle ABC and DEF;
BC = EF and ∠ACB ≅ ∠DFE
Hence:
If ∠ABC = ∠DEF, then ΔABC and ΔDEF are congruent by the ASA criterion.
If AC = DF, then ΔABC and ΔDEF are congruent by the SAS criterion.
Find out more on congruent figures at: https://brainly.com/question/1675117
I need help answering this ASAP
Answer:
"D"
if you multiply by Conjugate
the denominator would end up A^2 - b^2
the answer has 25 - 10x
that is D
Step-by-step explanation:
write 6x10x10x10x10 with an expont
Answer:
6x10^4
Step-by-step explanation:
A survey showed that, in one city, 20.7% of the population used
product X, 50% use product Y and among users Y, 36.5% use X. Randomized interview
However, a resident in that city, calculate the probability that that person
a) Use both X and Y;
b) Neither X nor Y
Answer:
Step-by-step explanation:
a) 0.5*0.365=18.25%
b) (100%-20,7%-50%)=29.3
An 8 sided die, which may or may not be a fair die, has 4 colors on it; you have been tossing the die for an hour and have recorded the color rolled for each loss. What is the probability you will roll a purple on your next toss of the die? Enter your answer as a simplified fraction or a decimal rounded to four decimal places.
Red Purple Yellow Orange
44 37 41 21
Answer:
0.2587 = 25.87% probability you will roll a purple on your next toss of the die.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In an experimental probability, which is the case in this question, the number of outcomes is taken from previous experiments.
In this question:
44 + 37 + 41 + 21 = 143 tosses.
37 purple.
What is the probability you will roll a purple on your next toss of the die?
[tex]p = \frac{37}{143} = 0.2587[/tex]
0.2587 = 25.87% probability you will roll a purple on your next toss of the die.
Ray’s weight increased by 11% in the last two years. If he gained 16.5 pounds, what was his weight two years ago?
Answer:
Ray weighed 150 pounds two years ago.
Step-by-step explanation:
11/100 = 16.5/x
11x = 16.5(100)
11x = 1,650
(11x)/11 = (1,650)/11
x = 150
About time that he should start going to the gym!
How many of each coin does he have?
_____nickels
_____quarters
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 indicating that their financial security was more than fair. Conduct the hypothesis test and compute the p-value. Round your answer to four decimal places. What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places.
Answer:
hey, how you're day going
Step-by-step explanation:
.................
Question 13 (Essay Worth 8 points)
Write the sum using summation notation, assuming the suggested pattern continues.
3, -12, 48, -192, + …
Is this sequence arithmetic or geometric? Explain your answer.
9514 1404 393
Answer:
geometric sequence
Step-by-step explanation:
The terms of the sequence have a common ratio of -12/3 = -4, so the sequence is geometric. The general term is ...
an = 3(-4)^(n-1)
so the sum can be written as ...
[tex]\displaystyle\sum_{n=0}^\infty3(-4)^n[/tex]
(Note the summation starts at n=0, corresponding to a first term of 3.)
g A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 11 of the plates have blistered. Does this provide compelling evidence for concluding that more than 10% of all plates blister under such circumstances
Complete Question
A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of times, and determines that 11 of the plates have blistered. Does this provide compelling evidence for concluding that more than 10% of plates blister under such circumstances?
A) State H_0 and H_a, (5 pts)
B) Test the hypothesis using the P-Value approach at a significance level of 4%: (15 pts)
Expert Answer
Answer:
a)[tex]H_0:p=0.10[/tex]
[tex]H_a:p>0.10[/tex]
b) We fail to reject Null hypothesis
Step-by-step explanation:
From the question we are told that:
Sample size n=100
No. with blistered x=11
a)
Generally the Hypothesis given as
[tex]H_0:p=0.10[/tex]
[tex]H_a:p>0.10[/tex]
b)
Since p=0.10
Therefore
[tex]p'=\frac{11}{100}[/tex]
[tex]p'=0.11[/tex]
Test statistics
[tex]Z=\frac{p'-p}{\sqrt{p(1-p)}}[/tex]
[tex]Z=\frac{0.11-0.10}{\sqrt{0.10*0.90/100}}[/tex]
[tex]Z=1.33[/tex]
From table
[tex]P-Value =0.092[/tex]
Therefore
P-value >0.04 significance level
Hence,We cannot conclude that at [tex]4\%[/tex] significance level the proportion is greater than [tex]10\%[/tex]
We fail to reject Null hypothesis
Im new, and i hope someone tells me the right answers!
A factor is a natural number that can be multiplied by another natural number to get a value. The greatest common factor refers to when one compares the factors of two numbers, the largest natural number that both numbers have in common is the number's greatest common factor.
In the case of ([tex]m^2[/tex]) and ([tex]m^4[/tex]), the greatest common factor is ([tex]m^2[/tex]) because there are no factors of ([tex]m^2[/tex]) that are larger than it. No number can have a factor larger than itself. Since ([tex]m^2[/tex]) is also a factor of ([tex]m^4[/tex]) it is the greatest common factor of the two numbers.
The access code for a vault consists of four digits. The first digit
must be even and the last digit cannot be a zero. How many possible
codes are there?
Answer:
5 * 10 * 10 * 9 = 4500
Step-by-step explanation:
Geometry workkkk I need help it’s due tonightttt
