Answer:
(a)
[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex] [tex]Pr(x = 1) = \frac{^7C_1 * ^3C_1}{45}[/tex] [tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]
(b)
[tex]E(x) = \frac{3}{5}[/tex]
Step-by-step explanation:
Given
[tex]n = 10[/tex] --- flashbulbs
[tex]k = 3[/tex] --- defective bulbs
[tex]r = 2[/tex] --- selected
Solving (a): The distribution of x
The total outcome is: [tex]^nC_r[/tex]
This gives:
[tex]^{10}C_2 = 45[/tex]
Having 3 defective bulbs means 7 are not.
When there is no defective bulb among the selected, the probability is:
[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex]
When 1 is defective:
[tex]Pr(x = 1) = \frac{^7C_1 * ^3C_2}{45}[/tex]
When both are defective
[tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]
So, the distribution is:
[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex]
[tex]Pr(x = 1) = \frac{^7C_1 * ^3C_1}{45}[/tex]
[tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]
Solving (b): The expected value
This is calculated as:
[tex]E(x) = \sum x * Pr(x)[/tex]
So, we have:
[tex]E(x) = x_1 * Pr(x_1) +x_2 * Pr(x_2) + ............... + x_n * Pr(x_n)[/tex]
The equation becomes:
[tex]E(x) = 0* Pr(x=0) +1* Pr(x=1) + 2 * Pr(x=2)[/tex]
[tex]E(x) = 1* Pr(x=1) + 2 * Pr(x=2)[/tex]
[tex]E(x) = Pr(x=1) + 2 * Pr(x=2)[/tex]
From the distribution in (a), we have:
[tex]E(x) = \frac{^7C_1 * ^3C_1}{45} + 2 * \frac{^3C_2}{45}[/tex]
[tex]E(x) = \frac{7 * 3}{45} + 2 * \frac{3}{45}[/tex]
[tex]E(x) = \frac{21}{45} + \frac{6}{45}[/tex]
[tex]E(x) = \frac{21+6}{45}[/tex]
[tex]E(x) = \frac{27}{45}[/tex]
Simplify
[tex]E(x) = \frac{3}{5}[/tex]
annual survey in which readers rate their favorite cruise ship. All ships are rated on a -point scale, with higher values indicating better service. A sample of ships that carry fewer than passengers resulted in an average rating of , and a sample of ships that carry or more passengers provided an average rating of . Assume that the population standard deviation is for ships that carry fewer than passengers and for ships that carry or more passengers. Round your all answers to two decimal places.
This question is incomplete, the complete question is;
Condé Nast Traveler conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service.
A sample of 37 ships that carry fewer than 500 passengers resulted in an average rating of 85.36, and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.40.
Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that carry 500 or more passengers. What is the value of the test statistic? Round your all answers to two decimal places.
Answer:
value of the test statistic is 4.13
Step-by-step explanation:
Given the data in the question;
fewer than 500 passengers more than 500 passengers
n₁ = 37 n₂ = 44
x'₁ = 85.36 x'₂ = 81.40
s₁ = 4.55 s₂ = 3.97
Now, to get the test statistics, we use the following formula;
z = (x'₁ - x'₂) / √( [tex]\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}[/tex] )
we substitute
z = ( 85.36 - 81.40 ) / √( [tex]\frac{(4.55)^2}{37} + \frac{(3.97)^2}{44}[/tex] )
z = 3.96 / √( [tex]\frac{20.7025}{37} + \frac{15.7609}{44}[/tex] )
z = 3.96 / √( 0.5595 + 0.3582 )
z = 3.96 / √0.9177
z = 3.96 / 0.957966596
z = 4.1337 ≈ 4.13
Therefore, value of the test statistic is 4.13
Can someone help me solve this
Answer:
[tex]y = {(x + 8)}^{3} - 9[/tex]
A computer professor is interested in studying the amount of time it would take students enrolled in the Introduction to Computers course to write and run a program in Matlab. The professor hires you to analyze the following results in minutes from a random sample of 9 students:
10 12 8 16 12 13 10 11 15
Required:
At the 0.05 level of significance, is there evidence that the population average time is greater than 10 minutes?
Answer:
Following are the solution to the given question:
Step-by-step explanation:
In this question, firstly we calculating the [tex]\bar{x} \ \ and \ \ s[/tex]
[tex]\bar{x}=11.89 \\\\s = 2.52\\\\n = 9\\\\\alpha=0.05\\[/tex]
[tex]H_0 : u \leq 10\\\\ H_1 : u > 10[/tex]
It is an upper test and testing the statistics:
[tex]t=\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}\\\\t=\frac{11.89-10 }{\frac{2.52}{\sqrt{9}}}\\\\t=2.25\\\\[/tex]
So, the test statistics [tex]t=2.25[/tex]
[tex]\alpha=0.05 \\\\ d.f = n-1\\\\[/tex]
[tex]=9-1\\\\=8[/tex]
critical value =2.306 ( using t-table ) [tex]critical\ value >\ test\ statistics , \ Fail\ to\ Reject\ H_0[/tex]
Decision: We should not reject the null hypothesis.
What is the distance between the points (4.10) and (-3,-14) on the coordinates plane?
Answer:
25 units
Step-by-step explanation:
use the distance formula to get the square root of 24² + 7²
this will give you the square root of 625, which is 25
What is x3 – 25x factored completely
Answer:
x(x2-25)=o
x=0;x=5 and -5
Answer:
[tex] {x}^{3} - 25x \\ = x( {x}^{2} - {5}^{2} ) \\ = x(x - 5)(x + 5)[/tex]
(x+iy)^4 -(x+iy)^2 +16=0
Answer:
below
Step-by-step explanation:
that is the procedure above
Josh's annual salary is $39.000. A total of $12.330.96 will be deducted for taxes and health insurance. He will receive his paycheck monthly in 12 equal installments. How much will he get paid with each paycheck?
Answer:
Step-by-step explanation:
without tax and insurance deduction- 3,250 (monthly)
with tax and insurance deduction-26,669.04/12=2,222.42 (monthly)
You measure 20 turtles' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 11.5 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight. Give your answer as a decimal, to two places
Answer: the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight = 4.23
Step-by-step explanation:
Formula for margin of error : [tex]E=\dfrac{z^*\times (Population\ standard\ deviation)}{\sqrt{Sample\ size}}[/tex]
, where z* = Critical z-value.
Given: population standard deviation = 11.5 ounces
Sample size = 20
Z value for 90% confidence level = 1.645
margin of error (E) = [tex]\dfrac{1.645\times11.5}{\sqrt{20}}[/tex]
[tex]\approx4.23[/tex]
Hence, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight = 4.23
The vertex of the parabola below is at the point (2, -5). Which of the equations
below could be the one for this parabola?
Change 10 miles per hour to meters per second (hint: you'll need to
change from miles to kilometers, then change kilometers to meters)
how do i do this work shown!!
Answer:
10 miles per hour = 0.1862 meter per second
Step-by-step explanation:
Given
Speed in miles per hour = 10 miles per hour
As we know
1 mile = 1609.34 meters
and 1 hour = 24*60 *60 seconds
Thus, 10 miles per hour in meter per second would be
10 * 1609.34/24*60 *60
= 0.1862 meter per second
Which expression is equivalent to 3/4x -1/4xy
Answer:
\frac{3+x\frac{-4}{4xy}}{4x}
4x
3+x
4xy
−4
Step-by-step explanation:
which of the following us the graph of f(x)=-0.5| x+3| -2
Compare the two linear functions listed below and determine which has a negative slope.
Answer:
Gift card
Step-by-step explanation:
Given
Function 1 and 2
Required
Which has a negative slope
For the first function (Gift card), we have the following observation.
As x increases from 0, 1, 2 and then 3
The values of y keep reducing
This means that the gift card function has a negative slope
For the second function (calculator rental)
We have:
[tex]c = 10 + 5m[/tex]
The slope of function [tex]y =mx + b[/tex] is m
So, by comparison
[tex]m=5[/tex]
5 is positive,
This means that the gift card function has a negative slope
If 25x2 – 35x – 18 is written as a2 – 7a – 18, what is a in terms of x?
a =
Answer:
a = 5x
Step-by-step explanation:
The value of an in terms of x will be a = 5x.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expressions are 25x² – 35x – 18 is written as a² – 7a – 18.
The value of an in terms of x will be calculated as:-
25x² – 35x – 18
a² – 7a – 18.
Compare the first term of the two equations,
25x² = a²
a = √25x²
a = 5x
To know more about an expression follow
https://brainly.com/question/20724072
#SPJ2
7. Your closet has 10 shirts for every 4 sweaters. Your closet has 40 shirts. How many sweaters are
in your closet?
Answer:
16 sweaters
Step-by-step explanation:
4=10
4=10
4=10
4=10
4x4=16
A study followed for 10 years a sample of 82,695 middle-aged men with no prior history of heart failure living in California. The daily number of minutes spent being sedentary (seated) was recorded in diaries and reported on regularly administered questionnaires. During the course of the study, a total of 3,473 men experienced heart failures. Participants with high sedentary time and low sedentary times were compared. The proportion experiencing a heart failure was higher in the group of men spending more time being sedentary.
This study is an example of:_________
a. longitudinal cohort study
b. case-control observational study
c. voluntary response sample or anecdotal data
d. completely randomized experiment
e. matched pairs / repeated measures experiment
f. cross-sectional sample survey
g. census (population data)
Answer:
f. cross-sectional sample survey
Step-by-step explanation:
- longitudinal cohort study is when the group of subjects that comprises the cohort is chosen based on a disease or injury and is then monitored over time at routine intervals. In this question, it's not the case as the sample of men were just picked and studied with no special group or cohort.
- If it was case-control observational study, the research would have started with identifying those who have heart failure and those who don't have heart failure but it wasn't the case and thus this is not correct.
- If this was voluntary response sample, it means the men would have been self chosen which means they volunteered to be part of the study if it was of interest to them. But this is not the case here.
- If it was completely randomized experiment, it means that the people sampled would have been randomly assigned to different treatments which was not so in this question.
- If it were to be match pairs experiment, it means the men sampled would be grouped into pairs and each pair will be assigned different treatments which didn't happen in this question.
- If it were to be cross-sectional sample survey, it means that data will be collected from a population of interest to make inferences from that population at a point in time. That is the case here because data about sedentary time or less was taken and compared to know the effect it had on heart failure.
- If it were census, it will just be about getting the size of the population without making inquiries about sedentary time.
emergency helpn please i dk wut they mean
Answer:
below
Step-by-step explanation:
that is the procedure above
The lines below are perpendicular. If the slope of the green line is -1/6, what is the slope of the red line?
Answer:
slope of red line=6
Step-by-step explanation:
Hi there!
We're given a set of perpendicular lines and the slope of the green line being -1/6
Perpendicular lines have slopes that are negative and reciprocal; if they are multiplied together, the result is -1
So to find the slope of the red line, we can use this formula (m is the slope):
-1/6m=-1
Multiply both sides by -6 (clears the fraction to get 1m on the left)
m=6
So the slope of the red line is 6
Hope this helps!
Is this answer correct? If not, which one is correct?
Answer:
correct
Step-by-step explanation:
factorise a2-17a+42
Answer:
(a-14) (a-3)
Step-by-step explanation:
Answer:
(a - 14) (a - 3)
Step-by-step explanation:
a² - 3a - 14 a + 42
a(a - 3) - 14 ( a - 3)
(a - 14) (a - 3)
On a coordinate plane, rhombus W X Y Z is shown. Point W is at (7, 2), point X is at (5, negative 1), point Y is at (3, 2), and point Z is at (5, 5).
What is the perimeter of rhombus WXYZ?
the answer is 4,13 of the perimeter
A 12 SIDED DIE WITH SIIDES LABLELED 1-12 ARE ROLLED ONCE. EACH NUMBER IS LIKELY TO BE ROLLED .WHAT IS THE PROBABILITY OF ROLLING A NUMBER GREATER THAN 10
Answer:
p=.1666
11 or 12
2 out of 12
2/12
1/6
p=.1666
Step-by-step explanation:
ABCD is a kite, find the value of y
Answer:
All triangles add to 180 degrees.
180 = 90 + 40 + angle ABX
angle ABX = 180 - 90 - 40
Angle y = 50
Step-by-step explanation:
Need help in understanding how to solve this problem.
>> Find an equation of the plane through (−2,3,2) and parallel to the plane 3x+y+z= 4
Answer:
Step-by-step explanation:
3x+y+z= 4
3x+ y = 4 - z
y = 4-z-3x
We then make parallel
y-2 = 4−z−3x
y-2 = 4-2 -z-3x
y-2 = 2-z-3x
y = -z-3x+2
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
Calculate the value of this investment at the end of the 5 years,
Answer:
The investment after 5 years is $ 662.45.
Step-by-step explanation:
Principal, P = $ 600
Time, t = 5 years
Rate of interest, R = 2 %
Time , t = 5 years
The amount after the time 5 years is
[tex]A = P \times \left ( 1+\frac{R}{100} \right )^t\\\\A = 600\left ( 1+0.02 \right )^5\\\\A = 662.45[/tex]
So, the investment after 5 years is $ 662.45.
Need help will give brainliest
Answer:
X=15
Step-by-step explanation:
line segment with length 18 is tangent and other one is secant so
[tex] {18}^{2} = 12(12 + x) \\ 324 = 144 + 12x \\ 324 - 144 = 12x \\ 180 = 12x \\ x = 180 \div 12 \\ x = 15[/tex]
Write the prime factorization of 4
Answer:
2 x 2
Explanation:
The prime numbers that multiply to 4 are 2 and 2.
Which type of sequence is shown? -2, 0, 2, 4, 6, . . .
Answer:
The type of sequence that is show is an arithmetic sequence
Step-by-step explanation:
A: A
B: B
C: C
D: D
Show work!
Answer: A
Step-by-step explanation:
Area of a triangle is base times height
We have a base made by point m and n with a length of 6
now the third point has to form a height which when put with the base, gets you 18
area of triangle is bh/2
so lets set height as h, 6x/2 = 18 6x = 36 x = 6
This means the point has to be 6 apart either left or right. Only point that matches this is a.
Please help me no links
Answer:
c
Step-by-step explanation:
The graph starts at 100 and decreases as it goes the following situations that were listed should be somewhat implying that something is decreasing. Since a and b are GAINING something then it can't be that because it is increasing, so we are left with choice c.
hope this helps!
