Answer:
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
Step-by-step explanation:
The probability of obtaining a defective 10-year old widget is 66.6%
p = 66.6% = 0.666
The probability of obtaining a non-defective 10-year old widget is
q = 1 - 0.666 = 0.334
The random variable will be the number of items that must be tested before finding the first defective 10-year old widget.
The geometric distribution is given by
[tex]$P(X = k) = p \times q^{k - 1}$[/tex]
Solving manually:
For k = 1:
[tex]P(X = 1) = 0.666 \times 0.334^{1 - 1} = 0.666 \times 0.334^{0} = 0.666[/tex]
For k = 2:
[tex]P(X = 2) = 0.666 \times 0.334^{2 - 1} = 0.666 \times 0.334^{1} = 0.2224[/tex]
For k = 3:
[tex]P(X = 3) = 0.666 \times 0.334^{3 - 1} = 0.666 \times 0.334^{2} = 0.0743[/tex]
For k = 4:
[tex]P(X = 4) = 0.666 \times 0.334^{4 - 1} = 0.666 \times 0.334^{3} = 0.0248[/tex]
For k = 5:
[tex]P(X = 5) = 0.666 \times 0.334^{5 - 1} = 0.666 \times 0.334^{4} = 0.0083[/tex]
For k = 6:
[tex]P(X = 6) = 0.666 \times 0.334^{6 - 1} = 0.666 \times 0.334^{5} = 0.0028[/tex]
Using Excel function:
NEGBINOMDIST(number_f, number_s, probability_s)
Where
number_f = k - 1 failures
number_s = no. of successes
probability_s = the probability of success
For the geometric distribution, let number_s = 1
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
As you can notice solving manually and using Excel yields the same results.
The equation 4x-45=y is used to find your profit y in dollars from buying $45 of supplies and washing cars for $4 what does the x stand for
After a series of major corporations admitted to large accounting irregularities, a public policy research institute conducts a survey to determine whether the public favors increased governmental regulation and oversight of corporations. Which of the following questions will deliver an unbiased response?
a. In light of the recent wave of shocking corporate accounting fraud, should government increase its regulation and oversight of corporations?
b. Should privately-owned companies be subjected to intrusive governmental regulation and oversight?
c. ls the government doing enough to protect American shareholders from corporate greed?
d. None of the above
Answer:
I think option B
Step-by-step explanation:
Should privately-owned companies be subjected to intrusive governmental regulation and oversight?
This question will produce an unbiased answer either a yes or a no. The question is simple and not too loaded and it is direct without including an inclination to bend to a particular direction. It will produce unbiased responses in that no comment was made about the admittance to large accounting irregularities.
Suppose f '' is continuous on (−[infinity], [infinity]). (a) If f '(−5) = 0 and f ''(−5) = −1, what can you say about f ? At x = −5, f has a local maximum. At x = −5, f has a local minimum. At x = −5, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = −5. (b) If f '(1) = 0 and f ''(1) = 0, what can you say about f ? At x = 1, f has a local maximum. At x = 1, f has a local minimum. At x = 1, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = 1.
Answer:
Step-by-step explanation:
a) The first derivative helps considering f decreases or increases. Also, when f'(x) = 0, the function gets local max/min depends on how it acts.
The second derivative helps determining the concave up/down.
At x = -5, f"(-5) = -1 <0 That means the function f have concave down. Also, it shows f increases before -5 and decreases after -5.
Hence f'(-5) = 0 shows f gets maximum at -5.
b) At the point where f" =0, the function has a reflecting point and we need more information to determine if f has a local max/min there.
Using concepts of critical points, it is found that:
a) At x = −5, f has a local maximum.
b) At x = 1, f has neither a maximum nor a minimum.
-----------------------
A critical value of a function f(x) is a value of [tex]x^{\ast}[/tex] for which: [tex]f^{\prime}(x^{\ast}) = 0[/tex].
The second derivative test is also applied:
If [tex]f^{\prime\prime}(x^{\ast}) > 0[/tex], [tex]x^{\ast}[/tex] is a minimum point.If [tex]f^{\prime\prime}(x^{\ast}) < 0[/tex], [tex]x^{\ast}[/tex] is a maximum point.If [tex]f^{\prime\prime}(x^{\ast}) = 0[/tex], [tex]x^{\ast}[/tex] is neither a maximum nor a minimum point.Item a:
[tex]f^{\prime}(-5) = 0, f^{\prime\prime}(-5) = -1[/tex], thus, a maximum point, and the correct option is:At x = −5, f has a local maximum.
Item b:
[tex]f^{\prime}(1) = 0, f^{\prime\prime}(1) = 0[/tex], thus, neither a maximum nor a minimum point, and the correct option is:At x = 1, f has neither a maximum nor a minimum.
A similar problem is given at https://brainly.com/question/16944025
Analysis showed that the mean arrival rate for vehicles at a certain Shell station on Friday afternoon last year was 4.5 vehicles per minute. How large a sample would be needed to estimate this year's mean arrival rate with 98 percent confidence and an error of ± 0.5?
Answer:
25
Step-by-step explanation:
use a Poisson process to model the arrival.
the mean rate of arrivals is λ=4.5
The standard deviation is calculated as:
σ==√λ =2.1213
The z-value for a 98% CI is z=2.3262.
If the 98% CI has to be within a error of 0.5 then:
Ul-Ll=2z*σ/√n=2*0.5=1
√n=z*σ=2.3262*2.1213=4.9346
√n=4.9346 and n = 4.9346^2=24.35 rounded to 25
The sample size needed is n=25.
The radius of a circle is 10.7 m. Find the circumference
to the nearest tenth.
Answer:
2 x [tex]\pi[/tex] x 10.7 = 67.2
Step-by-step explanation:
Step-by-step explanation:
c=2πr
c=2×π×10.7m
c=67.2m
so about 67
Solve for w: 2w<9+5w
Answer:
w > -3
Step-by-step explanation:
2w<9+5w
Subtract 5w from each side
2w-5w<9+5w-5w
-3w <9
Divide each side by -3 remembering to flip the inequality
-3w/-3 > 9/-3
w > -3
Answer:
w>-3
Step-by-step explanation:
g A cannonball is shot with an initial speed of 62 meters per second at a launch angle of 25 degrees toward a castle wall that is 260 meters away. If the wall is 20 meters tall, how high off the ground will the cannonball hit
Answer:
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Step-by-step explanation:
Given;
Initial speed v = 62m/s
Angle ∅ = 25°
Horizontal distance d = 260 m
Height of wall y = 20
Resolving the initial speed to vertical and horizontal components;
Horizontal vx = vcos∅ = 62cos25°
Vertical vy = vsin∅ = 62cos25°
The time taken for the cannon ball to reach the wall is;
Time t = horizontal distance/horizontal speed
t = d/vx (since horizontal speed is constant)
t = 260/(62cos25°)
t = 4.627 seconds.
Applying the equation of motion;
The height of the cannonball at time t is;
h = (vy)t - 0.5gt^2
Acceleration due to gravity g = 9.81 m/s
Substituting the given values;
h = 62sin25×4.627 - 0.5×9.81×4.627^2
h = 16.2264134736
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Which one of the following numbers is an irrational number?
Question 20 options:
A)
134∕675
B)
3.
C)
7.676767…
D)
8.12131415…
Answer:
B
Step-by-step explanation:
rational number means comparison between two numbers
eg: 1:3 or 1/3 or 0.333
irritional number does not
The one of the numbers is an irrational number that is A) 134 / 675
What are rational numbers, and irrational numbers?Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex]where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.
Irrational numbers are those real numbers which are not rational numbers.
Noted that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
For example
: 1:3 or 1/3
or 0.333
But irrational number does not.
The rational number means the comparison between two numbers
A) 134 / 675 = 0.19
B) 3.
C) 7.676767…
D) 8.12131415…
So, A) 134 / 675
This is an irrational number
Learn more about numbers here;
https://brainly.com/question/3151755
#SPJ2
Solve x-6y = 11 for y
Answer:
2
Step-by-step explanation:
Answer: y = 11 - x / -6
Step-by-step explanation:
X - 6y = 11
Since we are solving for y, we need to isolate the variable.
Move x to the other side of the equation.
- 6y = 11 - x
Now divide bith sides by -6 to cancel out -6y and get the variable y
-6y/ -6 = 11 - x/ -6
y = 11 - x / -6
Im not sure if it was solving for y, or if it was solve for x if y = 11
Determine the maximum r-value of the polar equation r = 3 + 3 cos theta
Answer:
Step-by-step explanation:
6
Last weekend, Lena worked 7.5 hours on Friday, 9.75 hours on Saturday, and 6.25 hours on Sunday.
She earns £8.60 per hour. How much did she earn in total?
Answer:202.1
Step-by-step explanation:
7.5hrs +9.75hrs+6.25hrs=23.5
8.60 X 23.5 =202.1 pounds
Help asap giving branlist!!!
Answer:
Option 2
Step-by-step explanation:
The first statement is false because the price for 10 gallons is about $37 from the graph. Using this same reasoning, the third statement is also false. The last statement doesn't make sense because the graph has nothing to do with the amount of miles driven. Therefore, the answer is the second statement. We can prove it by looking at the point (4, 15). This means that it costs $15 for 4 gallons, so then the price for one gallon will be 15 / 4 = $3.75.
During your journey, you develop an abscessed tooth and have to visit the dentist. You are prescribed an antibiotic with a dosage of 7.5 mg/kg every six hours. If you weigh 128 pounds and the antibiotic comes in 250 mg tablets, how many tablets should you take each day?
Answer:
I should take 10.44 tablets in a day, approximately 10.5 tablets.
Step-by-step explanation:
In order to solve this problem we need to convert the weight from pounds to kilograms, to do that we need to divide it by 2.205.
[tex]w = \frac{128}{2.205}\\w = 58.05 \text{ kg}[/tex]
Since I need to take 7.5 mg per kg of body weight, then in order to find the dosage we need to multiply the weight in kg by 7.5.
[tex]\text{dosage} = 58*7.5 = 435 \text{ mg}[/tex]
Since I need to take it every six hours and there are 24 hours in a day, we will have to take 4 dosages in a day, therefore we need:
[tex]\text{dosage(day)} = 435*6 = 2,610 \text{ mg}[/tex]
The antibiotic comes in 250 mg in tablets, therefore the number of tablets is:
[tex]tablets = \frac{2610}{250} = 10.44[/tex]
I should take 10.44 tablets in a day, approximately 10.5 tablets.
We know that if the probability of an event happening is 100%, then the event is a certainty. Can it be concluded that if there is a 50% chance of contracting a communicable disease through contact with an infected person, there would be a 100% chance of contracting the disease if 2 contacts were made with the infected person
Answer:
The correct answer to the following question will be "No". The further explanation is given below.
Step-by-step explanation:
Probability (Keeping the disease out of 1 contact)
= [tex]0.5[/tex]
Probability (not keeping the disease out of 1 contact)
= [tex]1-0.5[/tex]
= [tex]0.5[/tex]
Now,
Probability (not keeping the disease out of 2 contact)
= Keeping the disease out of 1 contact × not keeping the disease out of 1 contact
On putting the estimated values, we get
= [tex]0.5\times 0.5[/tex]
= [tex]0.25[/tex]
So that,
Probability (Keeping the disease out of 2 contact)
= [tex]1-0.25[/tex]
= [tex]0.75 \ i.e., 75 \ percent[/tex]
∴ Not 100%
Which of the lists of letters all have line symmetry? A, B, C, D W, X, Y, Z L, M, N, O S, T, U, V
Answer:
A, W, X, Y, M, O, T, U, V, C, D
Step-by-step explanation:
If you put a line through the middle, then the left and the right side will look the same
A card is drawn at random from a standard 52-card deck. Find the following probabilities: (2 points) a. The probability the card is a diamond or a face card. (2 points) b. The probability that the card is neither an ace nor a heart. (2 points) c. The probability that the card is a face card or a 3
Answer:
(a)[tex]\dfrac{11}{26}[/tex]
(b)[tex]\dfrac{9}{13}[/tex]
(c)[tex]\dfrac{4}{13}[/tex]
Step-by-step explanation:
Number of cards in a Standard Deck=52
(a)
Number of Diamonds (D)=13
Number of Face Cards(F) = 12
Number of Diamonds that are face cards = 3
[tex]Pr($that the card is a diamond or a face card)=P(D)+P(F)-P(D \cap F)\\=\dfrac{13}{52} +\dfrac{12}{52} -\dfrac{3}{52} \\=\dfrac{22}{52} \\=\dfrac{11}{26}[/tex]
(b)The probability that the card is neither an ace nor a heart.
Number of Aces (A)=4
Number of Hearts(H) = 13
Number of Hearts that are Aces = 1
[tex]Pr($that the card is a Ace or a Heart), P(A \cup H)=P(A)+P(H)-P(A \cap H)\\=\dfrac{4}{52} +\dfrac{13}{52} -\dfrac{1}{52} \\=\dfrac{16}{52} \\$Therefore, probability that the card is neither an ace nor a heart.\\=1-P(A \cup H)\\=1-\dfrac{16}{52}\\=\dfrac{36}{52}\\=\dfrac{9}{13}[/tex]
(c)The probability that the card is a face card or a 3
Number of 3 cards(T)=4
Number of Face Cards(F) = 12
[tex]Pr($that the card is a three or a face card)=P(T)+P(F)\\=\dfrac{4}{52} +\dfrac{12}{52} \\=\dfrac{16}{52} \\=\dfrac{4}{13}[/tex]
01
The list below shows the prices of T-shirts at a clothing store.
{8, 10, 10, 12, 15, 15, 18)
Which statement best describes the mean of this ser?
the difference between the least and greatest prices
the sum of the prices
the quotient of the difference between the least and greatest prices divided by 7
the sum of the prices divided by 7
dem
Answer:
the sum of the prices divided by 7
Step-by-step explanation:
The mean is the sum of the elements of a set, divided by the number of elements in the set. This set has 7 members, so its mean is ...
the sum of the prices divided by 7
perimeter.
6) A quadrilateral can have 2
reflex angles.
Answer:
False
Step-by-step explanation:
Answer:
A quadrilateral can't have 2 reflex angles
Step-by-step explanation:
A quadrilateral can't have 2 reflex angles because reflex angles > 180° so if you add two together, it is > 360°
Solve for X 10(x-1) = 8x-2
Answer:
X = 4 x
over 5 ( x − 1 ) − 1 5 ( x − 1 )
Answer:
x = 4
Step-by-step explanation:
10(x-1) = 8x-2
Distribute
10x-10 = 8x-2
Subtract 8 from each side
10x-10-8x = 8x-2-8x
2x-10 = -2
Add 10 to each side
2x-10+10 = -2+10
2x = 8
Divide each side by 2
2x/2 = 8/2
x = 4
3. The difference between two numbers is 5
Answer:
The difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s
Step-by-step explanation:
⇒ x(x-5) = 50
⇒ x2 - 5x - 50 = 0
⇒ x2 - 10x + 5x - 50 = 0
⇒ x (x - 10) + 5 (x - 10) = 0
⇒ (x+5) (x-10) = 0
⇒ (x+5) (x-10) = 0
⇒ x = -5 or 10
⇒ x = 10 (x = -5 , rejected)
Graph the image of the figure given the translation. 1. (x, y) → (x +4, y - 1)
Answer:
Y=(-1,0)
G=(0,1)
F=(-1,3)
Step-by-step explanation:
rearrange the equation t = vf - vi /a
to make acceleration appear on the left hand side
Answer:
a= (vf - vi)/t
Step-by-step explanation:
t = vf - vi /a
a* t =(vf - vi /a)*a
at = vf - vi
at/t = (vf - vi)/t
a = (vf - vi)/t
Hope it works
A pair of shoes usually sells for $70. If the shoes are 30% off, and sales tax is 5%, what is the total price of the shoes, including tax?
Answer:
The total price of the shoes including tax is 51.45
Step-by-step explanation:
You could go about this 2 ways.
One way is if the shoes originally cost $70 and they are now 30% off, it basically means that the discounted price of the shoes is 70% of the original cost, which is $49. Then to find the total price including tax, you need to find 105% of 49, because you are adding 5% to the discounted price(100). When you do the math, you should get the answer 51.45.
The other way to do it is by first finding 30% of 70, which is 21, and then subtracting that from the original price(70) to get the discounted price, $49. Then you need to find 5% of 49 and then add that to 49 to find the total cost w/ tax, which is 51.45.
The following simple linear regression analyzes the relationship between the number of classes students are taking (the independent variable, labeled in the following output as X[,2]) and the number of books they have in their backpack (the response) at randomly chosen times. Assume all relevant assumptions are met. Which of the following are correct interpretations of the slope?
a. Each additional class a student takes is associated with about a 58.7% increase in the number of books in their backpack on average.
b. Each additional class a student takes is associated with about an additional 0.587 books in their backpack on average.
c. Taking an additional class causes students to carry 0.587 extra books with them on average.
d. The population average number of books in a studentâs backpack is 0.587.
Answer:
The answer is B.
Step-by-step explanation:
Why do we say that the answer is B?
For each additional class there is a significant increase that represents a minimum value over a total of books, that is, 100% that will always remain, therefore the increase will be an additional average over the other "books" that are already in backpack.
Solve -3(2x - 9) = -3.
Answer:
X=4
Step-by-step explanation:
1. Distribute 3 to 2x and -9
2. You will get "6x-27 = -3"
3. Next, add 27 to -27 and -3
4. You will get "6x = 24"
5. Then, you will divide 6x and 24 by 6
6. You will get "6x/6 = 24/6"
7. The 6 will cancel the 6 in 6x.
8. Then, you will divide 24 and 6. which will give you the answer of 4
9. Add the "X=..." and...
10. You will get the answer of "X=4"
What is the value of X?
Answer:
x = 41 ft
Step-by-step explanation:
35(35+23) = 29(29+x)
2030 = 29(29+x)
70 = 29 + x
x = 41 ft
In the arcade game Skee Ball, players roll a ball up a ramp and receive 10 to 50 points based on where the ball lands. Players will attempt to aim the ball to receive higher scores, which are more difficult to achieve based on size and location. However, if a ball is rolled randomly up the ramp, the probabilities of the ball landing in different scoring areas are not equal. Assume the following probabilities for each possible score:
Score 10 Points 20 Points 30 Points 40 Points 50 Points
Probability 0.50 0.25 0.15 0.07 0.03
Assume that a player rolls three balls at random.
Required:
a. What is the probability of a total score of at least 100 points?
b. If the first ball scores 30 points, what is the probability of a total score of at least 100 points?
c. Are the events "the first ball scores 30" and the "total score is at least 100" independent? Why or why not??
d. What is the expected total score? What is the variance of the score on one roll?
Answer:
Step-by-step explanation:
a) sum of 100 can be achieved from following set of score
10,40,50. This score can be achieved in 3! ways
20,30,50. This score can be achieved in 3! ways
20,40,40. This score can be achieved in 4 ways
30,30,40. This score can be achieved in 4 ways
So,
P(score of 100)=
A college job placement center has requests from five students for employment interviews. Three of these students are math majors, and the other two students are statistics majors. Unfortunately, the interviewer has time to talk to only two of the students. These two will be randomly selected from among the five. What is the sample space for the chance experiment of selecting two students at random
Answer:
Step-by-step explanation:
The following is the information provided
number of students is 5
The number of math major = 3
The number of statistic major = 2
Label math students as A, B, C
And statistic students as D, E
The total number of ways to select two students from 5 students is 10
The sample space is S = {AB,AC,BC,AD,AE,BD,BE,CD,CE,DE}
Yes , in the sample space the events are equally alike
What is the probability that both selected students are statistics majors
The selected students of statistic major are DE
the probability that both selected students are statistics majors is [tex]\frac{1}{10}[/tex]
= 1/10
What is the probability that both students are math majors
The selected students of statistic major are AC,AB,BC
the probability that both selected students are math majors is [tex]\frac{3}{10}[/tex]
= 3/10
What is the probability that at least one of the students selected is a statistics major
Number of ways to select at least one of the students selected is a statistic major is {AD,AE,BD,BE,CD,CE,DE}
the probability that at least one of the students selected is a statistics major is [tex]\frac{7}{10}[/tex]
7/10
What is the probability that the selected students have different majors
Number of ways to select students with different major is {AD,AE,BD,BE,CD,CE,}
the probability that the selected students have different majors is [tex]\frac{6}{10}[/tex]
6/10
Mariah spent $9.50 on 9 pounds of limes and pears. Limes cost $0.50 per pound and pears cost $1.50 per pound. Let l be the number of pounds of limes and let p be the number of pounds of pears.
The system of linear equations that models this scenario is:
l + p = 9
0.5l + 1.5p = 9.5
How many pounds of each type of fruit did she buy?
Answer:
4 pounds of lime and 5 pounds of pears
Step-by-step explanation:
I + P = 9
0.5l + 1.5P = 9.5
I = 9 - P
0.5(9 - P) + 1.5P = 9.5
4.5-0.5P + 1.5P = 9.5
4.5 + P (1P) = 9.5
P = 9.5-4.5 = 5
I = 9 - 5 = 4
Answer: 4 pounds of lime and 5 pounds of pears
In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $13.$ What is the length of the hypotenuse of the triangle?
Answer:
AB = 2√106 ≈ 20.591
Step-by-step explanation:
The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs.
For median AM, we have ...
AM² = CM² +AC² = (BC/2)² +AC²
For median BN, we have ...
BN² = CN² +BC² = (AC/2)² +BC²
The sum of these two equations is ...
AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)
AM² +BN² = (5/4)(AB²)
The hypotenuse of triangle ABC is then ...
AB = √(4/5(AM² +BN²))
AB = 2√((19² +13²)/5)
AB = 2√106 ≈ 20.591