Answer:
The probability that on a randomly selected day the statistics professor will have five messages is 0.1755.
Step-by-step explanation:
Let the random variable X represent the number of e-mail messages per day a statistics professor receives from students.
The random variable is approximated by the Poisson Distribution with parameter λ = 5.
The probability mass function of X is as follows:
[tex]P(X=x)=\frac{e^{-5}\cdot 5^{x}}{x!};\ x=0,1,2,3...[/tex]
Compute the probability that on a randomly selected day she will have five messages as follows:
[tex]P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}[/tex]
[tex]=\frac{0.006738\times 3125}{120}\\\\=0.17546875\\\\\approx 0.1755[/tex]
Thus, the probability that on a randomly selected day the statistics professor will have five messages is 0.1755.
A children's roller coaster is limited to riders whose height is at least 30 inches and at most 48 inches. Write two inequalities that represent the height h of riders for the roller coaster.
Answer:
h≤48 h≥30
Step-by-step explanation:
A goat is tied to a peg in the ground. The rope is 3m long. What area of grass can the goat eat? (use the value 3.14 for pie)
Answer:
28.26 (Please mark as brainiest if you find it helpful )
Step-by-step explanation:Area the goat will eat is equal to the are of circle having radius 3m.
Area of circle = pi * r ^ 2
⇒ 3.14 * (3) ^ 2 → 3.14 * 9
⇒ 28.26
g(x) = x2 – 5x + 2.
Answer:
Use the quadratic formula:
a = 1 b= -5 c= 2
x = - -5 +-sqr root (25 - 4 * 1 * 2) / 2 * 1
x = 5 +-sqr root (25 - 8) / 2
x = 5 +- sqr root (17) / 2
x1 = 5 +4.1231056256 / 2
x1 = 4.5615528128
x2 = 5 -4.1231056256 / 2
x2 = 4.5615528128
Step-by-step explanation:
Question 2 (1 point)
How much does the prefix milli multiply the value of a base unit?
Answer:1000
Step-by-step explanation:
A 45 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1088
Answer:
The substance's half-life is 6.4 days
Step-by-step explanation:
Recall that the half life of a substance is given by the time it takes for the substance to reduce to half of its initial amount. So in this case, where they give you the constant k (0.1088) in the exponential form:
[tex]N=N_0\,e^{-k\,*\,t}[/tex]
we can replace k by its value, and solve for the time "t" needed for the initial amount [tex]N_0[/tex] to reduce to half of its value ([tex]N_0/2[/tex]). Since the unknown resides in the exponent, to solve the equation we need to apply the natural logarithm:
[tex]N=N_0\,e^{-k\,*\,t}\\\frac{N_0}{2} =N_0\,e^{-0.1088\,*\,t}\\\frac{N_0}{2\,*N_0} =e^{-0.1088\,*\,t}\\\frac{1}{2} =e^{-0.1088\,*\,t}\\ln(\frac{1}{2} )=-0.1088\,t\\t=\frac{ln(\frac{1}{2} )}{-0.1088} \\t=6.37\,\,days[/tex]
which rounded to the nearest tenth is: 6.4 days
Answer:
6.4
Step-by-step explanation:
I did it on the same site and got it correct
the average mark of candidates in an aptitude test was 138.5 with a standard deviation of 10.6. three scores extracted from the test are 178,122,100.what is the average of the extracted scores that are extreme value
Answer:
The average of the extracted scores = 133.33
Step-by-step explanation:
Given data the average mark of candidates in an aptitude test was 138.5 with a standard deviation of 10.6
mean of the aptitude test = 138.5
Standard deviation of the aptitude test = 10.6
Given three scores extracted from the test are 178,122,100
The average of the extracted scores = ∑x / n
The average of the extracted scores
= [tex]\frac{178 +122 +100}{3}[/tex]
= 133.33
Final answer:-
The average of the extracted scores = 133.33
What is the value of X ?
A-12
B-17
C-23
D-25
Step-by-step explanation:
25 answer by considering
The answer and how to solve it.
Answer:
B
Step-by-step explanation:
what is the output from the following machine when the input is 4
Answer:
4 - 7 = -3
-3 / 3 = -1
What is a word problem for 15 minus 28?
Answer:
A word problem for that would be Sam had 28 chocolates and Bob took away 15. How many does Sam have left?
Step-by-step explanation:
I don't know how to show work for writing a word problem. Sorry
Answer:
Step-by-step explanation:
Jane has $15 in her bank account. She wrote a $28 check for buying a fiction book. How much is her balance now?
If triangles DEF and NPQ are similar, what is the length of side d? As fraction or whole number.
The length of the side d would be 77/18.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
If triangles DEF and NPQ are similar, then
7/9 = d/ (11/2)
By cross multiply
9d = 7 x 11/2
d = 77/2 ÷ 9
d = 77/18
Thus, The length of the side d would be 77/18.
Learn more about ratios here:
brainly.com/question/186659
#SPJ2
How did governments pursue mercantilist policies?
Answer:
Most of the mercantilist policies were the outgrowth of the relationship between the governments of the nation-states and their mercantile classes
Step-by-step explanation:
In the British empire Mercantilism, an economic policy designed to increase a nation's wealth through ... Mercantilism did, however, lead to the adoption of enormous trade
Hope this helps. :)
An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a random variable with variance = 5.
a) What is the probability that at most 3 cars per year will experience a catastrophe?
b) What is the probability that more than 1 car per year will experience a catastrophe?
Answer:
(a) Probability that at most 3 cars per year will experience a catastrophe is 0.2650.
(b) Probability that more than 1 car per year will experience a catastrophe is 0.9596.
Step-by-step explanation:
We are given that the distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with variance = 5.
Let X = the number of cars per year that will experience the catastrophe
SO, X ~ Poisson([tex]\lambda = 5[/tex])
The probability distribution for Poisson random variable is given by;
[tex]P(X=x) = \frac{e^{-\lambda} \times \lambda^{x} }{x!} ; \text{ where} \text{ x} = 0,1,2,3,...[/tex]
where, [tex]\lambda[/tex] = Poisson parameter = 5 {because variance of Poisson distribution is [tex]\lambda[/tex] only}
(a) Probability that at most 3 cars per year will experience a catastrophe is given by = P(X [tex]\leq[/tex] 3)
P(X [tex]\leq[/tex] 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= [tex]\frac{e^{-5} \times 5^{0} }{0!} +\frac{e^{-5} \times 5^{1} }{1!} +\frac{e^{-5} \times 5^{2} }{2!} +\frac{e^{-5} \times 5^{3} }{3!}[/tex]
= [tex]e^{-5} +(e^{-5} \times 5) +\frac{e^{-5} \times 25 }{2} +\frac{e^{-5} \times 125}{6}[/tex]
= 0.2650
(b) Probability that more than 1 car per year will experience a catastrophe is given by = P(X > 1)
P(X > 1) = 1 - P(X [tex]\leq[/tex] 1)
= 1 - P(X = 0) - P(X = 1)
= [tex]1-\frac{e^{-5} \times 5^{0} }{0!} -\frac{e^{-5} \times 5^{1} }{1!}[/tex]
= 1 - 0.00674 - 0.03369
= 0.9596
You have been hired to assist in the data analysis at the court level (judge-level analysis will be done at a later time). You must use your knowledge of probability and conditional probability to help determine the likelihood of appeal and reversal for cases handled by different courts. Which outcome has the highest probability of occurring based on the data? a. A case in Domestic Relations Court being reversed b. A case in Common Pleas Court being reversed c. A case in Municipal Court being reversed d. There is not enough information to determine the answer
ANSWER: "There is not enough information to determine the answer". Option D is correct.
Step-by-step explanation:
For a case that was ruled by a court to be reversed by a higher court, they must be conditions in the ruling of the lower court that has been reconsidered by the higher court. This is regardless of the jurisdiction of the court or judge that ruled the case.
A case from all the courts in the options can be reversed by a higher court if the courts judgement lacks merit by the higher court, at any given times, irrespective of the court.
Please help me with this question!!
Answer:
IV
Step-by-step explanation:
Cosine is positive in quadrants I and IV.
Cosecant (also sine) is negative in quadrants III and IV.
The quadrant where cos > 0 and csc < 0 is quadrant IV.
Simplify 1 · 0 - . can someone please help out
Answer:
That would be just 0 because anything multiplied by 0 is 0.
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Volume of cylinder = πr²h
= (3.14)(4)(0.75)
= 9.4
Since she'll fill it half so
Amount of water to be filled = 4.7
A chemist needs a 20% solution of alcohol. How many liters of 15% solution should be added to 4 liters of 40% solution to get a 20% solution?
Answer:
16
Step-by-step explanation:
Let's call the liters x. We can write 0.15x + 0.4 * 4 = 0.2 (x + 4). When we solve for x we get x = 16 liters.
I NEED HELP PLEASE SOMEONE HELP ME
Answer:
2nd option is the correct answer
Step-by-step explanation:
3 times a number decreased by 6 is - 2
how many real solutions does the equation x2 − 9 = 0 have?
Answer:
Zero
Step-by-step explanation:
Because when you replace x with a number and solve it it doesn't have the same answer as x2 − 9 = 0.
I hope this helped. I am sorry if you get this wrong.
The mean of the data set(9,5,y,2,x) is twice the data set(8,x,4,1,3).what is (y-x)
Answer:
[tex]y-x = 16[/tex]
Step-by-step explanation:
Given
Set 1: (9,5,y,2,x)
Set 2: (8,x,4,1,3)
Required
(y - x)
First the mean values of set 1 and set 2 has to be calculated
For set 1
[tex]Mean _1 = \frac{(9+5+y+2+x)}{5}[/tex]
Collect like terms
[tex]Mean _1 = \frac{9+5+2+y+x}{5}[/tex]
[tex]Mean _1 = \frac{16+ y+x}{5}[/tex]
For set 2
[tex]Mean _2 = \frac{(8+x+4+1+3)}{5}[/tex]
Collect like terms
[tex]Mean _2 = \frac{8+4+1+3+x}{5}[/tex]
[tex]Mean _2= \frac{16+ x}{5}[/tex]
Given that the mean of set 1 is twice the mean of set 2;
[tex]Mean_1 = 2Mean_2[/tex]
[tex]\frac{16+ y+x}{5} =2 * \frac{16+x}{5}[/tex]
Multiply both sided by 5
[tex]5 * \frac{16+ y+x}{5} = 5 * 2 * \frac{16+x}{5}[/tex]
[tex]16+ y+x = 2 * (16+x)[/tex]
Open bracket
[tex]16+ y+x = 32 + 2x[/tex]
Subtract 16 from both sides
[tex]16+ y+x- 16 = 32 + 2x - 16[/tex]
[tex]16 - 16 + y+x = 32 - 16 + 2x[/tex]
[tex]y+x = 16 + 2x[/tex]
Subtract 2x from both sides
[tex]y+x-2x = 16 + 2x-2x[/tex]
[tex]y-x = 16[/tex]
Triangle QRS is dilated according to the rule DO,2 (x,y). On a coordinate plane, (0, 0) is the center of dilation. Triangle Q R S has points (negative 3, 3), (2, 4), and (negative 1, 1). What is true about the image ΔQ'R'S'? Select three options. Which statements are true? DO,2 (x,y) = (2x, 2y) Side Q'S' lies on a line with a slope of -1. QR is longer than Q'R'. The vertices of the image are closer to the origin than those of the pre-image. The distance from Q' to the origin is twice the distance from Q to the origin.
Answer:
Options A, B and E are correct
Step-by-step explanation:
From the information given above, we would draw a dilation that produces an image that is the same shape as the original image, but has a different size.
The scale factor is 2
QRS → Q'R'S' = (x,y) → 2(x,y)
The coordinates of ∆QRS
Q (-3, 3)
R (2, 4)
S (-1, 1)
To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In order words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.
2 (x,y) = (2x, 2y)
The coordinates of ∆Q'R'S' becomes:
Q' (-6, 6)
R' (4, 8)
S' (-2, 2)
To determine the statements that are true about the image ΔQ'R'S,
we would graph the coordinates of the two triangles.
Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.
See attached the diagram for better explanation.
Let's check out each options and compare it with diagram we obtained:
a) DO, 2 (x,y) = (2x, 2y)
A dilation about the origin with a scale factor 2 is described using the above notation.
Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)
R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)
S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)
This option is correct
b) Side Q'S' lies on a line with a slope of -1
Q' (-6, 6)
S' (-2, 2)
coordinate (x, y)
Slope = m = (change in y)/(change in x)
m = (6-2)/[-6-(-2)]
= 4/(-6+2) = 4/-4
m = -1
This option is correct
c) QR is longer than Q'R'
Length of QR (-3 to 2) = 5
Length of Q'R' (-6 to 4) = 10
QR is not longer than Q'R'
This option is false
d) The vertices of the image are closer to the origin than those of the pre-image
The scale factor determines how much bigger or smaller the dilation image will be compared to the preimage. In a transformation, the final figure is referred to as the image. The original figure is referred to as the preimage.
From the diagram, the vertices of the preimage (original image) are closer to the origin than those of the dilation image.
This option is false
e) The distance from Q' to the origin is twice the distance from Q to the origin.
The distance from Q' to the origin (6 to 0) = 6
The distance from Q to the origin (3 to 0) = 3
The distance from Q' to the origin = 2(the distance from Q to the origin)
This option is correct
Answer:
A,B and E is correct
Step-by-step explanation:
Two positive numbers have a difference of 8. The larger number is three more than twice the smaller. Find the two numbers.
Answer:
5 and 13
Step-by-step explanation:
Let x represent the smaller number. Then the larger number is 2x+3, and the difference is ...
(2x+3) -(x) = 8
x = 5
The two numbers are 5 and 13.
_____
Check
Twice the smaller number is 10. 3 more than that is 13, the larger number. Their difference is 13 -5 = 8.
If $5a+2b=0$ and $a$ is two less than $b$, what is $7b$?
Answer:
7b = 10
Step-by-step explanation:
We have that:
5a + 2b = 0
a is two less than b
So a = b - 2.
Replacing in the above equation:
[tex]5a + 2b = 0[/tex]
[tex]5(b - 2) + 2b = 0[/tex]
[tex]5b - 10 + 2b = 0[/tex]
[tex]7b = 10[/tex]
[tex]b = \frac{10}{7}[/tex]
7b
[tex]7b = 7\frac{10}{7} = \frac{70}{7} = 10[/tex]
7b = 10
What’s the correct answer for this question?
Answer:
107 meters
Step-by-step explanation:
Central angle = 123°
In radians
123° = 123π/180
123° = 2.147 radians
Putting in formula
S = r∅
S = (50)(2.147)
S = 107 meters
Please answer this correctly
Answer:
Opinion
Step-by-step explanation:
This is an opinion because it says "more exciting to visit than"
This implies the persons' own beliefs and is not a fact, because this is not true for everyone
The Sky Train from the terminal to the rental car and longterm parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution. What is the average waiting time (in minutes)
Answer:
Average waiting time = 4 minutes
Step-by-step explanation:
From this question, we are told that the sky train is supposed to arrive every 8 minutes.
Thus, the waiting time of the passengers for the train = 8 minutes.
Then, the average waiting time is simply the mean or 50th percentile of the total waiting time.
So, average waiting time = 50% × 8
Average waiting time = 4 minutes
Solve for x
There’s no options sorry ya’ll please answer I’m desperate
Answer & Step-by-step explanation:
The triangle shown is an isosceles triangles. Isosceles triangles have a pair of congruent angles which are found at the bottom. These angles are called the base angles. So, when you find the measurement of one of the base angles, then the other base angle will have the same measurement.
We can find the measurement of x by subtracting 130 from 180. We are doing this because all triangles have a sum measurement of 180°. After we do this, then we will divide that number by 2 to find the measurement of x.
180 - 130 = 50
Now, we divide 50 by 2.
50 ÷ 2 = 25
So, the measurement of x is 25°.
A company manager for a tire manufacturer is in charge of making sure there is the least amount of defective tires. If the tire manufacturing process is working properly, the average weight of a tire for a 4-door sedan is normally distributed with a mean of 22 pounds and a standard deviation of 0.76 pounds. The manager decides to reject a tire as underweight if it falls more than 1.5 interquartile ranges below the lower quartile of the specified shipment of tires. What proportion of tires will be rejected by this process?
Answer:
0.347% of the total tires will be rejected as underweight.
Step-by-step explanation:
For a standard normal distribution, (with mean 0 and standard deviation 1), the lower and upper quartiles are located at -0.67448 and +0.67448 respectively. Thus the interquartile range (IQR) is 1.34896.
And the manager decides to reject a tire as underweight if it falls more than 1.5 interquartile ranges below the lower quartile of the specified shipment of tires.
1.5 of the Interquartile range = 1.5 × 1.34896 = 2.02344
1.5 of the interquartile range below the lower quartile = (lower quartile) - (1.5 of Interquartile range) = -0.67448 - 2.02344 = -2.69792
The proportion of tires that will fall 1.5 of the interquartile range below the lower quartile = P(x < -2.69792) ≈ P(x < -2.70)
Using data from the normal distribution table
P(x < -2.70) = 0.00347 = 0.347% of the total tires will be rejected as underweight
Hope this Helps!!!
The proportion of the tires that would be denied for being underweight through the given process would be:
[tex]0.347[/tex]% of the total tires will be rejected as underweight.
Given that,
Interquartile Range [tex]= 1.5[/tex]
Standard Deviation [tex]= 0.76[/tex]
Considering Mean = 0
and Standard Deviation = 1
Since lower quartile = -0.67448
Upper quartile = +0.67448
IQ range = 1.34896
To find,
The proportion of tires would be rejected due to being underweight through the process would be:
1.5 of Interquartile Range = 1.5 × [tex]1.34896 = 2.02344[/tex]
Now,
1.5 of the IQ range below the lower quartile [tex]= (lower quartile) - (1.5 of Interquartile range)[/tex]
[tex]= -0.67448 - 2.02344[/tex]
[tex]= -2.69792[/tex]
The proportion of tires that would be under 1.5 of the interquartile range below the lower quartile:
[tex]= P(x < -2.69792)[/tex] ≈ [tex]P(x < -2.70)[/tex]
Using data through the Normal Distribution Table,
[tex]P(x < -2.70)[/tex] [tex]= 0.00347[/tex]
[tex]= 0.347[/tex]%
Thus, 0.347% of the total tires would be rejected as underweight.
Learn more about "Proportion" here:
brainly.com/question/2548537
A bag contains 4 green, 5 red, and 6 purple balls. The probability that all of them are red is?
Answer:
The percentage would be 20% (5x20=100)
Step-by-step explanation: