1. Not binomial: there are more than two outcomes for each trial.
Thus, option (B) is correct.
2. Procedure results in a binomial distribution.
Thus, option (B) is correct.
1. Not binomial: there are more than two outcomes for each trial.
In a binomial distribution, each trial can have only two outcomes (usually referred to as success and failure).
In this case, the procedure involves rolling a single die 53 times and keeping track of the "fives" rolled.
Since the outcome can be any number from 1 to 6 on each trial, it does not meet the criteria for a binomial distribution.
Thus, option (B) is correct.
2. Procedure results in a binomial distribution.
In this case, the procedure involves spinning a roulette wheel 7 times and keeping track of the winning numbers. The outcome of each trial is either a win or a loss, which satisfies the requirement for a binomial distribution.
Thus, option (B) is correct.
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Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. At α = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold? 8.92 6.99 5.54 5.73 6.38 5.51 6.45 7.50 8.48 5.56 6.90 6.46
Answer:
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
Step-by-step explanation:
We formulate our null and alternative hypotheses as
H0 u≤ 6 ug Ha : u > 6 ug
The significance level ∝ = 0.05
The test statistic used is
t = X` - u / s/ √n
which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.
The critical region t > t (0.05,11) = 1.796
We compute the t value from the data
Xi Xi²
8.92 79.5664
6.99 48.8601
5.54 30.6916
5.73 32.8329
6.38 40.7044
5.51 30.3601
6.45 41.6025
7.50 56.25
8.48 71.9104
5.56 30.9136
6.90 47.61
6.46 41.7316
80.42 553.0336
Now x` = ∑x/ n = 80.42/12 = 6.70
S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)
= 1/11 (553.034-538.948) = 1.2805
s= 1.1316
Putting the values in the test statistics
t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12
= 2.1698
The critical region t > t (0.05,11) = 1.796
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
Draw a Venn diagram and use the given information to fill in the number of elements in each region.
Answer: Check out the diagram below for the filled in boxes
14 goes in the first box (inside A, but outside B)
7 goes in the overlapping circle regions
5 goes in the third box (inside B, outside A)
3 goes in the box outside of the circles
==============================================================
Explanation:
[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.
n(A) = 21 means there are 21 items in A
n(B) = 12 means there are 12 items in B
We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]
It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.
--------
[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]
So there are 7 items in both regions.
This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.
Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.
Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.
The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.
Again the diagram is posted below with the filled in values.
A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
The filled Venn diagram is given below.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
n(A) = 21
This is the total of all the items included in Circle A.
n(B) = 12
This is the total of all the items included in Circle A.
n(A') = 8
The items that are not in circle A.
n(A U B ) = 26
The items that are in both circle A and circle B.
Now,
n (A U B) = n(A) + n(B) - n(A ∩ B)
26 = 21 + 12 - n(A ∩ B)
n(A ∩ B) = 33 - 26
n(A ∩ B) = 7
Thus,
The filled Venn diagram is given below.
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Kim is earning money for a trip. She has saved and she earns per hour babysitting. The total amount of money earned (y) after (x) number of hours worked is given by the equation . How many hours will she need to work in order to earn for her trip?
Answer:
what is the amount of money Kim earn per hour of babysitting? Also I need to know how much trip cost to find out how many hours she need to work.
Step-by-step explanation:
In Triangle A B C, what is the value of x? Triangle A B C. Angle A is (10 x minus 10) degrees, angle B is (8 x) degrees, angle C is (10 x + 8) degrees.
Answer:
6.5
Step-by-step explanation:
The sum of all angles in a triangle are 180 degrees.
=> 10x -10 + 8x + 10x + 8 = 180
=> 28x -2 = 180
=> 28x = 182
=> x = 6.5
So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees
Angle B = 8 x 6.5 = 52 degrees
Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.
55 + 52 + 73 = 55 + 125 = 180 degrees
Which of the following is equivalent to –2i(6 – 7i)?
Answer:
[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
Answer = A
Write 8:18 as a fraction in simplest form.
Ratio as a Fraction:
Fraction in Simplest Form:
Answer:
[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]
[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]
Step-by-step explanation:
Part 1: Writing a ratio as a fraction
A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,
Replace the colon with a divisor line or the divisor line with a colon (use the first portion to transform a ratio into a fraction and the second form to transform a fraction into a ratio).Therefore, 8:18 as a fraction is 8/18.
Part 2: Fraction in simplest form
To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.
8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.
Instead, if both numbers are even, divide by 2.
8/2 = 4
18/2 = 9
Check to see if the new numerator and denominator can reduce any further.
4/9 = 4/9
The fraction in simplest form is 4/9.
In a school, there are 25% fewer 11th graders than 10th graders, and 20% more 11th graders than 12th graders. The total number of students in 10th, 11th, and 12th grades in the school is 190. How many 10th graders are there at the school?
Answer:
There are 80 10th graders in the school
Step-by-step explanation:
Let the number of 10th graders be x
There are 25% fewer 11th graders
That mean x - 25% of x
x -0.25x = 0.75x
There are 20% more 11th graders than 12th graders
So if number of 12th graders = y, then
0.75x = y + 20/100 * y = y + 0.2y = 1.2y
Since ;
0.75x = 1.2y
then y = 0.75x/1.2 = 0.625x
So let’s add all to give 190
x + 0.75x + 0.625x = 190
2.375x = 190
x = 190/2.375
x = 80
In a simple regression analysis with age as the only explanatory variable, the effects of other factors, such as faminc, are
Answer:
In the error term.
Step-by-step explanation:
A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).
Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.
helppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
Brainliest!
Step-by-step explanation:
36x^-4y^2/5x^2y^-3z^-2
36y^5z^2/5x^6
make everything positive
find the value of each variable and the measure of each angle
Answer:
Left angle = 60°
Top angle = 120°
Right angle = 60°
Step-by-step explanation:
Use what you know about angle relationships to set up equations you can solve for each variable.
The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.
You have two variables, so you need at least two equations (I made three but only used two).
The work is in my attachment, comment of you have questions.
What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Here is the equation
[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]
In the order of operations parentheses go first so we get
[tex]20+3\times11+5+2\times16[/tex]
Next we do the multiplication
[tex]20+33+5+32\\[/tex]
And finally we add them all up
[tex]20+33+5+32=90\\[/tex]
Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is
Complete Question
In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:
A -1.645
B -2.066
C -2.000
D-1.960
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The population mean is [tex]p = 0.50[/tex]
The sample size is [tex]n = 64[/tex]
The number that met the standard is [tex]k = 24[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{24}{64}[/tex]
[tex]\r p =0.375[/tex]
Generally the standard error is mathematically evaluated as
[tex]SE = \sqrt{ \frac{p(1- p )}{n} }[/tex]
=> [tex]SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }[/tex]
=> [tex]SE = 0.06525[/tex]
The test statistics is evaluated as
[tex]t = \frac{ \r p - p }{SE}[/tex]
[tex]t = \frac{ 0.375 - 0.5 }{0.0625}[/tex]
[tex]t = -2[/tex]
Multiply the following complex numbers:
(7+2i)(2+3i)
Please don’t guess
Answer:
14 + 25l + 6l^2
Step-by-step explanation:
(7 + 2i) (2 + 3i)
=> 14 + 4l + 21l + 6l^2
=> 14 + 25l + 6l^2
This is the correct answer
This solid shape is made from 5 cubes. Which of the diagrams show the plan of the solid? Please help!
Answer:
A Maybe
Step-by-step explanation:
Cogntive identification
Unable to answer mathematically or analytically
The Plan of the solid shape is shown by : (A)
What is the Meaning of solid shape?A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.
A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.
solid shapes can take up space in the universe because they are more tangible and realistic.
In conclusion, the Plan of the solid shape is shown by : (A)
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what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?
Answer:
Approximately 3.05
Step-by-step explanation:
Using "compatible numbers" we can simply round these numbers to integer values. Let's make 76.32 => 76 and 24.98 => 25
So from here let's do 76/25 to get 3 R 1/25
1/25 as a decimal is .04
So far, we have 3.04. Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98. So we should consider an extra value in our decimal.
Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.
Thus our number will be 3.04 + .01.
Making our quotient approximately 3.05.
Cheers.
A video rental store keeps a list of their top 15 movie rentals each week. This week the list includes 6 action, 4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie?
Answer:
32/1125Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome of event/Total outcome.
If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.
If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;
Probability of selecting 2 comedies = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).
Probability of selecting 1 action movie = 6/15 = 2/5
Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125
Note that the rented movies will have to be returned hence reason for the replacement.
Determine the equation of the exponantial function with a common ratio of 2, a horizontal asymptote at y=4 and passin through the point (2,10).
Answer:
Step-by-step explanation:
STUCK Basic geometry A for senior year school
Answer:
(C) A reflection across a horizontal line and a horizontal translation
Step-by-step explanation:
We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.
Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.
Hope this helped!
a function includes the points (4, -3) and (-9,4). what fraction in lowest terms represents the output value of this function for an input of zero
Answer:
-11/13
Step-by-step explanation:
The equation of the line through these points can be written using the 2-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (4 -(-3))/(-9-4)/(x -4) -3
y = (-7/13)x +28/13 -3
For x=0, the value of y is ...
y = 28/13 -39/13 = -11/13
The output for an input of 0 is -11/13.
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?
Answer:
Speed of plane in still air is 270 mph
Wind speed is 30 mph
Step-by-step explanation:
Check the picture.
The speed of the plane in still air is 270 mph and the speed of the wind will be 30 mph.
What is the distance formula?The distance traveled by an object is the product of the speed of an object and the time taken.
Distance = speed x time
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.
Let the speed of the plane be x
The speed of wind be y
Distance covered with the wind = (x + y)t
1200 = (x + y)4
(x + y) = 1200/4
(x + y)= 300 .....(a)
Distance covered against the wind = (x - y)t
1200 = (x - y)5
(x - y) = 1200/5
(x - y) = 240 .......(b)
By solving both the equation
(x + y)= 300
(x - y) = 240
Therefore the values will be x= 270mph and y = 30 mph
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A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower that is 98 meters high. After traveling 83 meters, which statement is most accurate?
A. The plane needs to be about 15 meters higher to clear the tower.
B. The plane clears the tower with about 27 meters to spare.
C. The plane clears the tower with about 15 meters to spare.
D. The plane needs to be about 27 meters higher to clear the tower.
Answer:
D. The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).
The hypothenus is the distance travelled by the plane which is 83 meters (h)
The height of the tower is 98 Meters
We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.
According to Pythagorean theorem
(x^2) + (y^2) = h^2
y = √ (h^2) - (x^2)
y = √ (83^2) - (42^2)
y= √(6889 - 1764)
y= 71.59 Meters
The height from the plane's position to the top of the tower will be
Height difference = 98 - 71.59 = 26.41 Meters
So the plane should go about 27 Meters higher to clear the tower
In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. Question 9 (2.5 points) If 2000 students are randomly selected, how many would you expect to have a score between 250 and 305?
Answer:
The number is [tex]N =1147[/tex] students
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 281[/tex]
The standard deviation is [tex]\sigma = 34.4[/tex]
The sample size is n = 2000
percentage of the would you expect to have a score between 250 and 305 is mathematically represented as
[tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]
So
[tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]
[tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]
From the z table the value of [tex]P( z_2 < 0.698) = 0.75741[/tex]
and [tex]P(z_1 < -0.9012) = 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.57[/tex]
The percentage is [tex]P(250 < X < 305 ) = 57\%[/tex]
The number of students that will get this score is
[tex]N = 2000 * 0.57[/tex]
[tex]N =1147[/tex]
Suppose the radius of a circle is 5 units. What is its circumference?
Answer:
C≈31.42
Step-by-step explanation:
C=2πr
C=2xπx5
C≈31.42
pls mark as brainliest
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
Answer:
Step-by-step explanation:
Following the cardinal points as regards location of points, the sketch of Musah's movement can be as what is attached to this answer.
A poker hand consisting of 7 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly 3 face cards. Leave your answer as a reduced fraction.
Answer:
The probability is 2,010,580/13,378,456
Step-by-step explanation:
Here is a combination problem.
We want to 7 cards from a total of 52.
The number of ways to do this is 52C7 ways.
Also, we know there are 12 face cards in a standard deck of cards.
So we are selecting 3 face cards from this total of 12.
So also the number of cards which are not face cards are 52-12 = 40 cards
Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4
Thus, the required probability will be;
(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560
= 20,105,800/133,784,560 = 2,010,580/13,378,456
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want % confidence that the sample mean is within points of the population mean, and the population standard deviation is .
Answer: hello below is the complete question
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number
answer : 737 adults
Step-by-step explanation:
confidence interval = 90% = 0.9
( E ) = 4
standard deviation = 66
first we have to calculate the value of a
a = 1 - confidence interval
= 1 - 0.9 = 0.10 hence a / 2 = 0.05
next find the value of Z a/2 from table
Z[tex]_{0.05}[/tex] = 1.645
The number of Adults selected can be determined using this relation
N = [tex](Z_{a/2} * (s/E))^2[/tex]
= [tex](Z_{0.05} * ( 66/4))^2[/tex]
= 737
A number is chosen at random from 1 to 10. Find
the probability of selecting 4 or a factor of 6.
Step by step.
Answer:
1/2
Step-by-step explanation:
The possible outcomes are
1,2,3,4,5,6,7,8,9,10
Factors of 6 are 1,2,3,6
or a 4
1,2,3,4,6 are the outcomes we want
There are 5 "good" outcomes
P( 4 or a factor of 6) = "good" outcomes/ total
= 5/10
=1/2
Answer:
[tex]\boxed{\frac{1}{2} }[/tex]
Step-by-step explanation:
There are total 10 outcomes.
[tex]1,2,3,4,5,6,7,8,9,10[/tex]
The probability of selecting 4 is 1 outcome out of total 10 outcomes.
Factors of 6 are [tex]1,2,3,6[/tex].
These are 4 outcomes out of total 10 outcomes.
The probability of selecting 4 or a factor of 6 is:
[tex]\displaystyle \frac{1}{10} +\frac{4}{10} =\frac{5}{10} =\frac{1}{2}[/tex]
The graph below shows the quadratic function f, and the table below shows the quadratic function g.
x -1 0 1 2 3 4 5
g(x) 13 8 5 4 5 8 13
Which statement is true?
A.
The functions f and g have the same axis of symmetry and the same y-intercept.
B.
The functions f and g have different axes of symmetry and different y-intercepts.
C.
The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
D.
The functions f and g have the same axis of symmetry, and the y-intercept of f is less than the y-intercept of g.
Answer:
D
Step-by-step explanation:
The true statement is:
The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
As, per the graph and table is:
From the graph of f(x):
Axis of symmetry will be at x = 2
The maximum value of f(x) = 10
From the table of g(x):
Axis of symmetry will be at x = 2
The minimum value of g(x) = 4
thus, The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
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Given m = - 1/4 & the point (4, 5)which of the following is the point slope form of the equation?
Answer:
y - 5 = -1/4(x - 4)
Step-by-step explanation:
Point slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
To find the point slope form, plug in the point given and the slope.
y - y1 = m(x - x1)
y - 5 = -1/4(x - 4)
Find the distance of the translation.
Round your answer to the nearest hundredth.
