A single dice is rolled 4 times. Let X be the number of times face 6 occurs.
Draw the distribution of X.
What is the probability of face 6 showing at least 2 times.
Answers
The distribution of X is given below as:
X | P(X)
0 | 0.482
1 | 0.385
2 | 0.130
3 | 0.023
4 | 0.001
The probability of face 6 showing at least 2 times when rolling the dice 4 times is 0.154.
What is the probability?The distribution of X is determined as follows:
Number of trials (n) = 4
Probability of success (p) = probability of face 6 = 1/6
Probability of failure (q) = 1 - p = 5/6
For X = 0:
P(X = 0) = ⁴C₀ * (1/6)⁰ * (5/6)⁴
P(X = 0) ≈ 0.482
For X = 1:
P(X = 1) = ⁴C₁ * (1/6)¹ * (5/6)³)
P(X = 1) ≈ 0.385
For X = 2:
P(X = 2) = ⁴C₂ * (1/6)² * (5/6)²
P(X = 2) ≈ 0.130
For X = 3:
P(X = 3) = ⁴C₃ * (1/6)³ * (5/6)¹
P(X = 3) ≈ 0.023
For X = 4:
P(X = 4) = ⁴C₄ * (1/6)⁴ * (5/6)⁰
P(X = 4) ≈ 0.001
The probability of face 6 showing at least 2 times:
P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4)
P(X ≥ 2) ≈ 0.130 + 0.023 + 0.001
P(X ≥ 2) ≈ 0.154
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Related Questions
This is algebra!! I need help :(
Answers
The answer to this problem please someone help me
Answers
Answer:
The answer is 0.18 cubic meters
Answer:
.21 cubic meters
Step-by-step explanation:
L x W x H
jade has 4 bags of chips each bag has x amount of chips. How many chips are in total?
Answers
Answer:
x = x amount of chips in 1 bag
x about of chips in 1 bag times the 4 bags = x amount of chips in all 4 bags
question 23 (4 points) you will be expected to know the antiderivatives of the six trigonometric functions for the final. question 23 options: a) true b) false
Answers
The statement "you will be expected to know the antiderivatives of the six trigonometric functions for the final" is false because it is subjective and dependent on the specific requirements and expectations of your course or exam.
While it is true that knowledge of the antiderivatives of the six trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant) can be beneficial in calculus and integration.
Whether or not you will be specifically expected to know them for your final exam depends on your course syllabus and the instructions provided by your instructor.
It is important to consult your course materials, syllabus, or instructor to determine the specific content that will be covered on your final exam.
This will ensure that you allocate your study time and focus on the relevant topics that will be assessed.
Therefore, the correct option is (b) false, as the expectation of knowing specific antiderivatives of trigonometric functions for the final exam is not universally applicable and may vary depending on the course and instructor.
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The equation for the line that has a slope of −38 and passes through (0, 10) is please help me with this problem.
Answers
Answer:
y = -38x + 10Step-by-step explanation:
Slope- intercept form:
y + mx = bGiven
m = -38 and point (0, 10)As per given point, y-intercept is b = 10
So the equation is:
y = -38x + 10A statistics professor is giving a final exam for his class that, in the past, only 70% of
students have passed. The professor will be giving the final exam to 200 students.
Assuming a binomial probability distribution, what is the probability that more than 150
will pass the final exam? Round your answer to the nearest hundredth.
Answers
Using the concept of binomial probability, the chances that 150 students passes the exam is 0.05 to the nearest hundredth
From Binomial probabilitynumber of trials, n = 200
probability of success , p = 70% = 0.7
1 - p = 1 - 0.7 = 0.3
Number of successes , x = 150
The Binomial probability that more than 150 students passes the exam can be written as the sum of the individual probability for all whole numbers above 150 to 200.
Mathematically, we have ;
P(x > 150) = P(x=151) + P(x = 152) + ... + P(x = 200)
Applying the binomial probability formula to each value of x
\( \binom{n}{r} \times {p}^{r} \times ( {1 - p)}^{n - r} \)
Solving the problem manually is complex and time consuming, we could use a binomial probability calculator instead.
Using a binomial probability calculator :
P(x > 150) = 0.05059
The probability that more than 150 will pass the final exam is 0.05059, which is 0.05 rounded to the nearest hundredth.
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-16-4 = ?
4.? =
4.
So, -16-4=
Answers
Answer:
It's -16-4
Step-by-step explanation:
Therefore its negative mins a neg so its like a debt mins a debt so it remains a debt.
Therefore its- 20
Plzzz brainlest
Answer:
-16-4=20
can try photo math
App
just gotta take a picture of your questions and your
answers will pop up :)
A sticker company shipped a total of 289,005 stickers last month. This month, the company shipped 338,486 stickers. Estimate the total amount of stickers shipped both months.
Round to the nearest hundred thousand.
Answers
each platform varies in the number of videos or images that can be added for a carousel ad, but the range is limited to what number?
Answers
The maximum limit to add the videos or images in Carousel is 10MB and the aspect ratio to add the images or videos is 1:1
There are many applications that are present where the videos and images can be added in the websites. The maximum images in the in few website is nine, but in carousel is 10MB of size and also it can be added up to 1:1 ratio of aspect size. The Carousel also allows the user to add slides and images. It helps to add the graphical representation.
The size of the videos must be from 60 seconds to 30 seconds of size and also the video includes the visual templets that help the user to have the presentation in an effective ways. There are many templets that also helps the user to present in a professional way. The carousel is a cloud representation that helps to create the slideshow online and also present it in the blockage videos. The online photos and images can also be added.
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x+y=3
x^2+y^2=17
Solve the simultaneous equations
Answers
The possible solution set for the system is (- 1, 4) and (4, - 1).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the equations as -
x + y = 3
x² + y² = 17
Refer to the graph of the function attached. The points of intersection represents the possible solution set.
Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).
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2. I am thinking of a number. It is multiplied by 9. The product is 27. What is my number? (1 point)
On= 36
On=18
On=3
On=4
Answers
Answer:
\(x9 = 27 \\ x = 3\)
X=3
X9=27
With pleasure
Help with question plzzz
Answers
Determine if the triangles, ΔUVW and ΔBAC, are similar. If so, identify the similarity criterion.
A) AA similarity
B) SAS similarity
C) SSS similarity
D) not similar
Answers
Answer:
B). SAS similarity.
Step-by-step explanation:
In Δ WVU & ΔCAB,
UV/CA = 17/34 = 1/2
&
VW/AB = 14/28 = 1/2
∵ UV/CA = VW/AB = 1/2
& ∠V = ∠A (Given)
∵ ΔWVU ≅ ΔCAB (by SAS similarity)
consider the experiment of rolling two dice. let x be the value of the first roll and y the sum of the two dice. find e(x | y ). i.e., give the value of e(x | y )(y) for all y.
Answers
The conditional expectation E(X | Y = y) for all y is:
E(X | Y = y) = (y + 1) / 2.
To find the conditional expectation E(X | Y = y), we need to calculate the expected value of X given that the sum of the two dice is y.
Let's consider all possible values of y from 2 to 12 (the possible sums of rolling two dice):
For y = 2:
The only possible combination is (1, 1). In this case, X can only take the value 1. Therefore, E(X | Y = 2) = 1.
For y = 3:
The possible combinations are (1, 2) and (2, 1). In both cases, the value of X is 1. Therefore, E(X | Y = 3) = 1.
For y = 4:
The possible combinations are (1, 3), (2, 2), and (3, 1). In these cases, the value of X can be 1, 2, or 3. Taking the average, we have E(X | Y = 4) = (1 + 2 + 3) / 3 = 2.
Similarly, we can calculate the conditional expectations for y = 5, 6, 7, 8, 9, 10, 11, and 12:
For y = 5: E(X | Y = 5) = (1 + 2 + 3 + 4) / 4 = 2.5
For y = 6: E(X | Y = 6) = (1 + 2 + 3 + 4 + 5) / 5 = 3
For y = 7: E(X | Y = 7) = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5
For y = 8: E(X | Y = 8) = (2 + 3 + 4 + 5 + 6) / 5 = 4
For y = 9: E(X | Y = 9) = (3 + 4 + 5 + 6) / 4 = 4.5
For y = 10: E(X | Y = 10) = (4 + 5 + 6) / 3 = 5
For y = 11: E(X | Y = 11) = (5 + 6) / 2 = 5.5
For y = 12: E(X | Y = 12) = 6
In summary, the conditional expectation E(X | Y = y) for all y is given by:
E(X | Y = 2) = 1
E(X | Y = 3) = 1
E(X | Y = 4) = 2
E(X | Y = 5) = 2.5
E(X | Y = 6) = 3
E(X | Y = 7) = 3.5
E(X | Y = 8) = 4
E(X | Y = 9) = 4.5
E(X | Y = 10) = 5
E(X | Y = 11) = 5.5
E(X | Y = 12) = 6
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Which of the following is a core general business principle presented in this topic? Group of answer choices Walk the talk Taking a holistic perspective in decision-making yields the best results The customer rules Exchange information for inventory whenever possible All of the above
Answers
The core general business principle presented in this topic is "Taking a holistic perspective in decision-making yields the best results."
Among the answer choices provided, the principle that stands out as a core general business principle is "Taking a holistic perspective in decision-making yields the best results." This principle emphasizes the importance of considering all relevant factors, stakeholders, and potential impacts when making business decisions. It recognizes that decisions made in isolation or based solely on a narrow perspective may not yield optimal outcomes.
Taking a holistic perspective means considering the interconnectedness and interdependencies within the business environment, including the social, economic, environmental, and ethical aspects. It involves considering the long-term implications and potential consequences of decisions, as well as the potential impacts on various stakeholders, such as customers, employees, suppliers, and the wider community. By taking a holistic perspective, organizations can make more informed and well-rounded decisions that align with their values, promote sustainability, and contribute to long-term success. It involves analyzing and synthesizing diverse information, seeking multiple perspectives, and understanding the broader context in which decisions are made.
While the other answer choices, such as "Walk the talk," "The customer rules," and "Exchange information for inventory whenever possible," may also reflect important principles in business, they are not as comprehensive or universally applicable as the principle of taking a holistic perspective in decision-making. The latter encompasses a broader approach that considers multiple dimensions of business operations and decision-making, ultimately leading to better overall outcomes.
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7. In an orchestra, the ratio of trombones to violas is 4:6. There are 9 violas. Write and solve a proportion to
determine how many trombones are in the orchestra.
Answers
Answer: 6 trombones
Step-by-step explanation:
We can set up a proportion.
Let x be the number of trombones there are.
\(\frac{4 trombones}{6violas} = \frac{x trombones}{9 violas}\)
We can cross multiply:
4*9 = 6x
6x = 36
Divide both sides by 6:
x = 6
Compute the present value if future value (FV)=$4892, interest rale (r)=14.0%, and number of years (t)=16 (Do not round intemadiate caiciations round your answers to 2 decimal places, e 1
,g +
,32,16,1 -
Answers
The present value with interest rate is 14% is $1810.92.
The future value is $4892.
The interest rate is 14% per year.
The time period is 16 years.
To calculate the present value, we can use the following formula:
present value = future value / (1 + interest rate)**number of years
Plugging in the values for the future value, interest rate, and time period, we get:
present value = 4892 / (1 + 0.14)**16 = 1810.92
Therefore, the present value of $4892 if the interest rate is 14% and the number of years is 16 is $1810.92.
In words, the present value is calculated by dividing the future value by the factor that is 1 plus the interest rate raised to the power of the number of years. In this case, the future value is $4892, the interest rate is 14%, and the time period is 16 years. Therefore, the present value is $1810.92.
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Write an equation of the line that satisfies the given conditions. Give the equation (a) in slope-intercept form and (b) in standard form. m=− 3/4
(−2,4) (a) Write the equation in slope-intercept form.
Answers
a) The slope-intercept form is y = (-3/4)x + 5/2
b) The standard form is 3x + 4y = 10
How to find the linear equation?To find the equation of a line given the slope and a point, we can use the point-slope form of a linear equation:
(a) Slope-Intercept Form:
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope, and b represents the y-intercept.
Given that the slope (m) is -3/4 and the point (-2, 4) lies on the line, we can substitute these values into the equation:
y = mx + b
4 = (-3/4)(-2) + b
4 = 6/4 + b
4 = 3/2 + b
To isolate b, we subtract 3/2 from both sides:
4 - 3/2 = b
8/2 - 3/2 = b
5/2 = b
The equation of the line in slope-intercept form is:
y = (-3/4)x + 5/2
(b) Standard Form:
The standard form of a linear equation is given by Ax + By = C, where A, B, and C are integers, and A is positive.
To convert the equation from slope-intercept form to standard form, we can multiply through by 4 to eliminate the fraction:
4y = (-3)x + 10
Next, we rearrange the equation so that the x and y terms are on the left side:
3x + 4y = 10
The equation of the line in standard form is:
3x + 4y = 10
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A certain brand of coffee comes in two sizes.A 12.3-ounce package costs $2.99.A 33.9-ounce package costs $8.74. Find the unit for each size. Then state which size is the better buy based on the unit price. Round your answer to the nearest cent.
Answers
To get the unit price for the 12.3 ounce package =
$ 2.99/ 12.3 = $ 0. 243 per ounce
=$ 0.24 per ounce
To get the unit price for the 33.9-ounce package =
$ 8.74/ 33.9 = $ 0. 2558 per ounce
= $ 0.26 per ounce
The better price is based on the unit price is that which is lower
Hence it is the 12. 3 ounce package
You are the basketball team captain and T-shirts are to be ordered for your season. T-shirts with a number on the back cost $12. T-shirts with a name and number cost $16. You have $240 to spend on T-shirts for the team.
The equation 12x + 16y = 240 models the total cost, where x is t-shirts with a number on the back and y is t-shirts with a name and number on the back.
There are 12 members of the team who want their names and numbers on the back of their T-shirts. How many members will order a T-shirt with just their number on the back?
Answers
Answer:
20 12cost and the the rest 16
Step-by-step explanation:
What i the equation of a line that i parallel to the line y =2x 7 and pae through the point -2,4
Answers
The equation of a line y=2x+8.
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis
Looking at the given line,
y = 2x + 7
Compared with the slope-intercept equation,
Slope, m = 2
If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2
Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes
4 = 2 × - 2 + c
4 = - 4 + c
c = 4 + 4 = 8
The equation becomes y=2x+8.
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Select all segments parallel to FE.
HF
AB
FC
GH
ID
CD
BE
GJ
AJ
BC
IH
GE
AD
IJ
Answers
Answer: CB, DA, IJ, HG
Step-by-step explanation:
As long as the lines never intersect, they are parallel
Answer:
DONT CHEAT
Step-by-step explanation:
Simplify : a) 2(x 2 + y 2 ) + 3 ( x 2 − y 2 )
Answers
Answer:
8x2−8y2+6x−6y
Step-by-step explanation:
x2 means x squared
If the diagonals are congruent, then a quadrilateral is a parallelogram.
Answers
The congruence of diagonals alone is not sufficient to conclude that a quadrilateral is a parallelogram.
Why it is and what is quadrilateral?
This statement is not true.
While it is true that if the opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram, the congruence of the diagonals alone does not necessarily imply that the quadrilateral is a parallelogram.
A quadrilateral is a geometric shape that consists of four straight sides and four angles. The term "quadrilateral" comes from the Latin words "quadri" (meaning "four") and "latus" (meaning "side").
Some examples of quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids, and kites. Quadrilaterals can be convex, meaning all the interior angles are less than 180 degrees, or non-convex, meaning at least one interior angle is greater than 180 degrees.
Therefore, The congruence of diagonals alone is not sufficient to conclude that a quadrilateral is a parallelogram.
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Let f(x) represent the linear parent function.
Which descriptions match the given transformations?
Drag and drop the answers into the boxes..
f(x) - 15
15f (x)
f(x) is translated 15 units up.
f(x) is translated 15 units left.
f(x) is translated 15 units down. f(x) is vertically compressed by a factor of 15.
f (x) is vertically stretched by a factor of 15.
Answers
The given transformation of a function f(x) - 15 and 15 f(x) represents "f(x) is translated 15 units down and f(x) is vertically stretched by a factor of 15" respectively.
What are the transformation rules for the translation and dilation of a function?The translation transformation rule for a function is
1) f'(x) = f(x) + a; Vertical translation by 'a' units up.
f'(x) = f(x) - a; Vertical translation by 'a' units down.
2) f'(x) = f(x + a); horizontal translation by 'a' units left
f'(x) = f(x - a); horizontal translation by 'a' units right.
The dilation transformation rule for a function is
1) f'(x) = a f(x);
If a > 1, vertical stretch by a factor of 'a' units
If 0 < a < 1, vertical compression by a factor of 'a' units
2) f'(x) = f(ax);
If a > 1, horizontal compression by a factor of 'a' units
If 0 < a < 1, horizontal compression by a factor of 'a' units.
Calculation:It is given that f(x) represents the linear parent function.
The transformed functions are given as
f(x) - 15 and 15 f(x)
The transformation f(x) - 15 is a vertical translation of the function f(x) by 15 units down.
The transformation 15 f(x) is a vertical stretch by a factor of 15 units.
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Mona has 400 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?A rectangle that maximizes the endlosed area has a length of___yards and a width of_____yards.
Answers
A rectangle that maximizes the enclosed area has a length of 200 yards and a width of 400 yards. The maximum area is 80000 square yards.
Mona has 400 yards of fencing to enclose a rectangular area. To maximize the enclosed area, the 400 yards should be divided into two sides of equal length, with the remaining fencing used for the other two sides. This results in a length of 200 yards and a width of 400 yards, which maximizes the area of the plot. The maximum area that can be enclosed is 80000 square yards.
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A rectangle that maximizes the enclosed area has a length of 100 yards and a width of 100 yards.
To find the dimensions of the rectangle that maximize the enclosed area with 400 yards of fencing, we can use the following steps:
Let the length of the rectangle be L yards and the width be W yards.
The perimeter of the rectangle is given by P = 2L + 2W.
Since we have 400 yards of fencing, we can write the equation:
400 = 2L + 2W.
Solve for W:
W = 200 - L.
The area of the rectangle is given by A = L * W.
Substitute the expression for W from step 4 into the area equation:
A = L * (200 - L).
To maximize the area, we need to find the maximum value of A. Differentiate A with respect to L:
dA/dL = 200 - 2L.
Set dA/dL = 0 to find the critical points:
0 = 200 - 2L.
Solve for L: L = 100.
Substitute L back into the equation for W from step 4:
W = 200 - 100 = 100.
So, a rectangle that maximizes the enclosed area has a length of 100 yards and a width of 100 yards. The maximum area is A = L * W = 100 * 100 = 10,000 square yards.
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let $s n$ be the sum of the reciprocals of the non-zero digits of the integers from to $10^n$ inclusive. find the smallest positive integer $n$ for which $s n$ is an integer.
Answers
If Sₙ denotes the sum of the reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive , then the smallest positive integer n for which Sₙ is an integer is 63 .
The "Sₙ" be the sum of reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive ;
We Let \(K= \sum_{i=1} ^{9} \frac{1}{i}\) ,
On further examination , we get that , \(S_{1} =K+1\) ;
Since each digit "n" appears once and the number 1 appears for an extra time.
Now , we write S₂ .
So ,Each term of K will appear 10 times in the units place and 10 times in the tens place ,
So , we get \(S_{2} = (n10^{n-1})K+1\) ; and there are total "n" places ;
The denominator of K is written as \(D=2^{3} .3^{2} .5.7\) .
For Sₙ to be an integer, \(n10^{n-1}\) must be divisible by D , we must select "n" to be divisible by \(3^{2} .7\) .
And since need to find the smallest integer "n" , So , the n is \(3^{2} .7 = 63\) .
Therefore , For Sₙ to be an integer , the smallest positive integer n is 63 .
The given question is incomplete , the complete question is
Let Sₙ be the sum of the reciprocals of the non-zero digits of the integers from 1 to 10ⁿ inclusive. find the smallest positive integer n for which Sₙ is an integer .
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I don’t know how to give extra point because I’m new to this app but I would appreciate it if you could help
Answers
Answer:
n=-4
Step-by-step explanation:
First, subtract 3n on both sides. This results in -3=n+1. Then, subtract 1 on both sides. The answer is n=-4.
Answer:
B
Step-by-step explanation:
We have the equation:
\(3n-3=4n+1\)
Let's solve for n. To do so, we want to isolate it.
Let's use the subtraction property of equality to subtract 3n from both sides:
\((3n-3)-3n=(4n+1)-3n\)
The left side will cancel...
\(-3=(4n+1)-3n\)
Subtract on the right:
\(-3=1n+1\)
Remember that 1n is the same as just n. So:
\(-3=n+1\)
Now, let's use the subtraction property of equality again to subtract 1 from both sides:
\((-3)-1=(n+1)-1\)
The right side will cancel. Subtract on the left:
\(-4=n\)
Symmetric property:
\(n=-4\)
So, our answer is B.
And we're done!
Calculate the missing term. 32/24 = 20/___
Answers
Answer:
20/30
Step-by-step explanation:
Simplest form of 32/24= 4/3
Multiply both 4 and 3 by 10= 20/30
Hope this helps!
Which equation, together with y = -1. 5x + 3, makes a system with one solution?
Y= -1. 5x + 6
Y= -1. 5x
2Y= -3x + 6
2Y + 3x = 6
Y= -2x + 3
Answers
The equations that, together with y = -1.5x + 3, make a system with one solution are: 1. Y = -1.5x + 6, 4. 2Y + 3x = 6, 5. Y = -2x + 3
To find the equation that makes a system with one solution when paired with y = -1.5x + 3, we need to find an equation with a different slope and/or a different y-intercept.
Let's analyze each given equation:
1. Y = -1.5x + 6: This equation has the same slope as y = -1.5x + 3 but a different y-intercept, so it has one solution.
2. Y = -1.5x: This equation has the same slope as y = -1.5x + 3, and therefore has an infinite number of solutions (or is dependent), so it's not the answer.
3. 2Y = -3x + 6: To compare with the given equation, let's put it in the same format. Divide both sides by 2 to get Y = -1.5x + 3, which is the same as the given equation, so it's not the answer.
4. 2Y + 3x = 6: To compare with the given equation, let's put it in the same format. Divide both sides by 2 to get Y + 1.5x = 3. This equation has a different slope, so it has one solution.
5. Y = -2x + 3: This equation has a different slope and y-intercept, so it has one solution.
Thus, the equations that, together with y = -1.5x + 3, make a system with one solution are:
1. Y = -1.5x + 6
4. 2Y + 3x = 6
5. Y = -2x + 3
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