under what circumstances do you think it works well to approximate the binomial using the normal, considering the differences?
Answers
What is Normal Approximation to the Binomial Distribution?
In certain situations, such as when X∼B(n,p) and n is large and/or p is close to 1, the normal distribution can be utilized as a rough approximation to the binomial distribution (np, npq).
You must fulfill the requirements for a binomial distribution in order to compute the normal approximation to the binomial distribution:
There are n independent trials in a certain number.Any trial's results are either success or failure.Every trial has an equal chance of being successful.Remember that X∼B(n,p) if X is the binomial random variable. The normal distribution's shape should be comparable to the shape of the binomial distribution. The values np and nq must both be greater than five (np>5 and nq>5; the approximation is better if both are greater than or equal to 10), in order to guarantee this.
Then, the normal distribution with a mean of np and a standard deviation of \(\sqrt{npq}\) can be used to approximate the binomial. Keep in mind that q=1−p. Use x+0.5 or x0.5 to add 0.5 to x or subtract 0.5 from x for the best approximation. 0.5 is referred to as the continuity correction factor.
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Related Questions
Rua and Liz have a bag of 24 cherries. Liz keeps most for herself, but gives some to Rua. He complained, so she gave him five more. She then had one Cherry fewer than 1.5 times the number of cherries that Rua had. Write an equation and solve it to find how many cherries she gave to Rua at the start.
Answers
Answer:
8 cherries
Step-by-step explanation:
Let r represent the number of cherries Rua was given
24 - r - 5 = 1.5r - 1
Simplify and solve for r.
19 - r = 1.5r - 1
-2.5r = -20
r = 8
So Liz gave Rua 8 cherries at the start.
Rylan is a marketing director for a musician and is researching ways to improve the attendance at the concerts. Currently, the attendance averages 10,500 people with an average ticket cost of $45. In her research, she has discovered that when ticket prices are lowered by $1 then the attendance will increase by 300 people. She has a meeting scheduled with the President of Business Operations who has asked her to maximize revenue. She is trying to calculate a model, but is struggling to determine which one works. A(x) = (45 - x)(10,500 + 300x) B(x) = (45 - x)[10,500 + 300(45-x)]1) Which model should Rylan use? 2) Find the ticket price that will lead to the maximum revenue for the team. 3) What is this maximum revenue? To make matters more difficult, the President of Business Operations wants her to determine the revenue potential of $25 and $30 tickets.4) revenue for $25 tickets = 5) revenue for $30 tickets =
Answers
Answer:
Step-by-step explanation:
eight hundred and five thousandths in decimal numerals
Answers
Answer:
"0.805" is the correct answer.
Matilda has 16 3/4 hours to finish three consulting projects.how much time may she spend on each project ,if she plans to spend the same amount of time on each?
Answers
Time taken by Matilda on each project is \(5\frac{7}{12}\) hours.
According to the question we have been given that,
Total time taken by Matilda to complete the consulting projects = \(16\frac{3}{4}\) hours
First we will convert it into simple fraction which is
\(16\frac{3}{4} = \frac{67}{4} \\\) hours
Number of consulting projects = 3
And Matilda spends same amount of time to each of the project.
To find the time she spend on each project is by using unitary method
that is, 3 projects = \(\frac{67}{4}\) hours
1 project = \(\frac{67}{4} / 3\)
= 67/12
= \(5\frac{7}{12}\) hours
Hence time taken by Matilda on each project is \(5\frac{7}{12}\) hours.
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In a relay race, Aisha ran 1 and ¾ of a mile and Paula ran 1 and 5/12 of a mile. Who ran farther?
Answers
Answer:
Aisha ran farther
Step-by-step explanation:
Aisha - 1 9/12
Paula - 1 5/12
Make the denominator the same
Julie is tracking the growth of a plant for a science project. The height of the plant on the 2nd day she measured was 8 inches and on the 7th day, it was 20.5 inches find and interpret the rate of change.
Answers
This means that the plant grow at a rate of 2.5 inches per day.
Linear equationLinear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the height of the plant after x days.
The height of the plant on the 2nd day she measured was 8 inches. It is given by:
(2, 8)The height of the plant on the 7th day she measured was 20.5 inches. It is given by:
(7, 20.5)The rate of change (m) is:
\(m=\frac{y_2-y_1}{x_2-x_1} =\frac{20.5-8}{7-2} =2.5\)This means that the plant grow at a rate of 2.5 inches per day.
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HELP ASAPPPP DUDE PLS PLS PLSSSSSS NOOO LINKS
Answers
Answer:
Step-by-step explanation:
use 25,000*(1-0.15)^8 = $ 6812.26
WILL MARK BRAINIEST!!! 20 POINTS!!! Determine the equivalent system for the given system of equations. 4x − 5y = 2 10x − 21y = 10 4x − 5y = 2 3x − y = 4 4x − 5y = 2 24x − 47y = 22 4x − 5y = 2 10x + 3y = 15 4x − 5y = 2 14x + 26y = 12 plz show work, im bad at math.
Answers
Answer:
none of the options
Step-by-step explanation:
4x − 5y = 2 , 10x − 21y = 10
---------
the first equation is same in all answer choices, let's check which is equivalent to second, the easy way is to consider x/y ratio which is 10/ -21
4x − 5y = 2 , 3x − y = 4
no, ratio is 3/ -14x − 5y = 2 , 24x − 47y = 22
no, the ratio is 24/ -474x − 5y = 2 , 10x + 3y = 15
no, the ratio is 10/34x − 5y = 2 , 14x + 26y = 12
no, the ratio is 14/26an ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:1. if the diameter of the cone is 2 inches and the height is 6 inches, approximately what is the volume of vanilla ice cream in the cone? (round to nearest tenth) responses a 6.3 in3in36.3 in 3 b 2.1 in3in32.1 in 3 c 1.0 in3in31.0 in 3 d 4.2 in3
Answers
The volume of the vanilla ice cream in the cone is 4.18 cubic inches
The diameter of the cone = 2 inches
The radius of the cone = 2/1
= 1 inches
The height of the cone = 6 inches
The volume of the cone = (1/3) × π × r^2 × h
Substitute the values in the equation
= (1/3)π × 1^2 × 6
= 6.28 cubic inches
The ratio of vanilla and chocolate ice cream = 2:1
2x + x = 6.28
3x = 6.28
x = 6.28 / 3
x = 2.09
The volume of vanilla ice cream = 2x
= 2×2.09
= 4.18 cubic inches
Therefore, the volume of vanilla ice cream is 4.18 cubic inches
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find the indefinite integrals
Answers
Answer:
Below in bold
Step-by-step explanation:
∫ dx / (x^2√(9-x^2))
Substitute x = 3sinu and dx = 3cosu du
then the √(9-x^2) = √( 9 - 9sin^2u) = 3 cos u and u = arcsin(x/3)
= 3 ∫(csc^2 u du )/ 27
= 1/9 ∫(csc^2 u du
= -1/9 cot u
= -√9-x^2) / 9x.
Find the range of the data.
The ages of kids playing at a park.
4, 1, 3, 9, 6, 3, 2, 4
Range: [?]
![Find the range of the data.The ages of kids playing at a park.4, 1, 3, 9, 6, 3, 2, 4Range: [?]](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/b5HUFqPHUhWOnaCANbNcKJs2EpNPqDMO.png)
Answers
Answer:
8
Step-by-step explanation:
Range is found by taking the largest number and subtracting the smallest number
The largest number is 9
The smallest number is 1
9-1 =8
The range is 8
Answer:
8
Step-by-step explanation:
Range = highest value - lowest value
Range = 9 - 1
Range = 8
Let V be an inner product space and v, u,x,y,z EV such that vis orthogonal to u, x, y and z. Prove that v is also orthogonal to span{u.x,y,z}. (4) (b) Let u and v be orthogonal vectors. If u + vand u - v are orthogonal, show that | u ||=|| v ||. (5) (C) Given the vectors uz = (1,2,1,0), u2 =(3,3,3,0), u3=(2, -10,0,0), u =(-2,1,-6,2). i. Show that the vectors {ui, u2, 13, 14} form the basis for R4. ii. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R"spanned by the given set of vectors {uj, u2, 13, 14} .
Answers
Let's consider the subspace spanned by {u, x, y, z} where v is orthogonal to u, x, y, and z. We have to prove that v is also orthogonal to this subspace. We'll start with a fact that if any vector is orthogonal to a set of vectors, then it's also orthogonal to any linear combination of those vectors.
As all the vectors u, x, y, z are contained in the subspace, any linear combination of them will also belong to the subspace. Hence, it will also be orthogonal to v as all of the elements of the linear combination are orthogonal to v. Therefore, we can say that v is orthogonal to span{u.x,y,z}.
It is given that V is an inner product space and v, u, x, y, and z EV such that vis orthogonal to u, x, y, and z.Let's consider the subspace spanned by {u, x, y, z} where v is orthogonal to u, x, y, and z. We have to prove that v is also orthogonal to this subspace. We'll start with a fact that if any vector is orthogonal to a set of vectors, then it's also orthogonal to any linear combination of those vectors.
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What are the mean and median next 12 months pe ratios of the group? enter your answer as the mean multiple followed by the median multiple, comma separated with no spaces. For example: 25. 5x,15. 8x
Answers
The mean and median next 12 months PE ratios of the group are the mean multiple followed by the median multiple, comma-separated with no spaces.
The mean and median next 12 months PE ratios of the group can be found by following these steps:
1. Gather next 12 months PE ratios for each company.
2. Calculate mean by summing the ratios and dividing by total number.
3. Arrange ratios in ascending order.
4. Find the middle value(s) to determine the median.
5. Write the mean multiple followed by the median multiple, comma-separated with no spaces.
Therefore, the mean and median next 12 months PE ratios of the group are the mean multiple followed by the median multiple, comma-separated with no spaces.
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Which relation in the below table(s) represents a function?
Answers
The relation 2 represents a function.
In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.
To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.
The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.
If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.
We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.
Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.
Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.
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value of in the equation a=2+3+10
Answers
\(\huge{\boxed{\mathfrak{ANSWER}}} \)
\(a=2+3+10\)
\(a = 15 \)
\(\huge \pink {\overline{ \quad \quad \quad \quad \quad \quad \quad\quad \quad}}\)
Seven years ago, Mrs Grey decided to invest R18 000 in a bank account that paid simple interest at 4,5% p.a. 4.1.1 Calculate how much interest Mrs Grey has earned over the 7 years. 4.1.2 Mrs Grey wants to buy a television set that costs R27 660,00 now. If the average rate of inflation over the last 5 years was 6,7% p.a., calculate the cost of the television set 5 years ago. 4.1.3 At what rate of simple interest should Mrs Grey have invested her money 7 years ago if she intends buying the television set now using only her original investment of R18 000 and the interest earned over the last 7 years?
Answers
The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.
4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:
Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.
4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:
Cost 5 years ago = Cost now / (1 + Inflation rate)^Time
Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.
4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:
Rate = Interest / (Principal x Time)
Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.
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I need help figuring out the answer … I’m confused
Answers
1st step. Calculate the area of the parallelogram
We can use the following formula:
\(A=b\cdot h\)where,
base, b = 9 km
height, h = 5 km
Therefore,
\(A=9\cdot5=45\)The area of the parallelogram is 45 km^2
2nd step. Calculate the area of the triangle
Let's use this formula:
\(A=\frac{b\cdot h}{2}\)where,
base, b = 6 km
height, h = 3 km
Therefore,
\(A=\frac{6\cdot3}{2}=9\)The area of the triangle is 9 km^2
3rd step. calculates the ratio of the area of the parallelogram to the area of the triangle
\(r=\frac{A_P}{A_T}=\frac{45}{9}=5\)Answer: the area of the parallelogram is 5 times greater than the area of the triangle.
What is the slope of the line described by x+4y=3?
Answers
Answer:
so the answer is equation
Step-by-step explanation:
as you know the question is come from the linear equations and simple inqualities so the answer is this
Write your answer in simplest form
Answers
Answer:
-2 2/5
Step-by-step explanation:
- 3/5 + - 9/5 = -12/5
-12/5 = -2 2/5
Factor the given polynomial by removing the common monomial factor. 7x+21 7x+21=
Answers
The factored form of the polynomial 7x + 21, after removing the common monomial factor, is 7(x + 3)
we can first observe that both terms in the polynomial share a common factor of 7. We can factor out this common factor to simplify the expression.
Factoring out the common factor of 7, we get:
7(x + 3)
Therefore, the factored form of the polynomial 7x + 21, after removing the common monomial factor, is 7(x + 3)
In the given polynomial, we have two terms, 7x and 21, both of which are divisible by 7. By factoring out the common factor of 7, we are essentially dividing each term by 7 and simplifying the expression. This is similar to finding the greatest common factor (GCF) of the terms.
By factoring out the common factor of 7, we are left with the expression (x + 3), which represents the remaining factor after dividing each term by 7. The factored form 7(x + 3) indicates that the polynomial is equivalent to 7 times the binomial (x + 3).
Factoring out common factors is a useful technique in algebra that helps simplify expressions and identify patterns or common structures within polynomials.
It can also facilitate further algebraic manipulations, such as expanding or solving equations involving the factored expression.
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A number is between 10 and 15. It has prime factors of 2 and 3. What is the number?
Answers
The number in between 10 and 15 and having prime factors of 2 and 3 is 12.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
The integer between 10 and 15 are,
11,12,13,14
The prime factors of 2 and 3 will be given as,
\(2^{a} \times 3^{b}\) where a and b can be positive.
Since, 12 = 2² × 3¹
Thus, 12 is the only number that is the prime factor of 2 and 3 both.
Hence "The number between 10 and 15 and having prime factors of 2 and 3 is 12".
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the ratio of length to width is 4:3 what is the width of Michelle's room if the length of her room is 148 in
Answers
Answer
The width of Michelle's room = 111 inches.
Find the projection of v onto w if v = (-5,-2) and w = (1,-1).
Answers
The Projection of v onto w is (-3/2, 3/2).
The projection of v onto w is found by using the formula:proj_w(v) = (v · w / ||w||²) * w
Where v is the vector to be projected, w is the vector onto which we want to project v, and ||w||² is the magnitude of w squared.
To find the projection of v onto w if v = (-5,-2) and w = (1,-1), we first need to calculate the magnitude of w squared.||w||² = 1² + (-1)²= 2
Next, we need to calculate the dot product of v and w.v · w = (-5)(1) + (-2)(-1)= -5 - (-2)= -3
Now, we can use the formula above to find the projection of v onto w.proj_w(v) = (v · w / ||w||²) * w= (-3 / 2) * (1,-1)= (-3/2, 3/2)
Therefore, the projection of v onto w is (-3/2, 3/2).
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Need help don't know what to do!
Answers
Answer:
1) 15x+10=130 (corresponding angles)
15x=120
x=120/15
x=8
2) 60+128+x=180 (angle to straight line)
188+x=180
x=180-188
x=-8
3) 12x+8=13x+2
12x-13x=2-8
-x=-6
x=6
4) 115+16x+1=180 (co interior angles)
116+16x=180
16x=180-116
16x=64
x=64/16
x=4
please help me with this math question.
Answers
Answer:
Alejandro: The relationship is not a function because x = 1 has two different y-values.
Correct, it is referring to vertical line test
Step-by-step explanation:
Hope this helps!!
Clayton's bus ride to school is 3/4 of a mile and Prince's bus ride is 1/4 of a mile. How much longer is Clayton's bus ride than Prince's.
Answers
A taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional $0.20 for each mile traveled. The rule c = 0.20m + 2.00 describes the relationship between the number of miles m and the total cost of the ride c. What is the charge for a 1-mile ride? A)$0.20 B)$0.02 C) $2.20 D)$2.00
Answers
Answer:
c
Step-by-step explanation:
Any ride takes $2.00 and one mile takes $0.20.
Cost = $0.20 + $2.00
Cost = $2.20
PLEASE HELP CHIMESTRY!
Answers
Answer: There are 4 significant figures in this mass
Step-by-step explanation:
In the number 3 x 10^6 mg, there are four significant figures. The first three digits, 3, 1, and 0, are significant. The final digit, 6, is not significant because it is a rounded value. Therefore, there are four significant figures in this mass.
33=10∙q+r cual es el valor de q y r
Answers
Answer:
Q=33/10-r/10 R=33−10q
Step-by-step explanation:
Espero que sea correcto para ti también puedes hacerme más inteligente si es correcto
the distance from the center of the circle to the outer edge is called
Answers
The distance from the center of the circle to the outer edge is called radius of the circle.
Circle is a segment of line connected to it itself. It is a 2 dimensional structure measuring 360°. The outer edge of the circle is called circumference. Now, an interesting fact about the circle is that circumference is equi distant from the radius.
Therefore, be it any point on the circumference, it will be at the same distance from radius. If the radius is further extended to meet the opposite side of circumference, it will become a diameter. The total length of diameter however decreases as we move from center to top of the circle.
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