Answer:
a) The probability is 0.5557 = 55.57%.
b) The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.
c) Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean weight of 0.8616g and a standard deviation of 0.0518
This means that [tex]\mu = 0.8616, \sigma = 0.0518[/tex]
a) If 1 candy is reandomly selected, find the probability that it weights more than 0.8542g.
This is 1 subtracted by the pvalue of Z when X = 0.8542. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.8542 - 0.8616}{0.0518}[/tex]
[tex]Z = -0.14[/tex]
[tex]Z = -0.14[/tex] has a pvalue of 0.4443
1 - 0.4443 = 0.5557
The probability is 0.5557 = 55.57%.
b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.
Sample of 447 means that [tex]n = 447, s = \frac{0.0518}{\sqrt{447}} = 0.00245[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8542 - 0.8616}{0.0245}[/tex]
[tex]Z = -3.02[/tex]
[tex]Z = -3.02[/tex] has a pvalue of 0.0013
1 - 0.0013 = 0.9987
The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.
c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.
it takes Carly 39 minutes to walk 3 miles at that rate how long will it take Carly to walk 7 miles
The time it takes Carly to walk 7 miles is 91 minutes
How to determine how long will it take Carly to walk 7 milesFrom the question, we have the following parameters that can be used in our computation:
Time = 39 minutes
Distance = 3 miles
The speed can be calculated as
Speed = Distance/Time
Substitute the known values in the above equation, so, we have the following representation
Speed = 3 miles/39 minutes
So, we have
Speed = 1/13 miles per minute
From the question, we have
Distance = 7 miles
Recall that
Speed = Distance/Time
Make time the subject
Time = Distance/Speed
So, we have
Time = 7/(1/13)
Evaluate
Time = 91 minutes
Hence, the time is 91 minutes
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The graph of a linear equation passes through (0, -6) and (9, 0).
What is the equation?
Answer:
In standard form the equation would be
6x -9y = 54
Step-by-step explanation:
Let x = 0
-9y = 54 Divide both sides by -9
y = -6
(0,-6)
Let y = 0
6x = 54 Divide both sides by 6
x = 9
(9,0)
suppose the correlation coefficient is .4. what percentage of the total variation in salar can be explained by gender
If the correlation coefficient is 0.4, the total variation in salary can be explained by gender is 16%.
What is correlation coefficient?A statistical concept known as the correlation coefficient aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated correlation coefficient's value explains how well the expected and actual values match.
Correlation Value of the coefficient is always between -1 and +1. If the correlation coefficient value is positive, the two variables have a similar and same relationship. Otherwise, it shows how the two variables are different.
If the correlation coefficient (R) = 0.4
Coefficient of determination (R²) = (0.4)²
Coefficient of determination (R²) = 0.16
So that, the total variation in salary can be explained by gender is 16%.
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the center of a semisimple lie algebra {\displaystyle {\mathfrak {g}}}{\mathfrak {g}} is trivial proof. t/f
Answer:
False. The center of a semisimple Lie algebra is usually not trivial.
Step-by-step explanation:
The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.
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A basketball player makes 70 % of her free throws. When fouled, she gets to take 2 free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table:Number of free throws made 0 1 2Probability 0.09 0.42 0.49The probability that she makes at least one free throw isa.0.67b.0.91c.0.95d.1.00
The probability that she makes at least one free throw is b. 0.91. Probability theory is a branch of mathematics that is used to model and analyze random events.
Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
To find the probability that the player makes at least one free throw in two attempts, you can subtract the probability that she misses both free throws from 1. The probability that she misses both free throws is 0.09, so the probability that she makes at least one free throw is:
1 - 0.09 = 0.91.
Therefore, the correct answer is 0.91, or choice (b).
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Find an equation for (-8,1) parallel to x-4y=4
The required equation of the line passing through (-8, 1) and parallel to x - 4y = 4 is y = 1/4x + 1.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Slope of the given line x - 4y = 4
y = 1/4x - 1
m = 1/4
The slope of the parallel lines is always equal
Now,
Equation of the parallel line passing through the point (-8, 1) is given as,
y - y₁ = m (x - x₁)
y -1 = 1/4(x + 8)
y = 1/4x + 1
Thus, y = 1/4x + 1 is the needed equation for the line passing through (-8, 1) and parallel to x - 4y = 4.
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Factors 3x^4-5x^3+6x^2-15x completely over the set of integers
The Factors of 3x^4-5x^3+6x^2-15x completely over the set of integers will give 5(1-3x).
How can this be calculated?In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller
The expression can be broken down after the other as
[2x4 = 8] + [5x3=15] + [6x2=12]
= [8-15+12-15x]
=5-15x
then we can factorize as
5(1-3x)
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6a^3 - (1/9 b^4)
If A and B are 3
Answer:
Step-by-step explanation Let a =3 and b=3 we are given this information.
6a^3-1/9b^4
Substitute values for a=3 and b=3
=6(3)^3-1/9(3)^4
=6 x27-1/9 x 81
=162-9
153
reminder 3^3=27=3 x 3 x 3
reminder 3^4=81=3 x 3 x 3 x 3
b) If the marginal revenue function for output x is given by MR = C, where a, b, c, m and n are constant. mn (ax+b)² Prove that the demand function is p mn b(ax+b) C.
The demand function is given by the expression -
D{x} = mn(a²x + 2b + b²)
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the revenue function as follows -
f(x) = mn (ax + b)²
The revenue function is simply [x] multiplied by the demand function.
R{x} = x (D{x})
The revenue function is -
f(x) = mn (ax + b)²
So, the demand function can be written as -
mn(ax + b)² = x (D{x})
D{x} = {mn(ax + b)²}/x
D{x} = {mn(a²x² + b² + 2abx)}/x
D{x} = {a²x²mn + mnb² + 2bmnx}/x
D{x} = a²xmn + 2bmn + mnb²
D{x} = mn(a²x + 2b + b²)
Therefore, the demand function is given by the expression -
D{x} = mn(a²x + 2b + b²).
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If f(x)\ =\ x^{2}+3f(x) = x 2 +3 , find f(-2)f(−2) .
The solution for f(-2) in the function f(x) = x² + 3 is 7
How to determine the solution for f(x) in the function?From the question, we have the following equation that can be used in our computation:
f(x) = x 2 +3
To make the equation legible, we need to rewrite it
So, we have the following representation
f(x) = x² + 3
Also from the question, we have
f(-2)
This means that the value of x is -2, and we calculate f(x) when x = -2
Substitute the known values in the above equation, so, we have the following representation
f(-2) = x² + 3
So, we have the following equation
f(-2) = (-2)² + 3
Evaluate
f(-2) = 7
Hence, the solution is 7
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The plot below shows the volume of 11 river water samples collected by an ecologist. All measurements are rounded to the nearest 1/8 gallon.
The largest sample volume is 7/8 gallon.
What is volume?Space is occupied by every three-dimensional object. Its volume serves as a gauge for this area. The area contained by an object's boundaries in three-dimensional space is referred to as its volume. Another name for it is an object's capacity.
When filling an aquarium, water tank, or bottle with water, for example, knowing the volume of the container can help us calculate how much water is needed to fill it.
According to the information in the query.
The smallest sample has a 1/8 gallon volume.
Because
the volume of the largest sample/volume of the smallest sample equals 7/8/1/8
= 7/8× 8/1 = 7,
We can conclude that the volume of the largest sample is 7 times that of the smallest sample.
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Full question
The plot below shows the volume of 11 river water samples collected by an ecologist. All measurements are rounded to the nearest 1/8 gallon. How many times as great is the volume of the largest sample than the volume of the smallest sample?
there appears to be a strong positive correaltion between the number of firefighters at a fire and the amount of damage the fire does choose the statemnt that is most likely true a, b, or c? a. We should assign fewer firefighters to a fire to decrease the amount of fire damage. b. The more firefighters present, the less damage a fire is likely to cause. C. Bigger fires cause more fire damage and more firefighters are likely to be present at bigger fires.
The relationship between the quantity of firemen and the amount of damage brought on by a fire is, in fact, created by a third party. Thus, choice A is the best one.
Firefighter
A fireman is a first responder and rescuer who has received significant training in firefighting. They are primarily responsible for putting out dangerous flames that endanger life, property, and the environment as well as for rescuing humans and, in some circumstances, animals from perilous situations.
The third aspect
The numbers that divide 3 in three equal parts with no remainders are known as its factors. As is well known, the earliest odd prime number is three. The three components and their pair can be expressed in both good and negative ways. For illustration, the pair factor of 3 is shown.
It is true to say that a third party is to blame for the correlation between the number of firefighters and the amount of damage a fire causes. So, option A is the best choice.
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The factors of 3 are the numbers that split it into three equal pieces with no remainders. The oldest odd prime number is three, as is common knowledge. The three elements and their paired expressions have both positive and negative connotations. The pair factor of three is displayed as an illustration.
It is accurate to say that there is a third party at fault for the association between the quantity of firefighters and the scope of a fire. As a result, option A is the best one.
The total weight of a giraffe and her calf is 904 kilograms. How much does the calf weigh? Use a tape
diagram to model your thinking.
The Calf weigh about 75 kg.
How is weight calculated ?The force of gravity acting on an item is known as its weight, and it can be determined using the formula w = mg, which equals the mass times the acceleration of gravity. The newton is the SI unit for weight since it is a force.The gravitational force that pulls a body toward the earth or another celestial body; it is equal to the mass times the acceleration due to local gravity.We treat our weight as mass and use the unit kg to measure weight by presuming that the gravitational field is the same everywhere.The fundamental mass unit in the metric system is the kilogramme (kg). The mass of 1,000 cubic centimeters of water is extremely close to (and was originally meant to be exactly) one kilogram. The actual weight of a pound is 0.45359237 kg.Given data :
The total weight of a giraffe and her calf is 904 kilograms.
Weight of the giraffe is 829 kg
So the weight of the calf = Total weight - weight of giraffe
= 904 - 829 = 75
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write the equation in slope intercept form and graph using a table
X = 5
Answer:
y=5x+0
Step-by-step explanation:
wouldn't the equation be something like y=5x+0? If x=5 then x would be the slope. So then if the slope is 5 you'd start off your equation y=5x but there might not be a y-int for this equation because the equation only has an x and there is no y.
(Not sure if you understand it, but if it were to me I'd do something like this because there is only one number in the equation, hope this helps in some way....)
10. (04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? (1 point)
2x + y = 8
-x - 3y = -12
3y + 12
-3y + 12
3y - 12
-3y - 12
If you isolated x in the second equation to use the substitution method. -3y + 12 expression we substitute into the first equation.
What is Substitution Method ?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
The substitution method has three straightforward steps, which are listed below:
In any equation, determine the value of any one variable in terms of the other variable.Replace that in the other equation, then solve it.In any of the equations, replace the value of the second variable once more.2x + y = 8
-x - 3y = -12
__________
-3y + 12
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How many integral solution(s) is/are there for x if -69 ≤ 7x + 9 ≤ 49?
Answer:
To find the number of integral solutions for x in the given inequality, we can first solve the inequality to find the range of values that x can take on. To do this, we need to isolate the x term on one side of the inequality, so let's start by subtracting 9 from both sides of the inequality:
-69 ≤ 7x + 9 ≤ 49
-9 ≤ 7x ≤ 40
Next, we can divide both sides of the inequality by 7 to isolate the x term:
-9/7 ≤ x ≤ 40/7
The result of this calculation is a range of values for x, but we are looking for the number of integral solutions, which means we need to find the number of whole numbers that x can take on within this range. In this case, we can see that the range of possible values for x is from -1 to 5, and there are 5 whole numbers within this range (-1, 0, 1, 2, 3, 4, 5), so there are 5 integral solutions for x in this inequality.
In general, to find the number of integral solutions for x in an inequality of the form a ≤ bx + c ≤ d, where a, b, c, and d are constants, you can follow these steps:
1.Solve the inequality to isolate the x term on one side, by subtracting c from both sides and then dividing both sides by b. This will give you the range of possible values for x.
2.Count the number of whole numbers within this range to find the number of integral solutions for x.
Step-by-step explanation:
Two parallel lines are cut by transverse as shown suppose
Write and equation of a circle that has a diameter that passes through the points (3,0) and (7,6)
The equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x - 6*y +21 =0
Given that, the points (3,0) and (7,6)
(x1, y1) = (3,0) and (x2, y2) = (7,6)
We know that the formula for the equation of circle whose points of diameter are given is equal to :
(x - x1) * (x - x2) + (y - y1) * (y - y2)
So now,
(x - 3) * (x - 7) + (y - 0) * (y - 6) = x² + y² - 10*x - 6*y +21 =0
so the equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x - 6*y +21 =0
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Lakeside amusement park charges an entry fee plus $1.25 per ticket used to go on the rides. The entry fee is the same amount for everyone.
Louisa spent a total of $43.75 on the entry fee plus 25 ride tickets. Click “show your work” below and show calculations to determine how much Louisa paid for the entry fee.
Using mathematical operations, the amount that Louisa paid for the entry fee is $12.5.
What are mathematical operations?The basic mathematical operations include addition, subtraction, division, and multiplication.
These mathematical operations combine values, numbers, and variables with mathematical operands to solve mathematical problems.
For instance, the variable cost per ride ticket is given as $1.25. There are a total of 25 ride tickets spent by Louisa.
Mathematically, the total variable cost is the product of per unit cost and total ride tickets.
The total variable cost is subtracted from the total amount spent to determine the fixed entry fee.
Fee per ticket = $1.25
Total amount spent by Louisa = $43.75
The number of ride tickets = 25
The fixed entry fee per person = $12.50 ($43.75 - $1.25 x 25)
Thus, whereas, Louisa spent $1.25 per ride ticket, she spent $12.50 as the fixed entry fee.
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(x+1)=(7x-5) how do i solve this
Step-by-step explanation:
You start with x+1=7x-5
Basically you want all the x's on one side and all the constants on the other
(x+1)+5=(7x-5)+5, to get rid of the 5 on the right side
(x+6)-x=7x-x, to get rid of the x on the left side
We are now left with 6x=6
No we simplify, 6x/6=6/6
Now we have x=1, which is the answer
I hope this made sense.
x= 1.
Step-by-step explanation:1. Write the expression.[tex](x+1)=(7x-5)\\ \\x+1=7x-5[/tex]
2. Subtract "1" from both sides of the equation.[tex]x+1-1=7x-5-1\\ \\x=7x-6[/tex]
3. Subtract "7x" from both sides of the equation.[tex]x-7x=7x-6-7x\\ \\-6x=-6[/tex]
4. Divide both sides by "-6".[tex]\frac{-6x}{-6} =\frac{-6}{-6} \\ \\x=1[/tex]
5. Verify.[tex](1)+1=7(1)-5\\ \\2=7-5\\ \\2=2[/tex]
That's correct!
6. Conclude.x= 1.
A fair die is rolled three times. A 4 is considered "success," while all other outcomes are "failures." Find the probability of 3 successes.
The probability of getting 3 successes is 0.00463 Or 0.46%.
What is a binomial distribution in probability?In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is [tex]P(x) = ^nC_xp^xq^{n-x}[/tex] if the likelihood of success on a given trial is p.
Given, A fair die is rolled three times. Getting a 4 is considered 'success', while all other outcomes are 'failures'.
So, The probability(p) of getting a 4 on a die is (1/6), and hence the probability of failure(q) = 1 - 1/6 = 5/6.
Also given, n = 3.
Therefore, The probability of getting 3 successes is,
[tex]P(x = 3) = ^3C_0(1/6)^3\times(5/6)^0[/tex].
[tex]P(x = 3) = 1\times\frac{1}{216}\times1[/tex]
[tex]P(x = 3) = \frac{1}{216}[/tex].
So, the probability of 3 successes is 1/216.
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a survey of 1655 people who took trips revealed that 167 of them included a visit to a theme park. based on those survery results, a management consul
Based on the survey results, the proportion of people who took a trip that included a visit to a theme park is 167/1655 = 0.101. This means that approximately 10.1% of the people who took a trip included a visit to a theme park.
It is not clear what the management consultant is trying to do with this information. However, the proportion of people who took a trip that included a visit to a theme park can be used as a measure of the popularity of theme parks as a vacation destination.
It could also be used to estimate the demand for theme park tickets or to develop marketing strategies for theme parks.
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let be a scalar field and let be a vector field. describe each expression. 1. curl is [ select ] 2. grad(div ) is [ select ] 3. div(curl(grad ))) is
1) curl = del x
2) grad(div ) = del(div )
3) div(curl(grad )) = div(curl(grad))
What is Scalar field and Vector field?
1) The curl of a vector field is a vector field that describes the local rotational motion of the field. It is defined as the cross product of the del operator (a vector operator that operates on scalar and vector fields) and the vector field:
curl = del x
2) The gradient of the divergence of a vector field is a scalar field that describes the local rate of change of the divergence of the field. It is defined as the del operator applied to the divergence of the field:
grad(div ) = del(div ).
3) The divergence of the curl of the gradient of a scalar field is a scalar field that describes the local rate of change of the curl of the gradient of the field. It is defined as the divergence of the curl of the gradient of the field:
div(curl(grad )) = div(curl(grad)).
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determine the area (in units2) of the region between the two curves by integrating over the y-axis. x
The area of the region between the two curves by integrating over the y-axis, x = y² and x = 9 is 18 square units.
Total Area inclosed between line and Curve:The area where the "area under the curve" is common to both the straight line and the given curve is called the bounding area. Therefore, the area common to both can be found by subtracting the area under line T from the area under curve C. The x constraint for computing the area under the curve can be found by solving the system of equations for the coordinates of the intersection of the line and the curve.
We have given the curve , x = y² and line x = 9 and bounded region is A in above graph of x = y² and line x = 9.
Now, we determine the intersection points of curve and line,
put x = 9 in curve equation we get,
y² = 9 => y = +-√9
= + 3 or -3
Total area bounded by curve and line, A = integration of curve over y from y = -3 to y= 3
= ₋₃∫³x dy = ₋₃∫³y² dy = ₋₃[ y³/3]³
= [ (3)³/3 - (-3)³/3]
= 9 + 9 = 18
Hence, the required area is 18 square unit.
Complete question:
determine the area (in units2) of the region between the two curves by integrating over the y-axis. x = y² , x = 9
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 29 41
Does not like burritos 54 135
Total 110 205
Part A: What percentage of the survey respondents liked neither hamburgers nor burritos? Show all work. (3 points)
Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)
Part C: Which category has the lowest joint relative frequency? Show all work. (4 points)
A: 16.09 % of the survey respondents liked neither hamburgers nor burritos
B) 0.65 is the marginal relative frequency.
C) The lowest joint relative frequency of those who like Hamburgers but not burritos.
What is Marginal Frequency?The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single type of data.
Given:
Like Hamburgers Does Not Like Hamburgers Total
Likes burritos 39 38 77
Does not like burritos 95 33 128
Total 134 71 205
A) There are 33 such respondents.
So, percentage is
= 33/205 x 100
= 16.095
B) It will be the ratio of the sum of the customers that like hamburgers to the total number of respondents
So, the ratio is
= 134/205
= 0.65 :1
Part C: For this, we need to find the ratio of all the four data with the total.
Those who like Hamburgers and burritos
= 39/134
Those who like Hamburgers but not burritos
= 95/134
Those who like burritos but not Hamburgers
=38/71
Those who do not like burritos or Hamburgers = 33/71
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Using Euler's formula, how many
edges does a polyhedron with 20
faces and 12 vertices have?
[?] edges
Euler's Formula: F + V = E + 2
Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+9=13
X=
Marta conducts emissions inspections on cars. She finds that 8 % 8%8, percent of the cars fail the inspection. Let X XX be the number of cars Marta inspects until a car fails an inspection. Assume that the results of each inspection are independent. Find the mean and standard deviation of X XX. Round your answers to one decimal place.
There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.
What connection exists between the mean and the standard deviation?First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:
The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.
What is the standard deviation and mean formula?The mean is calculated as follows:
Mean = (all data values added together) / (number of data values)
However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.
The standard deviation equation is as follows:
Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":
No of the size of the data collection, the mean rises by precisely K.
No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.
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Select the correct answer.
The height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t. Find the eceleration at time t.
O A.
100-cos t
OB.
-sin t
O C.
-cos t
O D. 100-sin t
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Next
-sint is the acceleration at time t.
What is Acceleration?Acceleration is the rate of change of the velocity of an object with respect to time.
Given, the height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t.
We need to find the acceleration at time t.
s(t) = 100 + cos t.
To find the acceleration we have to differentiate the above equation.
d/dt=d/dt(100+cost)
=d/dt(100)+d/dt(cost)
=0+(-sint)
s'(t) = -sint.
Hence, the acceleration at time t is -sint.
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t on rn . 14. let t be a one-to-one linear transformation from a vector space v into rn . show that for u, v in v , the formula hu; vi d t .u/t .v/ defines an inner
The formula hu; vi d t .u/t .v/ defines an inner product on v because it is linear equation in u and v, symmetric, and positive definite.
The formula hu; vi d t .u/t .v/ defines an inner product on v because satisfies all of the requirements of an inner product. Specifically, it is linear in both u and v, meaning that ah; vi bh; vi for any scalar a and any two vectors u, v. This means that it is distributive over addition, so hu b c; v i d hu b; v i C hc; v i. It is also symmetric, so hu; v i d hv; ui, which is necessary for hu; ui to be considered a valid inner product. Finally, it is positive definite, meaning that hu; ui d k uk2 0 for all vectors u 6 d 0. This means that for any two vectors u, v, the inner product of hu; vi d t .u/t .v/ is a valid inner product on the vector space v.
Proof: Let u, v ∈ V .
1.hau b; v i d t .au b/t .v/ d at t .u/t .v/ bt t .v/ d ah; vi bh; vi
2. hu; vi d t .u/t .v/ is linear in v :
h u; av b i d t .u/t .av b/ d at t .u/t .v/ bt t .u/t .v/ d ah; vi bh; vi
3. hu; vi d t .u/t .v/ is symmetric:
h u; v i d t .u/t .v/ d t .v/t .u/ d hv; ui
4. hu; vi d t .u/t .v/ is positive definite:
h u; u i d t .u/t .u/ d k t .u/ k2 d k uk2 0 for all u 6 d
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t on rn . 14. let t be a one-to-one linear transformation from a vector space v into rn . show that for u, v in v , the formula hu; vi d t .u/t .v/ defines an inner product on v .