There are a total of 216 ways in which the waiter could serve the meal types.
Let the beef meal be denoted by B, chicken meal by C, and fish meal F. Now say the nine people order meals BBBCCCFFF respectively and say that the person who receives the correct meal is the first person. We will solve for this case and then multiply by 9 to account for the 9 different ways in which the person to receive the correct meal could be picked.
Now, we need to distribute meals BBCCCFFF to orders BBCCCFFF with 0 matches. The two people who ordered B's can either both get C's, both get F's, or get one C and one F.
If the two B people both get C's, then the three F meals left to distribute must all go to the C people. The F people then get BBC in some order, which gives three possibilities.
If the two B people both get F's, the situation is identical to the above and three possibilities arise.
If the two B people get CF in some order, then the C people must get FFB and the F people must get CCB. This gives 2*3*3 = 18 possibilities.
In total, we see there are 24 possibilities, so the answer is 9*24 = 216
Thus, there are a total of 216 ways in which the waiter could serve the meal types.
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Your question was incomplete. Check for missing part below-
Find the number of ways in which the waiter could serve the meal types to the nine people so that exactly one person receives the type of meal ordered by that person.
whats -3x + 4x please answer.
Answer: 1x
Step-by-step explanation:-3+4=1 and then add a x
Apples sell for $2
per pound and
oranges sell for $3
per pound.
Suppose Ben
bought 5 pounds of
fruit at a cost of
$12. How many
pounds of each
kind of fruit did
Ben buy?
Answer:
Step-by-step explanation:
apples=$2 per pound
oranges=$3 per pound
If Ben bought x pounds of oranges and five pounds of fruit in total, then he bought 5-x pounds of apples.
oranges price: 3x
apples price: 2(5-x)
Final Equation: 3x+2(5-x)=12
3x+10-2x=12
x+10=12
x=2 -> amount of oranges
input in apples equation
apples= (5-x)->(5-2)=3
Final answer: 2 pounds of oranges, 3 pounds of apples
I REALLY NEED HELP!! 50 POINTS
Find a point on the line and the line's slope.
y = 3 + 3 ( x + 4 )
point on the line: (____,____)
slope: _____
Answer:
Point on the line: (0, 15)
Slope: 3
Step-by-step explanation:
Step 1: Put the equation in slope-intercept form
The slope-intercept form is written like this: y = mx + b
m = slope
b = y-intercept
1. y = 3 + 3(x + 4) → y = 3x + 15
Step 2: Retrieve the values from the equation
y-intercept = 15
slope = 3
If me and my brother pay for grocerie and the total wa 443 and I pay 243 and he pay 200 but we get paid back 75 each how much hould I get paid
The total money I have to pay will be 168.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
If I and my brother pay for groceries and the total was 443.
If i pay 243 and get paid back 75
So the total I paid will be (243 - 75) = 168
Hence, the total money I have to pay will be 168.
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Write the statement "the sum of a number and 18.4 is at least −3.8" as an inequality.
−3.8 + b > 18.4
b + 18.4 ≥ −3.8
b + 18.4 ≤ −3.8
−3.8 + b < 18.4
Hence, he sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality is [tex](b+18.4)\geq -3.8[/tex].
What is the inequality?
An inequality is said to be sharp if it cannot be relaxed and still be valid in general.
Here given that,
The sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality.
Let [tex]b[/tex] be the number
As it is mentioned that the sum of [tex]x[/tex] and [tex]18.4[/tex] is at least [tex]-3.8[/tex].
Hence, the sum is greater or equal to [tex]-3.8[/tex]
i.e., [tex](b+18.4)\geq -3.8[/tex]
Hence, he sum of a number and [tex]18.4[/tex] is at least [tex]-3.8[/tex] as an inequality is [tex](b+18.4)\geq -3.8[/tex].
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Given the equation, y=3x, complete the table of values
x (input)
y (output)
-2
-1
0
1
2
Answer:
-2, -6
-1, -3
0,0
1,3
2,6
Step-by-step explanation:
nsd fbvdvjben ebtv
Step-by-step explanation:
when x is -2 y is y=3x
y=3×-2
y=-6 do that for all
The population of a city was 195 thousand in 1992. The exponential growth rate was 1.2% per year.
..
a) Find the exponential growth function in terms of t, where t is the number of years since 1992.
P(t)=____
well, we know that it was 195 in 1992, so "t" years later that'd be
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &195\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ t=years\dotfill &t\\ \end{cases} \\\\\\ A=195(1 + 0.012)^{t} \implies A =195(1.012)^t[/tex]
An officer printer prints 25 photos in 12.5 minutes. A home printer prints 15 photos in 6 minutes. Which printer is faster, How many more photos can you print in 12 minutes using the faster printer? You can print ____
more photos in 12 minutes using the faster printer.
Answer: The at home printer prints faster, and you can print 6 more photos with it than the office printer.
Step-by-step explanation:
25 ÷ 12.5 = 2
15 ÷ 6 = 2.5
2 x 12 = 24
2.5 x 12 = 30
A pharmacist asserts that more than 40% of prescribed medicines are derived from plants. They decide to test this assertion by computing the sample proportion for a random sample. The data results in a test statistic of z = 2.14 and a P- value of .0162. Test at a 5% significance level. a. State the hypotheses for their test. b. Briefly describe what the P-value is. c. Using the test statistic, how was the P-value found? d. Based on the P-value what conclusion should the pharmacist make? In particular, do they have enough evidence in support of their claim?
a. test statistic = 1.35
p-value = 0.198439
b. Support the null hypothesis.
So you have the hypothesis:
H₀:μ=4
H₁:μ≠4
with the sample information you calculate the statistic using the t-distribution with 14 (n-1) degrees of freedom:
t=x[bar] - μ ⇒ t= 4.8 - 4 = 0.8 = 1.347≅ 1.35
s/√n 2.3/√15 0.59
The p-value is defined as the probability corresponding to the calculated statistic (or of obtaining a value as extreme as the value of the statistic) if possible under the null hypothesis.
p-value: 0.198439
b.
Since the calculated p-value is greater than the significance level, you don't reject the null hypothesis.
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a ladder ft long leans against a vertical wall. if the lower end is being moved away from the wall at the rate of ft/sec, how fast is the height of the top changing (this will be a negative rate) when the lower end is feet from the wall?
The height of the top change when the lower end is feet from the wall by -4.5 ft/sec.
Given,
Assume that the horizontal floor is x and the vertical wall is y in distance (6 ft).
This creates a triangle, with the ladder serving as the 10 foot hypotenuse.
dy/dt = 6 feet per second.
Pythagoras' law states that there is a link between x and y.
(x²) + (y²) = (hypothenus²) = 10².
When both sides of the equation are distinct,
0 = 2x(dx/dt) + 2y(dy/dt)
(x/y) × (dx/dt) = dy/dt
y = √(10²) - (6²) = 8ft
Consequently, dy/dt = (6/8) × (6/1)= -4.5 ft/sec.
The rate is negative.
That is,
When the lower end is feet from the wall, the height of the top changes by -4.5 feet per second.
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focus on the means (mean). - what do you notice about the means of the sample means as the sample size increases from 1 to 100? - what would you expect the mean of the sample means to equal if n
As the sample size increases the mean is 100 , if n = 1000 , the mean of the sample means will be unchanged .
In the question ,
from the table we can observe that ,
if n = 1 , the mean is 97.656 ,
if n = 5 , the mean is 100.101 ,
if n = 10 , the mean is 100.006 ,
if n = 100 , the mean is 100.341 ,
from the table we notice that as the sample size increases from 1 to 100 , the means of the sample means are same that is 100 .
we can see that for every n , the mean is approximately equal to 100 ,
So , if n = 1000 , then the mean will also be approximately equal to 100 .
Therefore , the mean of the sample means will be unchanged .
The given question is incomplete , the complete question is
Focus on the means. What do you notice about the means of the sample means as the sample size increases from 1 to 100? What would you expect the mean of the sample means to equal if n = 1000 ?
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can someone help me really quick
Answer:
Step-by-step explanation:
12.50
Answer:
B
Step-by-step explanation:
constant of proportionality = 10/20 = 1/2
y/x = 1/2
y = 1/2x
y = 1/2 * 25
y = 25/2
y = 12.5
PLEASE ANSWER ASAP
Which statement correctly describe the data shown in the scatter plot?
Responses
The scatter plot shows no association.
The scatter plot shows no association.
The scatter plot shows a linear association.
The scatter plot shows a linear association.
The point (2, 14) is an outlier.
The point , left parenthesis 2 comma 14 right parenthesis, is an outlier.
The scatter plot shows a negative association.
"The scatter plot shows a linear association."
What is scatter plot ?
Several dots are plotted on horizontal and vertical axes to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences (called variables).
But how? Well, linear means: "arranged in or extending along a straight or nearly straight line." Which if you didn't notice.. All the points on the graph, make up a generally straight line.
"No association" means there is no line or association with any of the points. So, you'd pick that if the points were all over the graph in no order, line or combination; which isn't the case.
"Negative association" is when the top of the points come from the left of the graph lowering into the right. While Positive association would be from right to left. So, it couldn't be choice "Negative Association" since it's coming from right to the left of the graph.
"The point (2, 14) is an outlier." If you didn't know, an outlier is one dot out of a whole group. Think of it as if EVERYONE was wearing pink except one; who wore black. It's just the out of placed kind of dot; but it's supposed to be there. When you look at the graph, there is no dot or outlier at point (2,14) so, that's automatically out as well.
Ending with the last choice "The scatter plot shows a linear association." which is not just true but is the only one that'd make since.
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37. a confidence interval for the difference of two population means a) must pool the sample variances. b) may or may not pool the sample variances. c) cannot be used to test for equal population means. d) must have equal sample sizes.
The confidence interval of two populations means a) it must pool the sample variances
A confidence interval provides a range of possible values for the difference between two population means. For example, a 95% confidence level indicates that given 100 random samples from the population, you can expect about 95 samples to yield intervals that include the population difference.
If the confidence interval for the between-groups difference contains zero, it means that if you run the experiment again, it is likely that you will not find a difference between the groups. Two populations from which two independent samples are selected are known to have the same variance.
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A flower hop ha 18 red roe, 27 pink tulip and 36 white gardenia. The florit want to make identical bouquet with no flower left over. Each bouquet mut contain roe, tulip and white gardenia. What i the larget number of bouquet the florit can make?
The largest number of bouquet are 9
What is Highest Common Factor?
The greatest common factor is the biggest whole number shared by the supplied numbers. For example, the common factors of 10 and 20 are 1, 2, 5, and 10, with 10 being the greatest; so, the highest common factor of 10 and 20 is 10.
Solution:
Total Red Roses = 18
Total Tulip = 27
Toal White Gardenia = 36
To find the largest number of bouquet we need to use Highest Common Factor
HCF of (18, 27, 36) = 9
The largest number of bouquet are 9
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Hannah is driving along a highway at a speed of 60 miles per hour. Answer the questions below regarding the relationship between distance and time. The independent variable, x, represents the______________and the dependent variable is the________________, because the______________depends on the_____________. A function relating these variables is R(x)=______. So R(3) = , meaning after 3 _____________________________________________.
Variable, x, represents the independent variable and the dependent variable is the distance, because the distance depends on the time. A function relating these variables is R(x) = 60x. So R(3) = 180 miles, meaning after 3, a distance of 180 miles was covered.
What are dependent and independent variables?The dependent variable is the outcome or result that is being measured or observed, while the independent variable is the factor that is manipulated or changed to see its effect on the dependent variable.
Therefore, we can say that: the independent variable, x, represents the time and the dependent variable is the distance, because the distance depends on the time.
A function relating these variables is R(x) = 60x, representing the distance covered as a function of time at a constant speed of 60 miles per hour.
So, R(3) = 60 * 3 = 180 miles, meaning after 3 hours of driving, Hannah will have covered a distance of 180 miles.
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The independent variable x represents time in hours and the dependent variable R(x) represents distance in miles. The relationship between these variables is expressed by the function R(x) = 60x, signifying the distance (in miles) Hannah would have driven after x hours. For instance, R(3) equals 180, implying that after 3 hours, Hannah would have driven 180 miles.
Explanation:In this context, the independent variable, x, represents the time in hours and the dependent variable, R(x), is the distance in miles, because the distance depends on the time. A function relating these variables is R(x) = 60x. This is because Hannah's speed is 60 miles per hour, so the formula for distance (Rate x Time) becomes 60 times the number of hours (x). So R(3) equals 180, meaning after 3 hours, Hannah would have driven 180 miles.
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At one university, the mean distance commuted to campus by students is 19.0 miles, with a standard deviation of 4.2 miles. Suppose that the commute distances are normally distributed. Complete the following statements. (a) Approximately 95% of the students have commute distances between miles and miles. (b) Approximately 7 miles and 31.6 miles. of the students have commute distances between 6.4
The average commute for 95% of the students is between 19.0 and 4.2 miles.
The average distance is 19 miles.
Therefore, the standard deviation is 4.2 miles.
A) 2.7 = 19 - a(4.2)
where;
a deviates from the mean by a certain number of standard deviations. Thus;
a = (19 - 2.7) ÷ 4.2
a = 3
In a normal distribution, 3 standard deviations from the mean indicate that 95% of the data falls within that range.
B) The data are 2 standard deviations apart from the mean at the 95% confidence level. Thus;
CI = 19 ± 2(4.2)
CI = (18 - 10.2) OR (18 + 10.2)
CI = (7.8, 28.2)
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a flying squirrel jumped from a tree 11 feet in the air at an initial velocity of 9 feet per second
The maximum height reached is 21.125ft
The squirrel was at its highest point when, v=0, which occurred 2.25 seconds after it jumped.
Squirrel reaches the ground in 5.5 seconds.
What is the relation between height and velocity?
We can find velocity if equation of height is given by differentiating the equation with respect to time.
According to the given question:
The squirrel can only have reached its maximum height when its velocity equals zero.
If h=-2t^2+9t-11
Then dh/dT=v=-4t+9
A) Therefore ,at the maximum height, the velocity ,v=0.
That is, 4t=9 , consequently, t=2.25s
Therefore, when t=2.25s
h=-2(2.25)^2 + 9(2.25)-11
The maximum height reached is then h=21.125ft
B) As explained above, the squirrel was at its highest point when, v=0, which occurred 2.25seconds after it jumped.
C) The squirrel reaches the ground when h=0...
0=-2t^2+9t+11
-2t^2-2t+11t+11=0
-2t(t+1)+11(t+1)=0
(-2t+11)(t+1)=0, since t>0 for this problem...
-2t+11=0
-2t=-11
t=5.5 seconds.
Therefore, squirrel reaches the ground in 5.5 seconds.
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5. in a mixture of raisins and dates, the ratio by weight of raisins to dates is 7 to 3. how many pounds of raisins will there be in 7 pounds of this mixture?
The pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
It is given that:
In a mixture of raisins and dates, the ratio by weight of raisins to dates is 7 to 3
Let the common factor be x:
7x = raising
3x = dates
7x + 3x = 7
10x = 7
x = 7/10
7x = 7(7/10)
Raisin = 49/10 pounds
Thus, the pounds of raisins will there be in 7 pounds of this mixture is 49/10 pounds.
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A department store buys 200 shirts at a cost of $1400 and sells them at a selling price of $10 each. Find the percent markup.
The percent markup price is equivalent to 42.86%.
What is a expression? What is a mathematical equation? What is Equation Modelling?
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a department store buys 200 shirts at a cost of $1400 and sells them at a selling price of $10 each
Cost price of 200 shirts = C.P. = $1400
Selling price of 200 shirts = S.P = $(10 x 200) = $2000
Percentage markup = [(2000 - 1400)/1400] x 100 = (600/1400) x 100 = 600/14 = 42.86%.
Therefore, the percent markup price is equivalent to 42.86%.
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Answer: the answer would round up to 43
Step-by-step explanation:
HELP ME ASAP What is the best estimate of the solution to the system?
Answer:
(-3.4,2.7)
Step-by-step explanation:
The reason it's asking for an estimate, is because the intersection point is not on exact integer coordinates.
Start with the x-value of the intersection point. All options contain either -3.4 or -3.7. The x-value of the intersection point is closer to -3 than -4, so -3.4 is a better estimate.
Do the same with the y-value. Since the intersection point is closer to 3 than 2, 2.7 is the best estimate here.
Answer:
Last choice: (-3.4, 2.7)
Step-by-step explanation:
Well, you could actually solve the two line equations and arrive at the answer but that is not the intent of the question.
The solution of the two line equations is the point at which the two lines intersect
At this point the x value is closer to -3 than to -4. So the x value from the choices would be -3.4 rather than -3.7
We can eliminate 1st and 3rd choices
The y value is closer to 3 than it is to 2 so the y-value estimate would be 2.7
Correct choice: (-3.4, 2.7)
I have marked the solution point with an X in the attached image
An electrician charges a rate of $60 per hour plus a per job fee of $25. If
the electrician works on the weekend, he charges an additional 50% of
his hourly rate. Write an expression that represents the total cost for a
weekend job in 2 different ways.
The expression that represents the total cost on weekend job is 25x + 90y.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
Given that,
The hourly charge of the electrician is $60.
And, the job fee is $25.
The additional percent charged on weekend is 50%.
Suppose the number of jobs on weekend is x and the total hour worked is y.
Then, as per the given case, the following expression can be written for the weekend cost as,
25x + 60y + (50% of 60y)
= 25x + 60y + 50/100 × 60y
= 25x + 90y
Hence, the expression for the total cost for a weekend job is given as 25x + 90y.
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A triangle has two sides of lengths 6 and 9. What value could the length of the third side be? check all that apply.
The length of the 3rd side of the given triangle with 6 units and 9 units being the length of the 1st and 2nd side can be:
(B) 4 units
(C) 7 units
(F) 10 units
(E) 12 units
What is a triangle?A triangle is a polygon with three vertices and three sides.
The angles of the triangle are formed by the connection of the three sides end to end at a point.
The triangle's three angles add up to 180 degrees in total.
So, knowing that the third side of a triangle must be longer than the sum of the first two sides and shorter than the difference between the first two sides allows us to obtain:
x > (9-6) so x > 3 and x < (9+6) so x < 15
Based on these findings, the third side length can be chosen from B. 4, C. 7, F. 10, and E. 12.
Therefore, the length of the 3rd side of the given triangle with 6 units and 9 units being the length of the 1st and 2nd side can be:
(B) 4 units
(C) 7 units
(F) 10 units
(E) 12 units
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Complete question:
A triangle has two sides of lengths 6 and 9. What value could the length of the third side be? Check all that apply
A.15
B.4
C.7
D.2
E.12
F.10
throw two six-sided dice, one is fair and the other is unfair with probabilities given as Face : 1 2 3 4 5 6 Pobability : 1/9 1/9 1/9 1/9 3/9 2/9 The unfair die look the same as the fair die. Let X and Y be the number observed from the fair unfair dice, respectively. A)Find the joint distribution of X and Y
The joint distribution of X and Y probability is 1/6.
What is probability?
Probability is that the branch of arithmetic regarding numerical descriptions of however possible an occasion is to occur, or however possible it's that a proposition is true.
Main body:
Two dice are thrown S = { (i,j) / i, j =1:6}
a) X : Number observed from the fair die.
Y : Number observed from the unfair die.
P(X=1, Y=1) = 1/6 * 1/9 =1/54
Similarly we can obtained remaining probabilities.
P(X=2, Y=2 ) = 1/6 * 1/9 =1/54
P(X=3, Y=3 ) = 1/6 * 1/9 =1/54
P(X=4, Y=4 ) = 1/6 * 1/9 =1/54
P(X=5, Y=5 ) = 1/6 * 3/9 =3/54 = 1/18
P(X=6, Y=6 ) = 1/6 * 2/9 =2/54 = 1/27
the joint distribution of X and Y is =
⇒P(X=1, Y=1) = 1/6 * 1/9 =1/54 + P(X=2, Y=2 )+ P(X=3, Y=3 ) + P(X=4, Y=4)+
P(X=5, Y=5 ) +P(X=6, Y=6 )
⇒1/54 +1/54+1/54+1/54 +3/54+2/54
⇒ 9/54
⇒1/6
Hence the joint distribution of X and Y probability is 1/6.
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Aiko is enclosing a new rectangular flower garden with a rabbit garden fence. She has 40 feet of fencing.
A quadratic function in standard form that represents each area as a function of the width is; A = -x² + 20
How to solve quadratic word problems?We are told that she is enclosing a new garden and has 40 ft of fencing.
Now, let the two sides be labelled x and y.
We know that area of a rectangle is;
A = length * width
Thus;
A = xy
Now, since she has 40 ft of fencing, then it means that;
y = 0.5(40) - x
y = 20 - x
Thus, the area expressed in quadratic function formula is;
A = x(20 - x)
A = 20x - x²
A = -x² + 20
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Complete question is;
Write a quadratic function in standard form that represents each area as a function of the width.
Remember to defi ne your variables
Solve.
−5/6 = − 1/4 − 7/10 x
Enter your answer as a fraction in simplest form in the box.
x =
Answer:
-5/6=-1/4-7/10 x /×60
60×(-5/6)=60×(-1/4)+60(-7/10 x)
-50=-15-42 x
-50+15=-42 x
-35=-42 x
35=42 x
x=35/42
x=5/6
problem 1. monthly sales are independent normal random variables with mean 120 and standard deviation 5. (a) find the probability that exactly 4 of the next 6 months have sales greater than 120. (b) find the probability that the total of the sales in the next 4 months is greater than 500.
Probability - The answer to the problem is P(Y = 4) = 3/32
What is Probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Solution:
Mean = 120
Standard Deviation = 5
Z = (X - Mean)/Standard Deviation
Z = 1/2
(i) P(Y = 4) = 6/4 * (1/2)^2 * (1-1/2)^6-4
P(Y = 4) = 3/2 * 1/4 * 1/4
P(Y = 4) = 3/32
(ii)P(X > 500) = 1 - P(X ≤ 500)
= 1 - Φ(500; 480, 10)
= 1 - 0.9772
= 0.0228
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assume that x and y are independent. what are the expected value and the standard deviation of the points per game for the player?
The expected value and the standard deviation of the points per game for the player is -6.5 and 65.43 respectively.
Given:
In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played.
From the given table:
E ( X ) = 9.5 * 5 points
= 47.5
E ( Y ) = 5.4 * - 10
= -54
E ( X + Y ) = 47.5 + ( -54 )
= 47.5 - 54
= -6.5
SD ( X ) = 12.5 * 5
= 64.5
SD ( Y ) = - 11
SD ( X + Y ) = [tex]\sqrt{64.5^2 + (-11)^2}[/tex]
= 65.43
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Full question:
Is in the image uploaded.
Sketch the vector field F. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) F(x, y, z) = j - i At (-2, -2, -2) the vector is At (-2, -2, 2) the vector is At (-2, 2, -2) the vector is At (-2, 2, 2) the vector is At (2, -2, -2) the vector is At (2, -2, 2) the vector is At (2, 2, -2) the vector is At (2, 2, 2) the vector is
The sketching of the vector field is attached herewith.
Since we know the formula for the vector field is :
F(x, y, z) = -yi+ xj = xj -yi, where x and y are the magnitude and i and j are the unit vectors for the x and y - axis .Since we the points we are given with are:(-2, -2, -2) ,(-2, -2, 2) ,(-2, 2, -2),(-2, 2, 2),(2, -2, -2) ,(2, -2, 2),(2, 2, -2) , (2, 2, 2). So the filed vectors for individual points will be just substituting the magnitude of the individual axis :
F(-2, -2, -2) = -2j +2i
F(-2, -2, 2) = -2j +2i
F(-2, 2, -2) = -2j -2i
F(-2, 2, 2) = 2j +2i
F(2, -2, -2) = -2j-2i
F(2, -2, 2) = -2j -2i
F(2, 2, -2) = 2j -2i
F(2, 2, 2) = 2j -2i
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exercise 3.1.8: find example functions f and g such that the limit of neither f (x) nor g(x) exists as x!0, but such that the limit of f (x) g(x) exists as x!0.
the limit of f (x) g(x) exists as x!0 is exist.
functions f and g such that the limit of neither f (x) nor g(x) exists as x!0.function existance:-what is function existance ?
The EXISTS function returns a Boolean value to indicate whether a list contains at least one element.
let,
f(x) = 1 at x=Q
also, f(x) = -1 at x=Q'
now, g(x) = -1 at x = Q
also, g(x) = 1 at x = Q'
Here,
[tex]\lim_{n \to \infty} f(x)[/tex] and [tex]\lim_{n \to \infty} g(x)[/tex] does not exist.
but, f(x) + g(x) = (f+g)(x) = 0 at x = Q and also at x = Q'
⇒ (f+g)(x) = 0 ∀ x∈IR
⇒ [tex]\lim_{n \to \infty} (f+g)(x)[/tex] = 0 exist.
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