the polynomial will be 2x² + 11x+6, with degree less than 3 and be the subspace.
What is vector space?
A collection of vectors collected collectively and multiplied ("scaled") by scalars forms a vector space, also known as a linear space. Real numbers are typically thought of as scalars. Nevertheless, there aren't many instances of scalar multiplication with vector spaces using rational, complex, etc. numbers. Axioms and other preconditions must be met by the vector addition and scalar multiplication techniques. A space made up of vectors is referred to as a vector space when the addition of vectors is governed by the associative and commutative law and when vectors are multiplied by scalars is governed by the associative and distributive process.
W = span (9x-4-2x²,5+x+2x²)
Now, a(9x42x²)+b(5+x+2x²) = 0
⇒(9a+b)x+(2b-2a)x² + (5b-4a) = 0
⇒9a+b= 0; 2b2a = 0; 5b-4a=0
a = b =0
p(x)=(9x-4-2x²) + 2(5+x+2x²) = 9x-4-2x² + 10 + 2x + 4x² = 2x² + 11x+6
Hence the polynomial will be 2x² + 11x+6.
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Which system of linear equations has a solution of (1, –1)? y1 and y2 y1 and y3 y2 and y3 y2 and y4
The system of linear equations which has a solution of (1,-10) is y2 and y4
What are the 3 types of systems of a linear equation?Dependent: There are countless possible solutions to the system. The same lines are depicted on the equation graphs.
Independent: There is only one solution to the problem. The equations' graphs come together at a single point.
Inconsistent: There is no fix for the system.
What are the 3 solutions of systems of linear equation?There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method
line y2 cross line y4 at (1,-1)
Hence the solution is y2 and y4
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Given the following piecewise function,
f(3) =
f(8) =
f(-1) =
Answer:
f(3) = 5
f(8) = 3
f(-1) = 0
Step-by-step explanation:
Just plug in the number from the parentheses into the inequalities and whichever makes the inequality true plug into that equation so for example f(3) = ?
first plug 3 into the inequalities: 3 ≤ 0, 0 < 3 ≤ 5, 3 > 5
then find the one that's true which is: 0 < 3 ≤ 5
then plug into the equation that corresponds to that inequality: 2(3) - 1 → 6 - 1 = 5
write a paragraph explaining any similarities and differences for series solutions about ordinary points and series solutions about singular points.
Ordinary points: Point an is a regular point whenever functions p1(x) having p0(x) are logical at x = a.
Singular points: There are two types of singular points: regular and irregular.
Define the term series solutions for ordinary points?All those other points are common points except for the singular point x0=0.Every point is a regular point if P0 is a nonzero constant, as in Airy's equation, y″−xy=0. P1/P0 and P2/P0 are continuous at every point x0 that is not a zero of P0 for polynomials are continuous everywhere.Whenever functions p1(x) with p0(x) are analytical at x = a, point an is an ordinary point.
Define the term series solutions for singular points?Use the steps below to get a series solution centered on a regular solitary point x0. enter ∞ n=0 cn(x − x0)n+rinto the formula.
Since functions p1(x) with p0(x) are analytical at x = a, point an is an ordinary point. If p1(x) has a pole up to receive 1 at x = a and p0 has a pole with order up to 2 at x = a, then point an is a regular unique point. Point A is just an irregular singular point if left untreated.To know more about the singular point, here
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which could be the sides of a right triangle? a 2.5 cm, 6.5 cm, 6 cm b 2 cm, 2 cm, 5 cm c 1.5 cm, 2.5 cm, 4 cm d 2 cm, 3 cm, 5 cm
The option that could be the sides of a Right Triangle is 2.5 cm, 6.5 cm, 6 cm , the correct option is (a) .
In the question ,
it is given that ,
four options are given that have the three sides of the triangle ,
we have to select the sides that forms a right triangle .
If the sides form a right triangle , then
square of the longest side is equal to square of the other two sides .
In option (a) the sides are given as 2.5 cm, 6.5 cm, 6 cm .
So ,
(6.5)² = 6² + (2.5)²
42.25 = 42.25
Since LHS = RHS ,
So , Yes , the sides given in option (a) forms a right triangle .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
Which could be the sides of a right triangle ?
(a) 2.5 cm, 6.5 cm, 6 cm
(b) 2 cm, 2 cm, 5 cm
(c) 1.5 cm, 2.5 cm, 4 cm
(d) 2 cm, 3 cm, 5 cm
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let x represent the full length of a certain species of newt. assume that x has a normal probability distribution with mean 110.6 inches and standard deviation 4.9 inches. you intend to measure a random sample of n
If x represents the full length of a certain species of newts then, the mean of the sampling distribution and standard deviation are 216, and 0.31 respectively.
Central Limit Theorem for mean: When a random sample of size n is taken from a population with a mean and standard deviation, the sample mean approaches the normal distribution with mean and standard deviation σ/sqrt (n) as the sample size increases.
Sampling distribution of the sample mean:
using, Central Limit Theorem, the mean of the sampling distribution is μ_{x-bar} = 216.
The standard deviation of the population is σ = 3.1 and the sample size is n =103, people
The standard deviation σ/√n= 3.1/√103 =0.31.
As a result, the sample mean for the 103 sample size, following normal distribution has a mean of μ_{x-bar} = 216 and a standard error of μ_{x-bar} = 0.31.
x-bar ≈ N (216, 0.31)
μ_{x-bar} = 216
σ_{x-bar} =0.31
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(complete question)
Let X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with a mean of 110.6 inches and a standard deviation of 4.9 inches. You intend to measure a random sample of n = 103. find the mean of the sampling distribution and standard deviation.
Which of the following binary operations are closed? a. subtraction of positive integers b. division of nonzero integers c. function composition of polynomials with real coefficients d. multiplication of 2×2 matrices with integer entries ​
The goal is to determine whether or not the following binary operations are closed.
A. Subtraction of positive integers: Under normal substation operation, a set of positive integers is not near. Since 1∈Ζ⁺ and 2∈Ζ⁺ but (2-1) = ₋1∉Z⁺.
B. A division of nonzero integers: Non-zero integer set Z/{0} is not closed under the operation. Since 1∈Z/{0} and 2∈ Z/{0} but 1/2 ∉ Z/{0}.
C. Function composition of polynomials with real coefficients: The set of polynomials with real coefficients is closed when using the typical binary operator. Use the obvious conclusion that a polynomial is a combination of two polynomials [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since every polynomial coefficient is real, every polynomial's composition will also have real coefficients.
D. The multiplication of 2×2 matrices with integer entries: Under the action of standard matrix multiplication Μ₂ₓ₂ (Z), the collection of matrices with integer elements, is close.
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In the first week of July, a record 1,060 people went to the local swimming pool. In the second week,105 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 199 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the pool over these four weeks is 15%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
The number of people by the fourth week will be:
= 1060 - 105 + 145 - 199
= 901
The percentage decrease will be:
= (1060 - 901) / 1060 × 100
= 159/1060 × 100
= 15%
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Marta buys x candles and y books at a store.
• Each candle costs $6, and each book costs $14.
• She spends no more than $65.
• She buys more than 8 items total.
Create two inequalities using x and y to model the situation.
The two inequalities that models the situation are as follows:
6x + 14y ≤ 65
x + y > 8
How to use inequalities to model a situation?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Marta buys x candles and y books at a store.
Each candle costs $6, and each book costs $14.She spends no more than $65.She buys more than 8 items totalTherefore,
x = number of candlesy = number of booksHence, the inequalities are as follows:
6x + 14y ≤ 65
x + y > 8
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A faucet is used to add water to a large bottl that already contained some water. After 25 ounces of water. After it has been filling for 11 seconds, the gauge indicates the bottle contains 60 ounces of water. Let y be the amount of water in the bottle x t was turned on write a linear equation that models the amount of water in the bottle in terms of x. Oa. Y--5? 45 1 121 o d. Y-5x 49.
We insert m and c values inside the slope-intercept form to get a linear equation that expresses the volume of water in the bottle in terms of t: w = 5t + 5.
Explain Slope-Intercept Form of a Line?A line's equation can be expressed in standard form, slope-intercept form, and point-slope form.The slope-intercept form of the line passing through the points; (x1, y1) and (x2, y2) is; y = mx + cWhere x and y are really the coordinate points, c is really the y-intercept, and m is the slope of the line; m = (y2 - y1)/(x2 -x1).Let w be the quantity of water in the bottle after turning on the faucet.
The following points can be drawn from the provided statement:
(t1, w1) = (4, 25)
(t2, w2) = (11, 60)
The equation of a line's slope-intercept form is:
w = mt + c
Put the values to find slope m.
m = (w2 - w1)/(t2 -t1)
m = 60 - 25 / 11 - 4
m = 5
Put m = 5, t = 4 and w = 2 in equation of the line;
w = mt + c
25 = 5(4) + c
c = 5
We insert m and c values inside the slope-intercept form to get a linear equation that expresses the volume of water in the bottle in terms of t:
w = 5t + 5
Thus, the linear equation that models the amount of water in the bottle is w = 5t + 5.
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S
How could you show QR SR?
O A.
OB.
O C.
OD.
Use SAS to show triangle PRQ is congruent to triangle SRP
Use SAS to show triangle PRQ is congruent to triangle PRS
Use AAS to show triangle PRQ is congruent to triangle PRS
Use ASA to show triangle PRQ is congruent to triangle PRS
We prove that QR≅SR, using SAS to show triangle PRQ is congruent to triangle PRS. So option B is correct.
In the given question;
Given: PR bisects ∠QPS. PQ=12 units, and PS=12 units.
Prove: QR≅SR
We have to find how we prove QR≅SR.
As we can see that;
PQ = PS
Since PR is bisector.
So PR is common in both triangles PRQ and PRS.
PR=PR
Since PR is bisector.
So ∠PRQ=∠PRS
As we know that if two sides and one angle are congruent, then using the Side-Angle-Side (SAS) Theorem, the both triangle is congruent.
So ∠PRQ≅∠PRS
So QR≅SR
Hence, we prove that QR≅SR, using SAS to show triangle PRQ is congruent to triangle PRS. So option B is correct.
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HELP FAST WILL GIVE BRAINIEST
Answer:
first this is English
providential
slow congealed
innovative, effectual
more easy to
Give a big-o estimate for the number additions used in this segment of an algorithm. T := 0 for i := 1 to n for j := 1 to n t := t + i + j.
The big oh notation for the given algorithm that is T := 0 for i := 1 to n for j := 1 to n t := t + i + j will be O(n).
What is big oh notation?Big O notation is a type of mathematical notation that expresses how a function limits itself when the argument goes to zero or infinity. Big O Notation is a technique for expressing how time-consuming an algorithm is. As the input increases, it calculates how long it will take to perform an algorithm. In other words, it determines an algorithm's worst-case time complexity. The maximum runtime of an algorithm is expressed using the Big O Notation in data structures.
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PLEASE HELP ME WITH THIS QUESTION!!!
QUESTION ATTACHED BELLOW
THANKS IN ADVANCE!
Patrice is a star player for the UNC women's basketball team. She has injured her ankle and it is doubtful that she will be able to play. If she can play, the coach estimates they will score 78 points. If she is not able to play, the coach estimates they will score 62 points. The team doctor estimates there is a 60-40 chance she will play. Determine the number of points the team can expect to score. Play Not Play P(x) Outcome Expected Value:
If she can play, the coach estimates they will score 78 points. If she is not able to play, the coach estimates they will score 62 points. The team doctor estimates there is a 60-40 chance she will play.
Therefore, P(x) Outcome Expected Value: 71.6 %
Given in the question:
If she is playing, estimate score is 78 points.
If she is not playing, estimated score is 62 points.
chances : 60% to 40%
Therefore, the expected outcome value is :
P(X) = 78 × 60% + 62× 40%
= 71.6%
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the board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 5.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 41 randomly selected calls. the mean wait time was calculated to be 5.61 minutes. assuming the population standard deviation is 2.50 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 5.00 minutes with a 98% level of confidence?
In this case, the standard error would be standard error = 2.50 / sqrt(41) = 0.342 and the z-score would be z = (5.61 - 5.00) / 0.342 = 1.71
What is the z-score value?A z-score value is the numerical measured value of the relationship of a value to the mean of a group of values and it is measured in the terms of standard deviations from mean value.
What is the formula to measured the z-score value?The z-score is measured by formula z=(x- μ)/ a where x is the raw score, μ is the population mean and a is the population standard deviation. So to calculate z-score, we subtract the population mean from the raw score and divide it by the population standard deviation.
standard error = population standard deviation / sqrt(sample size)
standard error = 2.50 / sqrt(41) = 0.342
Next, you would need to calculate the z-score for the observed mean wait time of 5.61 minutes.
z = (observed mean - population mean) / standard error
z = (5.61 - 5.00) / 0.342
z= 1.71
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Write a linear function g with the values g(2) = 3 and g(6) = 5
Answer:
g(x)=1/2x+2
Step-by-step explanation:
the coordinates provided here are (2,3) and (6,5)
slope intercept form is g(x)=mx+b
m is slope and b is y intercept
We use slope formula to find slope y2-y1/x2-x1
5-3/6-2
2/4
1/2
Now we can find b by putting the values in
g(x)=1/2x+b
5=1/2(6)+b
5=3+b
-3 -3
2=b
g(x)=1/2x+2
Hopes this helps please mark brainliest
Christopher says that whenever you multiply a whole number by a fraction the product is either greater or less than the whole number. Do you agree with Christopher? Why or why not. If not provide an example.
Christopher's statement "whenever you multiply a whole number by a fraction the product is either greater or less than the whole number" is correct.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The statement made by Christopher is correct, this is because a fraction is always either greater or lesser than 1. And multiplying a fraction to a whole number will give result either greater or less than the whole number, depending upon the type of fraction it is.
If the fraction is a proper fraction, than the result will be less than the whole number.If the fraction is a improper fraction, than the result will be greater than the whole number.For example let's take the number 100,
Let's take a proper fraction, 2/5. Therefore, the result will be,
100 × (2/5) = 40
Let's take an improper fraction, 7/5. Therefore, the result will be,
100 × (7/5) = 140
Hence, Christopher's statement is correct.
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a researcher is interested in whether or not a significant trend exists regarding the popularity of certain music played at restaurants. a random sample of 50 customers from each of three restaurants is selected. the customers are asked to indicate which of three music types: country, jazz, and classical they preferred. the results are given for each restaurant by music category. do the results deviate significantly from what would be expected due to chance?
No the results did not deviate significantly from what would be expected due to chance.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
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FILL IN THE BLANK. In a simple regression analysis (where y is a dependent and x an independent variable), if the slope is positive, then it must be true that _____.
If the slope of a basic regression analysis—in which y is the dependent variable and x is the independent variable—is positive, then there must be a positive correlation between x and y.
What is regression analysis?Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. A statistical technique that demonstrates the link between two or more variables is regression analysis. The approach examines the connection between a dependent variable and independent variables, often represented in a graph. A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.
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Solve the equation. Check for extraneous solutions. 9 |9−8x|=2x+3 please show steps
Answer:
x = 0.6 , x = 2
Step-by-step explanation:
the absolute value function always gives a positive value, that is
| - a | = | a | = a
the expression inside the bars, however , can be positive or negative, so
9 - 8x = 2x +3 ( subtract 2x from both sides )
9 - 10x = 3 ( subtract 9 from both sides )
- 10x = - 6 ( divide both sides by - 10 )
x = 0.6
Or
- (9 - 8x) = 2x + 3
- 9 + 8x = 2x + 3 ( subtract 2x from both sides )
- 9 + 6x = 3 (add 9 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
As a check
substitute these values into the equation and if both sides are equal then they are the solutions.
x = 0.6
left side = | 9 - 8(0.6) | = | 9 - 4.8 | = | 4.2 | = 4.2
right side = 2(0.6) + 3 = 1.2 + 3 = 4.2= left side
-------------------------------------------------------
x = 2
left side = | 9 - 8(2) | = | 9 - 16 | = | - 7 | = 7
right side = 2(2) + 3 = 4 + 3 = 7 = left side
the solutions to the equation are x = 0.6 and x = 2
there are unknown number of oranges in a bag. seven oranges in the bag are stale. now you need to pick two oranges out of the bag. the probability to pick two stale oranges is 2/21. what is the total number of the orange in the bag?
The total number of oranges present in the bag was 21.
Explain the term probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages extending from 0% through 100% can be used to describe probabilities.For the stated question.
Let the total number of oranges in the bag be 'x'.
Total stale oranges = 7.
Thus,
Probability (first orange is stale) = Total stale oranges/ Total oranges.
Probability (first orange is stale) = 7/x
Probability (second orange is stale) = 6/(x - 1).
But, probability to pick two stale oranges is 2/21
7/x . 6/(x - 1) = 2/21
On solving,
x ² - x - 441 = 0
x = 21
Thus, the total number of oranges present in the bag was 21.
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the chi-square goodness of fit test assesses whether the observed counts of a categorical variable .
The chi-square goodness of fit test assesses whether the observed counts of a categorical variable follow a hypothetical proportion population distribution.
The chi-square fit test of goodness assesses whether the proportions of a category or individual outcome in a sample follow a hypothetical proportion population distribution.
In other words, if you take a random sample, the observed proportions follow the values suggested by theory.
Analysts often use the goodness-of-fit chi-square test to determine whether the proportions of categorical results are equal. Alternatively, the analyst can specify the proportions to include in the test.
Alternatively, this test can assess whether observed results follow a discrete probability distribution, for example, Poisson distribution.
As a hypothesis test, the chi-square test of goodness can be used to infer the entire population based on a sample.
Thus, it is true that the the chi-square goodness of fit test assesses whether the observed counts of a categorical variable follow a hypothetical proportion population distribution.
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a subcommittee of the citys planning dept suggests a different plan for the walkways in a city's new park. in the revised blueprint shown below, the walkways are shown in blue and parallel lines indicated by red arrowheads.The right angles of the rectangular park are marked, and the other two angle measures are given in red, find the measure of each numbered angle in the blueprint
The angles are ∠1=42°
∠2=48°
∠3=90°
∠4=42°
∠5=48°
∠6=132°
∠7=90°
∠8=48°
∠9=90°
∠10=132°
∠11=90°
∠12=90°
∠13=48°
∠14=48°
∠15=90°
∠16=90°
∠17=90°
∠18=48°
∠19=48°
∠20=90°
∠21=48°
∠22=42°
What is an angle?In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. Angles formed by two rays are located in the plane that contains the rays.
An angle in Plane Geometry is a figure formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angulus," which means "corner." The two rays are referred to as the sides of an angle, while the common endpoint is referred to as the vertex.
In Euclidean geometry, an angle is the figure formed by two rays known as the sides.
∠1=42°
∠1+∠2=90°
∠2=48°
In ΔABF,
∠2+∠3+42°=180°
48°+∠3+42°=180°
∠3=90°
∠4=42°
Now, ∠3+∠4+∠5=180°
90°+42°+∠5=180°
∠5=48°
∠5+∠6=180°
∠6=132°
∠7=90°
∠8=48°
∠7+∠9=180°
∠9=90°
∠10=132°
∠11+∠3=180°
∠11=90°
∠11+∠12=180°
∠12=90°
∠16=∠11=90°
∠12=15=∠90°
∠13=48°
∠14=48°
∠17=90°
∠1+∠17+∠18=180°
42°+90°+∠18=180°
∠18=48°
∠19=48°
Now, ∠19+∠20+42°=180°
∠20=90°
∠21=48°
Now, ∠21+∠22=90°
∠22=42°
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Given log_5 2≈0.4308 and log_527≈2.0478, evaluate the expressions. Note: you must use the given values and not values obtained from a calculator for those logarithms.
log_5 3
log_5 (27/50)
The solutions to the logarithm equations are;
1) Log₅3 = 0.6826
2) Log₅(27/50) = -0.383
How to solve logarithm Equations?
There are different rules of logarithm such as;
Product rule which is; Log a + Log b = Log (ab)
Quotient rule which is; Log a - Log b = Log(a/b)
Power rule which is; Log aˣ = x log a
We are given that;
Log₅2 = 0.4308
Log₅27 = 2.0478
We know that 27 = 3³. Thus;
Log₅27 = Log₅3³
Using power rule, we have;
Log₅3³ = 3Log₅3
Thus;
Log₅27 = 3Log₅3 = 2.0478
1) We want to solve Log₅3
We have;
3Log₅3 = 2.0478
Thus;
Log₅3 = 2.0478/3 = 0.6826
2) Log₅(27/50)
Using quotient rule, we have;
Log₅27 - Log₅50
This can also be expressed as;
Log₅3³ - Log₅ (25 * 2)
= 3Log₅3 - [2Log₅5 + Log₅2]
= 2.0478 - 2 - 0.4308
= -0.383
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The Terra family sold its heavily wooded land to
a lumber company for $350,000 at a rate of $700
dollars per acre. If the property averages 8 trees
per acre, which of the following is closest to the
number of trees on the land?
A.
63
B. 500
C. 3,500
D. 4,000
E. 5,608
Answer:
B
Step-by-step explanation: It is very simple. All you have to do is to do 350 000 divided by 700 which gives you 500. That's your answer!
I do not know
how to do fractions please help
Answer:
should be the first one because 12 is the common factor between the two of them(had to be 20 characters long so i could answer your question)
A local charity has put together 20 care packages for
people. Each package contains $15 worth of goodies
and $2.50 per food satchel added to it. If the charity
spent $800 on the care packages how many food
satchels were in each package? Write and solve an
equation for this scenario.
Answer:
The equation is 15x + 2.50y = 800, where x is the number of care packages and y is the number of food satchels. Solving for y, we get y = 32. Therefore, each package contained 32 food satchels.
Step-by-step explanation:
What is the average rate of change of the functionf(x)=20(14)x from x = 1 to x = 2? enter your answer, as a decimal, in the box. Do not round your answer.
The average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75 when the function f(x)=20(1/4)ˣ.
Given that,
We have to find what is the function f(x)=20(1/4)ˣ average rate of change from x = 1 to x = 2.
We know that,
Average rate of change(A(x)) of f(x) over a interval [a,b] is given by:
A(x)=(f(b)-f(a))/b-a
We get the function:
f(x)=20(1/4)ˣ
Now, the average rate of change from x = 1 to x= 2
At x = 1
Then;
f(1)=20(1/4)¹=5
At x = 2
Then;
f(2)=20(1/4)²=1.25
Substitute these in above formula we have;
A(x)=f(2)-f(1)/2-1=-3.75
Therefore, The average rate of change of the function f(x) from x = 1 to x = 2 is, -3.75 when the function f(x)=20(1/4)ˣ.
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let x denote the number of canon slr cameras sold during a particular week by a certain store. the pmf of x is x 0 1 2 3 4 px(x) 0.1 0.2 0.3 0.25 0.15
P(X = 4, Y = 2) = 0.055131
P(X = Y) = 0.35607
From the information given:
X represent no of Canon SLR
The PMF is given as:
X : 0 1 2 3 4
p(x) : 0.1 0.2 0.3 0.25 0.15
p = P(customers that purchase the camera & also purchase an extended warranty.
As a result, the conditional distribution Y provided X approaches a Binomial distribution with n = x and p = 0.55 as the parameter.
[tex]\frac{Y}{X}[/tex] ~ Bin ( n= x , p =0.55) y
= 0.1 ........ x and X = 0,1,2,3,4.
The condition probabilities Y given X is:
[tex]P (\frac{Y = 0}{X = 0} ) =1[/tex]
[tex]P (\frac{Y = 0}{X = 1} ) = 0.45 and P (\frac{Y = 1}{X = 1} ) =0.55[/tex]
[tex]P (\frac{Y = 0}{X = 2} ) = 0.2025 and P (\frac{Y = 1}{X = 2} ) =0.495, P (\frac{Y = 2}{X = 2} ) =0.3025[/tex]
[tex]P (\frac{Y = 0}{X = 3} ) = 0.091125 and P (\frac{Y = 1}{X = 3} ) =0.334125, \\P (\frac{Y = 2}{X = 3} ) =0.408375 and P (\frac{Y = 3}{X = 3} ) = 0.166375[/tex]
[tex]P (\frac{Y = 0}{X = 4} ) = 0.0.041006 and P (\frac{Y = 1}{X = 4} ) =0.0.200475, P (\frac{Y = 2}{X = 3} ) =0.367538[/tex]
[tex]P (\frac{Y = 3}{X = 4} ) = 0.299475 and P (\frac{Y = 4}{X = 4} ) =0.091506[/tex]
Now, the joint P.D (probability Dist.) of X & Y is expressed as:
[tex]P (\frac{Y = y}{X = x} ) = P (\frac{Y = y. X = x}{X = x} )[/tex]
[tex]P( X = x , Y = y) = P(\frac{Y = y}{X =x} ) * P(X =x)[/tex]
The Joint P.D is;
Y Total
0 1 2 3 4
X 0 0.1 0 0 0 0 0.1
1 0.09 0.11 0 0 0 0.2
2 0.06075 0.1485 0.09075 0 0 0.3
3 0.022781 0.083531 0.102094 0.041594 0 0.25
4 0.006151 0.030071 0.055131 0.044921 0.013726 0.15
Total 0.279682 0.372103 0.247974 0.086515 0.013726 1
(a)
P(X=4,Y=2)
From the table above:
P(X=4,Y=2)
= 0.055131
(b)
P(X= Y)
= (P = 0 , Y = 0) + P( X =1, Y =1) + P( X=2, Y=2) + P(X=3,Y=3) + P(X=4,Y=4)
= 0.1 + 0.11 + 0.09075 + 0.041594 + 0.013726
= 0.35607
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in a random sample of 38 restaurants it was found that the mean number of employees was 12.6 with a standard deviation of 2.4 employees. find the critical value used to test the claim that the mean number of restaurant employees is less than 15 at the 1% significance level.
Critical value used to test the claim that the mean number of restaurant employees is less than 15 at the 1% significance level is - 2.431
What is standard Deviation ?The square root of the variance is used to calculate the standard deviation, a statistic that gauges a dataset's dispersion from its mean. The variation from the mean of each data point is used to determine the standard deviation, which is equal to the square root of variance.
What is mean ?It is basically the average of the given numbers.
The given data is
Sample Size = n = 38
Sample mean = X = 12.6
Sample Standard deviation = S = 2.4
= n - 1 = 38 - 1 = 37
μ₀ = μ ≥ 15
μ₁ = μ < 15 ( left tailed )
d = 0.01
Hence, Critical value = - 2,431
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