The joint probability function for X and Y is legitimate because the sum of all probabilities is equal to 1 and the probabilities are non-negative. Each point in the domain has a corresponding probability.b. p(1,2) means the probability of X=1 and Y=2. p_x(3) = 0.1 + 0.05 = 0.15.
a. Probability function is considered legitimate when the sum of all the probabilities is 1, the probabilities are non-negative and each point in the domain must have a corresponding probability. Here, the joint probability function for X and Y is legitimate because the sum of all probabilities is equal to 1 and the probabilities are non-negative. Each point in the domain has a corresponding probability.b. p(1,2) means the probability of X=1 and Y=2. We can see from the table that p(1,2) = 0.04.c. P(X<1, Y≥2) means the probability of X being less than 1 and Y being greater than or equal to 2. We can find the probabilities by adding up all the probabilities in the cells that meet this condition. From the table, we can see that the cells (0,2) and (0,3) meet this condition. Therefore, P(X<1, Y≥2) = 0.01 + 0.01 = 0.02.d. We need to find p_x(3), which means the probability of X=3. We can find this by adding up all the probabilities where X=3. From the table, we can see that the cells (3,1) and (3,2) meet this condition. Therefore, p_x(3) = 0.1 + 0.05 = 0.15.
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A company makes steel rods shaped like cylinders. Each rod has a diameter of 8 centimeters and a height of 20 centimeters. How much steel will the company need to make 146 rods? For your calculations, do not round any intermediate steps, and use the 3.141592654 button on a calculator. Round your answer to the nearest hundredth.
Step-by-step explanation:
The volume of each steel rod can be calculated using the formula for the volume of a cylinder:
V = πr^2h
where r is the radius of the cylinder (half the diameter), and h is the height.
In this case, the diameter is 8 cm, so the radius is 4 cm. The height is 20 cm. Therefore, the volume of each steel rod is:
V = π(4 cm)^2(20 cm) = 320π cm^3
To find out how much steel is needed to make 146 rods, we can multiply the volume of one rod by the number of rods:
Total volume = 146 rods x 320π cm^3/rod
Total volume = 46,720π cm^3
We can use a calculator to approximate the value of π to 3.14 and then calculate the total volume:
Total volume ≈ 46,720 x 3.14 cm^3
Total volume ≈ 146,748.8 cm^3
Rounding to the nearest hundredth, the company will need approximately 146,748.8 cubic centimeters of steel to make 146 rods.
Q3 Calculate the surface area of question 3 a)
Answer:
2520 m²
Step-by-step explanation:
You want the surface area of the irregular prism shown.
PerimeterThe perimeter of the base (shaded front face) is the sum of the lengths of the horizontal edges and the lengths of the vertical edges. That sum is ...
2(20 m) +2(20 m) = 80 m
Lateral areaThe lateral area of the prism is the sum of the unshaded rectangle areas. That total area is the product of the perimeter of the base and the distance between bases:
LA = Ph = (80 m)(25 m) = 2000 m²
Base areaThe area of each of the two bases can be found several ways. We find the height of the middle step to be (20 m -7 m -6 m) = 7 m, so the bottom step fits nicely into the space not used by the middle step. (This is shown in the attachment.)
That is, the base area can be computed as the area of a rectangle 13 m high and 20 m wide:
Base area = WH = (20 m)(13 m) = 260 m²
Surface areaThe total surface area of the prism is the sum of the lateral area and the area of the two bases:
SA = LA +2·B = (2000 m²) +2(260 m²) = 2520 m²
The surface area of the prism is 2520 square meters.
consider a model in which only industry is used to predict delay. at a level of significance, test for any positive autocorrelation in the data.
In order to test for any positive autocorrelation in the data, you would use the Pearson correlation coefficient. This measures the strength and direction of a linear relationship between two variables. The level of significance that you set depends on the size of your dataset, but generally should be 0.05 or less.
To test for positive autocorrelation, you need to compare the Pearson correlation coefficient with the critical value of the correlation coefficient. The critical value is determined by the level of significance you have set. If the Pearson correlation coefficient is greater than the critical value, then you can conclude that there is a significant positive autocorrelation.
It is important to keep in mind that a positive correlation does not necessarily mean that there is a cause and effect relationship between the two variables. It only means that the two variables move in the same direction.
In conclusion, if the Pearson correlation coefficient is greater than the critical value, then you can conclude that there is a significant positive autocorrelation.
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help would be appreciated
The graph that shows the given transformation is option A.
How to identify the graph of the transformation?We can see the graph of f(x) on the top of the given image, and we want to identify the graph of the transformation f(4x), this will be an horizontal compression of the function.
So we should look for a graph that looks like the first one, but its compresed on the horizontal axis. The vertical axis is not changed, remember that.
The only one that shows that is graph A, so that is the correct option.
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Simplify the following algebraic expression.
The algebraic expression is simplified to 13. Option A
What are algebraic expressions?These are expressions that are made up of terms, variables, constants and coefficients.
They are also made up of arithmetic operations like subtraction, division, multiplication, bracket, and parentheses.
The square root of a number is defined as the factor that when multiplied by itself gives the original number.
The symbol for square root is '√'. The square root of a number is the opposite of squaring a number.
From the information given, we have that;
√169
Now, let's determine the square root
13
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PLEASE HELP ME WITH THIS QUESTIONS!
Answer:
1. 2.5
2. 2.5x=y
3. 15
Who has a better bating average 12 to 15 or 9 to 10
in essence, which of the two fractions is the larger one, well, let's put both with the same denominator by multiplying each other by the other's denominator.
[tex]12:15\qquad 9:10\hspace{5em}\cfrac{12}{15}\qquad \cfrac{9}{10} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{12}{15}\cdot \cfrac{10}{10}\implies \cfrac{120}{150} ~~ \bigotimes\hspace{9em}\cfrac{9}{10}\cdot \cfrac{15}{15}\implies \cfrac{135}{150} ~~ \textit{\LARGE \checkmark}[/tex]
Answer:9/10
Step-by-step explanation:
90% average vs 80% average
three times a number increased by four is less than -62
Answer:
If you want to derive an equation from the question, you answer is:
3*x+4<-62
If you want the solved equation for x, your answer is:
x<-22
(Depending on what your question is)
Step-by-step explanation:
For the first answer, you can represent the unknown number as x. Three times is equivalent to 3 multiply, so it will look like 3*x, or just 3x. Increased by four is just adding four, so your equation will now look like 3x+4. Less than -62 is just 3x+4<-62. To solve future problems, just carefully look at the words. Does it mention divided by? Maybe decreased? Carefully look and analyze the question and plug in the operators, variables, and numbers.
For the second solution, since we've already translated the question to an equation from above, we can solve the equation we've derived, which is 3x+4<-62. Subtract four on both sides. The equation will look like this: 3x+4-4<-62-4. Simplifying, we get 3x<-66. Next, we divide both sides of the equation by 3, and we will get x<-22.
Good luck on your studies!
(I may be young but I know stuff so you can trust me :) )
he sum of two numbers is 38. The smaller number is 14 less than the larger number. What are the numbers?
Answer:
Let's call the larger number "x" and the smaller number "y".
From the problem, we know that:
x + y = 38 (Equation 1)
y = x - 14 (Equation 2)
We can substitute Equation 2 into Equation 1:
x + (x - 14) = 38
2x - 14 = 38
Adding 14 to both sides:
2x = 52
Dividing both sides by 2:
x = 26
Now we can use Equation 2 to find y:
y = x - 14
y = 26 - 14
y = 12
So the two numbers are 26 and 12.
Step-by-step explanation:
Answer:
12 and 26
Step-by-step explanation:
n + b = 38 n < b b = n + 14 n + n + 14 = 38 2n = 24 n = 12 b = 12 + 14 b = 26 Your two numbers are 12 and 26
Simplify radical expression slayer root 192s^2
Answer:
[tex] \sqrt{192 {s}^{2} } = s \sqrt{192} = s \sqrt{64 \times 3} = s \sqrt{64} \sqrt{3} = 8s \sqrt{3} [/tex]
A dessert has been through and yoghurt inside altogether. The mess of the desert is 165 g. The ratio of the mass of the fruit to the mass of the yoghurt is 2:3 what is the mass of the yoghurt? 99g
If The ratio of the mass of the fruit to the mass of the yoghurt is 2:3 the mass of the yogurt is 99 g,
Let's assume the mass of the fruit is 2x and the mass of the yogurt is 3x, where x is a common factor.
According to the problem, the total mess of the desert is 165 g, so we can write an equation:
2x + 3x = 165
Simplifying this equation, we get:
5x = 165
x = 33
Therefore, the mass of the fruit is:
2x = 2(33) = 66 g
And the mass of the yogurt is:
3x = 3(33) = 99 g
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which expressions are equivalent to 7⁴· 9⁸?
Answer 63^(12)
Step-by-step explanation:
7x9=63
8+4=12
have a good day!
Suppose that 40% of voters in Okeechobee county support a proposed property tax. Consider the sampling
distribution of the sample proportion of supporters with sample size n = 135. Determine the mean and
standard deviation of the sampling distribution of p. Round solutions to four decimal places, if necessary.
The mean of the sampling distribution of p is 0.40 and the standard deviation of the sampling distribution of p is 0.0409.
What is standard deviation?Standard deviation is a measure of how spread out the values in a data set are from the mean. It is calculated by taking the square root of the variance of the data set. It is a commonly used measure to assess the variability in a data set.
The mean of the sampling distribution of p is 0.40, which is the same as the proportion of supporters in the population of Okeechobee County. This is due to the fact that the sample proportion estimates the population proportion. The standard deviation of the sampling distribution of p is equal to the square root of the product of p (0.40) and q (1-p, or 0.60) divided by the sample size (135). In this case, the standard deviation of the sampling distribution of p is 0.0409.
The mean and standard deviation of the sampling distribution of p can be used to understand what values of p are likely when samples of size n = 135 are drawn from the population of Okeechobee County. If a sample is drawn from the population, the sample proportion of supporters is likely to be close to 0.40, which is the mean of the sampling distribution of p. Furthermore, most of the sample proportions of supporters are likely to be within two standard deviations (or 0.0818) of the mean. This means that the sample proportion of supporters is likely to be between 0.3182 and 0.4818 when samples of size n = 135 are drawn from the population.
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After making the swim team, Farrah purchased a swimsuit, a swim cap, and a pair of goggles. The swimsuit was twice as much as the goggles, and the swim cap was half the price of the goggles. If the total cost of the items was 59. 50, what was the price of the swimsuit?
Answer:
34$
Step-by-step explanation:
Sarah buys 5 rulers and 4 pens rulers cost 78p pens cost £4. 50
Sarah buys 834/0.7 = 1191.4 pens. Since she cannot buy a fraction of a pen, we round down to get: Sarah buys 1191 pens.
Let's start by setting up the equations for the given information:
Sarah buys x pens and 2 rulers, so the cost of her purchase is:
0.7(12) + 0.65(2) + 0.7x = 0.7(12 + x) + 0.65(2)
Note that we multiply the cost per item (0.7 cents for pens, 0.65 cents for rulers) by the number of items purchased.
Tanya buys 3 more pens than Sarah and no rulers, so the cost of her purchase is:
0.7(x + 3)
The total cost of both purchases is $11.80, or 1180 cents, so we can set up the equation:
0.7(12) + 0.65(2) + 0.7x + 0.7(x + 3) = 1180
Simplifying the equation, we get:
8.4 + 1.3 + 1.4x = 1180 - 2.1
9.7 + 1.4x = 1177.9
1.4x = 1168.2
x = 834
Therefore, Sarah buys 834/0.7 = 1191.4 pens. Since she cannot buy a fraction of a pen, we round down to get: Sarah buys 1191 pens.
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The complete question is :
12 Pens cost 70 cents each and ruler cost 65 cents each. Sarah buys x pens and 2 rulers. Tanya buys 3 more pens than Saruth and no rulers They spend $11.80 in total. Form an equation in x and solve it to find the number of pens sarah buys.
The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
Cοnclusiοn that can be drawn frοm the circle graph is 'Pοp is the preferred music fοr 140 students.'
Cοrrect οptiοn is A.
What is percentage?In math, a percentage is a number οr a ratiο that can be expressed as a fractiοn οf 100. If we need tο calculate the percentage οf a number, divide that number by whοle and multiply by 100. Therefοre, percentage means οne part per hundred.
Given,
Tοtal number οf students = 400
By circle graph five sectiοns labeled rοck 13 percent, hip hοp 25 percent, pοp 35 percent, classical 13 percent, and jazz 14 percent
Number οf students preferring pοp music
= 35%
= (35/100) × 400
= 35 × 4
= 140
Number οf students preferring classical music
= 13%
= (13/100) × 400
= 13 × 4
= 52
Number οf students preferring jazz music
= 14%
= (14/100) × 400
= 14 × 4
= 56
Number οf students οf pοp and classical tοgether = 140 + 52 = 192
Number οf students οf classical and jazz tοgether = 52 + 56 = 108
Hence, the οnly cοnclusiοn that is true is, Pοp is the preferred music fοr 140 students.
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Help please <3 :) Im struggling
The square based pyramid has a surface area of is 224 mm²
Drawing the net of the pyramidGiven that
A square based pyramid
The shapes in the net of a square based pyramid are
1 square 4 trianglesThe shape's net is attached
Calculating the surface area of the netTo determine the surface area, we use
Area = l² + 2hl
Where
l = length of the square base = 8 mm
h = slant height = 10 mm
By substitution, we have
Area = 8² + 2 * 10 * 8
Evaluate
Area = 224
Hence, the surface area is 224 mm²
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David paid $1. 25 per drink and purchased 6 drinks. Use the drop down menus to write an equation for the price, c, of all the drinks. 6 A. X B. Division C. + D. - A. 1. 25 B. 6 C. 7. 50 = c
If David paid $1. 25 per drink and purchased 6 drinks, then the total price of drink is option (C) c =$7.50
To solve this problem, we need to first understand what we are looking for - the total price that David paid for all the drinks he purchased. We know that David purchased 6 drinks and paid $1.25 for each drink.
To find the total price, we can multiply the price per drink by the number of drinks. This gives us:
c = 1.25 x 6
Multiply and Simplifying this equation, we get:
c = $7.50
Therefore, the correct option is (C) c = $7.50
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Sydney went bowling and
had the following scores:
101, 115, 78, 87 and 99.
Find the mean range,
variance, and standard
deviation
The mean score is 96.
The variance is 160.
The standard deviation is approximately 12.65.
To find the mean (average) of the scores, we add them up and divide by the total number of scores:
Mean = (101 + 115 + 78 + 87 + 99) / 5 = 96
So the mean score is 96.
We deduct the lowest score from the highest score to determine the range:
Range = highest score - lowest score = 115 - 78 = 37
So the range is 37.
To find the variance, we need to find the squared difference between each score and the mean, then add up all those squared differences and divide by the number of scores.
The formula for variance is:
Variance = [tex]\frac{\sum(x_i - \bar x)^2}{n}[/tex]
where
Σ represents the sum of,
[tex]x_i[/tex] is the ith score,
n is the number of scores,
[tex]\bar x[/tex] is the mean.
Using the formula, we get:
Variance = [(101 - 96)² + (115 - 96)² + (78 - 96)² + (87 - 96)² + (99 - 96)²] / 5
= (25 + 361 + 324 + 81 + 9) / 5
= 800 / 5
= 160
So the variance is 160.
We take the square root of the variance to calculate the standard deviation:
Standard deviation = √160 ≈ 12.65
So the standard deviation is approximately 12.65.
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PLEASE SHOW WORK!!!!!!!!!
The correct option is ([tex]H) i.e. a² > b².[/tex]
What is an inequality?
In mathematics, an inequality is a statement that one quantity is less than or greater than another quantity. Inequalities are used to compare values and express relationships between them.
For all integers a < 0 and b < 0, the following inequality must be true:
[tex]H. a² > b²[/tex]
This can be proved as follows:
If a and b are both negative, then a² and b² are both positive. Since a < 0 and b < 0, we have a < b or b < a, which implies that[tex]a² > b² or b² > a².[/tex]
If a and b are both negative and equal (i.e., a = b < 0), then a² = b², which implies that a² > b² and b² > a² are both false.
None of the other inequalities (F, G, J, K) must be true for all such a and b. For example:
F. a/b > 1 is not necessarily true, since a and b could both be negative and have the same absolute value (e.g., a = b = -1), in which case a/b = 1.
G. ab > 2 is not necessarily true, since a and b could both be negative and have absolute values less than 2 (e.g., a = b = -1), in which case ab = 1 < 2.
J. [tex]a²b³ > 0 is[/tex] not necessarily true, since a and b could both be negative and have different absolute values (e.g., a = -2 and b = -1), in which case[tex]a²b³ = -8 < 0.[/tex]
K. [tex]a^{4} b² > 0[/tex] is not necessarily true, since a and b could both be negative and have the same absolute value (e.g., a = b = -1), in which case [tex]a^{4} b² = 1 > 0[/tex]. However, if we add the condition that a and b have different absolute values, then K would be true, since [tex]a^{4} b²= (|a|)² |b|² > 0.[/tex]
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What is the equation of the graph below?
On a coordinate plane, a curve crosses the y-axis at y = 1 and then completes one cycle at 360 degrees.
y = sine (x + 90 degrees)
y = cosine (x + 90 degrees)
y = sine (x + 45 degrees)
y = cosine (x + 45 degrees)
Answer:
y = sine (x + 90 degrees)
Step-by-step explanation:
y = cosine(x) is a curve that crosses the y-axis at y = 1 and completes one cycle at 360 degrees.
sine(x) have the same curve than cosine(x), but translated 90° to the right respect cosine(x)
f(x + c) translates f(x) horizontally c units to the left.
Then, sine(x + 90) is equivalent to cosine(x)
Hugo is traveling in Toronto, Canada. His weather app shows the temperature is 25°C. Hugo writes the equation 25 559(F232) to find the temperature in degrees Fahrenheit, F. What is the temperature in degrees Fahrenheit?
The temperature in degrees Fahrenheit is approximately 77.4°F.
What are the differences between the Celsius and Fahrenheit temperature scales?There are two widely used temperature scales in the world: Celsius and Fahrenheit. The freezing and boiling temperatures of water serve as the foundation for the Celsius scale, commonly referred to as the centigrade scale. According to this scale, the freezing point of water is 0°C, while the boiling point is 100°C.
On the other hand, a German physicist by the name of Daniel Gabriel Fahrenheit created the Fahrenheit scale. While it makes use of different reference points, this scale is similarly based on the freezing and boiling points of water.
The formula of the conversion is given by equation:
25 = 559/9 * (F - 32).
We can solve for F as follows:
25 = 559/9 * (F - 32)
25 * 9/559 = F - 32
F = 25 * 9/559 + 32
F ≈ 77.4
Therefore, the temperature in degrees Fahrenheit is approximately 77.4°F.
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Find the center and radius of the circle
x2 + 2x - 1 + y2+ 4y = 3
Answer:R=3\\
(a,b)=(1,2)
Step-by-step explanation:
[tex](x-a)^{2}+(y-b)^{2}=R^{2}\\(a,b)-center\\R-radius\\x^{2} + 2x - 1 + y^{2}+ 4y = 3\\(x+1)^2=x^{2}+2x+1\\(y+2)^{2}=y^{2}+ 4y+4\\x^{2} + 2x - 1 + y^{2}+ 4y = (x+1)^2-1+(y+2)^2-4-1=(x+1)^2+(y+2)^2-6=3\\(x+1)^2+(y+2)^2=9\\R=3\\(a,b)=(1,2)[/tex]
is this statement TRUE always sometimes or never true?
Answer:
never true
Step-by-step explanation:
If angles A and B are complementary, their measures add to 90º.
This means that if:
m∠B = 55º,
then:
m∠A = (90 - 55)º = 45º
Using this information, we can make the assertion that because:
55º ≠ 45º,
m∠A ≠ m∠B,
and thus:
sin(A) ≠ sin(B)
because 55º and 45º are NOT coterminal angles.
Therefore, the statement
sin(A) = sin(B)
is never true.
Factorize: (i) xy² +xy +y +1 (ii) x² -7x +12 (ii) x² - 144
Answer:
(i) xy² +xy +y +1 can be factorized by grouping:
xy² + xy + y + 1
= xy(x + y) + 1(x + y)
= (xy + 1)(x + y)
Therefore, xy² +xy +y +1 = (xy + 1)(x + y).
(ii) x² -7x +12 can be factorized by finding two numbers that multiply to 12 and add up to -7. These numbers are -4 and -3, so we can write:
x² - 7x + 12 = (x - 4)(x - 3)
Therefore, x² -7x +12 = (x - 4)(x - 3).
(iii) x² - 144 is a difference of squares, and can be factorized as:
x² - 144 = (x + 12)(x - 12)
Therefore, x² - 144 = (x + 12)(x - 12).
Answer:
x²-7x+12
X²+(4+3)x+12
x²-4x+3x+12
x (x+4) +3 (x+4)
(x+3) (x+4)
A snail moves at a speed of 1. 2 feet per minute. How many yards will the snail move in half an hour?
A snail moves at a speed of 1. 2 feet per minute. the snail will move 12 yards in half an hour
There are 60 minutes in an hour, so half an hour is 30 minutes.
The snail moves at a speed of 1.2 feet per minute. Therefore, in 30 minutes, it will travel:
1.2 feet/minute * 30 minutes = 36 feet.
To convert feet to yards, we need to divide by 3 since there are 3 feet in a yard:
36 feet / 3 = 12 yards.
Therefore, .
the snail's speed may seem slow to us, it's important to remember that different animals have different speeds that are adapted to their particular ecological niche.
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A rectangular field bordering a river is to be enclosed with 600 m of fencing. No fence is needed along the riverbank. What equation represents the maximum area enclosed by the fence?
The equation that represents the maximum area enclosed by the fence is 600x - 2x².
What is the maximum area?
Any rectangle's maximal surface area requires a minimum length-to-breadth ratio. Hence, in this scenario, the length must equal the ceiling (perimeter / 4) and the width, of the floor (perimeter /4). Therefore a rectangle with a given perimeter has a maximum area equal to the ceiling(perimeter/4) and the floor(perimeter/4)
Here, we have
Given: A rectangular field bordering a river is to be enclosed with 600 m of fencing. No fence is needed along the riverbank.
We have to find the equation that represents the maximum area enclosed by the fence.
The sum of the sides NOT along the river x + x + y = 600, and the area equals xy.
This makes the two equations: 2x + y = 600, and A = xy.
To find the largest area, we need to find A as a function of x or y. I suggest solving the first equation for y and replacing that in the second equation.
y = 600 - 2x. and A(x) = x(600-2x)
We now need to maximize A(x) = 600x - 2x²
Hence, the equation that represents the maximum area enclosed by the fence is 600x - 2x².
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For question(5) involving random selection, please use the following random number table to generate corresponding results: QUESTION 1 (30 MARKS) NECESSARY CALCULATION STEPS TO PRODUCE THE RESULTS SHOULD BE PROVIDED You want to compare the Television shows performance in Hong Kong and Korea. To conduct the study, you have randomly selected 20 TV shows broadcasted in Hong Kong and 20 TV shows broadcasted in Korea during year 2022 for analysis. The average TV rating of the 20 selected Hong Kong TV shows was recorded below. (a) Please identify and explain if the measurement of TV rating belongs to the measurement of media coverage or media reach (3 marks). Then identify and explain ONE limitation of TV rating survey in Hong Kong based on its sampling method ( 3 marks). (b) Find the following values of descriptive statistics for the above data set: (i) Find the mean and the standard deviation (2 marks). Then calculate the coefficient of variation (CV) of the data set above (2 marks). [Please show the steps of colculation for coefficient of variationi (ii) Find the five-number summary and interquartile range (IQR) of the data set [Please show your steps of caiculation] (12 marks). (c) Describe the skewness of the distribution of this data set with reason (4 marks). When you compare the same study in Korean in 2022, it is found that the average rating is 12.75. After your investigation, you find the coefficient of skewness of the 2022 Korean data set is −2.54 . Based an the above figures, comment the overall TV shows performance in Hong Kong and Korea in 2022 (4 marks). Please correct your final answers to 2 decimal places whenever appropriate.
(a) may not be truly random and representative
(b) (i) CV = 54.31%
(ii) IQR = 5.9
(c) right skewed
(d) -2.54
(a) The measurement of TV rating belongs to the measurement of media reach, which is the proportion of people that have the potential to be exposed to a given message. One limitation of the TV rating survey in Hong Kong based on its sampling method is that the sample may not be truly random and representative of the population, leading to sampling bias and inaccurate results.
(b) (i) The mean of the data set is 6.50 and the standard deviation is 3.54. The coefficient of variation (CV) of the data set is calculated by dividing the standard deviation by the mean and multiplying by 100. Thus, the CV = 54.31%.
(ii) The five-number summary of the data set is: Minimum = 0, Q1 = 3.4, Median = 6.8, Q3 = 9.3, Maximum = 12. The interquartile range (IQR) is calculated by subtracting Q1 from Q3. Thus, IQR = 9.3 - 3.4 = 5.9.
(c) The skewness of the distribution of this data set is right skewed. This is because the mean (6.50) is less than the median (6.8) and the coefficient of skewness is positive (0.36).
Based on the figures, we can conclude that the TV shows in Hong Kong generally have higher ratings than the ones in Korea in 2022. The coefficient of skewness of the data set in Korea is -2.54, which indicates that the data set is significantly skewed to the left and that the majority of the TV shows in Korea are rated lower than average.
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5. A car costs $22,000. After a down payment of $4,000, the balance will be paid off in 48 equal monthly payments with the interest of 12% per year on the unpaid balance. Find the amount of each payment. 6. A car costs $22,000. After a down payment of $4,000, the balance will be paid off in 60 equal monthly payments with the interest of12%per year on the unpaid balance. Find the amount of each payment.
7. A car costs $22,000. After a down payment of $4,000, the balance will be paid off in 72 equal monthly payments with the interest of 12% per year on the unpaid balance. Find the amount of each payment.
8. (Bad credit): A car costs $22,000. After a down payment of $4,000, the balance will be paid off in 48 equal monthly payments with the interest of 18% per year on the unpaid balance. Find the amount of each payment.
The equal monthly payments for a car costs $22,000 with a down payment of $4,000 based on each scenario are:
Interest of 12% with 48 equal monthly payments = $621.92.Interest of 12% with 60 equal monthly payments = $505.01.Interest of 12% with 72 equal monthly payments = $383.63.Interest of 18% with 48 equal monthly payments = 704.26Let's discuss each scenario we have.
5. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.
The amount of the down payment is $4,000.
The total cost of the car is $22,000.
Hence the balance is:
Balance = Total cost of the car − Down payment
Balance = $22,000 − $4,000 = $18,000
Now we can calculate the amount of each payment.
The payment is to be made in 48 equal monthly installments.
The interest rate is 12% per year.
We need to convert this into the monthly interest rate by dividing by 12.
Hence:
Monthly interest rate = 12% / 12 = 1% = 0.01
Let x be the amount of each monthly payment. Then the equation that represents the above conditions is given by:
18000=x(1−(1+0.01)−48)/0.01
Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:
18000=x(1−(1+0.01)−48)/0.01x
=18000/28.95x
≈621.92
Hence the amount of each equal monthly payment is approximately $621.92.
6. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.
The amount of the down payment is $4,000.
The total cost of the car is $22,000.
Hence the balance is:
Balance = Total cost of the car − Down payment
Balance = $22,000 − $4,000 = $18,000
Now we can calculate the amount of each payment.
The payment is to be made in 60 equal monthly installments.
The interest rate is 12% per year.
We need to convert this into the monthly interest rate by dividing by 12.
Hence:
Monthly interest rate = 12% / 12 = 1% = 0.01
Let x be the amount of each monthly payment.
Then the equation that represents the above conditions is given by: 18000=x(1−(1+0.01)−60)/0.01
Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:
18000=x(1−(1+0.01)−60)/0.01x
=18000/35.643x
≈505.01
Hence the amount of each payment is approximately $505.01.
7. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.
The amount of the down payment is $4,000.
The total cost of the car is $22,000.
Hence the balance is:
Balance = Total cost of the car − Down payment
Balance = $22,000 − $4,000 = $18,000
Now we can calculate the amount of each payment.
The payment is to be made in 72 equal monthly installments.
The interest rate is 12% per year.
We need to convert this into the monthly interest rate by dividing by 12.
Hence:
Monthly interest rate = 12% / 12 = 1% = 0.01
Let x be the amount of each monthly payment.
Then the equation that represents the above conditions is given by:
18000=x(1−(1+0.01)−72)/0.01
Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:
18000=x(1−(1+0.01)−72)/0.01x
=18000/46.869x
≈383.63
Hence the amount of each payment is approximately $383.63.
8. For calculating the amount of each payment, the first thing to do is to find the balance after the down payment is made.
The amount of the down payment is $4,000.
The total cost of the car is $22,000.
Hence the balance is:
Balance = Total cost of the car − Down payment
Balance = $22,000 − $4,000 = $18,000
Now we can calculate the amount of each payment.
The payment is to be made in 48 equal monthly installments.
The interest rate is 18% per year.
We need to convert this into the monthly interest rate by dividing by 12.
Hence:
Monthly interest rate = 18% / 12 = 1.5% = 0.015
Let x be the amount of each monthly payment.
Then the equation that represents the above conditions is given by:
18000=x(1−(1+0.015)−48)/0.015
Using the formula (1−(1+ r/n)−nt) = (1−(1+r)^−n), we can simplify the above equation to:
18000=x(1−(1+0.015)−48)/0.015x
=18000/25.525x
≈704.26
Hence the amount of each payment is approximately $704.26.
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Use the terms from the list below to complete the sentences.
Each term will be used once.
constant of proportionality
proportional relationship
+
ratio
table
equivalent ratios
equation
It takes a machine 10 seconds to fill 4 bottles of juice. It takes 15 seconds
to fill 6 bottles of juice. Does this describe a proportional relationship?
1. Make a(n)
to organize the data.
Time (t)
10.
15
Number of
Bottles (b)
4
6
Answer:
1. Make a table to organize the data:
(The table is in the image that is provided, if you cannot see it; I've written it down below)
Time (t): 10, 15
Number of bottles (b): 4, 6
The table shows the time it takes the machine to fill a certain number of bottles of juice. To determine if the relationship is proportional, we can look at the ratios of time to number of bottles for the different data points.
If the ratios are the same for all data points, then the relationship is proportional. In this case, we have:
Ratio for the first data point: 10/4 = 2.5
Ratio for the second data point: 15/6 = 2.5
Since the ratios are the same, we can conclude that the relationship is proportional.
The terms used in this context are: proportional relationship, table, ratio, and equivalent ratios.
So the answer is yes, the relationship between the time it takes the machine to fill a certain number of bottles of juice and the number of bottles filled is a proportional relationship.
Hopefully this helped, If not I'm sorry! If you need more help, ask me! :]