Divide €132 in the ratio 7:4
Answer:92.4
Step-by-step explanation:
4x+7x=132
10x=132
x=132/10
x=13.2
4x=4×13.2
=52.8
5x=7×13.2
=92.4
A bag contains 5 milk and 13 dark chocolates.
A sweet is selected at random.
What is the probability of choosing:
P(milk)
=
P(not milk)
=
Answer:P(milk) 5/18 - 27% ----------- P(not milk) 13/18- 73%
Step-by-step explanation:
total chocolates in the bag= 18 (5 milk chocolates + 13 dark chocolates= 18 chocolates in total)
to find percentages divide numerator by denominator ( 5/18 = 27%) (13/18=73%)
P(milk) - 27% chance you will get milk chocolate
P(not milk) 73% chance you will get dark chocolate
It is more likey to get dark chocolate
the average package of Oreos has 51 cookies. If there are 3 rows of Oreos in each package,how many cookies are in each row? what if there were four rows of cookies how many cookies would be in a package
Answer:
1/ 17 cookies in each row
2/ 68 cookies in a package
Step-by-step explanation:
We know
The package of Oreos has 51 cookies
1/
If there are 3 rows of Oreos in each package, how many cookies are in each row?
51 / 3 = 17 cookies
So, there are 17 cookies in each row.
2/
If there were four rows of cookies, how many cookies would be in a package?
We know each row has 17 cookies
17 x 4 = 68 cookies
So, there are 68 cookies in a package.
Linda buys candy that costs $6 per pound. She will buy less than 8 pounds of candy. What are the possible amounts she will spend on candy?
Use c for the amount (in dollars) Linda will spend on candy.
Write your answer as an inequality solved for c.
Answer:
$42
Step-by-step explanation:
Which graph shows a set of ordered pairs that represent a function?
On a coordinate plane, solid circles appear at the following points: (negative 2, 3), (negative 1, 2), (1, 1), (2, negative 1), (2, negative 3), (4, negative 5).
On a coordinate plane, solid circles appear at the following points: (negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4).
On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).
Answer:
On a coordinate plane, solid circles appear at the following points: (negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4).
Step-by-step explanation:
Marriyam was given $75 for a birthday present. She's going to use that gift, plus the earnings from her summer job, to buy a skateboard that costs $325. If her job pays I dollars per hour, how many hours does she need to work to buy the skateboard?
Answer:
250 hours
Step-by-step explanation:
Jeez can Marriyam get some more money per hour?
Ok, Marriyam is given 75 dollars so she only need to pay 325-75 = $250.
Since Marriyam earns 1 dollar an hour she need to work 250 hours.
Hopefully that helps.
If her job pays I dollars per hour, 250 hours does she need to work to buy the skateboard.
What is the equation?In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
Marriyam was given $75 for a birthday present.
She's going to use that gift, plus the earnings from her summer job, to buy a skateboard that costs $325.
The amount left she has to earn is;
= 325 - 75 = $250
If her job pays I dollars per hour, how many hours does she need to work to buy the skateboard is;
\(= 1\times 250\\\\=250\)
Hence, If her job pays I dollars per hour, 250 hours does she need to work to buy the skateboard.
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rebecca’s electric bill is a variable expense. what is the average amount she pays for electricity if she paid $135 in december, $129 in january, $99 in february, $120 in march and $140 in april?
The average amount Rebecca pays for electricity based on the given data is $124.60.
To calculate the average, we add up the amounts she paid in each month and then divide by the total number of months. In this case, the sum of her payments is $135 + $129 + $99 + $120 + $140 = $623. Dividing this sum by the total number of months (5), we get an average of $623 / 5 = $124.60. Calculating the average helps us determine the typical amount Rebecca pays for electricity based on the given data. It provides an overall picture of her average expenses in the specified period.
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There are 7 gloves in the lost & found box. There are 2 blue gloves, 3 green gloves,
1 black glove, and 1 brown glove. What fraction of the gloves are black?
Answer: 1/7
Step-by-step explanation:
There are total of 7 gloves
There is 1 black glove
So take 1 divided by 7
The Fraction is 1/7
At the beginning of a laboratory experiment, the temperature of a substance is -12.6 °C. During the experiment, the temperature of the substance decreases 7.5 °C. What is the final temperature of the substance?
!!!!SHOW YOUR WORK!!!!
Answer
20.1°C
Step-by-step explanation:
-12.6 °C - 7.5 °C =-20.1°C
Answer:
the initial temperature= -12.6⁰c
change in temperature= 7.5⁰c
the final velocity = x
-12.6-7.5=x
-20.1=x
so therefore the final temperature is -20.1
The area of a circle is 200.96 cm? What is the diameter of the circle? (Write only the
numeric answer no units)
Answer:
16 (well, more like 15.99)
Step-by-step explanation:
\( \sqrt{((200.96 \times 4) \div 3.14)} \)
What is -11 2/3x(-4 1/5)
Answer:
49x
Step-by-step explanation:
Answer:
-49x
Step-by-step explanation:
-11 2/3x (-4 1/5)
= -49x
Nikolai was curious if he could predict how many "likes" an internet video received based on how many views the video had. He took a random sample of videos and noticed a positive linear relationship between number of views and number of likes (both in thousands). Here is computer output from a least-squares regression analysis on his data:
Which of these is an appropriate least-squares equation for this model?
Answer:
likes
=0.420+0.034(views) (B) on khan academy
Step-by-step explanation:
Study the road plan shown in the figure. A service station will be built on the highway, and a road will connect it with Cray. How long will the new road be? A.54.2 mi B. 312 mi C. 46.2 mi D.400 mi
The length of the road that connects the service station with Cray is 46.2 mi.
How long will the new road be?
We need to apply the principle of similar triangles to obtain the length of the road that will connect the service station with Cray as shown in the image attached.
Hence;
The distance between Alba and Blare = 130 mi
The distance between Alba and Cray = 120 mi
Road connecting the service station with Cray =x
And;
120/130 = x/50
x = 46.2 mi
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The results of a survey asking 500 people about their favorite ice cream flavor are shown in the table.
Find the experimental probability of each outcome in the sample space. Enter your answers in the boxes.
Flavor Number of People
Chocolate 90
Vanilla 125
Strawberry 60
Mint Chip 50
Other 175
P(chocolate) =
%
P(vanilla) =
%
P(strawberry) =
%
P(mint chip) =
%
P(other) =
%
Chocolate = 18%
Vanilla = 25%
Strawberry = 12%
Mint Chip = 10%
Other = 35%
The explanation for me getting these exact percentages is because of the formulas given for calculating the percentages from specific numbers and real world problems like this. When you are trying to find the calculation precentages of these types of questions, you divide the number by the total surveyed and multiple by 100.
Example:
125 / 500 = 0.25
0.25 x 100 = 25%
So, this is also how I got the other numbers, just change the "125" to the other numbers.
The experimental probability of each outcome in the sample space are:
P(chocolate) = 18%, P(strawberry) = 12%, P(vanilla ) = 25%, P(mint chip) = 10% and P(other) = 35%
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Flavor Number of people
chocolate 90
strawberry 60
vanilla 125
mint chip 50
other 175
So, the Experimental probability are:
P(chocolate)= 90/ 500 x 100 = 18%
P(strawberry) = 60/ 500 x 100 = 12%
P(vanilla ) = 125/ 500 x 100 = 25%
P(mint chip) = 50/ 500 x 100 = 10%
P(other) = 175/ 500 x 100 = 35%
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Solve for x
Taking quiz now can’t find the right answer
This quadratic equation has a negative coefficient of (-16)2 - 4(2)(36) = -64. The line y = -x + 9 is not intersecting the circle (x - 4)2 + (y - 2)2 = 64 at any other location, proving that the quadratic has no real roots.
What is equation?The equals sign (=) is used in mathematical equations to denote equality between two assertions. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in mathematics. For instance, the equal sign places a space between the integers in the equation 3x + 5 = 14. The relationship between the two lines on either side of a character can be expressed mathematically. Frequently, the logo and the specific component of software are the same. such as, for example, 2x - 4 = 2.
The tangent line has a slope of -1/1 = -1 because the radius through point (6,4) has a slope of (4-2)/(6-4) = 1
(x - 4)^2 + (-x + 8)^2 = 64
By enlarging and condensing, we obtain:
2x^2 - 16x + 36 = 0
This quadratic equation has a negative coefficient of (-16)2 - 4(2)(36) = -64. The line y = -x + 9 is not intersecting the circle (x - 4)2 + (y - 2)2 = 64 at any other location, proving that the quadratic has no real roots.
The line must be tangent to the circle at the place because it does not cross the circle at any other points. (6,4). As a result, we can say that the circle (x - 4)2 + (y - 2)2 = 64 at the position on the line y = -x + 9 is tangent to it. (6,4).
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The cost of a video game increased in price from $20 to $39. What was the percent of the increase?
For this exercise you need to use the following formula to calculate the Percent of Increase:
\(PercentIncrease=\frac{Final\text{ }value-Starting\text{ }value}{|Starting\text{ }value|}\cdot100\)In this case, you can identify that (according to the information given in the exercise):
\(\begin{gathered} Starting\text{ }value=20 \\ Final\text{ }value=39 \end{gathered}\)Therefore, you can substitute values into the formula and evaluate. The result is:
\(\begin{gathered} PercentIncrease=\frac{39-20}{|20|}\cdot100=\frac{19}{|20|}\cdot100=95 \\ \end{gathered}\)The answer is: 95%
i need to know what 3x-2/3 equals
Answer: -2
(I hope this is what you meant)
Hope this helps!
Step-by-step explanation:
▬▬▬▬
10. Write the equation log328 -
a.
3
325 = 8
3/5
b. 3
in exponential form.
85 = 32
C.
3/5
32
= 8
d. S
83 = 32
The equation log328 is c.3/5 32 is 8.
How do you write in exponential form?The following examples illustrate how to express numbers raised to specific powers of their prime factors in order to write them in exponential form,
8 = 2 × 2 × 2 = 23. Therefore, the exponential form of 8 can be written as 2.... 72 = 2 2 2 3 3 = 23 32.... 121 = 112.
First, isolate the exponential expression. Step 2: Take the natural log from both sides. Step 3: Extract the x from the exponent using the properties of logs. Solve for x in step four.
The following examples illustrate how to express numbers raised to specific powers of their prime factors in order to write them in exponential form:
8 = 2 × 2 × 2 = 23. Therefore, the exponential form of 8 can be written as 2.... 72 = 2 2 2 3 3 = 23 32.... 121 = 112.
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The net of a solid is shown below:
Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square.
What is the surface area of the solid?
18 square inches
27 square inches
36 square inches
45 square inches
Answer:
The answer is 45 inches².
Step-by-step explanation:
First, you have to find the area of each triangle:
\(area = \frac{1}{2} \times base \times height\)
\(let \: base = 3 \\ let \: height = 6\)
\(area = \frac{1}{2} \times 3 \times 6\)
\(area = \frac{1}{2} \times 18\)
\(area = 9 \: \: {inches}^{2} \)
Assuming that the formula for surface area of pyramid is Surface area = base area(area of square) × 4(area of triangle):
\(base \: area = 3 \times 3 = 9\)
\(area \: of \: triangle = 9\)
\(s.a = 9 + 4(9)\)
\(s.a = 9 + 36\)
\(s.a = 45 \: \: {inches}^{2} \)
Please help with this algebra 1 question, it's in the attachments
y = 4(0.5)ˣ is the equation for the function that model the data
How to write the equation for the function that models the data?A. Exponential model is the model that best describes the data because there is a huge increase in the value of y as x decreases
B. The general form of the exponential function is y = abˣ
From the table, when x = 0, y = 4. Substitute the values into the function:
y = abˣ
4 = ab⁰ (Note: b⁰ = 1)
4 = a(1)
4 = a
a = 4
Also, from the table, when x = 1, y = 2. Substitute the values into the function:
2 = 4 × b¹
2 = 4b
4b = 2
b = 2/4 = 0.5
We can now write the exponential function for the data:
y = abˣ
y = 4(0.5)ˣ
Therefore, the equation for the function that model the data is y = 4(0.5)ˣ
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a sample assistant professors on the business faculty state supported institutions in ohio revealed the mean income to be $ 72,00 for 9 months
assistant professors on the business faculty at state-supported institutions in Ohio make, on average, between $69,263 and $74,737 for nine months.
In Ohio's state-supported institutions, the
average incom for a sample of assistant professors in the business faculty for nine months is $72,000.
Since the sample size is unknown, it is difficult to draw any definitive conclusions based on this statistic
. However, we can use this mean to estimate the probable range of incomes for assistant professors at these institutions by calculating a confidence interval.For example, if we use a 95 percent confidence level, we can assume that the real average income for assistant professors in the business faculty at Ohio's state-supported institutions falls within a certain range of values
. Based on the sample mean of $72,000 and a standard deviation of $5,000, the 95 percent confidence interval is $69,263 to $74,737. This means that we are 95 percent confident that the real average income for assistant professors falls within this range.The interval reflects the range of values that the true average could fall within, given the uncertainty of the sample data.
Therefore, we can infer that assistant professors on the business faculty at state-supported institutions in Ohio make, on average, between $69,263 and $74,737 for nine months.
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The mean income for sample assistant professors on the business faculty at state-supported institutions in Ohio is $72,000 for 9 months.
Based on the information provided, the mean income for sample assistant professors on the business faculty at state-supported institutions in Ohio is $72,000 for 9 months.
To better understand this, let's break it down step by step:
1. The mean income refers to the average income earned by assistant professors on the business faculty in Ohio.
2. The sample represents a group of assistant professors who were surveyed or studied.
3. The business faculty refers to the department or area of expertise these assistant professors specialize in.
4. State-supported institutions in Ohio are public universities or colleges that receive funding from the state government.
5. The $72,000 represents the average income earned by assistant professors on the business faculty in Ohio over a period of 9 months. It does not include income earned during the summer months.
6. It's important to note that this figure may vary for different individuals based on factors such as experience, qualifications, and position within the faculty.
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You have been asked to rename one of the quadrilaterals (square, parallelogram, rectangle, rhombus, or trapezoid). Which quadrilateral would you rename, and what would be its new name?
Answer:
I would rename the trapezoid. I would rename it a semi-hexagon, because it is basically half of a hexagon.
Find the measure of each marked angle.
The larger angle measures ___
The smaller angle measures ___
Answer:
(for angles laying on the same line, there sum is always supplementary)
(21x+3)° + (14x+2)° = 180°
21x + 3 + 14x + 2 = 180
35x + 5 = 180
35x = 180 - 5
35x = 175
x = 175 / 35
x = 5
larger angle = 108°
21x + 3
= 21 × 5 + 3
= 105 + 3
= 108°
smaller angle = 72°
14x + 2
= 14 × 5 + 2
= 70 + 2
= 72°
Step-by-step explanation:
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Describe how the graphs of square root and cube root functions are similar and how they are different.
Explain why they are different!!!
Answer:
Just as the square root is a number that, when squared, gives the radicand, the cube root is a number that, when cubed, gives the radicand. Cubing a number is the same as taking it to the third power: 23 is 2 cubed, so the cube root of 23 is 2.
Step-by-step explanation:
there i hope you understood
The graphs of Square root function only continues in one direction forever whereas the cube root function continues in two directions forever.
What is Square root function?"The principal square root function \(f(x) = \sqrt{x}\) (usually just referred to as the "square root function") is a function that maps the set of non negative real numbers onto itself."
What is Cube root function?"The cube root function \(f(x) = \sqrt[3]{x}\) is a continuous function, with no start or end point. Its domain is all real numbers."
The similarities in the graphs of square root function and cube root function are positive function (0,∞), x-intercept: intersects x-axis at (0, 0)
y-intercept: intersects y-axis at (0, 0).
The square root function only utilizes the positive square root. If both positive and negative square root values were used, it would not be a function. The cube root function can process both positive and negative values.
Hence, the graphs of Square root function only continues in one direction forever whereas the cube root function continues in two directions forever.
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12. the score on a standardized test for a certain year had a mean of 83 and a standard deviation of 6.3. the empirical rule shows the values where 68%, 95% and 99.7% of data occurs. give the low and high values for the 95% data range for this data.
This standardized test, the low value for the 95% data range is 70.4 and the high value is 95.6.
The empirical rule states that for a normally distributed data set, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this case, the mean score is 83 and the standard deviation is 6.3.
To find the low and high values for the 95% data range, we need to calculate two standard deviations and subtract/add them to the mean.
Two standard deviations would be 2 * 6.3 = 12.6.
Subtracting 12.6 from the mean gives us
83 - 12.6 = 70.4,
which is the low value for the 95% data range. Adding 12.6 to the mean gives us
83 + 12.6 = 95.6,
which is the high value for the 95% data range.
In conclusion, for this standardized test, the low value for the 95% data range is 70.4 and the high value is 95.6.
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1. Let the distribution of X be the normal distribution N (μ, σ2) and let Y = aX + b. Prove that Y is distributed as N (aμ + b, a2σ2).
2. Let X and Y be two independent random variables with E|X| < [infinity], E|Y| < [infinity] and E|XY| < [infinity]. Prove that E[XY] = E[X]E[Y].
1 Y is distributed as N(aμ + b, a^2σ^2), as desired.
2 We have shown that under these conditions, E[XY] = E[X]E[Y].
To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.
First, let's find the mean of Y:
E(Y) = E(aX + b) = aE(X) + b = aμ + b
Next, let's find the variance of Y:
Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2
Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.
We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:
E[XY] = ∫∫ xy f(x,y) dxdy
where f(x,y) is the joint probability density function of X and Y.
Then, we can use the fact that X and Y are independent to simplify the expression:
E[XY] = ∫∫ xy f(x) f(y) dxdy
= ∫ x f(x) dx ∫ y f(y) dy
= E[X]E[Y]
where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.
Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].
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Find the critical t-value that corresponds to 99% confidence. Assume 8 degrees of freedom
We can conclude that the critical t-value that corresponds to 99% confidence and 8 degrees of freedom is approximately 3.355. This means that if we conduct a t-test with these parameters and obtain a t-statistic greater than 3.355 or less than -3.355, we would reject the null hypothesis at the 99% confidence level.
To find the critical t-value that corresponds to 99% confidence and 8 degrees of freedom, we can use a t-distribution table or a calculator.
Using a t-distribution table, we can locate the row for 8 degrees of freedom and the column for a two-tailed 0.01 (1% divided by 2) significance level. The intersection of these values gives us a critical t-value of approximately 3.355.
Alternatively, we can use a calculator or software that has a built-in function for finding critical t-values. For example, using the function TINV(0.01,8) in Microsoft Excel, we get a critical t-value of approximately 3.355.
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can someone please help me w these using Addition and Subtraction of Fractions w Different Denominators? PLS PLS
Using addition and subtraction of the fractions with different denominators, we have the following:
1) 13/8
2) 1/8
3) 73/36
4) 29/35
5) 55/216
6) 43/48
7) 5/72
8) 13/8
9) 145/36
10) 275/56
11) 71/70
12) 3/7
How to add and subtract fractions with different denominators?For addition and subtraction of fractions with different denominators, we shall first find a common denominator by finding their LCM (Lowest Common Denominator):
1) 7/8 + 3/4:
LCM (the least common multiple) of 8 and 4 is 8.
Next, convert the fractions to get a common denominator:
7/8 + 3/4 = (7/8) + (3/4 * 2/2) = 7/8 + 6/8 = (7 + 6)/8 = 13/8.
2) 7/8 - 3/4:
The LCM of 8 and 4 is 8:
7/8 - 3/4 = (7/8) - (3/4 * 2/2) = 7/8 - 6/8 = (7 - 6)/8 = 1/8.
3) 1 1/12 + 17/18:
First, convert the mixed fraction to an improper fraction.
1 1/12 = (12/12 + 1/12) = 13/12
Find a common denominator for 12 and 18, which is 36.
13/12 + 17/18 = (13/12 * 3/3) + (17/18 * 2/2)
= 39/36 + 34/36 = (39 + 34)/36 = 73/36
4) 3/7 + 2/5:
3/7 + 2/5 = (3/7 * 5/5) + (2/5 * 7/7)
= 15/35 + 14/35 = (15 + 14)/35 = 29/35
5) 15/24 - 10/27 :
15/24 - 10/27 = (15/24 * 9/9) - (10/27 * 8/8)
= 135/216 - 80/216 = (135 - 80)/216 = 55/216
6) 7/12 + 5/16 :
7/12 + 5/16 = (7/12 * 4/4) + (5/16 * 3/3) = 28/48 + 15/48 = (28 + 15)/48 = 43/48
7) 15/27 - 5/24:
15/27 - 5/24 = (15/27 * 8/8) - (5/24 * 9/9) = 120/216 - 45/216 =
(120 - 45)/216 = 75/216 = 5/72
8) 1 1/4 + 3/8 :
1 1/4 = (4/4 + 1/4) =
5/4 + 3/8 = (5/4 * 2/2) + (3/8 * 1/1) = 10/8 + 3/8 = (10 + 3)/8 = 13/8
9) 11/4 + 23/18:
11/4 + 23/18 = (11/4 * 9/9) + (23/18 * 2/2)
= 99/36 + 46/36 = (99 + 46)/36 = 145/36
10) 29/8 + 9/7:
29/8 + 9/7 = (29/8 * 7/7) + (9/7 * 8/8)
= 203/56 + 72/56 = (203 + 72)/56 = 275/56
11) 2 13/35 - 1 5/14:
2 13/35 = (2 * 35/35) + 13/35 = 70/35 + 13/35 = 83/35
1 5/14 = (1 * 14/14) + 5/14 = 14/14 + 5/14 = 19/14
83/35 - 19/14 = (83/35 * 2/2) - (19/14 * 5/5)
= 166/70 - 95/70 = (166 - 95)/70 = 71/70
12) 2/3 + 1/21 - 2/7:
2/3 + 1/21 - 2/7 = (2/3 * 7/7) + (1/21 * 1/1) - (2/7 * 3/3)
= 14/21 + 1/21 - 6/21 = (14 + 1 - 6)/21
= 9/21 = 3/7
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Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index. Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1) was 25, and for the last seven quarters the price variance for XYC common (population 2) was 8. Assume that stock prices are normally distributed in the population. If a = 0.05, what is the observed value for the appropriate test statistics?
Select one:
a. 0.32
b. 1.77
c. 3.13
d. 9.77
Here the observed value for the appropriate test statistic is approximately 3.13 that is, option c.
In this scenario, Tamara Hill is comparing the price variance of the S&P 500 index (population 1) to the price variance of XYC common (population 2) to determine if the XYC common stock can be considered a 'low risk' issue.
To conduct the hypothesis test, we can use the F-test, which compares the variances of two populations. The test statistic for the F-test is calculated by dividing the sample variance of population 1 by the sample variance of population 2.
Given that the price variance for the S&P 500 index (population 1) is 25 and the price variance for XYC common (population 2) is 8, we can calculate the observed value for the test statistic as follows:
Test Statistic = (Sample Variance of Population 1) / (Sample Variance of Population 2)
= 25 / 8
≈ 3.125
Since we are given the significance level a = 0.05, we can compare the observed value of the test statistic to the critical value from the F-distribution table at a = 0.05 and appropriate degrees of freedom.
By comparing the observed value of the test statistic (approximately 3.125) to the critical value, we find that the observed value falls in the rejection region, indicating that the XYC common stock can be considered a 'low risk' issue.
Therefore, the observed value for the appropriate test statistic is approximately 3.13, which corresponds to option c.
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