The function which describes the zeroes of the graph of f(x) = 3x6 + 30x5 +75x42 is 5 with multiplicity 2 and 3 with multiplicity 4, the correct option is B.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
The function f(x) = 3x6 + 30x5 +75x42
Now,
We can factorize f(x) = 3x6 + 30x5 +75x4 by taking out the common factor of 3x4:
f(x) = 3x4(x2 + 10x + 25)
Then we can factorize the quadratic expression inside the parentheses by finding two numbers that multiply to 25 and add to 10. These numbers are 5 and 5, so we have:
f(x) = 3x4(x + 5)(x + 5)
To find the zeroes, we set f(x) equal to zero and solve for x:
0 = 3x4(x + 5)(x + 5)
This equation has two solutions: x = 0 and x = -5. However, x = 0 is a zero of multiplicity 4, because it makes x4 equal to zero four times. Similarly, x = -5 is a zero of multiplicity 2, because it makes (x + 5) equal to zero twice.
Therefore, by the function the answer will be 5 with multiplicity 2 and 3 with multiplicity 4
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The measure of an exterior angle of a triangle is always
A. Greater than its adjacent interior angle.
B. Less than its adjacent interior angle.
C.greater than either remote interior angle.
D.less than either remote interior angle.
A. Greater than its adjacent interior angle. The measure of an exterior angle of a triangle is always C. greater than either remote interior angle.
An exterior angle is formed by extending one side of a triangle. In a triangle, the exterior angle is equal to the sum of the two remote interior angles (the two angles that are not adjacent to the exterior angle).
Therefore, the exterior angle will always be greater than either one of the remote interior angles.
The exterior angle theorem states that when two sides of a triangle are adjacent, the resulting exterior angle is equal to the sum of the degrees of the two interior angles of the triangle. This theorem can be used to find the measure of an unknown angle in a triangle.
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Please write y = 4x -2
in Ax + By = C form
Then identify x-intercept, y-intercept, and slope
Thanks!
[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]
[tex]\begin{aligned} y &= 4x-2 \\ -4x+y &= -2 \end{aligned}[/tex]
Then, [tex]Ax+By=C \implies -4x+y=-2[/tex].
So, [tex]A=-4, B=1, C=-2[/tex].
Now, identify the x-intercept (y = 0):
[tex]y=4x-2\\0=4x-2\\2=4x\\x=\dfrac{2}{4}\\x=\dfrac{1}{2}\\ \therefore \left( \dfrac{1}{2} , 0 \right)[/tex]
y-intercept (x = 0):
[tex]y=4x-2\\y=4(0)-2\\y=2\\\therefore (0,2)[/tex]
Slope:
We know that [tex]y=4x-2[/tex]. the the slope [tex]m=4[/tex] (x coefficient).
[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\boxed{\mathfrak{answered \: by: \: akbarsdtazm}}}}[/tex]
About 6 randomly selected people were asked how long they slept at night. The mean time was 7 hours, and the standard deviation was 0.6 hour. Calculate the 80% confidence interval of the mean time by assuming that the variable is normally distributed. Provide only the value required below. Express your answer in 3 decimal places.a. te (negative value only):
The negative value requested (a. te) represents the lower end of the confidence interval minus the mean:
a. te = 6.639 - 7 ≈ -0.361 (rounded to 3 decimal places)
To calculate the 80% confidence interval for the mean sleep time, we'll use the following formula:
CI = mean ± (t * (standard deviation / √sample size))
Given:
- Mean time = 7 hours
- Standard deviation = 0.6 hour
- Sample size = 6 people
First, we need to find the t-value (t-score) for an 80% confidence interval and degrees of freedom (df) = sample size - 1 = 6 - 1 = 5. Using a t-distribution table or calculator, the t-value for a two-tailed test with 80% confidence (or 0.1 significance level) and df = 5 is approximately 1.476.
Now, plug in the values into the formula:
CI = 7 ± (1.476 * (0.6 / √6))
Calculate the margin of error:
Margin of error = 1.476 * (0.6 / √6) ≈ 0.361
So, the 80% confidence interval is:
Lower limit: 7 - 0.361 ≈ 6.639 hours
Upper limit: 7 + 0.361 ≈ 7.361 hours
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What is the component form of the vector that translates the top house figure to the bottom house figure?
(7, -2)
(6, -4)
(5, -1)
(-4, 5)
Answer:
Mark me the brainliest
Step-by-step explanation:
Okay, let's break this down step-by-step:
The top figure represents the original vector: (7, -2)
To translate it to the bottom figure: (6, -4)
We need to determine the component form of the translation.
The x-component is 7 - 6 = 1 (it decreased by 1)
The y-component is -2 - (-4) = -2 (it decreased by 2)
Therefore, the component form of the translation is: (1, -2)
So the translation vector that transforms the top figure (7, -2) into the bottom figure (6, -4) is (1, -2).
Does this make sense? Let me know if you have any other questions!
Show that 20 is not a solution of the inequality in the example. Explain what this means about Fidel’s driving this week.
20 is not a solution of the inequality as the value is greater than 400 rather being less than 400.
We have the inequality
26g < 400
Now, for g = 20
26g
=26(20)
= 520 > 400
So, 20 is not a solution of the inequality as the value is greater than 400 rather being less than 400.
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In circle M, MN = 3 and the length of NO = 37. Find the area shaded below.
-
Express your answer as a fraction times 7.
M
0
N
The shaded area on the circle in this problem is given as follows:
A = 13/2π.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
[tex]C = 2\pi r[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it is given as follows:
r = MN = 3.
Thus the circumference of the circle is of:
C = 6π.
NO = 5π/3, hence the proportion of the shaded area is given as follows:
p = (6π - 5π/3)/6π
p = (13π/3)/6π
p = 13/18.
Thus the area of the shaded region is given as follows:
A = 13/18 x π x r²
A = 13/18 x π x 9
A = 13/2π.
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Find Arc MAC
Above 107 is x-9
Image not to scale
The measure of arc AC in the circle shown above is determined as:
m(AC) =
How to Find the Measure of an Arc in a Circle?The circle shown above has information given that would be used in finding the measure of arc AC that is indicated.
Thus, we have to find the value of x as shown below:
110 + 107 + x - 9 = 360 [a full circle is equal to 360 degrees].
208 + x = 360
x = 360 - 208
x = 152
Measure of arc AC = x - 9
Measure of arc AC = 152 - 9
Measure of arc AC = 143°
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Damon will write an equivalent expression for 60xyz+36yz+24xy by dividing each term by a common factor and rewriting the expression as the product of a common factor and the sum of remaining factors.
Select three possibilities that he could use as the common factor for equivalent expression
The three possibilities that Damon can use as the common factor for equivalent expression are y(5xz + 3z + 2x), z(5xy + 3y + 2x) and xy(5z + 3 + 2z).
How to Solve the Problem?To discover a common figure for 60xyz+36yz+24xy, we have to be discover the Greatest Common Factor (GCF) of the coefficients 60, 36, and 24, and the factors x, y, and z.
The GCF of the coefficients 60, 36, and 24 is 12. Able to calculate out 12 from each term:
60xyz+36yz+24xy = 12(5xyz + 3yz + 2xy)
Presently, we ought to discover a common calculate for the remaining components, 5xyz + 3yz + 2xy. Here are three conceivable outcomes:
Calculate out y:
5xyz + 3yz + 2xy = y(5xz + 3z + 2x)
Calculate out z:
5xyz + 3yz + 2xy = z(5xy + 3y + 2x)
Calculate out xy:
5xyz + 3yz + 2xy = xy(5z + 3 + 2z)
So, Damon may utilize any of these three conceivable outcomes as the common calculate for an proportionate expression.
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Js need a simple answer
Answer:
the tenth letter of the alphabet.
Step-by-step explanation:
Js is just the plural version of J.
Answer:a simple answer
Step-by-step explanation:the question asks: "Js need a simple answer"
So what they need is "a simple answer"!
a pe class has 48 4848 students. one group of 24 2424 students chooses to play volleyball. the teacher then divides the remaining students into as many groups of 5 55 as possible to shoot baskets. after that, the remaining students (not on a volleyball or basketball team) climb the rock wall.
In this PE class with 48 students, one group of 24 students decides to play volleyball, leaving 24 students who will be shooting baskets. The teacher then divides the remaining 24 students into as many groups of 5 as possible, which results in 4 groups. Each group will have 5 students, and one student will be left without a group.
In this scenario, there are 48 students in the PE class. One group of 24 students chooses to play volleyball, leaving 24 students (48 - 24 = 24) remaining. The teacher then divides the remaining students into as many groups of 5 as possible to shoot baskets.
To determine how many groups of 5 can be formed, we'll divide the remaining students by 5:
24 ÷ 5 = 4 (with a remainder of 4)
So, the teacher can create 4 groups of 5 students each for shooting baskets. This accounts for 20 students (4 groups x 5 students = 20).
Since there were 24 students remaining after the volleyball group, and 20 of those students have been assigned to basketball groups, we're left with 4 students (24 - 20 = 4) who will climb the rock wall.
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Don't know how to solve and also really need to get this homework done so I can pass would greatly appreciate it
Answer:
See below
Step-by-step explanation:
11. This is a tangent-chord angle, which means the angle is half of the measure of its intercepted arc.
7x - 10 = (1/2) * 120
7x - 10 = 60
7x = 70
x = 10
12. This is a chord-chord angle, which means the angle is half of the sum of the measures of the arcs intercepted by the chord-chord angle and its vertical angle.
26x - 2 = (1/2) * (131 + 18x + 1)
26x - 2 = (1/2) * (18x + 132)
26x - 2 = 9x + 66
17x = 68
x = 4
13. This is a secant-tangent angle, which means the angle is half of the difference between the measures of the intercepted arcs.
5x - 5 = (1/2) * (190 - (13x - 7))
5x - 5 = (1/2) * (197 - 13x)
10x - 10 = 197 - 13x
23x = 207
x = 9
14. This is also a secant-tangent angle.
2x + 14 = (1/2) * (6 + 14x - 58)
2x + 14 = (1/2) * (14x - 52)
2x + 14 = 7x - 26
5x = 40
x = 8
Hope this helps!
Answer:
Step-by-step explanation:
a rectangular painting has a diagonal measure of inches and an area of square inches. use the formula for the area of a rectangle and the pythagorean theorem to find the length and width of the painting.
A rectangular painting has a diagonal measure of 20 inches and an area of 192 square inches. Using the formula for the area of a rectangle and the Pythagorean theorem the length and width of the painting are 8 inches and 24 inches respectively.
To solve this question, we will use the given information: the area of the rectangle (192 square inches) and the diagonal length (20 inches), along with the formula for the area of a rectangle and the Pythagorean theorem.
Step 1: Recall the formula for the area of a rectangle:
Area = length × width
We know that the area of the painting is 192 square inches. So, we have:
192 = length × width
Step 2: Recall the Pythagorean theorem for a right triangle:
a² + b² = c²
In this case, a and b represent the length and width of the rectangle, and c represents the diagonal. We know that the diagonal is 20 inches. So, we have:
length² + width² = 20²
length² + width² = 400
Step 3: Solve the system of equations:
192 = length × width
400 = length² + width²
We will solve the first equation for length:
length = 192 ÷ width
Step 4: Substitute the expression for length in the second equation:
(192 ÷ width)² + width² = 400
Step 5: Solve the equation for width:
width² - 400 = -(192 ÷ width)²
width⁴ - 400width² + 192² = 0
Step 6: Factor the equation and solve for width:
(width² - 64)(width² - 576) = 0
Two possible values for width are 8 and 24.
Step 7: Find the corresponding lengths:
If width = 8, then length = 192 ÷ 8 = 24
If width = 24, then length = 192 ÷ 24 = 8
So, the length and width of the painting are 8 inches and 24 inches.
The complete question is:-
A rectangular painting has a diagonal measure of 20 inches and an area of 192 square inches. use the formula for the area of a rectangle and the Pythagorean theorem to find the length and width of the painting.
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There is a pair of parallel sides in the following shape.
What is the area of the shape?
The area of the shape is 28 square units.
The shape you described is a trapezoid, which is a 4-sided shape with two parallel bases that are different lengths. The area of a trapezoid is given by the formula: A=21(b1+b2)h.
In this case we are given that;
b1=6, b2=8, and h=4.
Plugging these values into the formula, we get:
A=21(6+8)4
A=21(14)4
A=7×4
A=28
Therefore, by the area the answer will be 28 square units.
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T/F : Span{a1,a2} contains only the line through a1 and the origin, and the line through the a2 and the origin.
False.
The span of {a1, a2} is the set of all linear combinations of a1 and a2. A linear combination of two vectors is of the form c1a1 + c2a2, where c1 and c2 are constants.
The span of {a1, a2} is the set of all linear combinations of a1 and a2. A linear combination of two vectors is of the form c1a1 + c2a2, where c1 and c2 are constants.
If a1 and a2 are linearly independent, then the span of {a1, a2} is the plane that contains a1 and a2. If a1 and a2 are linearly dependent, then the span of {a1, a2} is the line that contains a1 and a2.
So, in general, the span of {a1, a2} does not contain only the line through a1 and the origin, and the line through a2 and the origin. It can be a line, a plane, or all of R^3, depending on whether a1 and a2 are linearly dependent or independent.
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Write the decimal −0.43 (the 3 is repeating) as a fraction in simplest form.
Answer:
Step-by-step explanation:
Let's call the repeating decimal x, so x = -0.433333...
We can write this as:
10x = -4.33333...
And if we subtract x from 10x, we get:
10x - x = 9x = -4
So, x = -4/9.
Therefore, the decimal -0.43 (the 3 is repeating) as a fraction in simplest form is -4/9.
PLEASE HELP ME. WILL MARK BRAINLEST!!!
The values of θ in the equation are determined as 225.6⁰ and 314.4⁰.
What is the value of θ in the equation?The value of θ is calculated as follows;
The given equation; -7 cos²θ + 7 = 16sinθ + 15
cos²θ + sin²θ = 1
cos²θ = 1 - sin²θ
- 7(1 - sin²θ) + 7 = 16sinθ + 15
-7 + 7sin²θ + 7 = 16sinθ + 15
7sin²θ = 16sinθ + 15
Let sinθ = x
Our new equation becomes;
7x² = 16x + 15
7x² - 16x - 15 = 0
solve for x using formula method;
x = 3 or -0.714
Sinθ cannot be equal to 3, so we choose -0.714
Sinθ = -0.714
θ = sin⁻¹(-0.714)
θ = -45.6⁰
Since θ must be greater than θ, the possible values of θ are in third quadrant and fourth quadrant.
θ = 180 + 45.6⁰ = 225.6⁰
θ = 360 - 45.6⁰ = 314.4⁰
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Read and answer the question circled in red
The sum of the numbers less than 3 is 5/4
What are fractions?Fractions are simply defined as part of a whole variable, element or number.
In mathematics, there are different types of fractions, they are;
Proper fractionsImproper fractionsSimple fractionsComplex fractionsMixed fractionsExamples of simple fractions are; 1/2, 1/3, 1/4
Examples of mixed fractions are; 2 1/3, 4 1/3
Examples of improper fractions are; 5/2, 4/2
From the information given, we have that;
the sum of the numbers less than 3 is written as
1/2 + 3/4
Add the values
2 + 3/4
Add the values
5/4
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What is the IQR of the aged, in years?
The IQR of the ages, in years include the following: B. 16.
How to interpret the box-and-whisker plot?Based on the information provided about the given box plot or box-and-whisker plot, the five-number summary for the given data set include the following:
Minimum (Min) = 12.First quartile (Q₁) = 22.Median (Med) = 32.Third quartile (Q₃) = 38.Maximum (Max) = 44.How to calculate the interquartile range (IQR)?In Mathematics and Statistics, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) of data set = Q₃ - Q₁
Interquartile range (IQR) of data set = 38 - 22
Interquartile range (IQR) of data set = 16.
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find the value of each variable
The value of the sides are;
x = 13
y = 13 √2
How to determine the valueTo determine the value of the identities, we have to note the know the trigonometric identities. They are;
sinecosinetangentsecantcosecantcotangentFrom the information given, we have that;
Using the tangent identity;
tan θ = opposite/adjacent
substitute the values, we get
tan 45 = x/13
cross multiply the values
x = 13
Using the sine identity
sin 45 = 13/y
y = 13 √2
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The graph of f is translated a whole number of units horizontally and vertically to obtain the graph of g.
The function f is defined by f(x) = |x|
Write down the expression for g(x)
An expression for the function g(x) include the following: g(x) = |x - 3| + 4.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In order to write an expression that models g(x), we would have to apply a vertical translation to f(x) by 4 units up and a horizontal translation by 3 units right;
g(x) = f(x - 3) + 4
g(x) = |x - 3| + 4
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Early civilizations used standard measuring pottery to measure volume. As recently at the 1800's in the U.S. units of measures varied from area to area. When California became a state in 1850, one of the first laws passed was to establish weights and measures standards.
What is the volume of the cylinder?
Based on the above, the volume of the cylinder is 16oπ cubic inches or 502.65 cubic inches
What is the volume of the cylinder?
For one to be able to know the volume of the cylinder, then we need to use this formula below:
Where:
Volume = π x r² x h
Where π = pi
r = radius
H= height
Since the base radius is 4 inches and that of the height is 10 inches, we can then placed them into the above formula:
Volume = π × 4² × 10
Volume = π × 16 × 10
Volume = 160 π or simply say 502.65 cubic inches
Therefore, the volume of the given cylinder is about 160π cubic inches.
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We want the margin of error to be 2% while we are 95% confident. What sample size is
needed?
The sample size needed for the margin of error to be 2% while we are 95% confident is 9604.
Margin of error = 2%
Confidence interval = 95%
The formula to calculate the margin of error is,
MOE = z σ/√n
Here z is the test statistic, σ is the population standard deviation and n is the sample size.
For a normal distribution,
z value for 95% confidence interval = 1.96
Population standard deviation = 1
Substituting,
0.02 = 1.96 / √n
√n = 1.96 / 0.02
n = (1.96/0.02)² = 9604
Hence the sample size is 9604.
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12. Lucy earned $400 and
$550 in interest the last 2
years. How much interest
must she earn this year so
that her average earnings
over the three year period
is more than $600?
Inequality:
Answer:
Answer:
Check Screenshot for answer and explanation
Step-by-step explanation:
The president of Babyorganics Inc., a baby food producer, claims that her company’s product is superior to her competitors because babies gain weight faster with her product. To test the claim, a survey was undertaken. Mothers of newborns were asked which baby food they intended to use. Those who responded that they would use Babyorganics or the competitor were asked to keep track of their babies’ weight over the next 2 months. There were 15 mothers who indicated that they would feed their babies Babyorganics and 25 who responded that they would feed their babies the competitor’s baby food. Each baby’s weight was recorded at the end of the two months. Can the president of Babyorganics conclude the competitor’s food is not as good for increasing baby weight?
Based on the information provided in the output below, what is the correct decision
Reject the null hypothesis at the 0.10 level of significance
Reject the null hypothesis at the 0.05 level of significance
Do not reject the null hypothesis at the 0.05 level of significance
Both a and b are correct
1. Choose a significance level (e.g., 0.05 or 0.10).
2. Perform a statistical test (e.g., t-test or ANOVA) to compare the mean weight gains of the two groups of babies.
3. Compare the p-value obtained from the test to the chosen level of significance.
Based on the information provided, we do not have the output or data necessary to determine whether to reject the null hypothesis or not. However, we can interpret the terms "hypothesis," "level," and "significance" in this context.
- Hypothesis: The president of Baby Organics Inc. has made a claim that her company's product is superior to her competitors because babies gain weight faster with her product. This is the alternative hypothesis, which is being tested against the null hypothesis that there is no difference in weight gain between babies fed Babyorganics and those fed the competitor's baby food.
Null Hypothesis (H0): There is no difference in weight gain between babies fed Babyorganics and those fed the competitor's food.
Alternative Hypothesis (H1): Babies fed Baby organics gain weight faster than those fed the competitor's food.
- Level: The significance level is a threshold that is set to determine whether the results of the survey are statistically significant. This threshold is usually set at 0.05 or 0.10, indicating a 5% or 10% chance of rejecting the null hypothesis when it is actually true.
- Significance: If the results of the survey are statistically significant at the chosen level of significance, it means that the observed difference in weight gain between babies fed Baby Organics and those fed the competitor's baby food is unlikely to have occurred by chance alone and is therefore likely to be a real effect.
Make a decision based on the comparison:
- If the p-value is less than or equal to the level of significance, reject the null hypothesis, which means there is evidence to support the claim that Baby organics lead to faster weight gain.
- If the p-value is greater than the level of significance, do not reject the null hypothesis, which means there is insufficient evidence to support the claim.
In order to determine whether the president of Baby Organics Inc. can conclude that the competitor's food is not as good for increasing baby weight, we would need to see the actual data and results of the survey.
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Which net represents this solid figure?
Right rectangular prism is the net which represents the solid figure required figure
In three-dimensional space, prisms is a polyhedron where two ends are similar.
We want to find the solid figure.
Solids or three-dimensional forms in geometry are objects that have the three dimensions (length, width, and height).
From the given choices;
right rectangular prism is required figure.
Therefore, right rectangular prism is required figure.
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which of the following methods takes unsystematic risk also into account for performance evaluation of portfolios?a) sharpe ratio b) treynor ratio c) fama's net selectivity d) both 'a' and 'c'-
The correct answer is option d) both 'a' and 'c'. The Sharpe ratio and Fama's net selectivity are performance evaluation measures that take into account unsystematic risk along with systematic risk.
The Sharpe ratio measures the excess return of a portfolio over the risk-free rate per unit of total risk (i.e., both systematic and unsystematic risk) and is given by:
Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Portfolio Standard Deviation
Fama's net selectivity, on the other hand, measures a portfolio's ability to generate returns over and above what would be expected based on its exposure to different factors (i.e., systematic risk) and its level of unsystematic risk. It is calculated as the difference between the portfolio's actual return and the return predicted by a multifactor model that takes into account the portfolio's exposure to different factors. Both of these measures account for unsystematic risk along with systematic risk, making them useful for evaluating portfolio performance. The Treynor ratio, on the other hand, only takes into account systematic risk and not unsystematic risk.
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A bin contains seven red chips, nine green chips, three yellow chips, and six blue chips. Find the probability of drawing a yellow chip, not replacing it, and then choosing a blue chip.
A)13/49
B)7/10
C)42/625
D)13/50
The probability of first drawing a yellow chip without replacement and then drawing a blue is equal to 3/100.
Probability of an event without replacementThe probability of an event without replacement implies that once an item is drawn, then we do not replace it back to the sample space before drawing another item.
total number of chips = 7 + 9 + 3 + 6
total number of chips = 25
yellow chips = 3
blue chips = 6
probability of drawing a yellow chip = 3/25
probability of drawing a blue without replacing the first yellow drawn = 6/24
probability of drawing a yellow without replacement and then a blue = 3/25 × 6/24
probability of drawing a yellow without replacement and then a blue = 3/100.
Therefore, the probability of first drawing a yellow chip without replacement and then drawing a blue is equal to 3/100.
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the mean and standard deviation of salaries of players on the denver broncos were recorded. is it appropriate to use the methods of this section to perform a hypothesis test about the mean salary of players in the national football league? if not, why not?
It's important to consider the terms "deviation," "players," and the context of the question. The mean and standard deviation of the salaries of players on the Denver Broncos have been recorded. You'd like to know if it's appropriate to use these methods to perform a hypothesis test about the mean salary of players in the National Football League (NFL).
In this case, it may not be appropriate to use the methods of this section to perform a hypothesis test about the mean salary of players in the NFL. The reason is, the data collected only represents the players on the Denver Broncos and not the entire population of NFL players. The standard deviation and mean of the Denver Broncos' salaries may not accurately represent the salary distribution of the entire league, as there might be variations among different teams.
To perform a hypothesis test about the mean salary of players in the NFL, it would be necessary to gather data from a representative sample of players across all teams in the league. This would allow for a more accurate estimation of the true mean salary and standard deviation within the entire population of NFL players.
In conclusion, while the data collected for the Denver Broncos players provides useful information about that specific team, it is not sufficient to draw conclusions about the mean salary of players in the entire NFL without obtaining a representative sample from all teams.
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Calculate the area and circumference of a circle with diameter 8cm explain by step by step
Answer:
Area = 50.24 cm^2
Circumference = 25.12 cm
Step-by-step explanation:
To calculate the area and circumference of a circle with a diameter of 8cm, you can follow these steps:
Recall that the diameter of a circle is the distance across the circle passing through its center. In this case, the diameter is given as 8cm.
Recall that the radius of a circle is half of its diameter. To find the radius, you can divide the diameter by 2:
radius = diameter/2
radius = 8cm/2
radius = 4cmTo calculate the area of a circle, use the formula:
area = πr^2
where π is the mathematical constant pi (approximately 3.14) and r is the radius.
Substituting the values we have:
area = 3.14 x (4cm)^2
area = 3.14 x 16cm^2
area = 50.24cm^2
Therefore, the area of the circle with diameter 8cm is 50.24 square centimeters.
To calculate the circumference of a circle, use the formula:
circumference = 2πr
where π is again the mathematical constant pi and r is the radius.
Substituting the values we have:
circumference = 2 x 3.14 x 4cm
circumference = 25.12cm
Therefore, the circumference of the circle with diameter 8cm is 25.12 centimeters.
Answer:
the area is about 50.26548
the circumference is about 25.13274
Step-by-step explanation:
Divide the diameter by 2 to get the radius (4)
Then use this equation to find the area A=\pi r^{2}
A=\pi 4^{2}
A=16\pi
A= about 50.26548
Then use this equation to find the circumference C=\pi d
C=8\pi
C= about 25.13274
Which equation represents the parabola with focus
(
1
,
4
)
and latus rectum of 4?
y
=
−
1
4
(
x
−
1
)
2
+
3
y
=
4
(
x
−
1
)
2
+
3
y
=
(
x
−
1
)
2
+
4
y
=
1
4
(
x
−
1
)
2
+
3
The equation of parabola with with focus (1,4)and latus rectum of 4 is given as y=(x−1)2+4, hence option C is correct.
We know that the focus of the parabola is at (1, 4), and the latus rectum is 4 units long. The latus rectum is the line segment that passes through the focus and is perpendicular to the axis of symmetry. Its length is equal to 4 times the distance from the focus to the directrix. Since the latus rectum is 4 units long, the distance from the focus to the directrix is 1 unit.
Therefore, the directrix is the horizontal line y = 3, which is 1 unit below the focus. The axis of symmetry is the vertical line x = 1. The standard form of the equation of a parabola with vertex at the origin, axis of symmetry along the x-axis, and focus at (p, 0) is:
x² = 4py
In this case, the vertex is (1, 0) and the focus is (1, 4). Therefore, we can write,
x - 1 = 4p(y - 0)
x - 1 = 4py
We know that the distance from the focus to the vertex is p, which is 4 units in this case. Therefore, the equation of the parabola is,
(x - 1)² = 16y
Simplifying this equation, we get,
y = (1/16)(x - 1)²
Therefore, the answer is C. y = (x - 1)²/16.
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Complete question - Which equation represents the parabola with focus (1,4) and latus rectum of 4?
A. y=−14(x−1)²+3
B. y=4(x−1)²+3
C. y=(x−1)²+4
D. y=14(x−1)²+3