Matthew can travel up to 150 miles for $50, assuming the cost of the limo ride remains constant at a $20 fixed cost plus $0.20 per mile. Let's say Matthew has $50 to spend on the limo ride.
We know that the cost per mile is $0.20, so we can set up an equation:
Cost = $20 + $0.20 x Distance
We can substitute $50 for Cost and solve for Distance:
$50 = $20 + $0.20 x Distance
$30 = $0.20 x Distance
Distance = $30 / $0.20
Distance = 150 miles
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deduce that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the slim. in particular, the sum cannot be uniformly distributed on the numbers from 2 to 12. g
We know that no matter how the two dice are biased, the numbers 2, 7, and 12 cannot be equally likely values for the sum. In particular, the sum cannot be uniformly distributed on the numbers from 2 to 12.
Explanation:
When we roll a fair die (i.e. an unbiased die), the probabilities of getting any one of the six possible numbers {1, 2, 3, 4, 5, 6} are equal to 1/6 each. But, when we use a biased die, the probabilities of getting any of the six possible numbers will no longer be equal. Some numbers will be more likely to occur, while others will be less likely to occur
For example:
if one of the dice has a weight in such a way that it always rolls a 6, then the probability of getting a sum of 2 will be zero, the probability of getting a sum of 7 will be 1/6, and the probability of getting a sum of 12 will be zero.However, if the dice are biased in some other way, we can still get non-zero probabilities for the sums of 2, 7, and 12. But, the probability of getting those three sums will not be the same. For instance, if one die is biased to always roll a 1, and the other die is biased to always roll a 6, then the probabilities of getting each of the sums 2, 7, and 12 are as follows:
P(2) = P(1, 1) = (1/6)² = 1/36
P(7) = P(1, 6) + P(6, 1) + P(2, 5) + P(5, 2) + P(3, 4) + P(4, 3) = 6(1/6)(1/6) = 1/6P(1
2) = P(6, 6) = (1/6)² = 1/36
So, the probability of getting a sum of 7 is six times as likely as getting a sum of 2 or 12. Therefore, the sum cannot be uniformly distributed on the numbers from 2 to 12.
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What is the value of angle X
Answer:
32
Step-by-step explanation:
A rental car company charges $74. 90 per day to rent a car and $0. 13 for every mile driven. Tyee wants to rent a car, knowing that:
He plans to drive 175 miles. He has at most $210 to spend. Write and solve an inequality which can be used to determine
�
x, the number of days Tyee can afford to rent while staying within his budget
Tyee can afford to rent the car for at most 2 days while staying within his budget.
Let x be the number of days Tyee can rent the car within his budget.
The total cost of renting the car will be the sum of the daily rental fee and the cost of miles driven:
Total cost = rental fee + (cost per mile x miles driven)
Using the given information, we can write the inequality:
74.90x + 0.13(175)x ≤ 210
Simplifying the expression, we get:
74.90x + 22.75x ≤ 210
97.65x ≤ 210
x ≤ 2.15
Therefore, Tyee can afford to rent the car for at most 2 days while staying within his budget.
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a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409.0 409.0 gram setting. it is believed that the machine is underfilling the bags. a 38 38 bag sample had a mean of 406.0 406.0 grams. a level of significance of 0.05 0.05 will be used. state the hypotheses. assume the variance is known to be 400.00 400.00 . enter the hypotheses:
The null and alternative hypotheses for the manufacturer of banana chips can be defined as:
H0: µ = 409 (Null Hypothesis)
Ha: µ < 409 (Alternative Hypothesis)
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409.0 409.0 gram setting. It is believed that the machine is underfilling the bags. A 38 bag sample had a mean of 406.0 grams. A level of significance of 0.05 will be used. State the hypotheses. Assume the variance is known to be 400.00. Enter the hypotheses.
The null and alternative hypotheses for the manufacturer of banana chips can be defined as:
H0: µ = 409 (Null Hypothesis)
Ha: µ < 409 (Alternative Hypothesis)
Where µ is the population mean of the weight of banana chips in a bag. The level of significance is 0.05. As the population variance is known, the z-test can be performed. To test the above hypotheses, we can calculate the test statistics as shown below :
z = (X - µ) / [σ / √(n)]
Where, X = Sample mean = 406, Population mean = 409, Population standard deviation = 20 (Square root of variance = √400) , Sample size = 38 substituting the given values, we get
= (406 - 409) / [20 / √(38)]z = -1.581
According to the z-distribution table, the probability of getting a value less than or equal to -1.581 is 0.0562. It means the p-value is 0.0562. Since the p-value (0.0562) > α (0.05), we fail to reject the null hypothesis H0.
Therefore, there is not enough statistical evidence to conclude that the bag filling machine is underfilling the bags at the 409-gram setting. Thus, the given statement is false.
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(1 point) in a baseball league of 10 teams, how many games are needed to complete the schedule if each team plays 9 games with each other?
Answer:
90
Step-by-step explanation:
In a baseball league of 10 teams, 405 games are needed to complete the schedule if each team plays 9 games with each other.
Each team must play 9 games against each other, and there are 10 teams in the baseball league. We'll need to figure out how many games that means each team will play.Each team will play 9 games against every other team, for a total of 9 x 9 = 81 games played by each team (including games they play against themselves).Since there are 10 teams in the league, the total number of games played will be:
81 x 10 = 810.
However, each game is played between two teams, so we must divide by 2 to get the total number of games:
810 / 2 = 405.So, there will be 405 games played in the league.
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how many acres are in a government rectangular survey that consists of the sw 1/4, ne 1/4, and nw 1/4 of section 13, blendon township?
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
We have,
In the Government Rectangular Survey System, a section is a square tract of land measuring 1 mile by 1 mile, covering an area of 640 acres.
Each section is divided into quarters.
If we consider the SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township, the total acreage can be calculated as follows:
SW 1/4:
This represents one-fourth of the section.
The SW 1/4 of Section 13 is 640 acres / 4 = 160 acres.
NE 1/4:
The NE 1/4 of Section 13 is also 160 acres.
NW 1/4:
The NW 1/4 of Section 13 is 160 acres.
To find the total acreage, add up the individual acreages:
160 acres (SW 1/4) + 160 acres (NE 1/4) + 160 acres (NW 1/4)
= 480 acres
Therefore,
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
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pls help Mariah sells her paintings which she frames using pieces of wood that are 1 inch wide . Her paintings come in difference sizes , but the width is always 1.5 times the height Write an equation to represent the total area of her paintings and their frames .
if u can pls draw the height and width :)
Step-by-step explanation:
Lets use A for area, W for width, and H for height (sorry in advance for bad handwriting, I am writing using a mouse)
Since area is equal to width times height, lets make an equation given what we already know.
A = W * H
Now lets use the given parameters to create a proper area equation, partially answering the question.
A = (H*1.5) * H, H*1.5 being the width
Now we have the frames to add to this equation
Since these frames are 1 inch thick, this adds one inch to the width and the height.
You use order of operations to assume that we are calculating this by multiplying the height by 1.5 first, then adding the one inch to the width and height.
So our final equation is:
A = ((h*1.5)+1) * (h+1)
Lets give some example values
Height is 6, width is 6*1.5, meaning width is 9
After, we add one to the height and the width, meaning the height is 7 and the width is 10.
Lets multiply these together, and the total square area is 70 inches squared.
please help me solve this geometry proof i’ll mark brainliest
BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)
What is triangle congruency?Triangle congruence: Two triangles are said to be congruent if their three corresponding sides and their three corresponding angles are of identical size.
You can move, flip, twist, and turn these triangles to produce the same effect. When relocated, they are parallel to one another.
Two triangles are congruent if they satisfy all five conditions for congruence.
They include the right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and angle-side-angle (SSS) (RHS).
So, in the given △DAB and △DCB:
AC = AC = Common
∠DAC = ∠BAC = AC is the angle bisector
∠DCA = ∠BCA = AC is the angle bisector
Then, △DAB ≅ △DCB under the ASA congruency rule,
Then, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)
Therefore, BC will be congruent to AD under the C.P.C.T rule (corresponding parts of congruent triangles.)
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match the quadratic equation with the easiest method that could be used to find the solutions.
The quadratic equation with the easiest method that could be used to find the solutions:
5x² + 24x + 21 = 0 :: Factoring
x² + 4x + 27 = 0 :: Completing the Square
x² + 8x + 15 = 0 :: Factoring
-3x² = -5x + 8 :: Dividing by x and simplifying gives Quadratic Formula
What is equation?An equation is a mathematical statement that uses an equal sign to show that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of an equation is to solve for the variable(s) that make the equation true.
Here,
The easiest method to find the solutions of a quadratic equation depends on the form of the equation and the tools available. Here are some common methods and when they are typically used:
Zero Product Property/Factoring: This method is used when the quadratic equation can be factored into two linear factors, each of which equals zero.
Square Root Property: This method is used when the quadratic equation is in the form of x² = a, where a is a positive number. For example, the equation x² = 9 can be solved using the Square Root Property: take the square root of both sides and remember to include both the positive and negative roots, giving x = ±3.
Completing the Square: This method is used when the quadratic equation is in the form of x² + bx + c = 0, where b and c are constants. Completing the square involves adding and subtracting a constant term to both sides of the equation to create a perfect square trinomial, which can then be factored and solved using the Square Root Property.
Quadratic Formula: This method is used when the quadratic equation is in the form of ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. The Quadratic Formula is x = (-b ± √(b² - 4ac)) / 2a.
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you randomly choose one of the chips. without replacing the first chip, you choose a second chip. find the probability of choosing a green chip, then a black chip.
The probability of randomly choosing a green chip, then a black chip without replacing the first chip is 1/6.
To explain, we need to consider the probability of choosing a green chip first, then a black chip. The probability of selecting a green chip is 1/3, since there are 3 green chips out of 9 chips in total. After selecting the green chip, there are still 8 chips left in the bag. Since there are 2 black chips, the probability of selecting the black chip is 2/8.
Therefore, the probability of randomly selecting a green chip, then a black chip without replacing the first chip is 1/3 * 2/8 = 1/6.
In conclusion, the probability of randomly choosing a green chip, then a black chip without replacing the first chip is 1/6.
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PLEASE HELP ASAP!! NEED THIS RIGHT NOW
A crafts worker is knitting a circular rug that has a diameter of 80 inches. He would like to put trim around the outer edge of the rug. If 1 inch = 2.54 centimeters, how many centimeters of trim would
he need? Use π = 3.14 and round to the nearest centimeter.
O 638 centimeters
O 254 centimeters
O213 centimeters
O 33 centimeters
Answer:254
Step-by-step explanation:
I just did it
Answer: 254
Step-by-step explanation: i did a test and it was right
Answer options
2 units
4 units
6 units
10 units
As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.
what is triangle ?Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.
given
The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.
To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.
As a result, we have:
sin 30° = (6/2x)
Adding two times to both sides:
2x * sin 30° = 6
Using sin 30°, which has a value of 0.5:
x = (6/(2 * 0.5)) = 6/1 = 6
Consequently, the side YZ is 6 units long.
As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.
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Aaliyah puts 42 gal of water into her fish tank . This is 60% of the total number of gallons the fish tank can hold how many total gallons of water can the fish tank hold
Answer:
58.8 gallons
Step-by-step explanation:
past data suggest that the score increase has astandard deviation of about 50 points. how large a sample of high school students would be needed to estimate the mean change in sat score to within 2 points with 95% confidence
382 students
To estimate the mean change in SAT scores to within 2 points with 95% confidence, you would need a sample of at least 382 high school students. This is because the margin of error (2 points) must be smaller than the standard deviation (50 points). Thus, we use the formula margin of error = (z-score) x (standard deviation/√n), where n is the sample size, to calculate the required sample size. Solving for n yields 382 students.
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On the first day of school, the principal said Chase had the chance to
3. Reasoning In Example 2, what happens to the
value of the dependent variable, a, the amount
still owed, when the value of the independent
variable, w, the number of weeks Ethan pays $5,
is increased by 1?
Answer:
In Example 2, the relationship between the dependent variable a, the amount still owed, and the independent variable w, the number of weeks Ethan pays $5, is given by the equation:
a = 100 - 5w
If we increase the value of w by 1, then the new value of w becomes w + 1. To find out what happens to the value of the dependent variable a, we substitute w + 1 for w in the equation:
a = 100 - 5(w + 1)
a = 100 - 5w - 5
Simplifying this expression, we get:
a = 95 - 5w
Comparing this expression to the original equation, we see that the value of the dependent variable a decreases by 5 when the value of the independent variable w is increased by 1. Therefore, if Ethan pays $5 for one more week, the amount still owed will decrease by $5.
the mean of eight numbers is 25. when two extra numbers are included the mean of the ten numbers is 24. find the mean of the two extra numbers.
The mean of eight numbers is 25, and when two extra numbers are included the mean of the ten numbers is 24. This means that the two extra numbers must be lower than 25 in order to bring down the mean of the ten numbers to 24.
To find the mean of the two extra numbers, we need to subtract the sum of the first eight numbers from the sum of all ten numbers.
The sum of the first eight numbers is 8 x 25 = 200, and the sum of all ten numbers is 10 x 24 = 240.
Subtracting 200 from 240 gives us 40.
Since there are two extra numbers, we need to divide 40 by 2 to find the mean.
the mean of the two extra numbers is 40 / 2 = 20.
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PLEASE HELP NEED IT DONE RN !!
Answer: rectangleular pyramid
Step-by-step explanation:
-1/x-1+2/x+5=1 State any restrictions on the variable if they exist
The solution to the equation is x = -2 if x ≠ 0.
The equation -1/x-1+2/x+5=1 can be rearranged to 2/x+1/x+5 = 0. To solve this equation, we must find the values of x for which the equation is true.
Since the equation involves dividing by x, we need to ensure that x is not equal to 0. Therefore, the restriction on the variable is x ≠ 0.
To solve the equation, we can first add -1/x to both sides to get 2/x + 5 = 1. Then, we can subtract 5 from both sides to get 2/x = -4. Finally, we can divide both sides by 2 to get x = -2.
Therefore, the solution to the equation is x = -2 if x ≠ 0.
To solve the given equation, we need to first find a common denominator. Here, the common denominator is (x - 1)(x + 5).-1(x + 5) + 2(x - 1) = (x - 1)(x + 5)Multiplying both sides by (x - 1)(x + 5), we get:-1(x + 5)(x - 1) + 2(x - 1)(x + 5) = (x - 1)(x + 5)(1)Expanding, we have:-x² - 4x + 5 + 2x² + 8x - 10 = x² + 4x - 5Simplifying,-x² + 2x² + x² - 4x + 8x + 4x + 5 + 10 - 5 = 0- x² + 8x + 10 = 0Rearranging, we have:x² - 8x - 10 = 0To solve the quadratic equation x² - 8x - 10 = 0, we use the quadratic formula. The formula is given byx = [-b ± sqrt(b² - 4ac)] / 2a Where a = 1, b = -8, and c = -10.Substituting these values, we get:[tex]x = [8 ± sqrt((-8)² - 4(1)(-10))] / 2(1)[/tex]
Simplifying = [8 ± sqrt(64 + 40)] / 2x = [8 ± sqrt(104)] / 2x = 4 ± sqrt(26)Therefore, the restrictions on the variable Are's ≠ 1 and x ≠ -5.
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Can someone help me with this aleks
I think the best way to do this is by splitting up the trapezoid into two shapes since it is not a regular trapezoid. We can make a split to form a small right triangle on the left and a regular trapezoid on the right.
Small right triangle on the left:
4 inch side length and 6 inch hypotenuse with the Pythagorean theorem will give us the missing side.
missing side = square root of 6^2-4^2 = [tex]2\sqrt{5}[/tex]
Then the area is [tex]\frac{1}{2}*4*2\sqrt{5}=4\sqrt{5}[/tex]
Regular trapezoid on the right:
Area will be [tex]\frac{6+(17-2\sqrt{5})}{2}*4=46-4\sqrt{5}[/tex]
Summing up the two areas to get the total we have [tex]4\sqrt{5}+46-4\sqrt{5}=46[/tex] in^2.
Which expression can be used to model the phrase "the sum of three and a number"?
O 3+x
O x-3
O 3-х
O x•3
Answer: "3 + x".
Step-by-step explanation:
luis wants to create a graph using powerpoint to show how much weight he lost after starting an exercise plan over six months. which type of graph should he use?
Luis wants to create a graph using PowerPoint to show how much weight he lost after starting an exercise plan over six months. The type of graph that Luis should use is a line graph.
What is a line graph?A line graph is a method of displaying data or information on a two-dimensional Cartesian plane. It is mostly used to display changes over time or trends. It is ideal for data that has a lot of numeric data or that change frequently over time.The line graph is made up of two lines, one horizontal and the other vertical, which connect the data points in a sequential order. It is best used for visual representation of data, as it provides the viewer with a simple, visual representation of the data.
The x-axis and y-axis of a line graph represent the independent and dependent variables, respectively. The x-axis is often used to represent the time or the data being analyzed, while the y-axis represents the numerical values that are being analyzed.To create a line graph using PowerPoint, you can use the Insert Chart button to add your data, then choose Line Graph as the type of chart you want to create. You can then customize the chart as you like, including changing the colors, fonts, and background.
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There are 20 students in a class. Everyone in the class scored 6 out of 10 in a test. What is the range of their scores?
The range of scores is 0 to 10. Since everyone in the class scored 6 out of 10, the lowest possible score is 0 and the highest possible score is 10.
The range is the difference between the highest and the lowest of the given scores. In this case, it's 4 (10-6).
Therefore, the range of scores is 0 to 10. It is important to note that the range is a measure of the spread of scores in a dataset, and in this case, the spread is from the lowest possible score of 0 to the highest possible score of 10.
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what are coordinate planes explain:
Answer:
a two-dimension surface formed by two number lines.
PLS HELP ME ASAP I WILL MARK THE BRAINLIEST!!!!
The fourth term of the arithmetic progression is found to be 29.
Explain about the arithmetic progression?A sequence is a collection of numbers that move from expression to term according to a specific pattern or rule.
You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequence data, quadratic sequences, and special sequences.
An ordered collection of integers with a shared distinction between each word is known as an arithmetic sequence.It constitutes an arithmetic sequence if we add as well as subtract by the same amount each time to create the sequence.The given equations are:
a1 = 5
an = 2[tex]a_{n - 1}[/tex] + 3
put n = 1, 2 , 3...
Second term will be:
a2 = 2[tex]a_{2 - 1}[/tex] + 3
a2 = 2[tex]a_{1}[/tex] + 3
Put the value of a1 = 5
a2 = 2*5 + 3
a2 = 13
Now, the common difference d = 13 - 5 = 8
a4 = a1 + (n - 1)d
a4 = 5 + (4 - 1)*8
a4 = 5 + 3*8
a4 = 29
Thus, the fourth term of the arithmetic progression is found to be 29.
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Which of the following limits are indeterminate forms?Given that lim x->a f(x)=0lim x->a g(x)=0lim x->a h(x)=1lim x->a p(x)=infinitylim x->a q(x)= infinity. THEN(a) lim x->a f(x)/g(x)= (b) lim x->a f(x)/p(x)=(c) lim x->a h(x)/p(x)=(d) lim x->a p(x)/f(x)=(e) lim x->a p(x)/q(x)=
In conclusion, the indeterminate forms among the given limits are
(a) lim x->a f(x)/g(x)
and
(e) lim x->a p(x)/q(x).
The indeterminate forms are expressions that cannot be directly determined or evaluated when approaching a specific limit. In calculus, there are several common indeterminate forms such as 0/0, ∞/∞, 0⋅∞, ∞−∞, 0^0, 1^∞, and ∞^0.
Let's analyze each given limit:
(a) [tex] lim x->a f(x)/g(x) = 0/0[/tex]: This is an indeterminate form because it is of the form 0/0.
(b) lim x->a f(x)/p(x) = 0/∞: This limit is not indeterminate; it equals 0 since the numerator is 0 while the denominator approaches infinity.
(c) lim [tex]x->a h(x)/p(x) = 1/∞[/tex]: This limit is not indeterminate; it equals 0 because the numerator is a constant value (1) and the denominator approaches infinity.
(d) [tex]lim x->a p(x)/f(x) = ∞/0[/tex]: This limit is not an indeterminate form, but rather an undefined form because division by zero is undefined.
(e) [tex] lim x->a p(x)/q(x) = ∞/∞[/tex]: This is an indeterminate form because it is of the form ∞/∞.
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how many different arrangements are there of eight peo- ple seated at a round table, where two arrangements are considered the same if one can be obtained from the other by a rotation?
The number of different arrangements of eight people seated at a round table, where two arrangements are considered the same if one can be obtained from the other by a rotation, is (8-1)!/2 = 7!/2 = 2,520.
To solve this problem, we use the formula for arranging objects in a circle, which is (n-1)!, where n is the number of objects. In this case, there are 8 people, so the formula gives us (8-1)! = 7! arrangements if we do not consider rotations.
However, we need to eliminate the arrangements that are the same due to rotations. Since there are 8 people, we can rotate the table 8 times and still get the same arrangement. Thus, we divide 7! by 8 to eliminate these duplicate arrangements, which gives us (7!)/8.
But we are not done yet, because there is an additional duplicate arrangement that is not eliminated by the division. Specifically, we can flip the table over and get another arrangement that is the same as the original. Since we do not want to count this duplicate, we divide (7!)/8 by 2, giving us the final answer of 2,520.
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650 of those surveyed said their favorite color was blue. if 65% of the students surveyed said their favorite color was blue, how many students were surveyed in total?
Answer:
let X be the value of the total students
[tex] \frac{65}{100} \times x = 650 \\ \\ \frac{65x}{100 } = 650 \\ if \: w \:e \: crossmultipl \\ 65x = 65000 \\ x = 65000 \div 65 \\ x = 1000[/tex]
20. while standard deviation and beta are both measures of risk, there are differences between the two. which of the following is correct? a. beta measures all risk b. beta measures only systematic risk c. beta measures only unsystematic risk d. standard deviation and beta are different, but both measure total risk
Standard deviation and beta are both measures of risk, however Beta is used to measure systematic risk. The correct answer is option (B), beta measures only systematic risk.
Standard deviation and beta are both measures of risk, however, there are differences between them. Standard deviation is a measure of the variation or dispersion of a set of data values. It shows the average deviation of each value from the mean. It is expressed in the same units as the original data.
Beta, on the other hand, is a measure of the systematic risk of an investment relative to the market as a whole. It reflects the extent to which the return on a particular security or portfolio moves with the overall market, and is often used in the Capital Asset Pricing Model (CAPM) to estimate the required rate of return for an investment. It measures the sensitivity of the security's returns to the market.
The systematic risk of an investment is the risk that is associated with the market as a whole, rather than with a particular security. It is often referred to as market risk because it is based on factors that affect the entire market, such as changes in interest rates, inflation, or economic conditions.
Unsystematic risk, on the other hand, is the risk that is specific to a particular security or industry, and is caused by factors that affect that particular security or industry, such as management changes, lawsuits, or other events that affect the company's operations.
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on a business retreat, your company of 32 businessmen and businesswomen go golfing. you need to divide up into foursomes (groups of 4 people): a first foursome, a second foursome, and so on. how many ways can you do this?
There are 4,845 ways to divide a group of 20 people into foursomes, and there are 1,800 ways to form foursomes with at least one Board member in each.
(a) The number of ways to divide a group of 20 people into foursomes can be calculated using the combination formula:
C(20,4) * C(16,4) * C(12,4) * C(8,4) * C(4,4)
where C(n,r) represents the number of ways to choose r items from a set of n items.
Plugging in the values, we get:
[C(20,4)] [C(16,4)] [C(12,4)] [C(8,4)] [C(4,4)] = 4,845,120
Therefore, there are 4,845,120 ways to divide the 20 people into foursomes.
(b) If we want to include one of the five Board members in each foursome, we can first choose the Board member for the first foursome (5 ways to do this), then choose the Board member for the second foursome (4 ways to do this), and so on. After choosing the Board members, we can then assign the remaining people to the foursomes in the same way as in part (a).
Therefore, the total number of ways to form the foursomes with one Board member in each foursome is:
5 [C(16,3)] [C(12,3)] [C(8,3)] [C(4,3)] = 1,254,720
Learn more about combinatorics here: brainly.com/question/13261685
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Complete question:
On a business retreat, your company of 20 businessmen and businesswomen go golfing.
(a) You need to divide up into foursomes (groups of 4 people): a first foursome, a second foursome, and so on. How many ways can you do this?
(b) After all your hard work, you realize that in fact, you want each foursome to include one of the five Board members. How many ways can you do this?