50 Points! Multiple Choice Algebra Question. The Related Graph Of A Quadratic Equation Is Shown At The (2024)

Mathematics College

50 Points! Multiple Choice Algebra Question. The Related Graph Of A Quadratic Equation Is Shown At The (1)

Answers

Answer 1

The solution of the quadratic equation is option C {-3, 2}.

What is solution of quadratic equation?

Numerous techniques, such as factoring, completing the square, and the quadratic formula, can be used to solve quadratic equations. The values of x that make a quadratic equation true are represented by the solutions to the equation, which are known as its roots or zeros.

In several disciplines, including physics, engineering, economics, and finance, quadratic equations are frequently employed to simulate real-world occurrences. They can be used to depict a variety of phenomena, including a projectile's motion, an electrical circuit's behaviour, a satellite's trajectory, the cost of production, and many more.

The solutions of the quadratic equation are the x-intercepts of the graph. That is the point at which the graph, crosses the x-axis.

For the given graph the x-intercepts are {-3, 2}.

Hence, the solution of the quadratic equation is option C {-3, 2}.

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Related Questions

1) (5,-5) (2,5)find the slope from the pair of points ​

Answers

Answer: slope = -10/3

Step-by-step explanation:

Answer:

slope = - [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, - 5 ) and (x₂, y₂ ) = (2, 5 )

m = [tex]\frac{5-(-5)}{2-5}[/tex] = [tex]\frac{5+5}{-3}[/tex] = [tex]\frac{10}{-3}[/tex] = - [tex]\frac{10}{3}[/tex]

How how much water can this container hold? Use 3.14 to approximate high battery to the nearest 100

Answers

A spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.

To solve the question :

The volume of a sphere = 4/3 πr³

Where,

π = mathematical constant pi and

r = radius of the sphere.

Given,

radius (r) = 8 cm and

π = 3.14,

Substituting the values of π and r to the volume equation

V = (4/3) x 3.14 x 8³

V = (4/3) x 3.14 x 512

V = 2688.53 cm³ (rounding off to the nearest hundredth)

Hence, a spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.

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Express 658.75 in standard form

Answers

Answer:

6.5875 × 10^2

Step-by-step explanation:

Standard form format is: a×10^b

A number is written in standard form when it is represented as a decimal number times a power of 10.

As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 10^8.

Example: Convert 459,608 to Standard Form

Move the decimal 5 places to the left to get 4.59608

a = 4.59608

We moved the decimal to the left so b is positive

b = 5

The number 459,608 converted to standard form is 4.59608 x 10^5

hope this helps <3

simplify the expression ^4√16x^12y^16
(show explanation please).

Answers

Answer: 2x^3y^4

Step-by-step explanation:

The expression ^4√16x^12y^16 can be simplified as follows:

^4√16 = 2, since 2^4 = 16

x^12 can be written as (x^3)^4, and ^4√(x^3)^4 = x^3

y^16 can be written as (y^4)^4, and ^4√(y^4)^4 = y^4

Therefore, ^4√16x^12y^16 simplifies to:

2x^3y^4

A bag contains 26 letters and 10 numerals. Robin draws two cards from the
bag. What is the probability that she draws 2 numerals?
OA. 1/7
O B. 1/14
O C.1/63
D. 2/13

Answers

Answer:

On the first draw, there are 10 numerals out of 36 cards.

P(first card is a number) = 10/36 = 5/18

On the second draw, there are 9 numerals out of 35 cards.

P(second card is a number) = 9/35

The probability of both events is the product:

P(both cards are numbers) = P(first card is a number) x P(second card is a number)

= 5/18 x 9/35

= 1/2 x 1/7 (cancel a 5 and a 9).

= 1/14

Malachi asks students in his class, "How long does it take you to get to school?" The histogram shows the data. Which statement best describes the distribution?

Answers

The data from the distribution shows a symmetric distribution.

When is the data from a distribution symmetric?

The data from a distribution can be described as symmetric when the values of the data are evenly distributed around its center point. This mans that if the data is folded along its center point and the two halves overlap perfectly, then the distribution is said to be symmetric.

In the histogram, we see an example of symmetric data because the center value that has the frequency of 10 ahs even distribution on both sides.

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Help with math problems

Answers

1. The solution to the system of equations is v = -3 and w = 4.

2. The solution to the system of equations is y = 6 and z = -2.

How to solve for -v + w = 7; v + w = 1?

To eliminate v, we can add the two equations:

(-v + w) + (v + w) = 7 + 1

2w = 8

w = 4

Substitute w = 4 into one of the equations to solve for v:

v + 4 = 1

v = -3

How to solve for y + z = 4; y - z = 8?

To eliminate z, we can add the two equations:

(y + z) + (y - z) = 4 + 8

2y = 12

y = 6

Substitute y = 6 into one of the equations to solve for z:

6 + z = 4

z = -2.

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solve the equation x^2+4x-11=0 by completing the square

Answers

To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:

Move the constant term to the right side of the equation:

x^2 + 4x = 11

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 + 4x + (4/2)^2 = 11 + (4/2)^2

Simplifying the left side:

x^2 + 4x + 4 = 11 + 4

Factor the perfect square on the left side of the equation:

(x + 2)^2 = 15

Take the square root of both sides of the equation:

x + 2 = ±√15

Solve for x by subtracting 2 from both sides:

x = -2 ± √15

Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.

For this answer the equation would be

2
+
4


1
1
=
0

On a standardized test with a normal distribution, the mean was 64.3 and the standard deviation was 5.4.
Approximately what percent of those taking this exam had scores between 58.9 and 69.7?
Responses
A 68.3%
B 38.2%
C 60.0%
D 34.1%

Answers

The percent of those taking this exam had scores between 58.9 and 69.7 is 34.1%

What is standardized test?

To find the number of standard deviations 58.9 and 69.7 are above and below the mean, find the difference between these two numbers and the mean, then divide by the standard deviation 5.4:

z1 = (58.9 - 64.3) / 5.4 = -0.996

z2 = (69.7 - 64.3) / 5.4 = 1.004

Since the absolute values of the z-scores are almost equal, we can approximate the area between them as half of the total area between -1 and 1 standard deviations.

Therefore, the approximate percentage of those taking the exam with scores between 58.9 and 69.7 is:

68% / 2 = 34%

Therefore, the correct option is D 34.1%.

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Alexandra is a head librarian in a city with a population of 1.8×106 residents. When her library system conducted a survey, they found that the average resident visits a library 1.5 times per year. How many total library visits per year does that work out to?
Write your answer in standard form. Do not use exponents. THE ANSWER IS 2,700,000 YOUR WELCOME...

Answers

The total number of library visits per year is 2.7 million, written in standard form as 2.7×106.

What is average?

Average refers to the central tendency or typical value of a set of numerical data, which is obtained by dividing the sum of the values by the total number of values. It is a commonly used statistical measure that helps to represent the general trend or level of a dataset. The average can be calculated for various types of data, such as income, age, weight, and test scores, among others.

According to the given information:

To calculate the total number of library visits per year, we need to multiply the average number of visits per resident by the total population:

Total number of library visits per year = average visits per resident x total population

Substituting the given values, we get:

Total number of library visits per year = 1.5 x 1.8×106

Multiplying, we get:

Total number of library visits per year = 2.7×106

Therefore, the total number of library visits per year is 2.7 million, written in standard form as 2.7×106.

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Simplify 6^2/6 x 6^12/6^8

Answers

Step-by-step explanation:

6^2 / 6^1 x 6^12 / 6^8 =

6^(2-1) x 6^(12-8) =

6^1 x 6^4 =

6^(1+4) = 6^5 or = 7776

What is the height of the cylinder?

5m diameter
13 m

Cylinder
10.5 m
12 m
13.9 m
9 m

Answers

As a result, the cylinder's height is roughly 1.65 metres as In the second line, we failed to deduct 39.27 from both sides.

what is cylinder ?

A cylinder is really a muti geometric shape made up of two circular bases that are congruent and parallel to one another, as well as a curving lateral surface that links the bases. It can be envisioned as a reasonable shape that is created by extending a circle perpendicular to the plane of the circle. Several advantageous characteristics of the cylinder, such as a constant bridge area over its whole length, make it suitable for a wide range of practical applications. For instance, a lot of different kinds of containers, such pipes and tubes, have cylindrical shapes. The following formula can be used to figure out the size of a cylinder:[tex]V = \pi r^2h[/tex] where V is the capacity, r is the circumference of the spherical base, and h is the cylinder's height.

given

We must apply the formula for a cylinder's surface area, which is: to determine the cylinder's height.

[tex]SA = 2\pi r^2 + 2\pi rh[/tex]

where SA stands for surface area, r for base radius, and h for cylinder height.

The cylinder has a radius of 2.5 m and a diameter of 5 m.

[tex]13 = 2\pi (2.5)^2 + 2\pi (2.5)h[/tex]

13 = 39.27 + 15.71h

-26.27 = 15.71h

h = -26.27/15.71 ≈ -1.67

In the second line, we failed to deduct 39.27 from both sides. When we do this, the height is given a positive value:

h = (13 - 39.27) / 15.71 ≈ 1.65

As a result, the cylinder's height is roughly 1.65 metres as In the second line, we failed to deduct 39.27 from both sides.

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Answer: 12m

Step-by-step explanation:

Test the following hypotheses by using the given sample information and α = .01. Assume the populations are normally distributed.
H0 : σ2 =σ2 Ha:σ2 >σ2 1212
n1 =10, n2 =11, s2 =562, s2 =1013 12

Answers

Since the calculated F-value of 0.555 is less than the critical value of 4.025, we fail to reject the null hypothesis.

What is null hypothesis?

A null hypothesisis a statement that establishes the equality of two expressions and frequently includes variables, constants, and mathematical operations.

The equal sign (=) is used to denote the space between the two sides, which are referred to as the left-hand side (LHS) and the right-hand side (RHS).

To test the given hypothesis, we will use the F-test for two variances.

The null and alternative hypotheses are:

H0: σ1² = σ2² (no difference in population variances)

Ha: σ1² > σ2² (population variance of first group is greater than that of second group)

The test statistic is calculated as:

F = s1² / s2²

Where s1² and s2² are the sample variances of the two groups.

The degrees of freedom for the F-distribution are df1 = n1 - 1 and df2 = n2 - 1.

Using the given sample information, we have:

n1 = 10, n2 = 11

s1² = 562, s2² = 1013

Therefore, the test statistic is:

F = s1² / s2² = 562 / 1013 = 0.555

The degrees of freedom are df1 = 9 and df2 = 10.

Using a significance level of α = 0.01 and the F-distribution tables or a calculator, the critical value for the right-tailed test with df1 = 9 and df2 = 10 is 4.025.

Since the calculated F-value of 0.555 is less than the critical value of 4.025, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population variance of the first group is greater than that of the second group at a significance level of α = 0.01.

We can conclude that there is not enough evidence to support the claim that σ1² > σ2².

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the perimeter of rectangle is 76m if one side is 16m what is the other side?​

Answers

Let's assume that the length of the rectangle is 16m (given in the question), and the width of the rectangle is "w" meters.

The formula for the perimeter of a rectangle is:

P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

We know that the perimeter of the rectangle is 76m, so we can substitute the values in the formula:

76 = 2(16 + w)

Simplifying the equation:

76 = 32 + 2w

Subtracting 32 from both sides:

44 = 2w

Dividing both sides by 2:

w = 22

Therefore, the width of the rectangle is 22 meters.

Answer: 22

Step-by-step explanation:

The formula for perimeter of a rectangle is side 1 + side 1 + side 2 + side 2. Side one is 16. This means that 16x2 is 32. Then, you realize there are 44 meters remaining. 44/2=22. The other side is 22.

[4x2+(5+1)]÷2 can I please get help :)

Answers

For the second question if are reading a book and you don’t know the word you should look at the glossary

If <2 is equivalent to (2x-8)• what is the value of c?

A 62•
B 35•
C 28•
D 18•

Answers

Answer: 18 (choice D)

Reason:

[tex]\angle 1 = 62^{\circ}[/tex] because of the vertical angles theorem.

Then angle 1 and angle 2 add to 90 degrees (the angles are complementary).

[tex]\angle 1 + \angle 2 = 90\\\\62 + (2x-8) = 90\\\\2x + 54 = 90\\\\2x = 90 - 54\\\\2x = 36\\\\x = 36/2\\\\x = 18\\\\[/tex]

Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
$

Answers

So, the total net amount the supermarket owes the wholesaler for the order is $231.61.

To find the total net amount that the supermarket owes the wholesaler for the order, we need to first calculate the cost of each item after the trade discount is applied, and then add up the costs of all the items.

For the 13 cases of organic vegetable soup, the list price per case is $18.90, and the trade discount is 39%. So, the discount amount per case is:

Discount amount = 39% x $18.90 = $7.37

The cost per case after the discount is:

Cost per case = $18.90 - $7.37 = $11.53

So, the total cost of 13 cases of organic vegetable soup is:

Total cost of vegetable soup = 13 x $11.53 = $149.89

Similarly, for the 4 cases of organic baked beans, the list price per case is $33.50, and the trade discount is 39%. So, the discount amount per case is:

Discount amount = 39% x $33.50 = $13.07

The cost per case after the discount is:

Cost per case = $33.50 - $13.07 = $20.43

So the total cost of 4 cases of organic baked beans is:

Total cost of baked beans = 4 x $20.43 = $81.72

Therefore, the total net amount the supermarket owes the wholesaler for the order is:

Total net amount = Total cost of vegetable soup + Total cost of baked beans

= $149.89 + $81.72

= $231.61

So, the total net amount the supermarket owes the wholesaler for the order is $231.61.

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A waiter made $288 in tips after waiting on 12 tables. What was the waiter’s average tip per table?

A$24
B$13
C$15
D$16

Answers

Answer:

24

Step-by-step explanation:

Answer:

A. $24

Step-by-step explanation:

Given:

total of $288number of values is 12 tables

Solve for average tip:

Average is the same as the meanTo solve you have add up the total and divide by the total number of values288 / 12 = 24

Answer:

Thus, the waiter's average tip per table is $24.

The answer is A.

If P(A)=0.3, P(B)=0.2 and P(A∩B)=0.2 determine the following probabilities:
(a) P(A')
(b) P(A∪B)
(c) P(A'∩B)
(d) P(A∩B')
(e) P[(A∪B)']

Answers

The probabilities are as follows:

(a) P(A')= 0.7

(b) P(A∪B) = 0.3

(c) P(A'∩B) = 0

(d) P(A∩B') = 0.1

(e) P[(A∪B)'] = 0.7

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7

(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3

(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0

(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1

(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7

Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.

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find the factors to this polynomials i need help SHOW YOUR WORK.

Answers

Answer:

hope this will help you...

someone help me plsss

Answers

The fraction of the panel left after cutting the hole is 11/12.

The correct answer choice is option C

What is the fraction of the panel is left?

Fraction left = (area of panel) - (area of hole) / (area of panel

Area of panel = 3 feet × 2 feet

= 6 square feet

Area of hole = 1 foot × ½ foot

= ½ square foot

So,

Fraction left = (area of panel) - (area of hole) / (area of panel

= (6) - (½) / (6)

= (5½) / (6)

= 11/2 ÷ 6

multiply by the reciprocal of 6

= 11/2 × 1/6

= 11/12

Ultimately, the fraction left is 11/12

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Round your answer to the nearest tenth of a degree

Answers

Answer:

57.8°

Step-by-step explanation:

SohCahToa

use sin^1 to get angle

sin^1(11/13)=57.7957725

to the nearest tenth=57.8°

HELP PLSZZZZSZZZZZZZZZZ need asap

Answers

Answer:

thursday

Step-by-step explanation:

there are 7 days in a week, and the multiple of 7 closest to 100 is 14, so after 98 days, it will be a monday. 3 days after monday is thursday, which is your answer. I hope this helps!

On the Y axis we have the profit from the trucking company and on the X axis we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less

B. Y intercept will be less and X intercept will be greater

C. Y intercept will be greater and X will be greater

D. Y intercept will be greater and X will be less

Answers

Therefore, the correct answer is A. Y intercept will be less and X will be less.

What is graph?

A graph is a visual representation of data that shows the relationship between two or more variables. Graphs are commonly used to display information in a way that is easy to interpret and analyze. They are often used in fields such as science, mathematics, economics, and engineering to help illustrate and explain complex data.

Here,

The introduction of a cost of 0.25 cents per mile for the driver would be an additional expense for the trucking company, and would affect their profit. This means that the profit values (on the y-axis) would decrease for each point on the graph. However, the miles traveled (on the x-axis) would remain the same as the cost of the driver is proportional to the distance traveled.

Therefore, the y-intercept of the graph (the profit when the truck has traveled zero miles) would be less than it was before, because the trucking company has a new cost that reduces their overall profit. However, the x-intercept (the point where the profit is zero) would remain the same, as this point is determined solely by the revenue and cost of the trucking company.

The slope of the graph would also be affected, as the profit now decreases at a faster rate as the miles traveled increase. The new slope would depend on the specific values of the revenue, costs, and driver expenses for the trucking company, but in general, it would be steeper than before.

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How can I solve this math problem within 5 minutes

Answers

The equation a² + b² = c² represents the Pythagorean theorem.

What is the Pythagorean theorem?

This is a theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.

To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:

If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):

Plug in the known values for a and b into the equation and solve for c.

Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.

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Kennedy has $0.81 worth of pennies and nickels. She has 9 more nickels than pennies. Write a system of equations that could be used to determine the number of pennies and the number of nickels that Kennedy has. Define the variables that you use to write the system

Answers

The system of equations that could be used to determine the number of pennies and the number of nickels that Kennedy has is 0.01b + 0.05d = 0.81

b = 9d

The variables used to write the system of equation is Number of pennies = b

Number of nickels = d

Write the equations that could be used to determine the number of pennies and nickels?

Let

Number of pennies = b

Number of nickels = d

0.01b + 0.05d = 0.81

b = 9d

Therefore, the variables are b for pennies and d for nickels.

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Problem Walk-Through
Stocks A and B have the following probability distributions of expected future returns:
Probability
0.1
0.2
0.5
0.1
0.1
A
(7%)
6
14
23
31
B
(39%)
0
23
25
45
a. Calculate the expected rate of return, FB, for Stock B (A = 12.90%.) Do not round Intermediate calculations. Round your answer to two decimal places.
%
b. Calculate the standard deviation of expected returns, GA, for Stock A (08= 21.64 %.) Do not round intermediate calculations. Round your answer to two decimal places.
%
Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places.
Is it possible that most investors might regard Stock B as being less risky than Stock A?
I. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
II. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
III. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
IV. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
V. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
-Select-
c. Assume the risk-free rate is 1.5%. What are the Sharpe ratios for Stocks A and B? Do riot round intermediate calculations. Round your answers to four decimal places.
Stock A:
Stock B:
Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?
I. In a stand-alone risk sense A is less risky than B. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and
hence be more risky in a portfolio sense.
II. In a stand-alone risk sense A is more risky than B. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and
hence be less risky in a portfolio sense.

Answers

A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market than Stock A.

What is Expeced return?

The profit or loss an investor can anticipate realising from an investment is known as the expected return. Calculating an expected return involves multiplying possible outcomes by their likelihood before adding the results. The expected return is computed by summing the results of multiplying all possible outcomes by the likelihood that each one will occur (as illustrated below).

Expeced return=Sum(probability*return)

Standard Deviation=[tex]\sqrt{sum(probability*(return-expected\ return)^2}[/tex]

Coefficient of Variation=Standard Deviation/Expected Return

1. Expected Returns:

Stock B=0.1*(-38%)+0.2*0%+0.5*21%+0.1*26%+0.1*36%=12.900%

2. Standard Deviation:

Stock A=[tex]\sqrt{(0.1*(-11\%-11.3\%)^2+0.2*(5\%-11.3\% +0.5*(13\%-11.3\%)^2+)^2 0.1*(18\%-11.3\%)^2} \\+0.1*(31\%-11.3\%)^2)[/tex]

= 10.120%

3. Coefficient of Variation:

Stock B=19.892%/12.9%=1.5420

4. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market

than Stock A.

5. Sharpe Ratio:

Stock A=(11.3%-3.5%)/10.120%=0.7708

Stock B=(12.9%-3.5%)/19.892%=0.4726

6. A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio

if it has a lower correlation to the market than Stock A.

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Sand dollars are animals that live buried in the sand of shallow coastal waters. The thin circular body of a sand dollar is usually 2 to 4 inches wide. Find the area of a sand dollar that is 3 inches wide.

Answers

The area of a sand dollar that is 3 inches wide is 7.0686 inch².

What is linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

Width of sand dollar's circular body = d = 3 inches

Radius of the sand dollar's circular body = r

r = d/2 = 3/2 = 1.5 inch

area of circle = πr²

So, the area of a sand dollar that is 3 inches wide:

A = 3.14 * (1.5)² = 7.0686 inch²

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A boat traveled 350 miles each way downstream and back. The trip downstream took 14 hours.
The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of
the current?

Answers

Answer:

The speed of the boat in still water is 15 mi/hr while the speed of the current is 10 mi/hr.

Step-by-step explanation:

Given: d = 350 miles

[tex]t_{ds}[/tex] = 14 hours

[tex]t_{us}[/tex] = 70 hours

Asked: Speed of the boat [tex]V_b[/tex] in still water and speed of the current [tex]V_c[/tex]

Solve:

Note that when the boat is going downstream, the current is helping the boat to speed up and when the boat is going upstream, the current is slowing it down.

Get the speed downstream

[tex]V_{ds} = V_b + V_c[/tex]

350mi/14hrs = [tex]V_b + V_c[/tex]

25 mi/hr = [tex]V_b + V_c[/tex]

Transpose to get the value of Vb

25 mi/hr - Vc = Vb ---equation 1

Get the speed upstream

[tex]V_{us} = V_b - V_c[/tex]

350mi/70hrs = Vb - Vc

5 mi/hr = Vb - Vc

Transpose to get the value of Vb

5 mi/hr + Vc = Vb ----equation 2

Equate equations 1 and 2

25 mi/hr - Vc = 5 mi/hr + Vc

Transpose

25 mi/hr - 5 mi/hr = Vc + Vc

20 mi/hr = 2 Vc

Divide both sides of the equation by 2

10 mi/hr = Vc

Vc = 10 mi/hr

From 25 mi/hr = [tex]V_b + V_c[/tex] we then solve the speed of the boat

25 mi/hr = Vb + 10 mi/hr

25 mi/hr - 10 mi/hr = Vb

15 mi/hr = Vb

Vb = 15 mi/hr

find the solution -b2+2b=0

Answers

The solutions to the equation -b² + 2b = 0 are b = 0 and b = 2.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), which are connected by an equals sign (=). The expressions on each side of the equals sign can be made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can be solved to find the value of the variable(s) that makes both sides of the equation equal.

To find the solution of -b²+ 2b = 0, we can use algebraic manipulation as follows:

-b² + 2b = 0

Factor out -b:

-b(b - 2) = 0

From this equation, we see that either -b = 0 or b - 2 = 0:

-b = 0 or b - 2 = 0

Solving for b in each case, we get:

-b = 0 --> b = 0

b - 2 = 0 --> b = 2

Therefore, the solutions to the equation -b² + 2b = 0 are b = 0 and b = 2.

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50 Points! Multiple Choice Algebra Question. The Related Graph Of A Quadratic Equation Is Shown At The (2024)
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