A stock has an expected return of 10.7 percent, its beta is .98, and the risk-free rate is 6.15 percent. What must the expected return on the market be?

Answers

Answer 1

The expected return on the market must be 10.7939%, or approximately 10.79%.

To find the expected return on the market, we can use the Capital Asset Pricing Model (CAPM), which relates the expected return of an asset to its beta and the expected return of the market.

The CAPM formula is as follows:

Expected Return = Risk-Free Rate + Beta * (Expected Return on the Market - Risk-Free Rate)

Given:

Expected Return of the stock = 10.7%

Beta of the stock = 0.98

Risk-Free Rate = 6.15%

Let's denote the expected return on the market as "E(Rm)".

Using the CAPM formula, we can plug in the given values and solve for E(Rm):

10.7% = 6.15% + 0.98 * (E(Rm) - 6.15%)

Let's simplify the equation:

10.7% - 6.15% = 0.98 * (E(Rm) - 6.15%)

4.55% = 0.98 * (E(Rm) - 6.15%)

Dividing both sides by 0.98:

4.55% / 0.98 = E(Rm) - 6.15%

4.6439 = E(Rm) - 6.15%

Adding 6.15% to both sides:

4.6439 + 6.15% = E(Rm)

10.7939% = E(Rm)

Therefore, the expected return on the market must be 10.7939%, or approximately 10.79%.

According to the CAPM, the expected return on a stock is determined by the risk-free rate, the stock's beta, and the expected return on the market. In this case, given the expected return of the stock, its beta, and the risk-free rate, we were able to calculate the expected return on the market using the CAPM formula.

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Related Questions

Solve for the exact solutions in the interval
List your answers separated by a comma, if it has no real solutions, enter DNE.

Answers

Answer:

[tex] \sqrt{2} \sin(3x) - 1 = 0[/tex]

[tex] \sqrt{2} \sin(3x) = 1[/tex]

[tex] \sin(3x) = \frac{ \sqrt{2} }{2} [/tex]

3x = π/4 + 2kπ or 3x = 3π/4 + 2kπ

x = π/12 + 2kπ/3 or x = π/4 + 2kπ/3

0 < π/12 + 2kπ/3 < 2π

0 < 1/12 + 2k/3 < 2

0 < 1 + 8k < 24

-1 < 8k < 23, so k = 0, 1, 2

x = π/12, 3π/4, 17π/12

0 < π/4 + 2kπ/3 < 2π

0 < 1/4 + 2k/3 < 2

0 < 3 + 8k < 24

-3 < 8k < 21, so k = 0, 1, 2

x = π/4, 11π/12, 19π/12

4 times the sum of a number and negative 5 is 12

Answers

4 times the sum of a number and negative 5 is 12.

We will have "x" represent "number."

So 4 times the sum of x and negative 5 is/equal to 12.

Sum is the answer to an addition expression, so the sum of x and negative 5 is x + -5 or x - 5.

So now we can easily put everything together.

4(x - 5) = 12

And if you want to solve this, we will first distribute:

4x - 20 = 12

Now we will add 20 to both sides:

4x = 32

Divide 4 to both sides:

x = 8

10. Order states to administer cefazolin 250 mg IM. Available is cefazolin 1 gram vial.
The directions state to add 3 mL of NS to obtain a concentration of 1 gram per
4mL. How many mL will the nurse administer?

Answers

Answer:

To administer 250 mg of cefazolin, we need to calculate the appropriate volume of the 1-gram vial to use.

First, we need to calculate the concentration of the solution after adding 3 ml of NS to the 1-gram vial:

1 gram cefazolin + 3 ml NS = 4 ml solution

1 gram cefazolin / 4 ml solution = 0.25 grams cefazolin per ml

Next, we can use dimensional analysis to calculate the volume of solution needed to provide 250 mg of cefazolin:

0.25 g cefazolin / 1 ml solution = 250 mg cefazolin / x ml solution

x = (250 mg cefazolin * 1 ml solution) / 0.25 g cefazolin

x = 1 ml solution

Therefore, the nurse will administer 1 ml of the cefazolin solution.

Step-by-step explanation:

Find the quadratic equation whose root is 2/3 and -3/4​

Answers

Answer:

12x^2 + 9x - 8 = 0

Step-by-step explanation:

To find the quadratic equation with roots 2/3 and -3/4, we can use the fact that if a quadratic equation has roots r and s, then it can be written in the form:

(x - r)(x - s) = 0

Expanding this equation gives:

x^2 - (r + s)x + rs = 0

So, for the roots 2/3 and -3/4, we have:

(x - 2/3)(x + 3/4) = 0

Expanding this equation gives:

x^2 + (3/4 - 2/3)x - (2/3)(3/4) = 0

Multiplying through by 12 to eliminate the fractions, we get:

12x^2 + 9x - 8 = 0

So, the quadratic equation with roots 2/3 and -3/4 is:

12x^2 + 9x - 8 = 0

QUESTION:-↓

The dimensions of a room are 12.5 m by 9 m by 7 m. there are 2 doors and 4 windows in the room; each door measures 2.5 m by 1.2 m and each window 1.5 m by 1 m. Find the cost of painting the walls at Rs. 3.50 per square meter.

no spam! ​

Answers

Given dimensions of the room:

Length: [tex]\displaystyle\sf 12.5 \,m[/tex]

Width: [tex]\displaystyle\sf 9 \,m[/tex]

Height: [tex]\displaystyle\sf 7 \,m[/tex]

Area of each wall:

[tex]\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2[/tex]

[tex]\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2[/tex]

[tex]\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2[/tex]

[tex]\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2[/tex]

Area of each door:

[tex]\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2[/tex]

Area of each window:

[tex]\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2[/tex]

Total area occupied by doors:

[tex]\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2[/tex]

Total area occupied by windows:

[tex]\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2[/tex]

Total wall area excluding doors and windows:

[tex]\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}[/tex]

[tex]\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6[/tex]

[tex]\displaystyle\sf = 275 - 6 - 6[/tex]

[tex]\displaystyle\sf = 263 \,m^2[/tex]

Cost of painting the walls:

[tex]\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50[/tex]

[tex]\displaystyle\sf = 263 \times 3.50[/tex]

[tex]\displaystyle\sf = 920.50 \,Rs[/tex]

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

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Ninety two passengers rode in a train coach seats cost 120 sleeper cost 285 total of the trip is 19,620 how many passengers purchased each ticket

Answers

Answer:

40 passengers in the coach seats and 52 passengers in the sleeper seats.

Step-by-step explanation:

Let's denote the number of coach passengers as "C" and the number of sleeper passengers as "S". We know from the problem statement that:

1. C + S = 92  (the total number of passengers)

2. 120C + 285S = 19,620  (the total cost of all tickets)

Now, we can solve these simultaneous equations.

One way to do this is by using substitution or elimination. However, the easiest way here might be to use the method of substitution, so let's solve the first equation for C:

C = 92 - S

Now we substitute C from the first equation into the second equation:

120(92 - S) + 285S = 19,620

11,040 - 120S + 285S = 19,620

165S = 8,580

S = 8,580 / 165

S = 52

Substitute S = 52 into the first equation to get C:

C = 92 - 52 = 40

So, there were 40 passengers in the coach seats and 52 passengers in the sleeper seats.

Judy made oatmeal cookies to take to a party. It took her 1 hour to make the dough and 1 hour and 17 minutes to bake all of the cookies. It was 5:53 P.M. when Judy finally took the last batch of cookies out of the oven. What time was it when Judy started making the cookies?

Answers

Judy started making the cookies at 3:25 P.M.

To determine the time Judy started making the cookies, we need to calculate the total time it took her to make the dough and bake the cookies.

Judy spent 1 hour making the dough and 1 hour and 17 minutes baking the cookies. To simplify the calculation, we convert the 17 minutes to hours by dividing it by 60. Thus, 17 minutes is equivalent to 17/60 hours, which is approximately 0.28 hours.

Now, we add the time spent making the dough (1 hour) and the time spent baking the cookies (1 hour + 0.28 hours) to get the total time.

1 hour + 1 hour + 0.28 hours = 2.28 hours.

Next, we need to determine the time difference between when Judy finished baking the cookies and when she started. Judy finished baking the cookies at 5:53 P.M., and it took her 2.28 hours to complete the process. Therefore, we subtract 2.28 hours from 5:53 P.M. 5:53 P.M. - 2.28 hours = 3:25 P.M.

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Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27). f(x) = -x3 - 4x2 + 3x. Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answers

The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

[tex]f(x) = -x^3 - 4x^2 + 3x[/tex].

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answer Please!!!!!!!!!

Answers

(a) 5.8% compounded annually: $ 3661.58

(b) 5.8% compounded semiannually: $ 3669.43

(c) 5.8% compounded quarterly: $3674.37

(d) 5.8% compounded monthly: $3676.35

(e) 5.8% compounded daily (ignore leap years): $3676.61

(a) The value of the investment at the end of 10 years with a 5.8% interest compounded annually can be calculated using the formula:

A = P(1 + r/n)^(nt)

where:

A is the final amount

P is the principal amount (initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

Plugging in the values, we have:

A = 2200(1 + 0.058/1)^(1*10)

A ≈ $3661.58

(b) With a 5.8% interest compounded semiannually, the formula becomes:

A = P(1 + r/n)^(nt)

Plugging in the values, we have:

A = 2200(1 + 0.058/2)^(2*10)

A ≈ $3669.43

(c) With a 5.8% interest compounded quarterly, the formula becomes:

A = P(1 + r/n)^(nt)

Plugging in the values, we have:

A = 2200(1 + 0.058/4)^(4*10)

A ≈ $3674.37

(d) With a 5.8% interest compounded monthly, the formula becomes:

A = P(1 + r/n)^(nt)

Plugging in the values, we have:

A = 2200(1 + 0.058/12)^(12*10)

A ≈ $3676.35

(e) With a 5.8% interest compounded daily, the formula becomes:

A = P(1 + r/n)^(nt)

Plugging in the values, we have:

A = 2200(1 + 0.058/365)^(365*10)

A ≈ $3676.61

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A box contains 4 red marbles, 8 white marbles, and 9 blue marbles. If a marble is randomly selected from the box, what is the probability that it is white? Express your answer as a fraction or a decimal number rounded to three decimal places, if necessary.

Answers

The probability of selecting a white marble from the box is approximately 0.381 or 8/21.

To find the probability of selecting a white marble, we need to determine the total number of marbles in the box and the number of white marbles specifically.The total number of marbles in the box is the sum of the red, white, and blue marbles:

Total marbles = 4 (red marbles) + 8 (white marbles) + 9 (blue marbles) = 21 marbles.

Now, we can calculate the probability of selecting a white marble by dividing the number of white marbles by the total number of marbles:

Probability of selecting a white marble = Number of white marbles / Total number of marbles = 8 / 21.

To express this probability as a decimal, we divide 8 by 21:

8 / 21 = 0.381.Rounded to three decimal places, the probability of selecting a white marble from the box is approximately 0.381.In fraction form, the probability can be written as 8/21.

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a cd player holds 5 CDs and each disc has 12 songs. If the CDs are changed randomly, find the probability that your favorite song is played first as a fraction

Answers

Answer:

The probability that your favorite song is played first is 1/60

Step-by-step explanation:

We assume that all 5 CDs have different songs so that only one of CDs will have our favorite song.

Then The probability that the CD that contains the song comes first will be,

(since there are 5 CDs)

1/5

And that CD has 12 songs, the probability that our favorite song will play first is then,

1/12

The total probability of our favorite song playing will be the product of these two, so,

P = (1/5)(1/12) = 1/60

P = 1/60

The probability that your favorite song is played first is 1/60

Determine the equation of the ellipse with foci... Please put the dots on the graph thats in the image. 100 points

Answers

Answer:

[tex]\frac{(x-7)^2}{8^2} + \frac{(y-2)^2}{17^2} = 1[/tex]

Step-by-step explanation:

Major axis length 2a

⇒ 2a = 34

⇒ a = 34/2

a = 17

General eq of ellipse:

[tex]\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]

centre : (h,k)

foci: (h, k+c) and (h,k-c)

Gn. foci : (7, 17) and (7, -13)

Comparing the above 2 lines,

h = 7,

k + c = 17   -eq(1)

k - c = -13   -eq(2)

eq(1) + eq(2):

(k + c) + (k - c) = 17 + (-13)

2k = 4

k = 2

sun k = 2 in eq(1):

2 + c = 17

c = 15

Also, c² = a² - b²

b² = a² - c²

= 17² - 15²

= 64

b² = 8²

b = 8

substituting in ellipse eq,

[tex]\frac{(x-7)^2}{8^2} + \frac{(y-2)^2}{17^2} = 1[/tex]

Answer:

[tex]\dfrac{(x-7)^2}{64}+\dfrac{(y-2)^2}{289}=1[/tex]

Step-by-step explanation:

As the foci of the ellipse have the same x-value, the ellipse is vertical.

The formula for a vertical ellipse is:

[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]

where:

b > ab is the major radius and 2b is the major axis.a is the minor radius and 2a is the minor axis.Center = (h, k)Vertices = (h, k±b)Co-vertices = (h±a, k)Foci = (h, k±c) where c² = b² - a²

Given the major axis is 34:

2b = 34b = 17b² = 289

The center of an ellipse is located at the midpoint between its two foci.

Given the foci are (7, 17) and (7, -13), the center of the ellipse is:

[tex](h, k) = (7, 2)[/tex]

As the formula for the foci is (h, k±c), then (k, h±c) = (7, 2±c). Therefore:

[tex]\begin{aligned}2\pm c &= 17, -13\\\pm c &= 15, -15\\c &= 15\end{aligned}[/tex]

The vertices are:

[tex]\begin{aligned}(h, k\pm b) &= (7, 2 \pm 17)\\& = (7, 19) \; \textsf{and}\; (7, -15)\end{aligned}[/tex]

To find the value of a, substitute the values of b and c into c² = b² - a²:

[tex]\begin{aligned}c^2&=b^2-a^2\\15^2&=17^2-a^2\\a^2&=\sqrt{17^2-15^2}\\a^2&=64\\a&=8\end{aligned}[/tex]

The co-vertices are:

[tex]\begin{aligned}(h \pm a, k) &= (7 \pm 8, 2)\\& = (-1,2) \; \textsf{and}\; (15,2)\end{aligned}[/tex]

Therefore:

a = 8 ⇒ a² = 64b = 17 ⇒ b² = 289h = 7k = 2

To find the equation of the ellipse, substitute these values into the formula:

[tex]\boxed{\dfrac{(x-7)^2}{64}+\dfrac{(y-2)^2}{289}=1}[/tex]

Major axis, 2b = 34Minors axis, 2a = 16Center = (7, 2)Vertices = (7, -15) and (7, 19)Co-vertices = (-1, 2) and (15, 2)Foci = (7, 17) and (7, -13)

Look at photo for question

Answers

[tex]x+3\geq0 \wedge 2x-6\not=0\\x\geq- 3 \wedge 2x\not=6\\x\geq-3 \wedge x\not =3\\x\in\langle-3,3)\cup(3,\infty)[/tex]

Review the work showing the first few steps in writing a partial fraction decomposition.



4x + 40 = A(x + 6) + B(x + 2)

4x + 40 = Ax + 6A + Bx + 2B

What is the partial fraction decomposition in terms of x?

Answers

The partial fraction decomposition of 4x + 40 in terms of x is: 4x + 40 = 8(x + 6) - 4(x + 2)

To find the partial fraction decomposition of the expression 4x + 40, we start by setting it equal to the sum of two fractions with unknown numerators and common denominators. In this case, the common denominator is (x + 6)(x + 2).

The equation is:

4x + 40 = A(x + 6) + B(x + 2)

Next, we distribute the factors on the right side of the equation:

4x + 40 = Ax + 6A + Bx + 2B

To simplify the equation, we combine like terms on the right side:

4x + 40 = (A + B)x + (6A + 2B)

Now, we can equate the coefficients of the like terms on both sides. Since the equation holds true for all values of x, the coefficients must be equal.

The coefficients of x on both sides of the equation are:

4 = A + B

The constant terms on both sides of the equation are:

40 = 6A + 2B

We have obtained a system of equations:

A + B = 4

6A + 2B = 40

We can solve this system of equations to find the values of A and B.

From the first equation, we have A = 4 - B.

Substituting this value of A into the second equation, we get:

6(4 - B) + 2B = 40

24 - 6B + 2B = 40

-4B + 24 = 40

-4B = 16

B = -4

Substituting the value of B back into the first equation, we find:

A + (-4) = 4

A - 4 = 4

A = 8

Therefore, the partial fraction decomposition of 4x + 40 in terms of x is:

4x + 40 = 8(x + 6) - 4(x + 2)

or, simplifying:

4x + 40 = 8x + 48 - 4x - 8

4x + 40 = 4x + 40

The original expression 4x + 40 is already decomposed into partial fractions, and it simplifies back to itself.

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The length of a new rectangular playing field is 3 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 516 ​yards, what are its​ dimensions?

Answers

The width of the rectangular playing field is 51 yards, and the length is 4(51) + 3 = 207 yards.

Let's assume the width of the rectangular playing field is 'x' yards.

According to the given information, the length is 3 yards longer than quadruple the width, which means the length is 4x + 3 yards.

The formula for the perimeter of a rectangle is P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.

Substituting the given values into the formula, we have 516 = 2((4x + 3) + x).

Simplifying the equation, we get 516 = 10x + 6.

By rearranging the equation, we have 10x = 516 - 6, which gives 10x = 510.

Dividing both sides by 10, we find x = 51.

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the manager of a store that specializes in selling tea desides to experiment with a new blend. she will mix some earl gray tea that sells for $5 per pound with some orange pekoe the that sells for $3 per pound to get 600 pounds of the new blend. the selling price is the new blend is to be $4.50 per pound. and there is to be no difference in revenue from selling the new brand versus selling the other types. how many pounds of earl gray tea and pekoe tea are required.​

Answers

Answer:

450 lb Earl Gray150 lb Orange Pekoe

Step-by-step explanation:

You want to know the number of pounds of each of Earl Gray and Orange Pekoe tea to make 600 pounds of mix that is valued at $4.50 per pound, if Earl Gray costs $5 per pound and Orange Pekoe costs $3 per pound.

Setup

Let x represent the number of pounds of Earl Gray tea in the mix. Then the value of the mix is ...

  5x +3(600 -x) = 4.50(600)

Solution

Simplifying, we have ...

  2x +1800 = 2700

  2x = 900 . . . . . . . . . subtract 1800

  x = 450 . . . . . . . . . divide by 2

  600 -x = 150 . . . find pounds of Orange Pekoe

The blend will consist of 450 pounds of Earl Gray, and 150 pounds of Orange Pekoe tea.

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In a forest you observed 22 eyes and 32 legs belonging to owls and foxes. a) How many owls and how many foxes are there? b) If on another day you saw 24 eyes and 38 legs, how many foxes and how many owls are there?​

Answers

Answer:

a) Let's say the number of owls is "x" and the number of foxes is "y".

Each owl has 2 eyes and 2 legs, so "x" owls would have 2x eyes and 2x legs.

Each fox has 2 eyes and 4 legs, so "y" foxes would have 2y eyes and 4y legs.

According to the problem, there are 22 eyes and 32 legs in total:

2x + 2y = 22 (equation 1)

2x + 4y = 32 (equation 2)

We can use these two equations to solve for "x" and "y".

Subtracting equation 1 from equation 2:

2x + 4y - (2x + 2y) = 32 - 22

2y = 10

y = 5

Substituting "y" = 5 into equation 1:

2x + 2(5) = 22

2x = 12

x = 6

Therefore, there are 6 owls and 5 foxes.

b) Let's use the same approach to solve for "x" and "y":

2x + 2y = 24 (equation 1')

2x + 4y = 38 (equation 2')

Subtracting equation 1' from equation 2':

2x + 4y - (2x + 2y) = 38 - 24

2y = 14

y = 7

Substituting "y" = 7 into equation 1':

2x + 2(7) = 24

2x = 10

x = 5

Therefore, there are 5 owls and 7 foxes.

reperesent the following rational number on number line​

Answers

The number line for the fractions given are as shown in the attached files

How to graph a number line?

In order for us to represent rational numbers on a number line, we will draw a line and mark a point on it representing rational zero. Positive rational numbers are usually represented to the right of 0 and negative rational numbers are usually represented to the left of 0.

Now, just as any integer can be represented on a number line, rational numbers can also be represented on a number line.

Thus, we have:

For -2/3 and 3/4, we have the number line as attached

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Yo help a brother out with this confusing algebra stuff

Answers

The equivalent expressions are given as follows:

(4x³ + 7x - 4) - (2x³ - x - 8): B.[tex](x^4 - 3x^2 + x) + (2x^4 + 4x - 7)[/tex]: C.2x³ - x² - 6x: A.

How to obtain the equivalent expressions?

Equivalent expressions are the expressions that have the same result, hence we must simplify each expression.

The first expression is given as follows:

(4x³ + 7x - 4) - (2x³ - x - 8).

Simplifying the like terms, we have that:

4x³ - 2x³ = 2x³.7x - (-x) = 7x + x = 8x.-4 - (-8) = -4 + 8 = 4.

Hence it is equivalent to expression B.

The second expression is simplified as follows:

[tex](x^4 - 3x^2 + x) + (2x^4 + 4x - 7) = 3x^4 - 3x^2 + x - 7[/tex]

The third expression is simplified as follows:

(x² - 2x)(2x + 3) = 2x³ + 3x² - 4x² - 6x = 2x³ - x² - 6x.

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I need to find which one is the equivalent expression

Answers

Answer:

  [tex]\dfrac{3^{10}}{3^{12}}[/tex]

Step-by-step explanation:

You want to identify the expression that is equivalent to 3^(-2).

Rules of exponents

The relevant rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

Application

This means you want to find the expression such that subtracting the bottom exponent from the top one yields -2.

  (3^-2)/(3^3) = 3^(-2-3) = 3^-5 . . . . . not equivalent

  (3^10)/(3^-12) = 3^(10 -(-12)) = 3^22 . . . . . not equivalent

  (3^3)/(3^22) = 3^(3-22) = 3^-19 . . . . . . not equivalent

  (3^10)/(3^12) = 3^(10-12) = 3^-2 . . . . . equivalent

__

Additional comment

If you consider that an exponent signifies repeated multiplication, you can see how this works.

  3^5 = 3×3×3×3×3

  3^3 = 3×3×3

Then (3^5)/(3^3) = (3×3×3×3×3)/(3×3×3) = 3×3 = 3^2

This is the same as 3^(5-3) = 3^2.

That is, the denominator exponent is subtracted from the numerator exponent. This shows you where the subtraction comes from.

As with many models, representation of negative numbers is not so easy. That doesn't mean the rule is not applicable. It just means it is somewhat more difficult to show with a physical representation.

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2x - 17 = 13, then x=?

Answers

2x=13+17
2x=30
X=30/2
X=15
Answer:

15

Step-by-step explanation:

We can use the properties of equality to find unknown variables.

Properties of Equality

The properties of equality (PoE) show us how we can manipulate an equation while maintaining equality. One of the most common properties of equality is the subtraction property of equality. The addition PoE says that if you add the same number to each side then the equation is still true. The other PoEs like subtraction, multiplication, and division PoEs work the same.

Solving for x

Using the PoEs above, we can solve for x. First, we need to rewrite the equation.

2x - 17 = 13

Then, add 17 to both sides using the addition PoE.

2x = 30

Finally, divide both sides by 2 using the division PoE.

x = 15

In this equation, x = 15. Additionally, this shows how we can manipulate equations to solve for x.

A group of five friends are long-distance runners who will be running in an upcoming marathon. To prepare for the marathon, each of the friends recorded the number of miles they ran each week for 12 weeks. The results of the friends' training are shown in the data set provided below. Which of the friends was the most consistent with the number of miles run each week during the training? Hint: You should not need to compute the standard deviation for each friend.

Answers

The most consistent friend with the number of miles run each week during the training is given as follows:

Caleb.

How to obtain the mean and the standard deviation of a data-set?

The mean of a data-set is given by the sum of all values in the data-set, divided by the cardinality of the data-set, which is the number of values in the data-set.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the cardinality of the data-set.

Looking at each value, we have that Caleb's values are quite close to each other, hence the sum of the differences squared is the smallest, and thus he has the lowest standard deviation.

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The following figure is a complex shape combined from a square and a rectangle. In the figure, suppose that b = 6, c = 8, and d =12. What is the perimeter of this complex figure?

Answers

Given that the figure is a combination of a square and rectangle, The perimeter of the complex shape is 52

What is meant by the perimeter and how do we solve for it?

The perimeter of a shape is the total length of all its sides.

In this case, the complex figure is made up of a square and a rectangle. The square has four sides of equal length, and the rectangle has two sides of equal length and two sides of different length.

We are given that b = 6, c = 8, and d = 12.

Perimeter = 2b + 2c + 2d

Perimeter = 2(b + c + d)

Perimeter = 2(6 + 8 + 12)

Perimeter= 2(26)

Perimeter = 52

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A rack of discount CD's are on sale for $9 each. If Mario buys � CD's, which expression shows the total cost?

Answers

Step-by-step explanation:

xcds ×9= $y

let x represent the number of cds mario bought

y represents the total amount he bought

A particle B moves along a curve whose parametric equations are as follows: X = 402 + 8t, y = 2 cos 3t, z = 2 sin 3t. The magnitude of the acceleration is,

Answers

The magnitude of the acceleration is a constant value of 18

What is magnitude of acceleration  ?

Each part of the location vector's second derivative must be calculated.

Given:

x = 402 + 8t

y = 2 cos(3t)

z = 2 sin(3t)

The position vector r(t) = (x, y, z)

First, let's find the velocity vector v(t) by taking the first derivative of each component:

v(t) = (dx/dt, dy/dt, dz/dt)

v(t) = (8, -6 sin(3t), 6 cos(3t))

Next, let's find the acceleration vector a(t) by taking the first derivative of each component of the velocity vector:

a(t) = (d²x/dt², d²y/dt², d²z/dt²)

a(t) = (0, -18 cos(3t), -18 sin(3t))

Finally, we can find the magnitude of the acceleration vector:

|a(t)| = √[(d²x/dt²)² + (d²y/dt²)² + (d²z/dt²)²]

|a(t)| = √[0² + (-18 cos(3t))² + (-18 sin(3t))²]

|a(t)| = √(324 cos²(3t) + 324 sin²(3t))

|a(t)| = √324 (cos²(3t) + sin²(3t))

|a(t)| = 18

Therefore, the magnitude of the acceleration is a constant value of 18.

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From the given parameters the magnitude of the acceleration is  18

How to determine the magnitude of acceleration?

Recall that the magnitude of acceleration is a physical term defined as the ratio of velocity variation to time, represented by the equation a = v/t. It is a vector quantity that includes both magnitude and direction

x = 402 + 8t

y = 2 cos(3t)

z = 2 sin(3t)

The position vector r(t) = (x, y, z)

But, the velocity vector v(t) by taking the first derivative of each component:

v(t) = (dx/dt, dy/dt, dz/dt)

v(t) = (8, -6 sin(3t), 6 cos(3t))

And  the acceleration vector a(t) by taking the first derivative of each component of the velocity vector:

a(t) = (d²x/dt², d²y/dt², d²z/dt²)

a(t) = (0, -18 cos(3t), -18 sin(3t))

Now, the magnitude of the acceleration vector:

|a(t)| = √[(d²x/dt²)² + (d²y/dt²)² + (d²z/dt²)²]

|a(t)| = √[0² + (-18 cos(3t))² + (-18 sin(3t))²]

|a(t)| = √(324 cos²(3t) + 324 sin²(3t))

|a(t)| = √324 (cos²(3t) + sin²(3t))

|a(t)| = 18

In conclusion,  magnitude of the acceleration is 18.

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Which of these shapes have rectangular cross sections when they are cut perpendicular to the base? Select three
options.

Answers

The three shapes that have rectangular cross-sections when cut perpendicular to the base are the rectangular prism, while the cylinder, cone, and sphere do not.

To determine which shapes have rectangular cross-sections when cut perpendicular to the base, we need to consider the properties of each shape.

Rectangular Prism: A rectangular prism has a rectangular base, and when cut perpendicular to the base, the cross-sections will also be rectangles. This is because the cuts will be parallel to the base, resulting in rectangular slices.

Cylinder: A cylinder has a circular base, and when cut perpendicular to the base, the cross-sections will be circles. This is because the cuts will be parallel to the circular base, resulting in circular slices. Therefore, a cylinder does not have a rectangular cross-section.

Cone: A cone has a circular base, and when cut perpendicular to the base, the cross-sections will be triangles. This is because the cuts will intersect the circular base at an angle, resulting in triangular slices. Therefore, a cone does not have a rectangular cross-section.

Sphere: A sphere is a perfectly round shape, and when cut perpendicular to any direction, the cross-sections will always be circles. Therefore, a sphere does not have a rectangular cross-section.

Based on the above analysis, the three shapes that have rectangular cross-sections when cut perpendicular to the base are the rectangular prism, while the cylinder, cone, and sphere do not.

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Enter the number that belongs in the green box

Answers

Answer:

? ≈ 33.40°

Step-by-step explanation:

using the Sine rule in the triangle

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex]

with a = 12.34, b = 7 , ∠ A = 76° , ∠ B = ? , then

[tex]\frac{12.34}{sin76}[/tex] = [tex]\frac{7}{sin?}[/tex] ( cross- multiply )

12.34 × sin? = 7 × sin76° ( divide both sides by 12.34 )

sin ? = [tex]\frac{7sin76}{12.34}[/tex] . then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{7sin76}{12.34}[/tex] ) ≈ 33.40° ( to the nearest hundredth )

the sum of two numbers is 40. when 3\1\4 times the larger number is subtracted from5\1\2 times the smaller, the difference is-25. find the two numbers.

Answers

Step-by-step explanation:

Not a very well written or posted question, but here is what I think it means:

x+ y = 25     re-arange to y = 25-x   and sub into the next equation:

5.5 y  -  3.25  x = -25

5.5 (25-x) - 3.25 x = - 25

137.5 - 5.5 -3.25x = -25

x= 18  4/7     then y = 6  3/7    

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval
4



8
4≤x≤8.

x

(

)
f(x)
4
4
2
2
5
5
4
4
6
6
8
8
7
7
16
16
8
8
32
32

Answers

In simplest form, the average rate of change of the function over the interval 4 ≤ x ≤ 8 is 751.75.

To find the average rate of change of the function over the interval 4 ≤ x ≤ 8, we need to calculate the difference in function values and divide it by the difference in x-values.

The function values corresponding to the given x-values are as follows:

x f(x)

4 225

5 446

6 887

7 1616

8 3232

To calculate the average rate of change, we use the formula:

Average Rate of Change = (Change in f(x))/(Change in x)

The change in f(x) over the interval is f(8) - f(4) = 3232 - 225 = 3007.

The change in x over the interval is 8 - 4 = 4.

Therefore, the average rate of change is:

Average Rate of Change = 3007/4 = 751.75.

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the length of a rectangular piece of steel in a bridge is 5 meter less than triple the width. the perimeter of the piece of steel is 46 meters. find the length of the piece of steel. find the width of the piece of steel.

Answers

The width of the piece of steel is 7m

What is perimeter of a rectangle?

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.

Perimeter is a math concept that measures the total length around the outside of a shape.

The steel takes the shape of a rectangle therefore the perimeter of the steel is the perimeter of the rectangle.

Perimeter of a rectangle is expressed as;

P = 2(l+w). where l is the length and w is the width.

l = 3w-5

p = 46

46 = 2( 3w-5+w)

3w -5 +w = 23

4w = 23 +5

4w = 28

w = 7m

Therefore the width of the steel is 7m

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