Use the Tree Diagram below to answer the following question.

Whats the probability that you will get a 15-inch monitor?

P(15-inch) = ?

a. 0
b. 1
c. 2/6
d. 3

50 points!

The value of the missing length of the enlarged triangle in the simplest form would be = 60mm.

To calculate the missing length, the formula for scale factor should be used such as follows;

Scale factor = Larger dimensions/smaller dimensions

length of ∆T = 10mm

length of ∆S = 3mm

scale factor = 10/3 = 3.33

If the width of ∆S = 18mm

width of ∆ T = 18×3.33

= 59.94 = 60mm

Learn more about scale factor here:

https://brainly.com/question/28339205

#SPJ1

Answer: A

Step-by-step explanation: -87

The critical value for a two-tailed test at the 0.05 significance level is 1.96.

The null hypothesis is that there is no difference in the proportion of men and women intending to vote for Donald Trump, and the alternative hypothesis is that there is a difference.

The test statistic is given by:

z = (p1 - p2) /√[(p×(1-p)×(1/n1 + 1/n2),

where p = (x1 + x2) / (n1 + n2) and x1 and x2 are the number of successes in samples 1 and 2 respectively, and n1 and n2 are the sample sizes of samples 1 and 2 respectively.

In this case, x1 = 120, x2 = 132, n1 = 250, and n2 = 240.

Plugging these values into the equation gives us z = 0.906.

Since the test statistic does not exceed the critical value, we fail to reject the null hypothesis. That is, there is not convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the 0.05 significance level.

Therefore, the critical value for a two-tailed test at the 0.05 significance level is 1.96.

Learn more about the critical value here:

https://brainly.com/question/14508634.

#SPJ5

The height of the tower is given as follows:

h = 22.5 ft.

Similar triangles are triangles that share these two features listed as follows:

The reflection means that the two triangles are similar in this problem, hence the proportional relationship for the equivalent side lengths is given as follows:

3/13.5 = 5/h

Then the height is obtained as follows:

3h = 5 x 13.5

h = 5 x 13.5/3

h = 22.5 ft.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{13\% of 50}}{\left( \cfrac{13}{100} \right)50}\implies 6.5[/tex]

Answer: 6.5

Step-by-step explanation: You can find the percent of a number by multiplying the two together such as 50(0.13). This will give you the answer of 6.5.

The graph is a function: A. yes

The domain of this function is: E. x ≥ -3.

The range of this function: G. all real numbers.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.

Range = {-∞, ∞} or all real numbers.

Read more on domain here: brainly.com/question/17440903

#SPJ1

Answer:

x + y = 3 and 3x - y = 1.

Step-by-step explanation:

For the equation x + y = 3, we can find the x-intercept by setting y = 0 and solving for x:

x + 0 = 3

x = 3

So the x-intercept is (3, 0). Similarly, we can find the y-intercept by setting x = 0 and solving for y:

0 + y = 3

y = 3

So the y-intercept is (0, 3). We can plot these two points and draw a straight line through them to represent the equation x + y = 3. The resulting line has a slope of -1 and a y-intercept of 3.

For the equation 3x - y = 1, we can find the x-intercept by setting y = 0 and solving for x:

3x - 0 = 1

x = 1/3

So the x-intercept is (1/3, 0). Similarly, we can find the y-intercept by setting x = 0 and solving for y:

3(0) - y = 1

y = -1

So the y-intercept is (0, -1). We can plot these two points and draw a straight line through them to represent the equation 3x - y = 1. The resulting line has a slope of 3 and a y-intercept of -1.

Now, we can visually determine the point where the two lines intersect, which represents the solution to the simultaneous equation. We can do this by looking at the graph and finding the point where the two lines intersect. Using the given range of values of x from -1 to +3, we can plot the two lines and find their intersection point:

[i dont know wheres the graph image but just show it so you can explain that]

The intersection point is approximately (1.1, 1.9), which is the solution to the simultaneous equation x + y = 3 and 3x - y = 1.

The location of point T on the number line is 3

From the question, we have the following parameters that can be used in our computation:

A = -6

B = 9

T = three-fifths of the distance from A to B.

Using the above as a guide, we have the following:

T = A + 3/5 *(B - A)

Substitute the known values in the above equation, so, we have the following representation

T = -6 + 3/5 *(9 + 6)

Evaluate

T = 3

Hence, the location is 3

Read more about distance at

https://brainly.com/question/28551043

#SPJ1

The direction angle of the vector with initial point (1, -1) and terminal point (7, 2) is approximately 26.57 degrees, found by calculating the arctangent of the ratio of the y and x components of the vector.

The direction angle of the vector v is the angle it makes with the positive x-axis, measured counterclockwise.

To find this angle, we need to calculate the difference between the y-coordinates and x-coordinates of the terminal and initial points of the vector, respectively. Then, we can use the arctangent function to find the angle.

Let's first find the components of the vector v

v = <7 - 1, 2 - (-1)> = <6, 3>

Now, we can find the direction angle as follows

θ = arctan(3/6)

θ = 0.4636 radians (in decimal form)

To convert this to degrees, we can multiply by 180/π

θ ≈ 26.57°

Therefore, the direction angle of the vector v is approximately 26.57 degrees.

To know more about direction angle:

https://brainly.com/question/28522105

#SPJ1

Answer:

128

Step-by-step explanation:

To translate the sentence into an equation, we can use the following formula: number / 8 = 16. This equation shows that we are dividing a number by 8 and getting a result of 16. To solve for the number, we can multiply both sides of the equation by 8. This gives us the equation number = 16 x 8, which simplifies to number = 128. Therefore, the solution to the equation is 128.

Answer:

128

Step-by-step explanation:

got it right on edge

Answer: 5.5 months

Explanation:

To calculate the number of months it will take to pay off your credit card balance, we can use the formula for the time it takes to pay off a balance with fixed monthly payments:

n = -log(1 - (r * b) / p) / log(1 + r)

where:n is the number of months it will take to pay off the balancer is the monthly interest rate (which is the annual percentage rate divided by 12)b is the balance owedp is the fixed monthly paymentFirst, let's calculate the monthly interest rate r:

r = 0.147 / 12 = 0.01225

Next, we can substitute the values into the formula:

n = -log(1 - (0.01225 * 2264) / 500) / log(1 + 0.01225)

Using a calculator, we can simplify this to:

n = 5.5 months

The solid formed when the right triangle is rotated around the side length of 5 is two cones with a radius of 1.5 units and a height of 1.8 units and 3.2 units.

The volume of the smaller cone is approximately 3.82 cubic units, and the surface area is approximately 20.94 square units.

The volume of the larger cone is approximately 6.04 cubic units, and the surface area is approximately 20.94 square units.

We have,

When the right triangle is rotated around the side length of 5, it forms two cones with different heights and radii.

Now,

r = base / 2 = 3 / 2 = 1.5 units

h = height = 4 units

Using the Pythagorean theorem,

l = √(1.5² + 4²) = √(18.25) ≈ 4.27 units

The first cone has a radius of 1.5 units and a height of 1.8 units (5 - 4.27)

The second cone has a radius of 1.5 units and a height of 3.2 units (5 - 1.8).

Now,

The volume of a cone.

V = (1/3)πr^2h

The surface area of a cone.

A = πrl + πr^2

For the first cone:

V = (1/3)π(1.5)²(1.8) = 3.82 cubic units

A = π(1.5)(4.27) + π(1.5)² = 20.94 square units

For the second cone:

V = (1/3)π(1.5)²(3.2) = 6.04 cubic units

A = π(1.5)(4.27) + π(1.5)² = 20.94 square units

Thus,

The solid formed when the right triangle is rotated around the side length of 5 is two cones with a radius of 1.5 units and a height of 1.8 units and 3.2 units.

The volume of the smaller cone is approximately 3.82 cubic units, and the surface area is approximately 20.94 square units.

The volume of the larger cone is approximately 6.04 cubic units, and the surface area is approximately 20.94 square units.

Learn more about cones here:

https://brainly.com/question/13798146

#SPJ1

The new coordinates of dilated rectangle by scale factor of 1/4 are J(1, 2), K(3, 2), L(3, 1), and M(1, 1) we can draw figure.

We are given the coordinates of the vertices of a rectangle J(4,8), K(12,8), L(12,4), and M(4,4).

To dilate the rectangle by a scale factor of 1/4, we need to multiply each coordinate by 1/4.

Multiplying each x-coordinate by 1/4

x-coordinate of J: 4 * 1/4 = 1

x-coordinate of K: 12 * 1/4 = 3

x-coordinate of L: 12 * 1/4 = 3

x-coordinate of M: 4 * 1/4 = 1

Multiplying each y-coordinate by 1/4

y-coordinate of J: 8 * 1/4 = 2

y-coordinate of K: 8 * 1/4 = 2

y-coordinate of L: 4 * 1/4 = 1

y-coordinate of M: 4 * 1/4 = 1

Therefore, the coordinates of the dilated rectangle are: J(1,2), K(3,2), L(3,1), and M(1,1).

Using these new coordinates, we can draw the dilated rectangle by plotting the four vertices on a coordinate plane.

The dilated rectangle has the same shape and orientation as the original rectangle, but it has been reduced in size by a scale factor of 1/4.

To know more about dilated rectangle:

https://brainly.com/question/28099065

#SPJ1

It will take the team 65 days to complete the maintenance of the entire sewage pipe

From the question, we have the following parameters that can be used in our computation:

Sewage pipe = 52 miles

Distance covered each day = 4/5 miles

Using the above as a guide, we have the following:

Number of days = Sewage pipe /Distance covered each day

Substitute the known values in the above equation, so, we have the following representation

Number of days = 52/(4/5)

Evaluate the quotient

Number of days = 65

Hence, the number of days is 65

Read more about unit rates at

https://brainly.com/question/19493296

#SPJ1

The  inequality given that the function f is increasing over it s domain

f(x²-2)<f (7x-8), Df =  (-∞,2) is: x ∈ (-∞,1) U (6,2).

We know the  values of x within the domain by setting the intersection points of the two functions f(x2-2) and f(7x-8).

f (x²-2) = f (7x-8)

So,

x²-2 = 7x-8

Simplify and find x

x² - 7x + 6 = 0

(x - 1)(x - 6) = 0

x = 1 or x = 6

The domain (-,2) is divided into the intervals (-,1), (1,6), and (6,2). Now let assess the interval endpoints because f is rising:

For x < 1:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) < 0

For 1 < x < 6:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) > 0

For x > 6:

x² - 2 < 7x - 8

x² - 7x + 6 < 0

(x - 1)(x - 6) < 0

Since f is rising across its domain the inequality f(x2-2) f(7x-8) has the following solution: x ∈ (-∞,1) U (6,2).

Therefore the inequality is  x ∈ (-∞,1) U (6,2).

Learn more about inequality here:https://brainly.com/question/25944814

#SPJ1

The solution to the inequality is x >= -2 for inequality 3x-5≥-11

The given inequality is 3x-5≥-11

Three times of x greater than or equal to minus eleven

x is the variable

3x - 5≥ -11:

Adding 5 to both sides, we get:

3x ≥ -6

Dividing both sides by 3, we get:

solution is  x≥-2

Therefore, the solution to the inequality is x >= -2.

To learn more on Inequalities click:

https://brainly.com/question/28823603

#SPJ1

Answer:A frequency table is a type of statistic used to organize and display data.

What is data set?

A data set is a collection of related data records or observations, usually containing information about a particular subject or area of study. Data sets can be used to analyze trends, make predictions, and provide insights into various phenomena. Data sets can be collected from a variety of sources, such as surveys, experiments, simulations, or other research methods. They are typically organized into tables and can include both quantitative and qualitative data.

It is a chart that shows how often something occurs within a given set of data. The categories in a frequency table are the different values or categories of data, and the frequencies are the number of times each category occurs.

Relative frequency is the ratio of the number of times a category occurs in the data set to the total number of values in the data set. It is usually expressed as a percentage or decimal. For example, if the data set contains 20 values and the category "A" occurs 5 times, the relative frequency of "A" is 25%.

Cumulative frequency is the sum of the frequencies up to a given point in the data set. It is used to show how many values are below or above a certain category. For example, if the data set contains 20 values and the category "A" occurs 5 times, the cumulative frequency of "A" is 5. This means that there are 5 values that are below or equal to "A" in the data set.

To know more about data set click-

brainly.com/question/14592520

#SPJ1

Brenda's class left for the field trip at 10:16 A.M.

We have,

Let's break down the time of Brenda's class field trip:

50 minutes to drive to the museum

3 hours and 45 minutes (or 225 minutes) at the museum

56 minutes to drive back to school

Adding up all of these times, we get:

50 + 225 + 56 = 331 minutes

So the field trip took a total of 331 minutes.

If the class arrived back at school at 3:47 P.M., and we subtract 331 minutes from 3:47 P.M., we can determine the time they left for the field trip:

3:47 P.M. - 331 minutes

= 10:16 A.M.

Therefore,

Brenda's class left for the field trip at 10:16 A.M.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The value of solution of the equation is,

⇒ tan x = 1 / 3

We have to given that;

The expression is,

⇒ - 2 tan (-x) = 5 tan (x) - 1

Now,, We can simplify as;

⇒ - 2 tan (-x) = 5 tan (x) - 1

⇒ - 2 (-  tan (x) ) = 5 tan (x) - 1

⇒ 2 tan (x) = 5 tan (x) - 1

⇒ 5 tan x - 2 tan x = 1

⇒ 3 tan x = 1

⇒ tan x = 1 / 3

Thus, The value of solution of the equation is,

⇒ tan x = 1 / 3

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

The present value of leasing the towers is $19,576,000 while the present value of erecting new towers is $20,273,000. Therefore, the company should lease the towers.

Step-by-step explanation:

The measure of ∠BPO is 48°.

Since PD bisects ∠BPA, we can say:

∠AOC = ∠BOC .

Thus, ∠ BOC = 42°

Since PB is tangent to the circle, PBO = 90°.

Looking at triangle PBO, we can say:

∠BPO + ∠PBO + ∠BOC = 180  (angles in a triangle add up to 180)

∠BPO + 90 + 42 = 180

∠BPO + 132 = 180

∠BPO = 180 - 32

∠BPO = 48°

Learn more about tangent to circle on:

https://brainly.com/question/9132922

#SPJ1

Complete Question

Check image attached

Note that the above prompt requires you to under stand what a W-4 form is  and how to complete one.

Rbecca needs to s tart by entering your personal information in boxes 1-4, including your name, address, Social Security number, and filing status. In this case, Rebecca Kate Foster's information is:

Box 1: Rebecca Kate Foster

Box 2: 1234 Main St.

Box 3: New York, NY 12345

Box 4: 123-45-6789

Box 5: Single

In box 6, write "1" since Rebecca only has one job.

Rebecca can claim the standard deduction or itemize deductions in box 7. She may benefit from itemizing deductions because she has donated $3,960 to charity in the last year.

Rebecca can claim whatever excess tax withholding she wants each paycheck in box 8. She may not need to withhold any further taxes because she has no dependents and is not married. If she prefers, she can leave this section blank.

Rebecca can claim any extra withholding for the year in box 9. If she anticipates to owing taxes at the end of the year, she may want to withhold more from each paycheck to prevent a hefty tax payment later. If she anticipates a reimbursement, she should withhold less. She can use the IRS's withholding calculator to determine the right amount.

Finally, sign and date the form in box 5 before submitting it to your company.

Learn more about W-4 Form at:

https://brainly.com/question/15507745

#SPJ1

Full Question:

Although part of your question is missing, you might be referring to this full question:

DIRECTIONS Read the scenario below and fill out the W-4 form using the information provided. Then, read the W-2 form and answer the questions that follow. W-4 Form Rebecca Kate Foster is starting a new job. She is 23 years old and graduated from college with no student loan debt. This is her only job, and she makes a salary that allows her to bring home $3,300 a month. She’s not married and has no children or anyone else who is supported by her income. Over the past year, she has given a total of $3,960 to charity. Her address is 1234 Main St., New York, NY 12345, and her Social Security number is 123-45-6789.

The match terminates as soon as the central heap runs out of cards whose factor are not present elsewhere, resulting in a score of 92 - falling short from 100.

It should be noted that to acquire a higher point achievement, alternative approaches can be tested; however, reaching beyond the hundred mark is not guaranteed.

Conversely, with each 20-game, the final outcome should contain 8 or fewer pieces in the tally pile since there are strictly 17 cards eligible to be shifted into this collection. Subsequently, due to the 138 maximum points potential (stated in part B), and the entire set amounting for 210 points - the minimum count for items within the discard pool will be 3 (as calculated from 20 - 17).

Learn more about word problem on

https://brainly.com/question/21405634

#SPJ1

(x+3)²+(y+7)²=169 is  the equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).

The equation of the circle if (-3,-7) is a point on the circle and the midpoint of the circle's diameter is (2,5).

The radius of the circle is 13

The equation of circle in standard form is (x-h)²+(y-k)²=r²

(h, k) is centre of circle

(-3, -7) is centre

(x+3)²+(y+7)²=13²

(x+3)²+(y+7)²=169

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

The return on equity (ROE) for a project financed with 100% equity or 50% equity and 50% debt, given different levels of earnings before interest and taxes (EBIT) are 20.3%, -5.4%, 36.2% and  -20.3% respectively. So, the correct answers are A), B), A) and A). if Galaxy Corp. proceeds with a recapitalization then  Basic earning power (BEP), Return on assets (ROA), Net income are likely to increase. The correct option is A), B) and E).

ROE = EBIT*(1 - T)/Total Equity

Where T is the tax rate and Total Equity is the amount of equity used to finance the project.

If the EBIT is $145,000, then

ROE = $145,000*(1 - 0.30)/$500,000 = 20.3%

Therefore, the answer is 20.3%. So, the correct answer is A).

If the EBIT is -$45,000, then

ROE = -$45,000*(1 - 0.30)/$500,000 = -5.4%

Therefore, the answer is -5.4%. So, the correct answer is B).

If the project is financed with 50% equity and 50% debt at an interest rate of 11%, then the cost of equity can be calculated as follows

Cost of Equity = EBIT*(1 - T)/Total Equity

Cost of Debt = Interest Rate*(1 - T)

Weighted Average Cost of Capital (WACC) = Cost of Equity*(Equity/Total Capital) + Cost of Debt*(Debt/Total Capital)

ROE = EBIT*(1 - T)/Total Equity

ROE = [$145,000*(1 - 0.30)/($500,0000.50)] + [$145,000(1 - 0.30)0.50/($500,0000.50)*(1 - 0.11)]

ROE = 36.2%

Therefore, the answer is 36.2%. So, the correct answer is A).

If the project is financed with 50% equity and 50% debt at an interest rate of 11%, and the EBIT is -$45,000, then

ROE = -$45,000*(1 - 0.30)/($500,0000.50) + [-$45,000(1 - 0.30)0.50/($500,0000.50)*(1 - 0.11)]

ROE = -20.3%

Therefore, the answer is -20.3%. So, the correct answer is A).

If Galaxy Corp. proceeds with the recapitalization, the cost of debt is likely to increase since the firm is issuing new long-term debt. Therefore, the cost of debt (rdrd) will increase.

However, the basic earning power (BEP) and return on assets (ROA) are likely to increase since the firm will have a higher proportion of debt in its capital structure, which will increase the financial leverage of the firm.

As a result, the net income of the firm may also increase. The cost of equity (rsrs) may or may not change depending on how the market perceives the increased financial risk associated with the higher debt level.

Therefore, the items that are likely to increase are Basic earning power (BEP), Return on assets (ROA), Net income. The correct answer is A), B) and E).

To know more about return on equity:

https://brainly.com/question/27821130

#SPJ1

--The given question is incomplete, the complete question is given

" Universal Exports Inc. is considering a project that will require $500,000 in assets. The project will be financed with 100% equity. The company faces a tax rate of 30%. What will be the ROE (return on equity) for this project if it produces an EBIT (earnings before interest and taxes) of $145,000?

20.3%

22.3%

13.2%

14.2%

Determine what the project’s ROE will be if its EBIT is –$45,000. When calculating the tax effects, assume that Universal Exports Inc. as a whole will have a large, positive income this year.

-7.6%

-5.4%

-6.3%

-5.7%

Universal Exports Inc. is also considering financing the project with 50% equity and 50% debt. The interest rate on the company’s debt will be 11%. What will be the project’s ROE if it produces an EBIT of $145,000?

36.2%

32.9%

24.7%

26.3%

What will be the project’s ROE if it produces an EBIT of –$45,000 and it finances 50% of the project with equity and 50% with debt? When calculating the tax effects, assume that Universal Exports Inc. as a whole will have a large, positive income this year.

-20.3%

-19.3%

-21.3%

-26.4%

Galaxy Corp. currently is financed with 10% debt and 90% equity. However, its CFO has proposed that the firm issue new long-term debt and repurchase some of the firm’s common stock. Its advisers believe that the long-term debt would require a before-tax yield of 10%, while the firm’s basic earning power is 14%. The firm’s operating income and total assets will not be affected. The CFO has told the rest of the management team that he believes this move will increase the firm’s stock price. If Galaxy Corp. proceeds with the recapitalization, which of the following items are also likely to increase? Check all that apply.

Basic earning power (BEP)

Return on assets (ROA)

Cost of debt (rdrd)

Cost of equity (rsrs)

Net income"--

The probability of yellow or has an odd number is 8/9

From the question, we have the following parameters that can be used in our computation:

Green = 1 to 3

Yellow = 1 to 6

This means that

Odd = 2 + 3

Odd = 5

So, we have

P(Yellow) = 6/9

P(Odd) = 5/9

P(Yellow and Odd) = 3/9

The probability of yellow or has an odd number is

P = 6/9 + 5/9 - 3/9

Evaluate

P = 8/9

Hence, the probability is 8/9

Read more about probability at

https://brainly.com/question/24756209

#SPJ1

The distance is given as 272.98 feet.

The measurement of the angle of depression relates to the formation between a horizontal line and the observer's sightline to an object or point that exists beneath their level.

Therefore, it demonstrates the formed degree between the observer's line of vision towards a subject and the horizontal flatness visible when looking downwards at it from afar.

This notion is prevalent throughout trigonometry and play a vital role in areas including surveying, navigation and architecture. The degrees obtained from this practice are generally calculated via angles, with a complete 90-degree measure indicative of viewing straight downward over the designated target.

Read more about Angle of Depression here:

https://brainly.com/question/27865363

#SPJ1

Answer:

Exponential decay is represented by the equation:

y = a * e^(-bx)

where:

y is the final value

a is the initial value

b is the decay rate

x is the time variable

The exponential decay rate, b, can be found by taking the natural logarithm (ln) of both sides of the equation, then rearranging to isolate the decay rate:

ln(y/a) = -bx

b = -ln(y/a)/x

So, to find the exponential decay rate, you would need to know the initial value (a), the final value (y), and the time elapsed (x). Then, you can use the formula above to calculate the decay rate, b.

The expressions "1+b" and "1-b" are not sufficient to find the exponential decay rate, as they do not contain enough information about the specific scenario or data set.

if this helps, can you please mark my answer brainliest?

The result of -3u + 5v is the vector (12, -34).

Let's start by defining the two given vectors u and v:

u = (1, 3)

v = (3, -5)

To find the dot product of two vectors, we need to multiply their corresponding components and then add up the results. The formula for the dot product of two vectors can be written as:

u · v = u₁v₁ + u₂v₂ + ... + uₙvₙ

where u₁ and v₁ are the first components of vectors u and v, u₂ and v₂ are the second components, and so on up to un and vₙ, which are the nth components.

Using this formula, we can find the dot product of u and v as follows:

u · v = (1)(3) + (3)(-5)

= 3 - 15

= -12

So, the dot product of vectors u and v is -12.

Next, we need to calculate -3u + 5v. To do this, we need to multiply each component of vector u by -3 and add it to the corresponding component of vector v multiplied by 5. We can write this as follows:

-3u + 5v = (-3)(u₁, u₂) + (5)(v₁, v₂)

= (-3)(1, 3) + (5)(3, -5)

= (-3, -9) + (15, -25)

= (12, -34)

To know more about vector here

https://brainly.com/question/29740341

#SPJ1