Which equation would be the best to solve by completing the square?

3x^2 + 4x = -2

x^2 + 8x = 20

x^2 + 11x = 40

x^2 = 36

Total pay = Regular pay + Overtime pay = $280 + $616 = $896. Therefore, if Lisa works 42 hours in one week, she would be paid $896

The first step is to calculate Lisa's regular pay for the week. We know that her regular hourly rate is $8 per hour. If she works 35 hours or less in a week, then her pay is simply her hourly rate times the number of hours worked. Therefore, her regular pay for a week where she works 35 hours or less would be:

Regular pay = $8/hour * 35 hours = $280

However, we know that Lisa worked 42 hours in one week, which is more than 35 hours. This means she also worked 7 overtime hours. According to the problem, Lisa is paid 11 times her regular salary for any overtime hours worked. This means her overtime pay for the 7 overtime hours would be:

Overtime pay = $8/hour * 11 * 7 hours = $616

To get Lisa's total pay for the week, we simply add her regular pay and overtime pay together:

Total pay = Regular pay + Overtime pay = $280 + $616 = $896

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The equation of the parabola with focus (4,5) and directrix y=-1 is

[tex](y-5)^2=4(x-4) or (y+1)^2=4(x-4).[/tex]

The equation of a parabola is defined by its focus and directrix. The focus is the point on the parabola that is used to determine its shape, while the directrix is the line used to determine its orientation. The equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex]. This equation can be expressed in terms of the focus and directrix by substituting the x and y values of the focus and directrix into the equation. Substituting the x value of the focus (4) into the equation gives us[tex](y-5)^2=4(4-4)[/tex], which simplifies to[tex](y-5)^2=0[/tex]. This equation can be rearranged to give us y=5, which is the y value of the focus. Substituting the y value of the directrix (-1) into the equation gives us [tex](y+1)^2=4(x-4)[/tex]. This equation can also be rearranged to give us y=-1, which is the y value of the directrix. Therefore, the equation of the parabola with focus (4,5) and directrix y=-1 is[tex](y-5)^2=4(x-4)[/tex] or[tex](y+1)^2=4(x-4)[/tex].

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The binomial probability distribution can be used to answer these questions. The formula for the binomial probability distribution is:
P(X=x) = C(n,x) * p^x * (1-p)^(n-x)
Where C(n,x) is the number of combinations of n items taken x at a time, p is the probability of success, and (1-p) is the probability of failure.

a. The probability that a single detection system will detect an attack is .86 (to 2 decimals).
b. If two detection systems are installed in the same area and operate independently, the probability that at least one of the systems will detect the attack is:
P(X>=1) = 1 - P(X=0)
P(X=0) = C(2,0) * .86^0 * (1-.86)^2 = .0196
P(X>=1) = 1 - .0196 = .9804 (to 4 decimals)
c. If three systems are installed, the probability that at least one of the systems will detect the attack is:
P(X>=1) = 1 - P(X=0)
P(X=0) = C(3,0) * .86^0 * (1-.86)^3 = .0027
P(X>=1) = 1 - .0027 = .9973 (to 4 decimals)
d. Based on the calculations, it is recommended that multiple detection systems be used. The probability of at least one system detecting an attack increases as the number of systems increases.

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The equation to represent the number of guests at your party is 150 + 6x = 282 where, the number of guests at the party, x is 22.

Let

Cost of renting a roller rink = $150

Cost per person = $6

Total charge of the party = $282

Number of persons at the birthday party = x

The equation:

150 + 6x = 282

subtract 150 from both sides

6x = 282 - 150

6x = 132

divide both sides by 6

x = 132/6

x = 22

Therefore, there are 22 guests at the birthday party.

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Answer:

360°

Step-by-step explanation:

If you travel around the outside of any polygon, the angels will add to 360

Helping in the name of Jesus.

The surface area of the triangular prism is 156.5 inches².

The surface area of a triangular prism can be found as follows:

Therefore, the prism is a triangular prism. The prism has two triangular base with side length 5 inches each. The height of the triangular bases are 4.3 inches each.

The height of the triangular prism is 9 inches. The surface area of the triangular prism is the sum of the whole individual area of each surface of the prism.

Hence,

surface area of the prism = bh + l(s₁ + s₂ + s₃)

Therefore,

surface area of the prism = 4.3 × 5 + 9(5 + 5 + 5)

surface area of the prism = 21.5 + 9(15)

surface area of the prism = 21.5 + 135

surface area of the prism = 156.5 inches²

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Answer:

Each of the diagonals is 16

Step-by-step explanation:

The diagonals of a rectangular are equal

The two diagonals are QS and RT

QS = RT

→ 30 - 2x = 9 + x

Subtract 30 both sides:
30 - 30 - 2x = 9  -  30 + x

- 2x  = -21  + x

Subtract x both sides
-2x - x = -21 + x  -  x

-3x = -21

x = -21/-3 = 7

So the diagonal RT = 9 + 7 =16

should be the same as diagonal QS
Qs = 30 - 2(7) = 30 - 14 = 16

Finally, we can express the answer in standard form by moving the decimal point one place to the left, and adjusting the exponent of 10 accordingly: 0.4192 × 10⁻⁹ = 4.192 × 10⁻¹⁰.

An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.

Here,

To subtract the given values in standard form, we need to make sure that the exponents of 10 are the same.

We can rewrite 4.57 × 10⁻¹⁰ as 0.457 × 10⁻⁹ (by moving the decimal point one place to the right) and rewrite 3.78 × 10⁻¹¹ as 0.0378 × 10⁻⁹ (by moving the decimal point one place to the right).

Now we can subtract the values:

(4.57 × 10⁻¹⁰) – (3.78 × 10⁻¹¹) = (0.457 × 10⁻⁹) – (0.0378 × 10⁻⁹)

= 0.4192 × 10⁻⁹

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The angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.

The 16-notch socket has a cylindrical shape with 16 notches or recesses machined into the interior of the socket. Each notch corresponds to a flat side of a 16-sided nut or bolt head. The notches are evenly spaced around the socket, providing a secure grip on the nut or bolt head and allowing for easy application of torque using a ratchet or wrench.

16-notch sockets are commonly used in automotive and industrial applications, particularly in heavy machinery where large bolts and nuts with 16-sided heads are often used. They are available in a range of sizes to fit different nut and bolt sizes and are typically made of durable materials such as chrome vanadium steel or high-grade aluminum.

Premise 1: Deondra is designing a 16-notch socket wrench.

Premise 2: The notches will be the same size.

Conclusion: Therefore, Deondra needs to know the angle measure for each notch.

To determine the angle measure for each notch, we can use the formula for the interior angle of a regular polygon, which is:

Interior angle = (n-2) x 180 / n

where n is the number of sides (or notches) in the polygon.

Applying this formula to a 16-sided polygon (or hexadecagon), we get:

Interior angle = (16-2) x 180 / 16

Interior angle = 1680 / 16

Interior angle = 105 degrees

Therefore, the angle measure for each notch in Deondra's 16-notch socket wrench should be 105 degrees.

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a) An equation in slope-intercept form representing the linear function is y = 12 + 6x.

b) If tomorrow’s practice is 60 minutes long, based on the slope-intercept equation above, the number of drills that Luna's team practice is 8.

The slope-intercept equation is a linear equation in slope-intercept form.

The slope-intercept equation is given as y = mx + b, where:

The number of minutes spent for warm-up practice = 12 minutes

The number of minutes spent per drill = 6 minutes

Let the number of drills per practice = x

Let the total number of minutes spent by the soccer team (length) per practice = y

y = 12 + 6x

The length for tomorrow's practice = 60 minutes

60 = 12 + 6x

60 - 12 = 6x

48 = 6x

x = 8

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Let's first find the total cost of transportation and admission tickets:

$200 (transportation) + $6.50 (admission ticket) x n (number of students) = $750

$6.50n = $550

n = 84.62

So, the maximum number of students that can go to the game is 84.62. However, we cannot have a fractional number of students, so we can round down to 84 students.

Now, let's find the cost of the meal for each student:

$2.50 (medium sandwich) + $2.00 (drink) + $1.50 (popcorn) = $6.00

If the booster club pays for a large sandwich, drink, and popcorn for each student, the cost will be:

$3.00 (large sandwich) + $2.50 (drink) + $2.00 (popcorn) = $7.50

The difference in cost between the two options is $1.50 per student.

To find how many more students can go to the game with the cheaper meal option, we can divide the total amount of money available ($750) by the difference in cost per student ($1.50):

$750 ÷ $1.50 = 500

So, with the cheaper meal option, the booster club can take 500/6 students = 83 students.

Therefore, the booster club can take 1 more student to the game if they pay for a medium sandwich, drink, and popcorn for each student.

How high the wall is to which the ladder reaches is 15 feet

To determine the height of the wall, we need to consider the Pythagorean theorem;

The theorem states that the square of the longest side of a triangle is equal to the sum of the squares of the two remaining sides of that triangle.

This is represented as;

a²= b² + c²

Such that ;

From the information given, we have that;

25² = 20² + c²

find the squares as substitute

c² = 625 - 400

subtract the values

c² = 225

c = √225

c = 15 feet

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Answer:

75%

Step-by-step explanation:

write it as a fraction first, so 15/20.

make the bottom number 100 to get the mark out of 100.

to do this, multiply the bottom by 5 (20x5=100) and then do the same to the top.

you get 75/100. this equals 75%

Answer:

75%

Step-by-step explanation:

In this question, 20 is the highest score you can get on the test so 20 is 100%. We will now want to divide 100 by 20.

100 ÷ 20 = 5

Each score Amore got on the test was worth 5% of the test.

We know he scored 15 on the text, so now we want to multiply 15 with 5.

15 × 5 = 75

Amore scored 75% on his test.

To compare the performance of MedStar Washington to other DC-based hospitals on overall satisfaction, we can use the (HCAHPS) survey data available on the Hospital Compare website.

The HCAHPS survey measures patients' perspectives of hospital care, including topics such as communication with doctors and nurses, the responsiveness of hospital staff, cleanliness and quietness of hospital environment, pain management, and medication communication.

To obtain the data for Medstar Washington and other DC-based hospitals (excluding Medstar Georgetown), you can follow these steps:

1) Go to the Hospital Compare website:

2) Click on "Find a Hospital."

3) Enter the city and state of the hospital you want to compare (e.g., Washington, DC) and click "Search."

4) Select "Patient Experience (HCAHPS) Survey" from the "Select a topic" drop-down menu.

5) Click on "Overall Hospital Rating" under the "Survey Summary Star Ratings" section.

6) Select the hospitals you want to compare and click "Compare."

7) You can view the survey results for each hospital on various dimensions of patient experience, such as communication with nurses, communication with doctors, the responsiveness of hospital staff, pain management, cleanliness and quietness, and overall hospital rating.

Based on the data, the administrator of MedStar Washington can identify areas of improvement and take necessary steps to enhance patient satisfaction.

For example, if the hospital is performing poorly in communication with nurses, the administrator can develop programs or training for nurses to improve their communication skills. If the hospital is struggling with pain management, the administrator can work with physicians and nurses to implement best practices and improve pain control.

It's worth noting that Hospital Compare data is based on self-reported patient experience, and other factors such as patient demographics, the severity of illness, and socioeconomic status can influence the scores.

Therefore, the data should be interpreted with caution, and administrators should use multiple sources of information to evaluate the quality of care in their hospitals

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Answer:

[tex]\large\boxed{ \sf Area = 25\ ft .^2}[/tex]

Step-by-step explanation:

We need to find out the area of the triangle which has a base of 12.5ft and s height of 4ft.

We know that the formula for calculating the area of the triangle is ,

[tex]\sf:\implies \pink{Area_{\triangle}=\dfrac{1}{2}\times (b)\times (h)}\\[/tex]

where,

F I G U R E : -

[tex] \setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){$\large\bf 4\ ft $}\put(2.8,.3){$\large\bf 12.5\ ft$}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\end{picture}[/tex]

Now on substituting the respective values, we have;

[tex]\sf:\implies Area = \dfrac{1}{2}\times (12.5) \times (4) \ ft.^2 \\[/tex]

Simplify,

[tex]\sf:\implies \underline{\underline{\boxed{\sf Area = \frak{25\ ft.^2} }}} \\[/tex]

Hence the area of the triangle is 25ft.²

The line of best fit for the given points is y = -1.35x + 9.62, where x is the independent variable and y is the dependent variable. This line represents the linear relationship between the two variables that best fits the given data.

To find the line of best fit for the given points, we can use linear regression. Using a calculator or statistical software, we obtain the following results:

Slope (m) = -1.35

Y-intercept (b) = 9.62

Therefore, the equation of the line of best fit is:

y = -1.35x + 9.62

Rounding to two decimal places, we get:

y = -1.35x + 9.62

The line of best fit for the given points is y = -1.35x + 9.62, which represents the linear relationship between the variables.

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a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is 0.095.

b. The probability that at most 23 of them live in cities with population greater than 100,000 people is 0.0332.

c. The probability that at least 22 of them live in cities with population greater than 100,000 people is 0.9876.

d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is 0.8782.

Let X be the number of Americans out of 34 who live in cities with population greater than 100,000 people.

Then X follows a binomial distribution with n = 34 and p = 0.6.

a. The probability that exactly 23 of them live in cities with population greater than 100,000 people is:

P(X = 23) = (34C₂₃) x (0.6)²³ x (0.4)¹¹ = 0.095

b. The probability that at most 23 of them live in cities with population greater than 100,000 people is:

P(X <= 23) = P(X = 0) + P(X = 1) + ... + P(X = 23)

= ∑(34Ci) x (0.6)^i x (0.4)^(34-i), i = 0 to 23

= 0.0332

c. The probability that at least 22 of them live in cities with population greater than 100,000 people is:

P(X >= 22) = 1 - P(X < 22) = 1 - P(X <= 21)

= 1 - ∑(34Ci) * (0.6)^i x (0.4)^(34-i), i = 0 to 21

= 0.9876

d. The probability that between 18 and 24 (including 18 and 24) of them live in cities with population greater than 100,000 people is:

P(18 <= X <= 24) = P(X <= 24) - P(X < 18)

= ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 24

- ∑(34 choose i) * (0.6)^i * (0.4)^(34-i), i = 0 to 17

= 0.8782

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7x ≤ 1, or x ≤ 1/7

(a) The probability that Thomas is selected for the position given that the company’s revenue did not improve is 4 out of 7.
(b) The probability that the company’s revenue will generally improve is the sum of the probabilities that Rachel, Sam and Thomas are hired multiplied by the probability that the company’s revenue will improve given that each individual is hired. This probability is given by (1/7)*(4/5) + (2/7)*(1/2) + (4/7)*(3/10) = 0.5.
(c) For the probabilities given for the second hiring process to be valid, the inequality x + 2x + 4x ≤ 1 must be satisfied. This inequality can be written as 7x ≤ 1, or x ≤ 1/7.

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The volume of the solid is the amount of space  value is k = 32.

What is volume in maths?.

Volume in mathematics refers to the quantity of space within a certain 3D object. A fish tank, for example, has measurements of 3 feet long by 1 foot wide and 2 feet high. If you increase the length, breadth, and height by 3x1x2, which is equal to six, you can calculate the volume.

The volume of the solid is represents in cubic units. Thus

     k = ∛v/4

    k³ = v/4

     v = 4k³    ( k≥0)

    when k = 1,  v = 4

  k = z,   v = 4.z³  = 32

 ∴ points (1,1) , (7,32) are on the graph.

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Tablespoons is an English unit for volume. This problem asks us to convert the given quantity into liters, a metric unit.  the correct order of conversions is explained below.

The correct order for the conversions to convert tablespoons to liters is as follows:

1 tablespoons -> 1/2 fluid ounce(fl oz)

1 fluid ounce->1/128 US gallon

1 US gallon -> 3.78541 liters

Therefore, to convert tablespoons to liters, we need to first convert tablespoons to fluid ounces, then fluid ounces to US gallons, and finally US gallons to liters. using these conversion factors, we can convert any given quantity in tablespoons to liters.

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Radius is the distance in a straight line from the centre of the circle to its circumference. The diameter is twice the radius. Therefore,  radius and diameter of the circle are 7 and 14 yards respectively.

The above figure is a circle. The area of the circle is given as 49π yard squared. The question want us to find the radius and diameter of the circle.

Hence,

area of a circle = πr²

where

Therefore,

area of the circle = 49π

Hence,

49π = π × r²

divide both sides by π

r² = 49

square root both sides

r = √49

r = 7 yards

The diameter of a circle is twice the radius.

Hence,

diameter of the circle = 7 × 2 = 14 yards

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The probability that x is at most 16 is 0.68, or 68%. This means that in this region, there is a 68% chance that the depth of the bioturbation layer in sediment is less than or equal to 16 centimeters.

To draw the density curve for x, we can use the formula for the uniform probability density function:

f(x) = 1 / (b - a), for a <= x <= b

where a = 7.5 and b = 20 are the minimum and maximum values of the interval, respectively

Therefore, the density curve for x is a horizontal line with height 1 / (20 - 7.5) = 0.08, between x = 7.5 and x = 20.

To find the probability that x is at most 16, we can calculate the area under the density curve from x = 7.5 to x = 16. This is equal to:

P(x <= 16) = ∫7.5^16 f(x) dx

= ∫7.5^16 0.08 dx (since f(x) is constant over this interval)

= 0.08(x) ∣7.5^16

= 0.08(16 - 7.5)

= 0.68

Therefore, the probability that x is at most 16 is 0.68, or 68%. This means that in this region, there is a 68% chance that the depth of the bioturbation layer in sediment is less than or equal to 16 centimeters.

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Manny's average speed in knots was approximately 11.9 knots. We simply used speed, distance and time formula.

To calculate the average speed in knots, we need to divide the distance sailed in nautical miles by the time taken in hours. So,

Average speed in knots = Distance / Time

Here, the distance is given as 500 nautical miles and the time is given as 42 hours.

Average speed in knots = 500 / 42

= 11.9 (rounded to one decimal place)

Therefore, Manny's average speed in knots was approximately 11.9 knots.

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The missing y value in the table can be found to be 19. 5.

To find the missing value, you need to find the relationship that x and y have with each other on the table.

We find that when 4 increases to 11, 2. 5 as y, increases to 9. 5. The difference in both is:

= 11 - 4                                                 = 9. 5  - 2.5

= 7                                                        = 7

We see this common difference again with 15 and 11 being 4 and the difference between the y - values of 13. 5 and 9. 5 being 4 as well.

The y value corresponding to 21 as x would be:

= ( 21 - 15 ) + 13. 5

= 19. 5

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Using the normal distribution, it is found that there is a 0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

[tex]Z=\frac{x-u}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s=\frac{\sigma}{\sqrt n}[/tex]

u=8.4, sigma=1.8 n=32 s=0.3182

The probability that their mean repair time is less than 8.9 hours is the p-value of Z when X = 8.9, hence:

Z=1.57

Z = 1.57 has a p-value of 0.9418.

1 - 0.9418 = 0.0582.

0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.

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:tan θ = sin θ / cos θ = (1/3) / [(2/3)√2] = √2 / 2cot θ = cos θ / sin θ = [(2/3)√2] / (1/3) = 2√2sec θ = 1 / cos θ = √3 / (2√2) = √6 / 4cosec θ = 1 / sin θ = 3cos θ = (2/3)√2tan θ = √2 / 2cot θ = 2√2sec θ = √6 / 4cosec θ = 3

Answer:Given, csc θ = 3 and θ lies in [0, π/2]We need to find the values of the remaining 5 trigonometric functions.Here is how we can find them:We know that csc θ = 3. csc θ = 1/sin θ. Hence, we can say sin θ = 1/csc θ = 1/3.In the first quadrant, sin θ is positive (All are positive except tan θ and cot θ). Hence, sin θ = 1/3, and cos θ = √(1 - sin²θ) = √(1 - 1/9) = √8/3 = (2/3)√2.The remaining trigonometric functions are:tan θ = sin θ / cos θ = (1/3) / [(2/3)√2] = √2 / 2cot θ = cos θ / sin θ = [(2/3)√2] / (1/3) = 2√2sec θ = 1 / cos θ = √3 / (2√2) = √6 / 4cosec θ = 1 / sin θ = 3cos θ = (2/3)√2tan θ = √2 / 2cot θ = 2√2sec θ = √6 / 4cosec θ = 3

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When p is the incenter of angle JKL, then by using the property of incenter, measures of the sides and the angles will be, JK = 21.2 units and KL = 26.63 units and JL = 28.33 units and M∠K = 36°

By the property of incenter, we know that PM = PN = PO = 7 units,

∠MJP = ∠OJP = 32° and ∠NLP = ∠OLP = 22°

By the triangle sum theorem, we can say that:

M∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

M∠NKP = 36°

From ΔJMP,

Tan(32°) = MP/MJ and Tan(32°) = 7/MJ

MJ = 7/tan(32°) and MJ = 11.20

From ΔPOL,

Tan(22°) = OP/OL and Tan(22°) = 7/OL and OL = 17.33

From ΔKNP,

Tan(36°) = NP/KN and Tan(36°) = 7/KN and KN = 9.63

Therefore, JK = MJ + MK = 21.2 units

KL = LN + KN = 26.63 units and JL = JO + OL = 28.33 units

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Part (a)

The error is that the 0.15 should be 0.85 because 1-0.15 = 0.85

If the laptop loses 15% of its value, then it keeps the remaining 85%.

Therefore, the formula should be [tex]a_n = 1500(0.85)^{n-1}[/tex]

I'm assuming the "$1,5000" should have been "$1,500".

===========================================

Part (b)

Plug n = 4 into the formula.

[tex]a_n = 1500(0.85)^{n-1}\\\\a_4 = 1500(0.85)^{4-1}\\\\a_4 = 1500(0.85)^{3}\\\\a_4 = 1500(0.614125)\\\\a_4 = 921.1875\\\\a_4 \approx 921.19\\\\[/tex]

The laptop's value is approximately $921.19 at the beginning of the 4th year.