HELP! BRAINLIST! THIS IS DUE IT IS END OF UNIT ASSESSMENT

Answer:

22(15)(12) + (1/2)(22)(10)(15) = 5,610 cm^2

The integral of f(x) can be found by using the substitution u = cos(x), du = -sin(x) dx. Thus, we have:

∫ (6 sin(2x) / cos(2x)) dx = -3 ∫ (2 sin(2x) / cos²(2x)) (-2cos(x)) dx

= 6 ∫ (sin(u) / u²) du

This integral can be evaluated using integration by parts, with u = sin(u) and dv = u⁻² du, giving:

6 ∫ (sin(u) / u²) du = -6 sin(u) / u + 6 ∫ (cos(u) / u) du

Substituting back u = cos(x), we have:

6 ∫ (sin(x) / cos²(x)) dx = -6 tan(x) + 6 ln |cos(x)| + C

Since tan(x) = sin(x) / cos(x) and cos²(x) = 1 - sin²(x), we have:

f(x) = 6 sin(x) / cos²(x) = 6 sin(x) / (1 - sin²(x)) = -6/(sin(x) - 1/sin(x))

Therefore, the general form of the primitive of f(x) is:

F(x) = -6 ln |sin(x) - 1/sin(x)| + C

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We know that the length of TU to the nearest tenth is 6.9 in

The figure is tangent to the circle at point U. Using the information given in the figure, we can conclude that segment ST is tangent to the circle at point T.

To find the length of TU, we can use the formula for the length of a tangent segment from a point outside the circle:

TU^2 = TS x TR

We know that TS = ST = 4 in. To find TR, we can use the Pythagorean theorem:

TR^2 = RS^2 - TS^2
TR^2 = 8^2 - 4^2
TR^2 = 48
TR = sqrt(48)

Now we can substitute the values we have found into the first formula:

TU^2 = 4 x sqrt(48)
TU = sqrt(4 x sqrt(48))
TU ≈ 6.9 in.

Therefore, the length of TU to the nearest tenth is 6.9 in.

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Therefore, the expression 250 * [tex]2^h[/tex] gives the number of bacteria in the colony after h hours, assuming that the initial number of bacteria is 250.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. Expressions can also include parentheses, brackets, and other symbols to clarify the order of operations. Expressions can be evaluated to obtain a numerical result or can be simplified using mathematical rules and properties to make them easier to work with. In algebra, expressions are often used to represent relationships between variables and to solve equations and inequalities.

Here,

In the given expression 250*[tex]2^h[/tex], the constant 250 represents the initial number of bacteria in the colony.

Since the number of bacteria doubles every hour, if we start with 250 bacteria at the beginning, after one hour we will have 250 * 2 = 500 bacteria. After two hours, we will have 500 * 2 = 1000 bacteria, and so on.

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Jasmine walks from the school to the post office, which is a distance of $2 - (-4) = 6$ blocks horizontally and 0 blocks vertically, so the distance is 6 blocks. Then she walks from the post office to the library, which is a distance of $2 - 2 = 0$ blocks horizontally and $-4 - 1 = -5$ blocks vertically, so the distance is 5 blocks.

The total distance of Jasmine's walk is the sum of the distances of each leg of her journey, which is $6 + 5 = 11$ blocks. Therefore, Jasmine walks 11 blocks in total.

If you have access to the information on the back of Ken's bank statement, you can calculate his revised statement balance by adding any credits and subtracting any debits from the previous statement balance.

Reconciling a bank account involves comparing the transactions in your own financial records with those listed on your bank statement. The goal is to ensure that the account balance in your financial records matches the balance reported by the bank.

To reconcile a bank account, you typically start with the ending balance on the previous bank statement, which becomes the beginning balance on the current statement. You then compare this balance with the transactions listed on the current statement, adding any credits (such as deposits or interest payments) and subtracting any debits (such as withdrawals or fees).

The resulting balance should match the ending balance listed on the current bank statement. If it does not match, then there may be errors or discrepancies in the account that need to be investigated. This can involve reviewing bank records, receipts, and other financial documents to identify any errors or missing transactions.

Reconciling your bank account on a regular basis is important for ensuring the accuracy of your financial records and identifying any issues or errors in a timely manner. It can also help you identify areas where you may be overspending or where you can save money by reducing fees or optimizing your financial habits.

Whether or not Ken's account reconciles depends on whether the calculated revised statement balance matches the bank's reported statement balance. If they match, then the account is reconciled. If they do not match, then there may be discrepancies in the account that need to be investigated and resolved.

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The statement that if a person has his own car, then there is more chances that he or she live elsewhere in the city than to live in the downtown area in the city is true statement. So, the option(a) is right answer for problem.

We have, a sample of sample size, n

= 200

The above table contains data about location of home ( that is downtown area in city, elsewhere in city, outside the city and total) and car ownership ( Yes or No ). Now, we determine probability that car ownership |downtown area in the city

= 10/70

= 1/7

probability that car ownership | elsewhere in the city = 15/70

= 3/14

Probability that car ownership | outside in the city = 35/60 = 7/12

As we see, 1/7 < 3/14 < 7/12

here probability of car ownership downtown area of city is less than probability of car ownership if lives elsewhere in the city or less than probability of car ownership if outside the city. So, statement (a) is true in this case. Also consider,

Probability that no car ownership | downtown area in the city = 60/70 = 6/7

Probability that no car ownership | elsewhere in the city = 55/70 = 11/14

Probability that no car ownership|outside the city = 25/60 = 5/12

As we see probabilities, 5/12 < 11/14 < 6/7

Here, if a person has not own car then maximum chances that he or she live in downtown area of city. So, statement (b) is false.

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Complete question:

The above figure complete the question. A local company is interested in supporting environmentally friendly initiatives such as carpooling among employees. The company surveyed all of the 200 employees at the downtown offices. Employees responded as to whether or not they own a car and to the location of the home where they live. The results are shown in the table above. Which of the following statements about a randomly chosen person from these 200 employees is true? responses

a) if the person owns a car, he or she is more likely to live elsewhere in the city than to live in the downtown area in the city.

b) if the person does not own a car, he or she is more likely to live outside the city than to live in the city (downtown area or elsewhere).

c) the person is more likely to own a car if he or she lives in the city (downtown area or elsewhere) than if he or she lives outside the city.

d) the person is more likely to live in the downtown area in the city than elsewhere in the city.

e) the person is more likely to own a car than not to own a car.

Answer: $532,000

Step-by-step explanation:

If the company is making $140,000 and they get 20% each year, we just multiply it by 20%, or 0.20, and get $28,000. So, we would multiply that by 14, the years the company operated, and then add it to the original $140,000.

28,000 x 14 = 392,000

392,000 + 140,000 = 532,000

So, over the course of 14 years, the company made a profit of $532,000.

To solve a Pythagorean triangle of 7 squared + 2 squared, you need to use the Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the unknown side, which we'll call x. So, we have:

7² + 2² = x²

Simplifying this equation, we get:

49 + 4 = x²

53 = x²

To find the value of x, we need to take the square root of both sides:

√53 = x

So the answer to the problem is √53. When you square root it, you get a decimal approximation of approximately 7.28.

In summary, to solve a Pythagorean triangle, you need to use the Pythagorean theorem and find the square root of the sum of the squares of the other two sides to find the length of the unknown side.

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The pickup truck wheel travels 37.7 inches farther in one revolution than the compact car wheel.

The distance traveled by a wheel in one revolution is directly proportional to the diameter of the wheel.

Since the diameter of the compact car wheel is 33 inches, its circumference (the distance traveled in one revolution) is 103.67 inches (C = πd). On the other hand, the radius of the pickup truck wheel is 19 inches, making its diameter 38 inches and its circumference 119.38 inches.

Therefore, the pickup truck wheel travels 15.71 inches more in one revolution than the compact car wheel (119.38 - 103.67 = 15.71). However, the question asks for the distance in inches farther, which means we need to subtract the circumference of the compact car wheel from that of the pickup truck wheel.

Hence, the answer is 37.7 inches (2 × 15.71 + 2 × 103.67 = 241.76 - 204.06 = 37.7).

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The number of cans that can be packed in a certain carton has correct statement as, Statements (1) and (2) together are not sufficient, option E.

Data sufficiency refers to evaluating and analysing a collection of data to see if it is sufficient to respond to a certain query. They are intended to assess the candidate's capacity to connect the dots between each question and arrive at a conclusion.

The size of each can is not revealed in statement 1 at all.

The size of the container is not disclosed in statement 2 at all.

We obtain two situations when we take into account both assertions. Case A: If the box is 1 x 1 x 2304 (inches) in size, then there are no cans that will fit within the carton.

Case B: If the box is 10 x 10 x 23.04 (inches) in size, then the carton can hold more than 0 cans.

The combined statements are insufficient because we lack clarity in our ability to respond to the target inquiry.

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Complete question:

What is the number of cans that can be packed in a certain carton?

(1) The interior volume of this carton is 2, 304 cubic inches.

(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

C. Both statements together are sufficient, but neither statement alone is sufficient.

D. Each statement alone is sufficient.

E. Statements (1) and (2) together are not sufficient.

The calculated value of the actual area of the playground is 5625π

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

A scale drawing of a playground had a scale of 15

This means that

Scale factor = 15/1

Evaluate

Scale factor = 15

The actual area of the park in meters squared is calculated as

Area = Area of scale * Scale factor²

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

Area = Area of scale * 15²

Using the area of circle, we have

Area = π5² * 15²

Evaluate

Area = 5625π

Hence, the actual area is 5625π

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Answer:

Answer: C) 19

We can solve this problem using the following chain of thought reasoning:

Step 1: We know that the ratio of Big Dogs to Small Dogs is 5 to 4. Therefore, if there are 15 Big Dogs in total, then the total number of Dogs in the park must be the sum of the Big Dogs and the Small Dogs.

Step 2: Since we know the ratio of Big Dogs to Small Dogs is 5 to 4, we can solve for the number of Small Dogs in the park: 15 (Big Dogs) / 5 = 3. Therefore, the total number of Dogs in the park is 15 + 3 = 18.

Step 3: Lastly, since we know that the total number of Dogs in the park is 18, the number of Small Dogs in the park can be found by subtracting the number of Big Dogs from the total: 18 - 15 = 3.

Therefore, the answer is C) 19 Small Dogs at the Dog Park.

Answer:

option B

Step-by-step explanation:

big : small

5 : 4

5 units= 15

1 unit= 15÷5

= 3

4 units= 3×4

= 12

there are 12 small dogs at the dog park

part a.

the percentage of eggs between 42 and 45mm is 48.48%

part b.

The median width is approximately (42+45)/2 = 43.5mm.

The median length is approximately (56+59)/2 = 57.5mm.

part c.

The width of grade A chicken eggs has a range of about 24mm.

part d.

I think its impossible to determine because we don't have the value for the standard deviation.

The second option should be correct.

A histogram is described as an approximate representation of the distribution of numerical data.

part a.

From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have  a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.

part b.

we have an  estimation  that the median of the width is 48mm and the median of the length is around 60mm.

part c.

Also from the histogram, we notice  that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.

In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.

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The inequality to describe the number of subscriptions Andre must sell to reach his goal is  3s + 25 ≥ C.

What are inequalities ?

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

here , we have,

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Assuming the cost of soccer cleats to be 'C' and the number of subscriptions to be 's'.

∴ The inequality that represents this situation is 3s + 25 ≥ C to real his goal.

Hence, The inequality to describe the number of subscriptions Andre must sell to reach his goal is  3s + 25 ≥ C.

The value of measure of angle WPN is,

⇒ m ∠WPN = 108°

We have to given that;

Parallel lines EN, BH, and RK, with transversal PW are shown.

And, m ∠ BMV = 108° and m ∠KVS = 72°

Now, We get by definition of vertically opposite angle;

m ∠ BMV = m ∠PWN = 108°

Hence, By definition of alternate angle we get;

⇒ m ∠PWN = m ∠WPN = 108°

Thus, The value of measure of angle WPN is,

⇒ m ∠WPN = 108°

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There are 15,660 different ways a committee consisting of 2 teachers and 2 students can be formed from 9 teachers and 30 students.

To find out how many different committees can be formed from 9 teachers and 30 students, if the committee consists of 2 teachers and 2 students, we will use the combination formula. The combination formula is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected.

First, let's find the number of ways to select 2 teachers from 9:
C(9, 2) = 9! / (2!(9-2)!) = 9! / (2! * 7!) = 36

Next, let's find the number of ways to select 2 students from 30:
C(30, 2) = 30! / (2!(30-2)!) = 30! / (2! * 28!) = 435

Now, to find the total number of ways the committee of 4 members can be selected, we simply multiply the number of ways to select teachers and students:
Total ways = 36 (ways to select teachers) * 435 (ways to select students) = 15,660

So, there are 15,660 different ways a committee consisting of 2 teachers and 2 students can be formed from 9 teachers and 30 students.

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Step-by-step explanation:

(10 x 6)/2 = 30 + 47 = 77

Answer:

C)4.192

Step-by-step explanation:

What is 524/125 written as a decimal?

We Take

524 divided by 125 = 4.192

So, the answer is C)4.192

To determine the exact distance and bearing of the island from Miami, we can use basic trigonometry and vector addition.

First, we need to break down the flight path into its components. The initial bearing of E 20 S can be broken down into an eastward component of 600 mph [tex]cos(20°) = 562.57[/tex] mph and a southward component of 600 mph [tex]sin(20°) = 208.38[/tex] mph.

After flying for 4 hours, the plane has traveled a distance of 600 mph × 4 = 2400 miles, with a displacement of 562.57 mph × 4 = 2250.28 miles eastward and 208.38 mph × 4 = 833.52 miles southward.

When the pilot adjusts the bearing to S 5'E, the plane travels 600 mph × 2 = 1200 miles with a displacement of 600 mph cos(5°) × 2 =996.18 miles eastward and 600 mph sin(5°) × 2 = 104.57 miles southward.

Finally, when the pilot adjusts the bearing to E 5°S, the plane travels 600 mph × 1 = 600 miles with a displacement of 600 mph cos(5°) = 598.31 miles eastward and 600 mph sin(5°) = 52.42 miles southward.

To find the total displacement from Miami to the island, we can add up the eastward and southward components:

Total eastward displacement = 2250.28 + 996.18 + 598.31 = 3844.77 miles

Total southward displacement = 833.52 + 104.57 + 52.42 = 990.51 miles

Using the Pythagorean theorem, we can find the total distance from Miami to the island:

[tex]Distance = sqrt((3844.77)^2 + (990.51)^2) =3985.21 miles[/tex]

To find the bearing from Miami to the island, we can use inverse trigonometry:

[tex]Bearing = tan^{-1} (\frac{990.51}{3844.77}) = 14.76°[/tex]

Therefore, you should tell the rescue authorities in Miami that you are approximately 3985.21 miles away from Miami and the bearing to the island is approximately N 75°E.

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The possible values of Y are 0, 1, 2, 3, and 4.

The number of female children in a family with four children can be any value between 0 and 4, inclusive.

To see why, we can consider all the possible outcomes of the family having four children, assuming that the probability of having a boy or a girl is 0.5 (assuming a binomial distribution).

There are 2 possibilities for the first child (boy or girl), 2 possibilities for the second child, 2 possibilities for the third child, and 2 possibilities for the fourth child, making a total of 2x2x2x2 = 16 possible outcomes.

Out of these 16 outcomes, we can count the number of outcomes that correspond to each possible value of Y:

If Y = 0, then all four children must be boys, which is 1 outcome.

If Y = 1, then there are 4 ways to have one girl (first, second, third, or fourth child).

If Y = 2, then there are 6 ways to have two girls (first two, first three, first four, second three, second four, or third fourth child).

If Y = 3, then there are 4 ways to have three girls (first three, first four, second four, or third four child).

If Y = 4, then all four children must be girls, which is 1 outcome.

Therefore, the possible values of Y are 0, 1, 2, 3, and 4.

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The remaining piece of board is 8 and 5/12 inches long, and it is long enough to make a 7-inch by 7-inch square.

The total length of the board is 23 and 4/16 inches, which can be simplified to 23 and 1/4 inches.

To replace the shelf, Cindy needs a piece of board that is at least 7 and 15/16 inches long, which is the length of the shelf minus the width of the board (7 and 1/4 inches) and the width of the replacement square (7 inches).

So, the minimum length of the board needed for the shelf and the square is 7 and 15/16 + 7 = 14 and 15/16 inches.

Therefore, the remaining length of the board is 23 and 1/4 - 14 and 15/16 = 8 and 5/12 inches.

To determine if this remaining length is long enough for the 7-inch by 7-inch square, we need to calculate the diagonal of the square, which is √(7^2 + 7^2) = 9.899 inches (rounded to three decimal places).

Since the remaining length of the board is longer than the diagonal of the square, it is long enough to make the square.

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The range of the data set is 19 hours. None of the options are correct.

The given data set represents the number of hours Raymond spent practicing the piano each week for several weeks: 24, 8, 6, and 5 hours. To calculate the range, follow these steps:

1. Identify the highest and lowest values in the data set.
  - The highest value is 24 hours.
  - The lowest value is 5 hours.

2. Subtract the lowest value from the highest value to find the range.
  - Range = Highest value - Lowest value
  - Range = 24 hours - 5 hours
  - Range = 19 hours

This means that there is a 19-hour difference between the maximum and minimum number of hours Raymond spent practicing the piano each week. None of the options (a. 8 hours, b. 2 hours, c. 5 hours, and 6 hours) provided matches the correct answer, which is 19 hours.

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Using the change of variables u = x and v = x + y, we transform the given region R into a rectangle S, and evaluate the integral as 9 (e^6 - 2e^4 + e^2 - 1).

We need to find a change of variables that maps the region R onto a rectangle in the uv-plane. Let's make the following substitutions

u = x

v = x + y

Then, the region R is transformed into the rectangle S defined by 0 ≤ u ≤ 1 and 0 ≤ v ≤ 2.

To find the limits of integration in the new variables, we can solve the equations 2[x] + 2y = 2 for x and y in terms of u and v

2[x] + 2y = 2

2u + 2v - 2[x] = 2

[x] = u + v - 1

Since [x] is the greatest integer less than or equal to x, we have

u + v - 1 ≤ x < u + v

Also, since 0 ≤ y ≤ 1, we have

0 ≤ x + y - u ≤ 1

u ≤ x + y < u + 1

u - x ≤ y < 1 + u - x

Now we can evaluate the integral using the new variables

∫∫R 9e^(2x+2y) dA = ∫∫S 9e^(2u+2v) |J| dudv

where J is the Jacobian of the transformation, given by

|J| = det [[∂x/∂u, ∂x/∂v], [∂y/∂u, ∂y/∂v]]

= det [[1, 1], [-1, 1]]

= 2

Therefore, the integral becomes

∫∫S 9e^(2u+2v) |J| dudv = 2 ∫0^1 ∫0^2 9e^(2u+2v) dudv

= 2 ∫0^1 [9e^(2u+2v)/2]_0^2 dv

= 2 ∫0^1 (9/2)(e^(4+2v) - e^(2v)) dv

= 2 (9/2) [(e^6 - e^2)/2 - (e^4 - 1)/2]

= 9 (e^6 - 2e^4 + e^2 - 1)

Therefore, the value of the integral is 9 (e^6 - 2e^4 + e^2 - 1).

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To evaluate the indefinite integral ∫x tan^2 x dx, we can use integration by parts.

Let u = x and dv = tan^2 x dx. Then, du/dx = 1 and v = ∫tan^2 x dx = tan x - x.

Using the formula for integration by parts, we have:

∫x tan^2 x dx = uv - ∫v du/dx dx
= x(tan x - x) - ∫(tan x - x) dx
= x(tan x - x) + ln|cos x| + C

Therefore, the indefinite integral of x tan^2 x dx is x(tan x - x) + ln|cos x| + C, where C is the constant of integration.
To evaluate the indefinite integral ∫x tan^2(x) dx, we can use integration by parts, which is defined as ∫udv = uv - ∫vdu.

First, let's choose our u and dv:
u = x, so du = dx
dv = tan^2(x) dx

To find v, we need to integrate dv. Since tan^2(x) = sec^2(x) - 1, we get:
v = ∫(sec^2(x) - 1) dx = tan(x) - x

Now, using integration by parts:
∫x tan^2(x) dx = x(tan(x) - x) - ∫(tan(x) - x) dx

Let's evaluate the remaining integral:
∫(tan(x) - x) dx = ∫tan(x) dx - ∫x dx
= ln|sec(x)| - (1/2)x^2 + C

So, the final answer is:
∫x tan^2(x) dx = x(tan(x) - x) - [ln|sec(x)| - (1/2)x^2] + C

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The runner's average speed is approximately 11.63 mph, which is slightly faster than 11 mph. So, the runner doesn't maintain exactly 11 mph throughout the entire race, but they are close.

If a runner completes a 6.2 mile race in 32 minutes, we can calculate their average speed by dividing the total distance by the total time.

6.2 miles ÷ 32 minutes = 0.194 miles per minute

To convert this to miles per hour, we need to multiply by 60 (the number of minutes in an hour):

0.194 miles per minute x 60 minutes = 11.63 miles per hour

So the runner must be running at an average speed of 11.64 miles per hour throughout the entire race in order to complete it in 32 minutes. This is an impressive pace and shows that the runner is very fit and capable of sustaining a fast speed for a relatively long distance.

A runner completes a 6.2-mile race in 32 minutes, and we are to determine if they maintain an 11 mph pace throughout the race. To do this, we need to convert the race time to hours and then divide the race distance by the time.

First, convert 32 minutes to hours:
32 minutes / 60 minutes/hour = 0.5333 hours

Next, calculate the average speed:
6.2 miles / 0.5333 hours ≈ 11.63 mph

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a. The actual area of the kitchen is 128 square feet.

b.  the couch measures 1.25 inches across in the scale drawing.

The scale is 1/4 inch = 2 feet,

meaning that in the drawing, each inch represents 8 feet (since 2 feet/0.25 inches = 8 feet/inch).

The kitchen in the drawing has an area of 2 square inches.

we apply  the scale factor to find the actual area in square feet,

1 inch in the drawing = 8 feet in real life

So, 2 square inches in the drawing = 2 x 8 x 8 = 128 square feet in real life.

Hence,  the actual area of the kitchen is 128 square feet.

we also apply  the scale factor to  find the couch measurement in the scale drawing,

1 inch in the drawing = 8 feet in real life

10 feet in real life = 10/8 = 1.25 inches in the drawing.

In conclusion,  the couch measures 1.25 inches across in the scale drawing.

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The population growth rate for 2019 would be 800 people.

The population size at the start of 2020 would be 149, 800 people.

The formula is:

Growth rate = rmax × Population × ( 1 - ( Population / Carrying Capacity ) )

Growth rate = 0.8 × 149,000 × ( 1 - ( 149, 000 / 150, 000) )

Growth rate = 0.8 × 149, 000 × 0. 0067

Growth rate = 800 people

The population size at the start of 2020 would therefore be:

=  Initial Population + Growth Rate

= 149, 000 + 800

= 149, 800 people

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To find the average temperature of the coffee during the first half hour, we need to find the temperature of the coffee at t = 0 (when the coffee is just brewed) and at t = 30 (after half an hour has passed).

At t = 0, T(0) = 20 + 75e^0/50 = 20 + 75 = 95 C. At t = 30, T(30) = 20 + 75e^-30/50 ≈ 42.5 C.

So, the temperature of the coffee decreases from 95 C to 42.5 C during the first half hour.

The average temperature during this time period can be found by taking the average of the initial and final temperatures:

Average temperature = (95 C + 42.5 C) / 2 = 68.75 C.

Therefore, the average temperature of the coffee during the first half hour is 68.75 C.

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For -10 as the value of k the equation k – 3(k + 5) – 0. 5 = 3(0. 25k + 4) is true.

Given equation is k – 3(k + 5) – 0. 5 = 3(0. 25k + 4)

To solve the equation, firstly we have to solve or open the brackets using the distributive property that is a(x + y) = ax +ay

Thus the equation becomes, k - 3k - 15 - 0.5 = 0.75k + 12

Then we have to take all the terms with k on one side and other on the other or segregate the like terms, the equation now is

k - 3k - 0.75k = 12 + 15 + 0.5

Simplify the equation by adding or subtracting the like terms.

-2.75k = 27.5

Then we divide the coefficient of k by the other side and get our answer

k = 27.5 ÷ (-2.75)

k = -10

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