integrate the following:
\( \displaystyle \int \: \tan(x) \cos(x) \: dx\)

​

The opportunity cost of knitting one more scarf can be determined by calculating the additional number of hats that could have been produced instead.The resulting number represents the foregone opportunity.

To calculate the opportunity cost of knitting one more scarf in terms of hats, we need to determine the number of hats that could have been produced instead. The concept of opportunity cost implies that by choosing to allocate resources to one activity, we forgo the potential benefits of an alternative activity.

Let's assume that the knitter's production plan allocates a certain number of resources to knitting scarves and hats. If the plan originally included a specific number of scarves and hats, we can calculate the opportunity cost by comparing the resulting production levels.

For example, if the knitter's plan initially included 10 scarves and 15 hats, and by knitting one more scarf, the production becomes 11 scarves and 15 hats, the opportunity cost of knitting that additional scarf would be 0.067, rounded to two decimal places. This means that by choosing to knit one more scarf, the knitter gives up the opportunity to produce approximately 0.067 hats.

It's important to note that the specific production plan and resource allocation will determine the exact opportunity cost in terms of hats. By considering the foregone alternative and calculating the difference in production levels, we can determine the opportunity cost of knitting one more scarf.

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Answer:

68x + 36y

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define expression

(19x + 4y) + (49x + 32y)

Step 2: Simplify expression

The company needs to sell 1.5 units of merchandise to make the maximum profit that implies 300.

What is profit ?

Profit is the financial gain that a business or an individual derives from a transaction or business activity, after deducting all costs and expenses. It is the difference between the amount earned and the amount spent to produce, sell, or provide goods or services. Profit is an important measure of business success and is used to evaluate the performance of a company, as well as to attract investors and secure financing.


According to the question:
To find the number of units of merchandise the company needs to sell to make the maximum profit, we need to locate the vertex of the parabola. Since the parabola opens downward, the vertex represents the maximum point on the graph.

From the graph, we can see that the vertex is located at (1.5, 7.5). This means that the company will make the maximum profit by selling 1.5 units of merchandise.

Therefore, the company needs to sell 1.5 units of merchandise to make the maximum profit.

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Answer:

Step-by-step explanation:

The numbers are either side from 1/10

To the left:

To the right:

Answer:

Just for fun, the probability of rolling a die 60 times and getting no ones is

(600)(5/6)60=0.0018% .

Step-by-step explanation:

This 10 ones is the value with the highest probability of occurring. It has a probability of  (6010)(1/6)10∗(5/6)50≈13.7% .

Answer:

the answer is 60 not 42 goodluck

Answer:

60

Step-by-step explanation:

i got it right on my test hope this helps sorry if it didn't

In a tesselation of the plane with congruent equilateral triangles, each vertex is shared by six triangles.

This can be visualized by imagining a single equilateral triangle as the center, surrounded by six other equilateral triangles that share a common vertex with the central triangle. Therefore, in this type of tesselation, each vertex is surrounded by six neighboring triangles.

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Answer:

-2

Step-by-step explanation:

15-8+-9

bodmas

15-8=7

7-9

=-2

The slope intercept form of equation of line is given by

y = 3x + 4

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If \(\theta\)  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  \(tan \theta\)

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

The given line is y = 3x - 8

Slope = 3

Slope of the line parallel to this line = 3

The line passes through the point (-2, -2)

Required equation of line

y - (-2) = 3(x - (-2))

y+2 = 3(x +2)

y+2 = 3x + 6

y = 3x + 6 - 2

y = 3x + 4

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The inequality represented in the graph attached is y ≥ (1/2)x + 3 and 3x - y > 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

The inequality represented in the graph attached is y ≥ (1/2)x + 3 and 3x - y > 2

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Answer:

14.88 + 12.19 = 27.07

Step-by-step explanation:

To me is looks like a visual glitch. I would do 14.88 + 12.19.

Answer:

14.88 + 12.19.

Step-by-step explanation:

Answer: (x - 1)(x + 1)^2(x - 4)^3

Step-by-step explanation:

First, remember that:

in expressions like: (x - b)^n

b is the value of x where the graph intersects the x-axis.

n can represent:

n = 1, the line just goes through the x-axis

n = 2, the line may change the direction (an inflection point), and touch the x-axis in one point.

n = 3, the line may have two inflection points when it intersects the x-axis.

Then we have the expression:

(x-b)(x-c)^2(x-d)^3

b is in the linear part, the graph crosses the x-axis linearly in x = 1.

c is in the quadratic part, the graph crosses the x-axis with one point of inflection at x = -1.

d is in the cubic part, the graph crosses the x-axis with two inflections in x = 4.

Then we can writhe the polynomial as:

f(x) = (x-1)(x-(-1))^2(x-4)^3 = (x - 1)(x + 1)^2(x - 4)^3

Answer:

(x - 1)(x + 1)^2(x - 4)^3

Answer:

1 minute = 1/6

2 minutes = 1/3

3 minutes =1/2

Step-by-step explanation:

one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag

the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag

to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3

The town of Newton is mapped on a coordinate grid with the origin being at City Hall . The cafe is located at the point (-3, 9) and the bookstore is located at (3, 1).  How far is it from the café to the bookstore?

Answer :10

4 balls in each group.

Step-by-step explanation:

you just divide 20 by 5, or add 5 times until you get 20.

Answer:

5 group of 4 balls

Step-by-step explanation:

Red balls : 20

5 Gym baskets

20 - 5      15

15 divided by 5    3

3 divided by 20     0.15

0.15 divided by 5     0.03

0.03 x 15   0.45

0.45 x 55 24.75

24.75 - 4.75    20

20 divided by 5   4

Answer is 4

BRAINLIEST PLS

Reason:

Direct proportion equations are straight lines that go through the origin.

Choices A through C are straight lines, but they don't go through the origin. Luckily, choice D fits both criteria mentioned above.

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}\)

Same reason as him.

Answer:

You will get paid $220.88

Step-by-step explanation:

Answer: 220.875

Step-by-step explanation:

Just multiply those two numbers

Answer:

there will only be one 3

Step-by-step explanation:

see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .

Answer:

-0.301

Step-by-step explanation:

Correct Question :-

If log 2 = 0.301 , find log 0.5

Solution :-

We are here given that the value of log 5 is 0.699 . Here the base of log is 10 .

\(\rm\implies log_{10}2= 0.301 \)

And we are supposed to find out the value of log 0.5 . We can write it as ,

\(\rm\implies log_{10}(0.5) = log _{10}\bigg( \dfrac{5}{10}\bigg)\)

Simplify ,

\(\rm\implies log _{10}\bigg( \dfrac{1}{2}\bigg)\)

This can be written as ,

\(\rm\implies log_{10} ( 2^{-1})\)

Use property of log ,

\(\rm\implies -1 \times log_{10}2 \)

Put the value of log 2 ,

\(\rm\implies -1 \times 0.301 =\boxed{\blue{-0.301}} \)

Hence the value of log (0.5) is -0.301 .

*Note -

Here here there was no use of log 5 in the calculation .

The correct statement is B. For all b, the equation Ax=b has a solution.

Since the columns of A are linearly independent, then the matrix A has full rank, and its column space is equal to the entire vector space in which it resides. This means that for any given vector b, we can find a linear combination of the columns of A that is equal to b, and therefore the equation Ax=b has a solution for all b.

Option A is incorrect, as there may be certain b vectors for which Ax=b has a solution.

Option C is incorrect, as the equation Ax=b may have a solution even when A has fewer columns than rows.

Option D is incorrect, as we can determine whether or not the equation Ax=b has a solution for all b by checking the rank of A.

Option E is incorrect, as the equation Ax=b may have a solution even when A has more columns than rows.

Option F is incorrect, as a square matrix may or may not have linearly independent columns, and therefore may or may not have a solution for all b.

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Answer:

390625

Step-by-step explanation:

Five multiplied by 5 8 times is rlly just 5^8

Answer:390,624

Step-by-step explanation:

5x5x5x5x5x5x5x5

The perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.

The perimeter of any object is the total sum length of its boundary.

The perimeter of a rectangle with length l units and width w units is given as:

Perimeter = 2(l + w) units.

In the question, we are given that the length of a rectangle is 5 3/5 inches and its width is half of its length. We are asked to find the perimeter of the rectangle.

The length of the given rectangle (l) = 5 3/5 inches = 28/5 inches.

The width of the given rectangle (w) = Half of length = 1/2 * 28/5 inches = 14/5 inches.

Thus, the perimeter of the rectangle = 2(l + b) = 2(28/5 + 14/5) inches,

or, the perimeter = 2(42/5) inches,

or, the perimeter = 84/5 inches,

or, the perimeter = 16.8 inches.

Thus, the perimeter of the rectangle that has a length of 5 3/5 inches, and the width as half of its length is 16.8 inches. Hence, option A is the right choice.

The given question is incorrect. The correct question is:

"The length of a rectangle is 5 3/5 inches. the width of the rectangle is half of its length. what is the perimeter of the rectangle?

(a) 16.8 inches

(b) 8.4 inches

(c) 2.8 inches

(d) 15.68"

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Answer:

∠6 = 78°.

Step-by-step explanation:

∠3 = 78°

∠2 and ∠3 are vertical angles, => ∠2 = ∠3 = 78°.

∠2 and ∠6 are corresponding angles, => ∠6 = 78°.

Answer:

\(\displaystyle 78° = m\angle{6}\)

Explanation:

As you can see, angles \(\displaystyle 6\:and\:3\)are alternate interiour angles, and accourding to the Alternate Interiour Angles Theorem, these angles are considered congruent, therefore seventy-eight degrees is also the measure of the sixth angle.

I am joyous to assist you at any time.

After solving the given  logarithmic expression we get

1. \(log_5 k + log_5 2 = log_5 (k\times2)\)

2. \(2 log_5 k = log_5 k^2\)

3. \(log_5 k - log_5 7 = log_5 (k/7)\)

4. \(log_3 k/log_3 5 = log_5 k/log_5 3\)

5. \(log_5 k + log_25 k = log_5 k^3\)

6.  \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 (k/5)\)

The power to which a number must be increased in order to obtain another number is known as a logarithm.

Following are the Four Basic Properties of Logs by using which we can solve the given expressions.

\(log_b(xy) = log_bx + log_by\\log_b(x/y) = log_bx - log_by\\log_b(xn) = n log_bx\\log_bx = log_ax / log_ab\)

Using logarithmic properties, we can rewrite each expression as follows:

1. \(log_5 k + log_5 2 = log_5 (k\times2)\)

2. \(2 log_5 k = log_5 k^2\)

3. \(log_5 k - log_5 7 = log_5 (k/7)\)

4. \(log_3 k/log_3 5 = log_5 k/log_5 3\)

5. \(log_5 k + log_25 k = log_5 k + 2 log_5 k\)

\(log_5 k + log_25 k = 3 log_5 k\)
\(log_5 k + log_25 k = log_5 k^3\)

6.  \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 k - 2 log_3 5\)

 \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 (k/5)\)

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Question

For each expression, give an equivalent expression that is of the form \(log_5(*)\), where * is an expression with numbers and possibly the variable k.

1. \(log_5\) k + \(log_5\) 2 =          2. 2 \(log_5\) k =

3. \(log_5\) k - \(log_5\) 7 =          4. \(log_3\)k / \(log_3\) 5 =

5. \(log_5\) k + \(log_{25}\) k =       6. \(log_3 k^2\)/\(log_3\) 25 =

Answer:

6cm

Step-by-step explanation:

The area of a square is s^2, where s is the length of one side.

s^2 = 36cm^2

s = \(\sqrt{36\\}\)cm

s = 6cm

Answer:

Step-by-step explanation:

Area of square = 36 cm²

      Side² = 36

Take square root,

√side² = √36 = √6*6

side = 6 cm

Answer:

I don't understand the question, but I think its 18°

Step-by-step explanation:

Answer:

12.8 cm

Step-by-step explanation:

8 cm = 5 km

? cm = 8 km

→ Find the multiplier between 5 and 8

1.6

→ Multiply 8 by the answer

8 × 1.6 = 12.8