if cot0=3/4 and the terminal point determined by 0 is in quadrant 3, then

a.  P(x) = 50x - 4000.1.

b. The company must sell at least 81 units of their product to have a positive profit.

c. The company should try to sell as many units as possible within the given range to maximize their profit.

A revenue function is a mathematical equation or formula that represents the amount of money a company or organization generates from the sale of its products or services. It is a function that relates the price of a product or service to the quantity sold and represents the total revenue earned by a company at a given price and level of production.

A profit function is a mathematical equation or formula that represents the amount of profit a company or organization generates from the sale of its products or services. It is a function that relates the price of a product or service, the cost of production, and the quantity sold and represents the total profit earned by a company at a given price and level of production.

In the given question,

(a) The profit function can be obtained by subtracting the cost function from the revenue function as follows:

R(x) = -0.1x + 150x

P(x) = R(x) - C(x)

P(x) = (-0.1x + 150x) - (100x + 4000)

P(x) = 50x - 4000.1

Therefore, the profit function is P(x) = 50x - 4000.1.

(b) To find the minimum number of units the company must sell to have a positive profit, we need to set P(x) greater than or equal to zero and solve for x:

P(x) ≥ 0

50x - 4000.1 ≥ 0

50x ≥ 4000.1

x ≥ 80.002

Therefore, the company must sell at least 81 units of their product to have a positive profit.

(c) To find the value of r that maximizes the profit, we need to find the derivative of the profit function and set it equal to zero:

P'(x) = 50

Setting P'(x) equal to zero, we get:

50 = 0

This equation has no solution, which means that the profit function has no maximum value within the given range. However, we can see that the profit function is increasing for all values of x, which means that the profit increases as the number of units sold increases. Therefore, the company should try to sell as many units as possible within the given range to maximize their profit.

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Answer:

0.6267

Step-by-step explanation:

See the picture.

Hope its clear.

Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:

A = the amount of money in the account after the specified time period

P = the initial principal amount (the amount deposited)

r = the annual interest rate (as a decimal)

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

t = the time period in years

In this case:

P = £4100

r = 13.55% = 0.1355

n = 1 (interest is compounded once per year)

t = 4 years

Plugging these values into the formula, we get:

A = £4100(1 + 0.1355/1)^(1*4)

A = £4100(1.1355)^4

A = £4100(1.6398)

A = £6717.58

Therefore, the amount of money in the account after 4 years will be £6717.58.

Answer:

Let's assume that Mr. Nkalle invested an amount of x in Scheme A and (20900 - x) in Scheme B.

The simple interest earned on Scheme A in 2 years would be:

SI(A) = (x * 9 * 2)/100 = 0.18x

The simple interest earned on Scheme B in 2 years would be:

SI(B) = [(20900 - x) * 8 * 2]/100 = (3344 - 0.16x)

The total simple interest earned in 2 years is given as N$3508:

SI(A) + SI(B) = 0.18x + (3344 - 0.16x) = 3508

0.02x = 164

x = 8200

Therefore, Mr. Nkalle invested N$8200 in Scheme A and N$12700 (20900 - 8200) in Scheme B. So the amount invested in Scheme B was N$12700.

The correct answer is C. A normal distribution is a symmetric probability distribution that is bell-shaped when graphed. When plotted on a horizontal scale, the curve starts on the horizontal axis, rises to a central peak, and then falls back to the horizontal axis.

The curve is symmetric, meaning that the left and right halves of the curve are mirror images of each other. The curve approaches the horizontal axis but never touches it, which indicates that there is a non-zero probability of observing values at any distance from the mean, although the probability decreases as the distance from the mean increases.

Normal distribution is a type of probability distribution that is commonly found in natural and social phenomena, where the majority of the observations tend to cluster around the mean, with fewer observations further away from the mean.

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Exchange rate calculation.

To find out the amount in Singapore dollars that Mr Li would need to give each of his five relatives 500 RMB each, we can follow these steps:

Calculate the total amount in RMB that Mr Li needs to give:

500 RMB/relative x 5 relatives = 2500 RMB

Convert the total amount in RMB to Singapore dollars using the given exchange rate:

2500 RMB x (S$100/RMB510.20) = S$490.64 (rounded to the nearest cent)

Therefore, Mr Li would need S$490.64 to give each of his five relatives 500 RMB each, given the exchange rate of S$100 to RMB510.20.

ChatGPT

Paul paid $1,635 in interest at the end of the loan.

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

The simple interest formula is:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time in years.

In this problem, P = $6,000, r = 0.0545 (since the interest rate is given as 5.45%), and t = 5 years. Plugging in these values, we get:

I = 6,000 * 0.0545 * 5 = $1,635

Therefore, Paul paid $1,635 in interest at the end of the loan.

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Answer: z = 210

Step-by-step explanation: Let's assume the original price of the present was x dollars.

Amanda agreed to pay 30% of the original price, so her contribution was 0.3x dollars.

The remaining amount to be paid is (1 - 0.3)x = 0.7x dollars.

Gabriel agreed to pay 2/5 of the remaining amount, so he paid (2/5)(0.7x) = 0.28x dollars.

The balance amount to be paid by Daniel is (1 - 0.3 - 2/5)(x) = 0.42x dollars.

When the price increased by 25%, the new price became 1.25x dollars.

We can set up an equation based on Amanda's contribution and solve for x:

0.3x = 63

x = 210

Therefore, the original price of the present was $210.

The solution for the given inequality "3x - 5 ≤ 7x + 1" in interval notaton is found out to be  (-1.5, ∞).

First of all, we will be simplifying  the inequality by subtracting 3x from both sides, we would get,

-5 ≤ 4x + 1

Next, we can subtract 1 from both the sides:

-6 ≤ 4x

Finally, we can divide both sides by 4:

-1.5 ≤ x

So the solution to the inequality is x ≥ -1.5.

Therefore, After xpressing the above inequality in interval notation, the solution is (-1.5, ∞), which means that x is greater than or equal to -1.5 and can take any value up to positive infinity.

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The complete question is :

Solve the inequality and express your answer in interval notation. Use decimal form for numerical values.

3x - 5 ≤ 7x + 1

The pairs of events of random integers are pairs of events are,

even and odd , negative and positive integers, zero and non-zero integers.

Two events are mutually exclusive if they cannot occur at the same time.

Selecting a random integer from -200 to 200,

Any two events that involve selecting a specific integer are mutually exclusive.

For example,

The events selecting the integer -100

And selecting the integer 50 are mutually exclusive

As they cannot both occur at the same time.

Any pair of events that involve selecting a specific integer are mutually exclusive.

Here are a few examples,

Selecting an even integer and selecting an odd integer.

Selecting a negative integer and selecting a positive integer

Selecting the integer 0 and selecting an integer that is not 0.

But,

Events such as selecting an even integer and selecting an integer between -100 and 100 are not mutually exclusive.

As there are even integers between -100 and 100.

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Answer:

We will use mathematical induction to prove the formula for the sum of arithmetic sequences:

For n=1, we have:

∑j=1^1(a + (j-1)d) = a

On the other hand, we have:

n/2(2a + (n-1)d) = 1/2(2a) = a

Thus, the formula holds for n=1.

Assuming the formula holds for n=k, we will prove that it holds for n=k+1.

We have:

∑j=1^(k+1)(a + (j-1)d) = (a + kd) + ∑j=1^k(a + (j-1)d)

Using the formula for n=k, we can write:

∑j=1^k(a + (j-1)d) = k/2(2a + (k-1)d)

Substituting this back into the first equation, we have:

∑j=1^(k+1)(a + (j-1)d) = (a + kd) + k/2(2a + (k-1)d)

Simplifying the right-hand side, we get:

∑j=1^(k+1)(a + (j-1)d) = 1/2(2a + (2k+1)d)

But (k+1)/2(2a + kd + d) = 1/2(2a + (2k+1)d), so the formula holds for n=k+1.

Therefore, by mathematical induction, the formula for the sum of arithmetic sequences is proved.

Answer:

To find the derivative of this function, we'll use the product rule and the chain rule. Let's begin by writing the function in a more readable form using parentheses:

y = e^x * csc(x) * (1 / x) * csc(x)

Now we can apply the product rule, letting u = e^x and v = csc(x) * (1 / x) * csc(x):

y' = u'v + uv'

To find u' and v', we'll need to use the chain rule.

u' = (e^x)' = e^x

v' = (csc(x) * (1 / x) * csc(x))'

= (csc(x))' * (1 / x) * csc(x) + csc(x) * (-1 / x^2) * csc(x) + csc(x) * (1 / x) * (csc(x))'

= -csc(x) * cot(x) * (1 / x) * csc(x) - csc(x) * (1 / x^2) * csc(x) - csc(x) * (1 / x) * csc(x) * cot(x)

= -csc(x) * [cot(x) * (1 / x) + (1 / x^2) + (cot(x) / x)]

Now we can substitute these into the product rule formula:

y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (1 / x) - (1 / x^2) - (cot(x) / x)] + e^x * (-csc(x) * cot(x) * (1 / x) * csc(x) - csc(x) * (1 / x^2) * csc(x) - csc(x) * (1 / x) * csc(x) * cot(x))

Next, we can simplify this expression. One way to do this is to factor out common terms:

y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (1 / x) - (1 / x^2) - (cot(x) / x)] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + (cot(x) / x)]

Now we can simplify further by combining like terms:

y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (2 / x) - (1 / x^2)] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + (cot(x) / x)]

= e^x * csc(x) * (1 / x) * csc(x) * [-2cot(x) / x - 1 / x^2 - cot(x) / x^2] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + cot(x) / x]

At this point, the derivative is simplified as much as possible.

(please could you kindly mark my answer as brainliest)

Answer:

To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:

∫[a,b] f(x) dx = F(b) - F(a)

where F(x) is the antiderivative of f(x).

First, we find the antiderivative of f(x):

F(x) = x^2 + (5/3)x + C

where C is the constant of integration.

Next, we evaluate F(5) and F(0):

F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C

F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C

Subtracting F(0) from F(5), we get:

∫[0,5] f(x) dx = F(5) - F(0)

= 25 + (25/3) + C - C

= 25 + (25/3)

= 100/3

Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.

Answer:

Regions 1 and 4

Step-by-step explanation:

There are 2 overlapping regions for A (coffee) and B(tea)

These are Region 4 which represents the adults who drink both coffee and tea but not cola

and

Region 1 which represents the adults who drink coffee, tea and cola

So combined these two regions we get all adults who drink both coffee and tea

Answer:

We can use the formula for compound interest to solve this problem:

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

where:

A = the amount of money in the account after t years

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

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

t = the number of years

Plugging in the given values:

P = $3,200

r = 0.031 (3.1% as a decimal)

n = 4 (quarterly compounding)

t = 8

A = 3200(1 + 0.031/4)^(4*8)

A = $4,100.53

Therefore, after 8 years, there will be $4,100.53 in the account.

Answer:

To find the probability of getting someone who tested positive given that he or she had the disease, we need to use the formula for conditional probability:

P(positive|disease) = P(positive and disease) / P(disease)

From the given data, we can see that there are 136 individuals who tested positive and actually had the disease. Therefore, P(positive and disease) = 136.

We can also see that there are a total of 136 + 8 = 144 individuals who actually had the disease. Therefore, P(disease) = 144.

Substituting these values into the formula, we get:

Simplifying, we get:

Rounding to three decimal places, we get:

Therefore, the probability of getting someone who tested positive given that he or she had the disease is approximately 0.944.

The equation of the tangent line is y = 2x + 2., and the equation of the normal line is y = -1/2 x + 2.

To find the equations of the tangent and normal lines to the curve y = x⁴ +  [tex]2e^{X}[/tex] at the point (0,2), we will need to find the slope of the curve at that point, and then use point-slope form to write the equations of the tangent and normal lines.

First, we can find the slope of the curve at the point (0,2) by taking the derivative of the function and evaluating it at x = 0:

y = x⁴ + [tex]2e^{X}[/tex]

y' = 4x³ +  [tex]2e^{X}[/tex]

y'(0) = 4(0)³ + 2e⁰ = 2

So the slope of the curve at the point (0,2) is 2.

Next, we can use point-slope form to write the equation of the tangent line. The point-slope form of a line will be given by:

y - y₁ = m(x - x₁)

where m will be the slope of the line and (x₁, y₁) is a point on the line.

For the tangent line at (0,2), we have:

y - 2 = 2(x - 0)

Simplifying, we get:

y = 2x + 2

So the equation of tangent line is y = 2x + 2.

To find the equation of the normal line, we need to find the negative reciprocal of the slope of the tangent line (since the slopes of perpendicular lines are negative reciprocals of each other). So the slope of the normal line will be:

m = -1/2

Using point-slope form again, the equation of the normal line is:

y - 2 = (-1/2)(x - 0)

Simplifying, we get:

y = -1/2 x + 2

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Answer:

1 cubic meter = 1000000 cm cubed

Step-by-step explanation:

[tex]1m^3*10^6=1000000cm^3[/tex]

Answer:

1 cubic meter = 10000000 cm cube

Answer:

The order from least to greatest is:

8.2 x 10^-7 < 5.8 x 10^-5 < 1.2 x 10^3 < 9.7 x 10^3 < 3.4 x 10^6

Answer:

it is already in the correct order

Step-by-step explanation:

A person who scored 25 points in this dataset would have a z-score of 0.99.

The mean can be calculated by adding up all of the scores and dividing by the number of scores:

(13 + 18 + 9 + 27 + 15 + 15 + 28 + 5 + 16 + 21 + 23 + 29 + 15 + 15) / 14 = 18

The standard deviation can be calculated using the formula:

sqrt(sum((x - mean)^2) / (n - 1))

where x is each score in the dataset, mean is the mean of the dataset, and n is the number of scores.

Using this formula, we get:

sqrt (((13-18) ^2 + (18-18) ^2 + (9-18) ^2 + (27-18) ^2 + (15-18) ^2 + (15-18) ^2 + (28-18) ^2 + (5-18) ^2 + (16-18) ^2 + (21-18) ^2 + (23-18) ^2 + (29-18) ^2 + (15-18) ^2 + (15-18) ^2) / (14 - 1))

= 7.05

Now we can calculate the z-score of a scores of 25 using the formula:

z = (x - mean) / standard deviation

where x is the score, we are interested in, mean is the mean of the dataset, and standard deviation is the standard deviation of the dataset.

Plugging in the values, we get:

z = (25 - 18) / 7.05 = 0.99 (rounded to two decimal places)

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Answer:

We are given the cost equations for Emma's and Madison's text message plans as:

Emma's Plan: y = 0.10x + 10

Madison's Plan: y = 0.15x

where y is the cost in dollars and x is the number of texts sent. We are also told that Emma and Madison paid the same amount in one month. Let's set the two equations equal to each other and solve for x:

0.10x + 10 = 0.15x

Subtracting 0.10x from both sides, we get:

10 = 0.05x

Dividing both sides by 0.05, we get:

x = 200

Therefore, Emma and Madison sent 200 text messages in one month to pay the same amount

Answer:

The right answer is below

Step-by-step explanation:

4.7 is the length of LJ

you thought

i was feeling you

Answer:

The answer is C

Step-by-step explanation:

Assuming this is a fair coin, the theoretical probability of the coin going on one side, let's say heads, is 50%, or 0.5. So what's the chance the coin lands head 5 times? To do this we do 0.5^5 OR 0.5*0.5*0.5*0.5*0.5. Both of these answers equal 0.03125. So C is the Answer. Hope this helps :D

When the graph of the equation y=a(x−2)(x+4) in the xy-plane is a parabola with vertex (c,d), then the value of d is equal to option (A) -9a

To find the vertex of the parabola, we need to complete the square by factoring out the constant term a and adding and subtracting a term that will allow us to write the quadratic in the form

y = a(x - h)^2 + k,

where (h,k) are the coordinates of the vertex. We have

y = a(x - 2)(x + 4) = a(x^2 + 2x - 8x - 8) = a[(x + 1)^2 - 9]

Expanding the square and factoring out the constant term a, we get

y = a[(x + 1)^2 - 9] = a(x + 1)^2 - 9a

Comparing this to the standard form of the quadratic, we see that the vertex is at (-1,-9a). The value of d is -9a

Therefore, the correct option is (A) -9a

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The probability that less than 8.4% of the individuals in the sample hold multiple jobs is approximately 0.0681 or 6.81%.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number outcomes.

To determine whether it is appropriate to use the normal approximation, we need to check whether the conditions for using the normal distribution are met.

We can use the following criteria:

The sample size is large enough: n × p ≥ 10 and n × (1 − p) ≥ 10

The observations are independent

Here, we are given that the sample size is n = 66. To check the first condition, we need to find the expected number of individuals who hold multiple jobs in the sample, which is given by:

np = 0.12 × 66 = 7.92

n(1-p) = 66 - 7.92 = 58.08

Both np and n(1-p) are greater than or equal to 10. So, the sample size is large enough and the first condition is met.

Additionally, we can assume that the observations are independent since the sample is random and represents less than 10% of the population of employed adults in the United States.

Therefore, it is appropriate to use the normal approximation.

To find the probability that less than 8.4% of the individuals in the sample hold multiple jobs, we need to standardize the sample proportion using the formula:

z = (p'- p) / [tex]\sqrt{(p(1-p) / n)}[/tex]

where p' is the sample proportion, p is the population proportion (0.12), n is the sample size (66), and sqrt represents the square root.

Substituting the values, we get:

z = (0.084 - 0.12) / [tex]\sqrt{((0.12)(1-0.12) / 66)}[/tex] = -1.496

Using a standard normal distribution table, we can find that the probability of z being less than -1.496 is approximately 0.0681.

Therefore, the probability that less than 8.4% of the individuals in the sample hold multiple jobs is approximately 0.0681 or 6.81%.

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Answer: tens

Step-by-step explanation:

The pairs of alternate interior angles are given as follows:

Alternate interior angles are pairs of angles that are formed when a transversal intersects two parallel lines. Alternate interior angles are located on opposite sides of the transversal and inside the parallel lines.

From the image given at the end of the answer, the parameters for this problem are given as follows:

Hence the pairs of alternate interior angles are given as follows:

As they are between lines l and k, on opposite sides of line t.

The diagram is given by the image presented at the end of the answer.

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Answer:

The absolute value of +98 is simply 98. So, | +98| = 98.

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

The absolute value of a number is its POSITIVE distance from 0, so as +98 is 98 away from 0, then |+98| = 98.

The graph demonstrates that local producers will provide 8,000 tonnes of apricots at the global price of $400 per tonne.

A graph is a visual representation of data that's frequently used to demonstrate how variables relate to one another or to show how trends change over time. Graphs can come in many various forms, including line graphs, bar graphs, pie charts, scatter plots, and more. Graphs are frequently used to simplify the presentation of complicated data in disciplines like economics, mathematics, science, and the social sciences.

given

The graph indicates that the cost of apricots in the globe is $400 per tonne. In the absence of the quota, the US would purchase 5,000 tonnes of apricots at the market rate. The United States will only be permitted to acquire 3,000 tonnes of apricots under the quota, though.

As a result of this quota, the United States will purchase 3,000 tonnes of apricots at the world price.

The graph demonstrates that local producers will provide 8,000 tonnes of apricots at the global price of $400 per tonne.

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