If the cost of producing each unit of a good is R17,00 which formulae will give the total cost (y) of producing z units of the good?​

The stability limit depends on the specific form of the equation, so you may need to adjust this value based on the specific equation you are working with.

The stability condition for the Euler's method applied to the equation

y' = f(x,y) is given by the following inequality:

|hf(x,y)| <= 1,

where h is the step size. To determine the largest step size for which Euler's method is stable, we need to find the maximum value of |hf(x,y)|. This maximum value is often referred to as the stability limit.

In your case, the equation is close to the simpler equation y' = a, which has the solution y = a*x + b. The stability limit for the Euler's method applied to this equation is 1, so we can take h <= 1 as the largest step size for which the method is stable. However, the stability limit depends on the specific form of the equation, so you may need to adjust this value based on the specific equation you are working with.

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Answer:

The rate of change is $21.5 per hour

Step-by-step explanation:

The rate of change can be found using the formula: (y^2 - y^1)/(x^2 - x^1).

(the exponents refer to which number. Y^2 refers to the y-axis number of the second number given)

So fill in the blanks:

(430 - 215)/(20– 10)

Now do the math:

430 - 215 = 215, 20 - 10 = 10

(215)/10

Divide:

215/10 = 21.5

Therefore, 21.5 is the rate of change!

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

Using the normal distribution, it is found that 6.3% of people received a higher score than Jose.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given by, respectively: \(\mu = 76.28, \sigma = 7.02\).

The proportion of people who received a higher score than Jose is one subtracted by the p-value of Z when X = 87, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{87 - 76.28}{7.02}\)

\(Z = 1.53\)

\(Z = 1.53\) has a p-value of 0.937.

1 - 0.937 = 0.063.

6.3% of people received a higher score than Jose.

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a) Probability of occurrence of evant A is equals to the 7/10.

P(not getting a white or a blue shirt), P(Aᶜ ) is equals the 3/10.

Probability of occurrence of evant B is equal to the 1/2.

b) The events A and B are not mutually exclusive

c) Mike's preference is to getting a white shirt with his size L.

We have a probabality based problem. Probability is defined as chance of occurrence of an event or result. It can be calculate as favourable outcomes divided by total possible outcomes. There is total number of avaliabile shirts = 20 i.e., total possible outcomes = 20

Mike is interested in getting a white or a blue shirt in size L. Let us consider two events :

A : Getting a white or a blue shirt

B: Getting a shirt in size L

a) Number of favourable outcomes to getting white or a blue shirt = 9 white or 5 blues

Probability ( Getting a white or a blue shirt) , P(A)

= 9/20 + 5/20 + 0 = 14/20 = 7/10

P(not Getting a white or a blue shirt), P(Aᶜ )

= 1 - P(A) = 1 - 7/10 = 3/10

ii) The number of favourable outcomes for event B, n(B) = 10

So, Probability of getting a shirt in size L, P(B)

= 10/20 = 1/2

b) Mutually exclusive events are defined as the events that can't happen at the same time. In other words AnB = 0 . Here, we see there is total 14 shirts which are in white or blue colors and 10 are in size L , So there is possibility that shirt is white or blue in colour and in size L , i.e, An B ≠0

So, events A and B are not mutually exclusive.

c) Event ,n( A u B )= n(A) + n(B) - n(A n B)

On the basis of all details, we conclude that Mike's preference is to choose white shirt with size L .

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Answer:

No, a 25-year-old job applicant cannot be two standard deviations below the mean

Step-by-step explanation:

There are two frequencies 25 and 65

Mean of the two frequencies = 25+65/2 = 45

Standard deviation =

\(\frac{65-25}{\sqrt{12} } \\= 11.55\)

Mean - 2 x standard deviation \(= 45 - 2 * 11.55 = 21.9\)

\(21.9 < 25\)

Thus, a 25-year-old job applicant cannot be two standard deviations below the mean

Answer: Rate of tree's height per year = 0.275 m per year.

Rate of tree's trunk per year = 0.025 m per year.

Step-by-step explanation:

Given data,

Exactly 120 years​ ago, students planted a tree in front of their school

Since​ then, the tree has grown 33 meters taller

The distance around the trunk has increased by 3 meters.

Define Unit rate :

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

So, we can write,

There are 2 various unit rates in this:

The increase of the tree's height per year

The increase of the tree's trunk per year

Let us assume,

The increase of the tree's height per year = x

The increase of the tree's trunk per year = y

we can solve it :

Rate of tree's height per year x = 33m / 120 years

                                                x = 0.275 m per year.

Rate of tree's trunk per year y = 3m / 120 years

                                              y = 0.025 m per year.

Therefore,

Rate of tree's height per year = 0.275 m per year.

Rate of tree's trunk per year = 0.025 m per year.

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The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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The angle measure explained in the solution.

Given that, a || b, we need to find the missing angles,

∠1 = 42° [vertically opposite angles]

∠3 = 62° [vertically opposite angles]

∠2 = 180°-(∠1+62°) [angle in a straight line]

∠2 = 76°

∠4 = ∠2 [vertically opposite angle]

∠4 = 76°

∠4 = ∠9 = 76° [alternate angles]

∠9 = ∠12 = 76° [vertically opposite angle]

∠3 = ∠ 6 = 62° [alternate angles]

∠ 6 = ∠7 = 62° [vertically opposite angle]

∠3 + ∠5 = 180° [consecutive angles]

∠5 = 118°

∠5 = ∠8 = 118° [vertically opposite angle]

∠4 + ∠10 = 180° [consecutive angles]

∠10 = 104°

∠10 = ∠11 [vertically opposite angle]

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Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

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Answer:

4.49% (rounded to 2 decimal places)

Step-by-step explanation:

Let the tax rate be r%

The tax paid on car = (Final Sale Price) - (Before Tax Price)

= 8652.60 - 8280 =  $372

Tax rate as a decimal = Tax/(Before Tax Price)

= 372/8652.60 ≈ 0.0449275  (rounded to 7 decimal places)

To find tax rate as percentage multiply the above by 100 to get tax rate as
0.0449 x 100 ≈ 4.49275% ≈ 4.49% (rounded to 2 decimal places)

After using ruler and following the steps described below

We get the standard position of 35 degree.

The given angle is = 35 degree

To draw standard position of angle:

We proceed it to draw by ruler

So, in order to get position,

Follow the following steps:

1: Draw a straight line with your ruler.

2: Place your protractor on the line and align the base of the protractor with the line.

3: Find the 35 degree mark on the protractor and make a small mark on the line at that point.

4: Move your protractor to the mark you just made.

5: Align the base of the protractor with the line and make another small mark on the line at the 35 degree mark.

6: Draw a straight line connecting the two points you just marked.

And there you have it! A 35 degree angle drawn on paper.

And after following these steps we get the standard potion angle 35 degree.

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Answer:

Multiply the normal price of the item by .25 and then subtract that from the normal price.

Step-by-step explanation

\(x -(x*.25)\)  

x is the item

Step-by-step explanation:

100%-25%= discounted price= 75%

You do the discounted price divided by 75 to find 1%

do that times 100 to find the pre-discounted price.

e.g

find the original price of a sweater when it was on sale of 25%. the sale price is £15.00.

£15.00 = 75%

15.00 divided by 75 = 1% =£0.20

£0.20 x 100 = pre-sale price = £20.00

The price of the sweater before the sale is £20.00.

You are welcome xx

Answer:

x = 29

Step-by-step explanation:

147 + 147 + 2x - 25 + 2x - 25 = 360

294 + 2x - 25 + 2x - 25 = 360

294 + 2(29) - 25 + 2(29) - 25 = 360

294 + 58 - 25 + 58 - 25 = 360

352 - 25 + 33 = 360

327 + 33 = 360

360 = 360

x = 29

Answer:

b option ..............

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

The probability that a person who tests positive actually has the disease is 0.006%

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

The probability that a person who tests positive actually has the disease is represented as

Probability = Incidence rate * False positive rate

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

Probability = 0.3% * 2%

Evaluate the products

Probability = 0.006%

Hence, the probability is 0.006%

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Answer:

The answer to this question can be defined as follows:

In part (i), the answer is "option d".

In part (ii), the answer is "option 2".

Step-by-step explanation:

Given:

Part (a)

\(\Rightarrow \bold{\frac{x^2+x-20}{x-4}=x+5}\\\\\)

Solve  the above equation:

\(\Rightarrow x^2+x-20=(x+5)(x-4)\\\\\Rightarrow x^2+x-20=(x^2-4x+5x-20)\\\\\Rightarrow x^2+x-20=x^2-4x+5x-20\\\\\Rightarrow \boxed{x^2+x-20=x^2+x-20}\\\)

Given:

Part (b)

\(\Rightarrow \bold{ \lim_{x \to \3} \frac{x^2+x-12}{x-3}= \lim_{x \to 3} (x+4)}\\\\\)

Solve the above equation:

factor of \(\Rightarrow x^2+x-20 =(x-3)(x+4)\)

\(\Rightarrow \lim_{x \to \3} \frac{(x-3)(x+4)}{x-3}= \lim_{x \to 3} (x+4)\\\\\Rightarrow \lim_{x \to \3} (x+4)= \lim_{x \to 3} (x+4)\\\\\)

apply limit value:

\(\Rightarrow (3+4)= (3+4)\\\\\Rightarrow 7= 7\)

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Answer:

Area = 130 ft^2

Step-by-step explanation:

Area =length * width

Perimeter = 2(L + W)

L=3+x

W= x

Perimeter= 2(3+x+x) =2(3 +2x)=6+4x=46 so x=10

L=3 +10= 13

W= 10

Area = 13* 10 130

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

C. Method 1 is an observational study because no attempt is made to influence results.

Step-by-step explanation:

Based on the descriptions provided: Method 1 is an observational study because no attempt is made to influence the results. Option 3 is the correct answer.

An observational study is a type of study where researchers observe and collect data without actively intervening or manipulating any variables.

Method 1 involves surveying shoppers and asking them about their detergent use and laundry cleanliness ratings. The researcher is merely collecting data without intervening or manipulating any variables. The study relies on the natural behavior of shoppers and their responses.

Method 2, on the other hand, involves actively creating soiled fabrics and washing them with different detergents. This intervention introduces an element of manipulation, making it more of an experimental study than an observational one.

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Step-by-step explanation:

Subtract the envelope weight from the total weight....this will result in the weight of the paperclips alone:

49.5 g - 2.43 g = 47.07 g   of paper clips

Then:

47.07 g   / ( .83 g /clip)  = 56.7 = ~ 57 clips

Answer:

40 dollars

Step-by-step explanation:

We can use a ratio to solve the problem

5 pounds         50 pounds

----------------  = -----------------

4 dollars            x dollars

Using cross products

5 * x = 4 * 50

5x = 200

Divide by 5

5x/5 = 200/5

x = 40

40 dollars

Step-by-step explanation:

\(\sf 5 \: pounds \longrightarrow 4 \: dollars\)

\(\sf 1\: pounds \longrightarrow \dfrac{4}{5} \: dollars\)

\(\sf 50\: pounds \longrightarrow \dfrac{4}{5}×50 \: dollars\)

\(\sf \longmapsto 40 \: dollars\)

Answer:y times 20 p

Step-by-step explanation:

Answer:

Step-by-step explanation:

b i think if not it should be a sorry if im wrong

The tutor that will earn more money in a week would be Zhen with the total income of =$1,080.

The total amount collected from pupils tutor by Zhen company = $2400

The 45% of $2400 = 45/100 × 2400

= 108000/100

= $1,080

The total amount collected from pupils Ryder tutored would be = $1080

The 45% of $1080 = 45/100 × 1080

= 48600/100

= $486

Therefore, the tutor that earned higher income is Zhen with an income of $1,080.

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Complete question:

Zhen and Ryder work as tutors at two different test-prep companies. In one week, Zhen earns 45% of the $2400 collected from the pupils tutors. Ryder earns 45% of the $1080 collected from the pupils she tutors the same week. Who earns more money in a week? Explain.

Answer: He will need 1 1/4 cups of butter

Step-by-step explanation:

1. We can do 28/8 to find how much we need to multiply our 1/2 cup of butter to keep the ratio of people to cups of butter the same. 28/8= 3 1/2

2. Then we can multiply 3 1/2 and 1/2 to get 1 1/4 cups of butter.

Joaquin requires 5.25 cups of butter to serve 28 people.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Given that the original recipe serves 8 people and requires 1/2 of a cup of butter but he needs it to serve 28 people.

Let the quantity of butter required for the new recipe be x.

To determine how much to multiply our 1/2 cup of butter in order to keep the same proportion of persons to cups of butter,

we can use the ratio of 28/8.

So, 8:1.5::28:x

⇒ 8x = 42

⇒ x = 5.25

Hence, Joaquin requires 5.25 cups of butter to serve 28 people.

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Answer:

A

Step-by-step explanation:

fog(x) = f(g(x) = f(1/2x) = 4x/(1+6x)