3


33 points


Given the bbjective Function:


Revenue =75x + 85y


and the critical points:


(0,0) (180, 120) (300,0)


Which critical point will yield a maximum revenue?


the (0,0)


the (180, 120)


the (300,0)


Cannot be determined with this information



Can be more than 1 answer

The curve joining the points P1, P2, P3, and so on is called the involute of a circle.

To construct the locus of the free end of the coir for unwinding through an angle of 360 degrees, as well as the normal and tangent at any point on the curve.

Here are the steps for construction:

1. Draw a line PQ that is tangent to the circle and is equal to the circumference of the circle. This line represents the coir being unwound.

2. Divide both the circle and the tangent line into the same number of equal parts. Label these divisions on the circle as 1, 2, 3, and so on. Similarly, label the divisions on the tangent line as 1', 2', 3', and so on.

3. Draw tangents at points 1, 2, 3, and so on on the circle. Mark the points where these tangents intersect the tangent line as P1, P2, P3, and so on.

The distance from each point Pi to the corresponding point i' on the tangent line should be the same as the distance from the center of the circle to the point i on the circle.

4. The curve joining the points P1, P2, P3, and so on is called the involute of a circle. This curve represents the locus of the free end of the coir as it unwinds.

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The process involves creating an initial circle that represents the drum, then using this to draw a horizontal line that's the same length as your first circle's circumference. Divide both into segments and draw lines (tangents) from one set of segments to the other. Points along these lines represent an unwound thread and create the involute when joined up. Tangents and normals can also be drawn onto this curve.

This question pertains to the mathematical concept of a curve locus, specifically the spiral curve produced by unwinding a coir from a drum. To draw this spiral curve (or 'involute'), start by sketching a circle representing the drum (with diameter 30mm). Next, calculate the circumference of this circle and draw a horizontal line of equivalent length. Then, divide this line and the circumference of your circle into the same number of equal sections. For each section in your circle, draw a line from the point of division to an equivalent point on your horizontal line. These lines are your tangents. Mark points on these lines which correspond to the distances covered by the unwound thread. Finally, join these points to create the involute of the circle.

For the part about drawing a normal and a tangent at any point on the curve: Pick a point on the curve. Remember that the tangent at a point on an involute is perpendicular to the line from the point to the centre of the original circle. A normal at any point on a curve is simply a line drawn perpendicular to the tangent at that point.

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The standard form of the given numbers is 207360 × 10¹⁷.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the numbers is  (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001)

Now standard form means we need to write the exponents form.

So,

5 x 6 x 4 x 8 x 3 x 2 x 4 x 9 = 207360

And

1,000,000 x  100000 x 10000 x 1000 x 100 x 10 x 0.1 x 0.001 = 10¹⁷

So, combine 207360 x  10¹⁷

Hence "The standard form of the given numbers is 207360 × 10¹⁷".

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The colorimeter detects the voltage created when sunlight penetrates the specimen, so the voltage created is exactly proportional to the absorbance of the sample.

When charged electrons (current) are forced through a conducting loop by the weight of an electrical raceway power source, they can perform tasks like lighting a lamp. In a nutshell, voltage equals pressure and is expressed in volts (V).

Here,

The voltage generated by the uv spectrophotometer is inversely proportionate to the amount of light present and linearly proportional to the sample's absorbance.

This indicates that as the sample's absorbance rises, so does the energy the colorimeter generates.

Similar to this, the voltage generated by the colorimeter rises as light strength falls.

The Beer-Lambert Law, which says that a sample's absorbance is directly proportional to its concentration of the absorbing substance and its path length and inversely proportional to incident light intensity, describes this connection.

The colorimeter detects the voltage created when sunlight penetrates the specimen, so the voltage created is exactly proportional to the absorbance of the sample.

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Answer:

the value of x= -90

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Answer:

$1,391.25

Step-by-step explanation:

Noon would be 12:00 PM which would be 4 hours ahead of 8:00 AM

We subtract $8,821 by $3,256 to get the amount earned between 8:00 AM and 12:00 PM

$8,821 - $3,256

= $5,565

The find the average taken in within those 4 hours we will have to divide the money earned by the hours

$5,565/4

= $1,391.25

Answer:

f(x)=12x

Step-by-step explanation:

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Answer:

-2

Step-by-step explanation:

=(0-2)/(3-2)

=-2/1

=-2

Answer:

-10,938

Step-by-step explanation:

Since it is below sea level then it’s negative.

Hope this help!

The two given angles add together to make a linear pair, which is 180 degrees.

(2x + 8) + (2x) = 180

4x + 8 = 180

4x = 172

x = 43

Angle ABC = 2(43) + 8 = 86 + 8 = 92 degrees

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A simple random sample of M&M plain candies weights (in grams) is given by the accompanying data.

A frequency histogram should be used to determine the distribution of weights of M&Ms. The mean and median will be determined. Finally, the better measure of central tendency to describe the weight of a plain M&M will be determined.A histogram, which is a graphical representation of data distribution, is a helpful method to display the weights of M&M plain candies. In a histogram, the frequency of occurrences of observations falling within a given category is depicted on the vertical axis, and the categories are listed on the horizontal axis.The shape of the distribution of weights of M&Ms will be determined from the histogram. The mean and median of the M&M weights will be calculated. The best measure of central tendency that describes the weight of an M&M will be determined by comparing the mean and the median.

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The equation in spherical coordinates is:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

What is Equation in Spherical Coordinates?

A mathematical equation that is represented in terms of the spherical coordinates of a point is known as an equation in spherical coordinates. A three-dimensional coordinate system known as spherical coordinates makes use of two angles, typically represented by symbols and a radial distance (r), and a coordinate system to find points in space.

\($r^2 = 81$\)

To represent the equation in spherical coordinates, we substitute the Cartesian coordinates \($x = r\sin(\phi)\cos(\theta)$, $y = r\sin(\phi)\sin(\theta)$, and $z = r\cos(\phi)$\) into the equation. After substitution and simplification, we have:

\($r^2\sin^2(\phi)\cos^2(\theta) + r^2\sin^2(\phi)\sin^2(\theta) + r^2\cos^2(\phi) = 81$\)

Since \(r^2 = 81,\) we can substitute it into the equation:

\($81\sin^2(\phi)\cos^2(\theta) + 81\sin^2(\phi)\sin^2(\theta) + 81\cos^2(\phi) = 81$\)

Finally, we divide the equation by 81 to simplify:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

So, the equation in spherical coordinates is:

\($\sin^2(\phi)\cos^2(\theta) + \sin^2(\phi)\sin^2(\theta) + \cos^2(\phi) = 1$\)

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Answer:

The answer to this question is 4,245

Step-by-step explanation:

Since the rocket is traveling at 283 per minute you would need to multiply 283 and 15 which would give you 4,245

283 X 15= 4,245

Answer:

The exact length of the third side would be 9.

Step-by-step explanation:

To find the length of the triangle, just add the height (6) and the base (3) which equals 9.

Answer:

8

Step-by-step explanation:

the denominator of 5/8 is 8

the denominator of 3/4 is 4

4 can be multiplied by 2 to get 8. If we multiply the entire fraction by 2/2, the fraction changes into 6/8

Now 5/8 and 6/8 share the same denominator and it's the smallest denominator shared between the two.

The function f(x) = x^4 + bx^2 + 1 has an inflection point at x = 0,

What is the inflection point?

An inflection point of a function is a point on the graph of the function where the concavity (curvature) of the graph changes. In other words, an inflection point is a point where the curve switches from being concave up to concave down, or vice versa.

The function f(x) = x^4 + bx^2 + 1 has an inflection point at x = 0, because the concavity of the graph changes at that point. To find the value of b such that the function has at least one inflection point over the interval (1,2), we can set x = 1 and x = 2 in the function and solve for b.

If we set x = 1, we get the equation f(1) = 1 + b + 1 = 0. Solving for b, we find that b = -2.

If we set x = 2, we get the equation f(2) = 16 + 2b + 1 = 0. Solving for b, we find that b = -9.

Since the function has an inflection point at x = 0 for any value of b, it will have at least one inflection point over the interval (1,2) for any value of b.

Therefore, the value of b can be any real number.

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The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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We can simplify the ratio by dividing the 3 numbers by 3, we will get the simplified ratio  34:33:29

We want to simplify the ratio:

102:99:87

To do so, we just need to divide all the numbers by the same integer, if we divide them all by 3 we will get:

102/3 = 34

99/3 = 33

87/3 = 29

Then we can rewrite the ratio as:

34:33:29

And these numbers do not have common factors, so we can't keep simplifying this.

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Answer:

X = 4.47  Y = 8.94

Step-by-step explanation:

2\(\sqrt{5}\)= 2.23606798

2.23606798 x 2 = 4.47213596

-------

4.47213596

4.47213596^2 + 4.47213596^2 = 8.94427192^2

8.94427192^2 = 80

Square root of 80 is 8.94

The volume of water in the cone-shaped paper cup is 25.12 cubic centimeters.

To calculate the volume of water in the cone-shaped paper cup, we can use the formula for the volume of a cone:

V = (1/3) * π * r^2 * h

Given:

Height of water (h) = 6 cm

Diameter of the top surface of water (2r) = 4 cm

First, we need to find the radius (r) of the top surface of the water. Since the diameter is given as 4 cm, the radius is half of that:

r = 4 cm / 2 = 2 cm

Now we can substitute the values into the volume formula and calculate the volume of water:

V = (1/3) * 3.14 * (2 cm)^2 * 6 cm

V = (1/3) * 3.14 * 4 cm^2 * 6 cm

V = (1/3) * 3.14 * 24 cm^3

V = 25.12 cm^3.

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If y is directly proportional to x, when x = 60, y = 6.

Proportional refers to a relationship between two quantities in which one quantity is a constant multiple of the other. In other words, if one quantity increases or decreases by a certain factor, the other quantity will also increase or decrease by the same factor.

Directly proportional is a specific type of proportionality where two quantities increase or decrease by the same factor. In other words, if one quantity doubles, the other quantity also doubles. If one quantity triples, the other quantity also triples, and so on.

In the given question,

If y is directly proportional to x, we can use the formula:

y = kx

where k is the constant of proportionality.

To find the value of k, we can use the given values:

y = kx

50 = k(500)

Solving for k:

k = 50/500

k = 0.1

Now that we know the value of k, we can use the formula to find the value of y when x = 60:

y = kxy = 0.1(60)

y = 6

Therefore, when x = 60, y = 6.

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Answer:

translation (x, y-9)

Step-by-step explanation:

Assuming that point J has the coordinates (0, 5),

the transformation  is a translation (x, y-9)

J (0,5) → J' (0, 5-9) → J' (0,-4)

K (2,6) → K' (2, 6-9) → K' (2,-3)

L (2,3) →  L' (2, 3-9) →  L' (2,-6)

M (1,3) → M' (1, 9-3)  → M' (1,-6)

Answer:

down 9

Step-by-step explanation:

Multicollinearity refers to a high correlation between two or more independent variables in a regression model.

When there is multicollinearity, the independent variables provide redundant or highly similar information to the model. This can cause issues in the regression analysis, such as unstable parameter estimates, difficulties in interpreting the individual effects of the variables, and decreased statistical significance.

In the context of the given options, multicollinearity is the term that describes the situation when there is a high correlation between independent variables. It indicates that the independent variables are not providing unique information to the model and are instead duplicating or overlapping in their explanatory power.

Variance inflation is related to multicollinearity, but it specifically refers to the inflation of the variance of the regression coefficients due to multicollinearity. Heteroskedasticity refers to the presence of non-constant variance in the error terms of a regression model. Multiple correlation refers to the correlation between a dependent variable and a combination of independent variables. Multiple interaction refers to the interaction effects between multiple independent variables in a regression model.

In summary, when there is a high correlation between independent variables, it is known as multicollinearity, indicating that the variables provide redundant information to the model.

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Answer: y-100= 0.25(x-160)

Step-by-step explanation:

Given: Charge per mile = $0.25

Total amount driver pays = $100

Number of miles he drove = 160 miles

Total cost = Flat fee +  ( Number of miles he drove) (Charge per mile) ...(i)

i.e. 100= Flat fee +  (160)(0.25)

⇒ Flat fee = 100 - (160)(0.25)

If y= total cost , x= number of miles, then

y= ( 100 - (160)(0.25))+ (x)(0.25)  [Substitute value of flat fee in (i)]

⇒ y= 100 - (160)(0.25)+ (x)(0.25)

⇒ y-100= (x)(0.25)- (160)(0.25)

⇒  y-100= 0.25(x-160)

Hence, the required equation:  y-100= 0.25(x-160)

Answer:

4

Step-by-step explanation:

Solving:

Checking:

Answer:

x = 3

Step-by-step explanation:

We divide the sides by 3 to get the triangle in question

Answer:

500

Step-by-step explanation:

let's say charlie sends x messages per month

he spends $50 + 0.05 for each x (message), which comes out to less than or equal to $75.

as an equation, this is

50 + 0.05 x ≤ 75

subtract both sides by 50 to isolate the variable and its coefficient

0.05 x ≤ 25

multiply both sides by 1/0.05 to isolate x

x ≤ 500

the maximum is therefore x = 500 messages

Answer:

x = 41°

Step-by-step explanation:

Complementary angles are angles that add up to 90°

y = x + 8

x + y = 90°

Plug in x+8° for y:

-Chetan K

The fraction of blue marble in the jar is [(1/2)x]/ (x+3) where x+3 is the total marbles.

This question involves basic arithmetic and fractions.

We know that a fraction means a part of a whole. It is of the form a/b where b is not equal to zero and a, b are numbers.

Now, here let the total number of marbles in the bar is x .

Then , the number of blue marbles is (1/2)x i.e. 1/2 of x.

Now, if three black marbles are added to the jar, the total number of marbles = x + 3.

So, fraction of blue marble in the jar = (no. of blue marble)/(no. of total members)

= [(1/2)x]/ (x+3).

Thus, the fraction of blue marble in the jar is [(1/2)x]/ (x+3) where x+3 is the total marbles.

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