What point in the feasible region maximizes the objective function?
x>0
Y≥0
Constraints
-x+3≥y
{ y ≤ ½ x + 1
objective function: C = 5x - 4y

The complete solution of the integral ∫ x · √(8 · x - x²) dx is equal to [- √(8 · x - x²)³ / 3] - (- 2 · x + 8) · √(8 · x - x²) + 32 · [ -  sin⁻¹ [(- 2 · x + 8) / 8]].

Some integrals cannot be resolved immediately or at least in few steps, requiring sometimes the resolution of some intermediate integrals. In this case, we have an integral of the form:

∫ x · √(a · x² + b · x + c) dx, where a, b, c are real constants.       (1)

The use of integral tables allows us to save time on resolution of integrals.

The solution of (1) can be found by using part integration several times. In accordance with the table of integrals, we find the following information:

∫ x · √(a · x² + b · x + c) dx = [√(a · x² + b · x + c)³ / (3 · a)] - [[b · (2 · a · x + b)] / (8 · a²)] · √(a · x² + b · x + c) - [[b · (4 · a · c - b²)] / (16 · a²)] ∫ [1 / √(a · x² + b · x + c)] dx

∫ [1 / √(a · x² + b · x + c)] dx = - (1 / √- a) · sin⁻¹ [(2 · a · x + b) / [√(b² - 4 · a · c)]]

Then, the complete solution of the integral is:

∫ x · √(a · x² + b · x + c) dx = [√(a · x² + b · x + c)³ / (3 · a)] - [[b · (2 · a · x + b)] / (8 · a²)] · √(a · x² + b · x + c) - [[b · (4 · a · c - b²)] / (16 · a²)] · [ - (1 / √- a) · sin⁻¹ [(2 · a · x + b) / [√(b² - 4 · a · c)]]]

If we know that a = - 1, b = 8 and c = 0, then the complete solution of the integral is:

∫ x · √(8 · x - x²) dx = [- √(8 · x - x²)³ / 3] - (- 2 · x + 8) · √(8 · x - x²) + 32 · [ -  sin⁻¹ [(- 2 · x + 8) / 8]]

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1. In 2005 12.6 out of every 50 employees were women

Total = 41232 employees

Estimate the number of women

41232* 12.6/50 = 10390.46 Women

Answer:

Step-by-step explanation:

x=40,y=60

Answer:

d X v = m

12.993 X 10.49 = 136.29657

Answer:

x-2 =0

x=2

now

putting the x value in p

we have,

p(2) = x2 + 2x +k

= 2×2 +2×2+k

= 4+4+k

= 8+k

so,

Either

8+k =0

k= - 8

Hello !

1. A quadratic equation results in the form: ax² + bx + c

2. Calculate the discriminant: Δ = b² - 4ac

3. Calculate x with the dicriminant: (-b ± √Δ) / 2a

Example:

3x² + 7x - 2 = 0 is a quadratic equation.

x = (-b ± √(b² - 4ac)) / 2a

= (-7 ± √(7² - 4*3*(-2))) / (2*3)

= (-7 ± √73)/6

Answer:

The critical value used is T = 3.747.

The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation.

Sample mean:

\(\overline{x} = \frac{127+174+157+120+161}{5} = 147.8\)

Sample standard deviation:

\(s = \sqrt{\frac{(127-147.8)^2+(174-147.8)^2+(157-147.8)^2+(120-147.8)^2+(161-147.8)^2}{4}} = 23.188\)

Confidence interval:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 5 - 1 = 4

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.98}{2} = 0.99\). So we have T = 3.747, which is the critical value used.

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 3.747\frac{23.188}{\sqrt{5}} = 38.856\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 147.8 - 38.856 = 108.944  

The upper end of the interval is the sample mean added to M. So it is 147.8 + 38.856 = 186.656.

The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).

Answer:

5, 6

Step-by-step explanation:

Answer:

Los números son:

6 y 5

Step-by-step explanation:

Planteamiento:

a * b = 30

a + b = 11

Desarrollo:

De la segunda ecuación del planteamiento:

a = 11-b    

Sustituyendo esta última ecuación en la primer ecuación del planteamiento:

(11-b)*b = 30

11*b + b*-b = 30

11b - b² - 30 = 0

-b² + 11b - 30 = 0

b = {-11±√((11²)-(4*-1*-30))} / (2*-1)

b = {-11±√(121-120)} /-2

b = {-11±√1} / -2

b = {-11±1} / -2

b₁ = {-11-1} / -2 = -12/-2 = 6

b₂ = {-11+1} / -2 = -10/-2 = 5

Comprobación:

6*5 = 30

6+5 = 11

Answer:

Answers: 40/60 and 400/600.

Step-by-step explanation:

Ok, these fractions are equivalent to 67%, and to 4/6.

Answer:

4

(0,4)

Step-by-step explanation:

The y-intercept is the y-value for when the line intersects with the y-axis. Another way to put this is also the y-value when x=0. This is easy to find when you have a graph because you can simply look to see where on the graph the line intersects with the axis. If you don't have the graph then you can plug 0 in for x in the equation and solve.

Answer:

p = packet of sweets

12p = 4.06

p = .3383333

p = .340

Answer:

A) 6.4

B) 13.2

C)26.5

D)154.3

E)282.4

F)0.3

Answer:

your answers from parts (a) and (b), write an equation for the line ... Find the slope and y-intercept of the line represented by each equation.

Step-by-step explanation:

does this help ;-;

Yes, this is an example of bias, specifically, response bias.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is an important concept in many fields, including mathematics, statistics, physics, and engineering, and is used to make predictions, analyze data, and make decisions under uncertainty.

Here,

Response bias occurs when the answers given by respondents in a survey do not accurately reflect their true opinions or beliefs. In this case, the question asked by the soft drink company is leading and suggestive, and it suggests that the company's product is superior to its rival's product. By framing the question in this way, the soft drink company is more likely to receive a positive response from respondents, even if they do not actually believe that the company's product is better than its rival's product.

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Answer:

201

Step-by-step explanation:

107^2+201=11650

Answer:

B

Step-by-step explanation:

The correct statement of the given ones are - the unit rate of best fudge is less than unit rate of candy cane.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is a table that shows the cost for fudge at candy lane. The graph represents the cost for similar fudge that best fudge shop sell.

The slope of straight line represented by the table -

m[1] = (16 - 8)/(2 - 1)

m[1] = 8

The slope of the line plotted on graph -

m[2] = (9 - 6)/(3 - 2)

m[2] = 3

The slope is the measure of unit rate. Therefore, the unit rate of best fudge is less than unit rate of candy cane.

The cost 3 pounds of fudge at best fudge shop = 3 x 3 = $9

The cost 1 pound of fudge at candy lane = $8

Hence, cost 3 pounds of fudge at best fudge shop is greater than the cost of a pound of fudge at sweet treats.

Therefore, the correct statement of the given ones are - the unit rate of best fudge is less than unit rate of candy cane.

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[Refer to the image attached for table and graph]

Answer:

you will need 30 aquariums to hold 10 gallons.

Step-by-step explanation:

3.10=30

10/3 aquariums will it take to hold 10 gallons.

Unit rate is defined as the ratio of two quantities used to find the amount associated with per unit of quantity.

Given that, an aquarium, holds 3 gallons of water, we need to find the number of aquariums will it take to hold 10 gallons,

So, 1 aquarium = 3 gallons

So, 1 gallon = 1/3 aquariums

So, 10 gallons = 10/3 aquariums

Hence, 10/3 aquariums will it take to hold 10 gallons.

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If it is ....

\(3 {x}^{2} - 2x + 1 = \)

The coefficient of x² is (( 3 ))

& the coefficient of x is (( -2 ))

_________________________________

If it is .....

\(3x - 2x + 1\)

\(x + 1\)

The coefficient of x² is (( zero 0 ))

& the coefficient of x is (( 1 ))

Answer:

I would identify the proportions of the corresponding sides, because that would allow you to identify whether or not the triangles are similar. You could also identify if two triangles are similar using

-SSS (side-side-side) which would tell you if all three corresponding sides are congruent

-SAS (side-angle-side) which would tell you if two sides and the angle between them are congruent

-ASA (angle-side-angle) which would tell you the two angles and the side between them are congruent

-AAS (angle-angle-side) which would tell you if two angles and a non-included side are congruent. You triangles may have all of these, or just one, but it will help you identify the similarity between triangles

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

Subtract 5x

Step-by-step explanation:

Cause then you would only get one x in the equation instead of 6x and 5x. Hope this helps!

Answer:

this is what i used as my answer on the advice i would give tucker for what to do as his first step.

Step-by-step explanation:

i would tell tucker to add 5 negative x-tiles because then he would be isolating the x variable and that would help him with not getting confused when gets to the part where he has to isolate the variable if he was to add 1 negative unit tile to both sides as his first step.

Either first step will isolate the variable.

The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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After solving the equations, we know that a total of 25 ladies attended the party.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

So, take dudes as x and ladies as y.

Now, form the required 2 equations as follows:
2x + y = 45 ...(1)

x + y = 35 ...(2)

Work on equation (2):

x + y = 35

x = 35 - y

Now, substitute x = 35 - y in equation (1):

2x + y = 45

2(35-y) + y = 45

70 - 2y + y = 45

-y = -25

y = 25

Since ladies were charged $1 for each ticket, then 25 ladies attended the party.

Therefore, after solving the equations, we know that a total of 25 ladies attended the party.

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Answer:

48,236.7

Step-by-step explanation:

40,000 + 8,000 + 200 + 30 + 6 + 7/10

7/10 can also be written .7

Answer:

sweefe

Step-by-step explanation:

EFEFEEa

The value of x = 2nπ,  (n ∈ Z) and

\(x=2(n\pi+(-1)^{n} \pi /6)\),  (n ∈ Z)

What are Trigonometric Identities?

Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables  being on both sides of an equation. Geometrically, these identities involve certain trigonometric functions(  similar as sine, cosine, tangent ) of one or  further angles.

According to question

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + cos(x) - 1 = 0

{ cos(2x) = 1 - 2sin²(x) }

cos(x) = 1 - 2sin²(x/2)

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + 1 - 2sin²(x/2) - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2) + 1 - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2)  = 0

⇒ sin(x/2)(- 2sin(x/2) + 1)  = 0

⇒ sin(x/2) = 0 , x = 2nπ (n ∈ Z)

and

⇒ sin(x/2) = 1/2 , \(x=2(n\pi+(-1)^{n} \pi /6)\) (n ∈ Z)

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