1
Apply the Linear Programming Theorem and interpret the results.
2) Answer the questions below for the following situation:
For a certain lawn, a landscaping contractor plans to use the least expensive combination of two brands of
fertilizer. A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates. A package of
Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates. The lawn requires at least 60 oz of
phosphates and 40 oz of nitrates. Which combination of the two brands should be used?
a. Translate the constraints into a system of inequalities.
b. Graph the system and label the vertices of the feasible set.
c. Apply the Linear Programming Theorem and interpret the results.
X

The 95% Confidence Interval for the mean number of defects per screen for all screens produced by this manufacturer is (1.447646, 2.352354)

Given Data:

3, 5, 0, 3, 5, 2, 5, 1, 0, 0, 0, 4, 2, 1, 0, 5, 1, 0, 1, 1, 0, 2, 0, 2, 1, 0, 2, 4, 4, 3, 2,

2, 3, 2, 1, 2, 1, 1, 4, 1, 1, 6, 0, 3, 1, 0, 2, 2, 1, 3

We calculate sample mean and standard deviation from given data.

Sample Mean, a = 2 (2) _ 95

-50

= 1.9

Sample Variance, $2 _ _(2 -x)2 _130.5

= 2.663265

n - 1

49

Sample std dev, s = V82 = v2.663265 ~ 1.631951

95% CI for u using Normal dist

Sample Mean = T = 1.9

Since sample size is large, sample standard deviation can be taken as an approx-

Limation of population standard deviation.

Population Standard deviation = o ~ 1.631951

Sample Size = n = 50

Significance level = 0 = 1- Confidence = 1 - 0.95 = 0.05

The Critical Value = za/2 = 20.025 = 1.96 (From z table)

Critical Values , 1za/2 = 41.96

Margin of Error = E = za/2 X -= 1.96 x 1.631951

0.452354

V50

Margin of Error, E = 0.

Limits of 95% confidence interval are given by:

Lower limit = I - E = 1.9 -0.452354 ~ 1.447646 ~ 1.448

Upper limit = I + E = 1.9 + 0.452354 ~ 2.352354 ~ 2.352

95% confidence interval is: T + E = 1.9 4 0.452354

= (1.447646, 2.352354)

95% CI using normal dist: (1.448 ) < < (2.352)

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Answer:

- 5/2 (z + 2)

Step-by-step explanation:

Distribute

- 7/2 z - 2 + z - 3

Subtract the numbers

- 7/2 z - 5 + z

Combine like terms

- 5/2 z - 5

Common factor

- 5/2 (z + 2)

Area of the base 'B' of a given rectangular prism is equal to 12 ft².

As given in the question,

For the given rectangular prism ,

Shape of the base is rectangle,

Length of the base of a rectangular prism = 4 ft

Width of the base of a rectangular prism = 3ft

Area of the base of a rectangular prism is given by

= ( length of the base ) × ( Width of the base)

Substitute the value of length and width of the base of the rectangular prism we get,

= ( 4 × 3 ) ft²

= 12 ft²

Therefore, area of the base 'B' of given rectangular prism is equal to 12 ft².

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Answer:

Step-by-step explanation:

the answer is 148 the reason is two angle interception

Step-by-step explanation:

The angle on top of x(x+4) is equal to 148.

The angle at x(x+4) = 180 -148 = 32

[tex]x(x + 4) = 32 \\ {x}^{2} + 4x = 32 \\ {x}^{2} + 4x - 32 = 0 \\ (x - 4)(x + 8) = 0[/tex]

x-4=0

x=4

x+8=0

x=-8

Using linear equation model, the change per week in the amount in the account is 20 dollars per week.

The starting amount of the money in the account is 350 dollars.

Omar is putting money into a checking account. y represent the total amount of money in the account (In dollars). x represent the number of weeks Omar has added money.

x and y are related with the equation y = 350 + 20x

The equation can be modelled to a linear equation.

Therefore,

y = mx + b

where

Therefore,  according to the equation, the change per week  in the amount if money is in the account is 20 dollars per week.  The slope is the rate of change.

The starting money amount of money in the account is the y-intercept of the equation which is 350 dollars

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Situations a and c can represent a proportional relationship. Options a and c are correct.

It is defined as the relationship between two quantities as one quantity increases the other quantity also increases and vice versa.

The following situations are found to represent proportionality using the concept of proportionality:

A) The total amount a babysitter makes who earns $10 an hour for babysitting r hours.

C) The total amount Andrew saves when he saves $24 a week for w weeks.

Thus, situations a and c can represent a proportional relationship. Options a and c are correct.

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The third congruent side is not included the side of angles thus it will be congruent by the AAS rule thus option (B) is correct.

If two figures are exactly the same in sense of their length side all things then they will be congruent.

In other meaning, if you can copy a figure then that copy and the original figure will be congruent.

As per the given two triangles,

The two angles are congruent.

The sides which are congruent in both triangles are not the common side of angles or not included in the side of angles thus it will be AAS congruency.

Hence "The third congruent side is not included the side of angles thus it will be congruent by the AAS rule".

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Choices made by consumer leads to financial irresponsibility are as follow:

As given in the question,

Choices made by consumer leads to financial irresponsibility are as follow:

When a person is spending money just on emotional feeling and buying large gifts for children which is beyond the budget. Due to this habits a person may have to take debt.

When a person is not saving enough money for the time of emergency, it can be a medical emergency then it is financial  irresponsible behavior.

When you are not making any budget and spending money ,it might possible at the end of the month or some time you have to face financial crises.

Don't compare yourself with anyone, this might lead you to take loan or debts which lead your life in facing financial trouble.

Therefore, choices made by consumer leads to financial irresponsibility are as follow:

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Answer:

Where the angle bisectors cross

Where the perpendicular bisectors cross

Explanation:

We can do cross multiplying through ratios:

310 feet / 10 secs = x feet / 12 secs

10x = 310 * 12

10x = 3720

x = 372 feet

OR

Divide 310 feet and 10 secs to get 31 feet in 1 sec

Multiply 31 ft and 1 sec to get 372 ft in 12 secs

The required expression is

(4/3)π(7)³

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

We are given to select the correct expression that gives the volume of a sphere with a radius of 7 units.

We know that,

the VOLUME of a sphere with radius 'r' units is given by

V=(4/3)πr³

Here, the radius of the given sphere is

r = 7 units.

Therefore, the volume of the sphere will be

V=(4/3)π(7)³

Thus, the required expression is

(4/3)π(7)³

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An equation to model this situation is M = t/3 + 3, which is shown in the graph attached below.

In order to solve this word problem, we would assign variables to the amount of time taken by Rick's bus ride and Matt's bus ride to school, and then translate the word problem into algebraic equation as follows:

Therefore, translating the word problem into an algebraic equation, we have the following;

M = 1/4(t) + 3

M = t/3 + 3

Based on the graph (see attachment) which models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride, we can logically deduce that the slope of the graph is 1/4 and the y-intercept is equal to 3.

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Answer:

-4/-5

Step-by-step explanation:

Gotchu bro

Answer:

4/5 or 0.8

Step-by-step explanation:

may i have the brainiest crown pls

Answer:

156

Step-by-step explanation:

36*3=108

8*-6=-48

108-(-48)=156

The solution of the expression 36(3) - 8(-6) will be 156.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 36(3) - 8(-6). the expression will be solved as below,

E = 36(3) - 8(-6)

E = 108 - ( -48 )

E = 108 + 48

E = 156

Hence, the solution will be 156.

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No, because it is plausible that she would make 3 or fewer shots by chance alone.

What is convincing evidence?

The proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent.

if our test statistic is: positive and greater than the critical value, then we have sufficient evidence to reject the null hypothesis and accept the alternative hypothesis. positive and lower than or equal to the critical value, we must accept the null hypothesis.

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Answer:

7x + 4,

8y - 3 > 13,

8a,

9 < 5x - 1

Step-by-step explanation:

Hello!

For this question it's important to know what form an expression takes, which is essentially a group of "things" (such as x, y, and numbers) that don't necessarily equal anything else, that would be an equation

In other words, an expression is a mathematical statement that does not include an = sign.

Answer:yesno

Step-by-step explanation:

yes

By the use of the law of conservation of mass, the mass of the aluminum chloride is  267 g.

We know that a chemical reaction occurs when there is the combination of two or more substances such that a new substances is formed. We have to put down the reaction equation in this case and we have;

[tex]4Al(s) + 3ZnCl_{2} (aq) ---- > 2Al_{2} Cl_{3}(aq) +3 Zn(s)[/tex]

Using the law of the combination of mass, the total mass of the reactants must be equal to the total mass of the products; Let the mass of the aluminum chloride formed be x

54 + 409.2 = 196.2 + x

x = (54 + 409.2) - 196.2

x = 267 g

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No, this solution is not valid because of wrong concept and wrong calculations as he solved  [tex]\frac{10^{-7} }{10^{-2} }[/tex]  as [tex]10^{-7 + (-2)}[/tex]  but it should be solved as [tex]10^{-7-(-2)}[/tex] .

These exponents can be split since they all share the same base, x. You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).

So according to it,

As they have same the base i.e. 10, we will subtract their power which would be like  [tex]10^{-7-(-2)}[/tex]  = [tex]10^{-5}[/tex] not the [tex]10^{-9}[/tex].

Hence, the solution is not valid due to the wrong concept and wrong calculations.

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Answer:

n = 8

Step-by-step explanation:

to solve this equation you must first isolate the variable

that is n

so first

add 2n to both sides to get rid of n on one of the sides

-4n + 2n + 14 = -2 - 2n + 2n

-2n + 14 = -2

now subtract 14 to both sides to isolate n

-2n + 14 - 14 = -2 - 14

-2n = -16

now divide everything by -2 to isolate n completely

(-2n)/(-2) = (-16)/(-2)

n = 8

that is your answer

Answer:

[tex]\boxed{\sf n=8}[/tex]

Step-by-step explanation:

[tex]\sf -4n+14=-2-2n[/tex]

Subtract 14 from both sides:-

[tex]\sf -4n+14-14=-2-2n-14[/tex]

Simplify:-

[tex]\sf -4n=-2n-16[/tex]

Add 2n to both sides:-

[tex]\sf -4n+2n=-2n-16+2n[/tex]

Simplify:-

[tex]\sf -2n=-16[/tex]

Divide both sides by -2:-

[tex]\sf \cfrac{-2n}{-2}=\cfrac{-16}{-2}[/tex]

Simplify:-

[tex]\sf n=8[/tex]

____________________

Hope this helps!

Have a great day!

Answer:

C

Step-by-step explanation:

Reciprocal functions have a general form of:

Let's see which of the given functions follow same form:

All the other functions are either linear or quadratic functions.

The amount after four years is £2649.79 .

Now we know that we need to obtain the rate for the compounding of the money and we need to recall that for the amount, we have;

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

A = amount

P = principal

r = rate

n = number of times compounded

t = time

For one year in which the interest is compounded annually;

2496.96 = 2448(1 + r)^1

2496.96/ 2448 = (1 + r)

1.02 = 1 + r

r = 1.02 - 1

r = 0.02 or 2%

Now after four years;

A = 2448(1 +  0.02)^4

A = £2649.79

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Answer:

13

Step-by-step explanation:

This is a special right triangle with side lengths 5-12-13 respectively.

If we can't remember the lengths we can use the following formula to calculate the lentgh of hypotenuse:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

the sum of square measure of both legs is equal to the square measure of hypotenuse

[tex] {5}^{2} + {12}^{2} = {c}^{2} [/tex]

25 + 144 = c^2

169 = c^2 find the root of both sides

13 = c, hypotenuse.

Part a:  The side of the square is found as 6 cm.

Part b: The side length of the square is found as 10 cm.

For the given dimensions for the question,

Part a: Area of square is same as area of rectangle.

Rectangle area = Length x breath

Rectangle area =  18 x 2

Rectangle area =  32 sq. cm

Now,

Area of square = Rectangle area

Area of square = side²

36 =  side²

side = √36

side = 6 cm.

Thus, the side of the square is found as 6 cm.

Part b: Side length of square.

Rectangle perimeter =  square perimeter

Rectangle perimeter =  2(length + width)

Rectangle perimeter =  2(18 + 2)

Rectangle perimeter =  40

square perimeter = 4 side

40 = 4 side

side = 40/4 = 10 cm.

Thus, the side length of the square is found as 10 cm.

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answer

microstates

Step by step explanation