the kenya agricultural research insistute suggested to a farmer to spread out at least 4800kg of a special phosphate and not less than 7200kg of a nitrogen fertilizer to raise productivity of crops in his fields. there are two sources to obtain these mixtures A and B. both of these are available in bags weighing 100 kg each and they cost 116, 400 respectively, while mixture B contains these ingredients equivalent to 50kg each. determine how many bags of each type the farmer should buy in order to obtain the required fertilizer at minimum cost.

Answer:

10000

Step-by-step explanation:

Answer:

1000

Step-by-step explanation: just add 100 100 times

9514 1404 393

Answer:

  29.15 in

Step-by-step explanation:

The area of a rectangle is given by the formula ...

  A = LW

Filling in the given information, we can find the missing side length.

  297 in² = (27 in)h

  h = (297 in²)/(27 in) = 11 in

The length of the diagonal can be found from the Pythagorean theorem.

  d² = 27² + 11² = 729 +121 = 850

  d = √850 = 5√34 ≈ 29.15476

The length of the diagonal is about 29.15 inches.

Answer:

54 lol not 40 its 20

Step-by-step explanation:

When applying a loan, Collateral can be beneficial to the borrower because:   (C). giving lenders protection against financial loss and more reason to approve loans

Loan is a form of debt incurred by an individual as a result of recieving money from an individual or organization that will repaid within a definite period.

collateral can be defined as any asset (example: car, house, land etc) that is offered by the borrower to the lender to secure a loan.

it is very important because the lender is secured that if you cant repay the loan he takes the asset.

In conclusion, when taking a loan, collateral is important.

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1: \(3n^{2}+9n+6\)

notice that each part is divisible by 3

\(3n^{2}\) ÷ 3 = \(n^{2}\)

9n ÷ 3 = 3n

6 ÷ 3 = 2

so it becomes \(3(n^{2} +3n+2)\)

3n can be rewritten as 2n+n

-you want to rewrite it into two numbers that multiply to the number that's alone (in this case 2)

which would get you

\(3(n^{2} +2n+n+2)\)

Now that it's rewritten, you can factor out n + 2 from the equation.

the answer is

3(n+2)(n+1)

And you can check that by multiplying (n+2)(n+1) which is \(n^{2} +2n+n+2\) and then each of those by 3, which is \(3n^{2} +6n+3n+6\) or \(3n^{2}+9n+6\), our origional equation

2: \(28+x^{2} -11x\)

So I rewrote this as \(x^{2} -11x+28\) (it's the same thing, just reordered using the commutative property)

now -11x can be rewritten as -4x-7x

(remember, the two numbers should multiply to equal 28, which is our constant.)

\(x^{2} -4x-7x+28\)

now we can factor out x from the first expression and -7 from the second

\(x(x-4)-7(x-4)\)

and lastly you factor out x-4,

which would give you

(x-4)(x-7)

Make sure to check your work and make sure it multiplies to \(x^{2} -11x+28\)

3: \(9x^{2} -12x+4\)

The first thing I notice when looking at this problem is that both 9 and 4 are perfect squares. Not only that, but they are the squares of 2 and 3, which are products of -12

So if you rewrite 9 as \(3^{2}\) and 4 as \(2^{2}\), the equation becomes

\(3^{2} x^{2} -12x+2^{2}\)

now that \(3^{2} x^{2}\) is ugly so it can be turned into \((3x)^{2}\)

and -12x can be rewritten as \(-2*3x*2\)

so our equation now looks like \((3x)^2-2*3x*2+2^{2}\)

There's a rule that says \(a^{2} -2ab+b^{2} = (a-b)^{2}\)

In our case, a=3x and b=2

so the final answer is

\((3x-2)^2\)

Answer:

Decreased by 19%.

-------------------------------

Decrease by of x 10% can be shown as a product of x and:

Same applies to the second decrease, then we get a final number:

It represent a one off decrease of:

Hence the answer is 19%.

Answer:

Step-by-step explanation:

100 - 100/10 = 90

90 - 90/10 = 91

100 - 81 = 19%

for a better understanding look at the figure

Answer:

(-5, -1)

General Formulas and Concepts:

Algebra I

Functions

Graphing

Solving systems of equations by graphing

Step-by-step explanation:

Where the 2 equations intersect is the solution to the systems of equations.

The circumference of a circle can be found using formula 2πr where r is the radius of circle.

What is the circumference of a circle?

A circle's or an ellipse's circumference is its perimeter. The circumference would be the length of the circle's arc, if the circle were opened up and straightened out to a line segment, in other words.

Suppose the radius of a circle is 5cm

So, we can find the circumference by using formula 2πr

     Circumference = 2 × π × 5 = 10π cm.

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Answer:

a) the mean percentage of defective item produced is 2.52 %

b) the standard deviation of percentage of defective item produced is 1.01%

Step-by-step explanation:

Given that;

the percentage of defective items produced was 2%, 1.4%, 4%, 3%, 2.2%.

sample size n = 5

a) Calculate the mean for these data

mean percentage of defective item produced will be;

\(x^{bar}\) = ∑x / n

\(x^{bar}\) = ∑x / n = ( 2% + 1.4% + 4% + 3% + 2.2% ) / 5

\(x^{bar}\)  = 12.6 / 5

\(x^{bar}\)  = 2.52 %

Therefore, the mean percentage of defective item produced is 2.52 %

b) Calculate the standard deviation for these data

Formula for standard deviation is;

S = √( (∑(x-\(x^{bar}\) )²) / (n-1) )

so we make a table;

x                   ( x - \(x^{bar}\) )%                ( x - \(x^{bar}\) )²%

2%                 -0.52                         0.2704

1.4%               -1.12                           1.2544

4%                  1.48                          2.1904  

3%                  0.48                         0.2304

2.2%.             -0.32                         0.1024

summation                                     4.048

so (∑(x-\(x^{bar}\) )² = 4.048%  

so we substitute the value into our equation;

S = √( (∑(x-\(x^{bar}\) )²) / (n-1) )

S = √( (4.048%) / (5-1) )

S = √( 4.048% / 4 )

S = √( 1.0121

S =  1.00598 % ≈ 1.01%

Therefore, the standard deviation of percentage of defective item produced is 1.01%

Answer:

See explanation. (I just sumbitted this exact assignment this morning, and i submitted something very similar to the example below!)

Step-by-step explanation:

The contrapositive of a conditional is the same as the converse of the inverse of the conditional.

The best way to prove/support this statement is to create an example. You should start by creating a conditional; you can then form the conditional's converse, inverse, and contrapositive. Here is an example:

Conditional: If C, then D. (starting statement)

Converse: If D, then C. (conditional reversed)

Inverse: If not C, then not D. (opposite of the conditional)

Contrapositive: If not D, then not C. (reversed opposite of the conditional)

Based on the information from the example you gave, you can conclude:

The converse of the inverse: If not D, then not C. (reversed opposite of the conditional)

Because: The converse is the conditional reversed (If D, then C). The inverse of the converse, in this case, would then make it the opposite (If not D, then not C).

I have not yet received a grade on this assignment, but I know the information is correct; the amount of explanation you need to give really depends on how your teacher grades. Personally, I just submitted an example (similar to the one above) that was color-coded to help show the different parts of each statement.

I hope this helps! :)

Answer: 853

Step-by-step explanation:

According to the Angle Addition Postulate, the measure of m∠ABD = 202°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠ABC=37°,

and m∠⁡C⁣B⁣D= 165⁢°.

So, according to the angle addition postulate;

m∠ABD = m∠ABC + m∠CBD

Substituting the values,

m∠ABD = 37° + 165⁢°

m∠ABD = 202°

Therefore, the angle measure of m∠ABD = 202°.

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The inequality that describes the problem is,

⇒ x + $49.95 < $120

Where, x represent the cost of the headset.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

Allie planned to spend up to $120 on a gaming mouse and headset. She spent $49.95 on a mouse.

Let x represent the cost of the headset.

Hence, We can formulate;

The inequality that describes the problem is,

⇒ x + $49.95 < $120

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Answer:

predictive value of a positive test = 18.18%

predictive value of a negative test = 94.03%

Step-by-step explanation:

Sensitivity = 60% = 0.6

Specificity = 70% = 0.7

Let True Positive = TP

True Negative = TN

False Negative = FN

\(Sensitivity = \frac{TP}{TP + FN} \\0.6 = \frac{TP}{TP + FN} \\0.6TP + 0.6FN = TP\\0.4TP = 0.6FN\\TP = 1.5 FN\)

\(Specificity = \frac{TN}{TN + FP} \\0.7 = \frac{TN}{TN + FP} \\0.7TN + 0.7FP = TN\\0.7FP = 0.3 TN\\TN = 7/3 FP\)

Prevalence = 10% = 0.1

Three hundred people are screened, \(T_{total} = 300\)

Total number of people having the disease, \(T_{disease} = ?\)

\(Prevalence = \frac{T_{disease} }{T_{total} } \\0.1 = \frac{T_{disease} }{300 }\\T_{disease} = 30\)

\(T_{disease} = TP + FN\\30 = TP + FN\)

But TP = 1.5 FN

30 = 1.5 FN + FN

30 = 2.5 FN

FN = 30/2.5

FN = 12

TP = 1.5 FN = 1.5 * 12

TP = 18

\(FP + TN = T_{total} - T_{disease} \\FP + TN = 300 - 30\\FP + TN = 270\\FP + \frac{7}{3} FP = 270\\\frac{10}{3} FP = 270\\FP = 27 * 3\\FP = 81\)

81 + TN = 270

TN = 189

To calculate the Predictive value of positive test (PPT)

\(PPT = \frac{TP}{TP + FP} * 100\\PPT = \frac{18}{18+81} * 100\\PPT = \frac{18}{99} * 100\\PPT = 18.18 \%\)

To calculate the Predictive value of negative test (PNT)

\(PPT = \frac{TN}{FN + TN} * 100\\PPT = \frac{189}{189+12} * 100\\PPT = \frac{189}{201} * 100\\PPT = 94.03 \%\)

Based on these considerations, it is necessary to assess the specific layout plan and the surrounding environment to determine whether the copier is suitably placed in room (3) at Hills Secondary.

To determine whether the copier is suitably placed in room (3) at Hills Secondary, we need to consider factors such as accessibility, noise, and convenience.

Firstly, we need to evaluate the accessibility of the copier in room (3). Is it easily accessible for all students and staff who need to use it? If the copier is located in a central position within the school or close to high-traffic areas, it would be considered suitable.

However, if it is tucked away in a corner or not easily visible, it may cause inconvenience and hinder access for users.

Secondly, we should consider noise levels. Copiers can be noisy machines, and if room (3) is located near classrooms or areas where students require a quiet environment, it may not be an ideal placement. Noise disturbances could disrupt learning activities and cause distractions.

Lastly, convenience plays an important role. Room (3) should be spacious enough to accommodate the copier and allow users to operate it comfortably. If the room is cramped or lacks proper ventilation, it may cause inconvenience for users and impact the overall workflow.

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$5000 would grow to $10,000 in 60 years

In order to determine the number of years it would take for $5000 to double, the rule of 72 can be used.

The rule of 72 is a rule of thumb that is used to determine the number of years it would take for the money in an account to double given the interest rate.

Rule of 72 = 72 / interest rate

72 / 1.2 = 60 years

In order to determine the number of years it would take $5,000 to grow to $10,000 in an account that yields 1.2% interest, divide 72 by the interest rate.

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Answer:

2/3pix³ or \(\frac{2}{3} \pi x^3\\\)

Step-by-step explanation:

This problem brothers on the mensuration of solid shapes, a cone.

we know that the expression for the volume of a cone is

\(volume= \frac{1}{3} \pi r^2h\)

let the radius r of the cone be= \(x\)

and the height h is =\(2x\)

we can now solve the expression that represents the volume of the cone, in cubic  units.

\(volume= \frac{1}{3} \pi *x*2x\\\volume= \frac{1}{3} \pi *2x^3\\\volume= \frac{2}{3} \pi x^3\\\)

Answer:

Lets suppose total number of tickets=X

so, 45= 60/100× X

X = 75

so total number of tickets are 75 therefore 75-67.5= 7 tickets have been sold

a) The probability that the computer will be fixed by either A or B is 58%.

b) The probability that it was fixed by B is 57.14%

Given data:

a)

To find the probability that the computer will be fixed by either A or B, we can use the principle of addition for probabilities.

The probability that A can fix the computer is 30% or 0.30, and the probability that B can fix the computer if A cannot is 40% or 0.40.

Therefore, the probability that either A or B can fix the computer is the sum of these probabilities:

P(A or B) = P(A) + P(B if A cannot) = 0.30 + (0.70 * 0.40) = 0.30 + 0.28 = 0.58

Therefore, there is a 58% probability that the computer will be fixed by either A or B.

b)

Let's denote event A as A fixing the computer and event B as B fixing the computer.

P(A) = 0.30 (probability A can fix the computer)

P(B|A') = 0.40 (probability B can fix the computer given that A cannot)

To find P(B|A), the probability that B fixes the computer given that it was fixed, use Bayes' theorem:

P(B|A) = (P(A|B) * P(B)) / P(A)

Since the computer is fixed, P(A) + P(A') = 1, so P(A) = 1 - P(A') = 1 - 0.30 = 0.70

P(B|A) = (P(A|B) * P(B)) / P(A)

P(B|A) = (1 * 0.40) / 0.70

P(B|A) = 0.40 / 0.70

P(B|A) ≈ 0.5714

Hence, if the computer is fixed, there is a 57.14% probability that it was fixed by B.

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Answer:

5.421 > 5.4

Step-by-step explanation:

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer:

ehfyuehruerfgr

Step-by-step explanation:

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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Both the domain and range of the transformed function are the same as those of the parent function.

What are Range and Domain?

The collection of all potential output values that a function can generate given its domain is known as its range.

The set of all potential input values for which a function is specified is referred to as its domain.

The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.

Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.

A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.

Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.

A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well

So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.

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Answer:

(1) The point estimate for the population mean is 4.925.

(2) Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

(3) Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

(4) As the level of confidence increases, the width of the interval increases.

Step-by-step explanation:

We are given that the following data represent the pH of rain for a random sample of 12 rain dates.

X = 5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68.

(1) The point estimate for the population mean is given by;

Point estimate, \(\bar X\) = \(\frac{\sum X}{n}\)

                            = \(\frac{5.20+5.02+ 4.87+5.72+ 4.57+ 4.76+4.99+ 4.74+ 4.56+ 4.80+5.19+ 4.68}{12}\)

                            = \(\frac{59.1}{12}\)  = 4.925

(2) Let \(\mu\) = mean pH of rainwater

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~  \(t_n_-_1\)

where, \(\bar X\) = sample mean = 4.925

             s = sample standard deviation = 0.33

            n = sample of rain dates = 12

            \(\mu\) = population mean pH of rainwater

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, \(\mu\) is ;

P(-2.201 < \(t_1_1\) < 2.201) = 0.95  {As the critical value of t at 11 degrees of

                                               freedom are -2.201 & 2.201 with P = 2.5%}  

P(-2.201 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 2.201) = 0.95  

P( \(-2.201 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(2.201 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

P( \(\bar X-2.201 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+2.201 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

95% confidence interval for \(\mu\) = [ \(\bar X-2.201 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+2.201 \times {\frac{s}{\sqrt{n} } }\) ]

                                      = [ \(4.925-2.201 \times {\frac{0.33}{\sqrt{12} } }\) , \(4.925+2.201 \times {\frac{0.33}{\sqrt{12} } }\) ]  

                                     = [4.715, 5.135]

Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

The interpretation of the above confidence interval is that we are 95% confident that the population mean pH of rainwater is between 4.715 & 5.135.

(3) Now, 99% confidence interval for the population mean, \(\mu\) is ;

P(-3.106 < \(t_1_1\) < 3.106) = 0.99  {As the critical value of t at 11 degrees of

                                               freedom are -3.106 & 3.106 with P = 0.5%}  

P(-3.106 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 3.106) = 0.99

P( \(-3.106 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(3.106 \times {\frac{s}{\sqrt{n} } }\) ) = 0.99

P( \(\bar X-3.106 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+3.106 \times {\frac{s}{\sqrt{n} } }\) ) = 0.99

99% confidence interval for \(\mu\) = [ \(\bar X-3.106 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+3.106 \times {\frac{s}{\sqrt{n} } }\) ]

                                     = [ \(4.925-3.106 \times {\frac{0.33}{\sqrt{12} } }\) , \(4.925+3.106 \times {\frac{0.33}{\sqrt{12} } }\) ]  

                                     = [4.629, 5.221]

Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

The interpretation of the above confidence interval is that we are 99% confident that the population mean pH of rainwater is between 4.629 & 5.221.

(4) As the level of confidence increases, the width of the interval increases as we can see above that the 99% confidence interval is wider as compared to the 95% confidence interval.

Answer:

4x\(\sqrt{6x}\)

Step-by-step explanation:

This can be written:

\(\sqrt{(3)(2)(2)(2)(2)xxx}\)  Pull out all the pairs. There are 2 pairs of 2 and 1 pair of x's

(2)(2)x\(\sqrt{(3)(2)x}\)  Clean up

4x\(\sqrt{6x}\)

Answer:

Personal Identification Number

Answer:

P.Personal

I .Identification

N . Number