Adirondack Savings Bank (ASB) has $5 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.(a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds.(b) How much (in dollars) should be allocated to each type of loan? 1) What is the total annual return (in dollars)?2) What is the annual percentage return?

Answer:

A

Step-by-step explanation:

Note: I suppose you typed the question wrong, thus I calculated the question in the picture

[tex]x = \frac{ - b + - \sqrt{{b}^{2} - 4ac} }{2} \\ = \frac{5 + - \sqrt{25 - 4 \times - 2 \times 1} }{2} \\ = \frac{5 + - \sqrt{25 + 8} }{2} \\ = \frac{5 + - \sqrt{33} }{2} [/tex]

The value of solution of quadratic function is,

⇒ x = (5 ± √33) / 2

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The quadratic function is,

⇒ x² - 5x - 2 = 0

Now, We can simplify as;

⇒ x² - 5x - 2 = 0

⇒ x = - (- 5) ± √(-5)² - 4×1×- 2 / 2

⇒ x = (5 ± √33) / 2

Thus, The value of solution of quadratic function is,

⇒ x = (5 ± √33) / 2

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Step-by-step explanation:

please type the question properly

Answer:

we need to factorise if imaginary number is in the denominator. no action is required if its in the numerator.

you can factorise an imaginary number by multiplying both the numerator and denominator by the conjuncate of the complex number

for instance,

we've given a complex number as follows

[tex] \frac{x}{3x + 4i} [/tex]

factorising

[tex] \frac{x}{3x + 4i} \times \frac{3x - 4i}{3x - 4i} [/tex]

as 3x -4i is the conjugate of 3x + 4i

and 4i is the imaginary number

[tex] \frac{ x(3x - 4i)}{9x {}^{2} - 4 {i}^{2} }[/tex]

and since i² = -1

[tex]\frac{ x(3x - 4i)}{9x {}^{2} + 4}[/tex]

hence factorised

Answer:

Percent who walk 45%

Percent in car 22.5%

Step-by-step explanation:

The total number of students is

36+26+18 = 80

Percent who walk is 36/80 = .45 =45%

Percent in car is 18/80 =.225= 22.5%

Answer:

Combine 4v_{5} and 2v_{5} to get 6v_{5}.

answer is a-circumcenter

The term that describes point J is Centroid.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Centroid:

The centroid is the point where the three medians of a triangle intersect.

A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

The centroid is also the center of mass of a triangle, and it is located two-thirds of the way along each median from the vertex to the midpoint of the opposite side.

Now,

From the figure,

We see that,

J is the point where the three medians of a triangle intersect.

Thus,

The term that describes point J is Centroid.

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Answer:

the number of students that enrolled after 15 year is 317

Step-by-step explanation:

The computation of the number of students that enrolled after 15 year is shown below;

We know that

Future value = Present value × (1 +rate of interest)^number of years

 = 100 × (1+8%)^15

= 100 × 1.08^15

= 317

Hence, the  number of students that enrolled after 15 year is 317

The same should be considered and relevant

Answer:

hat mather chosen to be mather

Answer:

x double bar = 4

LCL = - 2

UCL = 10

Step-by-step explanation:

The C - chart :

The control limit = xbar

xbar = mean = ΣX / n

The upper and lower control limit :

Xbar ± 3√xbar

Xbar = Σx / n = 100 / 25 = 4

Hence,

x double bar = 4

LCL = Xbar - 3√xbar = 4 - 3√4 = 4 - (3*2)

LCL = 4 - 6 = -2

UCL = Xbar + 3√xbar = 4 + 3√4 = 4 + (3*2)

LCL = 4 + 6 = 10

Answer: It's A.

You can see in the figure that:

BG=GD

<BGI=<OGD

GI=GO

Answer:

First table from left.

Step-by-step explanation:

Equal step of a half.

1,7

2,9

3,13

4,21

Step-by-step explanation:This is the linear function graph i plotted the points

Answer:

19.01%

Step-by- step explanation:

[tex]Percentage = \frac{1.35 billion }{ 7.1 billion } \times 100[/tex]

                [tex]= \frac{ 1.35 \ times 1, 000, 000, 000} {7.1 \times 1,000,000,000} \times 100\\\\\\=\frac{1.35}{7.1} \times 100 = 19.01 \%[/tex]

Answer:

The sequence converges to 1

Step-by-step explanation:

Given

[tex]\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},...[/tex]

Require

Description of the sequence

The given sequence follows:

[tex]\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},... \frac{n+1}{n+3}[/tex]

i.e.

[tex]T_n = \frac{n+1}{n+3}[/tex]

For every term,

[tex]\frac{n+1}{n+3} < 1[/tex]

In other words,

as the value of n increases, [tex]\frac{n+1}{n+3}[/tex] approaches 1

Hence, (c) is true

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

Answer:

X=2.

Step-by-step explanation:

3 times 2 is equal to 6, and 4 times 2 is equal to 8, 6+8=14.

Answer:

(8, 17)

Step-by-step explanation:

y= 3x -7 -----(1)

y= 2x +1 -----(2)

Substitute (1) into (2):

3x -7= 2x +1

Being x terms to one side, constant to the other:

3x -2x= 7 +1

x= 8

Substitute x= 8 into (2):

y= 2(8) +1

y= 16 +1

y= 17

∴ The solution is (8, 17).

Answer:

a. $0.13 / Ib.

Step-by-step explanation:

Slope of a line:

Suppose we have two data-points in a line. The slope is given by the change in the output divided by the change in the output.

In this question:

Input: weight(in pounds)

Output: Weekly cost to feed.

A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed.

Inputs: 0.5, 62.5

Outputs: 2, 10

Change in the outputs: 10 - 2 = 8

Change in the inputs: 62.5 - 0.5 = 62

Slope: [tex]m = \frac{8}{62} = 0.13[/tex]

So the correct answer is given by option A.

Answer:

0.13

Step-by-step explanation:

Step-by-step explanation:

everything can be found in the picture

Answer:

Non-linear

Step-by-step explanation:

While the difference in x terms remains constant at 1

The difference between y terms varies.

Answer:

Non-linear.

Step-by-step explanation:

Answer:

13.33

Step-by-step explanation:

Because it's only payment one we can easily figure out the interest portion

we first need the effective rate

.08/12= .006666667

We the just mulitply this by loan amount

2000*.006666667= 13.33

Step-by-step explanation:

its your answer

I hope it's help you

Mean = 24.47

Variance = 108.31

Standard deviation = 10.41

The probability distribution table has been attached to this response.

(1) To calculate the mean (m)

(a) First multiply each of the values of x by their corresponding probability values.

This is shown in the third column of the table.

(b) The sum of the results in the third column gives the mean of the distribution. i.e

m = ∑xP(x) = 11.52 + 9.36 + 3.15 + 0.44

m = 24.47

(2) To calculate the variance (σ²).

(a) First find the square of the difference between the values of x and the mean (m) calculated in (1b) above. i.e

(x - m)²

The result is shown in the fourth column of the table.

(b) Next, multiply each of the results in the fourth column (x - m)², by their corresponding probability values P(X = x). i.e

(x - m)²(P(X = x))

The result is shown in the fifth column of the table.

(c) Now find the variance (σ²) which is the sum of the results in the fifth column. i.e

σ² = ∑(x - m)²(P(X = x)) = 42.5411 + 0.8427 + 18.8330 + 46.0923

σ² = 108.3091

σ² = 108.31      [to 2 decimal places]

(3) To calculate the standard deviation (σ)

The standard deviation is the square root of the variance of the distribution. Calculate this by finding the square root of the result in (2c) above.

σ = √σ²

σ = [tex]\sqrt{108.31}[/tex]

σ = 10.4072

σ = 10.41        [to 2 decimal places]

Answer:

I did question no 2 , 4 , 5 , 6

from question attempt any two questions i did 4 and 5.

Step-by-step explanation:

Hope this helps u !!

Answer:

its answer is 3rd part

ABC-FED

Hey buddy I am here to help!

angle ABC = angle FED

Hope this answer helps!

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Answer:

The possible number that Hall could be thinking of is 144.

Step-by-step explanation:

Difference between 17 and the square root of my mystery number

This is represented by:

[tex]17 - \sqrt{x}[/tex]

is 5

Then:

[tex]17 - \sqrt{x} = 5[/tex]

What are two possible numbers that Hall could be thinking of?

We have to solve the equation, for x. So

[tex]17 - \sqrt{x} = 5[/tex]

[tex]\sqrt{x} = 12[/tex]

[tex](\sqrt{x})^2 = (12)^2[/tex]

[tex]x = 144[/tex]

The possible number that Hall could be thinking of is 144.

Answer:

If a point is reflected over the x-axis, the x- coordinate of the image remains the same as the pre-image and the y- coordinate is the opposite of the pre-image. ... If a point is reflected over both axes, both coordinates of the image are opposite of the pre-image.

Answer:

1. -4

Answer:

Question 1 = 256

Question 2 = ( 7, 8, 12)

Answer:

John attempted 500 passes this year

Step-by-step explanation:

To sum up the question, it is basically asking what number has 350 as 70% of it.

We know that:

350 is 70% of some number.

Convert 70% to fraction:

70% = 7/10

Divide:

350 ÷ 7/10 = 500

So 350 is 70% of 500

CHECK THE ANSWER:

10% of 500 is 50

To find 70% of 500, multiply:

50 x 7 = 350

I really hope this helps! Please ask me in case you’re confused.