You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house has a market value of $160,000. Your bank requires 1/5 of the market value as a down payment.
(a)
What is the amount (in $) of the down payment? $


(b)
What is the amount (in $) of the mortgage for which the Bradys are applying? $


(c)
Your bank offers the Bradys a 30-year mortgage with a rate of 5%. At that rate, the monthly payments for principal and interest on the loan will be $5.37 for every $1,000 financed. What is the amount (in $) of the principal and interest portion of the Bradys' monthly payment? $


(d)
What is the total amount (in $) of interest that will be paid over the life of the loan? $


(e)
Your bank also requires that the monthly mortgage payments include property tax and homeowners insurance payments. If the property tax is $1,710 per year and the property insurance is $1,458 per year, what is the total monthly payment (in $) for PITI (principal, interest, taxes, and insurance)? $


(f)
To qualify for the loan, bank rules state that mortgage payments cannot exceed 14 of the combined monthly income of the family. If the Bradys earn $3,750 per month, will they qualify for this loan?


Yes, they will http://qualify.
No, they will not qualify.


(g)
What monthly income (in $) would be required to qualify for this size mortgage payment? $

A) The number of cards that are in a complete deck of Set is; 81

B) The number of unique sets are; 36

a) We are given;

Number of shapes = 1, 2 or 3

Colour = Red, Purple or Green

Shape = Oval, Diamond or Squiggle

Shading = Hollow, Shaded or Striped

Now, since a set is formed by all 3 cards, then we can say that;

Number of cards in a complete deck of set = 3⁴ = 81 cards

(b) Let us first find all sets = 3² * 4 * 3 = 108.

Thus;

Unique sets = 108/3

= 36 unique sets.

(c) There are 3 ways to choose the number of the cards from the given order.  

For the second one, there 2 choices, and then there is only 1 choice.  Thus; Number of ways to choose the numbers = 3 * 2 * 1 = 6.  

For the other attributes;

Number of ways = 6 * 6 * 24 *6 ways.

Now, since the order of cards doesn't matter in a set, then the number of sets where all three cards are the same for exactly 0 attributes is;

(6 * 6 * 24 *6)/3! = 864 sets

(d) If all the colors are the same, then;

Number of sets = 6 * 24 * 6/3! = 144 sets.  

If all the numbers are the same, then there are 144 sets which is also same for shapes and shading. Thus;

The number of sets where all three cards are the same for exactly 1 attribute is; 4 * 144 = 576

(e) There are C(4, 2) = 6 ways of choosing two attributes.  

For each of the two attributes, there are 3 options.  

For the other two attributes, there are 3 ways of assigning the choices. Thus, number of sets = 6*3*3*3*3 = 486 sets.

(f) There are C(4,3) = 4 ways of choosing which attributes are the same.  There are 3*3*4 = 36 ways to assign which is which for each of these three attributes, and there are 4 ways to assign the choices for the fourth attribute. Thus;

The number of sets where all three cards are the same for exactly 3 attributes = 4*36*4 = 576 sets.

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The median of each of the sixteen​ samples, the sampling distribution of the medians are shown in the table.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have data:

40,40 40,45 40,47 40,53 45,40 45,45 45,47 45,53

47,40 47,45 47,47 47,53 53,40 53,45 53,47 53,53

We can find the sample mean, median, and probability:

sample median   probability   sample median      probability

40                                1/16                         46.5                          2/16

42.5                         2/16                        47                          1/16

43.5                                2/16                       49                          2/16

45                                1/16                          50                             2/16

46                              2/16                         53                             1/16

Thus, the median of each of the sixteen​ samples, the sampling distribution of the medians are shown in the table.

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Answer:

[tex]\huge\boxed{\sf y = -2x - 3}[/tex]

Step-by-step explanation:

m = -2

y = mx + c

(x,y) = (-5,7)

So, x = -5, y = 7

To find c, Put the values of x, y and m in the slope-intercept form.

7 = (-2)(-5) + c

7 = 10 + c

7 - 10 = c

-3 = c

c = -3

Now, put the values of m and c in the slope intercept form.

y = -2x - 3

[tex]\rule[225]{225}{2}[/tex]

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

The amount or the strength of force is called its magnitude.

Step-by-step explanation:

The amount or the strength of force is named magnitude.

Force is that the push or pull on an object with mass that causes it to alter its velocity. Force is an external agent capable of adjusting the state of rest or motion of a selected body. it's a magnitude and a direction.

The term which is true is magnitude. The magnitude of a force is expressed within the SI unit of force called Newton. 1 Newton is that the force which might make an object of 1 kilogram mass to  at a speed of 1 meter per second. Magnitude is essentially the most extent of size and also the direction of an object. Magnitude is employed as a typical think about vector and scalar quantities. Magnitude of earthquake is measured by Richter scale.

Hence the number or the strength of force is named its magnitude.

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How to determine whether or not the paired t test is appropriate for a two-sample hypothesis is: The  two samples are independent.

Two-sample hypothesis can be defined as  a test that is conducted on two samples  so as to determine whether the two samples are independent.

A  paired t-test is appropriate when the scores are of  equal subject or  equal variances.

Therefore how to determine whether or not the paired t test is appropriate for a two-sample hypothesis is: The  two samples are independent.

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Answer: 26

Step-by-step explanation:

to solve this series, we should find a pattern first.

if we look at the differences of each number, we can see that

4-1=3

8-4=4

13-8=5

19-13=6

to find the next number in the series, it would be 7 more than 19, since are counting upwards from 3.

Answer: 26

1 to 4 is 3

4 to 8 is 4

8 to 13 is 5

13 to 19 is 6

the next number should be 26

Combine like terms: [tex]6x^{3}[/tex] and [tex]4x^{3}[/tex] make [tex]10x^{3}[/tex]. At that point, disentangle constants: -8 + 6 rise to -2. Result:[tex]10x^{3} - 2x^{2} + 9x - 2[/tex].

To simplify the given expression, take after the arrangement of operations (PEMDAS/BODMAS):

Given expression: [tex]6x^{3} - 2x^{2} + 9x - 8 + 4x^{3} - 2x + 6[/tex]

Step 1: Combine like terms (terms with the same variable and example):

[tex]6x^{3} + 4x^{3} = 10x^{3}[/tex]

Step 2: Combine the steady terms:

-8 + 6 = -2

The expression presently gets to be:

[tex]10x^{3} - 2x^{2} + 9x - 2[/tex]

So, the disentangled expression is [tex]10x^{3} - 2x^[2} + 9x - 2.[/tex]

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The complete question:

Simplify the expression:

6 x 3-2x2+9x-8+4x3-2x+6

Answer:

b

Step-by-step explanation:

The effective elements to include in the introductions are statement of the topic, a relevant anecdote and a surprising fact about the topic. Therefore the option 1st, 2nd and 6th options are correct.

Introduction is the starting line or the opening hook or portion that attracts the readers attention which carries the relevant background of the information.

It is the statement which represents the main point of the following argument or the paragraphs.

There are many elements that included in the introductory part some of them are as follows:-

Therefore the option 1st, 2nd and 6th options are correct.

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Answer:

The first two, the fourth, and the last one are correct

Step-by-step explanation:

it just is.... so yeah

The standard deviation is 3.807.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

Given:

variance= 14.5

standard deviation = √variance

                               = √14.5

                              = 3.807

Hence, the standard deviation is 3.807.

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The dimensions of the circular cylinder of maximum volume inscribed in  sphere is r = 20.4 cm , h = 28.86 cm.

A sphere is a three dimensional round shaped figure , It has no vertices and the distance form the centre to any point on the sphere is same.

It is given that

A right circular cylinder is inscribed in a sphere

The circular cylinder has the maximum volume

Radius of the sphere is 25 cm.

Dimensions of the cylinder = ?

As it is a right cylinder.

The Pythagoras theorem can be applied

r² + (h/2)² = 25²

r² = 625 - h²/4

volume of the cylinder

=  πh(625 - h²/4)

= π(625 h - h³/4)

As the volume is maximum ,

so the derivative of the expression = 0

π(625 - 3h²/4) = 0

so h =  50 /√ 3

so r² = 625 - 2500 / (3 *4 )

r = 20.4 cm

h = 28.86 cm

Therefore the dimensions of the circular cylinder of maximum volume inscribed in a sphere is r = 20.4 cm , h = 28.86 cm.

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Hi !

[tex]f(x) = \frac{4}{x - 9} [/tex]

[tex]x-9[/tex] must be different from 0.

[tex]x -9 \ne0 \\ x \ne9[/tex]

[tex] = = > \: D_f=\mathbb{R}-\{9\}[/tex]

Have a nice day ;)

Answer:

There are 5 turning points

Step-by-step explanation:

The Income Statements under Absorption Costing and Variable Costing are as follows:

                                                       Absorption Costing     Variable Costing

Sales (19,500 units)                              $2,145,000               $2,145,000

Cost of goods sold                                $1,491,750               $1,365,000

Gross profit                                            $653,250                 $780,000

Selling and administrative expenses:

Fixed factory overhead                                          $162,500

Variable selling and

 administrative expenses    $296,400                  296,400

Fixed selling and

 administrative expenses       114,800    411,200    114,800   573,700

Net Income                                          $242,050                $206,300

The difference between Absorption Costing and Variable Costing is that the Ending Inventory costs under Variable Costing include only direct materials, direct labor, and variable factory overhead.  Absorption Costing includes all the variable factory costs plus fixed factory overhead (a period cost) in the Ending Inventory costs.

Sales (19,500 units)                              $2,145,000

Production costs (25,000 units):

Direct materials                $1,017,500

Direct labor                          487,500

Variable factory overhead 245,000

Fixed factory overhead       162,500

Total production costs      1,912,500

Cost per unit = $76.50 ($1,912,500/25,000)

Less Ending inventory        420,750               (5,500 x $76.50)

Cost of goods sold                              $1,491,750

Gross profit

Selling and administrative expenses:

Variable selling and administrative expenses $296,400

Fixed selling and administrative expenses 114,800 411,200

Sales (19,500 units)                              $2,145,000

Production costs (25,000 units):

Direct materials                $1,017,500

Direct labor                          487,500

Variable factory overhead 245,000

Total variable production costs  1,750,000

Cost per unit = $70 ($1,750,000/25,000)

Less Ending inventory       385,000               (5,500 x $70)

Cost of goods sold                              $1,365,000

Gross profit

Selling and administrative expenses:

Variable selling and

administrative expenses $296,400

Fixed factory overhead       162,500

Fixed selling and administrative expenses 114,800 411,200

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Answer:

y = 20°

x = 35°

Explanation:

Equation's:

   1) 2y + x + 105° = 180°

   2) 3x + x + 2y = 180°

Make y subject in equation 2

3x + x + 2y = 180

4x + 2y = 180

2y = 180 - 4x

y = 90 - 2x

Insert this into equation 1

2(90 - 2x) + x + 105° = 180°

180 - 4x + x + 105 = 180

-3x = -105

x = 35°

Find value of y

y = 90 - 2x

y = 90 - 2(35)

y = 20°

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{67 + x = 90^\circ}[/tex]

[tex]\mathsf{x+ 67 = 90^\circ}[/tex]

[tex]\large\textsf{SUBTRACT 67 to BOTH SIDES}[/tex]

[tex]\mathsf{x + 67 - 67 = 90^\circ - 67}[/tex]

[tex]\large\textsf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = 90 - 67}[/tex]

[tex]\mathsf{x = 23}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{x = 23}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

300

Step-by-step explanation:

if its 1:1 ratio, then its the same and so if there 300 bean seeds, there has to be 300 groundnut seeds

Rate of change for Function A is: 35

Rate of change for Function B is: 50

Difference is: 15.

Rate of change = change in y / change in x.

The graph for function B is a proportional graph, therefore, rate of change = y/x.

Using a point on the line, (1, 50), rate of change for function B = 50/1 = 50.

Function A is given as y = 35x. Rate of change, is 35.

The difference = 50 - 35 = 15.

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The coordinates of B is (-2, 3).

In geometry, translation is the movement of a point or shape from one position to another.

Here, The translation from ΔABC to ΔA'B'C' is (x, y) → (x + a, y + b)

Now, given coordinate

A ≡ (5, 1)      ⇒       A' ≡ (6, -2)

                             A' ≡ (1+5, 1 - 3)

                      On comparing this coordinate with translation coordinate

                       (x + a, y + b), we get

                          a = 1 and b = -3

Now translation coordinates is (x + 1, y - 3),

Now, Another coordinate;

B' ≡ (-1, 0)                   and the coordinate of B ≡ (x, y)

B' ≡ (-2+1, 3-3)

On comparing this coordinate with translation coordinate (x + 1, y - 3), we get

x = -2 and y = 3

Thus, the coordinates of B is (-2, 3).

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The answer to the question has to be filled into the blank as

This is described as the likelihood of the test correctly rejecting the null hypothesis on the basis that the alternative hypothesis is correct.

This question requires us to fill in the blank with the details that we have been given.

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Answer:

184cm²

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Divide the figure into two parts,

Part 1 : rectangle with, width = 7 cm and length = 20 cm

Area of part 1 :

[tex] \qquad❖ \: \sf \:20 \times 7[/tex]

[tex] \qquad❖ \: \sf \:140 \: \: {cm}^{2} [/tex]

Part 2 : Trapezoid with parallel sides - 7 cm and 4 cm,and height 8 cm

Area of part 2 :

[tex] \qquad❖ \: \sf \: \cfrac{1}{2} \cdot (7 + 4) \sdot(8)[/tex]

[tex] \qquad❖ \: \sf \:11 \times 4[/tex]

[tex] \qquad❖ \: \sf \:44 \: \: {cm}^{2} [/tex]

Area of whole figure =Area of part 1 + part 2

[tex] \qquad❖ \: \sf \:140 + 44 \: \: {cm}^{2} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \qquad❖ \: \sf \:area =184\: \: {cm}^{2} [/tex]

Answer:

12

Step-by-step explanation:

First solve the inside brackets.

[tex]3[6-(+2)]=3[6-2]\\\\=18-6\\\\=12[/tex]

Using the normal distribution, it is found that there is a 0.3192 = 31.92% probability that 20 customers will wait an average of less than 21 minutes to be seated.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 23.8, \sigma = 6, n = 20, s = \frac{6}{\sqrt{20}} = 1.3416[/tex]

The probability that 20 customers will wait an average of less than 21 minutes to be seated is the p-value of Z when X = 21, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{21 - 23.8}{6}[/tex]

Z = -0.47

Z = -0.47 has a p-value of 0.3192.

0.3192 = 31.92% probability that 20 customers will wait an average of less than 21 minutes to be seated.

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The lower class boundary for the third class is 0.50.

The lower class boundary of a class can be determined by calculating the average the upper limit of the previous class and the lower limit of the given class.

The lower class boundary = ( 1296 - 1295) / 2 = 0.50

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Answer:

the area of a square garden 3136cm what is the length of one side

In this problem, we're given an angle and two sides. Therefore, we should use a trigonometric function to solve for x.

Remember! SOH-CAH-TOA

We are given a 26 degree angle, looking from which we have the adjacent side and the hypotenuse. As such, we should use the cosine function.

cos(26) = x / 69

x = cos(26) * 69

x = 62.0168

x = 62.0

Hope this helps!

Step-by-step explanation:

Answer:

The third answer is correct.

Step-by-step explanation:

Answer:

[tex]82 = 525y2 \times 6112 =[/tex]

The perimeter of the hexagon is 180 ft.

The area of the hexagon is 2338.3 ft

The perimeter of the polygon can be found as follows:

The polygon is a regular hexagon.

Therefore,

perimeter of the hexagon = 30 × 6 = 180 ft

Area of the hexagon = 3√3 / 2 × s²

where

Therefore,

Area of the hexagon = 3√3 / 2 × 30²

Area of the hexagon =  3√3 / 2 × 900

Area of the hexagon = 450 × 3√3

Area of the hexagon = 2338.26859022

Area of the hexagon = 2338.3 ft

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