PART III
You operate a local mortgage & loan business with two other partners. Your role is to adjust
the prime interest rate for variable & fixed mortgages for your customers, as well as deal
with the length of a mortgage.
1. A client comes in looking to apply for a mortgage, but does not have any prior knowledge.
Answer the following questions to help them decide which type of mortgage to get.
(a) At most banking institutions, there are two types of mortgages available: fixed
mortgages and variable mortgages. Describe the difference between the two main
types of mortgages. Give one positive and one negative aspect of each type of
mortgage
(b) Banks will often advertise interest rates using the terminology prime plus/minus
percent. For example, if prime is 1.5%, then 2.5% might be advertised as prime plus
1%. Express 1.45% and 4.35% using the terminology of prime plus/minus percent
using Canada's current prime interest rate.
2. How many years will it take for your client to pay off a mortgage of $250,000 if he makes
month-end payments of $1,500? Assume a fixed interest rate of prime minus 0.5% over
the term of the whole mortgage. You may answer either by hand, or using the calculators
TVM buttons. If you use the calculator, ensure you write down all of your inputs for
full marks. No time diagram is necessary.
3. Your client borrows $250,000 and agrees to pay $1,500 at the end of every month for
a 5-year term. At the end of years, there is $200,000 remaining on the mortgage.
Use the calculator's TVM buttons to determine the fixed interest rate on this mortgage
(you will be unable to do this any other way). Write down all of your inputs, paying
careful attention to negative signs, for full marks. Express your final answer using prime
plus/minus terminology. No time diagram is necessary

Answer:

try b

Step-by-step explanation:

Answer:

The answer is A. g(x) = f(x) + 4

Answer:

1000000000000000005

Answer:

1000000000000005

Step-by-step explanation:

Answer:

the last one is an increase of $.22

Step-by-step explanation:

the last one is an increase of $.22

Answer:

Ai. Common ratio = 2/3

Aii. First term = 54

B. Sum of the first five terms = 422/3

Step-by-step explanation:

From the question given above, the following data were obtained:

3rd term (T3) = 24

6Th term (T6) = 64/9

First term (a) =?

Common ratio (r) =?

Sum of the first five terms​ (S5) =?

Ai. Determination of the common ratio (r).

T3 = ar²

T3 = 24

24 = ar²....... (1)

T6 = ar⁵

T6 = 64/9

64/9 = ar⁵......... (2)

The equation are:

24 = ar²....... (1)

64/9 = ar⁵......... (2)

Divide equation 2 by equation 1.

64/9 ÷ 24 = ar⁵ / ar²

64/9 × 1/24 = r³

8/27 = r³

Take the cube root of both side

r = 3√(8/27)

r = 2/3

Thus, the common ratio is 2/3

Aii. Determination of the first term (a).

T3 = ar²

3rd term (T3) = 24

Common ratio (r) = 2/3

First term (a) =?

24 = a(2/3)²

24 = 4a/9

Cross multiply

24 × 9 = 4a

216 = 4a

Divide both side by 4

a = 216/4

a = 54

Thus, the first term (a) is 54

B. Determination of the sum of the first five terms.

Common ratio (r) = 2/3

First term (a) = 54

Number of term (n) = 5

Sum of first five terms (S5) =?

Sn = a[1 –rⁿ] / 1 – r

S5 = 54[1 – (⅔)⁵] / 1 – ⅔

S5 = 54 [1 – 32/243] / ⅓

S5 = 54 (211/243) × 3

S5 = 54 × 211/81

S5 = 6 × 211/9

S5 = 2 × 211/3

S5 = 422/3

Thus, the sum of the first five terms is 422/3

Answer: 16

Step-by-step explanation:

All you have to do is plug 3.2 into the expression. So 5 * 3.2  is 16.

Answer: 4,405.66

Step-by-step explanation:

Add all the amounts together.

Answer:

$22.5

Step-by-step explanation:

10 kg=$4.50

50kg = x

(do cross multiplication)

10x =225

x=$22.5

Answer:

i don`t understand you

Step-by-step explanation:

but i think i phone...?

Answer:

ummm there is no other context did you mean to post a picture? All I could find was this

The Apple User Group Connection (AUGC) was established in 1985 by Apple and led by Apple employee Ellen Petry Leanse.

The probability that a randomly selected camper likes to have a cookout or swimming, but not both, is 0.10.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

The Venn diagram displays the campers’ preferences.

One circle is labeled S, 0.06,

the other circle is labeled C, 0.04,

the shared area is labeled 0.89,

and the outside area is labeled 0.01.

The probability that a randomly selected camper likes to have a cookout or swimming, but not both,

= 0.06 + 0.04

= 0.10

Therefore, 0.10 is the required probability.

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Let x be -b/2a

x = -193/2•(-16)

x = -193/-32

x = 6.03125

Now, plug this value of x into every x in the function and simplify. The max is the y value.

Can you finish?

The time at which the rocket will hit the ground to the nearest hundredth of seconds is 13 seconds.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

As per the given height of tower y in terms of time is seconds x

y = -16x² + 193x + 128

The height of the tower when the rocket hit the ground will be zero.

Thus, y = 0

0 = -16x² + 193x + 128

16x² - 193x - 128=0

By quadratic equation formula,

x = [-(-193) ± √((-193)²-4×16×(-128))]/ 2×16

x = [193 ± 213.168]/32

x = 12.69 and x = -0.63 since time can be never negative thus 12.69 seconds will be correct.

12.69 to the nearest hundred is 13.

Hence "The time at which the rocket will hit the ground to the nearest hundredth of seconds is 15 seconds".

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Answer:

a

Step-by-step explanation:

:P

Answer:

25

Step-by-step explanation:

trust me it's right it might be easier if you use paoer

Answer:

y=2

Step-by-step explanation:

y = 26

If you substitute x for -3 in the equation y = 6x + 8, your equation becomes:

y = 6(-3) + 8 now you can simplify it and solve for y

6 x -3 = -18

18 + 8 = 26

y = 26

Answer:

A

Step-by-step explanation:

Hope I helped

Answer:

The answer is A, $11.60

Step-by-step explanation:

0.66=spent 9 minutes

0.66x9=5.94

5.94+5.66=$11.60

Btw, luv ur profile pic uwu!

Answer:

C. Supplementary angles

Step-by-step explanation:

Supplementary angles always equal 180 degrees.

The answer is (C) because, the sum of both the angle is equals to 180° i.e they are pair of supplementary angles.

The first option is correct.

if we multiply the 34 and 12 so it comes 408

And according to first option, it we add 340 and 68 so it comes 408.

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Answer:

Yes, that's right:  the cross section will be a rectangle (but also a parallelogram).

Step-by-step explanation:

Answer: 1/12

Step-by-step explanation:

Answer:

ez pts tysm

Step-by-step explanation:

Answer:

no you scam me if I see what is promises I will help you

Answer: 12 1/3

hope this helps.. stay safe and have a great day

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

[tex]Length = 450\ m[/tex]

[tex]Width = 1200\ m[/tex]

Required

Determine the number of hectares  in this dimension

First, we need to calculate the area of the land

[tex]Area = Length * Width[/tex]

[tex]Area = 450m * 1200dm[/tex]

Convert dm to m

[tex]Area = 450m * 120m[/tex]

[tex]Area = 54 000 m^2[/tex]

[tex]1 hectare = 0.0001m^2[/tex]

So, we have:

[tex]1\ hectare = 0.0001m^2[/tex]

Multiply by 54000

[tex]Hectare = 0.0001 * 54000[/tex]

[tex]Hectare = 5.4[/tex]

Hence, there are 5.4 hectares

Answer:

y = 8x + 13

Step-by-step explanation:

slope-intercept form: y = mx + b

Given equation: [tex]y = -\frac{1}{8}x -2[/tex]

Second equation: unknown

Slope: unknown

Given point: (-2, -3)

When two lines are perpendicular, their slopes are negative reciprocals. So, since the slope(m) of the given line is [tex]-\frac{1}{8}[/tex], the slope of the line perpendicular to it is 8.

Now we know the slope of the line. To find the y-intercept, input the values of the slope and the given point into the equation format and solve for b:

y = mx + b

-3 = 8(-2) + b

-3 = -16 + b

13 = b

The y-intercept is 13.

Now that we know the slope and the y-intercept, we can write the equation:

y = 8x + 13

Hope this helps :)

Answer:

The first four terms of the sequence are: {-10,-23,-62,-179}

Step-by-step explanation:

Given recursive formula is:

[tex]a_n = 3a_{n-1}+7[/tex]

First term = a1 = -10

The first term is already known. In order to find the next terms, we will put n=2,3,4 in the recursive formula.

Putting n=2

[tex]a_2 = 3a_{2-1}+7\\a_2 = 3a_1+7\\a_2 = 3(-10)+7\\a_2 = -30+7\\a_2 = -23[/tex]

Putting n=3

[tex]a_3 = 3a_{3-1}+7\\a_3 = 3a_2+7\\a_3 = 3(-23)+7\\a_3 = -69+7\\a_3 = -62[/tex]

Putting n=4

[tex]a_4 = 3a_{4-1}+7\\a_4 = 3a_3+7\\a_4 = 3(-62)+7\\a_4 = -186+7\\a_4 = -179[/tex]

Hence,

The first four terms of the sequence are: {-10,-23,-62,-179}

Divide 4 wholes by 2/3 pieces to fnd number of pieces.

4 / 2/3

When you divide by a fraction, flip the fraction over then multiply:

4 x 3/2 = (4 x 3)/2 = 12/2 = 6

There are 6 pieces.

Answer:

6

Step-by-step explanation:

lets put this in terms of 3, because of 2/3. the number above the three will be divided by three to get to four. So if we multiply three by four to get twelve, we can put that over 3, and then find our answer. 12/3=4, so we know that is correct. and since we need to find how many 2/3 pieces we need, we divide 12/3 by 2/3 to get 6. so you need 6 2/3 pieces to get four wholes.

Answer:

Can give you the example then you have to figure out.

Step-by-step explanation:

We are assuming the center of the tower is at the origin, so we can use the standard form of a horizontal hyperbola centered at the origin: \displaystyle \frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1

​a

​2

​​  

​

​x

​2

​​  

​​ −

​b

​2

​​  

​

​y

​2

​​  

​​ =1, where the branches of the hyperbola form the sides of the cooling tower. We must find the values of \displaystyle {a}^{2}a

​2

​​  and \displaystyle {b}^{2}b

​2

​​  to complete the model.

First, we find \displaystyle {a}^{2}a

​2

​​ . Recall that the length of the transverse axis of a hyperbola is \displaystyle 2a2a. This length is represented by the distance where the sides are closest, which is given as \displaystyle \text{ }65.3\text{ } 65.3  meters. So, \displaystyle 2a=602a=60. Therefore, \displaystyle a=30a=30 and \displaystyle {a}^{2}=900a

​2

​​ =900.

To solve for \displaystyle {b}^{2}b

​2

​​ , we need to substitute for \displaystyle xx and \displaystyle yy in our equation using a known point. To do this, we can use the dimensions of the tower to find some point \displaystyle \left(x,y\right)(x,y) that lies on the hyperbola. We will use the top right corner of the tower to represent that point. Since the y-axis bisects the tower, our x-value can be represented by the radius of the top, or 36 meters. The y-value is represented by the distance from the origin to the top, which is given as 79.6 meters. Therefore,

x

2

a

2

−

y

2

b

2

=

1

Standard form of horizontal hyperbola

.

b

2

=

y

2

x

2

a

2

−

1

Isolate  

b

2

=

(

79.6

)

2

(

36

)

2

900

−

1

Substitute for  

a

2

,

x

,

and  

y

≈

14400.3636

Round to four decimal places

The sides of the tower can be modeled by the hyperbolic equation

\displaystyle \frac{{x}^{2}}{900}-\frac{{y}^{2}}{14400.3636 }=1,\text{or}\frac{{x}^{2}}{{30}^{2}}-\frac{{y}^{2}}{{120.0015}^{2} }=1

​900

​

​x

​2

​​  

​​ −

​14400.3636

​

​y

​2

​​  

​​ =1,or

​30

​2

​​  

​

​x

​2

​​  

​​ −

​120.0015

​2

​​  

​

​y

​2

​​  

​​ =1

The shape of hyperbolic cooling tower is a conic section that can be described with a formula equation.

a = 28.5, b ≈ 52.65

[tex]Equation \ of \ hyperbola;\ \dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]

Reasons:

The parameters of the hyperbolic cooling tower are;

Minimum diameter = 57 feet

The height at which the diameter occurs = 155 ft.

The diameter of the tower = 175 feet

Total height of the tower = 200 feet

Height at which the center of the hyperbola occurs = 155 feet

Solution:

The equation of a hyperbola is; [tex]\dfrac{(x - h)^2}{a^2} - \dfrac{(y- k)^2}{b^2} = 1[/tex]

The center of the hyperbola = (0, 155)

[tex]a = \dfrac{57}{2} = 28.5[/tex]

At y = 155,  

Therefore;

[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y -155)^2}{b^2} = 1[/tex]

At y = 200 feet [tex]x = \dfrac{75 \ feet}{2} = 37.5 \ feet[/tex]

Therefore;

[tex]\dfrac{37.5^2}{28.5^2} - \dfrac{(200 -155)^2}{b^2} = 1[/tex]

b² = 2769.0340909

b ≈ 52.62

The equation of the hyperbola is therefore;

[tex]\dfrac{x^2}{28.5^2} - \dfrac{(y-155)^2}{56.62^2} = 1[/tex]

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