MATHEMATICS HIGH SCHOOL

Mike is looking for a loan. He is willing to pay no more than an effective rate of 8.000% annually. Which, if any, of the following loans meet Mike’s criteria?Loan X: 7.815% nominal rate, compounded semiannually
Loan Y: 7.724% nominal rate, compounded monthly
Loan Z: 7.698% nominal rate, compounded weekly
a. Y only
b. X and Z
c. Y and Z
d. None of these meet Mike’s criteria.

Answers

Answer 1

Answer:

Answer:

b. X and Z

Step-by-step explanation:

Since, the effective annual rate is,

$i_a=(1+(r)/(m))^m-1$

Where r is the nominal rate per period,

m is the number of periods in a year,

For loan X,

r = 7.815 % = 0.07815

m = 2,

Thus, the effective annual rate,

$i_a=(1+(0.07815)/(2))^2-1$

$=(1+0.039075)^2-1$

$=1.07967685563-1=0.07967685563=7.967685563\% \approx 7.968\%$

Since, 7.968\% < 8.000 %

Thus, Loan X meets his criteria.

For loan Y,

r = 7.724%= 0.07724

m = 12,

Thus, the effective annual rate,

$i_a=(1+(0.07724)/(12))^(12)-1$

$=(1.00643666667)^(12)-1$

$=1.08003395186-1=0.08003395186=8.003395186\% \approx 8.003\%$

Since, 8.003 > 8.000 %

Thus, Loan Y does not meet his criteria.

For loan Z,

r = 7.698% = 0.07698

m = 52,

Thus, the effective annual rate,

$i_a=(1+(0.07698)/(52))^(52)-1$

$=(1.00148038462)^(52)-1$

$=1.07995899887-1=07995899887=7.995899887\% \approx 7.996\%$

Since, 7.996 % < 8.000 %

Thus, Loan Zmeets his criteria.

Hence, option 'b' is correct.

Answer 2

Answer:

Answer:

X and Z

Step-by-step explanation:

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What is the loss percentage incurred by a company when it buys an asset for rs. 1,50,000 and sells it for rs. 75,500?

Answers

The loss percentagea company incurs when buying an asset for rs. 1,50,000 and selling it for rs. 75,500 is 49.7%.

The loss percentage is calculated by subtracting the selling price from thepurchase price , then dividing that result by the purchase price, and finally multiplying by 100 to get the percentage format. In this case, it's a business scenario involving the purchase and sale of an asset, so the formula is appropriate

You can use it as follows:

Loss% = [(1,50,000 - 75,500) / 1,50,000] * 100

When you calculate the expression in the square brackets you get 0.497, or 49.7%.

So, in the provided scenario, the company incurred a loss percentage of 49.7%.

This means that the company lost nearly half of the initial value of the asset when they sold it.

Learn more about the topic of Loss Percentage here:

brainly.com/question/30938251

#SPJ11

Answer:

percentage incurred [(75,500-150,000)/150000]*100=49,666=49,6%

Step-by-step explanation:

the problem says "one side of the triangular garden is 42.0 ft. the angles on each end of this side measure 66 degrees and 82 degrees. find length of fence needed to enclose the garden." please help meeee

Answers

Draw out a triangle with one side labeled 42 feet, and the two adjacent angles 66 and 82.
When using the law of sines, you want to label the sides of your triangle a, b, c, and the angles of your triangle A, B, C.
First, label the triangle. To make this easy, I'll tell you what I labeled them so you can follow along.
The side labeled 42 feet is side "a", and the angle opposite this side is angle A
66 degrees is angle B, and the side opposite this angle is side b
82 degrees is angle C, and the side opposite this angle is side c.

We know two angles of the triangle, 66 and 82. We also know that a triangle is made up of 180 degrees. To find the angle A, we can subtract angle B and angle C from 180.

A = 180 - 66 - 82 = 32

a = 42 b = ? c = ?
A = 32 B = 66 C = 82

Now we can start using the Law of Sines to solve for sides b and c.
the law of sines says:

sin(A) = sin(B) = sin(C)
a b c

we know a, A, and B, and we are looking for "b" so we can substitute those values into sin(A)/a = sin(B)/ b

sin(32) = sin(66)
42 b

cross multiply:
b sin(32) = 42sin(66)
divide both sides by sin(32)
b = 42sin(66) ≈ 72.4
sin(32)

We can do the same thing for side c.
sin(A) = sin(C)
a c

sin(32) = sin(82)
42 c

c sin(32) = 42sin(82)

c = 42sin(82) ≈ 78.5
sin(32)

The 3 sides are 42.0 feet, 72.4 feet, and 78.5 feet. To find the length of the fence needed to enclose the garden, simply add the three sides up.

42.0 + 72.4 + 78.5 = 192.9 feet

CD HI MN RS what's next?

Answers

Just look on the alphabet.

a b CD e f g HI j k l MN o p q RS t u v WX y z

We choose 2 letters, then skip 3 letters. So the next two letters are WX - the answer.

If you had 13 cookies and you gave and even amount to 4 friends would you have any cookies left over

Answers

Answer:

yes

Step-by-step explanation:

every person would get 3 and be 1 left.

Answer:

Yes

Step-by-step explanation:

If you gave each friend 2 cookies, then you gave away 8 and would have 5 left over.

The midpoint of a segment is (−6,−5) and one endpoint is (1,3). Find the coordinates of the other endpoint.A. (8, 11)
B. (8, -13)
C. (-13, -13)
D. (-13, 11)

Answers

Answer: C. (-13, -13)

Step-by-step explanation:

The midpoint (x,y) of a line segment having two end points (a,b) and (c,d) is given by :-

$x=(a+c)/(2)\ ;\ y=(b+d)/(2)$

Given : The midpoint of a segment is (-6,-5) and one endpoint is (1,3).

Let the coordinates of other end point be (a,b) then , we have

$-6=(a+1)/(2)\ ;\ -5=(b+3)/(2)\n\n\Rightarrow\ a+1=2*-6\ ;\ b+3=2*-5\n\n\Rightharrow\ a+1=-12\ ;\ b+3=-10\n\n\Rightarrow\ a=-12-1\ ;\ b=-10-3\n\n\Rightarrow\ a=-13,\ ;\ b=-13$

Hence, the coordinates of the other endpoint = (-13,-13)

C. (-13,-13)
You take the x of the midpoint and equal it to the formula of the midpoint so it will be -6 = 1+x/2 so 1st you times 2 by 6 because you wanna get rid of 2 so it will -12 Then when you move 1 so x is alone it will be -1 so -12-1= -13
Same thing for y

Milli plans to rent a room for her birthday party for $40. The catering charge is $12 per person but there is no charge for Milli's meal since she is the guest of honor. If Milli has $100 to spend on her birthday party, how many guests can she invite?

Answers

Since Milli has $100 to spend on her birthday party and she will pay $40 so the remaining money left for her party is $60. For the $60 left she will then pay $12 for each guest for catering. Divide $60 by $12, the answer is 5. Therefore Milli will have 5 guests for her birthday.

Answer:

Step-by-step explanation:

proof in the picture.

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