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posledela
3 years ago
14

The population of a certain animal species you are studying decreases at a rate of 3.5% per year. Only 80 of the animals in the

habitat remain after 3 years of conducting your research. What was the initial amount of animals
Mathematics
1 answer:
almond37 [142]3 years ago
7 0
The function:
f ( x ) = x * 0.965^t
where x is the initial amount and t is the number of the years
80 = x * 0.965^3
80 = x  *  0.89632
x = 80 : 0.89632 ≈ 89
Answer:
<span>The initial amount of animals was </span><span>89.

Hope this helps :)</span>
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Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7.25% interest rate. They purchased 3 points and
Vikentia [17]

Answer:

119 months

Step-by-step explanation:

In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.

We proceed to answer the;

Mathematically,

The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments

We lost out the important values given in the question as follows:

Amount of Mortgage - $675,250

Tenure - 30 Years

The Rate of interest without points = 7.25%

The number of points = 3 points

The rate of interest with the 3 points = 6.875%

The amount to be paid for purchasing the discount point is now calculated below;

Since 1 discount point = 1% of mortgage value;

Therefore, 3 discount points = 3% of mortgage value

The amount paid is thus = 3% of $675,250 = $20,257.5

To calculate Monthly payment without points, we use the mathematical formula;

M = P[r(1+r)^n/((1+r)^n)-1)]

Where M

Is monthly payment, r is the interest rate, n is the number of months.

According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months

M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40

To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875

Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91

Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48

Break Even = Purchase cost of Discount Points / Monthly savings

= $20,257.5 / $170.48

= 119 Months

Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months

6 0
3 years ago
Sandy wants to make a punch recipe with 2 parts pineapple juice to 6 parts ginger ale if you wants to increase the recipe using
Blizzard [7]

Answer:

24

Step-by-step explanation:

If you go from 2 parts pineapple to 8, thats a 4x increase. Therefore 6x4=24 (6 from the Ginger)

4 0
3 years ago
GUYS PLEASE HELP
Volgvan

Answer:

10 minutes

Step-by-step explanation:

Since you can do 6 flyers each minute, the rate would go at 6x, with x being minutes. You initially did 80, so the equation for you would be y=6x+80.

Your friend's equation would be y=4x+100, because he initially had 100 done and is now getting 4 done per minute.

If you put the 2 equations in your calculator, the intersection will happen at x=10, showing that you and your friend will have an equal number of flyers at 10 minutes.

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3 years ago
Find the slope of the line passing through these points: (5,2) and (-10,12)
Marat540 [252]

Answer:

-2/3

Step-by-step explanation:

The slope of a line is found by

m= (y2-y1)/(x2-x1)

   = (12-2)/(-10 -5)

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3 years ago
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Blababa [14]

Step-by-step explanation:

to find mean

add all numbers, then divide by how many set they given

to find median

you need to arrange them ascending order

then what is the number in the middle

to find mode

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6 0
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