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stellarik [79]
3 years ago
13

On 1st September 2014 there were 5400 trees planted in a wood.

Mathematics
1 answer:
Aliun [14]3 years ago
3 0

Answer:

1. a = 5400

2. r = 0.96

3. Percentage decrement = 65.4%

Step-by-step explanation:

Given

N = ar^t

Solving (a): Write down the value of a

a implies the first term

And from the question, we understand that the initial number of trees is 5400.

Hence,

a = 5400

Solving (b): Show that r = 0.96

Using

N = ar^t

When a = 5400, t = 1 i.e. the first year and N = 5184

Substitute these values in the above expression

5184 = 5400 * r¹

5184 = 5400 * r

5184 = 5400r

Solve for r

r = 5184/5400

r = 0.96

Solving (c): Show that the trees has decreased by over 65% in 2040

First, we need to calculate number of years (t) in 2040

t = 2040 - 2014

t = 26

Substitute 26 for t, 5400 for a and 0.96 for r in N = ar^t to get the number of trees left

N = 5400 * 0.96^26

N = 1868.29658019

N = 1868 (approximated)

Next, we calculate the percentage change as thus:

%Change = (Final - Initial)/Initial * 100%

Where the initial number of trees =5400 and final = 1868

%Change = (1868 - 5400)/5400 * 100%

%Change = -3532/5400 * 100%

%Change = -3532%/54

%Change = -65.4%

The negative sign indicates a decrements or reduction.

Hence, percentage decrement = 65.4% and this is over 65%

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Crazy boy [7]

Answer:

B: 8 7/8 Lbs

Step-by-step explanation:

answer = 15\frac{1}{8} -3\frac{1}{2} -2\frac{3}{4}

step 1 find a common denominator

common denominator - 8

* apply *

\frac{1^*^1}{8^*^8} =\frac{1}{8} \\\\\frac{1^*^4}{2^*^4} =\frac{4}{8} \\\\\frac{3^*^2}{4^*^2} =\frac{6}{8}

now we have

15\frac{1}{8} -3\frac{4}{8} -2\frac{6}{8}

step 2 make each fraction a improper fraction

We can do this my multiplying the big number by the denominator and adding that to the numerator.

15*8=120\\120+1=121\\\frac{121}{8} \\\\3*8=24\\24+4=28\\\frac{28}{8} \\\\2*8=16\\16+6=22\\\frac{22}{8}

now we have

\frac{121}{8} -\frac{28}{8} -\frac{22}{8}

Now we can subtract

remember when subtracting fractions you only subtract the numerators. ( so we keep the denominator as 8 )

so 121 - 28 - 22 = 71

so the answer is \frac{71}{8}

finally we want to change the answer back into a mixed fraction

To do this we divided 71 and 8

8 can go into 71 8 times

8 * 8 = 64

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We're left with 8\frac{7}{8}

5 0
3 years ago
Harper works at an electronics store as a salesperson. Harper earns a 6% commission on the total dollar amount of all phone sale
agasfer [191]

<u>Answer:</u>

The system of equations are

x + y = 2600   …….equation (1)

and, 6x + 5y = 13700  ……equation (2)

<u>Explanation:</u>

Let x = amount of sales of phone;

y = amount of sales of computer

For phone, 6% of sales is 6% of x, or 6% * x = 0.06x.

Similarly for computer,

5% of y = 0.05y

Given the total sales; x + y = 2600

And commission; 0.06x + 0.05y = 137; or 6x + 5y = 13700

Therefore the system of equations are

x + y = 2600   …….equation (1)

6 x + 5 y = 13700  ……equation (2)

7 0
3 years ago
Jade wants to buy a $200,000 term life insurance policy. She is 34 years old. Using the premium table, what is her annual premiu
AnnZ [28]

Premium rates are usually for  premium per fixed face value. Jade's annual premium for a 10 year policy is given by Option b: $1,202

<h3>How to calculate the total annual premium for $x ?</h3>

If its given that the annual premium is $p per $y face value, then we can calculate the annual premium for $1 face value and then use it to calculate annual premium for $x.

Using proportions, we get:

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For given case, from the tables, we see that for age 34, and 10 year life insurance for female gender , there is annual premium of 6.01 per $1000 face value.
Thus, we have p = 6.01, y = 1000

Since Jade wants to buy Life insurance for $200,000, thus, x = $200,000

Putting it in the above derived formula, we get:

\rm \$x\:face\: value : \$\dfrac{p \times x}{y} \: annual \: premium\\\\\rm \$200000\:face\: value : \$\dfrac{6.01 \times 200000}{1000} \: annual \: premium\\ = \$1202 \: annual \: premiun

Thus, Jade's annual premium for a 10 year policy is given by Option b: $1,202

Learn more about calculating annual premium cost here:

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4 0
2 years ago
6. [(69 - 9) + 23]4<br> how do u solve this
Andru [333]
Always do the parentheses first. In this case, there are two parentheses, so do the parentheses inside the other parentheses first. After that, it’s just simple addition, subtraction, and multiplication.

(69-9)= 60

(60+23)= 83

83x4= 332
8 0
3 years ago
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