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polet [3.4K]
3 years ago
14

Help pls pls pls pls pls pls

Mathematics
1 answer:
Lynna [10]3 years ago
6 0

Answer:

an = 52(1.06)^(n-1).

Step-by-step explanation:

After 6 years there are 70 and after 8 years there are 79 so the common ratio can be calculated:

After 6 years : a6 = a1 r^(6 - 1) = a1 r^5 and after 8 it is a1 r^(7)   where a1 is the number of raccoons in year 1.

So we have a1 r^7 / a1 r^5    

= r^2 = 79/70

r = 1.06 to the nearest hundredth.

To find the number in year 1 we have:

a1 (1.06)^5 = 70

a1 = 70 / (1.06)^5

a1 =  52 raccoons.

So an = 52(1.06)^(n-1).

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Civil an airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. the airport
vekshin1

Answer:

<em>The shortest possible length for the service road is 2.88 miles.</em>

Step-by-step explanation:

According to the below diagram, A, B and C are the positions of airport, shopping center and factory respectively.

Given that,  AB= 3.6 miles, BC= 4.8 miles and AC= 6.0 miles

In right triangle ABC

tan(\angle ACB)=\frac{AB}{BC} \\ \\ tan(\angle ACB)= \frac{3.6}{4.8}=0.75\\ \\ \angle ACB= tan^-^1(0.75)=36.8698.... degree

The shortest possible length for the service road from the shopping center to the highway that connects the airport and factory is BD.

That means, \triangle BCD is also a right triangle in which \angle BDC=90\°, Hypotenuse(BC)= 4.8 miles and BD is the opposite side in respect of \angle DCB or \angle ACB.

Now in right triangle BCD

Sin(\angle ACB)=\frac{BD}{BC}\\ \\ Sin(36.8698...)=\frac{BD}{4.8}\\ \\ BD=4.8*Sin(36.8698...)=2.88

So, the shortest possible length for the service road is 2.88 miles.

4 0
4 years ago
What is the answer to 12,8,10,6
maw [93]

Q1) From 12 m to 18 m

It is a percentage increase

Percentage change = (18-12)/12 × 100

= 6/12 × 100

= 50%


Q2) From 27 days to 30 days

It is a percentage increase

Percentage change = (30-27)/27 × 100

= 3/27 × 100

= 11.1%


Q3) From $48.50 to $38.80

It is a percentage decrease

Percentage change = ($48.50 - $38.80)/48.50 × 100

= 9.7/48.50 × 100

= 20%


Q4) From 25 lb to 12 lb

It is a percentage decrease.

Percentage change = 25-12/25 ×100

= 13/25 × 100

= 52%


Q5) from 10mm to 3mm

it is a percentage decrease.

Percentage change = (10-3)/10 ×100

= 7/10 × 100

= 70%


Q6) From $875 to $1000

It is a percentage increase.

Percentage change = (1000-875)/875 × 100

= 125/875 ×100

= 14.3%


Q7) from $18.1 to $22.50

It is a percentage increase

Percentage change = (22.50-18.10)/18.10 × 100

= 4.4/18.10 × 100

= 24.3%

Q8) From 32 people to 3040 people

It is a percentage increase.

Percentage change = (3040-32)/32 × 100

= 3008/32 × 100

= 9400%


Q9) From 28 stray cats to 5 stray cats.

It is a percentage decrease.

Percentage change =(28-5)/ 28 × 100

= 23/28 × 100

= 82%


Q10) From 12 words to 90 words.

It is a percentage increase.

Percentage change = (90-12)/12 × 100

= 78/12 ×100

= 650%

Q11) From 47 mph to 35 mph

It is a percentage decrease

percentage change = (47 - 35)/47 × 100

= 13/47 × 100

= 25.5%


Q12) From 8 computers to 15 computers

It is a percentage increase

percentage change = (15-8)/8 × 100

= 7/8 × 100

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4 0
3 years ago
The distance from the center of a round table top to the edge of the table top is 4 ft. What is the area of. the table top
vladimir2022 [97]
<span>I am not sure on this one but I am sure someone will answer soon! :)</span>
7 0
4 years ago
Help me please thanks​
Zarrin [17]

FORMULA:

  • Pythagorean property —: h² = b² + p², where h = hypotenuse, b = base, p = perpendicular.

ANSWER:

By pythagorean property,

  • x² = 25² + 100²
  • x² = 625 + 10000
  • x² = 10625
  • x = √10625
  • x = 103 cm rounded.

Hence, the length of x is 103 cm.

8 0
3 years ago
Write a quadratic equation to represent the circle graphed on the right
Ivahew [28]

Answer:

<h2>The standard form: x² + (y + 1)² = 25</h2><h2>The general form: x² + y² + 2y - 24 = 0</h2>

Step-by-step explanation:

The equation of a circle:

(x-h)^2+(y-k)^2=r^2

(h, k) - center

r - radius

We have the center (0, -1) and the radius r = 5   <em>(look at the picture)</em>.

Substitute:

(x-0)^2+(y-(-1))^2=5^2\\\\x^2+(y+1)^2=25

<em>use (a + b)² = a² + 2ab + b²</em>

x^2+y^2+2y+1=25             <em>subtract 25 from both sides</em>

x^2+y^2+2y-24=0

5 0
4 years ago
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