If 450 birds have to fit evenly into 18 enclosures and there are 3 enclosures in each section of the zoo how many birds are in each section of the zoo?

(a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

The Continuous Compounding formula for the principal P , rate of interest r , and time t is

A = P×[tex]e^{rt}[/tex]

In the question ,

it is given that

Part(a)  

the amount deposited (P) = $5200

rate percent (r) = 3.7% = 3.7/100 = 0.037

time = 9 years

Amount = 5200×[tex]e^{0.037\times9}[/tex]

= 7254.76

the future value after 9 years is $7254.76   .

Part(b)

the effective rate is calculated using the formula

effective rate = [tex]e^{r}[/tex] - 1

effective rate = [tex]e^{0.037}[/tex] - 1

= 1.03769 - 1

= 0.03769

= 3.769%

Part(c)

the time to reach $10000 is calculated using the formula

10000 = 5200[tex]e^{0.037\times t}[/tex]

[tex]e^{0.037\times t}[/tex] = 10000/5200

[tex]e^{0.037\times t}[/tex] = 100/52

taking ㏑both the sides , we get

0.037×t×㏑(e) = ㏑(100/52)

0.037t = 0.65392

t = 0.65392/0.037

t = 1.76735

t ≈ 1.77 years

Therefore , (a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

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The domain of the inverse function is, x ≥ 8, x is greater than equal to 8.

What is domain and range?

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Given: A square root function has a domain of x≥2 and a range of y≥8.

We have to find the domain of it's inverse.

Since, The range of the inverse function's original function, f, is its domain. This also implies that the domain of the inverse function of the original function f is the range of that function.

Therefore, y [tex]\geq[/tex] 8 is the domain of inverse function.

Replace y with x.

Hence, the domain of the inverse function is  x ≥ 8.

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Answer: $54,742.75

Step-by-step explanation:

Each year you need to multiply the employee's current salary by 4% (in decimal form this is 0.04). Then you add the result to their current salary.

Year 1

40000 * 0.04 = 1600

40000 + 1600 = 41600

Year 2

41600 * 0.04 = 1664

41600+ 1664 = 43264

Year 3

43264 * 0.04 = 1730.56

43264+ 1730.56 = 44994.56

Year 4

44994.56 * 0.04 = 1799.78

44994.56+ 1799.78 = 46794.34

Year 5

46794.34 * 0.04 = 1871.77

46794.34+ 1871.77 = 48666.11

Year 6

48666.11 * 0.04 = 1946.64

48666.11+ 1946.64 = 50612.75

Year 7

50612.75 * 0.04 = 2024.51

50612.75+ 2024.51 = 52637.26

Year 8

52637.26 * 0.04 = 2105.49

52637.26+ 2105.49 = 54742.75

Frodo ran 132/35 miles in one hour.

Given, that Frodo ran 2(1/5) miles in 7/12 of an hour.

Now, 2(1/5) miles = 7/12 hour

11/5 miles = 7/12 hour

7/12 hour = 11/5 miles

1 hour = (11/5)×(12/7)

1 hour = 132/35 miles

So, Frodo ran 132/35 miles in one hour.

Hence, Frodo ran 132/35 miles in one hour.

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There are no extraneous solutions when plugging -7 into x-5=2(x+1).

So extraneous solutions means the solutions that you get by solving an equation, but after you try plugging it back into your original equation, the solution does not work.

Now we have our solutions of x=7, and we just need to check whether it is extraneous or not. We can do this by taking x=1 and plugging it back into your original equation  x - 5 = 2(x + 1)

x - 5 = 2(x + 1)

-7 - 5 = 2(-7 + 1)

-12 = -14 + 2

-14 + 14

0 = 0

We end up getting that 0 = 0 which is correct,

Thus, there are no extraneous solutions.when plugging -7 into x-5=2(x+1).

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Answer: 7 hours

Step-by-step explanation:

525 x 4.5= 2362.5

2362.5 / 6= 393.75

393.75 / 60= 6.5625

Hello..!

¿What is consumidores terciarios?

They are the ones that feed on carnivores and their parasites.

An example:

When we see a dead bird, a week goes by and then there are only the bones, since as it says they feed on dead birds, that is, they eat everything without leaving anything, whether they are birds, cows or people.

Answer:

I'm not sure if to answer is Spanish or English so here's both:

Spanish: Los organismos que comen consumidores secundarios se llaman consumidores terciarios y son carnívoros que comen carnívoro.

English: Tertiary consumers are organisms that eat secondary consumers

The component  describes a country of capitalism is All economic decisions made by government.

According to a common understanding, capitalism is an economic system in which individual actors own and control property according to their interests and where supply and demand freely set market prices in a way that benefits society. The fundamental quality of capitalism is the desire to make a profit.

Capital, which developed from capitale, a late Latin term based on caput, meaning "head," is where the word "capitalism" originates. Chattel and cattle, both of which allude to moveable property, also have their roots in capital (only much later to refer only to livestock).

A capitalist economy allows for the private ownership and control of capital assets like mines, railroads, and factories. It also allows for the purchase of labor for monetary wages, the accrual of capital gains to private owners, and the allocation of prices.

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The completion of the chart showing the hourly pay, gross pay, and hours worked by four JA Company employees, including the total wages for the week is as follows:

Employee       Hourly Pay  Hours Worked  Gross Pay

Jalen Smith         $9.25              40                $370.00

Kiara Grays         $9.45              32                $302.40

Tatiana Michel    $9.75              42               $429.00

Kisha Sil              $9.50              36               $342.00

Total wages                                                 $1,443.40

The gross pay for each employee is the product of the hourly pay and the hours worked.

For the employee, who worked 42 hours, the overtime pay is calculated at the double the regular hourly rate, which can also be described as double time.

The total wages are the addition of each employee's gross pay for the week.

Employee       Hourly Pay  Hours Worked  Gross Pay

Jalen Smith         $9.25              40              $370.00 ($9.25 x 40)

Kiara Grays         $9.45              32              $302.40 ($9.45 x 32)

Tatiana Michel    $9.75              42              $429.00 ($9.75 x 40 + (2 x 2 x $9.75)

Kisha Sil              $9.50              36              $342.00 ($9.50 x 36)

Total wages                                                $1,443.40

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The equation of the parabola is y = -x² + 12x - 27

Parabola is the locus of a point such that the same distance from a fixed line, called the directrix, and a fixed point (the focus) is the same.

The equation of a parabola is in quadratic form. Hence it is given as:

y = ax² + bx + c

At point (-5, 0):

0 = a(-5²) + b(-5) + c

25a - 5b + c = 0      (1)

At point (9, 0):

0 = a(9²) + b(9) + c

81a + 9b + c = 0      (2)

At point (10, 30):

30 = a(10²) + b(10) + c

100a + 10b + c = 30     (3)

Solving equations 1, 2, 3 gives: a = -1, b = 12, c = -27

The equation of the parabola is hence y = -x² + 12x - 27

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Answer:

first solve for y and simplify

y+5=[tex]\frac{2}{3} x[/tex]+4/3

y=[tex]\frac{2}{3} x[/tex]+4/3-5

y=[tex]\frac{2}{3} x[/tex]-11/3

Now graph this

y intercept=(0,-11/3)

use the slope to find another point

(3,-1.667)

draw a line using both points

Answer:

[4] Function

[5] Not a function

[6] Function

Step-by-step explanation:

    The vertical line test is a test to determine if the line graphed is a function. Taking a vertical line, you move it left and right through the graph. If, at any point, there are two or more intersections in the vertical line, the graph is not a function.

     4 and 6 pass the test meaning they are functions, 5 does not.

The annual percentage yield (APY) of Rocio is 3.11 %

What is Annual Percentage Yield?

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest.

Given data ,

Deposit amount of Russ = $ 3200

Interest rate R = 3.1 %

And it is given that the interest rate is compounded daily , so

Interest rate R = 3.1 % / 365

                       = 0.031 / 365

                       = 0.000084

Now , The annual percentage yield (APY) is calculated as

The interest amount = 3200 x ( 1 + 0.000084 )³⁶⁵

                                 = 3200 x ( 1.000084 )³⁶⁵

                                 = 3200 x 1.031133

                                 = 3299.6272

                                 ≈ 3299.627

Therefore , the interest will be

= 3299.627 - 3200

= $ 99.627

Now , the annual percentage yield (APY) is given by

= Interest / Deposit

= 99.627 / 3200

= 0.03113

≈ 3.11 %

Hence , annual percentage yield (APY) of Rocio is 3.11 %

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Answer:

Step-by-step explanation:

0.2

Answer:

0.2

Step-by-step explanation:

i did it :)

Answer:

Three people have phones and use social media

Step-by-step explanation:

1/5 of 30 is 6

1/2 of 6 is 3

Answer:

-188

Step-by-step explanation:

The cost for 1 hot dog is $2.25  and the cost for 1 bag of potato chips is  $1.5   .

In the question ,

it is given that ,

a vendor is selling  hot dogs and bags of potato chips ,

the customer bought 5 hot dogs and 4 bags of potato chips for $17.25

let the cost of 1 hot dog = h    and

let the cost of 1 bag of potato chips = p

So , the equation is 5h + 4p = 17.25

and another customer buys , 2 hot dogs and 2 bags of chips

So , the equation is , 2h + 2p = 7.50

2p = 7.50 - 2h

and 4p = 15 - 4h

Substituting 4p = 15 - 4h in the equation 5h + 4p = 17.25 , we get

5h + 15 - 4h = 17.25

h + 15 = 17.25

h = 17.25 - 15

h = 2.25

and 4p = 15 - 4h

4p = 15 - 4(2.25)

4p = 15 - 9

4p = 6

p = 6/4

p = 1.5

Therefore , The cost for 1 hot dog is $2.25  and the cost for 1 bag of potato chips is  $1.5   .

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The circumference of ΔAOC, ΔAOB and ΔABC are  4√2(1+√2), 2(√5+3) and 2(3+√5+2√2) units respectively and area of ΔAOC, ΔAOB and ΔABC are 8,4 and 12 square units respectively.

The perimeter of a triangle can be calculated by simply adding the length of all the sides.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

There are three triangle in the given diagram namely ΔAOC, ΔAOB and ΔABC.

We will find the area and circumference of each of the triangle.

First we find area of each triangle.

Area of ΔAOC = 1/2*CO*AO = 1/2*4*4 = 8 square units.

Area of ΔAOB = 1/2*BO*AO = 1/2*2*4 = 4 square units.

Area of ΔABC = 1/2*BC*AO = 1/2*6*4 = 12 square units.

Now, we will find circumference of each triangle.

Since,  ΔAOC, ΔAOB are right angled triangle

⇒    AC = [tex]\sqrt{AO^{2}+OC^{2} }[/tex] = [tex]\sqrt{4^{2}+(-4)^{2} }[/tex] = [tex]\sqrt{32}[/tex] = 4√2 units.

and AB = [tex]\sqrt{AO^{2}+OB^{2} }[/tex] = [tex]\sqrt{4^{2}+2^{2} }[/tex] = [tex]\sqrt{20}[/tex] =2√5 units.

Circumference of ΔAOC = AC+CO+AO = 4√2+4+4 =4√2+8 = 4√2(1+√2) units.

Circumference of ΔAOB = AB+BO+AO = 2√5+2+4 =2√5+6=  2(√5+3)units.

Circumference of ΔABC = AB+BC+AC = 2√5+6+4√2 = 2(3+√5+2√2)units.

Therefore, circumference of ΔAOC, ΔAOB and ΔABC are  4√2(1+√2), 2(√5+3) and 2(3+√5+2√2) units respectively and area of ΔAOC, ΔAOB and ΔABC are 8,4 and 12 square units respectively.

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Answer:

r=65° S=66° t=81°

Step-by-step explanation:

R=180-(99+16)° triangle has 180° R=65° to find S 180-(65+33+16)=S S=66

T=180-(33+66) T=81°

1584 hands(combination) contains two 3s and two 5s.

The query serves as an example of combination (also known as selections).

Two 3s are to be selected from 4 = 4C2

                                                        = 6

Two 5s are to be selected from 4 = 4C2

                                                        = 6

No. of cards in standard deck = 52

No. of remaining cards = 52 - 4 - 4

                            = 44

No. of remaining cards to be selected = 5 - 2 - 2

                                                                = 1

No. of last selection = 44C1

                                 = 44

Total selection = 44 * 6 * 6

                        = 1584

Hence, total hands is 1584.

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The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

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777.6 cubic ft is the volume of the shed that Lorie ordered to hold her gardening supplies.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given the data in the question;

To determine the volume of the shed, plug the given values into the above formula and simplify.

V = w × h × l

V = 12 ft × 3 1/5 ft × 20.25 ft

V = 12 ft × 3.2 ft × 20.25 ft

V = 12 ft × 64.8 ft²

V = 777.6 ft³

Therefore, the volume of the shed is 777.6 ft³.

Option B is the correct answer.

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An expression for the area of △KNM is = 1/2 x 2b x a

Given,

In the question:

In triangle KNM ;

The length of the base (MK) = 2b

and, height of the triangle is= a

To write an expression  for the area of △KNM .

Now, According to the question:

We know that :

Area of triangle is = 1/2 x base x height

The length of the base (MK) = 2b

and, height of the triangle is= a

Plug all the values in the area of triangle :

Here, Area of triangle is = 1/2 x 2b x a

Hence, An expression for the area of △KNM is = 1/2 x 2b x a.

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After the subtraction, the simplified value is 16 hours : 9 minutes : 22 seconds

Subtraction

Subtraction means the process of finding the difference between two or more numbers.

Given,

Here we have the timings.

9h 24min 13s

-6h 45min 9s

Now, we have to perform the subtraction on it and also write it in the simplified form.

In order to perform the subtraction, we have to convert the given timings into decimal form, then we get,

=> 9h 24min 13s = 9.4036

Similarly, the second one is converted as decimal form, like

=> - 6h 45min 9s = -6.7525

Now, we have to perform the subtraction on it,

=> 9.4036 - (-6.7525)

=> 16.1561

Now, we have to convert this into time format, then we get,

=> 16 hours : 9 minutes : 22 seconds

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Answer:

(0,2)

(3,0)

Step-by-step explanation:

The total costs for the first year, $690 , the second year $560, the third year $442, and all the years $1692 in dollars and cents

Depreciation cost for the first year:

Depreciation = $15,000 × 0.046

Depreciation = $690

Depreciation cost for the second year:

Depreciation= $14,000 × 0.04

Depreciation = $560

Depreciation cost for the third year:

Depreciation= $13,000 × 0.034

Depreciation= $442

Total depreciation:

Total depreciation =$690 + $560 + $442

Total depreciation = $1,692.

Therefore the total depreciation is $1,692

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1) In first circle radius is 3yard and diameter is 6 yard

2) In second circle radius is 46 inch and diameter is 92 inch

3)In third circle radius is 23 ft and diameter is 46ft

What's the radius solution?

The radius formula is easily obtained by halving the circle's diameter. The line segment created when we join a point on a circle's circumference to its exact center is referred to as the ring's radius. The radius of a circle is the separation between its center and circumference.

What is diameter, for instance?

If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to the diameter of a circle, which is the line segment that extends from one end of the circle to the other end while passing through the center of the circle.

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Step-by-step explanation:

3410 students were surveyed. It was found that the ratio of full-time students to part-time students was 7:4 How many full-time students were there? How many part-time students were there?

7 + 4 = 11

3,410/11 = 310

full time: 310 * 7 = 2,170

part time: 310 * 4 = 1,240

Answer:

140 bows

Step-by-step explanation:

hope this helps :)