A sewer line slopes 1/4" per foot grade. Calculate the total fall in 30 feet.

Answer:

Part 1) The exponential function is equal to [tex]y=1,350(0.95)^{x}[/tex]

Part 2) The population in 2010 was  [tex]992\ fish[/tex]

Step-by-step explanation:

Part 1) Write an exponential decay function that models this situation

we know that

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

y ----> the fish population of Lake Collins since 2004

x ----> the time in years

a is the initial value

b is the base

we have

[tex]a=1,350\ fish[/tex]

[tex]b=(100\%-5\%)=95\%=0.95[/tex]

substitute

[tex]y=1,350(0.95)^{x}[/tex] ----> exponential function that represent this scenario

Part 2) Find the population in 2010

we have

[tex]y=1,350(0.95)^{x}[/tex]

so

For [tex]x=(2010-2004)=6\ years[/tex]

substitute

[tex]y=1,350(0.95)^{6}=992\ fish[/tex]

Final answer:

The exponential decay function for the fish population in Lake Collins is P(t) = 1350 * e^(-0.05t). Using this, the estimated fish population in 2010 is about 1,000.

Explanation:

We need to write an exponential decay function to model the decreasing fish population in Lake Collins and then use it to find the population in 2010.

To create an exponential decay function, we can use the formula P(t) = P0 * e^(rt), where:

P(t) is the population at time t,

P0 is the initial population,

r is the rate of decay (as a negative value), and

t is the time in years since the initial count.

Given the initial population of 1,350 fish in 2004 and a decay rate of 5% per year, we can write the function as:

P(t) = 1350 * e^(-0.05t)

To find the population in 2010, we first calculate the time passed since 2004, which is 6 years. Thus, t = 6:

P(6) = 1350 * e^(-0.05*6)

Calculating this gives us:

P(6) ≈ 1350 * e^(-0.3) ≈ 1350 * 0.740818 ≈ 1000 (rounded to the nearest whole number)

Therefore, the fish population in 2010 was approximately 1,000 individuals.

Answer:

a) Function

b) Not a function

c) Function

d) Not a function

Step-by-step explanation:

a) Domain = { 7,-6,2}

   Range = {5,0,3}

It is a function as every value in domain has some and unique value mapped to it in Range

b)

Domain = { 7,-6,2}

   Range = {5,0,-2,3}

It is not a function as -6 value in domain has two values mapped to it in Range

c)

Domain = { 7,2}

   Range = {-6,-7}

It is a function as every value in domain has some and unique value mapped to it in Range

d)

Domain = { 7,-6}

   Range = {5,0,3}

It is not a function as 7 value in domain has two values 3 and 5 mapped to it in Range

Answer:

54 ft^2

Step-by-step explanation:

Bathroom area is 15 ft^2

The kitchen is twice the bathroom

2*15 = 30 ft^2

Kitchen: 30 ft^2

Front door: 9ft^2

The total is all the areas added together

Total = bathroom + kitchen + front door

         = 15 ft^2     + 30 ft^2  + 9 ft^2

         = 54  ft^2

Step-by-step explanation:

After taking the square root:

x + 2 = ±2

Notice that x + 2 can also equal -2, because (-2)² = 4.

Answer:

F. Hyperbola

Step-by-step explanation:

In each napped, you'll have a parabola, combined they form an hyperbola.

It's one of the various shapes that can be produced by a plane intercepting a right circular cone, as you can see in the attached picture.

Each plane intersection is different, based on the angle and the position it passes through.

I hope that helps.

Answer:

hyperbola

Step-by-step explanation:

apeex

Answer:

25% = 1/4

Step-by-step explanation:

It is 25% because there are 4 outcomes that you can get which are

HT, TH, HH, TT

H = Head

T = Tail

and out of the four outcomes, there is one that will be Head first and Tails on the second flip. So 1 out of 4 = 25%

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-9)^2+y^2=4\implies (x-\stackrel{h}{9})^2+(y-\stackrel{k}{0})^2=2^2~\hfill \stackrel{center}{(9,0)} \\\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{2})^2=4\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{2})^2=2^2~\hfill \stackrel{center}{(3,2)}[/tex]

Check the picture below.

well, its radius didn't change, anyhow, you know what to check out.

Answer:

The circle moves left and up

Step-by-step explanation:

The circle's center changes from (9, 0) to (3,2) and the radius stayed the same.

The large dog and small boy working together will take 2/3 hour to destroy Mr McGregor's garden.

To solve this problem, we can add the rates at which the large dog and the small boy work together:

Large dog's rate = 1 garden / 2 hours = 1/2 garden per hour

Small boy's rate = 1 garden / 1 hour = 1 garden per hour

Combined rate = 1/2 garden per hour + 1 garden per hour = 3/2 gardens per hour

Now, we can use the combined rate to find the time it would take for the large dog and the small boy to destroy Mr. McGregor's garden:

Time = 1 garden / Combined rate = 1 garden / (3/2 gardens per hour) = 2/3 hour

Learn more about Working together to complete a task here:

https://brainly.com/question/37863997

#SPJ11

Answer:

yellow b/c there are the most

Step-by-step explanation:

m<6 = 180° - m<3

m<6 = 180° - 130°

m<6 = 50°

Answer: m6 equals 50 degrees

Step-by-step explanation: Since AB and CD are parallel u just solve for m2 which is the same as m6 which would be 180-130=50

Answer:

  see below

Step-by-step explanation:

If you haven't memorized it so you know it already, it takes about 10 seconds with your calculator to discover that ...

  arccos((√3)/2) = β = 30°

This fact matches only one answer choice.

Answer:

d. 3x³ and 2x³

Step-by-step explanation:

In standard form, the terms of a polynomial expression are written in order of descending powers of the variable. There will be only one term for any given power of the variable.

Here, there are two terms that have x to the third power. These terms must be combined to write the expression in standard form. They are the only terms that can be combined: 3x³ + 2x³ = 5x³.

Answer:

D. 2(√{x} + √{x - 2})

Step-by-step explanation:

As hinted in the question, we have to simplify the denominator.

To understand it easier, let's imagine we have x - y in the denominator.  If we multiply it with x + y we'll get x² - y², right?  Check the next line:

(x - y) (x + y) = x² + xy -xy - y² = x² - y²

If we have the square of those nasty square roots, it will be much simpler to deal with.  So, let's multiply the initial fraction using x+y, but with the real values:

[tex]\frac{4}{\sqrt{x} - \sqrt{x - 2} } * \frac{\sqrt{x} + \sqrt{x - 2}}{\sqrt{x} - \sqrt{x - 2}} = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} }[/tex]

Then we simplify:

[tex]\frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(x) - (x - 2) } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{ 2 } = 2(\sqrt{x} + \sqrt{x - 2})[/tex]

Answer is D. 2(√{x} + √{x - 2})

Answer:

b = 17

Step-by-step explanation:

Since PQ = RQ then ΔPQR is isosceles and QS is a perpendicular bisector

Hence PS = RS = 17 ⇒ b = 17

Answer:   [tex]32\pi[/tex] cubic units.

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:

[tex]r=\frac{8units}{2}\\\\r=4units[/tex]

Since you already know that height and  the radius, you can substitute them into the formula. Then, the volume of this cone is:

[tex]V_{cone}=\frac{1}{3}\pi (4units)^2(6units)[/tex]

[tex]V_{cone}=32\pi \ units^3[/tex]

Answer: 48

Step-by-step explanation:

Answer:

option C

Step-by-step explanation:

Area of the triangle=4x²+4x+1

Answer:

x = -9

Step-by-step explanation:

Multiply both sides by √(x - 6) to eliminate the fraction:

√(3x) = 3√(x - 6)

Now square both sides:  

3x = 9(x - 6), or 3x = 9x - 54.  

Combining the x terms results in -6x = -54, and thus x = 9.

Answer:

The correct answer is option D.  x = 9

Step-by-step explanation:

From the attached question we get an expression,

√3x/√(x - 6) = 3

To find the solution of given expression

√3x/√(x - 6) = 3

Squaring both side we get,

3x/(x - 6) = 9

3x = 9 * (x - 6)

3x = 9x - 54

9x - 3x = 54

6x = 54

x = 54/6 = 9

Therefore the correct option is D.  x = 9

 The answer is C. I have the work for it in the image bellow

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

4.6

Step-by-step explanation:

We are given the results of a survey of patients at a hospital of their blood type, categorized by their gender.

We are to find the percentage of patients with blood type AB among all patients.

Number of patients with blood type AB = 33

Total number of patients = 714

Percent of patients with blood type AB = [tex] \frac { 3 3 } { 7 1 4 } \times 100 [/tex] = 4.6

Answer:

7ab+5

Step-by-step explanation:

add like terms (3ab+4ab=7ab)

5 doesn't have a like term so it stays by itself

Hey there! :)

3ab + 4ab + 5

In order to simplify this, we must add like terms. In addition, when simplifying, you can ONLY add like terms.

Since both "3ab" & "4ab" contain "ab," you are able to combine them together!

When combining like terms, you only add the numerical value, not the letters.

This leaves us with : 7ab + 5

Therefore, your answer is 7ab + 5

~Hope I helped!~

Answer:

6√2.

Step-by-step explanation:

The two radii are equal length and form a right angle, so the resulting triangle is 45-45-90.  Therefore, the length of the chord (the hypotenuse of the triangle) is 6√2.

Answer:

90.51 (rounded to the nearest hundredth)

Step-by-step explanation:

We can use trigonometry to figure this out

sin = opposite side / hypothenuse

The 45° angle's opposite side is a leg of the triangle

sin 45 = leg / 128

sin 45 * 128 = (leg / 128 ) * 128

0.7071 * 128 =  leg

90.51 = leg

Answer:

b

Step-by-step explanation:

Answer:

  (x, y) = (7/12, 11 1/6)

Step-by-step explanation:

A graph will show you the solution is near (x, y) ≈ (0.6, 11.2). For an exact answer, an algebraic solution is indicated.

Subtracting the second equation from the first gives ...

  0 = 12x -7

  7/12 = x

Substituting for x in the second equation gives ...

  y = 2(7/12) +10 = 7/6 +10

  y = 11 1/6

Answer:

Step-by-step explanation:

<EAF is a central angle. Its measure is 12o

Arc EF has angular measure of 12 degrees as well.

The formula for the arc length in cm is

Arc length = (given arc angle/360) * 2 * pi * r

r = 30 cm which is given

Given arc angle = 12 degrees.

Arc length = (12/360) * 2* pi * r

Arc length = 1/30 * 2*pi * 30

Arc length = 6.28

Answer:

33.75

Step-by-step explanation:

Step 1- Find the decimal form of 35%

Step 2- When you find that multiply that by 25

Step 3- When you find the answer to step 2 add that to 25

That is your answer

Final answer:

The price that Fred will pay the groomer the next time when his dog has a haircut is  $33.75.

Explanation:

The question asks us to calculate the new price Fred will pay for his dog's haircut after the groomer increases the price by 35%. To find the new price, we'll use the formula for calculating percentage increase, which is: New Price = Original Price + (Original Price * Percentage Increase).

First, convert the percentage increase to a decimal by dividing it by 100, so 35% becomes 0.35. Then, multiply the original price of $25 by 0.35 to find the amount of the increase, which is $8.75.Finally, add the increase to the original price to find the new price, which is $25 + $8.75 = $33.75. So, Fred will pay $33.75 the next time his dog has a haircut.

Answer:

26

Step-by-step explanation:

80 divided by three = 26.666666

26 times 3 = 78

2 leftover

The number sticker each student get is 26 and the number stickers teacher got is 2.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, three friends buy one pack of 80 stickers.

Now, number of stickers each friend = 80/3

3|80|26

  78
_____
   2

Therefore, the number sticker each student get is 26 and the number stickers teacher got is 2.

To learn more about the division visit:

https://brainly.com/question/1575906.

#SPJ5

Step-by-step answer:

Given:

Geometric sequence with

second term, T2 = 6

third term, T3 = 12

Wants to have the explicit and recursive rules.

Solution:

common ratio, r = 12/6 = 2

Therefore the first term, T1

= second term /r

= 6/2

=3

Thus the absolute rule is

Tn = T1 *r^(n-1)      where T1 = 3, r=2.  Check: T3 = T1*2^(3-1) = 3*2^2=12 ...good

The recursive rule (depending on the previous term)

Tn = Tn-1*r = 2*Tn-1

The explicit rule for the sequence is a_n = 3 * 2^(n-1), and the recursive rule is a_n = a_(n-1) * 2. These were determined by identifying the common ratio of the sequence as 2.

In a geometric sequence, each term is generated by multiplying the previous term by a common ratio. Given the second term (6) and third term (12) in the sequence, we can identify the common ratio by dividing the third term by the second term. So, 12 divided by 6 equals 2. Therefore, the common ratio is 2.

So, the explicit rule (the nth term) of this sequence would be: a_n = a_1 * r^(n-1) = 6 / 2 * 2^(n-1) = 3 * 2^(n-1).

The recursive rule for the sequence would be: a_n = a_(n-1) * r = a_(n-1) * 2.

To summarize, we determined the common ratio to be 2 by dividing the third term by the second term. We then used this ratio to create the explicit and recursive rules for the geometric sequence.

https://brainly.com/question/34721734

#SPJ3

Answer:

Jackie's total contribution the school would be $18.00

Step-by-step explanation:

Jackie's contribution to the school bazaar = a batch of baklava

No. of pieces in a batch = 12 pieces

Price of one piece = $1.50

CASE: All baklava is sold

No. of pieces of Baklava sold = 12 pieces

Price of 12 pieces of Baklava = no. of pieces * Price of one piece

= 12 * $1.50

= $18.00

Answer:

It depends on how you define an outcome.

Usually, the outcomes are considered to be the number showing on the top face of the die (number cube) when it comes to rest on a horizontal surface. If that is how you define outcomes, then the sample space is the set of numbers 1–6: {1, 2, 3, 4, 5, 6}.

Step-by-step explanation:

"This experiment" covers a lot of territory. The student could be checking to see if the die stays on the table or falls to the floor. The student could be experimenting to see if the die changes color or makes a certain kind of noise. The experiment could involve the number of times the die rolls over to a new face before it comes to rest. Until the experiment is properly defined, the sample space is unknown.

If the experiment is to see what number shows on the top face of the die at rest on a horizontal surface, then the sample space is presumably the set of numbers 1 through 6.

Answer:

  B. 40/61

Step-by-step explanation:

There are 40 spots out of the 61 in the lot with numbers greater than or equal to 22. The probability of choosing one of them at random is 40/61.

_____

About the answer choices

61/21 and 61/40 are both numbers that are greater than 1. A probability is always a number between 0 and 1 (inclusive), so these answers can be rejected immediately.

There are 21 spots with numbers less than 22, so 21/61 is the probability of choosing one of those. That is not what the question is asking for.