MATHEMATICS HIGH SCHOOL

Suppose the population of trout in a certain stretch of a river is 4000. In about how many years will the population of trout be 700 if the decay rate is 35%? Use the equation 700 = (4000)(0.65)x and round the value of x to the nearest year.

Answers

Answer 1

Answer:

Answer: 4 years

Step-by-step explanation:

The exponential decay equation is given by :_

$y=A(1-r)^x$ , where A is the initial population and r is the rate of decay in x years .

The initial population of trout in a certain stretch of a river =4000

The rate of decay = 35% =0.35

To find the number of years (x) for the population of trout be 700, we put all the values of the above equation, we get

$700=4000(1-0.35)^x\n\n\Rightarrow700=4000(0.65)^x\n\n\Rightarrow (0.65)^x=(700)/(4000)\n\n\Rightarrow(0.65)^x=0.175\n\n\text{Taking log on both sides, we get}\n\n\Rightarrow x\log(0.65)=\log(0.175)\n\n\Rightarrow x(-0.187086643357)=-0.756961951314\n\n\Rightarrow x=(-0.756961951314)/(-0.187086643357)\n\n\Rightarrow\ x=4.0460502029\approx4\text{ years}$

Answer 2

Answer: 4.97991230017 years is the final answer. I would suggest rounding your answer to the nearest tenth, so 5 years should be your correct answer.

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A group of students surveyed chose baseball as their favor sport in the ratio 3:8 A) if 132 students were surveyed, find the number of students that chose soccer as their favorite sport.

B) if 56 students chose soccer as their favorite sport, find the number of students that chose baseball as their favorite sport.

Answers

Answer:

For Part A answer is 96

For Part B answer is 21

Step-by-step explanation

Let ratio be x

number of student to choose baseball as their favor sport = 3x

number of student to choose soccer as their favor sport =8x

Total students (in terms of x ) =

3x +8x = 11x

Part (A) 11x = 132

x = 12

number of student with soccer = 8 (12) = 96

Part B

Number of students with Soccer = 8x (in terms of x )

8x = 56

x =7

Number of students with baseball = 3x = 3(7) = 21

49.5 baseball

82.5 soccer

A fishery is an area with the specific purpose of controlling fish populationsfor commercial or recreational fishing. Population dynamics describe how a
fish population changs over time. The population is changed by birth, death,
and migration of fish. While the supply of fish (population growth) can be
modeled with a linear equation, so can the demand of fish (the amount caught).
In one commercial venture, fishermen recorded their daily catch in an ocean
fishery. Using their data, the demand model for the total number y of fish caught
for x days is y = 349x + 50. What is the meaning of the slope?

Answers

Using linear function concepts, it is found that the slope of 349 means that each day, the number of fish caught increases by 349.

A linear function is modeled by:

$y = mx + b$

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

In this problem, the equation for the number of fish caught after x days is given by:

$y = 349x + 50$

The slope is of 349, which means that each day, the number of fish caught increases by 349.

You can learn more about linear function concepts at brainly.com/question/16302622

The cost y (in dollars) to rent a pickup truck is proportional to the number x of hours that the pickup truck is rented. It costs $100 to rent the truck for 4 hours. Write an equation that represents the cost to rent a pickup truck for x hours?

Answers

Answer:

Step-by-step explanation:D∧M a\\

Final answer:

The cost to rent the truck is directly proportional to the number of hours it's rented for. We determine the constant of proportionality to be $25 per hour. Therefore, the equation representing the cost of renting the truck for 'x' hours is y = 25x.

Explanation:

The subject of your question pertains to Mathematics, specifically with relation to a concept called proportionality. In this particular case, the cost of renting a pickup truck (y in dollars) is proportional to the number of hours the truck is rented (x). Since we know that the truck costs $100 for 4 hours, we can use these values to establish a ratio which can be represented as an equation. The ratio of cost to hours is $100/4 hours which simplifies to $25/hour. This is the constant of proportionality. Therefore, the equation that represents the cost to rent the pickup truck for x hours is y = 25x. This equation delineates that for every hour the truck is rented, the cost increases by $25.

Learn more about Proportionality here:

brainly.com/question/29184295

#SPJ12

Please can someone answer this for me, ive asked so many questions on here and they never get answered, I need the help rn this is like the last thing I can think of Given f(x) = ax – b, what is f-1(x)?
A) x - b a
B) x + b a
C) 1 ax - b
D) 1 ax + b

Answers

Answer:

Step-by-step explanation:

So we have the function:

$f(x)=ax-b$

And we want to find its inverse.

To find the inverse of a function, we need to: 1) change f(x) and x, 2) change f(x) to f⁻¹(x), and 3) solve for f⁻¹(x) for the inverse.

So, flip f(x) and x:

$x=a{f(x)-b$

Change:

$x=a {f^(-1)(x)-b$

Solve. Add b to both sides. The right side cancels:

$x+b=a{f^(-1)(x)$

Divide both sides by a:

$f^(-1)(x)=(1)/(a)(x+b)$

So, our answer is D.

What is halfway between pi and 2pi?

Answers

We are asked to determine the number that is haflway between pi and 2 pi. to determine the number, we can separate pi and get whats between 1 and 2 (coefficients of pi). The midpoint is 1.5 which is equal to 3/2. Hence, adding pi, the final answer is 3pi/2.

Answer:

3π/2 is halfway between π and 2π.

Step-by-step explanation:

We have been asked to find the value that is halfway between π and 2π.

In other words, we have to find the mid value of π and 2π.

This is equal to the average of π and 2π.

Average of two numbers a and b is given by

$\text{Average}=(a+b)/(2)$

a = π, b = 2π

Hence, the average or mid value of the given numbers is

$\text{Mid value}=(\pi+2\pi)/(2)$

Simplifying, we get

$\text{Mid value}=(3\pi)/(2)$

Hence, 3π/2 is halfway between π and 2π.

The list of multiples for 6 is infinite.
True or False?

Answers

Answer:

True

Step-by-step explanation:

As there are infinite numbers, the list of multiples are also infinite.

Multiples of 6 : 6, 12 , 18 , 24 ..............

Answer:

True; yes.

Step-by-step explanation:

Think about it, what does etc, etc mean? It means repetitive-a pattern, in a sort of way. So here are some multiples of 6:

6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150,156,162,168,174,180,186,192,198,204,210,216,222,228,234,240,246,252,258,264,270,276,282,288,294, etc.

As you can see, all I'm doing is adding 6 to every step I go. So when you say there is an infinite number, then these multiples are going to be infinite.

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