You realize that more than 8000 gallons per year was a lot of water to waste with a leaky faucet. You fixed your faucet so that it now takes 11 minutes longer to fill a cup of water than it did when it leaked 1 fluid ounce 30 seconds. How many gallons will the faucet waste in 1 year?

Answer:

[tex]y=420\cdot (0.79)^x[/tex]

The value of the function after 5 years would be 129.

Step-by-step explanation:

We have been that a population of 420 animals decreases at an annual rate of 21%. We are asked to write an exponential function for our given problem.

We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,

a = Initial value,

b = For decay b is in form [tex]1-r[/tex], where, r represents decay rate in decimal form.

[tex]r=21\%=\frac{21}{100}=0.21[/tex]

[tex]y=a\cdot (1-r)^x[/tex]

[tex]y=420\cdot (1-0.21)^x[/tex]

[tex]y=420\cdot (0.79)^x[/tex]

Therefore, our required function would be [tex]y=420\cdot (0.79)^x[/tex].

To find the value of the function after 5 years, we will substitute [tex]x=5[/tex] in our function.

[tex]y=420\cdot (0.79)^5[/tex]

[tex]y=420\cdot 0.3077056399[/tex]

[tex]y=129.236368758[/tex]

[tex]y\approx 129[/tex]

Therefore, the value of the function after 5 years would be 129.

Answer:

10.

Step-by-step explanation:

We are asked to find the estimation of 492.6 divided by 48.

First of all, we will round 492.6 to nearest hundreds and 48 to nearest tens.

Since tens digit of 492.6 is greater than 5, so we will round up to nearest hundred as: [tex]492.6\approx 500[/tex]

Since ones digit of 48 is greater than 5, so we will round up to nearest tens as: [tex]48\approx 50[/tex].

Now, we will find the quotient as:

[tex]\frac{500}{50}=10[/tex]

Therefore, an estimation of 492.6 divided by 48 would be 10.

Answer:

The potential energy of the 10-kg object is 294 joules .

Step-by-step explanation:

As given

The potential energy of an object is jointly related with the mass of the object and the height of the object.

Let the potential energy of an object is denoted by P.E .

Mass of the object = m

Height of the object = h

Than

[tex]P.E \propto mh[/tex]

P.E = mgh

Where g is the accleration due to gravity .

As given

A 40-kg object is 2 meters off the ground. The potential energy of the object is 784 joules.

Put the value in the P.E = mgh

784 = g × 2 × 40

784 = 80g

[tex]g = \frac{784}{80}[/tex]

g = 9.8 joules per kg meter .

As given

A 10-kg object is 3 meters off the ground.

Put the value in  P.E = mgh

P.E = 10 ×  9.8 × 3

P.E = 294 joules

Therefore the potential energy of the 10-kg object is 294 joules .

The range of a function is the set of all possible output values. For the quadratic function f(x)=3x²+6x-9, because it forms an upward opening parabola, its range will start from its vertex point and continue to infinity. The range of this function will be y ≥ -6.

This student is asking about the range of a given quadratic function. In the context of mathematics, the term 'range' refers to the set of all possible output values (y-values) of a function. For your function, f(x) = 3x² + 6x - 9, this is a quadratic function, so it forms a parabola when graphed. Given the positive coefficient of x², the parabola opens upwards.

Therefore, the lowest point (also known as the vertex) of the parabola will provide the minimum value of the range - since the parabola continues indefinitely upwards, there's no maximum value. For a quadratic function in the form f(x) = ax² + bx + c, you can find the x-coordinate of the vertex using the formula -b/2a.

Applying this to your function, we get x = -6 / (2*3) which simplifies to -1. You can then substitute this x-value into the function to find the minimum y value: f(-1) = 3*(-1)² + 6*(-1) - 9 = -6. Thus, the range of the function f(x) = 3x² + 6x - 9 is y ≥ -6.

https://brainly.com/question/29145252

#SPJ3

Answer:

(A)

Step-by-step explanation:

Scott cycled for 10 minutes in first week, 15 minutes in second week,20 minutes in third week and 25 minutes in the fourth week which maintains a consistency in the line as there is consistent slope when drawn on a graph.

On, the other hand, harry cycled for 10 minutes in first week, 20 minutes in second, 40 minutes in third and 80 minutes in fourth week in which there is no consistency in the timings according to the weeks. Therefore, only, scott's method is linear as the number of minutes increased by an equal factor every week.

To express 31% as a fraction in its lowest form, divide 31 by 100 and simplify the resulting fraction.

To express 31% as a fraction in its lowest form, we need to convert the percent to a decimal first. We do this by writing 31% as a fraction with a denominator of 100 and dividing the numerator by the denominator: 31/100. To reduce the fraction to its lowest form, we find the greatest common divisor (GCD) of the numerator and denominator, which is 1. Dividing both the numerator and denominator by 1, we get the fraction 31/100 in its lowest form.

the answer is 9 hope it helps

Answer:I can't answer it without measurements. Sorry

Step-by-step explanation:

Answer:

Lian is 12 years old and Ella is 8 years old.

Step-by-step explanation:

Lian and her younger sister Ella are 4 years apart.

The sum of their ages is 20.

Let L be Lian’s age in years.

Let E be Ella’s age in years.

The system of linear equations that models the scenario is:

[tex]L-4=E[/tex] this gives [tex]L=E+4[/tex]

[tex]L+E=20[/tex]

Putting L=E+4 in the second equation

[tex]E+4+E=20[/tex]

[tex]2E=20-4[/tex]

[tex]2E=16[/tex]

So, [tex]E=8[/tex]

Now we have , L+E=20

[tex]L+8=20[/tex]

So, [tex]L=12[/tex]

Therefore, Lian is 12 years old and Ella is 8 years old.

Answer:

Line

Step-by-step explanation:

Answer:  The answer is (a) Timeline.

Step-by-step explanation:  We are given four options out of which one is the cause and effective graphic organiser that best identifies why we use gasoline in our cars today and what we might use as fuel in the future.

The best option is Timeline, because they show the order of events, an event's place in history and identify events which lead up to, or cause, other events.

Flowcharts does not serve the purpose, because they do not clearly identifies the cause.

Thus, the correct option is (a).

A flow chart would be the best graphic organizer to identify why we use gasoline in our cars today and potential future fuels, as it clearly presents causes and effects in a non-linear way.

The type of cause and effect graphic organizer that would be most effective in identifying why we use gasoline in our cars today and what we might use as fuel in the future is a flow chart. A timeline would be helpful in demonstrating a chronological progression of fuels, but a flow chart allows you to clearly lay out causes and effects in a non-linear way, which is more suitable for this topic as it involves multiple possibilities for future fuels. It can visually present the reasons why we use gasoline now and the different options we have for future fuels, alongside their possible effects or outcomes.

https://brainly.com/question/32113051

#SPJ6

Answer:

Step-by-step explanation:

69d+5,000

Answer:

Each question had 4 points.

Step-by-step explanation:

Let the questions be x points each. As both Gretchen and Ezia received equal scores, we can write the equation as:

18x+19=15x+31   (Let the questions be x points each)

Solving for x;

[tex]18x-15x=31-19[/tex]

=> [tex]3x=12[/tex]

Dividing both sides by 3;

x = 4

Hence, each question had 4 points.

The fraction 1/15 is a repeating decimal because, when converted, it results in the repeating pattern 0.0666..., where the digit 6 repeats indefinitely.

When the fraction 1/15 is converted to a decimal, it results in the repeating decimal 0.0666..., where the digit 6 repeats indefinitely.

This happens because 1 divided by 15 gives a quotient of 0.0666..., and the 6 in the decimal representation repeats infinitely.

In other words, the division process doesn't terminate or end, and the same pattern of digits repeats endlessly after the decimal point.

This repeating pattern signifies that the fraction 1/15 cannot be expressed as a finite decimal and will always have repeating digits when written in decimal form.

Therefore, 1/15 is classified as a repeating decimal rather than a terminating one.