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Given the age in years, t, of a water-transport pipe, the formula R = 17 + 4 t can be used to predict the rate of water leakage (in gallons per minute) from the pipe as it carries water from the headquarters of a farming cooperative to farmland a mile away. What is the meaning of the constant 17 in the function R ?A. Initially the pipe leaks at 4 gallons per year.
B. Initially the pipe leaks at 17 gallons per year.
C. Initially the pipe leaks 17 gallons.
D. Initially the pipe leaks at 4 gallons per minute.
E. Initially the pipe leaks 4 gallons.
F. Initially the pipe leaks at 17 gallons per minute.

Answers

Answer 1

Answer:

Answer: F. Initially the pipe leaks at 17 gallons per minute.

Step-by-step explanation:

Given the equation below:

R = 17 + 4t

Where R is the rate of leakage in gallons per minute,

And t is the age of pipe in years.

The rate of leakage at time t = 0 ( initial rate of leakage )

R(0)= 17 + 4(0)

R(0)= 17 gallons per minute.

Therefore the initial rate of leakage is 17gallons per minute

Answer 2

Answer:

Final answer:

The constant 17 in the function R = 17 + 4t represents the initial rate of water leakage from the pipe when it is brand new. The correct answer is option C. Initially the pipe leaks 17 gallons.

Explanation:

The constant 17 in the function R = 17 + 4t represents the initial rate of water leakage from the pipe when it is brand new. This means that option C. Initially the pipe leaks 17 gallons is the correct answer.

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jay simplified the expression 3 x (3 +12 / 3) -4. for his first step ,he added 3 + 12 to get 15. what was jay's error? find the correct answer

Answers

you should be dividing 12/3

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best reate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 10 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 3 flights arrive late.

Answers

Answer:

There is a 32.22% probability that at least 3 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives on time, or it arrives late. This means that we can solve this problem using binomial probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)$

In which $C_(n,x)$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And $\pi$ is the probability of X happening.

In this problem, we have that:

There are 10 flights, so $n = 10$ .

A success in this case is a flight being late. 80% of its flights arriving on time, so 100%-80% = 20% arrive late. This means that $\pi = 0.2$ .

(a) Find the probability that at least 3 flights arrive late.

Either less than 3 flights arrive late, or at least 3 arrive late. The sum of these probabilities is decimal 1. This means that:

$P(X < 3) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)$

$P(X = 0) = C_(10,0).(0.2)^(0).(0.8)^(10) = 0.1074$

$P(X = 1) = C_(10,1).(0.2)^(1).(0.8)^(9) = 0.2684$

$P(X = 2) = C_(10,2).(0.2)^(2).(0.8)^(8) = 0.3020$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778$

Finally

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222$

There is a 32.22% probability that at least 3 flights arrive late.

Final answer:

The problem is solved by calculating the probability of the complementary event (0,1,2 flights arriving late) using the binomial distribution, then subtracting this from 1 to find the probability of at least 3 flights arriving late.

Explanation:

This problem is typically solved by using a binomial probability formula, which is used when there are exactly two mutually exclusive outcomes of a trial, often referred to as 'success' and 'failure'.
Here, our 'success' is a flight arriving late. The probability of success, denoted as p, is thus 20% or 0.2 (since 80% arrive on time, then 100%-80% = 20% arrive late). The number of trials, denoted as n, is 10 (the number of randomly selected flights).
We want to find the probability that at least 3 flights arrive late, in other words, 3,4,...,10 flights arrive late. The problem can be solved easier by considering the complementary event: 0,1,2 flights arrive late. Then subtract the sum of these probabilities from 1.

The binomial probability of exactly k successes in n trials is given by:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
Where C(n, k) is the binomial coefficient, meaning choosing k successes from n trials.
We calculate like so:
P(X=0) = C(10, 0) * (0.2)^0 * (0.8)^10
P(X=1) = C(10, 1) * (0.2)^1 * (0.8)^9
P(X=2) = C(10, 2) * (0.2)^2 * (0.8)^8
Sum these up and subtract from 1 to get the probability that at least 3 flights arrive late. This gives the solution to the question.

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I don’t know what answer to put for increasing and decreasing.

Answers

Answer:

Increasing: (2, ∞) Decreasing: (-∞,2)

Step-by-step explanation:

Think of the parabola (just for visualization purposes) as the direction of a rubber ball being thrown from above. The ball starts to decrease in position, eventually hitting the ground, and then starts to increase back to the orginal height and beyond.

So, because parabolas extend infinitely in both the positive and negative direction, we can use intervals to express the parts of the graph where it increases and decreased.

The minimum value point, or vertex is the point where the parabola changes direction. The vertex is visibly at (2,-4). So, the interval for decreasing would be (-∞,2) and increasing would be (2,∞)

Note: We use the symbol "[" to indicate that a value is included in the interval.

Because infinity is a concept and not a number, we have to use the non-inclusive version of it: "(" (simple parentheses) to indicate that infinity is NOT included in the interval, but it simply keeps extending in both directions.

I hope this helps you out.

What is 1/4 * 32 I need help please

Answers

Answer: 8

Step-by-step explanation: Think of the 32 in this problem as 32/1.

So rewriting, we have 1/4 × 32/1.

Now, the 4 and 32 cross-cancel to 1 and 8.

So we have 8/1 or just 8.

What is the y-coordinate of the point that divides the directedline segment from J to K into a ratio of 2:3?

K(8,11)

J(-3,1)

*7

*-6

*5

*-5

Answers

Answer:

(D)5

Step-by-step explanation:

Given the point J(-3,1) and K(8,11).

The line segment that divides the segment from J to K in any given ratio can be determined using the formula.

$P(x,y)=\left((mx_2+nx_1)/(m+n) ,(my_2+ny_1)/(m+n)\right)$

In the given case:

$(x_1,y_1)=(-3,1), (x_2,y_2)=(8,11)$ , m:n=2:3

Since we are to determine the y-coordinate of the point that divides JK into a ratio of 2:3, we have:

$(my_2+ny_1)/(m+n)=(2*11+3*1)/(3+2)\n\n=(22+3)/(5)\n\n=(25)/(5)\n\n=5$

The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.

The correct option is D.

Answer:

The answer is actually C(5) not D

Step-by-step explanation:

Compute Lenny's estimated tax payment for the third quarter. He is self-employed and he expects to earn $40,800.00 this year. His estimated income tax rate is 19%.

Answers

Answer:

Lenny's tax payment for the year will be $7,752

(The third quarter payment would be $1,938)

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Problems.

Taxes are calculated once a year based on your yearly income. That being said we can look at Lenny's income for the year ($40,800) and multiply that by 0.19 (19%) to calculate his tax payment for the year.

$$40,800 * 0.19 = $7,752$

So Lenny's tax payment for the year will be $7,752 . The question asks for payment for the third quarter but as mentioned above tax is calculated yearly.

That being said if you would like to know how much it would be quarterly we can simply divide the tax payment by 4.

$7,752 / 4 = 1,938$

So the third quarter payment would be $1,938

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

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