20. An airport, a factory, and a shopping center are at the vertices of a right triangle formed by three highways. The airport and factory are 6.0 miles apart. Their distances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service road will be constructed from the shopping center to the highway that connects the airport and factory. What is the shortest possible length for the service road? Round to the nearest hundredth​

a) The height of the ball after 2 seconds is 7.6 metres.

b) The given function is f(x) = (x - 2).

a) The inverse function of f(x) is g(x) = x + 2.

b) A farmer has 600 metres of fencing to enclose a rectangular area and divide it into 14 sections.

a) The total area enclosed can be expressed as a function of the length of the rectangle x as A(x) = 300x - x².

b) The domain of the area function is (0, 300) and its range is [0, ∞).

a) h(t) = -4.9t² + 13.1t + 1 When the time, t = 2 seconds;

the height of the ball, h(t) =h(2) = -4.9(2)² + 13.1(2) + 1= -4.9(4) + 26.2 + 1= -19.6 + 27.2= 7.6 metres

Therefore, the height of the ball after 2 seconds is 7.6 metres.

b) h(t) = -4.9t² + 13.1t + 1When the height of the ball, h(t) = 0.5 metres; we can write the equation as:

0.5 = -4.9t² + 13.1t + 1

Rearranging,4.9t² - 13.1t + 0.5 - 1 = 0i.e. 4.9t² - 13.1t - 0.5 = 0

Solving using the quadratic formula, t = [-(-13.1) ± √(13.1² - 4(4.9)(-0.5))]/(2(4.9))= [13.1 ± √(171.61)]/9.8≈ 0.138 and t ≈ 2.23

Thus, the ball reaches a height of 0.5 metres twice, at approximately 0.14 seconds and 2.23 seconds.

The given function is f(x) = (x - 2).

a) We can find the inverse of a function by interchanging x and y and then solving for y.

Here, f(x) = (x - 2) so we can write it as x = (y - 2)

Interchanging x and y: x = (y - 2)

Solving for y, we get: y = x + 2

Hence, the inverse function of f(x) is g(x) = x + 2.

b) Domain and range of the function and its inverse

The domain of f(x) is all real numbers. (i.e. -∞ < x < ∞)

The range of f(x) is all real numbers. (i.e. -∞ < f(x) < ∞)

The domain of g(x) is all real numbers. (i.e. -∞ < x < ∞)

The range of g(x) is all real numbers. (i.e. -∞ < g(x) < ∞)

The steps of the solution are given below:

Therefore, the inverse function of f(x) is g(x) = x + 2.

The domain of f(x) is all real numbers, and its range is all real numbers.

Similarly, the domain and range of g(x) is all real numbers.

A farmer has 600 metres of fencing to enclose a rectangular area and divide it into 14 sections.

Let x be the length and y be the width of the rectangle.

a) Write an equation to express the total area enclosed as a function of the length x.

Perimeter of the rectangle = Total fencing = 600 metres2(x + y) = 600i.e. x + y = 300

Solving for y, we get:

y = 300 - x

Thus, the area of the rectangle is A(x) = xy = x(300 - x) = 300x - x²

Therefore, the total area enclosed can be expressed as a function of the length of the rectangle x as A(x) = 300x - x².

b) Determine the domain and range of the area function.

The domain of the function is the set of all possible values of x, which in this case is the set of all positive real numbers. (i.e. 0 < x < 300)

The range of the function is the set of all possible values of A(x), which in this case is the set of all non-negative real numbers. (i.e. 0 ≤ A(x) < ∞)

Therefore, the domain of the area function is (0, 300) and its range is [0, ∞).

The steps of the solution are given below:

Therefore, the total area enclosed can be expressed as a function of the length of the rectangle x as A(x) = 300x - x². The domain of the area function is (0, 300) and its range is [0, ∞).

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Answer: I think B is the answer.

Step-by-step explanation:

Answer:not sure but

Step-by-step explanation: you can multiply each box, so lets say we have 20 times 7cm you multiply that and you get your answer, so put that a side

and once you multiply in each box add the numbers up and that should get your answer and make sure to add the "cm" at the end

Answer:

sorry but your question can't be solved any further because it doesn't have any like termsand you can't add40x and4y together it's impossible unless you multiply

Given a fixed vector b and a vector x is a solution to Qx = b, it is required to prove that every solution to the equation is in the form x = xh + xp where xh is a particular solution to Qx = b and xp is a solution to the equation Qxp = 0.

Let xh be a particular solution to Qx = b, so that Qxh = b.

Now consider the homogeneous equation Qx = 0.

This is an m × n system of homogeneous linear equations in the n unknowns x1, x2, ..., xn, whose coefficient matrix is Q.

Since xh is a solution to the equation Qx = b, it follows that the equation Q(x - xh) = Qx - Qxh = b - b = 0.

This means that x - xh is a solution to the homogeneous equation Qx = 0.

Now any solution to Qx = b is of the form x = xh + xp, where xp is any solution to the homogeneous equation Qxp = 0.

Thus, every solution to the equation is in the form x = xh + xp, as required.

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The calculated p-value is 0.016, which is significant. However, it does not strongly suggest that the population standard deviation (sigma) is less than 12.1.

In hypothesis testing, the p-value is used to determine the strength of evidence against the null hypothesis. In this case, the null hypothesis is that the population standard deviation (sigma) is equal to 12.1. The alternative hypothesis would be that sigma is less than 12.1.

A p-value of 0.016 means that if the null hypothesis were true (sigma = 12.1), there is a 1.6% chance of obtaining a sample with a standard deviation of 10.394 or lower. Typically, a p-value below a chosen significance level (e.g., 0.05) is considered statistically significant. However, in this case, the p-value of 0.016 is still relatively close to the significance level, indicating a moderate level of evidence against the null hypothesis.

Therefore, based on the given information, we can conclude that the p-value of 0.016 is significant, but it does not strongly suggest that the population standard deviation is less than 12.1. Strong evidence would require a smaller p-value, further away from the significance level, to support the alternative hypothesis.

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Answer:

yes.

................................

You need help with anything??

Answer:

1. 3

2. 1

Step-by-step explanation:

Answer:

1.3. now mark brainlieet plsssssssssss like you said you would

The pair (6, 3) in R, (6, 4) in R, and (C, 3) in R couldn't be matched with any pair in S, so they are not included in the composition relation RS.

To find the composition relation RS of R with S, we need to combine the ordered pairs in R and S in a way that the second element of each pair in R matches the first element of the pair in S.

Let's perform the composition:

R = {(2, 1), (6, 3), (6, 4), (C, 3)}

S = {(1, y), (1, 2), (2, w), (3, z)}

To form RS, we match the second element of each pair in R with the first element of each pair in S:

(2, 1) in R matches with (1, y) in S, so we combine them to form (2, y).

(2, 1) in R matches with (1, 2) in S, so we combine them to form (2, 2).

(6, 3) in R doesn't match with any pair in S.

(6, 4) in R doesn't match with any pair in S.

(C, 3) in R doesn't match with any pair in S.

Therefore, the composition relation RS is: RS = {(2, y), (2, 2)}

The pair (6, 3) in R, (6, 4) in R, and (C, 3) in R couldn't be matched with any pair in S, so they are not included in the composition relation RS.

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Answer

672 meters²

Step-by-step explanation:

2×(18×12 + 18×4 + 12×4) = 672 meters²

hope this helps :))

Answer:

function 2

Step-by-step explanation:

i looked at the table, and since t (which is the x-coordinate in this case) was 0, that means that 5.25 is the y-coordinate and is greater than 5 in the first equation.

Answer:

Step-by-step explanation:

455

Answer:

Answer is Option A

Step-by-step explanation:

the things people do for points smh :/

The rectangular equation which represents the parametric equations; x = t^(¹/2) and y = 4t is; y = 4x2, for x ≥ 0.

From the task content, it follows that the parametric equations given are;

Hence, it follows that; t = x² and y= 4t

Ultimately, upon substitution of x² for t; the resulting rectangular equation is; y = 4t².

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Answer:

y= -x+1

y=4x_14

solution

-x+1=4x-14

-x-4x= -14-1

-5x= -15

-5x/-5= -15/-5

x=3

while y=4x-14

y=4(3)-14

y=12-14

y= -2

Answer:

Both solutions are correct

Step-by-step explanation:

Given

Expression:

[tex]14x - 2x +3 = 3(5x + 9)[/tex]

See attachment for Clare and Lins' solution

Required

Determine if they are correct or not

[tex]14x - 2x +3 = 3(5x + 9)[/tex]

Open bracket

[tex]14x - 2x + 3 = 15x + 27[/tex]

Collect like terms

[tex]14x - 2x -15x = -3 + 27[/tex]

[tex]-3x = 24[/tex]

Divide by -3

[tex]x = \frac{24}{-3}[/tex]

[tex]x = -8[/tex]

Both solutions are correct

Answer:

the answer is A. 6 1/3 feet

Step-by-step explanation:

There are 12 inches in a foot. 12 x6=72 r of 4

there are 12 inches in a foot 12÷4=3. 1/3 of a foot

6 + 1/3= 6 1/3

Answer:

n/a

Step-by-step explanation:

how does it feel

Answer:

A. 223 were not playing volleyball

B. 12 books on each shelf with 3 books left over..

C. 12.15$ a day

D. 12.15 miles per day.

Step-by-step explanation:

A. Subtract 20 from 243.

B. Since books cant be divided into fractions, you take 243 divided by 20, which is 12.15. However, we have to say 12 with 3 leftover because books isn't money, a distance measure, etc. and cannot be cut into pieces.

C. 243 / 20 is 12.15

D. 243 / 20 is 12.15

Answer:

y=6x+7

Step-by-step explanation:

Answer: d. y= -2 2x+y= -3

Step-by-step explanation: Hope this help :D

The Set of all ideals of R₁×R₂, denoted as I₁×I₂, is an ideal of R₁×R₂, and it is also an ideal of R₁ and R₂ separately.

To prove that the set of all ideals of R₁×R₂, denoted as I₁×I₂, is an ideal of R₁×R₂, we need to demonstrate that it satisfies the necessary properties of an ideal.

1. Closure under addition: Let (a, b) and (c, d) be two elements in I₁×I₂. We need to show that their sum, (a, b) + (c, d), is also in I₁×I₂. Since both (a, b) and (c, d) are in their respective ideals, this implies that a+c is in I₁ and b+d is in I₂. Therefore, (a+c, b+d) is in I₁×I₂, showing closure under addition.

2. Closure under scalar multiplication: Let (a, b) be an element in I₁×I₂ and (r, s) be an arbitrary element in R₁×R₂. We need to show that their scalar product, (a, b)(r, s), is in I₁×I₂. Since a is in I₁, and R₁ is a ring with identity, we have ar is in I₁. Similarly, since b is in I₂ and R₂ is a ring with identity, we have bs is in I₂. Therefore, (ar, bs) is in I₁×I₂, demonstrating closure under scalar multiplication.

3. Contains additive identity: The additive identity in R₁×R₂ is (0, 0). Since both I₁ and I₂ are ideals, they contain their respective additive identities. Therefore, (0, 0) is in I₁×I₂.

Since the set of all ideals of R₁×R₂, denoted as I₁×I₂, satisfies closure under addition, closure under scalar multiplication, and contains the additive identity, it meets the definition of an ideal of R₁×R₂.

Additionally, since I₁×I₂ is a subset of both I₁ and I₂, it is an ideal of R₁ and R₂ individually.

In conclusion, the set of all ideals of R₁×R₂, denoted as I₁×I₂, is an ideal of R₁×R₂, and it is also an ideal of R₁ and R₂ separately.

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The given statement, "predictive modelling and lifetime value modelling are the same" is false. What is Predictive Modeling?

Predictive modeling is a technique for forecasting the probability of a certain event taking place in the future. It entails using current and past data to forecast the future events. In predictive modeling, you use known outcomes of historical data to determine whether specific patterns are likely to recur in the future. What is Lifetime Value Modeling? Lifetime Value Modeling is a method of forecasting the long-term earnings and profit of a business. It's a strategy for calculating the cumulative amount of profit generated by a customer over the life of their relationship with a company. Lifetime Value Modeling is used to decide the most effective ways to engage with consumers, such as personalized deals or special promotions, to maximize their lifetime value to the company by encouraging them to purchase more often and spend more during each transaction.

Predictive modeling and lifetime value modeling are distinct concepts that serve different purposes. Predictive modeling is used to forecast the future occurrence of specific events, whereas lifetime value modeling is used to calculate the long-term value of a customer to a company. So, the given statement is false.

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Answer:

C

Step-by-step explanation:

(c + 1)(c+1) = c² + c + c + 1 = c² + 2c + 1

Answer:

Step-by-step explanation:

You need to use vertex form of a quadratic to solve this.

Consider the vertex to be [tex](h,k)[/tex]

Another way of representing a quadratic is in "vertex form":

[tex]f(x) = a(x-h)^2+k[/tex]

Now all you have to do is solve for a.  You know that the vertex is [tex](0,2)[/tex] and you have know the point of [tex](1,8)[/tex].  Now, all you have to do is plug in these values and solve for a.

[tex]8 = a(1-0)^2+2\\8=a(1)^2+2\\8=a+2\\a=6[/tex]

Now you know the equation is [tex]f(x) = 6(x-0)^2+2[/tex] , but you need it in quadratic form.  All you have to do is solve is distribute the 6:

[tex]6x^2+2[/tex]

You get:

a = 6

b = 0

c = 2

Please mark this as brainliest if it satisfies your question

Answer:

36

Step-by-step explanation:

There are 30 red marbles and the ratio of black to yellow is 4/5, so 4/5=orange/green=orange/30.

30 is 6 times 5, so black=6 times 4=24. There are 24 black marbles.

Total of black and yellow=24+30=54.

40% of the marbles are green so 60% are black/yellow. Also 60% is 54 marbles.

60% is 60/100=3/5 so 3/5 of the total is 54 marbles, therefore 1/5 is 54/3=18 and 2/5 is the number of red marbles=2 times 18=36 red marbles.

to be honest i can't think of anything original for the visual thing, but i think the pi chart from the person above me would work well

Answer: 36

Step-by-step explanation: 2/5 of marbles are red, and 4:5 ratio is multiplied by 6 because there are 30 yellow marbles and so 3/5 of the marbles are 54 and 2/5 are 36. For visual model draw a pi chart with 40% red, 33% yellow, and 27% black.

Answer:

13.93

Step-by-step explanation:

see attached for explanation

The second quartile for the numbers 231, 423, 521, 139, 347, 400, 345 is 347. The median value is the second quartile

. So, when the numbers are arranged in ascending order, 347 is in the middle.

The following measures of variability is dependent on every value in a Set of data:

Standard deviation is the measure of variability that is dependent on every value in a Set of data.

Standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

Among these statistics, the Interquartile range is unaffected by outliers. The IQR is the distance between the first quartile (Q1) and the third quartile (Q3), which represents the middle 50% of the data.

The interquartile range (IQR) is unaffected by outliers because it only uses the values of the data points located at the 25th and 75th percentile of the data set to measure variability.

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Answer:

a part of the population that represents the entire population

Step-by-step explanation:

Answer:

I think it is the second option

I hope it helps you  

Answer: 150m

Step-by-step explanation: you first remove 5 from 20 to get what you should multiply for your triangle then you get 15 and multiply it by 12 to get 180 then you divide by 2 since it’s a triangle, to get 90 then you find the area of the rectangle by multipling 5 by 12 to get 60 then 60+90=150

Answer:

150 meters

Step-by-step explain

    He formula for a triangle is a=bh/2.  it ends up being a=12x15/2=90.

    The formula for a rectangle is 12x5=60.

    You take both and add them together and you get 150.

    So the answer is 150 meters.