Mia removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by f(x) = 10x2 −19x + 6, where x is time in minutes. Which of the following equations will reveal the time in minutes when the trough is empty?

True. The linear regression model is commonly used for descriptive purposes, such as identifying and quantifying relationships between variables.

True. While a linear regression model can be valuable for descriptive purposes, such as understanding relationships between variables, its predictive value can be limited. This is because linear regression models make assumptions about the linearity of the relationship between variables and may not capture more complex patterns in the data. Additionally, factors like outliers, multicollinearity, and overfitting can negatively impact the model's predictive accuracy. Therefore, it is important to consider these limitations when using a linear regression model for prediction purposes. However, its predictive value is limited as it assumes a linear relationship between variables and does not account for complex interactions or non-linearities in the data. Other predictive models, such as machine learning algorithms, may be more effective in predicting outcomes.

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The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

2.6 minutes

Step-by-step explanation:

Speed of Bob = 8 km/hr

Speed of Shannon = 10 km/hr

Distance of practice course = 1.7 km

As time = (distance)/(speed), so

Time taken by Bob to cover the distance, t1 = 1.7/8=0.2125 hours

Time taken by Shannon to cover the distance, t2 = 1.7/10= 0.17 hours

As t1 > t2, so, Bob takes more time than Shannon to complete the course.

t1-t2= 0.2125-0.17 = 0.0425 hours = 0.0425 x 60 minutes= 2.55 minutes.

On rounding up to tenth digit, t1-t2 = 2.6 minutes.

Hence, It takes 2.6 minutes more time for Bob to complete one trip around the course than Shannon

On average, a tourist would have to wait for approximately 19.01 minutes for service if they are not served immediately.

To calculate the average waiting time for a tourist, we need to consider the arrival rate of tourists and the time it takes to serve them. The arrival rate is given as one tourist every 15 minutes. This means that, on average, the interarrival time between two tourists is 15 minutes.

The service time is given as an average of 5.455 minutes per tourist. Since there are three employees on duty, the service rate is three times the individual service time, which is 3 * 5.455 = 16.365 minutes per tourist.

Using Little's Law, we can calculate the average waiting time (W) using the formula W = (L - 1) * T, where L is the average number of tourists in the system (including those being served) and T is the average time spent in the system.

The average number of tourists in the system (L) can be calculated by dividing the arrival rate (λ) by the service rate (μ), L = λ/μ.

Given that λ = 1/15 tourists per minute and μ = 1/16.365 tourists per minute, we have L = (1/15) / (1/16.365) = 16.365/15 ≈ 1.091.

Finally, substituting L = 1.091 and T = 5.455 minutes into the formula, we get W = (1.091 - 1) * 5.455 = 0.091 * 5.455 ≈ 0.495 minutes, which is approximately 19.01 minutes.

Therefore, the correct answer is b. 19.01 minutes.

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Given:

The table of values of a linear function.

To find:

The equation of linear function in slope intercept form.

Solution:

The slope intercept form of a linear function is:

\(y=mx+b\)

Where, m is the slope and b is the y-intercept.

If a linear function passes through two point, then the equation of the linear function is:

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Consider any two points from the given table. Let the two points are (-6,12) and (-5,14). So, the equation of the linear function is:

\(y-12=\dfrac{14-12}{-5-(-6)}(x-(-6))\)

\(y-12=\dfrac{2}{-5+6}(x+6)\)

\(y-12=\dfrac{2}{1}(x+6)\)

\(y-12=2x+12\)

Adding 12 on both sides, we get

\(y-12+12=2x+12+12\)

\(y=2x+24\)

Therefore, the slope intercept form for the given linear function is \(y=2x+24\).

Answer:

C) 88

Step-by-step explanation:

20 out of 50 is same ratio as:

Applied to the number 220 we get:

So expected number is 88

Correct answer choice is C

Answer:

24

Step-by-step explanation:

24

The total number of different costumes possible is 24 if  Anita has a costume wardrobe that consists of 2 pairs of tights, 3 T-shirts, and 3 scarves.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Anita has a costume wardrobe that consists of 2 pairs of tights (1 white pair and 1 black pair), 3 T-shirts (1 pink, 1 blue, and 1 green), and 3 scarves (1 silver, 1 gold, and 1 white).

The costume consists of either a pair of tights or a T-shirt with a scarf:

In this case total number of ways = 2×3×3 = 18

Pair of tights and a T-shirt without a scarf:

In this case total number of ways = 2×3 = 6

Total number of different costumes are possible:

= 18 + 6

= 24

Thus, the total number of different costumes possible is 24 if  Anita has a costume wardrobe that consists of 2 pairs of tights, 3 T-shirts, and 3 scarves.

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Answer:

MRT or TRM

Step-by-step explanation:

RT and MR meet at point R. Point R must be included in the final angle as well as the endpoints of RT and MR. The resulting angle is thus MRT, or TRM

Answer:  2144

Step-by-step explanation:

v = 4/3pir³

v = 4/3 (3.14) (8)³

v = 4/3 (3.14)(512)

v ≈ 2144

Answer:

2,143.57 cubit units.

Step-by-step explanation:

To find the volume of the sphere, use the formula given below.

Volume = 4/3π r³

Use this formula, the value given for the radius, and 3.14 for  to find the volume.

Volume = 4/3π r³

             ~~ 4/3 (3.14) (8 units)³

             ~~ 2,143.57 cubic units

Therefore, the approximate volume of the sphere is 2,143.57 cubic units.

Answer:

112.765789 ect

Step-by-step explanation:

The pound as a unit of mass , 14 x (1ounce)= 14 ounce.

The British imperial and American customary systems of measurement both utilize the pound as a unit of mass. The international avoirdupois pound, which is legally defined as exactly 0.45359237 kilograms and is divided into 16 avoirdupois ounces, is the definition that is currently most frequently used.

The avoirdupois pound is represented by the worldwide standard symbol, lbm (for the majority of pound definitions), (mostly in the U.S.),  and  (particularly for the apothecaries' pound).

The currency came from the Roman libra (hence the abbreviation "lb"). The Dutch term pond, the Swedish word pund, and the German word pfund are all cognates of the English word pound.

Older and no longer in use, these units (replaced by the metric system).

Hence, 14 x (1ounce)= 14 ounce.

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Answer:start on (0,1) and go up two and left three. keep going until you run out of room. then, draw a line through the points.

Step-by-step explanation:

gg

The complete question is,

Use the drawing tool(s) to form the correct answers on the provided graph.

Graph the system of equations given below on the provided graph.

2x– 3y = –18

3x + y = -5

A graph can be described as a pictorial representation or a diagram that methodically describes data or values.

In math, a graph can be described as a pictorial representation or a diagram that methodically describes data or values. The points on the graph often characterize the connection between two or more things.

2x– 3y = –18

3x + y = -5

Transforming the equation in slope-intercept form

2x-3y= -18

-3y= -2x-18

-3y= -(2x+18)

3y=2x+18

y=(2x+18)/3

And for equation 2

y= -5-3x

For plotting the graph, the online graphing calculator  can be utilized.

The points can be estimated by putting negative and positive values of x in both equations.

The graph exists attached as a picture.

As we can see from the graph that two lines intersect at (-3,4) so it stands for the solution of the provided system of linear equations.

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the only critical point of the function is a local minimum, which is located at (3, -3). The answer is (3, -3, -32).

To find the local maxima, local minima, and saddle points, if any, for the function z = 3x² + 3y² − 18x + 18y + 1, we need to find the critical points of the function. The critical points of a multivariable function are the points at which the partial derivatives are zero or do not exist. We can then use the second partial derivative test to determine whether each critical point is a local maximum, local minimum, or saddle point.To find the partial derivatives, we differentiate the function with respect to x and y and set each derivative equal to zero: ∂z/∂x = 6x - 18 = 0 ⇒ x = 3 ∂z/∂y = 6y + 18 = 0 ⇒ y = -3So the critical point is (3, -3).To find the second partial derivatives, we differentiate each of the partial derivatives with respect to x and y: ∂²z/∂x² = 6, ∂²z/∂y² = 6, ∂²z/∂x∂y = 0At the critical point, these become: ∂²z/∂x² = 6, ∂²z/∂y² = 6, ∂²z/∂x∂y = 0So we have: D = ∂²z/∂x² * ∂²z/∂y² - (∂²z/∂x∂y)² = (6)(6) - (0)² = 36Since D > 0 and ∂²z/∂x² > 0, the critical point is a local minimum.

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The critical point is neither a local maximum nor a local minimum. we can say that there is a saddle point at (3,-3,28). Hence, the point coordinates in the form of (∗,∗,∗) are (3,-3,28).

Given function is z = 3x² + 3y² - 18x + 18y + 1.

Here, we need to find the local maxima, local minima, and saddle points, if any using symbolic notation and fractions where needed.

To find them, first, we need to find the partial derivatives of the function with respect to x and y.

So, the partial derivative of z with respect to x is:d/dx z = 6x - 18

The partial derivative of z with respect to y is:

d/dy z = 6y + 18

Now, we need to equate both these derivatives to zero to find critical points:

6x - 18 = 0 => x = 3and6y + 18 = 0 => y = -3

Now, we need to find the second-order partial derivatives to check whether the critical points are maxima, minima, or saddle points.

So, the second-order partial derivative of z with respect to x is:

d²/dx² z = 6

The second-order partial derivative of z with respect to y is:

d²/dy² z = 6

And the second-order partial derivative of z with respect to x and y is:

d²/dxdy z = 0

Now, we can use the second derivative test to find whether the critical points are maxima, minima or saddle points.

6 is positive and d²/dxdy z = 0.

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Answer:

y=C-Ax÷B

Step-by-step explanation:

Ax+By=C

-Ax -Ax

By= C-Ax

—————

B

y=C-Ax

——–

B

Answer:

\(-\frac{6}{100}\)

Step-by-step explanation:

Well first 0.06 is equal to \(\frac{6}{100}\) since 6÷100 is 0.06.

Now since it's actually -0.06, then we get \(-\frac{6}{100}\)

Answer:0.06 but positive

Step-by-step explanation:

At STP (standard temperature and pressure), the molar volume of an ideal gas is 22.4 L/mol. To calculate the grams of Ne (neon) gas in 25.0 L, we first need to find the moles of Ne gas and then convert it to grams using its molar mass.

1. Find moles of Ne:
25.0 L Ne * (1 mol Ne / 22.4 L) = 1.1161 mol Ne

2. Convert moles to grams:
Ne has a molar mass of 20.18 g/mol.
1.1161 mol Ne * (20.18 g/mol) = 22.51 g Ne

Answer: There are 22.51 grams of Ne contained in 25.0 L of Ne gas at STP.

Part B:
To find the volume in liters occupied by 32.0 g of Ar (argon) gas at STP, we first need to find the moles of Ar gas and then convert it to volume using the molar volume at STP.

1. Find moles of Ar:
Ar has a molar mass of 39.95 g/mol.
32.0 g Ar * (1 mol Ar / 39.95 g) = 0.8010 mol Ar

2. Convert moles to volume:
0.8010 mol Ar * (22.4 L/mol) = 17.94 L Ar

Answer: 32.0 g of Ar gas occupies 17.94 liters at STP.

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The main bearing clearance (in mm) in a certain type of engine is a random variable with a probability density function (PDF).

A probability density function (PDF) is a mathematical function that describes the likelihood of a continuous random variable taking on a specific value within a given range. In this case, the main bearing clearance in a certain type of engine is a continuous random variable, and its PDF provides information about the probability distribution of the clearance values.

To fully describe the main bearing clearance's PDF, we would need the specific mathematical expression for the function. The PDF should satisfy two conditions: it must be non-negative for all values of the clearance, and the total area under the curve of the PDF must equal 1, as the probability of the clearance being within the entire possible range is 1 (100%).

Without the specific form of the PDF, we cannot provide further details, such as the mean, variance, or other properties of the main bearing clearance's probability distribution.

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Answer:

D

Step-by-step explanation:It is a straight line

If on january 1, year 1, billy co signed a three-year lease for office space The amortization expense on this leasehold improvement that Billy should  record for Year 2 is: $1,000.

Since we were told that the new overhead lighting fixtures is the amount of $2,000 now let determine the  Amortization expense using this formula

Amortization expense = New overhead lighting fixtures / 2 years

Let plug in the formula

Amortization expense =  $2,000 /2

Amortization expense = $1,000

Therefore the  Amortization expense  is the amount of $1,000.

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The complete question:

On January 1 , Year 1, Billy Co. signed a three year lease for office space. The lease required monthly rent of 8,000 for the first year. 8,100 for the second year and 8,200 for the 3rd year. Billy has the option to renew the lease for a fourth year at 8,300 per month. On January 1, Year 2, Billy permanently installed new overhead lighting fixtures at a cost of $2,000. How much amortization expense on this leasehold improvement should Billy record for Year 2?

Answer:

HDE is the semicircle

EH is the diameter

Answer:

p ≥  -5

Step-by-step explanation:

Hope this helps!

The value of x and y in the equation is as follows:

x  = 8

y = -1

The expressions can be solved using the law of exponentials. Therefore, let's breakdown the expressions and solve for x and y as follows;

\(\frac{b^{x} }{b^{y} } = b^{9}\)

\(b^{x-y} = b^{9}\)

Therefore,

x - y = 9

\(\frac{(b^{x}.b^{2} )}{b^{3y} }=b^{13}\)

Therefore,

\(b^{x + 2 - 3y} = b^{13}\)

x + 2 -3y = 13

x - 3y = 13  -2

x - 3y = 11

Therefore,

x - y = 9

x - 3y = 11

subtract the equations

-2y = 2

y = 2 / -2

y = -1

Hence,

x = 9 + y

x =9 - 1

x = 8

Therefore,

x = 8 and y = -1

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Answer:

Equivalent

Step-by-step explanation:

Look at 6/18.  18 divided by 6 is 3, which is the denominator.  6 divided by 6 is 1, so the numerator.  So 1/3.  

The two fractions 1/3 and 6/18 are equivalent, As 6/18 cancels out to 1/3.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

We know, Two or more than two fractions are equivalent if when written in the simplest form they are equal.

Given, Are two fractions (1/3) and (6/18).

Now, 1/3 is already in simplest form,

Now, 6/18 can be canceled out by 6 which equals 1/3.

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Option (b) is the correct choice as the combination of shapes used to create the 3D figure is Two regular pentagons and five congruent rectangles.

The 3D figure can be created using two regular pentagons and five congruent rectangles. The given figure has a congruent regular polygon as its base. As given, it has 10 sides, which means it is a decagon. Therefore, the regular polygon is a decagon. It has five rectangular sides connected to the base.

All these rectangles are congruent and have a length greater than their width. Therefore, it can be concluded that the combination of shapes used to create the 3D figure is Two regular pentagons and five congruent rectangles.

Hence, option (b) is the correct choice.

The figure has a congruent regular polygon as its base. The base of the figure is a regular polygon with 10 sides, which means it is a decagon. Therefore, the regular polygon is a decagon.The figure has 5 rectangular sides connected to the base.

All these rectangles are congruent and have a length greater than their width. Therefore, the combination of shapes used to create the 3D figure is two regular pentagons and five congruent rectangles.

Each of the pentagons acts as a base to the rectangular sides, which are congruent to each other.

Hence, option (b) is the correct choice as the combination of shapes used to create the 3D figure is Two regular pentagons and five congruent rectangles.

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Answer:

mean: 65

median: 9

Step-by-step explanation:

You take all the numbers you have and add them up. Make it simple by adding smaller numbers together. Then once you have the total which is 65 you divide it by the total of numbers you have and then round because after dividing you get 8.125 and the safest way to round is to 9.

Answer:

2 1/3 cups for each hiker

Step-by-step explanation:

8bags x 3.5 cups in each bag =28 cups in total
28 cups shared among 12 hikers = 28/12 = 2 1/3 cups for each hiker