A kitchen sink faucet streams 0.5 gallons of water in 10 seconds. A bathroom sink faucet streams 0.75 gallons of water in 18 seconds. Which faucet will fill a 3-gallon container faster?

The statement about That by increasing the sample size, the amount of sampling error will be decreased is true.

Given that,

That by increasing the sample size, the amount of sampling error will be decreased

Sampling error is inversely related to sample size. Therefore, if we expand the size of our sample, the likelihood of sampling error is reduced and the results are more trustworthy. The standard error is the term used to describe the sampling error that is most frequently utilized (SE). A measurement of the range of estimations around the "actual value" is the standard error. You get a lower return by increasing the sample size beyond what you already have because the added accuracy won't make much of a difference.

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The final answer is that any amount of 4 cents or 5 cents can be obtained using only 4 and 5 cent coins, as long as there are enough coins available to do so.

The smallest amount that can be made is 4 cents,

With a single 4 cent coin.

The next smallest amount is 5 cents, With a single 5 cent coin.

From there,

We can add additional 4 cent coins to make 8 cents, 12 cents, 16 cents, and so on.

We can also add a single 5 cent coin to make 9 cents, 13 cents, 17 cents, and so on.

Using these strategies,

We can make any amount of 4 cents or 5 cents, as long as we have enough coins to do so.

For example, if we have four 4 cent coins and one 5 cent coin, we can make 21 cents,

Start with the 5 cent coin

Add a 4 cent coin to make 9 cents

Add another 4 cent coin to make 13 cents

Add another 4 cent coin to make 17 cents

Add the final 4 cent coin to make 21 cents

Therefore,

4 cents or 5 cents can be obtained using only 4 and 5 cent coins.

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False.

The statement is not necessarily true. The number of levels of observed x-values does not have to be equal to the order of the polynomial in x that you want to fit.

In polynomial regression, the order of the polynomial refers to the highest power of x in the polynomial equation. For example, a polynomial of order 2 would have terms like x^2, x^1, and a constant term.

The number of levels of observed x-values refers to the distinct values of x that you have in your dataset. It represents the range or diversity of x-values observed.

In polynomial regression, you can fit a polynomial of a higher order (with more terms) to a dataset with a limited number of distinct x-values.

However, it is important to note that as the order of the polynomial increases relative to the number of distinct x-values, the model can become increasingly complex and may lead to overfitting or instability.

Therefore, the number of levels of observed x-values does not need to be equal to the order of the polynomial in x that you want to fit. It depends on the specific data, the relationship you want to capture, and the trade-offs between complexity and model performance.

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Answer:

q = infinite amount of solutions

Step-by-step explanation:

Step 1: Write equation

8q + 12 = 4(3 + 2q)

Step 2: Solve for q

--------------------------------------------------------------

We see here that you can plug in any number q and it would render the equation true. You can also look at it as 2 linear lines that are same, and the same line has infinite amount of solutions.

Step 3: Check

Plug in q to verify it's a solution.

8(0) + 12 = 4(3 + 2(0))

0 + 12 = 4(3 + 0)

12 = 4(3)

12 = 12

8(1) + 12 = 4(3 + 2(1))

8 + 12 = 4(3 + 2)

20 = 4(5)

20 = 20

We also see in the check step that any value q works.

The solution to the equation 8q + 12 = 4(3 + 2q) is Q can be any real number.

We have,

To solve for Q in the equation 8q + 12 = 4(3 + 2q), we can follow these steps:

Step 1: Distribute the 4 to the terms inside the parentheses:

8q + 12 = 4 * 3 + 4 * 2q

Simplifying further:

8q + 12 = 12 + 8q

Step 2: Combine like terms on both sides of the equation:

8q + 12 = 12 + 8q

Step 3: Subtract 8q from both sides of the equation to isolate the q term:

8q - 8q + 12 = 12 + 8q - 8q

Simplifying further:

12 = 12

Step 4: Since both sides of the equation are equal, the equation is true for all values of q.

This means the solution is all real numbers.

Therefore,

The solution to the equation 8q + 12 = 4(3 + 2q) is Q can be any real number.

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Answer:

15/2 i think

Step-by-step explanation:

180+72=252

Step-by-step explanation:

an angel can be a large or as wide up to 360 then it is a circle

from the center out one way is 180

the same from the center the other way is 180

The complete factorization of 3x⁵- 75x³ is:- 3x³(x + 5)(x - 5)

How to solve factor?

To factor completely the expression 3x⁵ - 75x³, we can first factor out the greatest common factor (GCF) of the two terms, which is 3x³:

3x³(x² - 25)

Next, we can factor the expression inside the parentheses using the difference of squares formula:

3x³(x + 5)(x - 5)

Therefore, the complete factorization of 3x⁵ - 75x³ is:

3x³(x + 5)(x - 5)

We can check that this is the correct factorization by using the distributive property of multiplication and verifying that the product of the factors is equal to the original expression:

3x³(x + 5)(x - 5) = 3x³(x² - 25)

= 3x³x² - 3x³(25)

= 3x⁵ - 75x³

So the factorization is correct.

In summary, to factor completely an expression like 3x⁵ - 75x³, we should first factor out the GCF and then look for further factorization opportunities using various factorization techniques such as the difference of squares formula, the sum or difference of cubes formula, or the quadratic formula. It's important to remember to check our work by multiplying the factors back together to ensure that we get the original expression.

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If the data set { (0, 1), (1,6), (2, 8), (4,9), (5,7) } was obtained from the launch of a rocket, it could represent the relationship between time and the altitude or velocity of the rocket during different stages of the launch.

The data set can be interpreted in the context of a rocket launch. The x-values, representing time, indicate the progression of time during the launch. The corresponding y-values can be seen as either the altitude or velocity of the rocket at those specific times. From the data, we can observe that the rocket starts at an initial altitude of 1 unit (at time 0). As time progresses, the altitude or velocity of the rocket increases, reaching its peak at time 2, where the altitude or velocity is 8 units. This could indicate a stage of the rocket's ascent where it is accelerating rapidly.

After the peak, the altitude or velocity starts to decrease. This could represent a change in the rocket's behavior, such as the start of the descent or a decrease in acceleration. The data suggests that the rocket gradually decreases in altitude or velocity, with a final reading of 7 units at time 5.

Overall, the data set could represent the altitude or velocity profile of a rocket during different stages of its launch, showing the initial ascent, peak altitude or velocity, and subsequent descent or decrease in velocity.

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The arithmetic mean is 59.

What is arithmetic mean?

It is the sum of collection of numbers divided by the count of the numbers.

Conider AB is the nuber satisfying the condition. Hence,

\(10A+B=A+B+A\times B\\9A=A\times B\\\)

Since AB is a two digit number hence, \(A\neq 0\\\). Hence, divide both sides by \(A\).

\(9=B\)

Hence, B is 9 and A can take any value from 1 to 9.

Hence, numbers are 19, 29, 39, 49, 59, 69, 79, 89,99.

Now, calculate arithmetic mean as follows:

\(AM=\frac{Sum \ of \ numbes}{Count \ of \ numbers}\\=\frac{19+29+39+49+59+69+79+89+99}{9}\\=59\)

Hence, arithmetic mean of numbers is 59.

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The (x, y) coordinates of point P are approximately (31.19, 20.67).

It is stated that the point P lies at a distance of r = 37 units from the origin and forms an angle of θ = 35° with respect to the x-axis, we can use trigonometry to find the x and y coordinates.

Using the trigonometric definitions, we have,

x = r * cos(θ) = 37 * cos(35°) ≈ 31.19

y = r * sin(θ) = 37 * sin(35°) ≈ 20.67

Therefore, the approximate (x, y) coordinates of point P are (31.19, 20.67). The coordinates (31.19, 20.67) represent the position of point P in the Cartesian coordinate system based on the given distance and angle measurements.

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Complete question - A point P lies in a plane and is a distance of r = 37 units from the origin of a Cartesian coordinate system. If the line joining the point and the origin makes an angle of = 35° degrees with respect to the x-axis, what are the (x, y) coordinates of the point P?

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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Answer:

45

Step-by-step explanation:

Answer:

4.00(x)+1.50(y)=5050

Step-by-step solution:

4.00x800=3,200

1.50x1225= 1838

1838+3200 is 5038

Answer:

\(sinC = \frac{7}{25}\\~\\cosC = \frac{24}{25}\\~\\tanC = \frac{7}{24}\)

Step-by-step explanation:

To get the sine of a non-right angle C in a right triangle, just divide the side opposing C by the long side. To get the cosine, divide the sides at C (shorter by longer). To get the tangent, divide the sine by the cosine.

Let's go:

\(sinC = \frac{7}{25}\\~\\cosC = \frac{24}{25}\\~\\tanC = \frac{7}{25} / \frac{24}{25} = \frac{7}{24}\)

Answer:

sin(7/25), cos(24/25), tan(7/24)

Step-by-step explanation:

The sin, cos, and tan are found through the sides of the triangle.

The acronym SOH CAH TOA can be used to find which goes where.

S = sin

C = cos

T = tan

O = opposite

A = adjacent

H = hypotenuse

since it asks to use  angle C you start from there, for sin its O/H hint by the SOH the rest are the same.

Answer:

Hello,

Step-by-step explanation:

heigth of the equilateral triangle:

\(h=3*\dfrac{\sqrt{3}}{2}\)

Area of the triangle:

\(A=\dfrac{6*3\sqrt{3} }{2*2} =\dfrac{9\sqrt{3} }{2} \\\\\)

Area of the disk:

\(S=\pi*4^2=16\pi\\\\\)

Probability:

\(p=\dfrac{9\sqrt{3} }{2*16*\pi}=0.15506125....\approx{15.5\%}\)

Answer:

Step-by-step explanation:

The height of the triangle is given as 6.5, the base is given as 6, therefore, the area of the triangle is:

\(A=\frac{1}{2}(6)(6.5)\\A=19.5\)

The area of the circle is:

\(A=\pi(4)^2\\A=16\pi\\A=50.26548\)

Divide the area of the triangle by the area of the circle:

\(\frac{19.5}{50.2654}*100=38.8\)%

Answer:

solution is (3,-1/2)

Step-by-step explanation:

Answer:

Assuming she has to do all of that before she leaves she needs to start at 4:40pm

Step-by-step explanation:

All of the things needed to do before she leaves equals 80 min and that is 1 hour and 20 min. Subtract that from 6:00pm and you get 4:40pm.

(Ps there is no number line)

The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

average speed for walking = 4.5 km/h

average speed for cycling = 23.2 km/h

Answer:

\(\frac{31}{(5x+2)^2}\)

Step-by-step explanation:

See image for quotient rule

f(x)= numerator = 3x-5

g(x)= denominator = 5x+2

so we have

\(\frac{(5x+2)(3x-5)'-(3x-5)(5x+2)'}{(5x+2)^2}\\(3x-5)'=3\\(5x+2)'=5\\\frac{(5x+2)(3)-(3x-5)(5)}{(5x+2)^2}\\\frac{15x+6-(15x-25)}{(5x+2)^2}\\\frac{31}{(5x+2)^2}\)

When diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

Step 1: Create an equation that connects a sphere's volume to radius as the first step.

V = 4/3*π*r³

Step 2: Calculate each side's derivative in respect to time (Let the time be "t").

(d/dt)V = (d/dt)(4/3*π*r³)

dV/dt = 4πr²*dr/dt

Step 3: The problem description informs us that the diameter is 600 m, hence r must be 30 mm.

Additionally, it is stated that now the radius of a sphere is expanding at a rate of 2 mm/s; as a result, dr/dt must equal 2 mm/s.

We are interested in dV/dt, or the rate of change of the sphere's volume.

dV/dt = 4π(30mm)²*(2mm/s)

dV/dt = 22,620 mm³/s

So, when diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

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Answer:

Slope: \(-\frac{1}{2}\)

y-intercept: \((0,2)\)

Look below for graph.

Step-by-step explanation:

\(y=2-\frac{1}{2}x\\y=\frac{-1}{2}x+2\)

Hope this helps!

\(\text {-TestedHyperr}\)

Answer:

9.75

Step-by-step explanation:

Answer:

the last option

you get cos^2(135)-sin^2(135) =cos(270)

The exact value of cos 270° is 0 as this correlates to the x-coordinate on the unit circle for a 270° angle.

The question is asking for the exact value of cos 270°. In Trigonometry, we have the unit circle which defines cosine and sine of angles based on the coordinates of points on the circle. On the unit circle, cos 270° is equivalent to the x-coordinate of the point where the angle intercepts the unit circle.

The angle of 270° corresponds to the point on the unit circle where the x-coordinate is 0 and the y-coordinate is -1. Therefore, the exact value of cos 270° is 0.

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Answer: Para convertir un decimal a una fracción, coloque el número decimal sobre su valor posicional. Por ejemplo, en 0.6, el seis está en el lugar de las décimas, entonces colocamos 6 sobre 10 para crear la fracción equivalente, 6/10. Si es necesario, simplifica la fracción.

Step-by-step explanation:

Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.

Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.

So for example, if the salaries of any 5 faculty members are as follows:

$10,000 , $50,000 , $80,000 , $150,000 , $160,000

Mean= (10,000+50,000+80,000+150,000+160,000) / 5

Mean= $90,000

Median= (5+1) / 2

Median= 6/2

Median= 3rd value

As the data is already arranged in ascending order, Median is $80,000

Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.

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Answer: The second one

There is a significant gap in south Africa between the wealthiest and poorest individuals.

It is a technique which is used to measure that captures the level of in equality for a given variables and population.It varies between 0 and 1.so 1 being perfectly inequal and 0 being perfectly equal.It is used to rank countries based on their income per capita , life expectancy and education development.

The Gini index measure income inequalities between poor and rich.

The formula we use given below

Gini Index= A/A+B

Where  A= area above Lorenz line

           B= area below Lorenz line

Lorenz is a graphical method for an economic inequality model taking the population percentage on X-axis and wealth on Y-axis.

It is the ratio of area between perfect equality line (A) divided by total area under perfect equality line (A+B).

Now we reach at this result

In south Africa the Gini index is more than 60.The higher the Gini index shows the higher the income inequality between rich and poor.

In Norway, given that the Gini index is less than 30 income inequality between rich and poor is lower.

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Brenna would take 20 min to cut the same wood into sixths.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let x be the rate at which Brenna cuts the wood in a single piece,
So, She can cut a log into thirds in 10 min.
x = 3/10

x = 0.3 cuts per minute for single wood,

Now,
time took to cut the same wood into 6 pieces
= 6 / x
= 6 / 0.3
= 20 min

Thus, Brenna would take 20 min to cut the same wood into sixths.

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Answer:

\(\sf a) y^{\frac{5}{3}}\\\\b) x^{\frac{-1}{5}}\\\\c)w^{\frac{7}{8}}\)

Step-by-step explanation:

Radical to exponent form:

   \(\sf \boxed{\sqrt[n]{x}=x^{\frac{1}{n}} }\)

\(\sf a) \sqrt[3]{y^5}=y^{5*\frac{1}{3}} =y^\frac{5}{3}\)

\(\sf b) \dfrac{1}{\sqrt[5]{x} }=\dfrac{1}{x^{\frac{1}{5}}}=x^{\frac{-1}{5}}\)

\(\sf c) \sqrt[8]{w^7}=w^{7* \frac{1}{8}}=w^{\frac{7}{8}}\)