A tanker truck fills the gas station’s reservoir at the rate of 1212 gallons per minute.
If the reservoir was empty and it is now 35 gallons full, how long has the tanker been filling the reservoir?
Round your answer to the nearest tenth. Enter your answer in the box.

how meny minutes

Step-by-step explanation:

Answer:

10 dance class

Step-by-step explanation:

The correct option is (d) a student needs to take 10 dance classes to learn the routine. Step-by-step explanation: Given that each dance class is hour and a student takes hours to learn a dance routine. We are to select the TRUE statement. Thus, a student needs 10 dance classes to learn the dance routine.

Answer:

330°

Step-by-step explanation:

angle subtended=11×360/12=11×30=330°

the limit of the sequence \(an = (n^2 - 1)/(n^2 + 1\)) as n approaches infinity is 1.

To find the limit of the sequence given by \(an = (n^2 - 1)/(n^2 + 1)\), we can analyze the behavior of the sequence as n approaches infinity.

Let's simplify the expression by dividing both the numerator and denominator by n^2:

\(an = (n^2/n^2 - 1/n^2)/(n^2/n^2 + 1/n^2)\)

  \(= (1 - 1/n^2)/(1 + 1/n^2)\)

As n approaches infinity, the terms \(1/n^2\) approach zero, so we have:

an = (1 - 0)/(1 + 0)

  = 1

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To find the mean and standard deviation of the corrected pH measurements, we can use the following formulas:

Corrected Mean = (Original Mean + Correction Factor) * Multiplication Factor

Corrected Standard Deviation = Original Standard Deviation * Multiplication Factor

The correction factor is 0.3 and the multiplication factor is 1.4. Therefore, the corrected mean is:

Corrected Mean = (4.8 + 0.3) * 1.4 = 7.14

And the corrected standard deviation is:

Corrected Standard Deviation = 1.2 * 1.4 = 1.68

Therefore, the mean of the corrected pH measurements is 7.14 and the standard deviation is 1.68.

In summary, to find the corrected mean and standard deviation of the pH measurements, we need to add the correction factor (0.3) to the original mean, multiply the result by the multiplication factor (1.4), and multiply the original standard deviation by the multiplication factor. The corrected mean is 7.14 and the corrected standard deviation is 1.68.

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The amount borrowed at 8% is $4000, at 10% is $12,000 and at 12% is $8000

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

let x be the amount borrowed at 8%

y be the amount borrowed at 10%

and z be the amount borrowed at 12%

total money borrowed = x+y+z = 24000 equation 1

also x+y = 2z equation 2

substitute 2z for x+y in equation 1

2z+ z = 24000

3z = 24000

z = 24000/3

z= $8000

the interest rate paid on z = 12/100× 8000 = $960

the interest paid on y = 10/100 × y

the interest paid on x = 8/100 × x

total interest paid = 960+10y/100+8x/100= 2480

10y/100+8x/100= 2480-960

10y/100+8x/100= 1520

multiply all terms by 100

8x+ 10y = 15200 equation 3

x+ y = 2z = 2× 8000

x+y = 16000 equation 4

using elimination method

8x+10y = 152000 equation 5

8x+8y = 128000 equation 6

subtract equation 6 from 5

2y = 24000

y = $12000

substitute 12000 for y in equation 4

x+12000= 16000

x = 16000-12000

x = $4000

therefore the amount borrowed at 8%, 10% and 12% are $4000, $12000, $8000 respectively.

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Answer:

in order of going down:
1) 77
2) 103
3) 77
4) 37
5) 53

Step-by-step explanation:

Answer:

77°

103°

77°

37°

Step-by-step explanation:

The outer quadrilateral in black is a rectangle because of the angles it has at the vertices.

Look at the upper green line. It intersects the vertical sides of the outer rectangle.

The upper green line intersects the left vertical segment of the outer rectangle at a 103° angle. That makes the top yellow box 77°.

The top yellow box is an angle of a quadrilateral.

360 - 77 - 66 - 114 = 103

The second yellow box is 103°.

The third yellow box is 77°.

The bottom yellow box is 180 - 66 - 77 = 37°

the volume of the cone is 94.2 cubic feet

The percentage of children that were at the party is 15%.

The number of people in the party is 60 people.

The number of adult in the party is 51 adults.

percentage is a ratio that can be expressed as a fraction of 100.

85% of the people at the family party are adult.

Therefore,

let

x = total number of people at the party

The party has only adult and children.

number of children = 9

a.

percentage of children in the party = 100% - 85% = 15%

b.

Let's find the total number in the party using the number of children

15 / 100 × x = 9

15x / 100 = 9

cross multiply

900 = 15x

x = 900 / 15

x = 60

c.

Let's find the number of adult in the party

number of adult in the party = 60 - 9 = 51 adults

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Answer: 590

Step-by-step explanation: 17$ is 17% and times that by 3 because of the 3 weeks, then you have 68$ and I just added 300 to the rest and then just subtracted 68$

What can I say exept your not welcome :D

Answer:There were a large shadow of looming

Step-by-step explanation:

i believe im not really sure sorry

Answer:

"The woods in the distance were a large shadow looming before Mary."

Step-by-step explanation:

This example of figurative language is a metaphor.

The story directly compares the woods to a large shadow without using like or as. The comparison is made to better show the reader how dark and intimidating the woods were to Mary.

Based on the results, the comparison of the overall performance of the portfolios, from best to worst, is: from "Portfolio 1, Portfolio 2, Portfolio 3". Therefore, the Option C is correct.

We have,

To calculate the weighted mean of the RORs for each portfolio, we need to multiply each ROR by its corresponding investment amount, sum the products, and divide by the total investment amount:

Weighted mean ROR for Portfolio 1:

= ((3.9% x $1,250) + (1.7% x $575) + (10.6% x $895) + (-3.2% x $800) + (8.1% x $1,775)) / ($1,250 + $575 + $895 + $800 + $1,775)

= 5.12%

Weighted mean ROR for Portfolio 2:

= ((3.9% x $950) + (1.7% x $2,025) + (10.6% x $1,185) + (-3.2% x $445) + (8.1% x $625)) / ($950 + $2,025 + $1,185 + $445 + $625)

= 0.04464053537

= 4.46%

Weighted mean ROR for Portfolio 3:

= ((3.9% x $900) + (1.7% x $2,350) + (10.6% x $310) + (-3.2% x $1,600) + (8.1% x $2,780)) / ($900 + $2,350 + $310 + $1,600 + $2,780)

= 0.03550251889

= 3.55%

Based on the results, the comparison of the overall performance of the portfolios, from best to worst, is: from "Portfolio 1, Portfolio 2, Portfolio 3". Therefore, the Option C is correct.

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complete question:

Calculate the weighted mean of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?

A)Portfolio 1, Portfolio 3, Portfolio 2

B) Portfolio 2, Portfolio 3, Portfolio 1

C) Portfolio 1, Portfolio 2, Portfolio 3

D) Portfolio 3, Portfolio 2, Portfolio 1

The value of (x + y) in parallelogram ABCD is equal to 150°.

Since ABCD is a parallelogram and ∠ADC is equal to 105°. Additionally, side AB in parallelogram ABCD is produced to point E. This ultimately implies that, angle C (∠C) and angle D (∠D) are adjacent angles of parallelogram ABCD:

∠C + ∠D = 180° (supplementary angles).

x + 105° = 180°

x = 180 - 105

x = 75°

Based on alternate interior angles theorem, ∠y is congruent to ∠x. Therefore, we have the following:

∠y ≅ ∠x

y = 75°

(x + y) = (75 + 75)

(x+ y) = 150°.

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Answer:

The answer is that x is equal to 33⁰

An ogive is used to plot cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class when displaying quantitative data. Option B.

An ogive is a graph that represents a cumulative distribution function (CDF) of a frequency distribution. It shows the cumulative relative frequency or cumulative frequency of each class plotted against the upper limit of the corresponding class. In other words, an ogive can be used to represent data through graphs by plotting the upper limit of each class interval on the x-axis and the cumulative frequency or cumulative relative frequency on the y-axis.

An ogive is used to display the distribution of quantitative data, such as weight, height, or time. It is also useful when analyzing data that is not easily represented by a histogram or a frequency polygon, and when we want to determine the percentile or median of a given set of data. Based on the information given above, option B: "Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class" is the correct answer.

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Answer:

\(percentage = \frac{56}{145} \times 100\)

56/145×100

0.386...×100

38.6%

There is insufficient evidence to substantiate the publisher's claim at the 0.05 level of significance.

To determine if there is sufficient evidence to substantiate the publisher's claim, we need to conduct a hypothesis test.

Let's assume the null hypothesis is that the proportion of readers who own a personal computer is equal to 0.32.

The alternative hypothesis is that the proportion is greater than 0.32.

We can use a one-tailed z-test for proportions to test the hypothesis.

At the 0.05 level of significance, the critical z-value for a one-tailed test is 1.645.

If our calculated z-value is greater than 1.645, we reject the null hypothesis and conclude that there is sufficient evidence to support the publisher's claim.

Assuming we take a random sample of readers and find that 350 out of 1000 readers own a personal computer, the calculated z-value can be computed as:

\(z = (p - P) / \sqrt( P(1-P) / n )\)

where

p = sample proportion = 350/1000 = 0.35

P = hypothesized proportion = 0.32

n = sample size = 1000

z = (0.35 - 0.32) / sqrt( 0.32 * 0.68 / 1000 )

z = 1.42

Since the calculated z-value (1.42) is less than the critical z-value (1.645), we fail to reject the null hypothesis.

Therefore, there is insufficient evidence to substantiate the publisher's claim at the 0.05 level of significance.

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The donation to the chi-square test statistic for men who named business networking as the most important factor is 4.29.

To calculate the donation to the chi-square test statistic for men who named business networking as the most important factor, we need to calculate the anticipated frequency and the donation for that cell.

The anticipated frequency for a cell is calculated as

anticipated frequency) = ( row aggregate) *( column aggregate)/( grand aggregate)

The row aggregate for the" business networking" row is 105, the column aggregate for the men is 1000, and the grand aggregate is 2000. thus, the anticipated frequency for the cell corresponding to men who named business networking is

anticipated frequency) = ( 105) *( 1000)/( 2000) = 52.5

To calculate the donation, we use the formula

donation) = (( observed frequency- anticipated frequency) 2)( anticipated frequency)

For men who named business networking, the observed frequency is 45. Plugging in the values, we get

donations = (( 45-52.5) 2)(52.5) = 4.29

thus, the donation to the chi-square test statistic for men who named business networking as the most important factor is 4.29

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Answer:

12

Step-by-step explanation:

\( \frac{3}{8} = \frac{?}{32} \)

8*4=32

3*4=12

Answer:

x = - 15

Step-by-step explanation:

Given

\(\frac{x}{5}\) = 5 + \(\frac{x-9}{3}\)

Multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

3x = 75 + 5(x - 9) ← distribute and simplify right side

3x = 75 + 5x - 45

3x = 5x + 30 ( subtract 5x from both sides )

- 2x = 30 ( divide both sides by - 2 )

x = - 15

As a check

substitute x = - 15 into the equation and if both sides are equal then it is the solution.

left side = \(\frac{-15}{5}\) = - 3

right side = 5 + \(\frac{-15-9}{3}\) = 5 + \(\frac{-24}{3}\) = 5 - 8 = - 3

Thus x = - 15 is the solution

The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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It provides a range of values within which the true percentage is likely to fall with a 90% level of confidence based on the Sample data.

Based on the confidence interval of (0.42, 0.48), the claim that is not supported is that less than 42% of all women do not find time to focus on their own health. This is because the lower bound of the interval is 0.42, indicating that at worst, 42% of all women do not find time to focus on their own health. Therefore, any claim that suggests a lower percentage is not supported by the confidence interval.

On the other hand, the confidence interval does support claims that suggest the percentage of women who do not find time to focus on their own health is at least 42% and no more than 48%. For example, a claim that states "between 42% and 48% of all women do not find time to focus on their own health" is supported by the confidence interval.

It is important to note that the confidence interval does not tell us anything about the actual percentage of women who do not find time to focus on their own health. Rather, it provides a range of values within which the true percentage is likely to fall with a 90% level of confidence based on the sample data.

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Answer:

it is dot 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello here is an solution

The domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=(x+1)/6x+7

Let f(x)=y

(x+1)/6x+7=y

x+1=y(6x+7)

x+1=6xy+7y

6xy-x=7y-1

x(6y-1)=7y-1

Divide both sides by 6y-1

x=7y-1/6y-1

So f⁻¹(x)=1-7x/6x-1

The domain is (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6}

The range is (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6}

Hence, the domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

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The equation of the tangent line to the graph y = x^3 - 3x + 1 at the point (2,3) is y = 7x - 11.

To find the equation of the tangent line, we need to determine both the slope and the y-intercept. The slope of the tangent line is equal to the derivative of the function evaluated at the given x-coordinate. Taking the derivative of y = x^3 - 3x + 1, we get y' = 3x^2 - 3.

Evaluating the derivative at x = 2, we have y'(2) = 3(2)^2 - 3 = 9. Therefore, the slope of the tangent line is 9.

Next, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) represents the given point on the graph. Plugging in the values (2,3) and m = 9, we obtain y - 3 = 9(x - 2).

Simplifying the equation, we get y = 9x - 18 + 3, which simplifies further to y = 9x - 15. Hence, the equation of the tangent line to the graph y = x^3 - 3x + 1 at the point (2,3) is y = 7x - 11.

In summary, the equation of the tangent line to the graph y = x^3 - 3x + 1 at the point (2,3) is y = 7x - 11. This line has a slope of 7 and intersects the y-axis at -11. The tangent line represents the instantaneous rate of change of the function at the given point and serves as an approximation of the function's behavior near that point.

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Answer:

a) The amplitud of the plain wave is 25, b) The wave length of the plain wave is \(\frac{\pi}{2}\), c) The frequency of the plain wave is \(\frac{\pi}{60}\), d) The speed of propagation of the plain wave is 0.082.

Step-by-step explanation:

A plain wave is modelled after the following mathematical model as a function of time and horizontal position. That is:

\(y(t, x) = A \cdot \sin (\omega\cdot t - \frac{2\pi}{\lambda}\cdot x)\)

Where:

\(y(t, x)\) - Vertical position wave with respect to position of equilibrium, dimensionless.

\(A\) - Amplitude, dimensionless.

\(\omega\) - Angular frequency, dimensionless.

\(\lambda\) - Wave length, dimensionless.

After comparing this expression with the equation described on statement, the following information is obtained:

\(A = 25\), \(\omega = 120\) and \(\frac{2\pi}{\lambda} = 4\)

a) The amplitude of the plain wave is 25.

b) The wave length associated with the plain wave is found after some algebraic handling:

\(\frac{2\pi}{\lambda} = 4\)

\(\lambda = \frac{\pi}{2}\)

The wave length of the plain wave is \(\frac{\pi}{2}\).

c) The frequency can be calculated in term of angular frequency, that is:

\(f = \frac{2\pi}{\omega}\)

Where \(f\) is the frequency of the plain wave.

If \(\omega = 120\), then:

\(f = \frac{2\pi}{120}\)

\(f = \frac{\pi}{60}\)

The frequency of the plain wave is \(\frac{\pi}{60}\).

d) The speed of propagation is equal to the product of wave length and frequency:

\(v = \lambda \cdot f\)

Given that \(\lambda = \frac{\pi}{2}\) and \(f = \frac{\pi}{60}\), the speed of propagation is:

\(v = \left(\frac{\pi}{2} \right)\cdot \left(\frac{\pi}{60} \right)\)

\(v \approx 0.082\)

The speed of propagation of the plain wave is 0.082.

The linear speed of the smaller Ferris wheel is 40.8 meters per minute.  The linear speed of larger Ferris wheel is 71.4 meters per minute.

When a body rotates, each point on it moves in a circle. The point on the circumference of the Ferris wheel travels the farthest distance in a single rotation compared to other points. Hence, the linear velocity of a point on the circumference is directly proportional to its distance from the center.

The angular speed of both Ferris wheels is the same i.e., 3 rotations per minute. The smaller Ferris wheel has a radius of 8 meters and the larger has a radius of 14 meters.

To find the linear speed of the Ferris wheel, we use the formula v = rω.

Linear velocity of the smaller Ferris wheel:

(8 m)(3 rotations/min) = 24π m/min ≈ 40.8 m/min.

Linear velocity of the larger Ferris wheel:

(14 m)(3 rotations/min) = 42π m/min ≈ 71.4 m/min.

The larger Ferris wheel would feel 30.6 m/min ≈ 0.5 m/s faster than the smaller Ferris wheel.

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Answer:11 hours tutoring and 3 hours landscaping

Step-by-step explanation:

Answer:

Inequality 1) y≤15−x; shade down

Inequality 2) y≥20− 22/13x; shade up

Possible solution: (13,1)

*Alexa could work 13 hours tutoring and 1 hour landscaping.

Step-by-step explanation:

Hope I helped ^U^

The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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The solution of expression is,

⇒ (6 + a⁴b) / a²b²

We have to given that,

An expression to solve is,

⇒ 6/a²b² + a²/b

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, WE can simplify the expression as,

⇒ 6/a²b² + a²/b

Take LCM;

⇒ (6 + a² × a²b)  / a²b²

⇒ (6 + a⁴b) / a²b²

Therefore, The solution of expression is,

⇒ (6 + a⁴b) / a²b²

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Answer:

Wrong values are plotted in the question statement graph.

Please find correct graph.

Step-by-step explanation:

Given that:

\(y =x+3\) and \(-1<x<5\)

i.e. we can put a value of x in the equation which is greater than -1 and lesser than 5.

OR

we can say, the points where x = -1 and x = 5 will not be included in the graph (they will be shown as hollow circle).

Now, let us put the values one by one:

x = -1, y = -1 + 3 =2

x = 0, y = 0 + 3 = 3

x = 1, y = 1 + 3 = 4

x = 2, y = 2 + 3 = 5

x = 3, y = 3 + 3 = 6

x = 4, y = 4 + 3 = 7

x = 5, y = 5 + 3 = 8

Therefore, the table of values become:

\(\begin{center}\begin{tabular}{ c c } x & y\\ -1 & 2\\ 0 & 3 \\ 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ 4 & 7 \\5 & 8\\\end{tabular}\end{center}\)

Points (-1, 2) and (5, 8) will not be included in the graph.

Please find attached corrected graph.