you just built a large pool and you have to figure out how much it will cost to fill it with water. the pool is 10 ft wide. if the water company charges $0.02 per gallon, how much will it cost to fill the pool?

There are 43,560 square feet in an acre. There are 640 acres in a square mile. There are approximately 3.78541 liters in a gallon. There are approximately 0.26417 gallons in a liter.

(a) To convert acres to square feet, multiply the number of acres by 4840 (the number of square yards in an acre) and then by 9 (the number of square feet in a square yard).

(b) To find the number of acres in a square mile, multiply the number of square miles by 640 (the number of acres in a square mile).

(c) To convert gallons to liters, multiply the number of gallons by 3.78541 (the conversion factor between gallons and liters).

(d) To convert liters to gallons, divide the number of liters by 3.78541.

(a) To convert acres to square feet, we multiply the number of acres by the conversion factor 4840 square yards per acre, and then multiply by 9 to convert square yards to square feet. The formula is: square feet = acres * 4840 * 9.

(b) To determine the number of acres in a square mile, we multiply the number of square miles by the conversion factor 640 acres per square mile. The formula is: acres = square miles * 640.

(c) To convert gallons to liters, we multiply the number of gallons by the conversion factor 3.78541 liters per gallon. The formula is: liters = gallons * 3.78541.

(d) To convert liters to gallons, we divide the number of liters by the conversion factor 3.78541 gallons per liter. The formula is: gallons = liters / 3.78541.

Performing the calculations:

(a) Square feet in an acre: 4840 * 9 = 43,560 square feet.

(b) Acres in a square mile: 1 * 640 = 640 acres.

(c) Liters in a gallon: 1 * 3.78541 = 3.78541 liters.

(d) Gallons in a liter: 1 / 3.78541 ≈ 0.26417 gallons.

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a.  the student must pay $2197.50 in interest. b.  the future value of the loan is $4197.50.

a. To calculate the interest, we can use the formula:

Interest = Principal x Rate x Time

Given:

Principal (P) = $2000.00

Rate (R) = 12.25% = 0.1225 (converted to decimal)

Time (T) = 9 months

Using the formula, we have:

Interest = $2000.00 x 0.1225 x 9

Interest = $2197.50

Therefore, the student must pay $2197.50 in interest.

b. To find the future value of the loan, we can use the formula:

Future Value = Principal + Interest

Given:

Principal (P) = $2000.00

Interest = $2197.50

Using the formula, we have:

Future Value = $2000.00 + $2197.50

Future Value = $4197.50

Therefore, the future value of the loan is $4197.50.

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Answer:

16

Step-by-step explanation:

9-9:9 +9 - 9 :9 =

9 - 1 +9 - 1 =

8 +9 - 1 =

17 - 1 =

16

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This integral is quite complex and does not have an analytical solution is 2pi ∫\(0^2\) \(e^{-r sin(\theta)\)) r (1 - 2\(r^2\)\(cos^{2}(\theta)\) (2\(-r^2\)) dr dtheta

To evaluate the triple integral of e^(x-y) over the region enclosed by the surfaces z=\(x^2-1, z=1-x^2, y=0,\) and y=8, we will use the cylindrical coordinates since the region is symmetric about the z-axis.

In cylindrical coordinates, we have:

x = r cos(theta)

y = r sin(theta)

z = z

The limits of integration for r, theta, and z are as follows:

0 <= r <= 2

0 <= theta <= 2pi

\(x^2\)-1 <= z <= 1-\(x^2\)

Substituting the cylindrical coordinates into the integral, we get:

∫∫∫ e^(x-y) dv = ∫∫∫ \(e^{(r cos(\theta) - r sin(\theta))\)r dz dr dtheta

Now, we need to determine the limits of integration for z in terms of r. Solving for z in the two equations that define the boundaries of the region, we get:

z =\(x^2\)- 1 -> z = \(r^2\)\(cos^2(\theta)\) - 1

z = 1 - \(x^2\) -> z = 1 - \(r^2\) \(cos^2(\theta)\))

Thus, the limits of integration for z become:

\(r^2 cos^2\)(theta) - 1 <= z <= 1 -\(r^2\) \(cos^2(\theta)\)

Substituting these limits into the integral and performing the integrations, we get:

∫∫∫ \(e^{r cos(\theta)\) - r sin(theta)) r (1 - \(r^2\) \(cos^2(\theta)\)) - \(r^2\) \(cos^2(\theta))\) dz dr dtheta

= ∫\(0^8\)∫\(0^2\)pi ∫\(0^2\) \(e^{r cos(\theta)\) - r sin(theta)) r (1 - 2\(r^2\) \(cos^2(\theta))\)dz dr dtheta

= 2pi ∫\(0^2\) \(e^{-r sin(\theta))\)r (1 - 2\(r^2\) \(cos^2(\theta))\) (2-\(r^2\)) dr dtheta

This integral is quite complex and does not have an analytical solution. Therefore, we need to evaluate it numerically using a computer or calculator.

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By using compound interest, there will be$554.68in the account after 2 years.

Compound interest is interest that is calculated on the original principal of a loan or deposit, as well as on any accumulated interest from previous periods.

Compound interest is calculated using the following formula:

Compound interest = P * (1 + r/n)^(nt) - P

To calculate the total amount in the account after 2 years, we can use the following formula:

Total amount = P * (1 + r/n)^(nt)

In this formula, P is the principal amount (the initial deposit of $500), r is the annual interest rate (5.2%), n is the number of times that interest is compounded per year (12 in this case, since the interest is compounded monthly), and t is the number of years for which the interest is compounded (2 in this case).

Substituting the given values into the formula, we get:

Total amount = $500 * (1 + 0.052/12)^(12*2) = $554.68

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Answer:

(0,4)

Step-by-step explanation:

System of Equations:

\(\left \{ {{12x-5y=-20} \atop {x+4=y}} \right.\)

x= y-4 .... Change format so you can substitute to first equation

12(y-4)-5y=-20 .... Plug in x= y-4  to first equation

12y - 48 -5y = -20 ..... Distributed

7y -48 =-20 .... Added like terms

7y=28 .... Added 48 to both sides

y=4

.... Plug y into the second equation to find x

x + 4=y

x +4 = 4 .... Plugged in y

x = 4-4 .... Subtracted 4 from both sides

x=0

Your answer is (0,4)

Hope this helps:)

Answer:

Step-by-step explanation:

In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.

Answer:

4

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

Three consecutive even integers can be represented by x, x+2, x+4.  The sum is 3x+6, which is equal to 108.  Thus, 3x+6=108.  Solving for x yields x=34.  However, the question asks for the largest number, which is x+4 or 38.  Please make sure to answer what the question asks for!

You could have also plugged in the answer choices.  If you plugged in 38 as the largest number, then the previous even integer would be 36 and the next previous even integer 34.  The sum of 34, 36, and 38 yields 108.

We have the lease of a building is for 10 years with an annual rent of $48 000.

We first determine the 7.5% for the first 5 years, for that we add the cost of the rent for 5 years, that is:

In 5 years the rent will be of $240 000, now we find the 7.5%:

Her commision for the first 5 years is going to be of $18 000.

Now we determine the 5% for the next 3 years, for this we determine the rent for 3 years:

The rent for 3 years adds $144 000, now we determine the 5%:

From this we have that the commission for the next 3 years will be of $7200.

And finally, we determine the rent for the two remaining years:

We have that the last two years the rent will be of $96000, now we determine the 3.5% of her commission during that time:

From this we have her commission for the last two years will be of $3360.

Finally we add all of the values of the commissions she will get:

From this we have that the total commision money she will be getting during those 10 years will be $28 560.

Answer:

20

Step-by-step explanation:

Answer:

\((i). \\ { \tt{area = 2(\frac{1}{2} \times base \times height}} )\\ = 4 \times 3 \\ = 12 \: sq \: units \\ \\ (iii). \\ = \frac{1}{2} \times 8 \times 6 \\ = 24 \: sq \: units \\ \\ (ii). \\ = \frac{1}{2} \times 12 \times 5 \\ = 30 \: sq \: units\)

We can say that the value of k will be equal to the y-coordinate of the center of the circle (since k represents the y-coordinate of the center).

To answer this question, we need to use the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

Where h and k represent the coordinates of the center of the circle, and r represents the radius. In this case, we are given that the circle has center (h, k) and radius 10. So we can write:

(x - h)^2 + (y - k)^2 = 10^2

We are asked to find the value of k. To do this, we need to look at the equation of the circle and notice that the y-coordinate is paired with k. This means that we can isolate k by rearranging the equation as follows:

(y - k)^2 = 10^2 - (x - h)^2

y - k = ±√(10^2 - (x - h)^2)

k = y ±√(10^2 - (x - h)^2)

Since we don't have any information about the x-coordinate, we can't solve for a specific value of k. However, we can say that the value of k will be equal to the y-coordinate of the center of the circle (since k represents the y-coordinate of the center). Therefore, the answer is:

k = y

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The polynomial 2x^3 - 4x^2 + 3x - 7 has the remainder is -1, and the quotient is 2x^2 + 3.

To find the quotient and remainder of a polynomial, follow these steps:

Arrange the polynomials in descending order of degrees.

Divide the term with the highest degree of the dividend polynomial by the term with the highest degree of the divisor polynomial. This will be the first term of the quotient.

Multiply the divisor polynomial by the first term of the quotient and subtract the result from the dividend polynomial.

Bring down the next term from the dividend polynomial.

Repeat steps 2 to 4 until all the terms of the dividend polynomial are exhausted or the degree of the remaining polynomial is lower than the degree of the divisor polynomial.

The resulting polynomial after the division process is complete is the remainder.

The terms obtained during the division process form the quotient polynomial.

For example, let's divide the polynomial 2x^3 - 4x^2 + 3x - 7 by the polynomial x - 2.

The term with the highest degree in the dividend polynomial is 2x^3, and the term with the highest degree in the divisor polynomial is x.

Dividing 2x^3 by x gives 2x^2, which is the first term of the quotient.

Multiply (x - 2) by 2x^2, giving 2x^3 - 4x^2.

Subtracting 2x^3 - 4x^2 from the dividend polynomial gives 3x - 7.

Bring down the next term, which is 3x.

Dividing 3x by x gives 3, which is the next term of the quotient.

Multiply (x - 2) by 3, giving 3x - 6.

Subtracting 3x - 6 from the remaining polynomial gives -7 + 6 = -1.

Since the degree of -1 is lower than the degree of x - 2, the division process is complete.

The remainder is -1, and the quotient is 2x^2 + 3.

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Answer:

Is "y (x-4) squared +6":     y = (x-4)^2 + 6?

If so,

x = y^(1/2) - 6^(1/2) + 4

Step-by-step explanation:

y^(1/2)= (x-4) + 6^(1/2)

(x-4) = y^(1/2) - 6^(1/2)

x = y^(1/2) - 6^(1/2) + 4

£1 = 99.72 rupees -> £450 = 44874 rupees.

As the post office only has 500 rupee papers, once we calculate out the result, we have to round down to the nearest whole number.

The amount of rupee papers we can change out is : 44874 : 500 = 89.748 (papers)
We round down to 89 papers.

Null hypothesis (H0): The global mean temperature in the current year is not lower than the global mean temperature in 1998 (μ ≥ 14.3°C).

Alternative hypothesis (H1): The global mean temperature in the current year is lower than the global mean temperature in 1998 (μ < 14.3°C).

As a climatologist, you can formulate the null and alternative hypotheses for testing whether the global mean temperature in the current year is lower than the global mean temperature in 1998. Here are the hypotheses:

Null hypothesis (H0): The global mean temperature in the current year is not lower than the global mean temperature in 1998.

H0: μ ≥ 14.3

Alternative hypothesis (H1): The global mean temperature in the current year is lower than the global mean temperature in 1998.

H1: μ < 14.3

In statistical terms, the null hypothesis assumes that the population mean temperature in the current year is greater than or equal to 14.3 degrees Celsius (or not lower than the temperature in 1998). The alternative hypothesis, on the other hand, suggests that the population mean temperature in the current year is lower than 14.3 degrees Celsius (lower than the temperature in 1998).

To test these hypotheses, you will need to gather more data and conduct appropriate statistical tests. The preliminary sample mean of 15.1 degrees Celsius will serve as a starting point, but further analysis will be necessary to make a conclusive determination.

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The probability of selecting a score greater than X = 50 from a normal population with μ = 60 and σ = 20 is approximately 0.3085, which corresponds to answer choice b).

To determine the probability of selecting a score greater than X = 50 from a normal population with μ = 60 and σ = 20, we need to calculate the z-score and find the corresponding probability using the standard normal distribution table or a statistical calculator.

The z-score can be calculated using the formula:

z = (X - μ) / σ

Substituting the values:

z = (50 - 60) / 20

z = -0.5

Using the standard normal distribution table or a calculator, we can find the probability corresponding to a z-score of -0.5.

The correct answer is b) 0.3085, as it corresponds to the probability of selecting a score greater than X = 50 from the given normal distribution.

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Answer:

River C: 2,600 miles

River D: 3,000

Step-by-step explanation:

Since beside a 400 mile difference they are the same just subtract 400 and divide it by 2 then add 400 to find river d

Answer:

C) 3

Step-by-step explanation:

To find the slope given a table with points, use the formula:
\(\frac{y_2-y_1}{x_2-x_1}\)

Use the points:

(-2,-2) and (-1,1)

\(\frac{1+2}{-1+2}\)

simplify

3/1

=3

So, the slope is 3.

Hope this helps! :)

Answer:

Your answer is 37.7

Step-by-step explanation:

C=2πr=2·π·6≈37.69911

Given that radius of circle is 6m and taking π = 3.14, the circumference of circle is equal to 37.68m.

The circumference of a circle is the length of the boundary of a circle. It is measured by the formula 2πr where, r is the radius of the given circle. The radius of a circle is the length of the line segment joining any point on the circle to the center of the circle.

Given in the question,

radius = r = 6m

take π = 3.14

circumference of a circle = 2πr = 2 * 3.14 * 6 = 37.68m

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Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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it would be beneficial to analyze other variables such as gender and opinion on the topic for a more comprehensive understanding of the local political opinion.

If the standard deviation of the ages is zero, then all individuals in the sample must have the same age of 25 years old. This means that the sample is not diverse and may not be representative of the entire neighborhood's opinion on the political topic. Therefore, conclusions drawn from this sample may not accurately reflect the opinions of the entire population. It is important to ensure that the sample is diverse and representative to make valid conclusions about a sensitive political topic.
Based on the data you collected, which includes age, gender, and opinion on the local sensitive political topic, you calculated the average age to be 25 years old and the standard deviation of the ages to be zero years old. This means that all individuals in your neighborhood are exactly 25 years old. Since there is no variation in age, it would be beneficial to analyze other variables such as gender and opinion on the topic for a more comprehensive understanding of the local political opinion.

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The maximum area to enclose a rectangular pasture with one side of the pasture up against a river is equal to 500,000 square feet.

As given in the question,

Let 'x' represents the length of the rectangular pasture

And 'y' represents the width of the rectangular pasture

Condition:

One side of the pasture is up against a river

Perimeter of the rectangular pasture with one side up against river

= x + 2y

⇒ 2000 = x + 2y

⇒x= 2000 - 2y

Area of the rectangular pasture

=( 2000 - 2y )( y )

= - 2 ( y² - 1000y)

= -2( y² - 1000y + 250000 - 250000 )

= -2 (y - 500 )² + 500, 000

Maximum area is at y = 500

Maximum area is 500,000

Therefore, the maximum area of the given rectangular pasture is 500,000 square pasture.

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Answer:

2/3 pounds of peanuts and

1/3 pound of cashews for every 1 pound of the mixture.

Step-by-step explanation:

Let x = the pounds of peanuts

Let 1-x = the pounds of cashews.

3x + 4.5(1 - x) = 3.5  Distribute the 4.5

3x + 4.5 - 4.5x = 3.5  Combine like terms

-1.5x + 4.5 = 3.5  Subtract 4.5 from both sides

-1.5x = -1  Divide both sides by -1.5

x = 2/3  This is the pounds of peanuts

1-x

1 - 2/3 = 1/3  This is the pounds of cashews.

Answer:2

Step-by-step explanation:

Answer: 22

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x\)

It is FALSE to state that if a researcher is interested determining if there is a relationship betweenethnicity and job type, then a Chi- Square Goodness of Fit test can be   used.

A Chi-Square Goodness of Fit test is not   appropriate for determining the relationship between ethnicity and job type.

This test is used to assess thedistribution of categorical variables within a single population or sample,   comparing observed frequencies with expected frequencies.

To examine the relationship between ethnicity and job type, a Chi-Square test of independence   or another suitable statistical test, such as logistic regression,would be more appropriate.

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Answer:

Simplifying

10x + 44 = 8X + -23

Reorder the terms:

44 + 10x = 8X + -23

Reorder the terms:

44 + 10x = -23 + 8X

Solving

44 + 10x = -23 + 8X

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-44' to each side of the equation.

44 + -44 + 10x = -23 + -44 + 8X

Combine like terms: 44 + -44 = 0

0 + 10x = -23 + -44 + 8X

10x = -23 + -44 + 8X

Combine like terms: -23 + -44 = -67

10x = -67 + 8X

Divide each side by '10'.

x = -6.7 + 0.8X

Simplifying

x = -6.7 + 0.8XStep-by-step explanation: