TANK A large tank is currently holding 12,000 gallons of water. The water will drain at a constant rate of 100 gallons per minute until the volume of water in the tank is 4,000 gallons. Write an equation to find the number of minutes m it will take for the specified amount of water to drain.

Answer:

1a. Let’s assume that the length of the north side of the house is represented by ‘x’. Then the polynomial that represents the length of the north side of the house is x.

1b. There is no expression to simplify.

2a. Your cousin is not correct.

2b. The length of the north side of the house is represented by ‘x’ and not by ‘9y+2y’. Therefore, your cousin is not correct.

The polynomial stated by the cousin as the length of the north side of the house, 9y + 2y, simplifies to 11y. Thus, the cousin is not correct. Polynomials and simplifying expressions are part of basic algebra skills.

Based on your cousin's statement, the polynomial representing the length of the north side of the house is 9y + 2y. To determine the correctness of this polynomial, we must first simplify the expression. By combining like terms (terms with the same variable and exponent), the expression simplifies to 11y. So, the length of the north side is represented by 11y, not 9y + 2y. Hence, your cousin's statement is not correct.

Understanding how to combine like terms, simplify expressions, and handle polynomials is an important part of basic algebra skills. Polynomials can be used to represent many real world quantities such as the length of a side of a house as in this problem. Remember that it is crucial to perform all calculations accurately to avoid errors.

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The Difference in the amounts that Tsion and Ibrahim paid for their watches is £3.85.

To find the difference in the amounts that Tsion and Ibrahim paid for their watches, we need to convert the prices to the same currency. We can use the exchange rates given to convert both prices to pounds.

1 Singapore dollar = £0.58

72 Singapore dollars = 72 x £0.58 = £41.76

1 Hong Kong dollar = £0.09

399 Hong Kong dollars = 399 x £0.095 = £37.91

Therefore, Tsion paid £41.76 for the watch and Ibrahim paid £37.91 for the same model of watch.

To find the difference in the amounts paid, we can subtract the smaller amount from the larger amount:

£41.76 - £37.91 = £3.85

Therefore, the difference in the amounts that Tsion and Ibrahim paid for their watches is £3.85.

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Answer: 70%

Step-by-step explanation:

obviously 7/10 gives you 70%

Answer:

70%

Step-by-step explanation:

If 3 of the pins were knocked down, that means 7 pins were still standing.

Next, to find what percent 7 is of 10, divide 10 by 100 to get 0.1.

0.1 is 1% of 10, so we need to divide 7 by 0.1 to find the percentage, which is 70.

The zero's of the polynomial 4x² - 4x - 8 are as follows:

x = 2 or x = -1

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. In other words, the zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

Therefore, let's find the zero's of the polynomial.

4x² - 4x - 8 = 0

divide through by 4

x² - x - 2 = 0

x² + x - 2x - 2 = 0

x(x + 1) -2(x + 1) = 0

(x - 2)(x + 1) = 0

Therefore,

x = 2 or x = -1

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The zeros of polynomial 4x² - 4x - 8, are 2 and -1. The relationship between the zeros and coefficients are 1 and -2.

Let the given polynomial be p(x) = 4x² - 4x - 8

To find zeros, take p(x) = 0

Factorizing the equation,

4x² - 4x - 8 = 0

4(x² - x - 4) = 0

x² - 2x + x- 2 = 0

x(x-2) + 1(x-2) = 0

(x-2) (x+1) = 0

∴ x=2 and x=-1

The roots of 4x² - 4x- 8 are 2 and -1

Relationship between the sum of zeros and coefficients:

-Coefficient of x/ coefficient of x²

(-1) + 2 = -(-4)/4 = 1

Relation between the product of zeros and coefficients:

Constant/ coefficient of x²

(-1) × 2 = -8/4 = -2

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There are 6,227,020,800 ways in which Aaron can arrange the 13 songs on the playlist.

To determine the number of ways Aaron can arrange the 13 songs on the playlist, we can use the concept of permutations. Since the order of the songs matters (i.e., each arrangement is different), we can use the formula for permutations.

The number of ways to arrange n items in a specific order is given by n factorial, denoted as n!. The factorial of a number n is the product of all positive integers less than or equal to n.

In this case, Aaron has 13 songs to arrange on the playlist, so the number of arrangements can be calculated as:

13! = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Calculating this expression, we find:

13! = 6,227,020,800

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The coordinates of point P that represents the weighted average of the set of points are (-8/5, y).

Given that point A weighs 3 times as much as point C. This implies that the weight of point C is 1, and the weight of point A is 3.

To find the weighted average of the points, we can use the formula:

[tex]P = \dfrac{(w_1 \times A + w_2 \times B + w_3 \times C)}{(w_1 + w_2 + w_3)}[/tex]

where P is the weighted average point, w₁, w₂, and w₃ are the weights of points A, B, and C, respectively, and A, B, and C are the coordinates of the points.

Substituting the given values, we have:

P = (3 × (-5) + 0 + 1 × 7) / (3 + 1 + 1)

P = (-15 + 7) / 5

P = -8/5

Therefore, the coordinates of point P that represents the weighted average of the set of points are (-8/5, y).

The y-coordinate cannot be determined without additional information.

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According to the Census 2000, the overall American Indian and Alaska Native population had a younger median age compared to the national median age. The national median age in 2000 was 35.3 years, whereas the median age for the American Indian and Alaska Native population was 26.3 years.

This can be attributed to several factors, including higher fertility rates and lower life expectancies in some American Indian and Alaska Native communities. Additionally, many Native American tribes have a strong cultural emphasis on family and community, which can contribute to larger family sizes and a younger overall population. It is important to note that these demographic trends may have shifted in the years since the Census 2000, and that there is significant diversity within the American Indian and Alaska Native population in terms of age, geography, and culture.

it is clear that the American Indian and Alaska Native population had a younger median age in 2000 compared to the national median age.

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Answer:5$

Step-by-step explanation:

The length of Alice’s step is 0.6 m.

The length of Basil’s step is 0.8 m.

Since Basil takes 100 fewer steps than Alice to walk 240 m;

the number of steps Basil takes = (240/A) - 100.

Basil's step is 20 cm longer than Alice's step;

B = A + 0.2

The distance each person walks is calculated as;

A(240/A) = (A + 0.2) [(240/A) - 100]

240 = 240 - 100A + 48/A - 20

0 =  - 100A + 48/A - 20

100A - 48/A = -20

100A² - 48 = -20A

100A² + 20A - 48 = 0

Solve for A using formula method;

A = 0.6 m

Basil's step length:

B = 0.6 + 0.2

B = 0.8 m

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Answer:

Step-by-step explanation:

if 32 was originally there now some left and 21 are left we can pit it into a subtraction equation.

32-?=21

we can also make an addition equation

21+?=32

we know that ?= 11 because of commen scene.

Answer: 32-(__)=21

Step-by-step explanation:

I like to think of what I'm given to be the left side, and what's after to be the right side. If there are 32 originally, then you take some away (since 21 is fewer than 32), that's subtracting by some number. Then, we have 21 left so put 21 on the right side. To solve, subtract the 21 from the 32 and add the unknown over to get (__)=9

By finding the inverses we can see that:

Two functions g(x) and g⁻¹(x) are inverses if:

g⁻¹(g(x)) = x

Here we know that the function g is defined by:

g={(-8, -3), (-3, 2), (3, 0), (5, 6)}

And we want to find:

g⁻¹(-3)

On the table we can see that g(-8) = -3, then:

g⁻¹(-3) = -8

And we have:

h(x) = -2x + 13

Evaluating on the inverse we should get:

h(h⁻¹(x)) = x

            = -2*h⁻¹(x)   + 13 = x

Solving for the inverse:

h⁻¹(x) = (x - 13)/-2

Now we can get the product:

(h⁻¹*h)(3) = (-2*3 + 13)(3 - 13)/-2

              = 7*5 = 35

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Step-by-step explanation:

The triangles are similar. Writing a proportion:

(3x − 5 + 10) / 28 = (3x − 5) / 20

Cross multiply:

20 (3x − 5 + 10) = 28 (3x − 5)

Simplify and solve:

20 (3x + 5) = 28 (3x − 5)

5 (3x + 5) = 7 (3x − 5)

15x + 25 = 21x − 35

60 = 6x

x = 10

False. The symbol x¯ represents the population mean of all possible sample means of size n.

The symbol x¯ (x-bar) represents the sample mean, not the population mean of all possible sample means of size n. The population mean of all possible sample means of size n is denoted by μ (mu). The sample mean, x¯, is calculated by taking the average of the observations in a specific sample.

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The dimensions of the deck are 26 meters by 16 meters and 84 meters of fencing will need to be purchased for the deck and pool area.

Let's denote the width of the deck as 'x'.

The length of the pool is 20 meters, and the width is 10 meters.

The combined area of the pool and the deck is 264 square meters.

The area of the pool is length times width: 20 × 10 = 200 square meters.

The area of the deck is (20 + 2x)(10 + 2x) - 200 square meters. We subtract 200 square meters to account for the area of the pool.

Therefore, the polynomial equation representing the given information is:

(20 + 2x)(10 + 2x) - 200 = 264

(200 + 40x + 20x + 4x^2) - 200 = 264

4x²+ 60x = 264

4x² + 60x - 264 = 0

Factoring out a common factor of 4:

4(x² + 15x - 66) = 0

Factoring the quadratic equation:

(x + 18)(x - 3) = 0

The width of the deck is x = 3 meters.

The dimensions of the deck can be found by adding twice the width to the length and width of the pool:

Length of the deck = 20 + 2x = 20 + 2(3) = 26 meters

Width of the deck = 10 + 2x = 10 + 2(3) = 16 meters

Therefore, the dimensions of the deck are 26 meters by 16 meters.

To calculate the length of fencing required, we need to consider the perimeter of the deck.

Perimeter of the deck = 2×(Length of the deck + Width of the deck)

Perimeter of the deck = 2 × (26 + 16)

Perimeter of the deck = 2 × 42

Perimeter of the deck = 84 meters

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The pollster should survey approximately 2,401 U.S. voters to estimate the true proportion of voters who oppose capital punishment with 95% confidence and a margin of error of 2%.

In order to estimate the true proportion of U.S. voters who oppose capital punishment with a 95% confidence level and a margin of error of 2%, the pollster should survey approximately 2,401 voters.



To calculate the sample size needed for this estimation, we can use the formula:

n = (Z² * p * q) / E²

where n is the sample size, Z is the z-score corresponding to the confidence level (in this case, 1.96 for 95% confidence), p is the estimated proportion of voters who oppose capital punishment, q is the estimated proportion of voters who support capital punishment (which is 1-p), and E is the desired margin of error (in this case, 0.02).

Assuming a conservative estimate of p = q = 0.5, we can plug in the values and solve for n:

n = (1.96² * 0.5 * 0.5) / 0.02² ≈ 2,401

Therefore, the pollster should survey approximately 2,401 U.S. voters to estimate the true proportion of voters who oppose capital punishment with 95% confidence and a margin of error of 2%.



In conclusion, to estimate the true proportion of U.S. voters who oppose capital punishment with a 95% confidence level and a margin of error of 2%, the pollster should survey approximately 2,401 voters. This sample size calculation is based on the formula for calculating sample size using the z-score, estimated proportions, and desired margin of error

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Answer: It means Undo

Step-by-step explanation:

The second term in the sequence is 0.

To solve the problem, we can use the fact that each term after the second is the sum of the two preceding terms. Let's call the first term a and the second term b. Then, according to the problem, we have:

a = 3 (the first term is 3)

b = ?

c = a + b = 3 + b

d = b + c = b + (3 + b) = 2b + 3

e = c + d = (3 + b) + (2b + 3) = 3b + 6

We also know that the fifth term is 3, so we can set e equal to 3 and solve for b:

3b + 6 = 3

3b = -3

b = -1

Therefore, the second term in the sequence is 0, since each term after the second is the sum of the two preceding terms and the first term is 3.

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[tex](\stackrel{\stackrel{ adjacent }{x}}{-3}~~,~~\stackrel{\stackrel{ opposite }{y}}{-\sqrt{7}})\hspace{5em}\textit{let's find the \underline{hypotenuse}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{-3}\\ o=\stackrel{opposite}{-\sqrt{7}} \end{cases}[/tex]

[tex]c=\sqrt{ (-3)^2 + (-\sqrt{7})^2}\implies c=\sqrt{ 9 + 7 } \implies c=\sqrt{ 16 }\implies c=4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{4}}~\hfill[/tex]

No, the variances are not similar enough to use the pooled t test. The ratio of the two variances (25/8) is greater than 3, which is the typical cutoff for determining similarity of variances. Therefore, an alternative method such as the Welch's t-test or a non-parametric test should be used to compare the means.

To determine if the variances are similar enough to use a pooled t-test, you can perform an F-test for equality of variances. Follow these steps:

1. Calculate the F statistic by dividing the larger variance by the smaller variance: F = var2 / var1 = 25 / 8 = 3.125.

2. Determine the degrees of freedom for each group: df1 = 10 - 1 = 9 and df2 = 10 - 1 = 9.

3. Check the F critical value for the given degrees of freedom and chosen significance level (e.g., 0.05) using an F-distribution table or a calculator. For df1 = 9 and df2 = 9 at a 0.05 significance level, the F critical value is approximately 3.18.

4. Compare the calculated F statistic to the F critical value: 3.125 < 3.18.

Since the F statistic is less than the F critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, the variances are similar enough to use the pooled t-test to evaluate differences in the means. The answer is yes.

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The area of the part of the plane 2x + 5y + z = 10 that lies in the first octant is 8√6/5 square units.

The first octant is the region of space where x, y and z are all positive. We need to find the area of the surface of the part of the plane 2x + 5y + z = 10 that lies in the first octant.

To find the surface area, we need to first parameterize the surface. We can do this by fixing one variable and expressing the other two in terms of it. Let's fix x:

2x + 5y + z = 10

Solving for z, we get:

z = 10 - 2x - 5y

Now, we can express y in terms of a parameter t:

y = t

And we can express z in terms of x and t:

z = 10 - 2x - 5t

So the parameterization of the surface is:

r(x, t) = (x, t, 10 - 2x - 5t)

To find the surface area, we need to compute the magnitude of the cross product of the partial derivatives of r with respect to x and t:

|∂r/∂x x ∂r/∂t| = |<1, 0, -2>| x |<0, 1, -5>| = |<2, 1, 1>|

= √(2^2 + 1^2 + 1^2) = √6

So the surface area is:

∫∫ √6 dA

where the double integral is over the region in the first octant where 2x + 5y + z = 10. We can express this region as:

0 ≤ x ≤ 5

0 ≤ y ≤ (10 - 2x)/5

0 ≤ z ≤ 10 - 2x - 5y

So the integral becomes:

∫₀^₅ ∫₀^(10-2x)/5 √6 dz dy dx

Evaluating this integral, we get:

∫₀^₅ ∫₀^(10-2x)/5 √6 dz dy dx = √6 ∫₀^₅ ∫₀^(10-2x)/5 dz dy dx

= √6 ∫₀^₅ (10-2x)/5 dy dx

= √6 ∫₀^₅ 2 - (2/5)x dx

= √6 [2x - (1/5)x²] from 0 to 5

= √6 [10 - (1/5)(25)]

= √6 (8/5)

= 8√6/5

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If Harper divides 12 baby carrots evenly among her 3 pet hamsters, Harvey, Hammy, and Flo, then each hamster would get 4 baby carrots. However, since Flo ate 2 baby carrots right away, she would only have 2 baby carrots left.


When Harper divides a package of 12 baby carrots among her 3 pet hamsters, each hamster gets 4 baby carrots. But since Flo eats 2 baby carrots right away, she is left with only 2 baby carrots. This means that Harvey and Hammy also have 4 baby carrots each, as they did not eat any carrots. It's important to divide food equally among pets, as it ensures that every pet gets an equal share of nutrients.


In conclusion, Harper divided 12 baby carrots among her 3 pet hamsters equally, but Flo ate 2 baby carrots right away. Therefore, Flo was left with only 2 baby carrots, while Harvey and Hammy had 4 baby carrots each. Dividing food equally among pets is important to ensure that every pet gets a fair share of nutrients.

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Answer:a

Step-by-step explanation:s

The center is (1,0), thus the center lies on the x-axis, the radius is 3 units and the radius of the circle is the same with x² + y² = 9.

The radius is half the diameter of a circle and the center of the circle is a point from which all distance to the edge of the circle is equal.

The equation that represents the center of the circle equation is (x - h)² + (y - k)² = r², where h,k represents the center and r is the radius.

Our circle in this form is: (x − 1)² +(y − 0)² = 3. Thus, h = 1, k = 0, r = 3. The standard form is y² + (x − 1)² = 9.

We can conclude that the center is (1,0), thus the center lies on the x-axis, the radius is 3 units and the radius of the circle is the same with x² + y² = 9.

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Answer: 54, 63, 72

Step-by-step explanation: Well let's multiply 9 till 75 so 9(1), 18(2), 27(3), 36(4), 45(5), 54(6), 63(7), 72(8). The underlined numbers are ones that are divisible by 3. Hope this helps! :)

There are 720 different completed answer sheets possible, where no blanks are allowed.

In this problem, we have 6 questions and 6 different answers to match with each question. We need to determine how many different completed answer sheets are possible, where no blanks are allowed. To solve this, we'll use combinatorics and permutations.

To find the number of different completed answer sheets, we can consider each question as a distinct entity. Let's label the questions as Q1, Q2, Q3, Q4, Q5, and Q6. Similarly, let's label the answers as A1, A2, A3, A4, A5, and A6.

Since each question needs to be matched with a different answer, we can think of this as a one-to-one mapping between the questions and answers. In other words, we want to find the number of permutations of the answers that satisfy the matching condition.

The first question (Q1) can be matched with any of the 6 answers (A1, A2, A3, A4, A5, or A6). Once Q1 is matched, the second question (Q2) can be matched with any of the remaining 5 answers. Similarly, the third question (Q3) can be matched with any of the remaining 4 answers, and so on.

Using the fundamental principle of counting, we can multiply the number of choices available for each question.

The number of possible completed answer sheets is given by:

Number of completed answer sheets = 6 * 5 * 4 * 3 * 2 * 1 = 720.

So, there are 720 different completed answer sheets possible, where no blanks are allowed.

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The Panthers have the largest overall size hat for their players based on the mean calculation. The mean is the best measure of center to compare the two teams because it takes into account all the data and provides a representative value of the central tendency.

To determine which team has the largest overall size hat for their players, we need to find the team with the highest average hat size. The best measure of center to compare the two teams would be the mean, as it provides a representative value of the central tendency of the data.
To calculate the mean for each team, we need to add up all the hat sizes and divide by the number of players on the team. For the Cougars, the sum of the hat sizes is 308.5 and there are 14 players, so the mean hat size is 22.04 inches. For the Panthers, the sum of the hat sizes is 333 and there are also 14 players, so the mean hat size is 23.79 inches.
Based on these calculations, we can see that the Panthers have the largest overall size hat for their players, with an average hat size of 23.79 inches compared to the Cougars' average hat size of 22.04 inches.
In conclusion, the Panthers have the largest overall size hat for their players based on the mean calculation. The mean is the best measure of center to compare the two teams because it takes into account all the data and provides a representative value of the central tendency.

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Both of Nick's bags weigh 41 kilograms combined.

In mathematical terms, if we let W1 be the weight of the first bag and W2 be the weight of the second bag, then the total weight of both bags can be expressed as W1 + W2.

Substituting the given values, we get:

Total weight of both bags = 24 + 17 = 41 kilograms.

This is a simple addition problem that involves adding the weights of two bags to find the total weight.

The complete question is:

Nick is going on vacation. one of his bags weighs 24 kilograms. the other bag weighs 17 kilograms. how much do both of nick's bags weigh combined?

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Answer:

he correct answer is c. vD = -7 vs = 5.

The Doppler shift equation is:

f = f' (v - vD) / (v - vS)

Where:

f is the frequency detected

f' is the frequency emitted

v is the speed of sound

vD is the velocity of the detector

vs is the velocity of the source

In this case, the source is traveling at 5 m/s away from the detector, the detector is traveling at 7 m/s toward the source, and there is a 3 m/s wind blowing from the source toward the detector.

The velocity of the detector is negative because it is moving towards the source. The velocity of the source is positive because it is moving away from the detector.

Therefore, the values that should be substituted into the Doppler shift equation are:

vD = -7

vs = 5

Step-by-step explanation: