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An NFL playing field is a rectangle. The length of the field (excluding end zones) is 40 yards more than twice the width. The perimeter of there playing field is 260 yards. What are the dimensions of the field in yards?

Answer:

9÷ 1/2 = 9 • 2/1 = 18 bags of trail mix

Step-by-step explanation:

You can solve this problem using division.  Since there are 9 pounds of trail mix to divide up, you would start with 9 pounds and divide it by 1/2 pound to find the number of bags you could make (use the reciprocal of the divisor 1/2)

Answer:

$3,096

Step-by-step explanation:

To find the total interest Mr. Quesada will pay, we need to first calculate the total amount he will pay back, and then subtract the original amount borrowed.

The total amount Mr. Quesada will pay back over 24 months is:

$629 x 24 = $15,096

Subtracting the original loan amount, we get:

$15,096 - $12,000 = $3,096

So Mr. Quesada will pay a total of $3,096 in interest over the course of the loan.

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

arrange the numbers in the other of magnitude

:

2.4,3.3,5.2,5.8,7,7.6,8.4,8.6,9.7

then check for the middle number(s)

median = 7

Answer:

Domain:  (0, positive infinity)

Step-by-step explanation:

6x^2 / x greater than or equal to 0

6x^2 = 0

x = 0

So, the answer is ( 0, positive infinity)

The equations of the two given planes are\(\[\begin{aligned} 10x+4y-5z&=-27 \\ 13x+10y-15z&=-75 \end{aligned}\]\)

We will solve the above two equations simultaneously to get the intersection point. By assuming that the intersection point is\(\[\left( x,y,z \right)\]\)

Now, we will solve this system of equation by the elimination method. We will eliminate x to get the equation in terms of y and z:

\(\[\begin{aligned} &\ 10x+4y-5z=-27 \\ &\ 13x+10y-15z=-75 \\\implies&\ 26x+8y-10z=-54 &&\text{(Multiplying first equation by 2)} \\ &\ 13x+10y-15z=-75 \\\implies&\ 13x+5y-5z=-27 &&\text{(Subtracting equation 1 from 2)} \end{aligned}\]\)

Now, we will solve these equations to get the values of y and z. To do this, we will multiply equation 2 by 2 and subtract equation 1 from it:

\(\[\begin{aligned} &\ 26x+10y-10z=-54 \\ -&\ (26x+8y-10z=-54) \\ =&\ 2y=0 \\ \implies&\ y=0 \end{aligned}\]\)

Similarly, we will multiply equation 2 by 3 and subtract equation 1 from it to get the value of z:

\(\[\begin{aligned} &\ 39x+15y-15z=-81 \\ -&\ (26x+8y-10z=-54) \\ =&\ 13x-7z=-27 \\ \implies&\ 13x-7z=-27 \\ \implies&\ 13x=7z-27 \end{aligned}\]\)

Now, we will substitute the value of y and z into any one of the given equations to get the value of x:

\(\[\begin{aligned} 10x+4y-5z&=-27 \\ 10x+4\left( 0 \right)-5\left( \frac{7x-27}{13} \right)&=-27 \\ 130x+0-35\left( 7x-27 \right)&=-351 \\ \implies x&=-10 \end{aligned}\]\)

Hence, the coordinates of the intersection point are \(\[\left( -10,0,-5 \right)\]\) A

The parametric equations of the line are \(\[\begin{aligned} x\left( t \right)&=-10t \\ y\left( t \right)&=0 \\ z\left( t \right)&=-5t \end{aligned}\]\)

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If each side of a square is increasing at a rate of 7 cm/s, then the rate of increasing the area of the the square when the area of the square is 64 cm square is 112 centimeter square per second

The rate of change of length with respect to the time = 7 cm per second

That is

dl / dt = 7 cm per second

The area of the square = l^2

Where l is the length of the square

The rate of change area with respect to the time is

dA / dt = 2l dl/dt

The area is given that 64 centimeter square and the side will be 8 cm

Substitute the values in the equation

dA / dt = 2 × 8 × 7

= 112 centimeter square per second

Therefore, the rate of increasing the area is 112 centimeter square per second

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Answer:

12.17secs

Step-by-step explanation:

Given the equation that models the height as y=-16x^2+187x+93

The rocket will hit the groung at y = 0

The equation becomes;

0 =-16x^2+187x+93

16x^2-187x-93 = 0

Factorize

x = 187±√187²-4(16)(-93)/2(16)

x = 187±√34,969+5952/32

x = 187±√40,921/32

x = 187±202.29/32

x = 187+202.29/32

x = 389.29/32

x = 12.17secs

Hence the required time that t will take is 12.17secs

Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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the equation for the given values of the variables. m+n for m=(7)/(6) and n=-(7)/(9) is 7/18.

To evaluate the expression m + n for the given values of m and n, substitute the values of m and n into the expression and perform the addition.

Given: m = 7/6 n = -7/9

Substituting the values: m + n = (7/6) + (-7/9)

To add the fractions, we need a common denominator. The least common multiple of 6 and 9 is 18.

Converting the fractions to have a common denominator: m + n = (7/6)(3/3) + (-7/9)(2/2) = (21/18) + (-14/18)

Now, we can add the fractions: m + n = (21 - 14)/18 = 7/18

Therefore, when m = 7/6 and n = -7/9, the value of m + n is 7/18.

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The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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The set of positive integers (n) that satisfy the given condition, (n) is an odd integer is {1, 3, 5, 7, 9, 11, ...}.

All odd integers are integers that cannot be evenly divided by 2. Therefore, if (n) is an odd integer, it must be in the form of (n) = 2k + 1, where k is any integer.

To find all positive integers (n) that satisfy this condition, we simply need to plug in different values of k until we get positive values for (n).

For example, when k = 0, we get (n) = 2(0) + 1 = 1. This is a positive integer and satisfies the condition of being an odd integer.

When k = 1, we get (n) = 2(1) + 1 = 3. This is also a positive integer and satisfies the condition of being an odd integer.

We can continue this process and find that all positive integers that satisfy the condition of being an odd integer are given by (n) = 2k + 1, where k is any non-negative integer.

Therefore, the set of positive integers (n) that satisfy the given condition is {1, 3, 5, 7, 9, 11, ...}.

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Answer:

it's commutative property of addition

Step-by-step explanation:

commutative property is when we can change the position or swap the numbers when adding or multiplying any two numbers.

The Laplace transform of the differential equation 5y'' - 2y' + 4y = sinh(at), y(0) = -2, y' = 2, is Y(s) = a/(s^2 - a^2) / (5s^2 - 2s + 4), where Y(s) represents the Laplace transform of y(t). This is the algebraic equation obtained by applying the Laplace transform to both sides of the given differential equation.

To transform the differential equation 5y'' - 2y' + 4y = sinh(at), y(0) = -2, y' = 2 into an algebraic equation using Laplace transforms, we will take the Laplace transform of each term on both sides of the equation.

Let's denote the Laplace transform of y(t) as Y(s), where s is the Laplace variable. The Laplace transform of the derivative y'(t) will be denoted as Y'(s), and the Laplace transform of the second derivative y''(t) will be denoted as Y''(s).

Taking the Laplace transform of each term on both sides of the equation:

L[5y'' - 2y' + 4y] = L[sinh(at)]

Applying the linearity property of Laplace transforms and the derivatives property:

5L[y''] - 2L[y'] + 4L[y] = L[sinh(at)]

Now, let's substitute the Laplace transforms of y''(t), y'(t), and y(t) using the notation introduced earlier:

5s^2Y(s) - 2sY(s) + 4Y(s) = L[sinh(at)]

Simplifying the equation:

5s^2Y(s) - 2sY(s) + 4Y(s) = a/(s² - a²)

Now, we can rearrange the equation to solve for Y(s):

Y(s)(5s² - 2s + 4) = a/(s² - a²)

Y(s) = a/(s² - a²) / (5s² - 2s + 4)

Therefore, Y(s) = a/(s²- a²) / (5s² - 2s + 4) is the algebraic equation obtained by taking the Laplace transform of the given differential equation.

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Answer: A

Step-by-step explanation:

Looks like A, since it's the altitude.

Answer:

it is irrational number

the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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The probability that the top card is the king of spades or the bottom card is the queen of spades is  \(\frac{1}{26}\)

There are 52 cards in a deck of cards. There is only one king of spades in a deck of cards, and only one queen of spades. Therefore, the probability of getting the king of spades as the top card is 1/52 and the probability of getting the queen of spades as the bottom card is also 1/52.

There are no other restrictions for drawing a card in this problem. So the probabilities are additive.

P (king of spades as top card or queen of spades as bottom card) = P(king of spades as top card) + P(queen of spades as bottom card)

P (king of spades as top card or queen of spades as bottom card) =  \(\frac{1}{52}\) +  \(\frac{1}{52}\)

\(P = 2/52\)

Reducing \(\frac{2}{52}\) to lowest terms, we get,

P (king of spades as top card or queen of spades as bottom card) = \(\frac{1}{26}\)

Hence, the probability that the top card is the king of spades or the bottom card is the queen of spades is  \(\frac{1}{26}\).

Probability is the likelihood of an event occurring. The values are between 0 and 1. The closer it is to 1, the greater the probability.

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Answer:

6+ 45 = 500 #!_ djdjbdkeknf

Let it be x

ATQ

\( \\ \sf \longmapsto \: 3x - (6) = 45 \\ \\ \sf \longmapsto \:3x = 45+6 \\ \\ \sf \longmapsto \:3 x = 51 \\ \\ \sf \longmapsto \: x = \dfrac{51}{3} \\ \sf \longmapsto \: x=17\)

Answer:

Reflexive Property

Step-by-step explanation:

Reflexive Property: A quantity is congruent (equal) to itself.

AB = AB

Answer:

Reflexive Property

Step-by-step explanation:

The reflexive property states that any real number, a, is equal to itself. That is, a = a. So, AB=AB

The profit-maximizing level of output can be determined by finding the quantity where the difference between (TR) and (TC) is maximized.the (Π) can be calculated by subtracting the (TC) from the (TR).

To find the profit-maximizing level of output, we need to identify the quantity at which the difference between total revenue (TR) and total cost (TC) is maximized. This occurs when the marginal revenue (MR) equals the marginal cost (MC). Since total revenue is the product of price (P) and quantity (Q), and the given information provides a revenue function, we can differentiate the total revenue function with respect to quantity to find the marginal revenue function. Equating the marginal revenue to the marginal cost, we can solve for the quantity that maximizes profit.

Once the profit-maximizing level of output is determined, we can calculate the total profit (Π) by subtracting the total cost (TC) from the total revenue (TR) at that level of output. In other words, Π = TR - TC. Plugging in the quantity obtained from part (a) into the revenue and cost functions, we can evaluate the total profit. However, without specific values for the constants in the revenue and cost functions (such as 22 and 0.5 in the total revenue function and 1/3, -8.5, 50, and 90 in the total cost function), it is not possible to provide the exact calculations in this context.

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To compute a basis of the eigen space corresponding to eigen value -2, we need to find the null space of the matrix A + 2I, where A is the 3x3 matrix and I is the identity matrix.

The null space will give us the basis vectors of the eigen space

To find the eigen space corresponding to the eigen value -2, we start by constructing the matrix A + 2I, where A is the given 3x3 matrix and I is the 3x3 identity matrix. Next, we solve the homogeneous system of linear equations (A + 2I)x = 0, where x is a vector. The solutions to this system form the null space of the matrix A + 2I.

By finding a basis for this null space, we can obtain the basis vectors of the eigen space corresponding to the eigen value -2.

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Answer: A. 7

Step-by-step explanation:

3y-2=19

3y-2+2=19+2 (add 2 to both sides)

3y=21

3y/3=21/3 (divide by 3 on each side)

y=7

The given series is:[infinity] (−1)n2n 4n(2n)! n = 0The sum of this series can be found as follows:The given series can be written in summation notation as follows:∑ n=0 ∞ (−1)n2n 4n(2n)!

This can be rearranged as follows:∑ n=0 ∞ (−1)n (4n) / [(2n)!]Therefore, this series can be represented as the Maclaurin series of cos 2x, where x = 2 (because the series is represented as 4n instead of 2n).Therefore, the sum of the series is cos (2 × 2) = cos 4.The sum of the given series is cos 4. The given series can be written in summation notation as follows:∑ n=0 ∞ (−1)n2n 4n(2n)!

This can be rearranged as follows:∑ n=0 ∞ (−1)n (4n) / [(2n)!]Therefore, this series can be represented as the Maclaurin series of cos 2x, where x = 2 (because the series is represented as 4n instead of 2n).Therefore, the sum of the series is cos (2 × 2) = cos 4. The sum of the given series is cos 4.

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Answer:

hi people of the 21 century

Step-by-step explanation:

The indefinite integral of x^2 ln(1 + x) dx is evaluated as a power series using the formula for the power series expansion of ln(1 + x). The resulting power series has a radius of convergence of 1.

To evaluate the indefinite integral of x^2 ln(1 + x) dx as a power series, we can use the formula for the power series expansion of ln(1 + x):

ln(1 + x) = ∑(-1)^(n+1) (x^n) / n

where ∑ represents the sum from n=1 to infinity.

Substituting this into the integral, we get:

∫ x^2 ln(1 + x) dx = ∫ x^2 ∑(-1)^(n+1) (x^n) / n dx

= ∑(-1)^(n+1) ∫ (x^(n+2)) / n dx

= ∑(-1)^(n+1) (x^(n+3)) / (n(n+3))

To find the radius of convergence, we can use the ratio test:

|((x^(n+4)) / ((n+1)(n+4))) / ((x^(n+3)) / (n(n+3)))| = |x| lim(n→∞) (n/(n+1)) = |x|

The series will converge if this limit is less than 1, so the radius of convergence is 1. Therefore, the power series expansion of the indefinite integral is:

∫ x^2 ln(1 + x) dx = ∑(-1)^(n+1) (x^(4+n)) / (n(n+3)) with radius of convergence 1.

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A jet-liner is a type of plane not a model one word hyphenated but two words total.

A jet-liner is a type of plane that is specifically designed for passenger transportation on long-haul flights. It combines the efficiency and speed of a jet engine with a spacious cabin to accommodate a large number of passengers.

Jet-liners are commonly used by commercial airlines to transport people across continents and around the world. These planes are characterized by their high cruising speeds, advanced avionics systems, and extended range capabilities.

They are equipped with multiple jet engines, typically located under the wings, which provide the necessary thrust to propel the aircraft forward. Jet-liners also feature a pressurized cabin, allowing passengers to travel comfortably at high altitudes.

The design of jet-liners prioritizes passenger comfort, with amenities such as reclining seats, in-flight entertainment systems, and lavatories. They often have multiple seating classes, including economy, business, and first class, catering to a wide range of passengers' needs.

Overall, jet-liners play a crucial role in modern air travel, enabling efficient and comfortable transportation for millions of people worldwide.

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The reason why the number of failures and successes in two population proportions must be up to 10 is because it is important to have many of samples from both populations.

This refers to the probability displayed that a parameter will exist between a pair of values around the mean.

It measures the extent to which one can be certain or uncertain about ones sampling method. Confidence Intervals are usually constructed using levels of 95% or 99%.

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Answer: So we can assume that the two samples are independent.

The limit of the given expression as δx approaches 0 is 0.

To find the limit of the expression lim δx→0 sin^6(δx) - 12δx, we can use some trigonometric identities and algebraic manipulation.

Using the identity sin(2θ) = 2sin(θ)cos(θ), we can rewrite the expression:

lim δx→0 (sin^2(δx))^3 - 12δx

Next, we can use another trigonometric identity sin^2(θ) = 1 - cos^2(θ) to further simplify:

lim δx→0 ((1 - cos^2(δx))^3 - 12δx

Expanding the cube and rearranging the terms:

lim δx→0 (1 - 3cos^2(δx) + 3cos^4(δx) - cos^6(δx) - 12δx)

Now, we can consider the limit as δx approaches 0. Since all the terms in the expression except for -12δx are constants, they do not affect the limit as δx approaches 0. Therefore, the limit of -12δx as δx approaches 0 is simply 0.

lim δx→0 -12δx = 0

Therefore, the limit of the given expression as δx approaches 0 is 0.

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