during a football​ game, a quarterback tried to gain yards but was tackled for a loss of yards. what integer represents this​ result?

The evaluation of ∫30(4f(t) - 6g(t)) dt given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8 is -80.

Given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8.

Let us evaluate ∫30(4f(t) - 6g(t)) dt.

Therefore,∫30(4f(t) - 6g(t)) dt = ∫30(4f(t) dt - 6g(t) dt) = 4 ∫30f(t) dt - 6 ∫30g(t) dt

Now, using the given values in the question we can say that,∫30(4f(t) - 6g(t)) dt = 4 ∫30f(t) dt - 6 ∫30g(t) dt = 4 (-8) - 6(8) = -32 - 48 = -80

Therefore, the evaluation of ∫30(4f(t) - 6g(t)) dt given that ∫150f(t) dt = -7, ∫30f(t) dt = -8, ∫150g(t) dt = 4, and ∫30g(t) dt = 8 is -80.

Note: The given integrals ∫150f(t) dt, ∫30f(t) dt, ∫150g(t) dt, and ∫30g(t) dt are only intermediate steps in order to evaluate the final integral.

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Answer:

1st: False

2nd: True

Step-by-step explanation:

Note:
The similarity ratio of two triangles can only be determined if the corresponding side lengths are in proportion.

If only the angles are given, then there is no way to know the lengths of the sides, and therefore the similarity ratio cannot be determined.

For 1st question:

Sides are not given,

So, the answer is False.

For 2nd question:

Sides are given,

\(\triangle XYZ \sim \triangle ABG\)

\(\frac{XY}{AB}=\frac{4}{2}=\frac{2}{1}\)

\(\frac{YZ}{BG}=\frac{3}{1.5}=\frac{2}{1}\)

\(\frac{XZ}{AG}=\frac{5}{2.5}=\frac{2}{1}\)

Since all the sides length are proportional.

So, the answer is True.

Using the long division method, it is proved that (x + 2) is a factor of (x³ + 8), because the result of the remainder is 0.

To show that (x + 2) is a factor of (x³ + 8) using long division, we can divide (x³ + 8) by (x + 2) and see if the remainder is 0. If the remainder is 0, then (x + 2) is a factor of (x³ + 8). Here's how the long division would look:

        x² - 2x + 4

x+2 | x³ + 0x² + 0x + 8

      - (x³ + 2x²)

    --------------------

         -2x² + 0x + 8

       - (-2x² - 4x)

         ---------------

              4x + 8

            - (4x + 8)

              --------

                 0

Since the remainder is 0, we can conclude that (x + 2) is a factor of (x³ + 8).

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Answer:

n(u)= 29

girl =n(g) =15

boys n(b)=?

n(b)= n(u)_n(g)

= 29-15

= 14

therefore .°. male= 14

female= 15

Answer:

it 15,000

Step-by-step explanation:

I hope it work

Answer:

B. 3.14

C. .33

E. 3.46

remember rational number are can be measured from decimals and even fractions.

Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

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The researcher cannot conclude that the correlation is significant at the .05 level.

The answer to the question that requires the inclusion of the term "150" is shown below: A researcher was interested in the relationship between how far students live from her classroom and how long it takes those students to walk to class.

She randomly selected 20 students and asked them each (1) how many feet away from this class do you live (measured as distance from entrance of class building to entrance of student’s home) and (2) how long does it take you to walk to class (measured in minutes)? The researcher computed a correlation of r = -.45.

The null hypothesis is stated as follows:H0: ρ = 0 (there is no correlation between how far students live from the classroom and how long it takes those students to walk to class)

The alternative hypothesis is stated as follows: Ha: ρ ≠ 0 (there is a correlation between how far students live from the classroom and how long it takes those students to walk to class)Degrees of freedom (df) = n - 2, where n is the sample size of 20 students.

Assuming α = .05, the critical values of r for a two-tailed test would be ± .444.

Therefore, if the calculated correlation coefficient is greater than the critical value of r, reject the null hypothesis. If the calculated correlation coefficient is less than the negative critical value of r, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

The calculated correlation coefficient of r = -.45 falls between the critical values of ± .444. Therefore, we fail to reject the null hypothesis.

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The rate of change of h(x) with respect to x when x=2 is -3. To find d/dx, we need to take the derivative of the function h(x) and evaluate it at x=2.

h(2) tells us that when x=2, h(x)=4.

h'(2) tells us that the slope of the tangent line to the graph of h(x) at x=2 is -3.

So, we can use this information to find d/dx as follows:

h(x) = y

dy/dx = h'(x)

We know that when x=2, y=h(2)=4.

We also know that the slope of the tangent line to the graph of h(x) at x=2 is h'(2)=-3.

So, we can write the equation of the tangent line at x=2 as:

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

y = -3x + 10

Now we can take the derivative of y with respect to x to find d/dx:

d/dx (y) = d/dx (-3x + 10)

d/dx (y) = -3

Therefore, d/dx = -3.

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Answer:

Step-by-step explanation:

y= 3+x/2

2y= 6+x

put x+1

y= 7/2

now put this value in first equation

x=4

By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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Answer:percantage spent on other things = 30%

Step-by-step explanation:

Percentage spent on other things = Money spent on other things/ Total money x `100/ 1

Money spent on rest things = Total money - ( Money spent on ice cream + Money spent on pizza)

100 -(25+ 45)

100-70= Rs 30

Percentage spent on other things = Money spent on other things/ Total money x `100/ 1

= Rs 30/ Rs 100 x 100

0.3 x 100 = 30%

Answer:

the distance cycled by Kayden in one hour is (y/15) km, in terms of y.

Step-by-step explanation:

If Kayden cycles 4 km in y minutes, we need to first convert y minutes to hours.

There are 60 minutes in an hour, so there are 60/y hours in y minutes.

Therefore, Kayden cycles at a speed of 4 km/(60/y) hours = (4y)/60 km/hour.

To find the distance cycled by Kayden in one hour, we can simply multiply this speed by 1 hour:

Distance = speed × time = ((4y)/60) × 1 = (4y)/60 km.

Simplifying, we get:

Distance = (2y)/30 km = (y/15) km.

Therefore, the distance cycled by Kayden in one hour is (y/15) km, in terms of y.

Answer: See explanation

Step-by-step explanation:

x=-(2-2*the square root of 6)/5, about 0.58

or

x=-(2+2*the square root of 6)/5, about -1.38

The values of the x from equation  \(5x^2+4x-4=0\) are  x = 0.5798 and -1.38.

Given that:

Equation:  \(5x^2+4x-4=0\)

To find the values of x that satisfy the equation \(5x^2+4x-4=0\), use the quadratic formula:

\(x = \dfrac{ -b \± \sqrt{b^2 - 4ac}}{ 2a}\)

Compare the equation with \(ax^2 + bx + c = 0\).

Here, a = 5, b = 4, and c = -4.

Plugging in the values to get,

\(x = \dfrac{-4 \± \sqrt{4^2 - 4 \times 5 \times (-4)}}{2 \times 5} \\x = \dfrac{-4 \± \sqrt{16 +80}}{10} \\x = \dfrac{-4 \± \sqrt{96}}{10}\\x = \dfrac{-4 \± {4\sqrt6}}{10}\)

So the solutions for x are calculates as:

Taking positive sign,

\(x = \dfrac{-4 + {4\sqrt6}}{10}\\x = \dfrac{-4 + {9.798}}{10}\\\)

x = 5.798/10

x = 0.5798

Taking negative sign,

\(x = \dfrac{-4 - {4\sqrt6}}{10}\\x = \dfrac{-4 - {9.798}}{10}\\\)

x = -13.798/10

x = -1.38

Hence, the exact solutions for the equation  \(5x^2 + 4x - 4 = 0\)  are x = 0.5798 and -1.38.

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Answer:

3 times 5 times 5

Answer: 130 marks

Step-by-step explanation:

There are 4 marks for every correct answer and there are 4 marks for each correct answer:

= 35 * 4

= 140 correct marks

There are -1 marks for every incorrect answer and there are 10 incorrect answers:

= 10 * -1

= -10 marks

Total score = 140 - 10

= 130 marks

Answer:

130 marks

Step-by-step explanation:

Area of the rectangle is 15\(x^{11}\) - 27\(x^{7}\) - 21\(x^{5}\) + 6\(x^{4}\).

To find the area of the rectangle, we need to multiply its length by its width. In this case, the width is given as 3x^4, and the length is given as 5\(x^{7}\)-9\(x^{3}\)-7x+2. Therefore, the area of the rectangle can be calculated as:

Area = width x length

Area = 3\(x^{4}\)(5\(x^{7}\)-9\(x^{3}\)-7x+2)

To simplify this expression, we need to distribute the 3x^4 term into the parentheses:

Area = 15\(x^{11}\) - 27\(x^{7}\) - 21\(x^{5}\) + 6\(x^{4}\)

This is the final expression for the area of the rectangle in terms of x. We can see that the degree of the polynomial is 11, which means that the area of the rectangle is a high-degree polynomial. The area also contains both positive and negative terms, which means that it can take on both positive and negative values depending on the value of x.

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1) Substituting into point-slope form, the equation of the line is y-6=⅓(x-3), which rearranges to:

So, we can now substitute in the coordinates of each of the options to see which point lies on the line.

So, the answer is (4) (-6, 3)

2) Substituting into point-slope form, the equation of the line is y - 5 = ¾(x-2), which rearranges to:

So, we can now substitute in the coordinates of each of the options to see which point lies on the line.

So, the answer is (1) (6, 8).

Answer:

$21

Step-by-step explanation:

First, find the price without the discount by adding 12 to 30:

30 + 12

= 42

To find the original cost of each game, divide 42 by 2

42/2

= 21

So, each game was originally $21

Answer:

x= 13

Step-by-step explanation:

Its a right angle = 90 degrees so add them both up to 90 degrees to find x

Answer:

0630 is the only thing I can come up with.

the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).

To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.

Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.

Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.

Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

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Answer:

\(y=2x+3\)

Step-by-step explanation:

Sure hope this helps you

The difference between the Lagrangian and Eulerian descriptions of a flow field lies in the perspective they take to analyze the motion of fluid particles.


1. Lagrangian description: Focuses on tracking individual fluid particles as they move through the flow field.
2. Eulerian description: Analyzes fluid properties at fixed points in space, disregarding individual particle motion.
3. Both descriptions represent the same physical phenomenon - fluid flow.
4. Material derivative: Connects the Lagrangian and Eulerian descriptions by relating the rate of change of a property in the Lagrangian frame to the rate of change in the Eulerian frame.

The two descriptions are related in the sense that they both represent the same physical phenomenon, i.e., the flow of fluid. However, they use different approaches to study the flow. To connect the Lagrangian and Eulerian descriptions, we can use the material derivative, which relates the rate of change of a property in the Lagrangian frame to the rate of change in the Eulerian frame.

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The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

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H satisfies all three subspace properties, it is a subspace of R³.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

Let H be the set of all vectors of the form 4t, where t is any real number. We want to find a vector v in R³ such that H = Span{v}.

Let v = [4,0,0]. Then any scalar multiple of v will be of the form [4t,0,0], which is an element of H. Thus, H is contained in Span{v}.

Conversely, any vector in Span{v} can be written as a scalar multiple of v, which is of the form [4t,0,0] and therefore an element of H. Thus, Span{v} is contained in H.

Therefore, we have H = Span{v}.

This shows that H is a subspace of R³ because Span{v} is a subspace of R³ (since v is in R³) and H = Span{v}. To show that H is a subspace of R³, we need to verify the three subspace properties:

The zero vector of R³ is in H: The zero vector of R³ is [0,0,0], which is of the form [4t,0,0] when t = 0. Therefore, the zero vector is in H.

H is closed under vector addition: Let u and w be vectors in H. Then u = [4t₁,0,0] and w = [4t₂,0,0] for some t₁, t₂ in R. The sum u + w is [4t₁+4t₂,0,0], which is also an element of H. Therefore, H is closed under vector addition.

H is closed under scalar multiplication: Let u be a vector in H and let c be a scalar in R. Then u = [4t,0,0] for some t in R. The scalar multiple cu is [4ct,0,0], which is also an element of H. Therefore, H is closed under scalar multiplication.

Therefore H satisfies all three subspace properties, it is a subspace of R³.

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Answer:

Answer:2, 6,9, 8

Step-by-step explanation:

Left to right

The exponential function that models the logistic function, f(x)= 80/(1+4\((2)^{-x}\)), for small values of x is 80(\(2^{x}\)).

Hence, the correct option is D.

To determine which exponential function models the given logistic function for small values of x, we can analyze the behavior of the function as x approaches negative infinity.

As x approaches negative infinity, the term \((2)^{-x}\) approaches infinity, and as a result, the denominator of the logistic function, 1 + 4\((2)^{-x}\), approaches infinity. This causes the entire fraction to approach 0.

Therefore, for small values of x, the logistic function approaches the value of the numerator, which is 80.

Out of the given options, the exponential function that represents this behavior is 80(\(2^{x}\))

Hence, the correct option is D.

The question is '' Which exponential function below models the logistic function, f(x)= 80/(1+4\((2)^{-x}\)), for small values of x?

A. 16(\(4^{x}\))

B. 80(\(4^{x}\))

C. 16(\(2^{x}\))

D. 80(\(2^{x}\)) ''.

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