-3 * f(-8) + 7 * g(2)

The velocity of the cart b is found as 20/23 ft/s over the pulley.

For the given data in the question.

q's velocity is 2 feet per second.

Rope length is 39 feet.

Assume x is the distance between A and Q. (refer the image).

Assume y is the distance between Q and B. (refer the image).

As a result of the image,

x² + 12² = L²

Now, with respect to time t, differentiate the above equation.

2x(dx/dt) + 0 = 2L.(dL/dt)

For x = 5 ft and L = 13 ft

dL/dt = (5×2)/13 = 10/13

In the case of B,

y² + 12² = (39 - L)² ; from diagram.

Differentiating now,

2y(dy/dt) + 0 = -2(39 - L).(dL/dt)

At x = 5 ft and y = 23 ft.

dy/dy = -20/23

(A negative sign indicates the opposite direction)

Thus, the velocity of cart b is found as 20/23 ft/s.

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The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).

Let's simplify the given expression step by step using the given terms:
Expression:

\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

First, while this can be solved by calculating each individual area, let's do it in a smarter way.

Notice that there are two outer parts shaded, and two inner parts shaded.

When we add all of those, we get half of the larger circle.

So we only need to calculate the area of the larger circle and then divide it by two.

Remember that the area of a circle is:

A = pi*r^2

where:

pi = 3.1416

r = radius of the circle.

In the image, we can see that the diameter of the larger circle is 8ft.

And we know that r is half of the diameter, then:

r = 8ft/2 = 4ft

Now we can replace those values in the area of the larger circle and get:

A = 3.1416*(4ft)^2 = 50.27 ft^2

Half of that is:

A/2 = 21.14 ft^2.

That is the area of the shaded regions.

Marcos is 45 years old, Betiana is 9 years old, and Sabrina is 18 years old.

Let's start by defining the variables for each person's age

Marcos' age = M

Betiana's age = B

Sabrina's age = S

From the problem statement, we know

S = 1/3 (B + M)

B + S = M - 18

M + B + S = 72

We can use equation (1) to substitute S in equation (2)

B + (1/3)(B + M) = M - 18

Multiplying both sides by 3

3B + B + M = 3M - 54

Simplifying

4B = 2M - 54

We can also use equation (1) to substitute S in equation (3)

M + B + (1/3)(B + M) = 72

Multiplying both sides by 3:

3M + 3B + B + M = 216

Simplifying

4M + 4B = 216

Now we have two equations with two unknowns

4B = 2M - 54

4M + 4B = 216

Solving for B in the first equation

B = (2M - 54)/4

B = (M - 27)/2

Substituting in the second equation

4M + 4((M - 27)/2) = 216

Simplifying:

4M + 2M - 54 = 216

6M = 270

M = 45

Substituting M = 45 in the equation we found for B

B = (45 - 27)/2 = 9

Finally, using equation (1) to find S

S = 1/3 (B + M) = 1/3 (9 + 45) = 18

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Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer: Write the numerical expression. 6 times the sum of 12 and 8. That would make 54

Write the numerical expression. The difference between 8 forty-sevens and 7 forty-sevens. Write your answer with no spaces. This would be 100.

(23⋅32⋅13 2⋅31x 27o)

Step-by-step explanation:

Answer:

I'd man good luck I need points

Answer:

Your balance is 1,513.02.

Step-by-step explanation:

The coefficient of determination given the correlation coefficient is 0.81.

Correlation is used to measure the linear relationship between two variables. When the correlation coeffienient is negative, it means that the variables have a negative correlation. This means that the two variables move in opposite directions.

The coefficient of determination is used to measure the variation between the two variables being measured.

The coefficient of determination = correlation coeffienct²

-0.9² = 0.81

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Answer:

6.333

Step-by-step explanation:

3x=2y+19

3x=2(0)+19

3x/3=19/3

x=6.333

D. horizontal translation 3 unites left.

Answer:

251 miles

Step-by-step explanation:

To answer this, we first must subtract the total Bill ended up paying by the base fee:

222.77 - 16.95 = 205.82

Now, we divide this total by 82 cents:

205.82 / 0.82 = 251

So, Bill drove the truck 251 miles

Hope this helps :)

The height equal to the given rectangle couldn't be found due to the reason of more information is needed. Therefore the required answer for the question is Option D.

So, the Probability density function is portrayed graphically as a rectangle where   (b-a) is the base and 1/(b-a)  is the required height.

Probability density function refers to the method that helps to define the random variable's probability within a distinct range of values as opposed to taking one value.

then,

the height of the rectangle for a uniform probability distribution should be 1/(b-a)

The height equal to the given rectangle couldn't be found due to the reason of more information is needed. Thus the correct answer is Option D.  

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grad(f) = (3x/(x²+y²+z²)) i + (3y/(x²+y²+z²)) j + (3z/(x²+y²+z² )) k This vector field has a magnitude that is inversely proportional to the distance from the origin.

A function's gradient vector field is a vector field that points in the direction of the function's maximum rate of change at every point in space. The following is a definition of the gradient vector field for a scalar function f(x, y, z):

grad(f) is equal to (f/x) i, (f/y) j, and (f/z) k, where i, j, and k are the unit vectors in the respective x, y, and z directions.

To find the inclination vector field of f(x, y, z) = 3√(x²+y²+z²), we want to take the halfway subordinates of f as for x, y, and z, and afterward structure the slope vector field utilizing the above condition.

The gradient vector field of f is, therefore, as follows: f/x = 3/2 * (2x)/(x²+y²+z²) = 3x/(x²+y²+z²); f/y = 3/2 * (2y)/(x²+y²+z²) = 3y/(x²+y²+z²); f/z = 3/2 * (2z)/(x²+y²+z²);

grad(f) = (3x/(x²+y²+z²)) i + (3y/(x²+y²+z²)) j + (3z/(x²+y²+z² )) k This vector field has a magnitude that is inversely proportional to the distance from the origin.

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Answer:

B. T = -7.7h + 24.1

Step-by-step explanation:

if you plug in the height for h which is 1 you get T=-7.7(1)+24.1 ,  and T would equal 16.4 which is the same temperature you get in the word problem

Answer:

160

Step-by-step explanation:

If the scale factor is 4, we would have to multiply the height and width by 4

4*5=20

4*4=16

Now to find the area of the triangle using the formula (20*16)/2

That equals to 160

The point of concurrency determined by the three altitudes of any triangle is called the orthocenter of the triangle.

The orthocenter is the intersection of the three altitudes of the triangle. It is a point on the plane of the triangle that is equidistant from the three sides of the triangle.

To find the orthocenter of a triangle, you can draw the altitudes of the triangle and find the point where they intersect. The orthocenter is the point of concurrency for the three altitudes.

An orthocenter of a triangle is a point where the three lines that are perpendicular to the sides of the triangle intersect. These lines are called altitudes of the triangle.

Alternatively, you can use the following formula to find the coordinates of the orthocenter:

Let's say that the vertices of the triangle are A(x1, y1), B(x2, y2), and C(x3, y3). The coordinates of the orthocenter (H) can be found using the following formula:

Hx = ( (y1 - y3) (x1^2 + y1^2 - x3^2 - y3^2) - (y1 - y2) (x1^2 + y1^2 - x2^2 - y2^2) ) / (2 * (y1 - y3) - 2 * (y1 - y2))

Hy = ( (x1 - x3) (x1^2 + y1^2 - x3^2 - y3^2) - (x1 - x2) (x1^2 + y1^2 - x2^2 - y2^2) ) / (2 * (x1 - x3) - 2 * (x1 - x2))

Therefore, The point of concurrency determined by the three altitudes of any triangle is called the orthocenter of the triangle

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Answer:

\(\displaystyle{\text{possible rational roots} = \pm 1, \pm \dfrac{1}{2}, \pm 3, \pm \dfrac{3}{2}, \pm 9, \pm \dfrac{9}{2}, \pm 27, \pm \dfrac{27}{2}}\)

Step-by-step explanation:

Rational Root theorem is when we divide the factors of last term by the factors of first term:

\(\displaystyle{\text{possible rational roots} = \dfrac{\text{factors of the coefficient of last term (constant)}}{\text{factors of lead coefficient (coefficient of first term)}}}\)

Our constant (last term) is -27. The factors of -27 can be ±1, ±3, ±9, ±27

Our lead coefficient is 2. The factors of 2 can be ±1 and ±2.

Hence:

\(\displaystyle{\text{possible rational roots} = \dfrac{\pm 1, \pm 3, \pm 9, \pm 27}{\pm 1, \pm 2}}\\\\\displaystyle{\text{possible rational roots} = \pm 1, \pm \dfrac{1}{2}, \pm 3, \pm \dfrac{3}{2}, \pm 9, \pm \dfrac{9}{2}, \pm 27, \pm \dfrac{27}{2}}\)

All of these are possible roots, meaning that not all of them are real roots of the equation, just a possibility.

Answer:

    x = 54

Step-by-step explanation:

Let x be the "mystery number."

If we divide x by 6000 [(x/6000)] and then multiply by 41 [(x/6000)*41] and then add 0.31 [(x/6000)*41 + 0.31], the result is 0.679:

  (x/6000)*41 + 0.31 = 0.679

 ( 41x/6000) + 0.31 = 0.679

( 41x/6000) = 0.369

     x = (0.369*(6000))/41

    x = 54

Answer:

Step-by-step explanation:

Rewrite without absolute value for the given conditions:

1) y = |x−3|+|x+2|−|x−5|, if x > 5

  y = x-3 + x + 2 - (x-5)

  y = x + 4

2) y = |10-x|, if x<10

   y = 10 - x

In both cases, the value of x is held to values that make the absolute value notation redundant, so they can be removed.

===============

Write the absolute value equations in the form x−b=c (where b is a number and c can be either number or an expression) that have the following solution sets:

1) All numbers such that x≤5

x≤5 kinda does it for me.  X can be any number less than or equal to 5.  Ta da. (?)

2) All numbers such that x≤−14.

x ≤ -14

Same comment.  I'm not sure what is being asked.

a) the rate per second is 14 feet per second.

b) The linear function that reflects the distance you run is d = 14x because we already know that the rate per second is 14 feet per second.

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0. Nonetheless, calculus and linear algebra are also used to represent linear functions. The function notation is the only distinction. It is also important to understand an ordered pair expressed in function notation. When an is an independent variable on which the function depends, the expression f(a) is referred to as a function. A straight line on a graph of a linear function has the equation or formula;

from the question:

A. The slope of the linear function y = 14x + 50 equals the rate per second. We can determine the slope of this function to be 14 by using the slope-intercept form of a linear function, which is y = mx + b, where m is the slope. The pace per second is 14 feet per second as a result.

B. We will refer to the distance you cover after x seconds as d. (in feet). Your linear function will take the form d = mx because you are starting at 0 feet, where m is the rate per second. The linear function that reflects the distance you run is d = 14x because we already know that the rate per second is 14 feet per second.

px + q = f(x) = y

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complete question:

You and a friend race each other. You give your friend a 50-foot head start. The distance y (in feet) your friend runs after x seconds is represented by the linear function y=14x+50. The table shows the distances you run.

Time (seconds) x : 2, 4, 6, 8

Distinct (feet) y : 38, 76, 114, 152

A. what is the rate per second?

B. Write a linear function that relates your distance to the number of seconds. In the same coordinate plane, graph the linear functions that represent the distances of you and your friend.

The student's height is 145cm and the average water depth in the pond is 110cm. Since the student is taller than the average water depth, they would not be at significant risk in the pond, as the water level would likely be below their head. However, it's always important to exercise caution and follow safety guidelines when around water, regardless of depth.

It is difficult to determine if the student is at risk in the pond. Height alone does not necessarily indicate swimming ability or water safety knowledge. However, if the student is not a strong swimmer or lacks knowledge of water safety, they may be at risk in any body of water, including one with an average depth of 110cm. It is important for all individuals to take precautions when swimming, such as wearing a life jacket and staying within their comfort and skill level in the water.

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To determine if the student has a risk in the pond based on their height, we need to consider the relationship between the student's height and the water depth.

In this scenario, the student's height is 145 cm, while the average water depth in the pond is 110 cm.

If the water depth is lower than the student's height, it means that the student's head will remain above the water surface, and there is no immediate risk of drowning due to water submersion. In this case, the student's height of 145 cm is greater than the water depth of 110 cm, indicating that the student's head would be above the water, and they would not face an immediate risk in terms of being submerged.

However, it is important to note that other factors could pose a risk in a pond or any body of water, such as the presence of strong currents, slippery surfaces, or the individual's swimming ability. It is crucial to consider these additional factors and exercise caution when in or near bodies of water, regardless of height.

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To determine the possible values of x that make the triangle with sides x, x, and 6 an acute triangle, we need to consider the triangle inequality theorem.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the longest side is given as 6. Therefore, the sum of the lengths of the other two sides (both x) must be greater than 6.

Mathematically, we can express this as:

2x > 6

Dividing both sides of the inequality by 2, we have:

x > 3

So, any value of x greater than 3 will make the triangle valid.

In interval notation, the solution would be x ∈ (3, ∞) or x > 3.

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The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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Answer:

It's B

Step-by-step explanation:

-a +5a-a =3a

+4-6=-2

= 3a-2

Answer

the answer is a

Step-by-step explanation:

hehe

Therefore, the expression for each wk in terms of the dataset (x1, y1), ..., (xM, yM) and W1, ..., Wk-1, Wk+1, ..., WM is: wk = (Σ (xij * yj) - Σ (wk' * xij^2), for j = 1 to N and k' ≠ k) / Σ xij^2, for j = 1 to N

The expression for each coefficient wk can be derived by taking the partial derivative of the OLS objective function J(w) with respect to wk and setting it equal to zero:

dJ(w)/dwk = 2 * Σ (xij * (wk * xij - yj)), for j = 1 to N

Setting this equal to zero and solving for wk, we get:

wk = (Σ (xij * yj) - Σ (wk' * xij^2), for j = 1 to N and k' ≠ k) / Σ xij^2, for j = 1 to N

Therefore, the expression for each wk in terms of the dataset (x1, y1), ..., (xM, yM) and W1, ..., Wk-1, Wk+1, ..., WM is: wk = (Σ (xij * yj) - Σ (wk' * xij^2), for j = 1 to N and k' ≠ k) / Σ xij^2, for j = 1 to N

The solution for this problem involves taking the partial derivative of the objective function J(w) with respect to each w_k and setting it to zero. This will give us a set of M normal equations, one for each coefficient w_k (1 ≤ k ≤ M).

The general expression for each w_k can be written as:

w_k = (Σ(x_i(k)y_i) - Σ(x_i(k)Σ(x_i(j)w_j)) / Σ(x_i(k)^2) for 1 ≤ j ≤ M, j ≠ k

Here, the summations run over all data points in the dataset D. The expression calculates w_k by considering the relationship between the k-th input variable x_i(k) and the output variable y_i, while taking into account the contribution of other coefficients w_j.

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