An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $5990 and her stock in Company B was worth $2450. The stock in Company A has decreased 20% since last year and the stock in Company B has decreased 8%. What was the total percentage decrease in the investor's stock account?

[tex] \green{ \underline{ \underline{\mathsf{ {(x - y)}^{2} }}}}[/tex]

We have the values of x and y:

Plug in the values~

[tex] \green{\mathfrak{ {(5 -( - 1))}^{2} }}[/tex]

[tex] \green{\mathfrak{ {(5 + 1)}^{2} }}[/tex]

Use the identity:

[tex] \red{ \mathsf{(x + y)^{2} = {x}^{2} + {y}^{2} + 2xy }}[/tex]

[tex] \green{\mathfrak{ {5}^{2} + {1}^{2} + 2 \times 5 \times 1 }}[/tex]

[tex] \green{\mathfrak{ 25 + 1 + 10 }}[/tex]

[tex] \boxed{\green{\mathfrak{36 }}}[/tex]

Answer:

x = -1 and y = 3

Step-by-step explanation:

Let's solve your system by elimination.

−2x−9y=−25;−4x−9y=−23

Multiply the second equation by -1, then add the equations together.

(−2x−9y=−25)

−1(−4x−9y=−23)

Becomes:

−2x−9y=−25

4x+9y=23

Add these equations to eliminate y:

2x=−2

x = -1

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

−2x−9y=−25

Substitute−1forxin−2x−9y=−25:

(−2)(−1)−9y=−25

−9y+2=−25(Simplify both sides of the equation)

−9y+2+−2=−25+−2(Add -2 to both sides)

−9y=−27

y = 3

The final answer to this integral is as follows: Integral x/(x^2 + 4)^2 dx = -1/8 (x^2 + 4)^-1 + C. Use C for the constant of integration.

An indefinite integral is a type of integral that does not have upper and lower limits, but rather simply requires finding the antiderivative of a function.

To evaluate an indefinite integral of the given function, follow these steps.

1. Separate the numerator of the function from the denominator, then rewrite the denominator as a perfect square.

2. Make a u-substitution by letting u = x^2 + 4.

Differentiate u with respect to x to get du = 2x dx.

3. Rewrite the integral in terms of u, making sure to substitute x dx with 1/2 du.

4. Simplify the integral by factoring out constants and substituting the value of u.

5. Integrate the function with respect to u.

6. Rewrite the final answer in terms of x.

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The resulting graph should look like a downward-facing parabola, opening towards the negative x-axis, with vertex at  [tex](7.5, 225),[/tex] crossing the x-axis at  [tex](0,0)[/tex] and [tex](15,0)[/tex]  , and reaching a maximum value of  [tex]450[/tex] at x=0 and x=15.

a) Since the perimeter of the rectangular fence is made up of the length, width, and two lengths of fencing, we can write:

Perimeter = 2(length + 2x) = 60

Simplifying this expression, we get:

Length [tex]+ 2x = 30[/tex]

Subtracting 2x from both sides, we get:

Length [tex]= 30 - 2x[/tex]

So, the expression for the length of the rectangular fence in terms of x is:

Length [tex]= 30 - 2x[/tex]

b) To find the area of the rectangular fence, we multiply the length and width together. Substituting the expression we found in part a for the length and the given width of 2x, we get:

Area  [tex]= (30 - 2x) * 2x[/tex]

Simplifying this expression, we get:

Area [tex]= 60x - 2x^2[/tex]

Factoring out a 2x, we get:

Area [tex]= 2x(30 - x)[/tex]

Expanding the brackets, we get:

Area [tex]= 60x - 2x^2[/tex]

So, the equation for the area of the rectangular fence in terms of x is  [tex]A(x) = 8x(15 - x).[/tex]

c) To sketch the graph of A versus x, we can plot some key points and use them to sketch the curve. First, we note that the domain of x is 0 to 15, since the length of the fence cannot be negative and cannot be greater than  [tex]30[/tex] (otherwise the width would be negative).

At x=0, A(x)=0, and at x=15, A(x)=0. So, we know that the curve must cross the x-axis at  [tex]x=0[/tex]  and  [tex]x=15[/tex] .

We can also find the vertex of the parabola, which occurs at x=7.5 by using the formula for the x-coordinate of the vertex, which is -b/2a, where a=-2 and b=60. So, the x-coordinate of the vertex is -60/(2*(-2))=15. The y-coordinate of the vertex is [tex]A(7.5)=225[/tex]  .

Finally, we can plot a few other points, such as x=5 (A(x)=200) and x=10 (A(x)=200), and connect the points with a smooth curve.

An outline of the graph is shown below:

    |    

 500|               x

    |             /

    |            /

    |           /

 250|----------/-------------

    |         /   \

    |        /     \

    |       /       \

    |      /         \

    |_____/___________\

        0   7.5   15

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Answer:

The values of x that satisfy the equation are x = 13 and x = 1. The values x = -29 and x = 42 do not satisfy the equation.

Answer:

b is the required ans of Qust

If the right rectangular prism is 2.75in by 4in by 16.5in, then the total surface area of the prism is (a) 244.75 in².

We know that the total surface area of a right rectangular prism is given by the formula ⇒ 2lw + 2lh + 2wh

Where ⇒  l, w, and h are length, width, and height of rectangular prism, respectively.

The dimensions of the rectangular prism is 2.75in by 4in by 16.5in,

Substituting the values of length , width and height , we get:

⇒ 2×2.75×4 + 2×2.75×16.5 + 2×4×16.5,

⇒ 22 + 90.75 + 132

⇒ 244.75

Therefore, the total surface area of the prism is 244.75 in²,the correct option is (a).

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The given question is incomplete, the complete question is

A right rectangular prism is 2.75 in by 4 in by 16.5 in. What is the total surface area of the prism?

(a) 244.75 in²

(b) 222.75 in²

(c) 122.375 in²

(d) 112.75 in²

By answering the presented question, we may conclude that 1.1.5: A inequality factor of 51 - 25 is a factor of 51 since 51 can be written as 25 x 2 + 1.

An inequality in mathematics is a link between two expressions or values that is not equal. As a result, inequality results from imbalance. An inequality in mathematics is a relationship between two values that are not equal. Equality and inequality are not the same thing. The not equal sign is often used to indicate that two values are not equal (). To contrast values, various disparities—no matter how small or large—are used. By changing the two sides until just the variables are left, many fundamental inequalities can be resolved. Yet, a variety of causes fuel inequality: On both sides, negative values are divided or added. Trade right and left.

1.1.1: Irrational number - 2.13131.... is a non-repeating, non-terminating decimal, which is a characteristic of irrational numbers.

1.1.2: Recurring decimal - None of the given numbers have a repeating decimal pattern, so this option is not applicable.

1.1.3: An uneven square number - None of the given numbers are perfect squares, so this option is not applicable.

1.1.4: An even prime number - The only even prime number is 2, which is not in the list. Therefore, this option is not applicable.

1.1.5: A factor of 51 - 25 is a factor of 51 since 51 can be written as 25 x 2 + 1.

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None of the statements are true; Hamilton circuits/paths and Euler circuits/paths are different concepts.

A Hamilton path is a path that visits every vertex of a graph exactly once, while an Euler circuit is a circuit that passes through every edge of a graph exactly once.

A Hamilton circuit is a circuit that passes through every vertex of a graph exactly once, while an Euler path is a path that passes through every edge of a graph exactly once.

Therefore, Hamilton circuits and Euler circuits are different concepts, as are Hamilton paths and Euler paths.

To add further explanation:

A Hamilton path can exist in a graph that does not have a Hamilton circuit. For example, a path that visits all vertices of a cycle graph except for one vertex is a Hamilton path, but the graph does not have a Hamilton circuit.

An Euler circuit can exist in a graph that does not have a Hamilton circuit or Hamilton path. For example, a graph with multiple connected components can have Euler circuits in each component, but it may not have a Hamilton path or circuit.

It is also possible for a graph to have both a Hamilton circuit and an Euler circuit. In this case, the graph is said to be both Hamiltonian and Eulerian.

Overall, the concepts of Hamilton and Euler circuits and paths are important in graph theory and have applications in various fields such as computer science, physics, and biology.

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The complete question is:

Which of the following statements about Hamilton and Euler circuits/paths are true?

The Hamilton path and Euler circuit are the same.

The Hamilton circuit and Euler circuit are the same.

The Hamilton circuit and Euler path are the same.

The Hamilton path and Euler path are the same.

Select all that apply.

The intersection of the given planes is $$(x,y,z) = (1,-y,-y)$$

The given planes are: $x+(y-1)+z=0$ and $-x+(y+1)-z=0$.We have to find the intersection of these two planes.Intersection of two planes can be found as follows:

First, convert the planes into parametric equations.$x+(y-1)+z=0$$\Rightarrow x = -y+1-z$$\Rightarrow (x,y,z) = (-y+1-z,y,z)$$(-x+(y+1)-z=0$$$$\Rightarrow x = y+1+z$$$$\Rightarrow (x,y,z) = (y+1+z,y,z)$So, we have,$$(x,y,z) = (-y+1-z,y,z) = (y+1+z,y,z)$$

This gives two equations,$$-y+1-z=y+1+z$$$$\Rightarrow -2y=2z$$$$\Rightarrow z=-y$$$$$$$$y+1+z=y$$$$\Rightarrow z=-1$$$$$$$$x = -y+1-z$$$$= -y+1-(-y)$$$$= 1$$

So, the intersection of the given planes is $$(x,y,z) = (1,-y,-y)$$

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sum_{k=2}^{26}\binom{26}{k}

To find out the value of the given expression, we will use the Vander monde's Identity which is as follows;\[\binom{m+n}{r} = \sum_{k=0}^r\binom{m}{k}\binom{n}{r-k}\]On comparing this with the given expression, we see that $m=n=26$, and $r=0, 1, 2, \cdots, 26$.Now we substitute these values in the given expression.\[\begin{aligned} 22\binom{26}{0} 21\binom{26}{1} 20\binom{26}{2} \cdots (-3)\binom{26}{25} (-4)\binom{26}{26} & = 22\binom{26}{26} - 21\binom{26}{25} + 20\binom{26}{24} - \cdots -3\binom{26}{3} + (-4)\binom{26}{2} \\ &= \binom{26}{26} - \left(\binom{26}{24} - \binom{26}{25}\right) + \left(\binom{26}{22} - \binom{26}{23}\right) - \cdots - \left(\binom{26}{4} - \binom{26}{3}\right) + \binom{26}{2} \\ &= \binom{26}{26} + \binom{26}{25} + \binom{26}{24} + \binom{26}{23} + \cdots + \binom{26}{4} + \binom{26}{3} + \binom{26}{2} \\ &= \sum_{k=2}^{26}\binom{26}{k} \end{aligned}\]Thus, we obtain $\sum_{k=2}^{26}\binom{26}{k}$ as the simplified value of the given expression.

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The sampling distribution of the sample mean amount of money in a savings account for University of Miami students is approximately normal, with a mean of 1100 and a standard error of 204.12.

The sampling distribution of the sample mean amount of money in a savings account is A. approximately Normal, with a mean of 1100 and a standard error of 204.12. This is because, according to the Central Limit Theorem, the sampling distribution of the sample mean tends to be Normal, regardless of the shape of the population distribution, as long as the sample size is sufficiently large. In this case, the sample size is 24, which is large enough for the sampling distribution to be approximately Normal. The mean of the sampling distribution is equal to the population mean, which is 1100, and the standard error is equal to the standard deviation of the population divided by the square root of the sample size, which is 1000/√(24) = 204.12.

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Answer:6g+32<80

Step-by-step explanation:

The solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0) is (1/(x+1))y^(x+1) = (1/2)x^2 - 1/2.

To find the solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0), we can use the method of separation of variables. This involves separating the variables x and y on opposite sides of the equation and then integrating both sides.

First, we can rewrite the differential equation as:
y^x dy = x dx

Next, we can integrate both sides of the equation:
∫y^x dy = ∫x dx
(1/(x+1))y^(x+1) = (1/2)x^2 + C

Now, we can use the initial condition (1,0) to solve for the constant C:
(1/(1+1))0^(1+1) = (1/2)(1)^2 + C
0 = 1/2 + C
C = -1/2

Therefore, the solution to the differential equation is:
(1/(x+1))y^(x+1) = (1/2)x^2 - 1/2

This is the solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0).

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The dimensions of the rectangle are:

width = 2x + 5

length = 4x+ 10

Here we know that the area of a rectangular piece of land is:

8x² + 40x + 50

Remember that for a rectangle of length L and width W, the area is:

A = L*W

So we can write:

L*W = 8x² + 40x + 50

We also know that the length is two times the width, so:

L = 2*W

Replacing that we get:

2*W*W = 8x² + 40x + 50

We an rewrite this as:

W² = (8x² + 40x + 50)/2

W² = 4x² + 20x + 25

Solving that for W we get:

W = √(4x² + 20x + 25)

W = √( 4x² + 2*2*5x + 5²)

W = √( (2x + 5)²)

W = 2x + 5

That expression represents the width, and the length is:

L  = 2*(2x + 5) = 4x + 10

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The net of this figure would be a square with four equilateral triangles on each of its sides.

To create the net of this figure we must analyze its sides and the joints of each of its faces. According to the above, we can conclude that this figure is made up of four equilateral triangular faces and a square at its base. To form the net of this figure, the most appropriate thing would be to start at the base and join the sides, in this case there would be four triangles, one on each side of the square. It is very important that the triangles are equilateral and have the same dimensions so that the pyramid can be formed correctly.

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B) PE = mgh = (2.2 kg)(10 N/kg)(2.0 m) = 44 J is the correct equation that shows that when a 2.2-kg book is lifted 2.0 m, its increase in gravitational potential energy is 44 J, given that g is equal to 10 N/kg in this case.

The gravitational potential energy of an object is directly proportional to its mass, height above the ground, and the acceleration due to gravity. In this case, a 2.2-kg book is lifted 2.0 m, and its increase in gravitational potential energy is to be calculated. The formula for gravitational potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the ground. Substituting the given values into the equation, we get PE = (2.2 kg)(9.8 m/s^2)(2.0 m) = 43.16 J, which means option D is the correct answer.

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Complete question:

Select the correct equations that show that when a 2.2- kg book is lifted 2.0 m its increase in gravitational potential energy is 44 j. (don't forget g, which can be expressed in units n/kg, equivalent to m/s2.)

A) PE = mgh = (2.2 kg)(9.8 m/s^2)(2.0 m) = 42.96 J

B) PE = mgh = (2.2 kg)(10 N/kg)(2.0 m) = 44 J

C) PE = mgh = (2.2 kg)(9.8 N/kg)(2.0 m) = 43.12 J

D) PE = mgh = (2.2 kg)(9.81 m/s^2)(2.0 m) = 43.16 J

E) PE = mgh = (2.2 kg)(10 m/s^2)(2.0 m) = 44 J

The domain for all variables is the set of integers.The correct answer is: ∀y ∃x (x+2y=1).

This statement is true because for any integer value of y, there exists an integer value of x that satisfies the equation x+2y=1. For example, if y=0, then x=1; if y=1, then x=-1; if y=2, then x=-3, and so on.

The other statements are not true for all integer values of x and y. For example, ∀x ∃y (x+2y=1) is not true because there are integer values of x for which there is no integer value of y that satisfies the equation (e.g. if x=2, then y= -0.5, which is not an integer). Similarly, ∃y ∀x (x+2y=1) and ∃x ∀y (x+2y=1) are not true because there is no single integer value of y or x that satisfies the equation for all integer values of x or y, respectively.

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The cost of the chemical increases over time by 6% every year, we found that an ounce of the chemical cost approximately $117.90 in 2018, which is 8 years after 2010.

a. The function C(x) models the cost in dollars of one ounce of a certain chemical used in a laboratory as a function of the number of years since 2010. The function is an exponential function with a base of 1.06, which means that the cost increases over time. Specifically, the cost increases by 6% every year because (1.06-1)*100% = 6%.

b. To find the cost of an ounce of the chemical in 2018, we need to substitute x = 8 into the formula. This is because 2018 is 8 years after 2010. So, we have:

C(8) = 75*(1.06)^8

We can evaluate this expression using a calculator to find that C(8) ≈ 117.90. Therefore, an ounce of the chemical cost approximately $117.90 in 2018.

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Answer:

a=180 b=180 and 914 c=180

Step-by-step explanation:

simple

The value of the expression for p=4 and q=-4 is 240. To factor the expression [tex]p^2q^2+pq-q^3-p^3,[/tex] we can use the factoring by grouping method.

First, we can factor out a common factor of pq from the first two terms and a common factor of [tex]q^3[/tex] from the last two terms:

[tex]p^2q^2 + pq - q^3 - p^3[/tex]

[tex]= pq(pq + 1) - q^3 - p^3 + q^3[/tex]

[tex]= pq(pq + 1) - p^3[/tex]

Now, we can factor the expression [tex]-p^3[/tex] by using the difference of cubes formula:

[tex]= pq(pq + 1) - (p)(p^2)[/tex]

[tex]= pq(pq + 1 - p^2)[/tex]

So the fully factored form of the expression is [tex]pq(pq + 1 - p^2).[/tex]

To find the value of the expression for p=4 and q=-4, we can substitute these values into the factored form:

[tex]pq(pq + 1 - p^2)[/tex]

[tex]= (4)(-4)((4)(-4) + 1 - (4)^2)[/tex]

= (-16)(-15)

= 240

Therefore, the value of the expression for p=4 and q=-4 is 240.

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The experiment conducted by Kathy has 16 different outcomes.

An even number is an integer that can be divided by two without a remainder. Even numbers are always divisible by two and are greater than or equal to zero. Examples of even numbers include 0, 2, 4, 6, 8, 10, 12, 14, 16 and so on.

This is because she flips a coin, which can either be heads or tails, and then rolls an 8-sided die, which can have any of the numbers 1 through 8 on the faces. Combining these two factors, the result is that there are 16 different outcomes in total.

The probability of her flipping heads and rolling an even number on the die is 1/8. This is because the probability of her flipping heads is 1/2 and the probability of her rolling an even number on the die is 1/2. When these two probabilities are multiplied together, the result is 1/8. This is the same as saying that the chance of her flipping heads and rolling an even number on the die is 1 out of 8, which can be written as a fraction in lowest terms as 1/8.

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3(-2x + 4) = -6x - 12 is the equation that has no solutions.

In mathematics, an identity is an equation that is true for all values of the variable(s) in the equation. An identity can be thought of as a special type of equation that does not have a specific solution, since every value of the variable(s) makes the equation true.

The equation that would have no solution is:

10x + 3 = 3 + 10x

This equation can be simplified as follows:

10x + 3 = 3 + 10x

10x - 10x + 3 = 3

0x + 3 = 3

3 = 3

We end up with a true statement, 3 = 3. However, this does not provide any information about the value of x. In fact, we can see that the equation 10x + 3 = 3 + 10x is true for all values of x. Therefore, this equation has no solution, since it does not restrict the value of x in any way.

The other three equations have a solution. For example, in the equation -8+16x = 16x - 8, we can simplify and solve for x as follows:

-8+16x = 16x - 8

-8 + 8 + 16x = 16x

16x = 16x

We end up with an identity, 16x = 16x, which is true for all values of x. Therefore, this equation has infinitely many solutions, since any value of x will make the equation true.

3(-2x + 4) = -6x - 12

-6x + 12 = -6x - 12

-6x + 6x  = - 12 - 12

0  = -24

0  ≠ -24

Therefore, 3(-2x + 4) = -6x - 12 is the equation that has no solutions.

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Complete question:

Which of the following equations would have no solution?

17 is the side of the square.

what is rectangle?

The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a form of quadrilateral. It is also known as an equiangular quadrilateral for this reason. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

Let the width=x mtr

So the length will be x+4 mtr

so the are of the rectangle will be=x(x+4)=240

x²+ 4x=240

x²+ 4x-240=0

  x = -5 , 13 meter

so the length= 13 + 4 =17 mtr

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Difference in water tank deliveries on a construction site in a 2-month period could be due to various factors, such as weather changes, project size, worker numbers, water sources, and equipment malfunctions.

One possible explanation for the difference in the number of water tank deliveries on a construction site in a 2 month period could be a change in the weather conditions, which could have affected the water needs for construction purposes. For example, if the weather was drier and hotter in one month, more water may have been needed to compensate for evaporation and to keep the site hydrated.

Other possible reasons for the difference in the number of water tank deliveries on a construction site in a 2 month period could include changes in the size or scope of the project, shifts in the number of workers on the site, or variations in the availability or quality of local water sources. Additionally, factors such as equipment malfunctions or supply chain disruptions could also impact the frequency of water tank deliveries.

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I hope this can help you out some

The volume of the wedge is π/8 cubic meters.

To find the volume of the wedge, follow these steps:
1. First, find the radius of the tree by dividing the diameter by 2.

Since the diameter is 2 meters, the radius (r) is 1 meter.
2. The angle of inclination of the second cutting plane is given as 45 degrees.

Since a full circle is 360 degrees, find the fraction of the circle that the wedge represents by dividing 45 by 360.

This gives us 45/360 = 1/8.
3. The volume of a cylinder can be calculated using the formula V = π[tex]r^2h,[/tex]

where r is the radius and h is the height.

In this case, the height of the wedge (h) is equal to the radius (r), which is 1 meter.

So, the volume of the whole cylinder (tree) would be V = π[tex](1^2)(1)[/tex]

= π cubic meters.
4. Now, multiply the volume of the whole cylinder by the fraction representing the wedge (1/8) to find the volume of the wedge: (1/8) × π = π/8 cubic meters.

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For the given function, all values c in [a, b] guaranteed by the Mean Value Theorem Note is lies on the expression of 15x⁴ - 240x² - 256

To determine whether the Mean Value Theorem can be applied to f on [0, 4], we need to check whether f satisfies two conditions: 1) f must be continuous on [0, 4], and 2) f must be differentiable on (0, 4). The first condition ensures that the function has no jumps or breaks within the interval, while the second condition ensures that the function has a well-defined slope at each point in the interval.

Next, we need to check if f is differentiable on (0, 4). To do this, we need to take the derivative of f(x) and check whether it exists and is continuous on (0, 4).

f(x) = (x² – 1) / (x² -4) f'(x) = [(x² -4)(2x) - (x² -1)(2x)] / (x² -4)² f'(x) = -4x / (x² - 4)²

We can see that the derivative of f(x) exists and is continuous on (0, 4) except for x = ±2, where it has a vertical tangent. However, these points do not affect the differentiability of the function on (0, 4).

To find the values of c, we can use the formula for the Mean Value Theorem:

f'(c) = [f(4) - f(0)] / (4 - 0)

We already found the derivative of f(x) to be f'(x) = -4x / (x² - 4)². Using this and plugging in the endpoints of the interval [0, 4], we get:

f'(c) = [-15/16] / 4 f'(c) = -15/64

To solve for c, we need to find the value(s) of x that satisfy the equation f'(x) = -15/64. We can simplify this equation to get:

-4x / (x² - 4)² = -15/64 64x = 15(x² - 4)² 0 = 15x⁴ - 240x² - 256

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Answer:

Below

Step-by-step explanation:

A) The derivative of the position function is the velocity function

    derivative =  19 - 3.72 t      at t = 1   this = 15.28 m/s

B)  unclear:    19 - 3.72a

C)    H= 0 when at surface

            0 = 19t - 1.86 t^2

                  Quadratic Formula shows t = 10.2 s

D )  it will come down at the same speed it went up (but opposite direction)         =       -19 m/s

The equation that describes the size of Richard's debt is absolute value of |-75| = 75 meaning that Richard has a debt of 75 dollars (second option)

The account balance is a negative number. A negative number is a number that is less than 0. A negative number has a minus in front of it. An example of a negative number is -75.

If the account balance is negative, it means that Richard has overdrawn his account and he is in debt. He owes the bank money.

The sign that is used to represent absolute value in mathematics is I I. The absolute value of I-75I is 75.

To learn more about absolute numbers, please check: https://brainly.com/question/23678275

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