A new television is marked down $75. If this is a 15% decrease what is the sale price

Answer:

3.987923694

Step-by-step explanation:

Quadratic formula and plug in the numbers:

T = (-45 +-(sqrt(2025+4800)))/-32

the object will be at a height of 0 feet  0.97 seconds and 4.53 seconds after it is propelled.

h(t) = -16t² + 45t + 75

-16t² + 45t + 75 = 0

using the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

a = -16, b = 45, and c = 75.

We then Substitute these values into the quadratic equation

t = (-(45) ± √((45)² - 4(-16)(75))) / (2(-16)

t = (-45 ± √(2025 + 4800)) / (-32)

t = (-45 ± √6825) / (-32)

We find the value of t using both the positive and negative square root:

t₁ = (-45 + √6825) / (-32)

t₂ = (-45 - √6825) / (-32)

t₁ =0.97 seconds

t₂=  4.53 seconds

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Answer:

The correct answer is 152

Answer:

It is a rational number.

Step-by-step explanation:

since it is not a perfect square therefore it does not have an exact square root. also any number that is positive or negative, positive or zero, and can be write as a fraction

We must compute the eigenvalues of a real-valued symmetric matrix to determine if it is indefinite

The determinant of a real-valued symmetric matrix cannot be used to determine whether or not the matrix is indefinite. The determinant of a matrix only provides information about the matrix's scaling factor; it does not provide information about the matrix's eigenvalues or curvatures.

We must compute the eigenvalues of a real-valued symmetric matrix to determine if it is indefinite. The matrix is considered indefinite if it has both positive and negative eigenvalues.

If all eigenvalues are positive, the matrix is positive definite; if all eigenvalues are negative, the matrix is negative definite.

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Answer:

C. 452.16 cm2

Step-by-step explanation:

A= π r^2 = π · 12^2 ≈ 452.38934 or 452.38

The closest answer to that listed is C

formula:(A = π r²)

π = 3.14

r(radius)^2= radius to the second power.

Answer:

The height of the pile is increasing at a rate of 16.72 feet per minute. To solve this problem, we need to use the volume formula for a right circular cone: V=pi/3 r²h. We know that the volume is 20 cubic feet per minute, the height is 14 feet and the radius of the base is 14 feet. So we can calculate the rate of change of the height by rearranging the formula to give v/(pi/3r²). So for our example, v/(pi/3*14²)=20/(pi/3*14²)=20/(3.14*196)=20/613.44=16.72 feet per minute.

They may choose to bring 4 chaperones or even more depending on their preferences and logistical constraints.

For the camping trip with 15 scouts, they will need at least 15/5 = 3 chaperones.

However, it's possible that they may want to have more than the minimum number of chaperones for additional supervision and safety. The number of chaperones they choose to bring may also depend on the ratio of chaperones to scouts that they want to maintain.

So, they may choose to bring 4 chaperones (1 chaperone for every 3.75 scouts), 5 chaperones (1 chaperone for every 3 scouts), or even more depending on their preferences and logistical constraints.

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Answer:

you're question is not clear enought

Step-by-step explanation:

I'm so confused.

The dilation of quadrilateral ABCD to form quadrilateral A'B'C'D' can be found to be a A. reduction.

A reduction is a transformation that decreases the size of a shape or figure while maintaining its shape and proportions. It involves scaling down all the dimensions of the figure by the same factor.

This can be achieved by multiplying the coordinates of each point in the figure by a scaling factor less than 1. A reduction is often used when creating scaled-down models, maps, or drawings.

As shown on the diagram, the dimensions of quadrilateral ABCD are larger than those of A'B'C'D' which shows that it was reduced.

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Answer:

3:9:24

Step-by-step explanation:

Answer:

105

Step-by-step explanation:36:10:1

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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Answer:

the answer is 4/-1

Step-by-step explanation:

because m= rise/run

Answer:

-2

Step-by-step explanation:

First, pick two points on the line; I am using (0, -1) and (-2, 3). Put it into point-slope form, like this: \(\frac{3 + 1}{-2 - 0}\) . Solve to get \(\frac{4}{-2}\), or -2. This is your slope. Another way to find it is to find one point on the line and count how many points it is up or down from the first point, in this case that number is 4, and how many to the right or left, which in this case is 2 to the left. Moving left is negative, so it becomes -2.

Answer:

a and b

no the definitions have opposite results

Step-by-step explanation:

Answer:

62.4

Step-by-step explanation:

Volume=L*w*h/3

V=5.2*4*9=187.2

187.2/3-62.4

Answer:

The volume of pyramid is

V = Base area x Height x 1/3

  = (5.2 x 4) x 9 x 1/3 = 62.4 (cm3)

Hope this helps!

:)

Answer:

Step-by-step explanation:

By the Isosceles Triangle Theorem, if 2 sides of a triangle are congruent to each other, than the angles opposite those sides are also congruent. We see by the markings on the triangle that WX and WY are congruent. That means that angle Y (which is across from WX) and angle X (which is across from WY) are the same measure. We can set them equal to each other  because of this:

6y - 2 = 4x + 20

But we have a problem because we have 2 unknowns.

Let's try this out: the Triangle Angle-Sum Theorem says that all the angles of a triangle have to add together to equal 180. That means that

52 + 6y - 2 + 4x + 20 = 180.

But we STILL have a problem with those 2 unknowns. BUT...

If angle X and angle Y are the same, then we don't need both 6y - 2 AND 4x + 20.  We only need 1 of those multiplied by 2 because they're the same measure. Changing things up a bit to reflect that:

52 + 2(4x + 20) = 180 and

52 + 8x + 40 = 180 and

8x = 88 so

x = 11.

That means that

4(11) + 20 = 64 which is the measure of both angles X and Y.

Let's check:

64 + 64 + 52 better equal 180. And it does, so we're good.

The value of x is found this way:

4x + 20 = 64 and

4x = 44 so

x = 11 which we already knew. Now for y:

6y - 2 = 64 and

6y = 66 and

y = 11 also.

Answer:

B. 5i + 12b < 100

Step-by-step explanation:

I used process of elimination on to figure this one out.

I first eliminated A because I knew the i should be next to the 5. I know this because i (ink) costs 5 dollars each.

I next eliminated D because this equation is looking to find the sum of the ink and the new brushes, not the ink plus the total cost equaling the brushes.

Finally, I eliminated C because Emily only has $100, so the cost of the ink (i) and the brushes (b) must NOT excede 100 dollars. From this, I can see that C states that the sum exceeds Emily’s $100 budget

This leaves us with B as the final answer

Hope this helps! Have a lovely rest of your day!

Answer:

The awnser is March 15th because every 12 days they are off at the same time

Step-by-step explanation:

First and foremost, it is important to note that human skin color is determined by a variety of factors, including genetics, environmental influences, and geographic location. In fact, skin color is the result of the amount and type of melanin pigment produced by specialized cells in the skin called melanocytes.

There are two main types of melanin pigment: eumelanin and pheomelanin. Eumelanin is responsible for producing darker skin colors, while pheomelanin produces lighter skin colors. However, the amount and distribution of these pigments can vary greatly between individuals, resulting in a wide range of skin tones.

Additionally, skin color can also be influenced by factors such as sun exposure, age, and hormonal changes. For example, prolonged sun exposure can lead to darker skin, while aging and hormonal changes can cause changes in skin pigmentation. Furthermore, it is important to note that skin color is not always clearly defined or easily categorized into specific shades. There can be a great deal of variation within a single skin tone, as well as overlap between different skin tones. This is due to the complex interplay of genetic and environmental factors that contribute to skin color.

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Answer:

x^{2} -3x=46

Step-by-step explanation:

First, we know that the area of the rectangle is L x W.

\(L= x+2\\W= x-5\\(x+2) * (x-5)=56\)

So, we would get \(x^{2} -5x+2x-10\)=56

\(x^{2} -3x=46\)

Answer:

-9v + 8

Step-by-step explanation:

Answer:

3 batches

Step-by-step explanation:

Given that :

Let Number of batches of cupcakes made = x

12 eggs was used to make x batches

Number of eggs used per batch = 4

If 4 eggs was used for a batch :

Number of batches of cupcakes made :

12 eggs / 4 eggs

= 3 batches

To determine the number of smaller boxes that would contain the same amount of cereal as a larger box, we set the expressions representing the cereal content equal to each other. Solving the equation, we find that 15 smaller boxes are required to match the cereal quantity in the larger box.

To find the number of smaller boxes that equal the same amount of cereal in a larger box, we need to equate the two expressions and solve for n.

Setting the expressions equal to each other:

10 + 6.3n = 7 + 6.5n

Simplifying the equation:

6.3n - 6.5n = 7 - 10

-0.2n = -3

Dividing both sides by -0.2:

n = -3 / -0.2

n = 15

Therefore, 15 smaller boxes would equal the same amount of cereal as the larger box.

The problem states that the expressions 10 + 6.3n and 7 + 6.5n represent the amount of cereal in the new larger box. The variable n represents the number of smaller boxes.

To find how many smaller boxes are equivalent to the larger box, we need to set the two expressions equal to each other and solve for n. This equation represents the balance between the amount of cereal in the larger box and the combined amount of cereal in the smaller boxes.

By simplifying the equation and solving for n, we find that 15 smaller boxes are needed to equal the same amount of cereal as the larger box.

This means that if the cereal manufacturer wants to package the same amount of cereal as the larger box, they would need to use 15 smaller boxes instead. This calculation helps the manufacturer determine the number of smaller boxes needed to maintain the same quantity of cereal while changing the box size.

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To solve this problem, we can use the method of Lagrange multipliers. This method allows us to find the maximum or minimum of a function subject to constraints.

In this case, the function we want to maximize is Z = 2x + 3y and the constraints are x = 24, y = 25, and 3x + 2y = 52.We begin by setting up the Lagrangian function, which is given by:L(x, y, λ) = Z - λ(3x + 2y - 52)where λ is the Lagrange multiplier. We then take the partial derivatives of the Lagrangian with respect to x, y, and λ and set them equal to zero.∂L/∂x = 2 - 3λ = 0∂L/∂y = 3 - 2λ = 0∂L/∂λ = 3x + 2y - 52 = 0Solving for λ, we get λ = 2/3 and λ = 3/2. However, only one of these values satisfies all three equations. Substituting λ = 2/3 into the first two equations gives x = 20 and y = 22. Substituting these values into the third equation confirms that they satisfy all three equations. Therefore, the maximum value of Z subject to the given constraints is Z = 2x + 3y = 2(20) + 3(22) = 84.

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The maximum value of Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, is 96.

To maximize the function Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, we will use the method of linear programming.

Let us first graph the equation 3x + 2y = 52.

The intercepts of the equation 3x + 2y = 52 are (0, 26) and (17.33, 0).

Since the feasible region is restricted by x ≤ 24 and y ≤ 25, we get the following graph.

We observe that the feasible region is bounded and consists of four vertices:

A(0, 26), B(8, 20), C(16, 13), and D(24, 0).

Next, we construct a table of values of Z = 2x + 3y for the vertices A, B, C, and D.

We observe that the maximum value of Z is 96, which occurs at the vertex B(8, 20).

Therefore, the maximum value of Z = 2x + 3y, subject to the conditions x ≤ 24, y ≤ 25, and 3x + 2y = 52, is 96.

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The amount you will pay back by the end of the term is; 162.18 dollar.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

\(a = p(1 + r)^{t}\)

Given that you borrow $101 at 7% compounded annually for seven years, then we have;

P = 101 dollar

Rate = 7%

Times = 7 yr

Therefore,

\(a = p(1 + r)^{t}\)

\(a = 101(1 + 0.07)^{7}\\\\a = 101 (1.07)^7\\\\a = $162.18\)

Hence, The amount you will pay back by the end of the term is; 162.18 dollar.

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Using proportions, it is found that she will pay $8.28 in total after the discount.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Before tax, the total price is given by:

P = 3.59 + 4.25 + 3.99 = $11.83.

She gets a 30% discount, hence the proportion she pays is 70% of this amount, hence:

P = 0.7 x 11.83 = $8.28.

She will pay $8.28 in total after the discount.

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The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

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Multiply 0.625/1 by 1000/1000 to get 625/1000. Reducing we get 5/8