Name
Date
- Sarah received a coupon for 15% off the total purchase price at a shoe store. Let p be the
original price of the purchase. Use the expression p-0.15p for the new price of the purchase.
Write an equivalent expression by combining like terms.

a) you would need $450,332.81 in your account at the beginning. b)  the total money that will be pulled out of the account is $600,000.

a) To calculate the amount needed in the account at the beginning, we can use the present value formula:

PV = PMT * ((1 - (1 + r)^-n) / r)

Where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of periods.

Plugging in the values, we get:

PV = 40000 * ((1 - (1 + 0.05)^-15) / 0.05)

PV = $450,332.81

Therefore, you would need $450,332.81 in your account at the beginning.

b) To calculate the total money that will be pulled out of the account, we can simply multiply the annual payment by the number of years:

Total money = PMT * n

Total money = 40000 * 15

Total money = $600,000

Therefore, the total money that will be pulled out of the account is $600,000.

c) To calculate the amount of money that is interest, we can subtract the initial investment from the total money pulled out:

Interest = Total money - Initial investment

Interest = $600,000 - $450,332.81

Interest = $149,667.19

Therefore, $149,667.19 of the money pulled out is interest.

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The equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.

A straight line can be used to symbolise a function that is linear, meaning that for each unit change in the input, the output (y) changes by a fixed amount (x). While a parabola can be used to depict a function, a quadratic function has an output (y) that changes by a non-constant amount for each unit change in the input (x). In other words, a quadratic function curves because of the squared term in its equation.

Given, the parabola has vertex at point (2, -11) and passes through the point (0, 5).

Thus, the equation of parabola in vertex form is:

y = a(x - 2)² - 11

Now, the parabola passes through the point (0, 5) we have:

5 = a(0 - 2)² - 11

5 = 4a - 11

16 = 4a

a = 4

Hence, the equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.

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Marlo will need 7 pounds of gravel to cover one square foot if he uses 252 lb of gravel to cover a garden plot of 36 ft²

In general, a pound (lb) is a unit of measurement for weight, which is commonly used in the United States and other countries that follow the imperial system of units. 1 pound is equal to 16 ounces or approximately 0.45 kilograms. The pound is derived from the Latin word "libra," which means balance or scales, and has been used as a unit of weight since ancient Roman times.

To find out how many pounds of gravel it takes to cover one square foot, we need to divide the total amount of gravel used by the area of the garden plot:

pounds per square foot = total pounds / area

In this case, Marlo used 252 lb of gravel to cover a garden plot of 36 ft², so:

pounds per square foot = 252 lb / 36 ft²

Simplifying this expression, we get:

pounds per square foot = 7 lb/ft²

Therefore, it takes 7 pounds of gravel to cover one square foot.

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None of the given numbers make the equation 8/y² + 2 true.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.

Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.

Substituting y=1 would give us:

8/1² + 2 = 8 + 2 = 10

So, 1 is not the answer.

Substituting y=2 would give us:

8/2² + 2 = 8/4 + 2 = 2 + 2 = 4

So, 2 is not the answer.

Substituting y=3 would give us:

8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888

So, 3 is not the answer.

Substituting y=4 would give us:

8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5

So, 4 is not the answer.

Therefore, none of the given numbers make the equation 8/y² + 2 true.

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The equation of the tangent line of f(x) = (ln x)⁴ at x = 4 is y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2.

We may calculate the derivative of a power function using the power rule of differentiation. Since many functions may be expressed as power functions or can be made simpler using power functions, the power rule is a helpful tool in calculus. We can quickly determine the derivatives of these functions using the power rule and apply them to issues in physics, economics, and engineering.

The slope of the tangent line at x = 4 is determined using the derivative as follows:

f(x) = (ln x)⁴

f'(x) = 4(ln x)³ (1/x)

At x = 4, we have:

f'(4) = 4(ln 4)³ (1/4) = (3/16)ln 2

Now, the equation of the tangent line is:

y - 256ln⁴ 2 = (3/16)ln 2(x - 4)

y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2

Hence, the equation of the tangent line of f(x) = (ln x)⁴ at x = 4 is y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2.

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On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.

In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).

On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.

For the given coordinates the range of x and y coordinates are:

x-coordinates range from -5 to 5

y-coordinates range from -40 to 50.

Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.

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the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.

How to solve the question?

To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:

AB' = AB x 3

where AB' is the length of AB after the dilation, and AB is the original length of AB.

However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:

AB²= AC²+ BC²

Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.

Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:

AB' = AB x 3

For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:

AB' = 5 x 3 = 15 units

Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.

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Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.

A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.

Both Jeremy and Aksa could be right, depending on how they are counting the cubes.

If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.

However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.

Therefore, the answer depends on the shape of the prism and how the layers are counted.

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Answer:

[tex]10 = -4( - 1) + b[/tex]

[tex]10 = 4 + b[/tex]

[tex]b = 6[/tex]

[tex]y = - 4x + 6[/tex]

The equation of the line in slope-intercept form is y = -4x + 6.

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is -4 and the line passes through the point (-1, 10), we can substitute these values into the equation.

Using the point-slope formula (y - y1) = m(x - x1), we can rewrite it as (y - 10) = -4(x - (-1)). Simplifying this equation, we get y - 10 = -4x - 4, and rearranging it, we have y = -4x + 6. Therefore, the equation of the line in slope-intercept form is y = -4x + 6.

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Answer:

Step-by-step explanation:

BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn

The discount allowed for a cash payment of GH 5,600.00 is given as follows:

GHC 280.00.

The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.

There is a 5% discount, hence the value of the discount is obtained as follows:

0.05 x 5600 = GHC 280.00.

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Answer:

B

Step-by-step explanation:

THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE

1. In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times. 2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. 3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. 4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker.

Speech is the act of expressing thoughts, ideas, or emotions through spoken words. It is a form of communication that allows individuals to convey information, share opinions, ask questions, and express feelings to others.

1. Three differences between the Robinson version and the Gage version of the speech are:

In the Robinson version, Truth says "I have as much muscle as any man" while in the Gage version she says "I have ploughed and planted, and gathered into barns, and no man could head me!".

In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times.

In the Robinson version, Truth refers to herself as a "colored woman" while in the Gage version she uses the term "African American".

2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. The differences between the two versions show how editors and publishers can change the meaning and impact of a text by making small modifications to it. Additionally, hearing both versions allows us to appreciate the nuances of language and dialect, and how different speakers can bring their own interpretations and emphasis to a text.

3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. For example, the reference to "colored women" in the Robinson version would have been seen as more confrontational and controversial in certain regions. Today, the differences may help us appreciate the diversity and complexity of language, and how it reflects the cultural and historical contexts in which it is spoken.

4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker. The dialect used in each version reflects the cultural and historical context of the time, and the different audiences that the speeches were intended for. By hearing the dialect of each version, we can better appreciate the ways in which language shapes our understanding of history and identity.

As for the next set of questions:

When women's rights activists spoke out, they were advocating for both white women and African-American women, although the experiences and struggles of African-American women were often ignored or marginalized within the movement.

Truth makes several distinct arguments in her speech, including that women deserve the same rights and respect as men, that the stereotype of women as weak and dependent is unjust, and that the experiences of African-American women are often overlooked in discussions of women's rights.

Truth is saying that women deserve equal rights and respect as men, and that the societal norms that limit women's opportunities and autonomy are unjust and unfounded.

Truth is arguing that women need to fight for their own rights, rather than waiting for men to give them these rights. She also emphasizes the importance of solidarity and mutual support among women.

Truth's speech reflects intersectionality by recognizing the ways in which race and gender intersect to create unique experiences of oppression and marginalization. She argues that the struggles of African-American women cannot be separated from the struggles of all women, and that a truly equitable society must address the needs and concerns of all marginalized groups. One passage that reflects this is when she says, "I have borne thirteen children, and seen most all sold off to slavery, and when I cried out with my mother's grief, none but Jesus heard me! And ain't I a woman?" This passage highlights the intersection of race, gender, and motherhood in Truth's experience.

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Answer:

3,4,5 is the answer

Step-by-step explanation:

for the explanation using pythagoras theoem

[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]

may you give me branliest as you promised

The third quartile range is the difference between the median height of the third grade class and the fourth grade class, so the answer is two times.

Answer: a) The exponential function that describes the amount in the account after time t, in years, is given by:

A(t) = Pe^(rt)

where P is the initial amount invested, r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

A(t) = 19665e^(0.068t)

b) To find the balance after 1 year, we substitute t = 1 in the above formula:

A(1) = 19665e^(0.068*1) = $20,983.88

To find the balance after 2 years, we substitute t = 2:

A(2) = 19665e^(0.068*2) = $22,429.45

To find the balance after 5 years, we substitute t = 5:

A(5) = 19665e^(0.068*5) = $29,137.27

To find the balance after 10 years, we substitute t = 10:

A(10) = 19665e^(0.068*10) = $43,127.22

c) The doubling time can be found using the formula:

t = ln(2)/r

where ln is the natural logarithm function. Substituting the given values, we get:

t = ln(2)/0.068 ≈ 10.20 years

Therefore, the doubling time is approximately 10.20 years.

Step-by-step explanation:

When electrons are lost, a cation is formed.

When electrons are gained, an anion is formed.

An atom can lose or gain electrons to form ions. An ion is an atom or molecule that has an unequal number of protons and electrons, which gives it a net electrical charge.

When an atom loses one or more electrons, it becomes positively charged because the number of protons in the nucleus is greater than the number of electrons. This type of ion is called a cation. Cations are formed when metals lose electrons because they have relatively low electronegativity, which means they don't hold onto their valence electrons as tightly.

On the other hand, when an atom gains one or more electrons, it becomes negatively charged because the number of electrons is greater than the number of protons. This type of ion is called an anion. Anions are formed when nonmetals gain electrons because they have relatively high electronegativity, which means they attract electrons more strongly.

Therefore, When electrons are lost, a cation is formed and When electrons are gained, an anion is formed.

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Answer:

When electrons are lost, a

✔ positive

 ion is formed.

When electrons are gained, a

✔ negative

 ion is formed.

Step-by-step explanation:

The answer is , (a)  For equation 1 Use the quadratic formula , (b) For equation 2 use of Factor out the common factor , (c) For equation 3 use of Complete the square.

A quadratic equation is a type of equation in algebra that contains a variable of degree 2, meaning that the highest power of the variable is 2.

Quadratic equations can have two real roots, one real root, or two complex roots, depending on the value of the discriminant (b² - 4ac). If discriminant is positive, equation has two real roots, if it is zero, equation has one real root (a "double root"), and if it is negative, equation has two complex roots.

Inga can use the following steps to solve the quadratic equation 2x² + 12x - 3 = 0:

Therefore, steps that Inga could use to solve quadratic equation are given:

Use the quadratic formula

Factor out the common factor

Complete the square

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According to the question the magnitude of the resulting force is 5.83.

Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.

The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.

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Suppose that the function h is defined as follows. -2 -1 h(x)= if – 2, the graph is given below: (see image)

A graph is a mathematical structure used to represent relationships between objects or entities. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices.

In a graph, the vertices represent the objects or entities being studied, while the edges represent the connections or relationships between them.

For example, in a social network graph, the vertices might represent individual users, and the edges might represent their connections (e.g. friendships) with other users.

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The number of square inches to make up half the cookie cake is 76.93 in² area.

The diameter of the circular cookie cake is 14 inches, so its radius will be r = 7 inches. Using the formula for area of circle we have:

area of cookies cake = 3.14 × 7 in × 7 in

area of cookies cake = 153.84 in²

half the area of the cookie cake = 153.84 in²/2

half the area of the cookie cake = 76.93 in²

Therefore, the number of square inches to make up half the cookie cake is 76.93 in² area.

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The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-4, 4} or -4 ≤ x ≤ 4.

Range = {-1, 1} or -1 ≤ y ≤ 1.

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Answer:

16.77 cm²

Step-by-step explanation:

Area of rectangle = L x W

L = 4.3 cm

Width = 3.9 cm

Let' solve

4.3 x 3.9 = 16.77 cm²

So, the area of the rectangle is 16.77 cm²

The image vertices of K′L′M′N′ under a rotation of 270° clockwise are:

K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0).

What is coordinates?

Coordinates are numerical values used to represent the position of a point in a particular space or system. coordinates are used to identify the position of a point in a given plane or space. Typically, two or three numbers are used to describe the location of a point in a two-dimensional or three-dimensional space, respectively.

To rotate a point by 270° clockwise about the origin, we can swap the coordinates and negate the new x-coordinate. Let's apply this transformation to each vertex of the polygon:

For point K(0, 0), we have K′(0, 0) (since the origin is its own image under any rotation).

For point L(5, 2), we have L′(−2, 5) (swapping the coordinates gives (2, 5), and negating the x-coordinate gives (−2, 5)).

For point M(5, −5), we have M′(5, 5) (swapping the coordinates gives (−5, 5), and negating the x-coordinate gives (5, 5)).

For point N(0, −3), we have N′(3, 0) (swapping the coordinates gives (−3, 0), and negating the x-coordinate gives (3, 0)).

Therefore, the image vertices of K′L′M′N′ under a rotation of 270° clockwise are:

=> K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)

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Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

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Answer:5

Step-by-step explanation: hope this helps