question attached
A. 5
B. 16
C. function is not defined for this value
D. 9

Question Attached A. 5B. 16C. Function Is Not Defined For This ValueD. 9

Answers

Answer 1

F(4)=9 is the value for this function.

What is piecewise function?

A function that is defined by numerous smaller functions across various time intervals is known as a piecewise function. The domain of a function is the sum of all the smaller domains, and each sub-function has its own formula and domain. The input value and the function that establishes that interval determine the function's output.

The typical functional notation, which represents the body of a function as an array of functions and related subdomains, can be used to define piecewise functions. Together, these subdomains must encompass the entire domain; frequently, it is also necessary for them to be pairwise disjoint, or constitute a partition of the domain.

x=4 is bigger than or equal to 0 because it.

we use the third function definition

F(x)=x+5.

Therefore, F(4)=4+5=9.

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Related Questions

Can someone help me to answer these questions pleases


Listen to Kerry Washington perform Sojourner Truth's speech Ain't I a Woman. Then go to ST's version at the Sojourner Truth Project's website. Compare the differences between Frances Gage's (the one Washington read) and Marius Robinson's earlier version (the one ST read). You can read them here.

Answer the following questions:

1. List 3 differences between the Robinson version and the Gage version of the speech.

2. Why do you think it is important to hear both versions of the speech?

3. How do you think the differences changed the way people (in the north and the south) understood the context of her speech? How about now?

4. How does hearing the differences in dialect change the way you think about the speech?


answer them in at least 10 sentences.

When women’s rights activists spoke out, who were they advocating for, white women or African-American women?

What are the distinct arguments that Truth makes in her speech?

What is Truth saying about women’s rights?

Who is going to give them these rights?

How does Truth’s speech reflect intersectionality?

What passages in the speech reflect this?

Answers

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.

What is speech?

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.

According to question:

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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please help me in this question is math,solve just d, e&f​

Answers

Step-by-step explanation:

a) factorize A

A = (2x-1)²+2(3-6x)(4x-7)-4x²+1

expand the terms

(2x-1)²-52x²+108x-41

factorize

(2x-1)²-(26x-41)(2x-1)

factor out the common factor 2x-1

-(2x-1)(24x-40)

A = -8(2x-1)(3x-5)

b) show that B = (3x-11)(2x-1)

6x²-25x+11

6x²-3x-22x+11

3x(2x-1)-11(2x-1)

(2x-1)(3x-11)

c) Expand and reduce A

(2x-1)²+2(3-6x)(4x-7)-4x²+1

-48x²+108x-40

d) Calculate A for x=0 and x=-1

when x=0 -48(0)²+108(0)-40

A=0

x=-1 -48(-1)²+108(-1)-40

A=-196

e) Reduce 2A-3B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-3(6x²-25x+11)

-96x²+216x-80-18x²+75x-33

-144x²+291x-113

f) Factorize 2A-B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-(6x²-25x+11)

-96x²+216x-80-6x²+25x-11

-102x²+241x-91

x=(241 + sqrt(20953))/204

x=(241 - sqrt(20953))/204

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Consider 8 = − 2/3x. Which is the BEST first step to take when solving the given equation?

A) Multiply each side by 3/2.


B) Multiply each side by −3/2.


C) Multiply each side by −2/3.


D) Add 2/3x to each side.

Answers

B) multiply each side by -3/2

if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?

Answers

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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The sum of 2 vector forces is <5, -3>. What is the magnitude of the resulting force?

Answers

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

What is magnitude?

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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find the missing terms 82,81,78,-,66,-
5,6,8,-,15,-​

Answers

To find the missing terms in the sequences: 82, 81, 78, -, 66, - and 5, 6, 8, -, 15, - we need to identify the pattern in each sequence.

For the first sequence (82, 81, 78, -, 66, -), we can see that each term is decreasing by 1, then decreasing by 13. So the missing terms are 63 and 60.

Therefore, the full sequence is: 82, 81, 78, 63, 66, 60.

For the second sequence (5, 6, 8, -, 15, -), we can see that each term is increasing by 1, then increasing by 7. So the missing terms are 11 and 22.

Therefore, the full sequence is: 5, 6, 8, 11, 15, 22.

The height distributions of two different classes at Dover elementary school are shown below both groups, have the same interquartile range how many times the third quartile range is the difference between the median height of the third grade class in the fourth grade class 1/4 1/2 two or four

Answers

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.

Marlo uses 252
lb of gravel to cover a garden plot of 36 ft2
How many pounds of gravel does it take to cover one square foot?

Answers

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

What does a pound mean?

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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Use the drop-down menus to complete the statements.



When electrons are lost, a
ion is formed.

When electrons are gained, a
ion is formed.

Answers

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:

Please help and hurry

Answers

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.

What is linear and quadratic equation?

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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A line has a slope of -4 and passes through the point (-1, 10). Write its equation in slope- intercept form.​

Answers

Answer:

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

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

[tex]b = 6[/tex]

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

Final answer:

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

Explanation:

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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What is the range of the relation whose graph is shown?

Answers

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

What is a domain?

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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Find the equation of the line tangent to the graph of f(x) = (In x)4 at x = 4.
y =
(Type your answer in slope-intercept form. Do not round until the final answer. Then round to
as needed.)

Answers

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.

What is differentiation?

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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HELP ASAP!!!!
The diameter of a circular cookie cake is 14 inches. How many square inches make up half of the cookie cake? Approximate using π = 3.14. 615.44 square inches 307.72 square inches 153.86 square inches 76.93 square inches

Answers

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

How to calculate for the half square inches 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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Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.

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

Answers

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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An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.

to close the expansionary gap, the government would need to increase or decrease spending by $ billion.

Answers

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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The sum of a number and three is no more than eight

Answers

Answer:5

Step-by-step explanation: hope this helps

<
The brain volumes (cm³) of 20 brains have a mean of 1128.4 cm³ and a standard deviation of 125.9 cm³. Use the
given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or
significantly high. For such data, would a brain volume of 1360.2 cm³ be significantly high?
Significantly low values are cm³ or lower.

Answers

Step-by-step explanation:

The range rule of thumb states that for data with a roughly bell-shaped distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Given that the standard deviation is 125.9 cm³, one standard deviation above the mean would be 1128.4 + 125.9 = 1254.3 cm³, and one standard deviation below the mean would be 1128.4 - 125.9 = 1002.5 cm³.

Thus, significantly low values would be 1002.5 cm³ or lower, and significantly high values would be 1254.3 cm³ or higher.

Since 1360.2 cm³ is higher than 1254.3 cm³, it would fall outside the range of one standard deviation above the mean and can be considered significantly high based on the range rule of thumb.

1:20 - salesman allows a 5% discount for cash payment. What will be the discount allowed for a ash payment of GH¢5,600.00? A. GH 250.00​

Answers

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

GHC 280.00.

How to obtain the discount?

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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The salaries of six bank employees are $37,000, $38,500, $35,000, $37,000, $45,000, $40,000, and $75,000.

Which statement is true?

Question 1 options:

Both the median and mode are appropriate measures of center.


The mean, median, and mode are all appropriate measures of center.


Both the mean and median are appropriate measures of center.


The median is the only appropriate measure of center.

Answers

The correct answer is: Both the mean and median are appropriate measures of center.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.

Here,

The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:

37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500

And there are seven salaries. Therefore, the mean is:

307,500 / 7 = 43,928.57

The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:

35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000

The median is the middle value, which is 40,000.

The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.

Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.

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7. Can the following be the lengths of the sides of a triangle?
a. 20 cm, 40 cm, 50 cm
b. 20 cm, 40 cm, 60 cm
c. 41 cm, 250 mm, 12 cm​

Answers

Answer:

B

Step-by-step explanation:

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

A bolynomial function has zeros √2, 4, and 6i. What is the minimum degree of the
polynomial function?
A. 6
B. 5
C. 4
D. 3

Answers

Answer:

C) 4

Step-by-step explanation:

In triangle BC, point D is on AC such that AD = 12 and CD = 12. If angle ABC = angle BDC = 90 degrees, then what is BD?

Answers

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

Jeremy and Aksa were finding the volume of this prism. They agreed that 4 layers can be added together to find the volume. Jeremy says that he can see on the end of the prism that each layer will have 16 cubes in it. Aksa says that each layer has 24 cubes in it. Who is right? Explain your answer.

Answers

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

What is 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.

According to the given information:

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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Choose scales for the coordinate plane shown so that you can graph the points J (5, 50), K(3, 50), L (4, -40), M (-2, 40), and N (-5, -10). on the x-axis use a scale of ____ units for each grid square. on the y-axis use a scale of ____ units of each grid square. complete the explanation for using these scales for each axis. the x-coordinates range from ____ to ____, and the y-coordinates range from ____ to ____.

Answers

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.

What is coordinate plane?

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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You want to be able to withdraw $40,000 each year for 15 years. Your account earns 5% interest.
a) How much do you need in your account at the beginning?
b) How much total money will you pull out of the account?
c) How much of that money is interest?

Answers

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.

How to determine  How much do you need in your account at the beginning

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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A car was valued at $38,000 in the year 1994. The value depreciated to $14,000 by the year 2004.
A) What was the annual rate of change between 1994 and 2004?
r =
Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r= %.
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2007 ?
value = $
Round to the nearest 50 dollars.

Answers

A) To find the annual rate of change, we can use the formula:

r = (V2/V1)^(1/n) - 1

where V1 is the initial value, V2 is the final value, n is the number of years, and r is the annual rate of change (expressed as a decimal).

Plugging in the given values, we get:

r = (14000/38000)^(1/10) - 1

r ≈ -0.1102

So the annual rate of change between 1994 and 2004 is approximately -0.1102.

B) To convert the rate to a percentage, we can multiply by 100:

r ≈ -11.02%

So the correct answer to part A written in percentage form is approximately -11.02%.

C) To find the value of the car in 2007, we can use the formula:

V = V0*(1+r)^n

where V0 is the initial value, r is the annual rate of change (expressed as a decimal), n is the number of years, and V is the final value.

We want to find the value in 2007, which is 3 years after 2004. So we plug in:

V0 = 14000 (since that was the value in 2004)
r = -0.1102 (the annual rate of change)
n = 3 (the number of years since 2004)

V = 14000*(1-0.1102)^3

V ≈ $9,679.65

Rounding to the nearest 50 dollars, we get:

value ≈ $9,700

Therefore, the value of the car in the year 2007 is approximately $9,700.

Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9

Answers

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.

What is Quadratic equation?

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:

Use the quadratic formula: Inga can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 2, b = 12, and c = -3.Factor out the common factor: Inga can factor out the common factor of 2 from the equation to get 2(x² + 6x - 3/2) = 0.Complete the square: Inga can complete the square by adding (6/2)² = 9 to both sides of the equation to get 2(x² +6x +9 -9/2) = 9.

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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Find the area of a rectangle with length 4.3 cm and breadth 3.9 cm

Answers

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

Suppose that ​19,665$ is invested at an interest rate of ​6.8% per​ year, compounded continuously.
​a) Find the exponential function that describes the amount in the account after time​ t, in years.
​b) What is the balance after 1​ year? 2​ years? 5​ years? 10​ years?
​c) What is the doubling​ time?

helppppppp

Answers

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:

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