Answer: 76 pages
Step-by-step explanation:
700 photo spaces = 100%
-The total
168 photo spaces = 24%
-The number of empty spaces in the album.
- Find 24% of 700:
70(10%) x 2 = 140
7(1%) x 4 = 28
140 + 28 = 168
532 photo spaces = 76%
- The number of photos in the album
700 - 168 = 532
Finding the number of pages.
-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.
532 ÷ 7 = 76.
Expand the expressions and simplify.
5(x + 4) + 3(x + 2) =
O
O
8x + 4
6x + 18
8x+ 26
7x - 18
Answer:
8x + 26
Step-by-step explanation:
Your aim is to get rid of the brackets...so do this
5(x + 4) + 3(x + 2)
5x + 20 + 3x + 6
5x + 3x + 20 + 6
8x + 26
hope this helps!
Please help with the answer!
Answer:
Step-by-step explanation:
2.1 so a
You just designed a new kind of cell phone, and now you want to put it up for sale. Each phone costs you
$100 to produce.
Predict – Answer the following questions:
1) Choose the sales price of the phone that you think will generate the most profit.
2) What could happen if you set the price too low?
3) What could happen if you set the price too high?
Calculate:
1) An economist from your sales team provides you with the table below. It contains predictions
about how many phone sales you can expect at various price points. Complete the other columns.
Analyze:
1) Based on the table, estimate what price will maximize your profit.
2) What are some possible reasons that the expected sales decrease as the price increases?
3) What is the x-intercept? What does that point represent?
Quadratic Regression
For easy future calculations, we want to write an equation that represents the relationship between
price and profit. Enter your data for x and y into a calculator. Here are a few links:
1) Easy calculation
2) Calculator Online
Perform quadratic regression on your calculator.
Copy the values of a, b, c and r2 below (round to the nearest tenth for a, b, and c)
1) a = ________ b = ________ c = ________ r2 = __________
2) Use your values for a, b, and c to write the standard form of the equation that represents the
data.
a. f(x) = ax2 + bx + c f(x) = x2 + x +
3) What is r2
, and what does it say about your equation?
4) Sketch a graph of your equation on the coordinate plane below. Make sure to label:
a. The axes and what they represent
b. The zero(s)
c. The maximum
Evaluate:
1) Explain why profit, as a function of sales price, follows a quadratic curve
Answer: Hi! Read the explanation below:
Brainliest?
Step-by-step explanation:
Predict:
Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).
If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.
If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.
Calculate:
See the table below.
Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)
100 20 2,000 2,000 0
120 18 2,160 1,800 360
140 16 2,240 1,600 640
160 14 2,240 1,400 840
180 12 2,160 1,200 960
200 10 2,000 1,000 1,000
Analyze:
Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.
As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.
The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.
Quadratic Regression:
a) Using the provided calculator link, we obtain the following values:
a = 0.05
b = -10
c = 500
r2 = 0.9
b) The standard form of the equation that represents the data is:
f(x) = 0.05x2 - 10x + 500
c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.
d) See graph below.
Graph of quadratic equation
Evaluate:
Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these
Solve x/ 2 < 4. Graph the solution
Answer:
The answer is x<8
Step-by-step explanation:
x/2<4
x<8
A bowl contained 33.4 grams of salt. Then, Charlie poured in another 58.09 grams. How much salt does the bowl contain now?
Find the area? For this shape pleae
Select the correct answer from each drop-down menu.
Chris purchased a new mattress for $1,399. He will need to pay $78 each month on his interest-free loan to pay off the total price of the mattress in 18
months. Separately, Chris sets aside $50 each month in a savings account, which currently shows a balance of $250.
Create an augmented matrix from a system of equations to help Chris determine when he can use monthly payments and savings to pay off the total
purchase price of the mattress,
Row 1
Row 2
Column 1
Column 2
>
Reset
Column 3
Next
>
>
Rewriting the equations in matrix form, we get:
[1 78/1399 | 1]
[50 1 | 1149/1399]
What is square matrix?
A square matrix is a matrix that has the same number of rows and columns. That is, a matrix A is square if A has dimensions n x n, where n is a positive integer.
To create an augmented matrix, we need to represent the system of equations in matrix form. Let x be the number of months it will take Chris to pay off the total purchase price of the mattress using monthly payments and savings. Then the system of equations is:
1399/18 + 78x = 1399
50x + 250 = 1399
The first equation represents the fact that the total price of the mattress must be paid off in 18 months using monthly payments, and the second equation represents the fact that Chris sets aside $50 each month in savings to put towards the purchase.
Rewriting the equations in matrix form, we get:
[1 78/1399 | 1]
[50 1 | 1149/1399]
This is the augmented matrix for the system of equations, where the leftmost columns represent the coefficients of the variables (1 for x in the first equation, 50 for x in the second equation, and 78/1399 for the monthly payment in the first equation), and the rightmost column represents the constants on the right-hand side of each equation.
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Column 1 Column 2 Column 3
Row 1-- 50 -1 -250
Row 2-- 78 1 1,399
I got it right on my test.
Your Welcome:)
What is the length of side AB?
The length of side AB is given as follows:
[tex]AB = \frac{6}{\sqrt{3}}[/tex]
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the angle of 30º, we have that:
AB is the opposite side.AC is the adjacent side.Hence the length of side AB is obtained as follows:
tan(30º) = AB/6
AB = 6 x tan(30º)
[tex]AB = 6 \times \frac{1}{\sqrt{3}}[/tex]
[tex]AB = \frac{6}{\sqrt{3}}[/tex]
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The value of the side AB is calculated as: AB = 6/√3
How to use trigonometric ratios?There are different trigonometric ratios used in right angle triangles which are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Looking at the given triangle, the value of AB can be gotten via the trigonometric ratio tan x. Thus:
AB = 6 * tan 30
AB = 6 * 1/√3
AB = 6/√3
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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.
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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Can someone help me with as many as possible (even one is ok) please
Answer:
7.30
Step-by-step explanation:
number 13 is simple subtraction.
How could expanded land acreage and pricing be viewed as some to be a bad thing
for the recovering Great Plains?
Increased land prices and acreage on the Great Plains could be seen as negative owing to potential ecological impact, as a disruption for Traditional communities and unsustainable resource use.
Why expanded land acreage and pricing in Great plains is considered negative?Ecological impact: Increased land acreage and price may cause habitat loss, biodiversity loss, soil erosion, and water pollution, all of which might be detrimental to the area's natural ecosystem.Disruption of traditional farming and ranching communities: Increasing land prices and greater parcel sizes may make it harder for small-scale farmers and ranchers to compete, which might result in the consolidation of land ownership and the eradication of traditional farming and ranching communities.Unsustainable resource use: Increasing land area might result in more water being used for irrigation, thereby worsening the Great Plains' water shortage problems.Loss of grasslands: The Great Plains are renowned for their distinctive grassland ecosystems, which are essential for biodiversity and carbon sequestration. More land being used for construction or agriculture might lead to the extinction of grasslands, which would have detrimental ecological effects.Degradation of the soil: Intensive agricultural techniques, such as monoculture and extensive chemical usage, may result in the loss of fertility and accelerated erosion of the soil. Long-term, this can have a negative effect on the sustainability and production of agricultural areas.Increased use of chemical inputs: Increasing land area may result in higher usage of chemical pesticides and fertilisers, which might impact regional ecosystems and contribute to environmental degradation.Danger of overproduction: Increased land acreage and pricing may lead to overproduction of agricultural products, which might lead to unstable prices, unstable farmer livelihoods, and potential market saturation.Potential for land speculation: Increasing land prices may encourage speculative investment, which might result in land being bought and retained for financial gain rather than for productive use. This could push up land prices even more and restrict access to land for local farmers and ranchers.Risks to wildlife and biodiversity: Include habitat fragmentation, the loss of wildlife corridors, and the displacement of native species, all of which might have an effect on the biodiversity and animal populations of the area.Learn more about land acreage and pricing here:
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Classroom A has a capacity of 50 students and is 70% occupied. Classroom B is 25% occupied. The ratio of the occupancy of Classroom A to Classroom
B is 5:3. How many students can fit in Classroom B?
Answer: Classroom B is 25% occupied. The ratio of the occupancy of Classroom A to Classroom B is 5:3. How many students can fit in Classroom B? 84 students.
Step-by-step explanation:
Graph the function.
f(x)=√x-4
Plot four points on the graph of the function: the leftmost point and three additional points. Then click on the graph-a-function button.
The four points on the graph of f(x) = √x-4 including the left most point are: (4,0), (5,1), (8,2), and (20,4).
Finding four points on the graph of the functionTo find points on the graph of f(x) = √x-4, we can choose values of x and find the corresponding values of y.
The leftmost point on the graph is when x is the smallest possible value, which is x = 4 (since we can't take the square root of a negative number). At x = 4, f(x) = √0 = 0, so the leftmost point is (4,0).
To find three additional points, we can choose values of x that are greater than 4 and find the corresponding values of y:
When x = 5: f(5) = √1 = 1, so the point is (5,1)
When x = 8: f(8) = √4 = 2, so the point is (8,2)
When x = 20: f(20) = √16 = 4, so the point is approximately (20.4)
So, four points on the graph of f(x) = √x-4 are: (4,0), (5,1), (8,2), and (20,4).
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find the missing terms 82,81,78,-,66,-
5,6,8,-,15,-
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.
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:
DeShawn and Ndiba each improved their yards by planting daylilies and ornamental grass. They
bought their supplies from the same store. DeShawn spent $80 on 1 daylily and 12 bunches of
ornamental grass. Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass. What is
the cost of one daylily and the cost of one bunch of ornamental grass?
The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.
System of the equations :A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values that satisfies all the equations in the system.
Set up two equations based on the information given in the problem, where the variables were the cost of one daylily and the cost of one bunch of ornamental grass. Use the substitution method to solve for variables.
Here we have
DeShawn spent $80 on 1 daylily and 12 bunches of ornamental grass.
Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass.
Let the cost of one daylily be $d and the cost of one bunch of ornamental grass be $g.
From the problem,
We can set up a system of equations based on the information given:
DeShawn's purchase: 1d + 12g = 80 ---- (1)
Ndiba's purchase: 5d + 2g = 52 --- (2)
We can solve this system of equations using substitution or elimination.
Here, we will use substitution:
Solving for d in terms of g from Deshawn's equation:
1d = 80 - 12g --- (3)
Substituting into Ndiba's equation:
=> 5(80 - 12g) + 2g = 52
=> 400 - 60g + 2g = 52
=> - 58g = - 348
=> g = 6
From (3)
1d = 80 - 12(6)
1d = 80 - 72
d = 8
Therefore,
The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.
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please help me in this question is math,solve just d, e&f
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
Please Mark Me Brainliest!
Solve for X
Please show step by step
(X - 4)^2 = 25
Answer: x = -1 and x = 9
Step-by-step explanation:
Lets solve this equation step by step
1. Simplify both sides of the equation
x^2 - 8x + 16 = 25
2. Subtract 25 from both sides
x^2 - 8x + 16 - 25 = 25 - 25
3. Factor the left side of the equation
(x + 1) (x - 9) = 0
4. Set the factors equal to zero
x + 1 = 0 or x - 9 = 0
Thus your answers are x = -1 and x = 9
You can check by inputting the values into the original equation
(-1 - 4)^2 = 25 and (9 - 4)^2 = 25
Please help
A space station is being built from 24 cubic modules. The space station can be any shape but the modules must be placed together so that entire faces match up with each other. Choose a tool to create two different plans for the space station. Explain why you chose the tool you selected.
100 Points! Algebra question. Use the following quadratic function: f(x)=x^2-4x+4. Photo attached with the rest of the question. Thank you so much!!
A.y-intercept: 4
axis of symmetry: x=2
x-coordinate of the vertex: 2
B.x f(x)
0 4
1 1
2 0
3 1
4 4
C. 5 | .
| .
| .
| .
|.
0 |_____________
0 1 2 3 4
What is intercept?An intercept refers to the point(s) at which a curve or line intersects an axis. For example, the x-intercept is where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.
What is vertex?A vertex is a point where two or more lines or curves meet. In the context of a parabolic curve, the vertex is the point at which the curve changes direction.
According to the given information:
A. The y-intercept occurs when x=0. Therefore, f(0) = 0² - 4(0) + 4 = 4. So the y-intercept is (0, 4).
The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients of x² and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Therefore, the equation of the axis of symmetry is x = 2.
To find the vertex, we use the fact that the vertex occurs at the axis of symmetry. So when x=2, f(x) = 2² - 4(2) + 4 = -4. Therefore, the vertex is at (2, -4).
B. We can use the vertex to make a table of values:
x f(x)
0 4
1 1
2 0
3 1
4 4
C. We can use the table of values to plot the points and sketch the graph of the function. The graph of the function is a parabola that opens upward, since the coefficient of x² is positive.
5 | .
| .
| .
| .
|.
0 |_____________
0 1 2 3 4
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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?
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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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.
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.
Liam is making
8 sculptures. Each
sculpture needs 2/3 yard of wire for the
base and another piece of wire for the
top. He uses 10 2/3 yards of wire in all.
How much wire is needed for the top of
each sculpture?
Mathematically, the quantity of wire Liam needs for the top of the 8 sculptures he is making is 5¹/₃ yards.
How is the quantity of wire for the top determined?The quantity of wire Liam needs for the top of the sculptures that he makes is determined using mathematical operations.
The four basic mathematical operations include addition, subtraction, division, and multiplication.
The total quantity of wire used = 10²/₃ yards.
The quantity of wire needed for each base = ²/₃ yards
The quantity of wire needed for each top = ²/₃ yards
The number of sculptures Liam is making = 8
²/₃ yards + ²/₃ yards = 1¹/₃ yards
8 x 1¹/₃ yards = 10²/₃ yards
8 x ²/₃ yards = 5¹/₃ yards
5¹/₃ yards x 2 = 10²/₃ yards
Therefore, the quantity of wire needed for the top will be 5¹/₃ yards.
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Please help with this math question!
Answer:
[tex]2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25[/tex]
Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^,
3/4 ≤ ≤ 3/2
The area of the region bounded by the curve [tex]r = {e}^{x} [/tex] and the specified sector is 1/4 [tex](e^{ \frac{3}{2} } - e^{ \frac{3}{4}} )[/tex].
What is area?
Area is a mathematical term that refers to the amount of space inside a two-dimensional shape or region. It is a measure of the extent or size of a surface or a planar region. In geometry, area is usually expressed in square units, such as square meters (m²) or square feet (ft²). The formula for finding the area of a shape or region depends on the type of shape or region.
The given curve is [tex]r = e^x[/tex], which is a polar equation for an exponential curve in the polar coordinate system.
The specified sector is the region enclosed by the rays emanating from the origin at angles 3/4 and 3/2 radians, as shown below:
To find the area of this region, we need to integrate the area element dA over the given sector,[tex]dA = \frac{1}{2} r^2 dθ[/tex] where θ varies from 3/4 to 3/2, and [tex]r = e^x[/tex]
.We can express r as a function of θ by solving the polar equation for x in terms of θ,
[tex]r = e^x \\ x = ln(r) \\ r = e^{(ln(r))} \\ r = r[/tex]
Therefore,
[tex]r = e^{ln(r)} = e^{(θ)}[/tex]
Substituting this into the area element,
[tex]dA = \frac{1}{2} (e^{(2θ)}) dθ[/tex]
Integrating this from θ = 3/4 to θ = 3/2, we get,
[tex]A = \int( \frac{3}{2} )( \frac{3}{4} ) \frac{1}{2} (e^{(2θ)}) dθ \\ =[ \frac{1}{4} (e^{(2θ)}]( \frac{3}{4} )^{( \frac{3}{4} )} \\ = \frac{1}{4} (e^{ \frac{3}{2} } - e^{ \frac{3}{4} }[/tex]
Therefore, the area of the region bounded by the curve [tex]r = e^x[/tex] and the specified sector is 1/4 [tex](e^{ \frac{3}{2} } - e^{ \frac{3}{4}} )[/tex].
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Correct question is "Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^x, 3/4 ≤ x ≤ 3/2."
Show that by the uniqueness theorem the linear transformation,
Y = aX + b, is also a normal random variable.
We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).
How to prove a normal random variableTo show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.
We can prove that it meets the mean condition this way:
E(Y) = E(aX + b) = aE(X) + b = aμX + b
Next, we can prove that it meets the variance condition thus:
Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2
Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.
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I'LL MARK THE BRAINLIEST!!!!!!
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.
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
Answer:
C) 4
Step-by-step explanation:
Justin says that x^-2and -x² are equivalent. Is he
correct? Justify your answer.
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^{-2}\implies \cfrac{1}{x^2}\hspace{5em} {\Large \begin{array}{llll} \ne \end{array}}\hspace{5em}-x^2[/tex]
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.