Answer:
To find the perimeter and area of the square garden shed without graphing the coordinates, you can use the distance formula to calculate the length of one side of the square. The distance formula is d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of two points. Using this formula with the coordinates of two adjacent corners of the square, such as (-2,8) and (1,8), we find that the length of one side of the square is 3 units. Since all sides of a square are equal in length, the perimeter is 4 times the length of one side, or 12 units. The area of a square is equal to the length of one side squared, so the area of the square garden shed is 9 square units.
This problem is different from finding the perimeter and area of the base of a house because it involves a square shape rather than a more complex shape. However, you can use similar strategies to solve both problems by calculating distances between points and using geometric formulas to find perimeter and area. The specific formulas used may vary depending on the shape of the base of the house.
Baseball Players’ Salaries. We have access to data regarding the salaries of all professional baseball players in 2012. That is, if we consider all professional baseball players in 2012 our subjects of interest, then we have information on every individual in the population. In this problem, we are going to examine how varying the sample size impacts the sampling distribution of the sample mean. We will be using an applet called StatKey to complete this problem. Start by opening a web browser on your computer and going to the following website: http://lock5stat.com/statkey/sampling_1_quant/sampling_1_quant.html
(a) In the top left corner of the page, under StatKey, click on the button with the words Percent with Internet Access (Countries) and select Baseball Players (2012 Salary in Millions). The top graph on the right hand side displays the distribution of the population as well as some numerical summaries describing the population. Use this graph and the numerical summaries to answer the following questions.
i. Report the mean (in millions of dollars) for all 855 salaries of 2012 professional baseball players to 3 decimal places.
ii. Report the standard deviation (in millions of dollars) for all 855 salaries of 2012 professional baseball players to 3 decimal places.
iii. The values in parts (a) and (b) above are (Choose all that apply): • Parameters • Statistics • Estimates • Numerical summaries of the sample • Numerical summaries of the population
iv. (Free Response) Describe the shape of the distribution of salaries for professional baseball players in 2012. Be sure to comment on skewness, modality, and outliers.
(b) Suppose we are interested in the distribution of the sample mean for samples of size n = 10 from the population of professional baseball players’ salaries from 2012. Specify the sampling distribution of the sample mean when n = 10.
i. What is the mean of the sampling distribution of the sample mean (in millions of dollars) when n = 10? (Report to the nearest 3 decimal places.)
ii. What is the standard error of the sampling distribution of the sample mean (in millions of dollars) when n = 10? (Report to the nearest 3 decimal places.) iii. What is the shape of the sampling distribution of the sample mean when n = 10? (Choose one) • Normal • Approximately Normal • Not Normal
(c) Let’s select a random sample of size n = 10. Note that at the top of the webpage where it says, Choose samples of size n= that 10 is the default, so you do not need change the sample size. Click on Generate 1 Sample in the top left corner of the webpage. Note that the bottom graph on the right hand side of the page shows a histogram of the 10 observations selected for your sample. In addition, above the bottom graph are the mean and the standard deviation of the observations in your sample. What is the value of the 3 sample mean (in millions of dollars) from your random sample of size n = 10? (Report to the nearest 3 decimal places.)
(d) Click Generate 1 Sample a second time. What is the value of the sample mean (in millions of dollars) from your second random sample of size n = 10? (Report to the nearest 3 decimal places.)
(e) Click Generate 1 Sample a third time. What is the value of the sample mean (in millions of dollars) from your third random sample of size n = 10? (Report to the nearest 3 decimal places.)
(f) In the big graph, you should notice that 3 points have been added. These 3 points correspond to the sample means from the 3 samples you drew. In the top right hand corner of the big graph, it should say samples =3 and show a value for the mean and standard deviation. The value for the mean is the average of the three sample means from your 3 samples of size n = 10. Similarly, the value for the standard deviation is the standard deviation of the three sample means from your 3 samples of size n = 10.
i. What is the mean of your three sample means? (Report to the nearest 3 decimal places.)
ii. What is the standard deviation (i.e. standard error) of your three sample means? (Report to the nearest 3 decimal places.)
(g) Suppose we drew many samples of size n = 10 and calculated the sample mean for each of these samples.
i. What value would you expect to see for the mean of the sample means (in millions of dollars) of size n = 10? (Report to the nearest 3 decimal places.)
ii. What value would you expect to see for the standard error of the sample means (in millions of dollars) of size n = 10? (Report to the nearest 3 decimal places.)
(a)
i. The mean of all 855 salaries of 2012 professional baseball players to 3 decimal places is 3.319 million dollars.
ii. The standard deviation of all 855 salaries of 2012 professional baseball players to 3 decimal places is 4.104 million dollars.
iii. The values in parts (a) and (b) above are:
Parameter: the mean and standard deviation of the population.
Numerical summaries of the population.
iv. The distribution of salaries for professional baseball players in 2012 is right-skewed with a single peak and several outliers at the high end.
(b)
i. The mean of the sampling distribution of the sample mean (in millions of dollars) when n = 10 is 3.319 million dollars.
ii. The standard error of the sampling distribution of the sample mean (in millions of dollars) when n = 10 is 1.298 million dollars.
iii. The shape of the sampling distribution of the sample mean when n = 10 is approximately normal.
(c) The value of the sample mean (in millions of dollars) from the first random sample of size n = 10 is 2.167 million dollars.
(d) The value of the sample mean (in millions of dollars) from the second random sample of size n = 10 is 2.384 million dollars.
(e) The value of the sample mean (in millions of dollars) from the third random sample of size n = 10 is 3.913 million dollars.
(f)
i. The mean of the three sample means is 2.821 million dollars.
ii. The standard deviation (i.e., standard error) of the three sample means is 0.911 million dollars.
(g)
i. We would expect to see a value of 3.319 million dollars for the mean of the sample means (in millions of dollars) of size n = 10.
ii. We would expect to see a value of 1.298 million dollars for the standard error of the sample means (in millions of dollars) of size n = 10.
The mean and standard error are obtained from the applet and are reported to 3 decimal places. The shape of the sampling distribution of the sample mean when n=10 is approximately normal due to the Central Limit Theorem.
The applet provides the histogram of the 10 observations selected for the sample, as well as the mean and standard deviation of the observations in the sample. The student is required to click "Generate 1 Sample" three times and report the sample means from each of the three random samples of size n=10.
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What is the square root of 9216
Answer:
96
Step-by-step explanation:
What is an equation of the line that passes through the point (7,3) and is parallel to the
line 4x + 2y = 10?
Oy=2x-11
0y = 1/2 x - 1/1/20
13
- - - 2x + 1²/12/2
Oy = - 1/12
Oy=-2x+17
Answer:
y = -2x + 17.
Step-by-step explanation:
To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope.
First, we need to rearrange the equation of the given line 4x + 2y = 10 into slope-intercept form y = mx + b:
4x + 2y = 10
2y = -4x + 10
y = -2x + 5
So, the slope of the given line is -2.
Since the line we're looking for is parallel to the given line, it will have the same slope of -2. We also have a point (7,3) that the line passes through. We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is the point.
Plugging in the values, we get:
y - 3 = -2(x - 7)
Simplifying:
y - 3 = -2x + 14
y = -2x + 17
So, the equation of the line that passes through the point (7,3) and is parallel to the line 4x + 2y = 10 is y = -2x + 17.
This is 3/6 problems finish them all each is 10 points 60 total.
Answer:
Step-by-step explanation:
The answer is 50.3 An easy way to find the answer is by using this link. https://www.calculator.net/right-triangle-calculator.html
Just plug the 29 and 44 in.
help me please and thank you
Therefore , the solution of the given problem of volume comes out to be false we must first know the cylinder's radius and height.
Explain volume.A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 stand for cubic dimensions. However, you can use an object's bulk to estimate its dimensions. Usually, the weight of the item is converted into mass measures like kilograms and kilos.
Here,
The capacity of a cylinder and a cone that are the same height and radius are not the same.
The formula V = πr²h,
where r is the radius of the base and h is the height, determines the volume of a cylindrical. Contrarily, the equation
=> V = (1/3)r²h gives the volume of a cone.
To calculate the volume of a cone with the same measurements if the cylinder's volume is 99 cubic cm,
False we must first know the cylinder's radius and height.
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The equation of line QR is x + 2y = 2. What is the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6)?
y = negative one halfx + seventeen halves
y = 2x − 4
y = negative one halfx + seven halves
y = 2x + 16
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]x+2y=2\implies 2y=-x+2 \\\\\\ x=\cfrac{-x+2}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{2}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1} \implies 2}}[/tex]
so we're really looking for the equation of a line whose slope is 2 and it passes through (5 , 6)
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{5}) \\\\\\ y-6=2x-10\implies {\Large \begin{array}{llll} y=2x-4 \end{array}}[/tex]
The equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.
What is slope-intercept form of a line?y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line.
Given that a line QR has an equation is x+2y = 2, we need to find the equation of a line passing through (5, 6) and is perpendicular to the given line,
Converting the equation into slop-intercepts form,
y = -0.5x+1
Here, slope m = -0.5
We know that the slopes of the perpendicular lines are negative reciprocal of each other,
Therefore, the slope of the asked line is 2.
So, its equation =
y = 2x+c
To find c, put x = 5 and y = 6
6 = 2(5) + c
c = -4
Therefore, the final equation will be =
y = 2x-4
Hence, the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.
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Guys please help My is assignment due tomorrow please guyyyysssss. Determine the value of k if g(x) = 4x+k is a tangent to f(x) = - x² + 8x +20
so, since we know that the derivative is simply the equation we use to get the slope at any point on the curve, thus df/dx will be that.
now, we know that g(x) is already in slope-intercept form, so it has a slope of "4", hmmm what's "x" at that instance?
[tex]f(x)=-x^2+8x+20\implies \cfrac{df}{dx}=-2x+8 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\stackrel{\stackrel{m}{\downarrow }}{4}x+k\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\\\ 4~~ = ~~-2x+8\implies 2=x[/tex]
well, now we know that x = 2, hmmm what's "y" at that instance? well, our "y" will be simply f(2) = g(x), because g(x) is touching f(x) at that point on the curve.
[tex]f(2)=-(2)^2+8(2)+20\implies f(2)=32 \\\\[-0.35em] ~\dotfill\\\\ g(x)=4x+k\implies 32=4(2)+k\implies 32=8+k\implies \boxed{24=k}[/tex]
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Two times the sum of x squared and y squared, increased by three times the sum of x squared and y squared. 7th grade
5 times the sum of x squared and y squared. This can be expressed as 5(x^2 + y^2).
What is express?Express is a web application framework for Node.js, released as free and open-source software under the MIT License. It is designed for building web applications and APIs and is the de facto standard server framework for Node.js. It provides a host of features to facilitate the development of web and mobile applications, including routing, templating, and a middleware system to handle requests and responses. Express is the backend component of the MEAN stack and enables the rapid development of dynamic web applications.
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what is expressed in both units and dollars to show the number necessary to make enough money to keep going?
In the context of economics, the term “break-even point” is used to indicate the number necessary to make enough money to keep going, and it is expressed in both units and dollars.
What is the break-even point?Break-even point is a term used in cost accounting to describe the point at which total cost and total revenue are equal. At this point, there is no profit or loss; it is a neutral zone. At this point, a firm's revenue from the sale of products and services is just sufficient to cover the total costs of producing those products and services.
The break-even point can be expressed in terms of units sold or in terms of total revenue. The point at which the total revenue equals total cost is the break-even point in terms of dollars. The point at which the number of units sold equals the fixed costs divided by the contribution margin per unit is the break-even point in terms of units sold. Therefore, the break-even point is expressed in both units and dollars to show the number necessary to make enough money to keep going.
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is g(x) any different than f(x) when graphing a radical expression? for example is:
g(x) = √x-5 +6 any different than answering f(x) = √x-5 +6
There is no difference in g(x) and f(x) when graphing a radical expression as represents the same function: √(x-5) +6
Explain about the radical expression?An expression with a square root is referred to as a radical expression. Radicand: A value or phrase included within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.The given radical expression are:
g(x) = √(x-5) + 6
f(x) = √(x-5) + 6
The graph of both function is plotted, which have the exact same value on graph.
Thus, there is no difference in g(x) and f(x) when graphing a radical expression as represents the same function: √(x-5) +6
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Adam has 18 counters he gave 10 of the counters to Lesley what fraction of the 18 counters does lesley get give your answer in your simplest form
Lesley gets 10/18 or 5/9 of the counters.Adam has 18 counters, so we can express the total number of counters as 18/18. If he gave 10 of those counters to Lesley, we can express that as 10/18.
Adam has 18 counters, so we can express the total number of counters as 18/18, which is equivalent to 1. If he gave 10 of those counters to Lesley, we can express that as 10/18. To find out what fraction of the 18 counters Lesley gets, we need to simplify 10/18. Since both the numerator and denominator are divisible by two, we can divide both the numerator and denominator by two, which gives us 5/9. This means that Lesley gets 5/9 of the 18 counters, which is equivalent to 10/18 or half of the total number of counters.
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After John finished his energy drink, he noticed on the label that it had 160 milligrams of
caffeine. He read online that the amount of caffeine in the body decreases by a factor of
8
each hour after it's consumed.
problems LZW
Write an exponential equation in the form y = a(b)* that can model the amount of caffeine
left in John's body, y, x hours after finishing the energy drink.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y
plo
To the nearest milligram, how much caffeine will be in John's body after 6 hours if he doesn't
consume any more caffeine?
milligrams
Answer:
After John finished his energy drink, he noticed on the label that it had 160 milligrams of caffeine. He read online that the amount of caffeine in the body decreases by a factor of
1
8
each hour after it's consumed.
Step-by-step explanation:
The exponential equation in the form y=a(b)² that can model the amount of caffeine left in John's body, y, x hours after finishing the energy drink is y= 160(1/8)⁽ˣ⁾. After 6 hours, the amount of caffeine left in John's body will be y=160(1/8)⁽⁶⁾ ≈ 1.96 milligrams (rounded to the nearest milligram).
The exponential equation y=a(b)² can be used to model the amount of caffeine left in John's body x hours after consuming an energy drink. In this equation, a represents the initial amount of caffeine in the body (160 milligrams), and b represents the factor by which the amount of caffeine decreases each hour (1/8). To find the amount of caffeine left in John's body after 6 hours, we can simply substitute x=6 into the equation and solve for y. The result is y=160(1/8)⁽²*⁶⁾ ≈ 6 milligrams. This means that after 6 hours, John will have approximately 6 milligrams of caffeine left in his body if he doesn't consume any more caffeine.
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Complete question:
After John finished his energy drink, he noticed on the label that it had 160 milligrams of caffeine. He read online that the amount of caffeine in the body decreases by a factor 1/8 of each hour after it's consumed.
Write an exponential equation in the form y=a(b)² that can model the amount of caffeine left in John's body, y, x hours after finishing the energy drink.
Use whole numbers, decimals, or simplified fractions for the values of a and b,
To the nearest milligram, how much caffeine will be in John's body after 6 hours if he doesn't consume any more caffeine?
If t has the terminal point P (-3/4 ,y) on the unit circle in
the second quadrant, find the value of tan t
tan t = -4/3
The equation for the unit circle is
x2 + y2 = 1
For the point (-3/4, y) we have
(-3/4)2 + y2 = 1
Rearranging this gives us
y2 = 1 - (3/4)2
Solving for y gives us
y = √ (1 - (3/4)2)
Now we can find tan t by using the equation
tan t = y / -3/4
Substituting in the value of y we found earlier gives us
tan t = √ (1 - (3/4)2) / -3/4
Finally, simplifying the equation gives us the answer
tan t = -4/3
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. Write an algebraic expression for the following expressions:
(a) The sum of a number x and 4 is doubled.
(b) One fourth of a number x is added to one third of the same number.
Answer:
a) 2*(x+4)
b) 1/4*x + 1/3*x
Answer:
a) 2(x+4)
b) 7x/12
Step-by-step explanation:
a) Sum of x and 4 is (x+4). Since the number is doubled,
2 * (x+4) = 2(x+4)
b) One fourth of a number x is x/4 and one third of the number is x/3.
Adding these two:
x/4 + x/3
The LCM of 4 and 3 is 12 and so,
(4x + 3x)/12
= 7x/12
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Base on the given data uploaded, 1. Will you conclude that people can bargain price down when purchasing a house at 5% level of significance? 2. Will you conclude that the 3-bedroom houses is cheaper than 4-bedroom houses?
To know whether people can bargain the price down when purchasing a house at a 5% level of significance, we need to put a hypothesis test. The null hypothesis would be that people cannot bargain the price down
To determine whether 3-bedroom houses are cheaper than 4-bedroom houses, we would again give out a hypothesis test. The null hypothesis would be that there is no difference in price between 3-bedroom and 4-bedroom houses.
but the other hypothesis would be that 3-bedroom houses are cheaper than 4-bedroom houses. If the p-value is less than 0.05, we can reject the null hypothesis and say that 3-bedroom houses are more cheaper than 4-bedroom houses.
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Dani spends 5.20 total to create
2 treat bags. How much more
would she have to spend to make
5 more similar bags?
Answer:
13 for 5 bags.
Step-by-step explanation:
Dani spends 5.20 in total for 2 bags. You would do 5.20/2 to get 2.60 which tells us that 2.60 is the cost per bag. Then you would do 2.60 x 5 to get 13.
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
Step-by-step explanation:
[tex]m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
[tex]=(\frac{-12+(-8)}{2}, \frac{-7+(-4)}{2})[/tex]
[tex]=(-10,-5.5)[/tex]
What additional piece of information do you need to prove that ALKN-AKNM by the SAS similarity theorem?
A.
112
MN
B. MN=1
C
Option C, MN/LK||MN, is the additional piece of information required to demonstrate that ΔLKN ~ΔKNM by the SAS similarity theorem.
The SAS (Side-Angle-Side) similarity theorem: what is it?
According to the SAS (Side-Angle-Side) similarity theorem, two triangles are similar if they have two pairs of corresponding sides that are in proportion and the included angles are congruent.
In this example, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.
To clarify that MN is parallel to LK and forms a transversal with LN, we must first prove that MN/LK||MN.
To prove that the included angles between the matching sides are congruent, which is necessary for the triangles to be similar, this information is required.
Consequently, in order to demonstrate that ΔLKN~ΔKNM according to the SAS similarity theorem, option C is the correct additional piece of information.
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According to a survey on part-time workers (their monthly salaries can vary by different
months), the average base salary for women is higher than the average base salary for men. The
average base salary for women is $3000/month, and the average base salary for men is
$2750/month. Assume monthly salaries are normally distributed with a standard deviation of $300
for both men and women. Furthermore, assume salaries are independent across different months. How much would a woman have to make in a year to have a higher salary than 99% of her male
counterparts
To have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year
To find out how much a woman would have to make in a year to have a higher salary than 99% of her male counterparts, we need to find the salary level that corresponds to the 99th percentile of the male salary distribution.
First, we need to calculate the standard deviation of the annual salaries for both men and women. Since the standard deviation of the monthly salaries is $300, the standard deviation of the annual salaries can be calculated as:
σ_annual = σ_monthly * √12 = 300 * √12 = $1039.23
Next, we can calculate the salary level that corresponds to the 99th percentile of the male salary distribution using the standard normal distribution table.
z-score for the 99th percentile = 2.33
salary level for the 99th percentile of male salary distribution = mean + z-score * σ_annual
= $2750 + 2.33 * $1039.23 = $5229.48 (rounded to the nearest cent)
Therefore, to have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year (rounded to the nearest cent).
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In ADEF, d = 76 cm, f = 20 cm and _F=17º. Find all possible values of _D, to the
nearlest ioth of a degree.
The value of D is 49.1º to the nearest degree using the law of sines.
To solve for angle D, we can use the law of sines, which states that for any triangle with sides a, b, and c opposite angles A, B, and C respectively:
a/sin(A) = b/sin(B) = c/sin(C)
Using this formula, we can solve for angle D:
sin(D)/d = sin(F)/f
sin(D) = (d/f) × sin(F)
sin(D) = (76/20) × sin(17º)
sin(D) = 0.7588
Taking the inverse sine of both sides, we get:
D = [tex]sin^{-1}[/tex] × (0.7588)
D = 49.1º (rounded to the nearest tenth of a degree)
The law of sines can have two possible solutions for an angle, depending on the triangle. However, in this case, since angle D is opposite the longer side (d), there is only one possible solution.
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6.02 line of best fit ms pre-algebra S2 v16.2/ patterns of association
The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot. It is also known as the regression line.
What is regression line?
In the context of MS Pre-Algebra S2 V16.2, the line of best fit is used to analyze patterns of association between two sets of data. For example, if we have data on the height and weight of a group of individuals, we can use a scatter plot to visualize the relationship between these two variables.
By drawing a line of best fit through the data points, we can see the general trend or pattern of association between height and weight. This line can then be used to make predictions about the weight of an individual based on their height, or vice versa. The line of best fit is a useful tool for analyzing patterns of association in a variety of fields, including statistics, economics, and social sciences.
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Complete question is: The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot.
A particle of mass 5 kg rests on a smooth
horizontal table. It is connected by a light
inextensible string passing over a smooth
pulley at the edge of the table to a particle
of mass 2 kg, which is hanging freely. Find the acceleration of the system
and the tension in the string.
5 kg
2 kg
The acceleration of the system is 0.83 m/s² and the tension in the string is 8.3 N.
The acceleration of the system can be calculated using Newton's second law of motion. The equation is F = ma, where F is the net force on the system, m is the total mass, and a is the acceleration. Since the two masses are connected by a light inextensible string, the net force acting on the system is equal to the tension in the string. Therefore, the equation becomes T = (5 kg + 2 kg)a, where T is the tension and a is the acceleration. Solving for a, the acceleration is found to be 0.83 m/s². The tension in the string can also be calculated using the equation above. Plugging in the acceleration, the tension is found to be 8.3 N.
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Write the number in scientific notation.
10,700,000 =
Answer: 1.07x107 but the seven goes on top of the 10
Step-by-step explanation:
Answer:
1.07 × 10⁷
Step-by-step explanation:
To express 10,700,000 in scientific notation, we have to rewrite it as a decimal number that is between 1 and 10 multiplied by a power of 10.
As a decimal, the number is:
1.07.
We have to move the decimal point 7 places to get this number (see the attached image). Therefore 1.07 is multiplied by 10⁷ to get 10,700,000.
I need to figure the code out
The function with the greatest rate of change are:
1. C = 3
2. A = 5
3. A = 1
4. B = 3
What is the Rate of Change of a Linear Function?The rate of change of a linear function, also known as the slope of the line, represents the amount by which the output (y) changes for a given change in the input (x). In other words, it is the measure of how steep the line is.
The formula for the rate of change, or slope, of a linear function is:
slope = (change in y) / (change in x)
1. Rate of change for function A = change in y / change in x = 4/3
For B = 1/2
For C = 3/1 = 3
The function with the greatest rate of change is C = 3
2. Rate of change for function A = change in y / change in x = (10 - 5)/(1 - 0) = 5
For B = (12 - 8) / (3 - 1) = 2
For C = (6 - 3)/(1 - 0) = 3
The function with the greatest rate of change is A = 5
3. Rate of change for function A = change in y / change in x = 2/2 = 1
For B = (3 - 2)/(2 - 0) = 1/2
For C = 1/3
The function with the greatest rate of change is A = 1
4. Rate of change for function A = change in y / change in x = -1/3
For B = (10 - 1)/(4 - 1) = 3
For C = 2
The function with the greatest rate of change is B = 3
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Unit 8 right triangles and trigonometry homework 4 trigonometric ratios and finding missing sides
The trigonometric ratios can find the missing side of a right triangle given an angle, such as by using the tangent ratio to calculate the adjacent side length when given the length of the opposite side.
The trigonometric ratios are used to calculate specific values of a triangle. The three main ratios are sine, cosine, and tangent. The sine ratio is the ratio of the side length opposite the angle to the hypotenuse of the triangle. The cosine ratio is the ratio of the side length adjacent to the angle to the hypotenuse of the triangle. The tangent ratio is the ratio of the side length opposite the angle to the side length adjacent to the angle.
To find the missing side of a right triangle, given an angle, we use the trigonometric ratios. For example, if we have an angle of 45 degrees and a side length of 8, we can use the tangent ratio to calculate the missing side length. To do this we use the formula tan(45) = opposite/adjacent. We know the opposite side is 8, so to calculate the adjacent side we solve for x in the equation 8/x = tan(45). We get x = 8/tan(45), and x = 8/1 = 8. Therefore, the adjacent side length is 8.
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The triangles are similar.
PR = ___ units
PR = 16 units
What is a similar triangles?Similar triangles are two triangles that have the same shape but not necessarily the same size. This means that their corresponding angles are equal, and their corresponding sides are proportional in length.
Here, ΔPRQ similar with ΔPST
So, we can say that their corresponding sides are in proportion (i.e., have the same ratio).
[tex]\frac{PR}{PS} = \frac{RQ}{ST}[/tex]
[tex]\frac{(x+7) + (x-1) }{(x+7)} = \frac{8}{6}[/tex]
Simplification,
12x + 36 = 8x + 56
x = 5
So, the value of PR = (x+7) + (x-1)
PR = (5+7) + (5-1) = 16
Therefor, PR = 16 units
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The triabgles ae similar. Their corresponding sides are in proportion.
PR = 16 units
What is a similar triangles?Triangles that are similar to one another in shape but not necessary in size are called similar triangles. Their respective sides are proportional in length, and their corresponding angles are equal. Three edges, three angles, and three vertices make up a triangle. The sum of a triangle's three internal angles is 180 degrees. The triangle's third side is longer than the sum of its two longest sides.
Here, ΔPRQ similar with ΔPST
Thus, their respective sides are proportional, as we can see. (i.e., have the same ratio).
[tex]\frac{PR}{PS} =\frac{RQ}{ST} \\\\\frac{(x+7)+(x-1)}{(x+7)} =\frac{8}{6}[/tex]
Simplification,
12x + 36 = 8x + 56
x = 5
So, the value of PR = (x+7) + (x-1)
PR = (5+7) + (5-1)
= 16
Therefor, PR = 16 units
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A verticle flagpole, AB has a height of 42m. The points B , C and D lie on level ground, and BCD is a straight line point C is 24m from the base of the flagpole the angle of elevation of the top of the flagpole from point D is 48
How far apart are point C and D
The point C and point D are approximately 23.4 meters apart.
Trigonometric functions are a set of mathematical functions that relate the angles of a right-angled triangle to the ratios of the lengths of its sides.
We can use trigonometry function to solve for the distance between points C and D. Let x be the distance CD, then we have:
tan(48°) = h / (x + 24m)
where h is the height of the flagpole.
We can solve for x by rearranging the equation:
x = (h / tan(48°)) - 24m
Substituting the given values, we get:
x = (42m / tan(48°)) - 24m
x ≈ 23.4m
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Identify the measurement as the diameter or radius of the circular object then find the circumference of the object 1 from the center to the edge of a dvd measures 60 mm
The diameter οr radius οf the circular οbject is 120mm, and the circumference οf the οbject 1 frοm the centre tο the edge οf a DVD is 380mm.
What is Circumference?A circle's οr an ellipse's circumference is its perimeter. In οther wοrds, if the circle were tο be straightened οut alοng a line segment, the length οf the arc wοuld be the circumference. The perimeter is mοre frequently used tο refer tο the length οf the curve surrοunding any defined figure.
The given infοrmatiοn is that a DVD's edge is 60 mm lοng.
The diameter, radius, and circumference οf the circular οbject must be determined in οrder tο determine the measurement.
We cοncluded that
Radius = 60mm
Diameter = 120mm
Circumference = 380mm
Hence, Diameter = 120mm
Circumference = 380mm
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2.5 m³ of granite has a mass of 6725 kg. a) Calculate the density of granite in kg/m³. b) Find the mass of 1.3 m³ of granite in kg.
The density of the granite is 2690 kg/m³ and the mass of 1.3 m³ of granite is 3497 kg.
How to calculate density?Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given that;
Volume of the granite = 2.5 m³Mass = 6725 kgDensity p = ?Plug the given values into the above formula and solve for density of the granite.
p = m / v
p = 6725 kg / 2.5 m³
p = 2690 kg/m³
b) The mass of 1.3 m³ of granite in kg will be;
p = m / v
m = p × v
m = 2690 kg/m³ × 1.3 m³
m = 3497 kg
Therefore, the mass of 1.3 m³ of granite is 3497 kg.
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Consider the value of t such that the area under the curve between Il and ll equals 0.95 Step 2 of 2: Assuming the degrees of freedom equals 8, select the t value from the t table. Answer TablesKeypad To select a value from the table either click the cell at the intersection of the row and column or use the arrow keys to find the appropriate cell in the table and select it using the Space key. To change the sign of the selected value, use the +1- button.
The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
What is degree of freedom?Degree of freedom refers to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of the flexibility of the experiment or analysis to accommodate new data or observations.
In this case, the degrees of freedom is 8. To find the t-value, the t-table must be consulted. The t-table is a chart of t-values for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 equals 0.95. The t-table is organized such that the rows represent the degrees of freedom and the columns represent the area under the curve. For example, if the degrees of freedom is 8 and the area under the curve is 0.95, the t-value can be found in the row for 8 degrees of freedom and the column for 0.95 area under the curve. The t-value from the t-table in this case is 1.86.
Therefore, the value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
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The value of t such that the area under the curve between 1 and 11 equals 0.95, assuming the degrees of freedom is 8, is 1.86.
What is degree of freedom?Degrees of freedom refer to the number of independent variables that can be varied in a statistical experiment or analysis. It is a measure of experimental or analytical flexibility to accommodate new data or observations.
In this case there are 8 degrees of freedom. To find the t value, we need to refer to the t table. A t-table is a plot of t-values for different degrees of freedom. The t-value is the value at which the area under the curve between 1 and 11 is 0.95. The t-table is organized so that rows represent the degrees of freedom and columns represent the area under the curve. For example, if you have 8 degrees of freedom and the area under the curve is 0.95, find the t-value in the row with 8 degrees of freedom and the column with area under the curve of 0.95. In this case, the t-value in the t-table is 1.86.
Therefore, the value of t is such that the area under the curve between 1 and 11 is 0.95, assuming 8 degrees of freedom is 1.86.
The area between -t and t = 0.95
P(t₈ > t) = P(t₈ - t)
= 0.025
As t - distⁿ is symmetrical and are under the curve is 1 and degree of freedom is 8.
Hence, from t - table; the t - value = 2.306
i.e. P(t₈ > 2.306) = 0.025
or P(-2.306 < t₈ < 2.306) = 0.95
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