The following data was collected in an experiment measuring the pressure of a gas (in atmospheres) as a function of temperature (in Kelvin). Temperature (K) Pressure (atm) 273.1 0.987 283.2 1.072 294.1 1.191 305.6 1.202 314.2 1.381 323.8 1.451 336.4 1.576 Plot this data in Excel with the independent variable on the x-axis and use Microsoft Excel to calculate the coefficient of determination (R2). Report the value of R2 here. Note: take care not to confuse the coefficient of determination R2 with R, the ideal gas constant. R2 is a statistical measure that we will include in graphs depicting linear relationships.
Answers
The coefficient of determination R2 calculated by Microsoft Excel is:
R2=0,974024991
To plot the given data in Excel, follow these steps: Create a scatter plot with temperature on the x-axis and pressure on the y-axis. To calculate R2 in Excel, add a trendline and check the 'Display R-squared value on chart' option.
Explanation:To plot the given data in Excel, follow these steps:
Create a scatter plot in Excel with the temperature data on the x-axis and the pressure data on the y-axis.Enter the given data into two columns in an Excel spreadsheet.Select the data and choose the scatter plot option from the chart types.Format the chart as desired.To calculate the coefficient of determination (R2) in Excel, follow these steps:
Add a trendline to the scatter plot.Right-click on the trendline and choose 'Format Trendline'.Check the 'Display R-squared value on chart' option.The calculated coefficient of determination (R2) will be displayed on the chart.
Related Questions
What is the value of 5 in 5,476,807,139
Answers
The value of 5 in 5,476,807,139 is five billion, as it is positioned in the billions place. This is explained by the concept of place value.
Explanation:The value of 5 in the number 5,476,807,139 refers to its place value in the numerical system. In this case, the 5 is in the billions place. This means that, in terms of place value, that 5 actually represents [5 × 1,000,000,000], which is 5,000,000,000 or five billion. The concept of place value is important in mathematics, it tells you how much each digit in a number is worth according to its position.
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My statistics book says there are 8 degrees of freedom for this data set. I don't understand how they got that number. # of Books Education Level 68 11 345 15 276 16 756 12 43 6 546 14 58 6 187 14 286 9 93 8 376 11 623 18 876 12 28 4 289 15
Answers
Answer:
It's a bit unclear with the table this way, but I count fifteen points, fifteen lines of the table, each a pair of numbers.
That's 15 degrees of freedom in the data. When modeling, each parameter in the model uses up one degree of freedom, so you'd use a smaller number of degrees of freedom when calculating t statistics, etc.
I need help asap! for a few questions of mine!
Find the slope of the line that passes through the following points. Simplify your answer.
(−6,9) and (−3,1)
Answers
[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-6)}}}\implies \cfrac{-8}{-3+6}\implies -\cfrac{8}{3}[/tex]
The volume of an open-top rectangular box is 4500 cc (cubic centimeters). The length of the rectangular base of the box is twice the width. What height will make the surface area as small as possible?
Answers
Answer:
The height that make the surface area as small as possible is 10 cm
Step-by-step explanation:
Let
L -----> the length of the base of the box
W -----> the width of the base of the box
H ----> the height of the box
we know that
The volume of the box is equal to
[tex]V=LWH[/tex]
we have
[tex]V=4,500\ cm^3[/tex]
so
[tex]4,500=LWH[/tex] ----> equation A
[tex]L=2W[/tex] ------> equation B
substitute equation B in equation A
[tex]4,500=(2W)WH[/tex]
[tex]4,500=2W^2H[/tex]
Solve for H
[tex]H=\frac{2,250}{W^{2}}[/tex] -----> equation C
The surface area of a open box is equal to
[tex]SA=2(L+W)H+LW[/tex] ----> equation D
Substitute equation B and equation C in equation D
[tex]SA=2(2W+W)(\frac{2,250}{W^{2}})+(2W)W[/tex]
[tex]SA=6W(\frac{2,250}{W^{2}})+2W^2[/tex]
[tex]SA=6(\frac{2,250}{W})+2W^2[/tex]
[tex]SA=\frac{13,500}{W}+2W^2[/tex]
Convert to function notation
[tex]f(W)=\frac{13,500}{W}+2W^2[/tex]
Find the derivative
[tex]f'(W)=-\frac{13,500}{W^2}+4W[/tex]
set equal to zero
[tex]f'(W)=0[/tex]
[tex]0=-\frac{13,500}{W^2}+4W[/tex]
Solve for W
[tex]\frac{13,500}{W^2}=4W[/tex]
[tex]W^3=\frac{13,500}{4}[/tex]
[tex]W=15\ cm[/tex]
Find the value of L (equation B)
[tex]L=2(15)=30\ cm[/tex]
Find the value of H (equation C)
[tex]H=\frac{2,250}{15^{2}}=10\ cm[/tex]
therefore
The height that make the surface area as small as possible is 10 cm
___________ Qualitative Inferential Descriptive Quantitative statistics consists of organizing and summarizing information collected, while ___________ qualitative quantitative descriptive inferential statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.
Answers
Answer:
Descriptive statistics consists of organizing and summarizing information collected, while inferential statistics use methods that generalize results obtained from a sample to the population and measure the reliability of the results.
Step-by-step explanation:
By definition, descriptive statistics summarize a given data set using measures of central tendency and measures of variability.
Measures of central tendency include:
mean. median. mode.Measures of variability include:
standard deviation. variance. the minimum and maximum variables.By definition, inferential statistics are used to make generalizations about a population from data samples.
For example, you might ask a sample of 100 people if they like shopping. You could make a bar chart of yes or no answers (descriptive statistics) or you could use your research and then, reason which is the percentage of the population that likes shopping (inferential statistics).
Descriptive statistics involve organizing and summarizing data, while inferential statistics use that data to make broader generalizations and measure their reliability. Qualitative data categorizes or describes attributes, while quantitative data involves numerical measurements.
Explanation:Descriptive statistics is a branch that deals with the organization and summarization of collected information. This can be done by graphing or using numbers like calculating the average. Examples of descriptors are the average temperature, the most popular car color or the average number of students in classes.
Inferential statistics, on the other hand, uses methods that generalize results obtained from a sample to the population and measure the reliability of these results. We use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study.
Next, we define qualitative data and quantitative data. Qualitative data are the result of categorizing or describing attributes of a population such as hair color, blood type, ethnic group, and so on. Quantitative data, on the other hand, are always numbers. They are the result of counting or measuring attributes of a population, like the amount of money, pulse rate, weight, number of people living in your town, and the number of students who take statistics.
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A football team gains 2 yards on the first play,loses 5 yards on the second play, loses 3 yards on the third play , and gains 4 yards on the fourth play. What is the teams overall gain or loss for all four plays show work
Answers
Answer:
2 yard loss
Step-by-step explanation:
When the team gains yards we use a positive value, and when the team loses yards we use a negative value. So the operation would be 2 -5 -3 +4 = -2, this means that the team had a 2 yard loss.
Describe the line segments. the cut sides of a wedge of apple pie: a) parallel b) intersecting c) skew
Answers
Answer:
They are intersecting line segments ⇒ answer b
Step-by-step explanation:
* Lets explain the types of the lines
- Parallel lines lie in the same plane and never intersect each other
- Intersecting lines are lines that meet each other in exactly one point
- Skew lines are lines that are in different planes and never intersect
* Now lets solve the problem
- The line segments that cut sides of a wedge of apple pie
∵ The wage of apple pie could represent a plane
∵ The line segments cut the sides of the wedge
∴ The lines are in the same plane
∵ Skew lines are in different planes and never intersect
∴ The lines can not be skew
∵ The line segments that cut sides of the wage must be intersected
at exactly one point
∵ Parallel lines never intersected
∴ The lines can not be parallel lines
∴ They are intersecting line segments
Please match this proof
Answers
Answer:
A, B, C, D, E
Step-by-step explanation:
AB ≅ AC and AD bisects ∠A
This is given information from the diagram and the statement.
∠BAD ≅ ∠CAD
This is from the definition of angle bisector.
AD ≅ AD
This is reflective property of congruence.
ΔABD ≅ ΔACD
From the previous three statements, side-angle-side congruence tells us the triangles are congruent.
∠B ≅ ∠C
Corresponding parts of congruent triangles are congruent.
Answer:
A.
B.
C.
D.
E.
refer to the attachment
The city of Madison regularly checks the quality of water at swimming beaches located on area lakes. Fifteen times the concentration of fecal coliforms, in number of colony forming units (CFU) per 100ml of water, was measured during the summer at one beach. 180 1600 90 140 50 260 400 90 380 110 10 60 20 340 80. What is the sample standard deviation?
Answers
Answer:
The sample standard deviation is 393.99
Step-by-step explanation:
The standard deviation of a sample can be calculated using the following formula:
[tex]s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex]
Where:
[tex]s=[/tex] Sample standart deviation
[tex]N=[/tex] Number of observations in the sample
[tex]{\displaystyle \textstyle {\bar {x}}}=[/tex] Mean value of the sample
and [tex]\sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex] simbolizes the addition of the square of the difference between each observation and the mean value of the sample.
Let's start calculating the mean value:
[tex]\bar {x}=\frac{1}{N} \sum_{i=1}^{N}x_{i}[/tex]
[tex]\bar {x}=\frac{1}{15}*(180+1600+90+140+50+260+400+90+380+110+10+60+20+340+80)[/tex]
[tex]\bar {x}=\frac{1}{15}*(3810)[/tex]
[tex]\bar {x}=254[/tex]
Now, let's calculate the summation:
[tex]\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=(180-254)^2+(1600-254)^2+(90-254)^2+...+(80-254)^2[/tex]
[tex]\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=2173160[/tex]
So, now we can calculate the standart deviation:
[tex]s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex]
[tex]s=\sqrt[ ]{\frac{1}{15-1}*(2173160)}[/tex]
[tex]s=\sqrt[ ]{\frac{2173160}{14}}[/tex]
[tex]s=393.99[/tex]
The sample standard deviation is 393.99
To find the sample standard deviation, use the formula standard deviation = √[ Σ(x - μ)² / (n - 1) ]. Follow the steps: find the mean of the data set, subtract the mean from each value and square the result, add all the squared deviations together, divide by (n - 1), and finally, take the square root of the result.
Explanation:To find the sample standard deviation, you can use the formula:
standard deviation = √[ Σ(x - μ)² / (n - 1) ]
where Σ represents the sum of the values, x is each value in the data set, μ is the mean of the data set, and n is the number of values in the data set.
Step 1: Find the mean of the data set. Add all the values together and divide by the number of values (15 in this case). This gives you a mean of 179.3333.
Step 2: Subtract the mean from each individual value in the data set, square the result, and add all the squared values together. This gives you a sum of squared deviations of 977733.3333.
Step 3: Divide the sum of squared deviations by (n - 1), where n is the number of values in the data set. Since there are 15 values, you divide by 14 to get 69838.0952.
Step 4: Take the square root of the result from Step 3. This gives you a sample standard deviation of approximately 264.1046.
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Some states are running out of license plate numbers. Delaware currently uses six-digit numbers in its license plate numbering system. The state of Washington recently stated that it needs to explore options to replace their current system of three numerical digits followed by three letters. New Jersey currently uses a system of one letter, two numerical digits, then three letters. How could the state of Washington change their license plate system to address the possible problem of running out of plate numbers? a. Washington can use 6 digits or letters for their numbering system. b. Washington can use more than 6 digits or letters for their numbering system. c. Washington can use 3 digits or 3 letters for their numbering system. d. Washington can use 6 letters for their numbering system.
Answers
Answer:
The answer is letter d
Step-by-step explanation:
This problem is a basic combinatory statistical problem:
Right now Washington uses 3 numerical digits (ranging from 0 to 9 each) and three letters (ranging from A to Z). So each number can be one in 10 and each letter can be one in 26 (the amount of numbers that the alphabet has).
Given n= the amount of possible licence plates and a= the amount of numbers ranging from 0 to 9 (10 possibilities) and b= the amount of letters ranging from A to Z (26 possibilities)
n=a*a*a*b*b*b=17.576.000
So if we switch one a to a b, we increment the amount of possible outputs, that is why when switching all the numbers to letters we exponentially increase the amount of possible license plantes.
The sun is an excellent source of electrical energy. A field of solar panels yields 16.22 watts per square feet. DETERMINE tha amount of electricity produced by a field of solar panels that is 305 feet by 620 feet
Answers
Answer: 11,658.45
Step-by-step explanation:
First multiply 305 x 620 to determine the square footage
divide that answer by 16.22 to get your answer
The required amount of electricity produced by a field of solar panels which is 305 feet by 620 feet, is 3,067,202 watt.
Given that,
A field of solar panels yields 16.22 watts per square foot.
T0 determines the amount of electricity produced by a field of solar panels that is 305 feet by 620 feet.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
A field of solar panels yields 16.22 watts per square foot.
The amount of electricity produced by a field of solar panels is 305 feet by 620 feet,
= 16.22 * 305 * 620
= 3,067,202 watt,
Thus the required amount of electricity produced by a field of solar panels that is 305 feet by 620 feet, is 3,067,202 watt.
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Connie and ron walked to a dock at 2 miles per hour, jumped in a boat and motired to dillons at 7 miles per hour. If the total distance was 14 miles and the trip took 3.25 hours in all, how far did they travel by boat?
Answers
Answer:
10.5 miles
Step-by-step explanation:
Let b represent the distance traveled by boat. The relation between speed, distance, and time is ...
time = distance / speed
We are told the total time and the total distance so we have ...
b/7 + (14-b)/2 = 3.25
2b +7·14 -7·b = 14·3.25 . . . multiply by 14
3.75·14 = 5b . . . . . . . . . . . .add 5b-14·3.25
b = 10.5 . . . . . . . . . . . . . . . divide by 5
They traveled 10.5 miles by boat.
_____
Check
10.5/7 +3.5/2 = 1.5 +1.75 = 3.25 . . . . the answer checks OK
They spent 1.75 hours walking 3.5 miles to the dock and 1.5 hours traveling 10.5 miles by boat.
Robert stands atop a 1,380-foot hill. He climbs down, reaching the bottom of the hill in 30 minutes. What is Robert’s average rate of elevation change in feet per minute?
A.
+460
B.
+46
C.
-46
or
D.
-460
Answers
Answer:
-46 feet/min
Step-by-step explanation:
Initial elevation = 1,380 ft
Final Elevation = 0 feet
Change in elevation
= Final elevation - Initial Elevation
= 0 - 1,380
= - 1,380 feet
Given that the journey took 30 min,
rate of descent = Change in elevation / time
= -1,380 / 30
= - 46 feet/min
A lion is running 75 feet per second and is 108 feet behind a wildebeest that is running at 66 feet per second. A lion can only maintain this speed for a very short period. How many seconds will it take lion to catch up to the wildebeest?
Answers
Answer:
12 seconds
Step-by-step explanation:
75 t=66t+108
75t-66t=108
9t=108
t=108/9=12
Answer:
The answer to your question is: 12 seconds
Step-by-step explanation:
Lion v = 75 ft/s
wildebeest = 66 ft/s and is 108 feet behind the lion
t = time = ?
Formula
v = d/ t solve for d d = vt
Process
lion d = 75t
wildebeest = d = 108 + 66t
Now
75t = 108 + 66t
solve for t 75t - 66t = 108
9t = 108
t = 12 s
Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 4 meters per second. If the slower runner has a 75-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
Answers
Answer:12.5 seconds
Step-by-step explanation:hconsidering Runner 1 with a speed of 10m/s
and Runner 2 with a speed of 4 m/s
the equation of displacement for a uniform movement is
x=V*t
so x1=V1*t
and x2=V2*t
and the problem condition is x2=x1+75m
so we proceed to solve the equations.
from equation 2 t=x2/V2
substituting in equation 1 we have
x1=V1(x2/V2) and then the 3 equation
x1=V1((x1+75m)/v2
finally x1=75*(V1/(V2-V1)) =75*(10/(10-4))=125m
then t=(x1/v1)=125/10=12.5 seconds
Answer:
12.5 seconds
Step-by-step explanation:
Speed of the first person = 10 meter per second
Speed of the second person = 4 meter per second
Relative velocity of faster person = 10 - 4 = 6 meter per second
since distance between both the person is = 75 meter.
Therefore, time to cover this distance by faster person = [tex]\frac{Distance}{Speed}[/tex]
[tex]\frac{75}{6}[/tex]
= 12.5 seconds.
Faster runner catches the slower runner after 12.5 seconds.
How to find the probability? Please show your work! Thanks!
Answers
Total shoppers 255.
Number of shoppers who did not shop at the store = 20+70 = 90
Probability = 90/255 = 0.353
Your friend said that there are exactly 12 different pairs of numbers with a difference of 12 and that he had found them all. How would you respond to him?
Answers
Answer:
See explanation
Step-by-step explanation:
I wouls say to my friend that he is incorrect, because there are infinitely many pairs of numbers with a difference of 12.
For example,
[tex]13-1=12\\ 14-2=12\\15-3=12\\16-4=12\\...[/tex]
Here we can increase the first and the second number by 1 and get their difference equal to 12 after this operation.
The same is possible with negative numbers:
[tex]-1-(-13)=12\\ -2-(-14)=12\\-3-(-15)=12\\ ...[/tex]
Actuall, we can do this with decimals too
[tex]12.5-0.5=12\\ \\13.4-1.4=12\\ \\12\dfrac{1}{8}-\dfrac{1}{8}=12\\...[/tex]
Such pairs of numbers are infinitely many (because there are infinitely many real numbers) and we cannot find all possible numbers with difference of 12.
In the continental United States the ratio of states that border an ocean to strays that don't border an ocean is 7:9. How many of the states border an ocean
Answers
so there are 48 states in the continental US and 7+9=16 which is a third of 48, so you have to multiply the numbers by 3
Bob and James are finishing the roof of a house. Working alone, Bob can shingle the roof in 14 hours. James can shingle the same roof in 18 hours. How long will it take them working together to shingle the roof? Round your answer to the nearest hundredth if necessary.
Please show work!
Answers
we know that Bob can do the whole job in 14 hours, how much of the work has he done in 1 hour only? well since he can do the whole lot in 14 hours in 1 hour he has only done 1/14 th of the job.
we know that James can do it in 18 hours, a bit slower, so in 1 hour he has done only 1/18 th of the job.
let's say it takes both of them working together say "t" hours, so in 1 hour Bob has done (1/14) of the work whilst James has done (1/18) of the work, the whole work being t/t or 1 whole, so for just one hour that'd 1/t done by both Bob and James.
[tex]\bf \stackrel{Bob}{\cfrac{1}{14}}~~+~~\stackrel{James}{\cfrac{1}{18}}~~=~~\stackrel{total~for~1~hour}{\cfrac{1}{t}} \\\\\\ \stackrel{\textit{using an LCD of 126}}{\cfrac{9+7}{126}=\cfrac{1}{t}}\implies \cfrac{16}{126}=\cfrac{1}{t}\implies 16t=126\implies t=\cfrac{126}{16} \\\\\\ \stackrel{\textit{7 hrs, 52 minutes and 30 seconds}}{t=\cfrac{63}{8}\implies t=7\frac{7}{8}}\implies \stackrel{\textit{rounded up}}{t=7.88}[/tex]
What is the equation of a line that contains the point (4, 0) and is parallel to x + y = 2?
Answers
Answer:
x + y = 4 or y = -x + 4
Step-by-step explanation:
0 = -1[4] + b
4 = b
y = -x + 4
If you want it in Standard Form:
y = -x + 4
+x +x
_________
x + y = 4 >> Line in Standard Form
* Since the rate of change [slope] is -1 and that parallel lines have SIMILAR SLOPES, -1 remains the same.
I am joyous to assist you anytime.
solve the system of equations y=3x.
y=x^2-4
Answers
Answer:
(x, y) = (-1, -3) or (4, 12)
Step-by-step explanation:
A graphing calculator can show the solutions to this system.
__
You can equate expressions for y and solve for x.
3x = x^2 -4
x^2 -3x = 4 . . . . add 4-3x
x^2 -3x +2.25 = 6.25 . . . . complete the square by adding (-3/2)^2 where -3 is the coefficient of x.
(x -1.5)^2 = 2.5^2 . . . . . . rewrite as squares
x -1.5 = ±2.5 . . . . . . . . . . take the square root
x = 1.5 ± 2.5 = -1, +4
y = 3x = -3, +12, respectively
Solutions are ...
(x, y) = (-1, -3) . . . . and . . . . (4, 12)
Find the coordinates of the midpoint HX. H (5 1/2, -4 3/4), X (2 1/4, 1 1/4)
Answers
Answer:
(3 7/8, -1 3/4)
Step-by-step explanation:
The midpoint is the average of the end point coordinates:
((5 1/2, -4 3/4) +(2 1/4, 1 1/4))/2
= (7 3/4, -3 1/2)/2 = (3 7/8, -1 3/4)
A rock is thrown at a window that is located 18.0 m above the ground. The rock is thrown at an angle of 40.0° above horizontal. The rock is thrown from a height of 2.00 m above the ground with a speed of 30.0 m/s and experiences no appreciable air resistance. If the rock strikes the window on its upward trajectory, from what horizontal distance from the window was it released?
Answers
Answer:
27.32 m
Step-by-step explanation:
We are given that
Height of window from the ground=18 m
Height of rock form the ground=2 m
Speed of thrown rock=30 m/s
We have to find the horizontal distance from the window from which rock was release.
Difference between window and rock=18-2=16 m
Initial vertical velocity component=[tex]30sin40^{\circ}=19.28 [/tex]m/s
Initial horizontal velocity component=[tex]30cos 40^{\circ}=22.98 m/s[/tex]
If the rock is reached to maximum height
Then, maximum height=[tex]\frac{v^2}{2g}=\frac{(19.28)^2}{2\times 9.8}=18.9731 m[/tex]
Time taken by rock to reach maximum height=[tex]\frac{v}{g}=\frac{19.28}{9.8}=1.96775 s[/tex]
Distance between window and maximum height at which rock reached=18.9731-16=2.973 m
Time to drop 2.973 m=[tex]\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\cdot 2.973}{9.8}}=0.77893 s[/tex]
Time to be at 16 m=1.96775-0.77893=1.189 s
Horizontal distance=[tex]1.189\times 22.98=27.32 m[/tex]
Hence, horizontal distance of rock from the window from which rock was released=27.32 m
The rock was released approximately 71.1 meters horizontally from the window. This calculation is based on the rock's initial speed of 30.0 m/s, launch angle of 40.0°, and the fact that it struck the window on its upward trajectory with no air resistance.
To solve this problem, we can use the kinematic equations of motion. We need to find the horizontal distance the rock was released from the window.
1. First, we can find the time it takes for the rock to reach its maximum height. We can use the following kinematic equation:
[tex]\[v_y = u_y + at\][/tex]
Where:
- [tex]\(v_y\)[/tex] is the final vertical velocity (0 m/s at the maximum height),
- [tex]\(u_y\)[/tex] is the initial vertical velocity (30.0 m/s, since it's thrown vertically),
- \(a\) is the vertical acceleration due to gravity (-9.81 m/s²),
- \(t\) is the time.
Rearrange the equation to solve for t:
[tex]\[0 = 30 - 9.81t\]\\\\[/tex]
[tex]\[t = \frac{30}{9.81} \approx 3.06 \, \text{s}\][/tex]
2. Now, we can find the horizontal distance using the horizontal motion equation:
[tex]\[d_x = u_x \cdot t\][/tex]
Where:
- [tex]\(d_x\)[/tex] is the horizontal distance we want to find.
- [tex]\(u_x\)[/tex] is the horizontal component of the initial velocity
[tex](30.0 m/s * cos(40°)).[/tex]
- \(t\) is the time calculated in step 1.
Plug in the values:
[tex]\[d_x = (30 \cdot \cos(40°)) \cdot 3.06 \approx 71.1 \, \text{m}\][/tex]
So, the rock was released approximately 71.1 meters horizontally from the window.
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Ari measured the density of quartz three times: 2.49 g/cm3, 2.56 g/cm3, and 2.72 g/cm3. The accepted value is 2.65 g/cm3. What is the percent error of Ari’s average measurement?
Answers
Answer:
The answer to your question is: 2.26%
Step-by-step explanation:
Data
densities 2.49 g/cm3, 2.56 g/cm3, 2.72 g/cm3
accepted value = 2.65 g/cm3
Process
mean = (2.49 + 2.56 + 2.72) / 3 = 7.77 / 3
= 2.59 g/cm3
% error = | approx. - exact| / exact x 100
% error = | 2.59 - 2.65 | / 2.65 x 100
% error = | -0.06| / 2.65 x 100
% error = 0.06/2.65 x 100
% error = 2.26 %
To find the percent error of Ari’s average measurement, find the average of the three measurements and use the formula: |(Accepted Value - Experimental Value)| / Accepted Value * 100%.
To find the percent error of Ari’s average measurement, we first need to calculate the average of the three measurements. Adding 2.49, 2.56, and 2.72 and dividing by 3 gives us an average density of 2.59 g/cm3.
To find the percent error, we use the formula:
Percent Error = |(Accepted Value - Experimental Value)| / Accepted Value * 100%
Substituting in the values, we get:
Percent Error = |(2.65 - 2.59) / 2.65| * 100%
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Can I get some help? How to find the indicated probability? Please explain or show your work. Thanks!
Answers
Answer:
the easyiest way for me to explain why the answer is A 0.077
Step-by-step explanation:
first add all your numbers it comes up to 1112 then youre going to take that number and put it aside then you dived 86 (the total for anyone at least 31+) and it gices you 0.077
Please please help me out...................
Answers
Answer:
y = [tex]\frac{1}{2}[/tex] x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, 3)
m= [tex]\frac{3-1}{4-0}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, 1) ⇒ c = 1
y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line
A ladder is leaning against a building. The ladder is 10m long and it is sitting on
the ground 4m out from the building. What is the angle that the ladder makes with
the ground?
Answers
Check the picture below.
make sure your calculator is in Degree mode.
The angle that the ladder makes with the ground would be 66.42 degrees.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are given that ladder is leaning against a building. The ladder is 10m long and it is sitting on the ground 4m out from the building.
The side adjacent to the angle is given, and the hypotenuse of the triangle is the unknown.
The cosine relation applies
Cos = Adjacent/Hypotenuse
We are given the hypotenuse = ladder length
Cos (∅)= (4 )/10
Cos (∅)≈ 2/5
(∅)≈ [tex]Cos^{-1}[/tex]2/5
(∅) = 66.42
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Plzzzzz help me quickly! 20 points to whoever gets correct and I will award brainiest! A lawn service company uses the function f(x) = 2.5x + 25 to determine the cost for x hours of service. What does the constant term in the equation represent?
A. the total number of hours of lawn service provided
B. the initial fee the company charges before providing lawn service
C. the total cost for the lawn service
D. the cost per hour of lawn service
Answers
Answer:
c
Step-by-step explanation:
it is the total cost for the lawn servic3
Answer:
B
Step-by-step explanation:
f(x)= the total of the equation
The constant term is the $25 which is what they charge along with the hours determined by x
Penny had a bag of marbles she gave 1/3 of them to Rebecca and 1/4 of the remaining marbles to John Penny then had 24 marbles left in the bag how many marbles the penny start with
Answers
Answer:
38
Step-by-step explanation:
1/3+1/4=7/12
7/12*24=12
24+12=26
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Paula knits hats. The number of hats h she can knit varies directly with the amount of yarn (y) in yards she has. The constant of proportionality is 42. H = 42y. What does the constant of proportionality, 42, represent in this problem?
- answer correctly
Answers
Answer:
42 = the number of hats Paula can knit from one yard of yarn
Step-by-step explanation:
The way this problem is written, the constant 42 is the multiplier of yards to get hats. That is, it has units of hats per yard, so represents the number of hats that can be knit from 1 yard of yarn.
_____
Comment on the problem
It seems more likely that the proportion should be written as ...
y = 42h
or
h = y/42
Then the constant would be the number of yards of yarn required for each hat.