2. The volume of gas in a container at a constant temperature varies inversely as the pressure.
(a) If the volume is 26 cubic centimeters at a pressure of 6 pounds, write an equation to represent this relationship.
Show work!! (3 points)
(b) Use your equation from part a to find the volume of a gas that has a pressure of 17. Round your answer to the
nearest hundredth if necessary. Show work!! (2 points work, 1-point answer)
Answers
\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\)
\(\stackrel{\textit{\boxed{v}olume varies inverse as the \boxed{p}ressure}}{v = \cfrac{k}{p}}\qquad \textit{we also know that} \begin{cases} v = \stackrel{cm^3}{26}\\ p=\stackrel{lbs}{6} \end{cases} \\\\\\ 26=\cfrac{k}{6}\implies 156=k~\hfill \underset{\textit{part a)}}{\boxed{v = \cfrac{156}{p}}} \\\\\\ \textit{when p = 17, what is "v"?}\qquad v = \cfrac{156}{17}\implies v = 9\frac{3}{17}\implies \underset{\textit{part b)}}{v\approx 9.18~cm^3}\)
26=k/6 is relationship which has volume is 26 cubic centimeters at a pressure of 6 pounds and volume is 9 cubic centimeters when pressure is 17.
What is Pressure?The perpendicular force per unit area, or the stress at a point within a confined fluid.
The volume of gas in a container at a constant temperature varies inversely as the pressure.
y varies inversely proportional with x
y=k/x
Volume v varies proportional with pressure.
So v=k/p
26=k/6
k=156.
Now we need to find volume when pressure is 17.
v=156/17
=9.17
=9
Hence 26=k/6 is relationship which has volume is 26 cubic centimeters at a pressure of 6 pounds and volume is 9 cubic centimeters when pressure is 17.
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Related Questions
How many solutions does the system of linear equations graphed below have?
A. No solution
B. 1 solution
B. Infinitely Many Solutions
Answers
HELP ASAP NO LINKS
What is the solution to the equation X=
56 8
co
O x = 448
Ox=64
O x = 48
Ox=7
Answers
Answer:
the answer is x=7 cause you have to divide 56 by 8 and that will give you 7 cause 8×7=56
The rate of interest on a loan is increased from 8.5% to 9% and the debtor has to pay Rs.25 more a year.how much is the loan.
Answers
Answer:
Step-by-step explanation:
0.09x - 0.085x = 25
0.005x = 25
x = 5000
The loan is for Rs 5000
In the paper airplane shown , ABCD=EFGH, m
Answers
Answer:
i would think it would be the same as angle bcd so 90
Step-by-step explanation:
A 2-column table with 9 rows. The first column is labeled year with entries 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013. The second column is labeled precipitation with entries 5.98, 6.05, 7.59, 5.27, 3.11, 7.18, 2.95, 7.22, 2.61. The table shows the precipitation in December, in inches, for Washington state from 2005 to 2013. What was the mean amount of precipitation during this time? Round to the nearest hundredth. 1.97 inches 2.61 inches 5.33 inches 5.98 inches
Answers
Answer:
5.33 inches
Step-by-step explanation:
Mean is another term for average. Therefore, we add up all precipitation items from Column B and divide by the total number of items (9):
\(5.98+6.05+7.59+5.27+3.11+7.18+2.95+7.22+2.61=47.96\)
\(47.96\div{9}\approx{5.33}\)
Pls help i dont understand :( will give Brainliest + 25 Points
Answers
Answer:
D
Step-by-step explanation:
Find the slope using the formula [ y2-y1/x2-x1 ]
2-2/-5-3
0/-8
0
Find the y-intercept using slope-intercept form [ y = mx + b ] and (3, 2)
y = 0x + b
2 = 0(3) + b
2 = b
Put everything we know into the final form.
y = 0x + 2
y = 2
Best of Luck!
change in y/change in x
y2-y1/x2-x1
2-2/-5-3
0/-8 = 0
The slope is 0 - the answer is d
because when 0x = 0, then you are left with y and only y
when the equation is x=, then the equation is undefined
but, when an equation is y=, that the slope is 0
Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years. a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer. b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03
Answers
Answer:
a. The 95% confidence interval is 0.799<p<0.847
b. The sample size n is 622
Step-by-step explanation:
A
P^ = 823/1000
= 0.823
At 95% confidence interval
P^ +- z-alpha/2√p^(1-p^)/n
z-alpha/2 = 1.96
When we insert values we get:
0.823+-1.96√0.823(1-0.823)/1000
= 0.823+-1.96√0.000145671
= 0.823+-1.96(0.012069)
= (0.8467, 0.7993)
The 95% confidence interval is 0.799<p<0.847
B.
We are to compute the sample size here.
The formula and full calculation has been done in the attachment.
4268.4x0.145671
= 621.78
= 622
n = 622
which number line shows the solution to the inequality -3x - 5 < -2 ?
Answers
Find the Interpret the mean absolute deviation of the data 1/4,5/8,3/8,3/4,1/2
Answers
The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.
To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:
Step 1: Find the mean (average) of the data set.
Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5
Step 2: Calculate the difference between each data point and the mean.
Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|
Step 3: Calculate the absolute value of each difference.
Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10
Step 4: Find the average of the absolute differences.
MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20
The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.
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PLEASE HELP
Two projectiles are shot vertically upward at the same instant.
Projectile A's height in feet, f(t), is represented in the table, where t is the seconds since the projectile was shot off
Projectile B's height at any time t is modeled by the function
h (t)=-16t^2 +96t
How do the times at which the projectiles begin their descents compare?
SEE PHOTO
Answers
Projectile B begins its descent 1 seconds before Projectile A does.
What is y-intercept?In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).
By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:
y-intercept = (0, 44).
Maximum height = (4, 300).
When t = 0, the y-intercept of Projectile B can be calculated as follows;
h(t) = -16t² + 96t
h(0) = -16(0)² + 96(0)
h(0) = 0.
For the maximum height, we have:
h(t) = -16t² + 96t
h'(t) = -32t + 96
32t = 96
t = 96/32
t = 3
Difference in time = 4 - 3
Difference in time = 1 seconds.
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— 7x(—8) help me plz
Answers
Answer: 56x
Step-by-step explanation: Multiply -8 by -7. Be sure to add your x at the end. VERY important.
I hope this helps you out! ♥
Answer:
\(56x\)
Step-by-step explanation:
\(-7x(-8)\)
The one and only thing you have to do in this question is to simplify.
\(-7x)(-8)\)
This equals
\(56x\)
Now you got your answer!
Hope this helps!
Please help if you can, this is due tomorrow.
In the diagram below, $\angle BAC=24^\circ$ and $AB=AC$.
If $\angle ABC=y^\circ$, what is the value of $y$?
[asy]
size(4.25cm);
pair a=(0,cos(pi/15)); pair b=(-sin(pi/15),0); pair c=-b; pair d=c+(1,0);
dot(a); dot(b); dot(c);
draw(c--a--b--c);
draw((2*a+3*b)/5-0.05*(cos(pi/15),-sin(pi/15))--(2*a+3*b)/5+0.05*(cos(pi/15),-sin(pi/15)));
draw((2*a+3*c)/5-0.05*(cos(pi/15),sin(pi/15))--(2*a+3*c)/5+0.05*(cos(pi/15),sin(pi/15)));
label(scale(0.75)*"$24^\circ$",a-(0,0.3),S);
label("$A$",a,N);
label("$B$",b,SSW);
label("$C$",c,S);
label(scale(0.85)*"$y^\circ$",b,NE);
[/asy]
Answers
The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
What is equation?Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.
From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.
This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.
In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
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Answer:
78
Step-by-step explanation:
Solve the following system of equations. 4x + 3y = -5
- 3x + 7y=13
Answers
Answer: 13
Step-by-step explanation:
4x+3y=-5 solve x :
4x = -3y + -5 | -3y
1x = -0.75y + -1.25 | : 4
-3x + 7y = 13 solve x :
-3x + 7y = 13 | -7y
-3x = -7y = 13 | : (-3)
Equalization Method Solution: -0.75y+-1.25=2.333y+-4.333
-0, 75y - 1,25 = 2,333y - 4, 333 solve y:
-0, 75y - 1,25 = 2,333y -4, 333 | -2,333y
-3, 083y - 1,25 = -4,333 | + 1, 25
-3. 083y = -3,088 | : (-3, 083)
y = 1
Plug y = 1 into the equation 4x + 3y = -5 :
4x + 3 · 1 | Multiply 3 with 1
4x + 3 = -5 | -3
4x = -8 | : 4
x = -2
So the solution is:
y = 1, x = -2
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Nancy started with 5 2/3 cups of flour. She used 2 1/3 cups of flour to make cookies. How much does she have left? *
Answers
Answer:
3 1/3
Step-by-step explanation:
5-2=3
2/3 - 1/3 = 1/3
3
+1/3
------
3 1/3
I hope this helps you :)
Brainliest please so i can level up please :)
Answer:ygfg
Step-by-step explanation:
PLEASE HURRY!! WILL GIVE BRAINLIEST!!!!
(Question is in the picture)
Answers
736
I hope this helps! :)
Answer:
736
Step-by-step explanation:
Fred and Gina are playing tennis. The first player to win 2 sets wins their match. Fred has a 3/5 chance to win each set while Gina has a 2/5 chance. What is the probability that the match goes three sets until someone wins?
Answers
Answer:
60/125 which can be reduced to 12/25
Step-by-step explanation:
Gina wins
2/5 * 2/5 = 4/25
3/5 * 2*5 * 2/5 = 12 /125
2/5 * 3/5 * 2/5 = 12/125
Fred Wins
3/5 * 3/5 = 9/25
2/5 * 3/5 * 3/5 = 18/125
3/5 * 2/5 * 3/5 = 18/125
P(3 sets) = (18 + 18 + 12 + 12)/125 = 60/125
P(2 sets) = (20 + 45)/125 = 65/125
I found the probability of 2 sets so I could add the results together to see if the probability totals 1. It does. This question is done correctly.
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 22 houses that sold in their neighborhood took an average time of 190 days to sell. The realtor also tell them that based on her prior experience, the population standard deviation is 72 days. Assume the number of days to sell a house has a normal distribution Find the lower bound of the 95% confidence interval for the mean sale time for all homes in the neighborhood.
Answers
Answer:
The lower bound of the 95% confidence interval for the mean sale time for all homes in the neighborhood is of 160 days.
Step-by-step explanation:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
\(M = 1.96\frac{72}{\sqrt{22}} = 30\)
The lower end of the interval is the sample mean subtracted by M. So it is 190 - 30 = 160 days
The lower bound of the 95% confidence interval for the mean sale time for all homes in the neighborhood is of 160 days.
The combined mean and variance of falary of 250 workers of city A and B are 560 and 5497
respectively, find the mean and variance of the salary in city A.
Answers
10-2 eeaaasadaddadeeee
Answers
Answer:thwe answer is 8
Step-by-step explanation:
Answer:88
Step-by-step explanation:
An important aspect of a federal economic plan was that consumers would save a substantial portion of the money that they received from an income tax reduction. Suppose that early estimates of the portion of total tax saved, based on a random sampling of 35 economists, had mean 26% and standard deviation 12%.
Required:
What is the approximate probability that a sample mean estimate, based on a random sample of n = 35 economists, will lie within 1% of the mean of the population of the estimates of all economists?
Answers
Answer:
0.3758 = 37.58% probability that a sample mean estimate will lie within 1% of the mean of the population of the estimates of all economists.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean 26% and standard deviation 12%.
This means that \(\mu = 26, \sigma = 12\)
Sample of 35:
This means that \(n = 35, s = \frac{12}{\sqrt{35}}\)
What is the approximate probability that a sample mean estimate, based on a random sample of n = 35 economists, will lie within 1% of the mean of the population of the estimates of all economists?
This is the p-value of Z when X = 26 + 1 = 27 subtracted by the p-value of Z when X = 26 - 1 = 25. So
X = 27
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{27 - 26}{\frac{12}{\sqrt{35}}}\)
\(Z = 0.49\)
\(Z = 0.49\) has a p-value of 0.6879
X = 25
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{25 - 26}{\frac{12}{\sqrt{35}}}\)
\(Z = -0.49\)
\(Z = -0.49\) has a p-value of 0.3121
0.6879 - 0.3121 = 0.3758
0.3758 = 37.58% probability that a sample mean estimate will lie within 1% of the mean of the population of the estimates of all economists.
85°
4X° + 21°
X =
degrees
Answers
4x°+21°=85°?
4x=85°-21°
4x°=64°
x°=64°÷4°
x=16°
Select the correct answer from each drop-down menu.
A candy company designs a package to hold chocolates. The height of the container is 13 inches and the diameter of its bottom is 9 inches.
9 in i
13 in
Which shape best models the package, and what is the approximate surface area of the package?
The best model for the package is a
The approximate surface area is
square inches.
Answers
The approximate surface area of the package is approximately 245.05 square inches.
The best model for the package is a cylinder.
To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.
The lateral surface area of a cylinder can be calculated using the formula:
Lateral Surface Area = 2πrh
where r is the radius of the base and h is the height.
The area of the circular base can be calculated using the formula:
Area of Base = \(πr^2\)
Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.
Using the given height of 13 inches, we can now calculate the surface area:
Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches
Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches
To find the total surface area, we add the lateral surface area and the area of the base:
Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches
Therefore, the approximate surface area of the package is approximately 245.05 square inches.
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For the figures shown, which information can be used to show that ABC DEF?
Select all that apply.
Answers
Answer:
D, C and A
Step-by-step explanation:
Had this test so i know the answer
The triangles ΔACB and ΔDFE are congruent if ∠F is 90°. Then the correct option is D.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Prove that the triangles ΔACB and ΔDFE are congruent.
AB = DE (Given)
BC = EF (Given)
∠ACB = ∠DFE = 90°
The triangles ΔACB and ΔDFE are congruent if ∠F is 90°. Then the correct option is D.
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Mina has 462 flowers if she wants to put nine flowers in each phase how many for vases will she have how many flowers will she have left over
Answers
A box contains 54 coins which are either 20-cent coins or 50-cent coins. If the total value of all the coins is $20.70, find the number of 20-cent coins in the box. LOF 1 11.
Answers
Number of 20-cent coins in the box are 33.
1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.
2. We can set up two equations based on the given information:
- x + y = 54 (since the total number of coins in the box is 54)
- 0.20x + 0.50y = 20.70 (since the total value of all the coins is $20.70)
3. We can multiply the second equation by 100 to get rid of the decimals:
- 20x + 50y = 2070
4. Now, we can use the first equation to express y in terms of x:
- y = 54 - x
5. Substitute the value of y in the second equation:
- 20x + 50(54 - x) = 2070
6. Simplify and solve for x:
- 20x + 2700 - 50x = 2070
- -30x = -630
- x = 21
7. Substituting the value of x back into the first equation:
- 21 + y = 54
- y = 33
8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.
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Scientists are preparing two satellites to be launched. The satellite, Space Explorer B, flies 74400 miles in 12 hours. The table below represents the number of miles, yy, that the satellite, Space Explorer A, flies in xx hours.
How much faster does Space Explorer B travel per hour than Space Explorer A?
Answers
The difference in speed between Explorer B and Explorer A is 600 miles per hour.
How much faster is the Space Explorer B?In order to determine how fast the satellites are travelling, the average speed of the satellites have to be calculated. Average speed is the total distance covered per time.
Average speed = total distance / total time
Average speed of Space Explorer B = 74,400 / 12 = 6,200 miles per hour
Average speed of Space Explorer A = 72,800 / 13 = 5,600 miles per hour
Difference in speed = 6,200 miles per hour - 5,600 miles per hour = 600 miles per hour.
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Will Give Brainliest if you anwser the question before 12:45
Answers
Answer:
\(\displaystyle \frac{1}{2}\)
General Formulas and Concepts:
Math
Converting to FractionsKCF - Keep Change Flip (Dividing Fractions)Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightStep-by-step explanation:
Step 1: Define
\(\displaystyle (\frac{(2.7 - 0.8) \cdot 2\frac{1}{3}}{(5.2 - 1.4) \div \frac{3}{70}} + 0.125) \div 2\frac{1}{2} + 0.43\)
Step 2: Compute
(Parenthesis) [Fraction] (Parenthesis) Subtract: \(\displaystyle (\frac{1.9 \cdot 2\frac{1}{3}}{3.8 \div \frac{3}{70}} + 0.125) \div 2\frac{1}{2} + 0.43\)(Parenthesis) [Fraction] Convert to fractions: \(\displaystyle (\frac{\frac{19}{10} \cdot \frac{7}{3}}{\frac{38}{10} \div \frac{3}{70}} + 0.125) \div 2\frac{1}{2} + 0.43\)(Parenthesis) [Fraction] Multiply/Divide: \(\displaystyle (\frac{\frac{133}{30}}{\frac{266}{3}} + 0.125) \div 2\frac{1}{2} + 0.43\)(Parenthesis) [Fraction] Divide: \(\displaystyle (\frac{1}{20} + 0.125) \div 2\frac{1}{2} + 0.43\)(Parenthesis) Convert to fraction: \(\displaystyle (\frac{1}{20} + \frac{1}{8}) \div 2\frac{1}{2} + 0.43\)(Parenthesis) Add: \(\displaystyle \frac{7}{40} \div 2\frac{1}{2} + 0.43\)Divide: \(\displaystyle \frac{7}{100} + 0.43\)Convert to fraction: \(\displaystyle \frac{7}{100} + \frac{43}{100}\)Add: \(\displaystyle \frac{50}{100}\)Simplify: \(\displaystyle \frac{1}{2}\)Write the equation in slope intercept form. y−4=3(x+2)
y=3x+2
y=3x+6
y=3x+10
y=3x−2
Answers
Answer:
y=3x+6
Step-by-step explanation:
multiplied 3 and (x+2), then added 4 to each side
plz help i will give brainliest
Answers
6x = 3x+2
Subtract 3x in both sides
3x=2 divide 3 in both sides and you get
X = 2/3
Simplify.
510√
2√
2√2
10√2
5√
Answers
Answer:if you know how to do this your smart and in two years if someone can Answer ill give you a mil in cash swear
Step-by-step explanation:
Answer:
√10/2
Step-by-step explanation:
I took le test