Write a direct proportion equation
that shows the price (y) for any
number of posters (x) that are $2.50
each.
A. y = kx
B. 2.50x = y
C. $2.50 = yx
D. 2.50y = x
Answers
Related Questions
Write 10x - 5y = -30 in slopeintercept form.
y =
X +
Answers
Answer:
\(y=2x+6\)
Step-by-step explanation:
Slope-intercept form is \(y=mx+b\).
Therefore, rearranging the given formula:
\(10x-5y=-30\)
\(-5y=-10x-30\)
\(\frac{-5y}{-5}=\frac{-10x}{-5}-\frac{30}{-5}\)
\(y=2x-(-6)\)
\(y=2x+6\)
Answer: y=2x+6
Step-by-step explanation:
A slope-intercept form is y=mx+b
Hence,
\(10x-5y=-30\\\\10x-5y+5y=-30+5y\\\\10x=-30+5y\\\\10x+30=-30+5y+30\\\\10x+30=5y\)
Divide both parts of the equation by 5:
2x+6=y
Thus, y=2x+6
Factor the following polynomial by factoring out the GCF.
6x4y2 – 9xy + 12x
Answers
(5,-4); y = 1/5 x - 4
Answers
y = 1/5x - 5 is the equation of slope-intercept form .
What is slope-intercept form explain?
A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible. This form is frequently known as the y = mx + b form.equation y = 1/5 x - 4
compare y = mx + c , m = 1/5
put points (5,-4) in equation
y = mx + c
- 4 = 1/5 * 5 + c
- 4 = 1 + c
c = -5
put value of c in equation
y = 1/5x - 5
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Find the percent increase in price per cheese stick.
Answers
Answer:
The answer is 80%
Step-by-step explanation:
BRAINLIEST PLEASEEEE
identify the graph that represents the given system of inequalities. also, identify two ordered pairs that are solutions to the system. y ≤ x 5 y ≤ 2x 3
Answers
Ordered pair (0, 6) and (2, 7) satisfy both inequalities in the system and are solutions to the system.
To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.
When we plot the graph of inequality separately:
y > x + 5:Draw a dashed line y = x + 5 (not including the line).Shade the region above the line.2. y ≥ 2x + 3:
Draw a solid line y = 2x + 3 (including the line).Shade the region above the line.The overlapping shaded region represents the solution to the system of inequalities.
To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:
Ordered pair 1: (0, 6)
Ordered pair 2: (2, 7)
These two points satisfy both inequalities in the system and are solutions to the system.
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The correct question is given below -
Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.
y > x + 5
y ≥ 2x + 3
Which of the following describes a situation in which it is safe to employ t-procedures
(a) n1=10, n2=40; both samples are moderately skewed.
(b) n1=10, n2=8; sample 1 is approximately normal, while sample 2 is skewed right.
(c) n1=6, n2=6; both samples are approximately normal.
(d) n1=35, n2=40; both samples are approximately normal, sample 2 has two outliers.
(e) It is safe to use t-procedures in more than one of the situations above.
Answers
The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.
option (c) is identified as the situation where it is safe to use t-procedures.
t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.
Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.
Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.
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perform the following calculations with the correct significant figures 0.0879/0.98
Answers
The correct significant figure of 0.0879/0.98 is 0.08989796. (rounded to six significant figures)
Significant FiguresThe meaningful digits in a measured or computed number are known as significant figures. They are used to convey the degree of uncertainty in a value and represent the accuracy of the measurement. You must first establish the number of significant figures in each value being utilized before you can execute a computation with significant figures. When doing the computation, use the same number of decimal places as the value with the fewest significant figures. The final step is to round the result to the appropriate number of significant digits.
According to the question
Both numbers in the calculation 0.0879/0.98 have four significant digits. The result, after performing the calculation, is 0.08989796. We look at the final digit (7) in the response to determine the right amount of significant digits to round to. The preceding digit (9) is rounded up if the digit is 5 or above. In this instance, the solution, rounded to six significant numbers, is 0.0899.
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Your hospital has just reset the safety stock level for sleeping pills to be 220 pills.
If your hospital consumes an average of 1,155 per day with a standard deviation of 81 pills, what is the chance that your hospital will run out of sleeping pills on any day? (Keep four decimal places in your answer, which should be a number not a percentage)
Answers
The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).
To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.
First, let's calculate the Z-score using the formula:
Z = (X - μ) / σ
Where:
X = consumption rate per day (1,155 pills)
μ = average consumption rate per day (1,155 pills)
σ = standard deviation (81 pills)
Z = (1,155 - 1,155) / 81
Z = 0
Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.
We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.
To find the probability of running out of sleeping pills, we subtract this probability from 1:
Probability of running out of sleeping pills = 1 - 0.5000
Probability of running out of sleeping pills = 0.5000
Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.
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What value of n makes the equation statement true? 12=n — 0.25(12+8n)
Give step by step work to prove your answer
Answers
Answer:
\(12 = n - 0.25(12 + 8n) \\ 12 = n - \frac{1}{4} (12 + 8n) \\ 12 = n - 3 - 2n \\ 12 + 3= n -2n \\ n = -15 \)
two integers have a sum of 2, and a difference of 12. find the two integers
Answers
==============================================================
Explanation:
Let x and y be the two integers where x > y.
The two integers have a sum of x+y and this is equal to 2, so x+y = 2. Solve for y to get y = -x+2
The two integers also have a difference of 12, so x-y = 12. Plug in y = -x+2 and solve for x
x-y = 12
x - ( y ) = 12
x - ( -x+2 ) = 12 ... replace y with -x+2
x + x - 2 = 12
2x - 2 = 12
2x - 2+2 = 12+2 .... adding 2 to both sides
2x = 14
2x/2 = 14/2 .... divide both sides by 2
x = 7
Use this x value to find y
y = -x+2
y = -7+2
y = -5
--------------------------------------
As a check,
x+y = 7+(-5) = 7-5 = 2 ... we get a sum of 2
x-y = 7-(-5) = 7+5 = 12 ... and get a difference of 12
the answers have been confirmed
Instructions 1 Given the following information, answer the questions. Output per worker is 100 K VN The savings rate is 20%. The depreciation rate is 4%. Question 1 1 pts Calculate output per worker il capitale workeris 40.000 0 DO Question 2 1 pts Calculate Investment per werkeri coital per workers O,000. Hint Use your answer to the previous question D Question 3 1 pts Calculate the amount of depreciation or worker cooper workeris 40,000 D Question 4 1 pts Calculate netestit capital or workeris 40.000 Question 5 1 pts Is capital per weer growing, tating or staying the son of capitale workers 40.000 Grow For Site D Question 1 pts Castle capitair wurer D Question 7 1 pts Calculate net investment if capital per worker is 360,000.
Answers
The answers based on the given information:
1. Output per worker (Y/L) is given as 100. Capital per worker (K/L) is given as 40,000.
2. Investment per worker (I/L) can be calculated using the savings rate (s). I/L = s * (Y/L). Since the savings rate is 20% (0.20), I/L = 0.20 * 100 = 20.
3. Depreciation per worker can be calculated using the depreciation rate (d) and capital per worker (K/L). Depreciation per worker = d * (K/L). Since the depreciation rate is 4% (0.04), Depreciation per worker = 0.04 * 40,000 = 1,600.
4. Net investment per worker can be calculated by subtracting depreciation per worker from investment per worker. Net investment per worker = (I/L) - Depreciation per worker = 20 - 1,600 = -1,580.
5. Since the net investment per worker is negative, capital per worker is decreasing.
7. If capital per worker is 360,000, net investment can be calculated by multiplying the savings rate by the new output per worker (assuming it stays the same) and then subtracting the depreciation. Net investment = (s * (Y/L)) - (d * 360,000) = (0.20 * 100) - (0.04 * 360,000) = 20 - 14,400 = -14,380.
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Evaluate the expression 2 x (3 + 1) + 2.
Answers
Applying the distributive property the given expression is equal to 10.
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±ac Commutative: a . b = b. a Associative: a(b+c)= c(a+b) Identity: b.1=bFor evaluating the given question, you should apply the distributive property.
See that the question gives 2*(3 + 1) + 2. Thus, from the distributive property, you have:
2*(3 + 1) + 2
6+2+2
8+2 =10
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A farmer saw some chickens and pigs in a field. He counted 45 heads and 146 legs. Determine exactly how many chickens and pigs he saw.
Answers
Answers:
17 chickens and 28 pigs
=======================================================
Explanation:
c = number of chickens
p = number of pigs
There are 45 heads, so c+p = 45. This solves to p = 45-c.
Since chickens have 2 legs and pigs have 4, this means there are 2c legs from all the chickens and 4p legs from all the pigs. In total there are 2c+4p legs.
Set this equal to 146 to get the second equation
2c+4p = 146
Then plug in p = 45-c and solve for c
2c+4p = 146
2c+4(45-c) = 146
2c+180-4c = 146
-2c+180 = 146
-2c = 146-180
-2c = -34
c = -34/(-2)
c = 17
There are 17 chickens.
p = 45-c
p = 45-17
p = 28
And there are 28 pigs.
------------------
Check:
c+p = 17+28 = 45 heads
2c+4p = 2*17+4*28 = 34+112 = 146 legs
The answers are confirmed.
WILL GIVE BRAINLIEST
CAN SOMEONE GIVE A EXPLAINATION ABOUT CLOSURE PROPERTY WITH A SIMPLE EXAMPLE THAT IS EASY TO UNDERSTAND
Answers
Explanation:
A set is "closed" for a particular operation if performing that operation on members of the set always gives a member of the set.
closed example
For example, the set {0, 1} is closed for multiplication:
0 × 0 = 0
0 × 1 = 0
1 × 1 = 1 . . . all result values are members of the set
Performing multiplication on any two members of the set gives a member of the set.
__
not closed example
The same set {0, 1} is not closed for addition:
0 +0 = 0
0 +1 = 1
1 +1 = 2 . . . not a member of the set
Performing addition on any two members of the set does not always give a member of the set.
_____
Additional comment
Sometimes you are asked to demonstrate closure of a particular set using a particular example. As we see with addition, above, some examples may seem to demonstrate closure, while another example may prove the set is not closed. In short, you can demonstrate that the set is closed for a particular operation on a particular example, but that does not demonstrate closure in general.
Consider the series ∑n=1[infinity]an where an=(5n−8)2n(3n 4)2n in this problem you must attempt to use the root test to decide whether the series converges
Answers
Applying the root test to the series ∑n=1[infinity]an, where an=(5n−8)2n(3n 4)2n, reveals that the series converges.
To determine the convergence of the series using the root test, we need to consider the limit of the absolute value of the nth root of the general term, as n approaches infinity. In this case, the general term is an=(5n−8)2n(3n 4)2n. Taking the nth root and absolute value, we have:
lim┬(n→∞)〖|an|^(1/n) 〗= lim┬(n→∞)〖|(5n−8)^(2n(3n 4)2n) 〗^(1/n) 〗
Simplifying the expression inside the limit:
|(5n−8)^(2n(3n 4)2n) 〗^(1/n) = |5n−8|^(2(3n 4)) = (5n−8)^(6n-8)
Now, as n approaches infinity, the base (5n−8) grows infinitely large, and since the exponent (6n-8) is also positive, the limit of the expression becomes infinity.
Therefore, lim┬(n→∞)〖|an|^(1/n) 〗= ∞.
Since the limit is greater than 1, according to the root test, the series ∑n=1[infinity]an diverges.
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Find the surface area of a sphere with radius, r = 10 in.
Answers
Answer: ~1256.64
Step-by-step explanation:
The equation for the surface area of a sphere is 4πr². So you would substitute 10 in for r which would then be 4π10². That will get you 1256.63706 but rounded it would be approximately 1256.64.
Answer: \(\text{400}\pi \ \text{square inches}\)
Step-by-step explanation:
Given: The radius of the sphere = 10 in.
The formula to calculate the surface area of the sphere is given by:
\(\text{Surface Area}=4\pi r^2\), where r is the radius of the sphere.
For r = 10 in. we have
\(\text{Surface Area of the sphere}=4\pi (10)^2\)
\(\implies \text{Surface Area of sphere}=4\pi (100)\)
\(\implies \text{Surface Area of the sphere}=\text{400}\pi \ \text{square inches}\)
\(400\pi =1256.64 \ \text{square inches}\)The class average on a statistics exam is 80 with a standard deviation of 4. Which of these best represents the percentage of students who scored between 68 and 82 on the exam?
Answers
Answer:
Subtract than divide
Step-by-step explanation:
Can someone help really fast with this question
Answers
The answer that describes the polygon RSTU is as follows:
QuadrilateralTrapezoidHow to find a quadrilateral?A quadrilateral is a polygon with 4 sides. Therefore, let's use the properties to find the name of the shape RSTU as follows:
The polygon has 4 sides therefore, it is a quadrilateral.
The quadrilateral has opposite side parallel to each other. The opposite sides are RS and TU.
A trapezoid is a quadrilateral with only one pair of opposite side parallel to each other.
Therefore, the shapes that defines the polygon are as follows:
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Move a number to each box to create an equation to solve 8/100+9/10 =
Answers
The solution of the given fraction can be gotten through filling the boxes with the following values respectively;
8/100 + 9/10 = 98/100
What is a fraction?A fraction is defined as the representation of a part of a whole value in the form of a numerator and denominator.
The given fraction;
8/100 + 9/10 = ?
Find the lowest common multiple of the denominator = 100.
= 8/100 + 9/10
= 8 + 90/100
= 98/100
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when a 99% confidence interval is calculated instead of a 95% confidence interval, with n being the same, the margin of error will be
Answers
The margin of error will be larger for a 99% confidence interval than for a 95% confidence interval, assuming the same sample size and level of variability in the data.
Explain your answer further indetail?The margin of error is the range of values above and below the point estimate within which the true population parameter is likely to fall.
A higher level of confidence requires a larger margin of error. This is because as the level of confidence increases, the range of values that contains the true population parameter becomes wider.
For example, a 95% confidence interval has a margin of error of plus or minus two standard errors of the point estimate.
Increasing the confidence level to 99% would require a wider range of values, and therefore a larger margin of error, such as plus or minus three standard errors of the point estimate.
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help me with this ques. (need solution and answer both) thanks so much <3
Answers
Answer:
1.) 27a^11 + 18a^9 -72a^7
2.) 6p^4q^3 - 10p^3q + 4p^2q3
Step-by-step explanation:
1.) Distribute and do the math
-9a^5 x (-3a^6) - 9a^5 X (-2a^4) - 9a^5 x 8a^2
27a^11 + 18a^9 -72a^7
2.) Distribute and do the math
2pq^2q x 3p^2q^2 - sp^2q x 5p + 2p^2q x 2q^2
6p^4q^3 - 10p^3q + 4p^2q3
2 exterior angle bisector intersect an interior angle bisector at a point. What is the name of the point?
Answers
Answer:
Exterior angle bisectors of the side △ABC at vertices B and C intersect at D. Find ∠BDC if ∠BAC=40∘
Step-by-step explanation:
Can someone help me?
Answers
Answer:
1 feet
Step-by-step explanation:
15-14
a study will be conducted to investigate whether there is a difference in the mean weights between two populations of raccoons. random samples of raccoons will be selected from each population, and the mean sample weight will be calculated for each sample.
Answers
Based on the information provided, it appears that a study will be conducted to compare the mean weights of two populations of raccoons.
To do so, random samples will be selected from each population, and the mean weight of each sample will be calculated. By comparing the mean sample weights of the two populations, researchers can determine whether there is a significant difference in the mean weights between the two groups.
It is important to note that the use of random samples helps to ensure that the results are representative of the entire population and reduces the risk of bias in the study.
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Rodney is an avid ice hockey fan. Each Saturday he visits the Sydney Ice Hockey Arena to watch his beloved team compete. He and his partner have season tickets and sit in the 4th row back from the rink. Last Saturday evening, while watching a game, Rodney was struck in the face by an ice puck that was hit from the field of play. This occurred even though there was a one (1) metre high hard clear plastic screen that surrounded the rink to protect spectators. The incident caused Rodney serious injury. In the fifteen (15) years Rodney has been attending the Sydney Ice Hockey Arena, he has only ever seen a puck hit from the field of play into the crowd on ten (10) occasions and nobody before has ever been injured. The organisers claim they are not responsible for Rodney’s injury.
Rodney wants to sue the organisers of the ice hockey match for negligence. Do you think he will succeed? Explain why/why not.
Answers
Rodney can sue the organizers of the ice hockey match for negligence. The reason is that the organizers did not provide proper safety measures even after knowing that the spectators are at high risk of injury.
In the given situation, the one-meter high hard clear plastic screen surrounding the rink was not enough to protect the spectators. The organizers of the ice hockey match have the responsibility of ensuring the safety of the spectators. While they did put up a hard clear plastic screen, it was not enough to protect Rodney. They should have taken additional measures such as erecting a higher barrier or providing protective gear to the spectators. Since Rodney has been attending the matches for fifteen years and has only seen a puck hit into the crowd on ten occasions.
The organizers knew the potential risk and should have taken steps to prevent such an incident. The fact that no one was injured in the past does not absolve the organizers of their responsibility. It is their duty to ensure the safety of the spectators at all times. In this case, they failed to take adequate safety measures, which resulted in Rodney's injury. Therefore, Rodney has a valid case of negligence against the organizers of the ice hockey match. In conclusion, Rodney can sue the organizers of the ice hockey match for negligence because they failed to provide proper safety measures to prevent an incident such as this from occurring. Therefore, Rodney has a strong case of negligence against the organizers of the ice hockey match, and he is likely to succeed in his claim. The organizers should take this opportunity to review their safety measures and ensure that such incidents are prevented in the future.
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A history professor decides to give a 12-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than 0.10. What score should be set as the lowest passing grade? Group of answer choices
Answers
Answer:
we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10
Step-by-step explanation:
From the given information;
Sample size n = 12
the probability of passing a student who guesses on every question is less than 0.10
In a alternative - response question (true/false) question, the probability of answering a question correctly = 1/2 = 0.5
Let X be the random variable that is represent number of correct answers out of 12.
The X \(\sim\) BInomial (12, 0.5)
The probability mass function :
\(P(X = k) = \dfrac{n!}{k!(n-k)!} \times p^k\times (1-p)^{n-k}\)
\(P(X = 12) = \dfrac{12!}{12!(12-12)!} \times 0.5^{12}\times (1-0.5)^{12-12}\)
P(X = 12) = 2.44 × 10⁻⁴
\(P(X = 11) = \dfrac{12!}{11!(12-11)!} \times 0.5^{11}\times (1-0.5)^{12-11}\)
P(X =11 ) = 0.00293
\(P(X = 10) = \dfrac{12!}{10!(12-10)!} \times 0.5^{10}\times (1-0.5)^{12-10}\)
P(X = 10) = 0.01611
\(P(X = 9) = \dfrac{12!}{9!(12-9)!} \times 0.5^{19}\times (1-0.5)^{12-9}\)
P(X = 9) = 0.0537
\(P(X = 8) = \dfrac{12!}{8!(12-8)!} \times 0.5^{8}\times (1-0.5)^{12-8}\)
P(X = 8) = 0.12085
\(P(X = 7) = \dfrac{12!}{7!(12-7)!} \times 0.5^{7}\times (1-0.5)^{12-7}\)
P(X = 7) = 0.19335
.........
We can see that,a t P(X = 9) , the probability is 0.0537 which less than 0.10 but starting from P(X = 8) downwards the probability is more than 0.01
As such, we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10
Suppose that we flip a fair coin until either it comes up tails twice or we have flipped it six times. What is the expected number of times we flip the coin
Answers
The expected number of times the coin is flipped is 3.75.
What is Probability?Probability refers to the chance of occurrence of an event.
Let E be an event. Then, the probability of E = P(E)
=> P(E) = \(\frac{Number Of Favourable Outcomes Of E}{Total Number Of Outcomes}\)
Now,
When the coin is flipped two times, Total number of outcomes = 4 Total number of Favorable outcomes = 1P(Tail coming up twice) = \(\frac{1}{4}\)
When the coin is flipped three times,Total number of outcomes = 8 Total number of Favorable outcomes = 2P(Tail coming up twice) = \(\frac{2}{8}\)
When the coin is flipped four times,Total number of outcomes = 16Total number of Favorable outcomes = 3P(Tail coming up twice) = \(\frac{3}{16}\)
When the coin is flipped five times,Total number of outcomes = 32Total number of Favorable outcomes = 4P(Tail coming up twice) = \(\frac{4}{32}\)
When the coin has been flipped six times,P(Tail coming up twice) = \(1-\frac{1}{4}-\frac{2}{8}-\frac{3}{16}- \frac{4}{32} = \frac{3}{16}\)
Therefore, the expected number of times coin is flipped = \(2(\frac{1}{4}) + 3(\frac{2}{8}) + 4(\frac{3}{16} )+5(\frac{4}{32} )+6(\frac{3}{16} ) =\frac{15}{4} = 3.75\)
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The van der Waals equation of state is p=
V
m
−b
RT
−
V
m
2
a
. (a) Show that the van der Waals equation can be written in the form of a virial equation of state in powers of 1/V
m
: pV
m
=RT(1+
V
m
B
+
V
m
2
C
+…) where the virial coefficients B and C are
B=b−
RT
a
C=b
2
Hint: You will need to use the Taylor expansion of (1−x)
−1
(when x is small):
1−x
1
=1+x+x
2
+⋯ (b) Measurements of argon gave B=−21.7 cm
3
⋅mol
−1
and C=1.200×10
3
cm
6
⋅mol
−2
for the virial coefficients at T=273 K. What are the values of a and b in the corresponding van der Waals equation of state? Use R=8.2057×10
−2
dm
3
⋅atm⋅K
−1
⋅mol
−1
for the gas constant. (c) Using calculated van der Waals constants a and b, estimate the Boyle temperature for argon. Hint: At Boyle temperature and V
m
→[infinity], we have
d(1/V
m
)
dZ
=0
Answers
a) pV_m = RT(1 + ((-RT / a) - b)V_m - (a / V_m) - b^2 / V_m) this equation can be written in the form of a virial equation of state in powers of 1/V_m.
b) a ≈ 1.673 cm^6·atm·mol^(-2)
c) The Boyle-temperature for argon can be estimated using the calculated van der Waals constants as V_m approaches infinity.
Step by step:
(a) To show that the van der Waals equation can be written in the form of a virial equation of state, we start with the given van der Waals equation:
p = (RT / (V_m - b)) - (a / V_m^2)
We can rewrite this equation by multiplying both sides by V_m:
pV_m = RT - bV_m - (a / V_m)
Now, let's substitute B and C in terms of a and b:
B = b - (RT / a)
C = b^2
Substituting these values into the equation, we have:
pV_m = RT - (RT / a)V_m - (a / V_m) - bV_m - b^2 / V_m
Rearranging terms, we get:
pV_m = RT(1 + ((-RT / a) - b)V_m - (a / V_m) - b^2 / V_m)
This equation can be written in the form of a virial equation of state in powers of 1/V_m.
(b) Given that B = -21.7 cm^3·mol^(-1) and C = 1.200×10^3 cm^6·mol^(-2), and using R = 8.2057×10^(-2) dm^3·atm·K^(-1)·mol^(-1), we can substitute these values into the equations for B and C:
-21.7 = b - (8.2057×10^(-2) / a) (Equation 1)
1.200×10^3 = b^2 (Equation 2)
From Equation 2, we can solve for b:
b = ±√(1.200×10^3)
Since b cannot be negative according to the van der Waals equation, we take the positive square root:
b = √(1.200×10^3) = 34.64 cm^3·mol^(-1)
Now, substituting this value of b into Equation 1, we can solve for a:
-21.7 = 34.64 - (8.2057×10^(-2) / a)
Solving for a, we find:
a = (8.2057×10^(-2)) / (34.64 + 21.7)
a ≈ 1.673 cm^6·atm·mol^(-2)
(c) To estimate the Boyle temperature, we use the condition:
d(1/V_m) / dZ = 0
At Boyle temperature, V_m approaches infinity. Taking the derivative, we have:
d(1/V_m) / dZ = (2a / V_m^3) - b = 0
Solving for V_m, we get:
V_m = (2a / b)^(1/3)
Substituting the values of a and b that we calculated earlier, we can find V_m:
V_m = (2(1.673) / (34.64))^(1/3)
V_m ≈ 2.519 dm^3·mol^(-1)
Therefore, the Boyle temperature for argon can be estimated using the calculated van der Waals constants as V_m approaches infinity.
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angelina drove at an average rate of 80 kph and then stopped 20 minutes for gas. after the stop, she drove at an average rate of 100 kph. altogether she drove 250 km in a total trip time of 3 hours including the stop. which equation could be used to solve for the time $t$ in hours that she drove before her stop?
Answers
Angelina drove for 0.83 hours (or approximately 50 minutes) before her stop.
The equation that could be used to solve for the time $t$ in hours that Angelina drove before her stop is:
$80t + 100(3 - t - \frac{1}{3}) = 250$
Let's break down the information given. Angelina drove at an average rate of 80 kph for a certain amount of time, which we want to find. After that, she stopped for 20 minutes (or $\frac{1}{3}$ of an hour) for gas. Then, she continued driving at an average rate of 100 kph. The total trip time, including the stop, was 3 hours.
To solve for the time Angelina drove before her stop, we can set up an equation based on the distance she traveled. The distance traveled at 80 kph is given by $80t$, where $t$ represents the time in hours. The distance traveled after the stop at 100 kph is $100(3 - t - \frac{1}{3})$, where $3 - t - \frac{1}{3}$ represents the remaining time after the stop.
The sum of these distances should equal the total distance traveled, which is 250 km. Therefore, we set up the equation $80t + 100(3 - t - \frac{1}{3}) = 250$.
By solving this equation, we can find the value of $t$, which represents the time in hours that Angelina drove before her stop.
To solve the equation, we can start by simplifying the expression on the right side:
$80t + 100(3 - t - \frac{1}{3}) = 250$
First, we can simplify the expression $3 - t - \frac{1}{3}$:
$3 - t - \frac{1}{3} = 2\frac{2}{3} - t = \frac{8}{3} - t$
Now, we substitute this expression back into the equation:
$80t + 100(\frac{8}{3} - t) = 250$
Next, we distribute the 100 to both terms inside the parentheses:
$80t + \frac{800}{3} - 100t = 250$
Combining like terms:
$-20t + \frac{800}{3} = 250$
To isolate the variable $t$, we can subtract $\frac{800}{3}$ from both sides:
$-20t = 250 - \frac{800}{3}$
To simplify the right side, we need a common denominator for 250 and $\frac{800}{3}$, which is 3:
$-20t = \frac{750}{3} - \frac{800}{3}$
Subtracting the fractions:
$-20t = \frac{-50}{3}$
Finally, we divide both sides by -20 to solve for $t$:
$t = \frac{\frac{-50}{3}}{-20} = \frac{50}{60} = \frac{5}{6}$
Therefore, Angelina drove for $\frac{5}{6}$ or 0.83 hours (or approximately 50 minutes) before her stop.
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Someone please help me
Answers
Answer:
m∠B ≈ 28.05°
Step-by-step explanation:
Because we don't know whether this is a right triangle, we'll need to use the Law of Sines to find the measure of angle B (aka m∠B).
The Law of Sines relates a triangle's side lengths and the sines of its angles and is given by the following:
\(\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}\).
Thus, we can plug in 36 for C, 15 for c, and 12 for b to find the measure of angle B:
Step 1: Plug in values and simplify:
sin(36) / 15 = sin(B) / 12
0.0391856835 = sin(B) / 12
Step 2: Multiply both sides by 12:
(0.0391856835) = sin(B) / 12) * 12
0.4702282018 = sin(B)
Step 3: Take the inverse sine of 0.4702282018 to find the measure of angle B:
sin^-1 (0.4702282018) = B
28.04911063
28.05 = B
Thus, the measure of is approximately 28.05° (if you want or need to round more or less, feel free to).