6 1/2+2/3+3/4 calcution with distribution
Answers
By the distribution property 6(1/2 + 2/3+3/4) = 23/2
Distribution Property:According to the distributive property, multiplying the difference or aum of numbers will be equivalent to multiplying the individual parts of the difference or sum.
The expression that can explain the above rule is A ( B+ C) = AB + AC
Here we have
6(1/2 + 2/3+3/4)
By distribution property
=> 6(1/2 + 2/3+3/4)
= 6(1/2) + 6(2/3)+ 6(3/4)
= 3 + 2(2) + 3(3/2)
= 3 + 4 + 9/2
= 7 + 9/2
= (14+9)/2 [ add 7 and 9/2 by taking 2 as LCM ]
= 23/2
Therefore,
By the distribution property 6(1/2 + 2/3+3/4) = 23/2
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Complete Question:
1. Find the value of this fraction computation: 6(1/2 + 2/3+3/4)
Related Questions
THE SUM OF TWO NUMBERS IS 54. IF THE SMALLER NUMBER IS 6 LESS THAN THE BIGGER ONE, FIND THE NUMBERS. (STEP BY STEP PLZ)
Answers
Answer:
24 and 30
Step-by-step explanation:
The sum of two numbers is 54. Let's use the variables x and y to represent theses numbers:
x + y = 54
The smaller number is 6 less than the bigger one. Let's say that x is the smaller number and y is the bigger number:
y - 6 = x
Now we know that x is equivalent to y - 6. So, let's replace x with y - 6 in the original equation:
x + y = 54
y - 6 + y = 54
Combine like terms:
2y - 6 = 54
Now we can solve for y:
2y - 6 = 54
Add 6 to both sides of the equation to isolate the 2y:
2y = 60
Divide both sides by 2 to find the value of y:
y = 30
Now that we know the value of y, we can solve for x:
y - 6 = x
30 - 6 = x
24 = x
The value of the two numbers is 24 and 30.
For this experiment you have been randomly assigned to a group consisting of you and one other person. You do not know now, nor will you ever know, who this other person is. For this experiment all you have to do is distribute your 10 points into two accounts. One account called KEEP and one account called GIVE. The GIVE account is a group account between you and your group member. For every point that you (or your group member) put in the GIVE account, I will add to it 50% more points and then redistribute these points evenly to you and your group member. The sum of the points you put in KEEP and GIVE must equal the total 10 points. Any points you put in the KEEP account are kept by you and are part of your score on this experiment. Your score on the experiment is the sum of the points from your KEEP account and any amount you get from the GIVE account. For example, suppose that two people are grouped together. Person A and Person B. If A designates 5 points in KEEP and 5 points in GIVE and person B designates 10 points to KEEP and 0 points to GIVE then each person’s experiment grade is calculated in this manner: Person A’s experiment grade = (A’s KEEP) + 1.5(Sum of the two GIVE accounts)/2 = 5 +(1.5)(0+5)/2= 5 + 3.75 = 8.75. Person A’s score then is 8.75 out of 10. Person B’s experiment grade = (B’s KEEP) + 1.5(Sum of the two GIVE accounts)/2 = 10 +(1.5)(0+5)/2 = 10 + 3.75. Person B’s score then is 13.75 out of 10. (you can think of any points over 10 as extra credit) In this module’s activity you were asked to make a decision about how to invest your resources (points). This activity is a classic strategic game where the good of the individual is at odds with the good for the group. These problems are pervasive in risk management. For example, a physician who is trained to treat diseases may be reluctant to discuss alternative treatments with a patient when the physician is sure that a specific treatment is the only truly viable treatment. Nonetheless, you have learned in this course that physicians (or an agent of the physician) must have this discussion and bow to the will of the patient even if, in the physician’s judgment, the patient chooses an alternative treatment which is likely to be superfluous. In this way, informed consent and patient education are nuisances to the physician but are very important to protect the group (maybe a hospital or surgical group) from liability. In light of recent events another example is warranted. Individuals may choose to not get vaccinated since they do not want to bear the risk of any possible adverse side-effects of a vaccine. This is perfectly reasonable to do so. The problem arises when large groups of people choose to not get vaccinated thus making the impact of the disease relatively larger than need be if everyone would choose to take a vaccine (remember our first cost-benefit experiment). This implies that individual’s rights to choose not to vaccinate are at odds with what is good for the group of individuals. These types of problems are common in risk management. Discussion: (If you post your answers to each of the four questions below before the deadline, you will get the full ten points for the discussion. The questions do not need to be answered mathematically or with a calculation. If you feel the need to use mathematics to make a calculation, then you are free to do so but the questions are merely asking you for a number and how you arrived at that number. If you do not do any calculations to arrive at the number, just say how you arrived at the number. (There are no incorrect answers.) 1. In this activity how did you arrive at your decision on the keep-give split? 2. What is the best outcome of this situation for you? 3. What is the best outcome of this situation for the group? 4. Can you see any parallels with this game and how risk management strategies work? Explain.
Answers
1. I based my decision on allocating points to maximize my own score, while also considering the potential benefits of contributing to the group fund.
2. The best outcome for me would be allocating the minimum points required to the GIVE account, while putting the majority in the KEEP account. This would ensure I receive the most points for myself.
3. The best outcome for the group would be if both participants maximized their contributions to the GIVE account. This would create the largest group fund, resulting in the most redistributed points and highest average score.
4. There are parallels with risk management strategies. Individuals may act in their own self-interest, but a larger group benefit could be achieved if more participants contributed to "group" risk management strategies like vaccination, safety protocols, insurance policies, etc. However, some individuals may free ride on others' contributions while benefiting from the overall results. Incentivizing group participation can help align individual and group interests.
Theoreticiant (s) credited with developing the mathematical models that predict population growth in each of two competing species a. Rosenzweig and MacArthur
b. Vorhuis c. Gouse
d. Lolka and Voera
Answers
The mathematicians credited with developing the mathematical models that predict population growth in each of two competing species are Rosenzweig and MacArthur(OPTION A).
These two scientists developed a theory known as the "competitive exclusion principle," which states that two species competing for the same resources cannot coexist indefinitely. Instead, one species will eventually outcompete and displace the other species.
Rosenzweig and MacArthur's model is based on the Lotka-Volterra equations, which are a set of differential equations that describe the dynamics of predator-prey relationships. They extended this model to include two competing species and developed the concept of the "ecological niche" – the specific set of environmental conditions under which a species can survive and reproduce.
Their model predicts that the two species will reach a stable equilibrium, where their populations remain relatively constant over time. However, the exact outcome of the competition depends on several factors, including the initial population sizes of the two species, the relative strengths of their ecological niches, and the availability of resources.
Overall, Rosenzweig and MacArthur's mathematical model has been influential in the field of ecology, providing a framework for understanding how competing species interact and how ecosystems evolve over time.
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Simplify the following expressions by factoring using the greatest common factor:
1. 17mn – 5mnx + 15mx
2. 4rst +18rst – 34rst
3. 12ax + 20bx + 32cx
Answers
Answ
Step-by-step explanation:
−42−5i 2y−1(y−2)(y−2)
What is the probability of a blue on this spinner? Be sure to reduce.
Answers
Answer: 3/8
Step-by-step explanation:
there are 8 slots and three of them are blue if you need decimal form then here: 0.375. The percentage is: 15% i think
I hope i helped you! :)
There are 3 blue in the spinners and total of spinners are 8
The cost of admission to a festival was $112 for 9 children and 3 adults. The admission was $108 for 8 children and 3 adults in another festival. How much was the admission for each child and adult?
Answers
Answer:
cost of admission for each child was $4.00, and each adult was $25.33
Step-by-step explanation:
When solving questions like these , I like to break down the problem so I understand it better.
Let x ---> cost of the admission for each child
Y ---------> cost of the admission for each adult
9x+3y = 112 ---> equation A
8x + 3y = 108 ---> equation B
Subtract B from A
9x+3y=112
-8x+3y = 108
x = 112-108
x = 4
Find value of y by substituting value of x into equation
9(4)+3y=112
Solve for y
36+3y = 112
3y = 112=36
3y = 76
y = 25.33
I need to show my work please help and I’m in 7th grade i don’t know why it says highschool
Answers
Answer:
green sugar...................
because ....
1 1/2 =3/4....
In a recent National Survey of Drug Use and Health, 2312 of 5914 randomly selected full-time US college students were classified as binge drinkers.
If we were to calculate a 99% confidence interval for the true population proportion p that are all binge drinkers, what would be the lower limit of the confidence interval? Round your answer to the nearest 100th, such as 0.57 or 0.12. (hint: use Stat Crunch to calculate the confidence interval).
Answers
The lower limit of the 99% confidence interval for the true population proportion of binge drinkers cannot be determined without additional information.
To calculate the lower limit of the 99% confidence interval for the true population proportion of binge drinkers, we need to know the sample proportion and the sample size. While the information provided states that 2312 out of 5914 randomly selected full-time US college students were classified as binge drinkers, we don't have the specific sample proportion.
Additionally, the margin of error is required to calculate the confidence interval. Without these values or the methodology used to calculate the interval, we cannot determine the lower limit. It is important to note that the confidence interval is influenced by the sample size, sample proportion, and the desired level of confidence. Without more information, we cannot compute the lower limit of the confidence interval.
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Consider the following counter-espionage puzzle to find whether there is a spy among n guests at a party. Every spy knows everyone else’s name but nobody will know theirs. Fortunately, if you ask any person at this event the name of any other person (other than yourself), they’ll tell you honestly whether they know. The non-spies will do so because they’re good, honest people, and the spy will do so because they want to seem like they fit in. So all you need to do is ask every pair at the party whether each knows the other’s name, right? Here’s the problem. If the spy happens to notice you doing this, they’ll get spooked and leave. You’ll need to ask as few questions as possible. Describe a protocol for finding a spy that: 1. Finds the spy if there is one. 2. Uses 3(n − 1) or fewer questions of the form "do you know that person’s name?" Your protocol should be recursive. Prove by induction on n that your protocol satisfies the two properties above. [Hint: By asking a single "what’s their name" question, you can always eliminate one person as a potential spy. You just need to figure out what to do after that...]
Answers
Total Questions = 3(n/2 - 1) + n/2 = 3n/2 - 3/2 + n/2 = 2n - 3/2. The recursive protocol guarantees that the spy can be found if there is one (Property 1) and uses 3(n - 1) or fewer questions (Property 2) for any number of guests n, as proven by induction.
Using a recursive protocol, we can follow these steps to solve the counter-espionage puzzle and locate the spy among the n partygoers:
Case in Point (n = 2):
Ask A and B, any two guests, if they know each other's names.
B is not the spy if A says "Yes." B is the spies otherwise.
Case Recursive (n > 2):
With roughly equal numbers of guests, divide the n guests into two groups, A and B.
Apply the protocol one group at a time to each group recursively.
Assume that one or both of the spies in group A and group B are identified by the recursive calls.
Now, we have to figure out which group has the spy or whether there is a spy between the two groups.
Consolidating the Findings:
Ask one guest from group A and one guest from group B if they know each other's names for each pair of guests.
The spy is part of the larger group if at least one pair answers "Yes" while the other responds "No."
There is no spying between the two groups if each pair in either group responds with either "Yes" or "No." In this instance, the group that was identified as having a spy during the recursive calls must contain the spy.
Final Outcome:
Divide the larger group into two subgroups and recursively apply the protocol if there is a spy in that group.
Keep going in this recursive manner until either a spy is found or it is determined that no guests have a spy.
We can use induction on n to demonstrate the efficiency and effectiveness of the protocol:
Case in Point (n = 2):
The spy is correctly identified among two guests by the protocol. It only asks one question, which is the bare minimum.
Step Inductive:
Consider the case of (n + 1) guests, assuming that the protocol functions properly for n guests.
Divide the guests (n + 1) into two groups with approximately n/2 members each. This can be accomplished by selecting n/2 guests at random from one group and distributing the remaining guests to the other.
Apply the protocol one group at a time to each group recursively. Using a maximum of 3(n/2 - 1) questions per group, this correctly identifies any spies within each group, according to the induction hypothesis.
Asking each pair of guests, one from each group, if they know each other's names brings the results together. This calls for n/2 inquiries.
The spy is part of the larger group if at least one pair responds incorrectly (one says "Yes" and the other says "No"). The larger group only has (n + 1)/2 guests in this instance.
During the recursive calls, the spy must be in the group identified as having a spy if all pairs respond with the same answer (either both "Yes" or "No"). There are maximum n guests in this group.
As a result, in the worst-case scenario, the number of questions that are asked are as follows:
The total number of questions is 3(n/2 - 1), plus n = 3n/2 - 3/2, plus n = 2n - 3/2.
As a result, the protocol ensures that the spy can be located if there is one (Property 1) and employs three questions (n - 1) or fewer (Property 2) for any number of guests n, as demonstrated by induction.
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Find g(x), where g(x) is the translation 4 units left and 9 units up of f(x) = x².
Write your answer in the form a(x - h)² + k, where a, h, and k are integers.
g(x)= ______
Answers
02.03 Focus Questions
What are linear equations and functions?
What are the different ways of representing a linear function?
How are key features of a linear function identified and interpreted from a graph?
How are key features of a linear function identified and interpreted from a table?
How are key features of a linear function identified and interpreted from an equation?
How are key features of a linear function identified and interpreted from a description?
Answers
Linear functions are those whose graph is a straight line and it has the following form. y = f(x) = a + bx.
There are several ways to represent a linear function such ad word form, function notation, tabular form, and graphical form.
The key features of a linear function identified and interpreted from a description as an increasing linear function results in a graph that slants upward from left to right and has a positive slope.
What is a linear function?A linear function can be expressed as a point slope or a line with a slope intercept. The ordered pairs will represent points on the line where a table of values representing the function is provided. According to the values in the table, the gradient of the line is a ratio of rise to run. The gradient and initial value of the function are shown in slope intercept form.
A graph with a positive slope and a left-to-right slope is produced by an increasing linear function. A graph with a negative slope and a left-to-right slant is produced by a decreasing linear function. A graph with a constant linear function looks like a horizontal line.
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Lisa kicked a ball against the wall at the indicated angle. What is the measure, in degrees, of <1?
Answers
Answer:
68°
Step-by-step explanation:
since the ball is placed or comes from a straight line (which is the wall) it means that when you add all those angles the final answer has to be 180 because angles in a straight line add up to 180°
68°+44°+1=180
112°+1=180
1=180-112
=68°
I hope this helps
The measure of ∠1 is 68 degrees.
We have Lisa who kicked a ball against the wall at the indicated angle.
We have to determine the measure of the angle 1 in degrees.
What is the angle of a straight line ?A straight line has an angle of 180 degrees.
According to question, we have -
∠3 = 68 degrees
∠2 = 44 degrees
Therefore -
∠3 + ∠2 + ∠1 = 180
68 + 44 + ∠1 = 180
112 + ∠1 = 180
∠1 = 180 - 112
∠1 = 68 degrees
Hence, the measure of ∠1 is 68 degrees.
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does it make sense that the number of cats falling from the 5th floor would be greater than those of the 4th? why or why not?
Answers
No, it does not make sense that the probability of cats falling from the 5th floor would be greater than those of the 4th. The force of gravity is the same regardless of the floor, so the number of cats falling should be the same no matter what floor they start from.
The force of gravity is a constant force that is the same on all floors. This means that the same amount of force is acting on the cats, no matter which floor they start from. Therefore, the number of cats falling from the 5th floor should be the same as the number falling from the 4th floor. The number of cats falling from a higher floor may be greater if there are extra factors, such as wind, that could affect their fall, but the force of gravity does not change with the floor. Therefore, it does not make sense for the number of cats falling from the 5th floor to be greater than those of the 4th
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The subtotal for a TV was $1,029.99. What does that mean?
Answers
Parv has a $50 gift card he uses the gift card to buy a pack of games for 9. 99. He also wants to buy n movies. Each movie cost 3. 99. Which inequality describes how many movies part can buy?
Answers
The inequality that describes how many movies Parv can buy is: n ≤ 10.025
Let's denote the number of movies Parv wants to buy as n. We are given that each movie costs $3.99. To determine the inequality that describes how many movies Parv can buy, we need to consider the amount of money he has remaining after purchasing the pack of games.
Parv starts with a $50 gift card and spends $9.99 on a pack of games. The remaining amount on the gift card is $50 - $9.99 = $40.01.
Now, let's consider the cost of n movies. Each movie costs $3.99, so the total cost of n movies would be n * $3.99.
Since Parv wants to buy the movies using the remaining amount on his gift card, we can set up the inequality:
n * $3.99 ≤ $40.01
This inequality states that the total cost of n movies, represented by n * $3.99, must be less than or equal to the remaining amount on the gift card, which is $40.01.
Simplifying the inequality further, we have:
3.99n ≤ 40.01
Now, if we want to solve for n, we can divide both sides of the inequality by 3.99:
n ≤ 40.01 / 3.99
Calculating this value, we have:
n ≤ 10.02506265664
Therefore, the inequality that describes how many movies Parv can buy is:
n ≤ 10.025
This means that Parv can buy a maximum of 10 movies, as he cannot purchase a fractional part of a movie.
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b. Factorize using middle term break 3d2 - 16dc – 12c2
Answers
Step-by-step explanation:
Given
3d² - 16dc - 12c²
Using middle term break
= 3d² - (18 - 2 )dc - 12c²
= 3d² - 18dc - 2dc - 12c²
= 3d( d - 6c) - 2c( d - 6c)
= ( d - 6c) ( 3d - 2c)
Hope it helps and have a great day onwards ❤
Answer:
= 3d² - (18 - 2 )dc - 12c²
= 3d² - 18dc - 2dc - 12c²
= 3d( d - 6c) - 2c( d - 6c)
= ( d - 6c) ( 3d - 2c)
Step-by-step explanation:
if y varies directly as x and y=7 when x=3 , find y when x=7
Answers
By Direct Variation, value of y is 49/3.
What is Direct Variation?
When two variables are related in a way that one is a constant multiple of the other, this is referred to as direct variation. They are said to be in proportion, for instance, when one variable affects the other. The equation has the form b = ka if b is directly proportional to a. (where k is a constant).
Direct variation, by definition, has the form shown below:
y=kx
Where k is the constant of proportionality.
Given the information in the problem , you can find k
7 = 3K
K = 7/3
Now you can find y when x=7 as following:
y = (7/3)x
Substitute values. Then:
y = ( 7*7)/3
y = 49/3
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If you like hot weather, would you rahter go to a majorca in august,where the average temperature is 80 f , or to rome where the average temperature is 27 c use the formula c = 5(f- 32) divided by 9
Answers
Since I like hot weather, I would rather go to Rome with a temperature 27-degree c than to Majorca with an average temperature of 80F.
How do you Convert from Degree to Farhenhite and Vice versa?The temperature is converted from Celsius to Fahrenheit using this formula. Scales of temperature offer a means of determining how warm or frigid a body is. Temperature scales include Celsius and Fahrenheit. The Formula of celsius to Farhenhite is F= 9/5×C+ 32.
To compare the temperatures of both the places, we will first convert them to similar Units so that the comparison becomes easy. We will Change both the units to the Farhenhite unit as follows.
The temperature of Rome:
F = 9/5×27+32
F= 80.6
Therefore the temperature of Majorca is 80F and that of Rome is 80.6. More temperature means more hot weather. Therefore Roma will be hotter in August than Majorca.
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In Manchester, 3 of the 18 radio stations play country music.
What is the probability that a randomly selected station will play country music?
Write your answer as a fraction or whole number.
P(country) =
Answers
Answer:
There is a one in six chance that a randomly selected radio plays country music.
Step-by-step explanation:
There is a 3/18 chance but that can be simplified if you divide both sides by 3 to get 1/6
Iris's checking account pays simple interest at 4% per year. She has $180 in her account. Write a linear function to model the amount of money in her checking account at any time t.
A(t)=
Answers
The amount of money in Iris's checking account can be modeled by a linear function of the form:
y = mt + b
where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.
In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:
y = 0.04t + 180
For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.
Need help with this question
Answers
the first is 1 and the second is -4
Russel has a biased coin for the which the probability of getting tails is an unknown p. He decide to flip the coin n and writes the total number of times X he gets tails. How large should n be in order to know with at least 0.95 certainty that the true p is within 0.1 of the estimate X/n ? What if he wants 0.99 certainty?
Answers
n should be a whole number, we round up to the nearest integer, giving n = 540. Therefore, if Russel wants 0.99 certainty, n should be at least 540.
To determine how large n should be in order to have a certain level of certainty about the true probability p, we can use the concept of confidence intervals.
For a binomial distribution, the estimate of the probability p is X/n, where X is the number of successes (in this case, the number of times tails is obtained) and n is the number of trials (the number of times the coin is flipped).
To find the confidence interval, we need to consider the standard error of the estimate. For a binomial distribution, the standard error is given by:
SE = sqrt(p(1-p)/n)
Since p is unknown, we can use a conservative estimate by assuming p = 0.5, which gives us the maximum standard error. So, SE = sqrt(0.5(1-0.5)/n) = sqrt(0.25/n) = 0.5/sqrt(n).
To ensure that the true p is within 0.1 of the estimate X/n with at least 0.95 certainty, we can set up the following inequality:
|p - X/n| ≤ 0.1
This inequality represents the desired margin of error. Rearranging the inequality, we have:
-0.1 ≤ p - X/n ≤ 0.1
Since p is unknown, we can replace it with X/n to get:
-0.1 ≤ X/n - X/n ≤ 0.1
Simplifying, we have:
-0.1 ≤ 0 ≤ 0.1
Since 0 is within the range [-0.1, 0.1], we can say that the estimate X/n with a margin of error of 0.1 includes the true probability p with at least 0.95 certainty.
To find the value of n, we can set the margin of error equal to the standard error and solve for n:
0.1 = 0.5/sqrt(n)
Squaring both sides and rearranging, we get:
n = (0.5/0.1)^2 = 25
Therefore, n should be at least 25 to know with at least 0.95 certainty that the true p is within 0.1 of the estimate X/n.
If Russel wants 0.99 certainty, we need to find the value of n such that the margin of error is within 0.1:
0.1 = 2.33/sqrt(n)
Squaring both sides and rearranging, we get:
n = (2.33/0.1)^2 = 539.99
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Which expression is equivalent to (2)−3(4)0 ?
A = (12)×(12)×(12)×4
B= (12)×(12)×(12)×1
C= (−2)×(−2)×(−2)×1
D= (−2)×(−2)×(−2)×4
Answers
Answer:
if any number power of 0 is 1
so, (4)^0 =1
if any number power of -1 is equal to one divide this number.
like;
a^(-1) = 1/a
Therefore,
2^(-3) = 2^(-1) x 2^(-1) x 2^(-1)
= 1/2 x 1/2 x 1/2
Hence solution of 2^(-3). (4) ^0 is,
1/2 x 1/2 x 1/2 x 1
Find the distance between the points G(-5, 4)andH2, 6).The exact distance between the two points is
Answers
The formula to calculate the distance between two points in the cartesian plane is the following:
\(\begin{gathered} d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} \\ \end{gathered}\)replacing:
\(\begin{gathered} d=\sqrt{\left(2-(-5)\right)^2+\left(6-4\right)^2} \\ d=\sqrt{\left(7\right)^2+\left(2\right)^2} \\ d=\sqrt{49+4} \\ d=\sqrt{63} \\ d=7.94 \end{gathered}\)The distance between the two points is 7.94 units
PLEASEEEEEEEEEW HELPPPPPPPPPPPPPP PLEASEEEEEEEEEEEE I NEED THE ANSWERS RIGHT NOW SOMEONE PLEASEEE
using the expression x+3 write one equation that has one solution, one equation that has no solution, and one equation that has infinitely many solutions.
Answers
One solution:
y = 3x+2
y=2x+4
No solution:
y=3x+2
y=3x+1
Infinitely:
y=2x+4
y=4x+8
Answer:
One solution: x + 3 = 2x
No solution: x + 3 = x
Infinitely many solutions: x + 3 = 2 ( 0.5x + 1.5 )
Step-by-step explanation:
1 ) x + 3 = 2x
x = 3
2 ) x + 3 = x
No Solution...
3 ) x + 3 = 2 ( 0.5x + 1.5 )
\(x\) ∈ \(R\)
Hope this helps! :)
please help me im despreratei need help
Answers
Solve the compound inequality, graph the solution set, and write in interval notation. SHOW ALL STEPS! 6x - 3x + 12 or 5x – 6 > 3x + 2
Answers
Answer
- The solution of this compound inequality is x < 3 OR x ≥ 4
- The graph of this solution is attached below
- The interval notation is (-∞, 3) OR [4, ∞)
Explanation
The compound inequality to be solved is
6x - 3 < x + 12 OR 5x - 6 ≥ 3x + 2
To solve this, we solve each of the pair one at a time for the two-part solution
6x - 3 < x + 12
6x - x < 12 + 3
5x < 15
Divide both sides by 5
(5x/5) < (15/5)
x < 3
OR
5x - 6 ≥ 3x + 2
5x - 3x ≥ 6 + 2
2x ≥ 8
Divide both sides by 2
(2x/2) ≥ (8/2)
x ≥ 4
So, the solution is
x < 3 OR x ≥ 4
So, this solution says that x is less than 3, but greater than or equal to 4.
For the graph, Note that
In graphing inequality equations, the first thing to note is that whenever the equation to be graphed has (< or >), the circle at the beginning of the arrow is usually unshaded.
But whenever the inequality has either (≤ or ≥), the circle at the beginning of the arrow will be shaded.
This solution tells us that the wanted parts are numbers less than 3 and numbers greater than 4.
Also, in writing inequalities as interval, the signs (< or >) indicate an open interval and is written with the bracket () while the signs [≤ or ≥] denote a closed interval which is denoted by the brackets [].
x < 3, that is, x ranges from negative infinity to just before 3.
x < 3 is (-∞, 3)
x ≥ 4, that is, x ranges from 4 to infinity
x ≥ 4 is [4, ∞)
Hope this Helps!!!
PLSSS HELP!! (Determine the value of x.)
Answers
Answer:
X=4
Step-by-step explanation:
(2x-5)+(4x-1)=7x-10
2x-5+4x-1=7x-10
6x-6=7x-10
6x=7x-4
x=4
Suppose a parole board has to decide whether a prisoner, a convicted murderer, is to be released. The null hypothesis would state that the prisoner has not been rehabilitated. Which one of the following decisions and outcomes represents a Type I error? The prisoner is released and kills a family of five in cold blood within 48 hours. The prisoner is released and becomes a model citizen, The prisoner is denied release when in fact he has been totally rehabilitated The prisoner is denied release and continues to get into trouble within the prison and to spend time in solitary confinement
Answers
The decision and outcome that represents a Type I error in this scenario is if the prisoner is released and kills a family of five in cold blood within 48 hours. A Type I error occurs when the null hypothesis is rejected even though it is actually true. In this case, if the parole board releases the prisoner based on the hypothesis that they have been rehabilitated but in reality, they have not been rehabilitated, it would result in a Type I error. The prisoner's release would lead to a tragic outcome, which could have been avoided if the null hypothesis had not been rejected.
Learn more about Type I error here:
https://brainly.com/question/24320889
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I need all parts of 2) done. (a, b, c, and d.)
Answers
your equations for part a) are semi-correct, let's recall that the x-axis has the number of cows and y-axis is how long it takes.
if the setup for Wesly is 0.3 hours, then he takes 0.2(1) for one cow and for a second one is 0.2(2) and so on, that'll be 0.2x, and how long it takes will be "y".
so we're looking at
y = 0.3 + 0.2xy = 0.4 + 0.05xnow let's do part c)
\(\begin{cases}y=0.3+0.2x\\\\ y=0.4+0.05x \end{cases}\qquad \implies \stackrel{\textit{substituting on the 2nd equation}}{\underset{y}{0.3+0.2x}~~ = ~~0.4+0.05x} \\\\\\ 0.2x=0.1+0.05x\implies 0.15x=0.1\implies x=\cfrac{0.1}{0.15}\implies \boxed{x=\cfrac{2}{3}} \\\\\\ \stackrel{\textit{substituting the 1st equation}}{y=0.3+0.2(\frac{2}{3})}\implies \boxed{y=\cfrac{13}{30}}\)
now le's do part b), Check the picture below.
now onto part d)
does it make any sense?
well, let's look at the picture, with the closeup
the blue line touches the red line and then it keeps on going UP, meaning, after they touch each other, it takes more hours on the blue line than it'd on the red line, so the red line takes less hours after that intersection, why's that?
well, the machine takes longer to setup, because he has to grab the mechanical pieces, put them together, assemble any parts, hook it up to the barn maybe, and so forth, however, once he's done with all that jazz, the machine can milk a cow in 0.05 of an hour, something he'd take 0.2 by himself, that machine is four times faster, hell yeah.
you can think of say hmm a tractor for plowing a land for say corn, same thing, it takes a while to setup maybe even weeks, but once is going it moves like a bee, plus it doesn't get tired, you simple give it some tune up and more gas and off you go.
I bet Wesley after milking about 5 cows, he's going to go watch Pokemon for a few to relax a bit, the machine won't.
