Answer:
7.07
Step-by-step explanation:
Angle M is 63 degrees because all 3 angles must add to 180.
Now use the law of sines:
sin(90)/x = sin(63)/6.3
Cross multiply: 6.3 sin (90) = x sin (63)
Divide by sides by sin (63): (6.3 sin (90))/sin (63) = x
Use a calculator: 7.07
<span>1.
Given that a study uses statistical methods to conclude that there is an
association between the weights of cars and the amounts of fuel
consumption.
This means that the study established a correlation between </span><span>the weights of cars and the amounts of fuel
consumption.
But, </span>a<span><span> correlation between variables, however, does
not automatically mean that the change in one variable is the cause of
the change in the values of the other variable.
</span>
Therefore, the conclusion by the study that adding weight to a car is
what makes it consume more fuel is wrong because The conclusion is based on a correlation that implies causality.
</span><span>2.
Given that a recent government agency found that 89% of people that owned a car
were above the poverty line, while only 8% of people that did not own a
car were above the poverty line. They concluded that owning a car kept
people out of poverty and started a program to give cars to people below
the poverty line.
We can see that the problem with the study is
that the government agency automatically assumed that the correlation
between the variables implies causality.
</span><span>3.
Given that a government agency produced a study in which they randomly chose 100
students just beginning college to determine what percentage of students
who begin college graduate with a degree. After four years they
identified that 23 had dropped out of college, 45 had graduated, and 20
were still pursuing their degree.
Notice that the number of final sample is less than the number of the initial sample.
Therefore, What is wrong with this poll is that some of the sample data are missing.
</span>
<span>4.
Given that a shampoo company recently paid a consulting firm to produce a study to
determine if using their product resulted in cleaner hair than other
brands.
As can be noticed the study is based on the self interest of the shampoo company.
Therefore, the thing wrong with this study is that it is a self-interest study.
</span><span>5.
Given that a survey was recently quoted to support the news that the number of
trees in the United States is increasing. Upon further research it was
found that the survey was fully funded by a logging company.
As can be seen, the logging company funded the survey in other to justify their activities
Therefore, the problem with this survey is that it is a self-interest study.
</span>
<span>6.
Given that a radio station sent a letter in the mail to 1000 randomly chosen
residents within its broadcast area. The letter contained one dollar and
a survey. The survey asked recipients to track their radio habits over a
week. The survey was to be filled out and sent back in to the radio
station.
Here, the major problem with this study is the problem of non-response.
There
is every possibility that not all the mails will be delivered either
way.
Therefore, a problem with the study is that a nonresponse occurred.
</span><span>7.
Given that the fire department in California decided to take a poll to see if
residents would pay a monthly fee for their services. They polled 22
people in the state and concluded that residents were not willing to pay
a monthly fee.
As can be seen, a sample of 22 people is too small to refrect the views of the population of a state.
Therefore, what is wrong with this poll is that the conclusion is based on a small sample.
</span><span>8.
Given that a campaign manager created a survey to see if the candidate could be
elected into office. The survey randomly chose 1,832 voters and asked
them whom they would vote for. Of those surveyed, 953 people responded
that they would vote for the candidate. Because there are 87,403 voters
in the area, the results mean that 45,466 people would vote for this
candidate.
As can be seen, the surveyor concluded that a similar
proportion of voters responded that they would vote for
the candidate, would vote for his
candidate. This is a precise number and surveys do not usually result in
a presice number but in a proportion with an allowed margin of error.
Therefore, a problem with the study is that the result is a precise number.
</span>
<span>9.
Given that a hospital did a ten-year study on patients who used its services. One
thousand patients were randomly selected and followed over a period of
ten years to determine the average number of visits per year. By the end
of the ten year period some of the patients had left the area.
As
can be seen, because some of the patients had left the area, the
problem with the poll is that some of the sample data are missing.
</span><span>10.
Given that a city council had a proposal for a new traffic light at an
intersection that had a recent accident. The council decided to take a
poll of 284 randomly selected residents and asked if they would support
the construction. Of those polled, 219 stated that they would support
the new traffic light and 45 said they would not.
</span><span>Notice that the number of final sample is less than the number of the initial sample. (i.e. 219 + 45 = 264 which is less than 284)
Therefore, </span><span><span><span>the problem
with the study</span> is that some of the sample data are missing.</span></span>
Answer:
Step-by-step explanation:
If you factor the first one you get 
The 6x times 5 gives 30x, added to 30x, the middle term so it works.
For the 2nd one you know the factoring has to be 
so its easy to multiply to get 48x as the middle term.
