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3 years ago

Which is equivalent to √3/√8 when denominator is "rationalized"?

Mathematics

1 answer:

TEA [102]3 years ago

4 0

Step-by-step explanation:

$\dfrac{\sqrt3}{\sqrt8}=\dfrac{\sqrt3\cdot\sqrt2}{\sqrt8\cdot\sqrt2}=\dfrac{\sqrt{3\cdot2}}{\sqrt{8\cdot2}}=\dfrac{\sqrt6}{\sqrt{16}}=\dfrac{\sqrt6}{4}$

$\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{a}=b\iff b^2=a\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\\sqrt{16}=4\ \text{because}\ 4^2=16$

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Given each scenario, identify an appropriate type of chart or plot that you would use to determine the answer. (e.g. pie chart,

satela [25.4K]

Answer:

a) dot plot

b) scatter plot

c) bar graph

d) scatter plot

e) histogram

f) pie chart

g) pie chart

Step-by-step explanation:

a) Cholesterol level for 100 males is observed, there is no grouping of people based on different range of cholesterol level, so the best chart for this dataset of 100 males will be a dot plot that shows all the 100 men’s cholesterol level on the chart and helping in depicting the trend as well.

b) For correlation of two factors the best graph is the scatter plot. If the direction of scatters is from lower left to upper right, then the relation is positive. But if the direction of the scatter points is from upper left to lower right then the relation is negative. Thus the best graph for it is scatter plot

c) A bar graph helps to plot the years on the x axis and the harvest on the y axis. A bar for each year is plotted and the length of the bar helps identify the value of yearly harvest.

d) For correlation of two factors the best graph is scatter plot. If the direction of scatters is from lower left to upper right, then the relation is positive. But if the direction of the scatter points is from upper left to lower right then the relation is negative.

Note: After question d) I have divided the questions into e), f) and g) as can be understood.

e) We want to understand the distribution of yearly household incomes in Tippecanoe County for 2012.

In order to understand the distribution of the household income a histogram can be used for the same. Continuous intervals of income can be formed. The bars of each range can be drawn and the distribution can be observed. If each range has same proportion of people the distribution is uniform, is it is lower at the extreme values and higher at the middle values then the distribution is normal and so on, such interpretations can be drawn from such a graph.

f) A poll of 200 undergraduates was taken. The respondents were asked to list all the modes of transportation used going from their home to campus.

Each mode of transportation can form one segment of pie chart. Thus pie chart helps in this kind of categorical data. Each segment size in the pie circle corresponds to the proportion of people in that segment.

g) What is the percentage of Indiana vehicles that are small passenger cars, large passenger cars, trucks, SUVs, and other types?

A pie chart can show the percent of each type of categories of cars. Each segment size in the pie circle corresponds to the proportion of people in that segment

Hope this helps!

3 0

2 years ago

Which is faster 15 feet per second or 12 miles per hour

Ierofanga [76]

12 miles per hour, it’ll be 17.6 feet per second.

6 0

2 years ago

Read 2 more answers

What is the inverse function of f(x)= 4- x/6

Westkost [7]

Answer:

$f^{-1}(x) = 6(4-x) = 24-6x$

Step-by-step explanation:

Let $y=f(x)$ and swap x and y:

$x = 4 - \frac{y}{6}$

Then, rearranging for y:

$x+\frac{y}{6} = 4$

$\frac{y}{6}= 4-x$

$y= 6(4-x) = 24-6x$

6 0

2 years ago

Aldos coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Aldo $4.15 per pound, and type of

bogdanovich [222]

Let A represent amount of Type A coffee pounds used.

Let B represent amount of Type B coffee pounds used

A + B = 156

B = 156 - A

A = 156 - B

5.80A + 4.65B = 826.60

580 (156 - B) + 4.65B - 826.60 = 0

904.8 - 5.80B + 4.65B - 826.60 = 0

904.8 - 1.15B - 826.60 = 0

78.2 - 1.15B = 0

78.2/1.15 = 1.15B/1.15

68 = B

B = 68 pounds of Type B coffee

There's many more steps you can take to check and etc but am too lazy to put down sorry.

3 0

2 years ago

Suppose that one person in 10,000 people has a rare genetic disease. There is an excellent test for the disease; 98.8% of the pe

nirvana33 [79]

Answer:

A)The probability that someone who tests positive has the disease is 0.9995

B)The probability that someone who tests negative does not have the disease is 0.99999

Step-by-step explanation:

Let D be the event that a person has a disease

Let $D^c$ be the event that a person don't have a disease

Let A be the event that a person is tested positive for that disease.

P(D|A) = Probability that someone has a disease given that he tests positive.

We are given that There is an excellent test for the disease; 98.8% of the people with the disease test positive

So, P(A|D)=probability that a person is tested positive given he has a disease = 0.988

We are also given that one person in 10,000 people has a rare genetic disease.

So, $P(D)=\frac{1}{10000}$

Only 0.4% of the people who don't have it test positive.

$P(A|D^c)$ = probability that a person is tested positive given he don't have a disease = 0.004

$P(D^c)=1-\frac{1}{10000}$

Formula: $P(D|A)=\frac{P(A|D)P(D)}{P(A|D)P(D^c)+P(A|D^c)P(D^c)}$

$P(D|A)=\frac{0.988 \times \frac{1}{10000}}{0.988 \times (1-\frac{1}{10000}))+0.004 \times (1-\frac{1}{10000})}$

P(D|A)= $\frac{2470}{2471}$ =0.9995

P(D|A)= $0.9995$

A)The probability that someone who tests positive has the disease is 0.9995

(B)

$P(D^c|A^c)$ =probability that someone does not have disease given that he tests negative

$P(A^c|D^c)$ =probability that a person tests negative given that he does not have disease =1-0.004

=0.996

$P(A^c|D)$ =probability that a person tests negative given that he has a disease =1-0.988=0.012

Formula: $P(D^c|A^c)=\frac{P(A^c|D^c)P(D^c)}{P(A^c|D^c)P(D^c)+P(A^c|D)P(D)}$

$P(D^c|A^c)=\frac{0.996 \times (1-\frac{1}{10000})}{0.996 \times (1-\frac{1}{10000})+0.012 \times \frac{1}{1000}}$

$P(D^c|A^c)=0.99999$

B)The probability that someone who tests negative does not have the disease is 0.99999

8 0

3 years ago