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2 years ago

Solve the following equation by completing the square

Mathematics

1 answer:

Ganezh [65]2 years ago

7 0

Answer is (x-1)and (x-2).First make the equation 3x^2- 9x+6=0. then divide both sides by 3 and then the two factors are (x-1)(x-2)

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The frequency distributions of two data sets are shown in the dot plots below.

fredd [130]

Answer:

1st, 4th and 6th statements are true.

Step-by-step explanation:

We have been given two dot-plots and we are asked to select all the true statements about given dot plots.

Let us write all the data points of both dot plots.

Data set 1:

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 7.

Data set 2:

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4.

1. The mean of data set 1 is greater than the mean of data set 2.

Let us find mean of both data sets.

$\text{Mean of data set 1}=\frac{1+1+1+1+1+2+2+2+2+2+2+2+2+3+3+3+4+4+7}{19}$

$\text{Mean of data set 1}=\frac{45}{19}$

$\text{Mean of data set 1}=2.3684\approx 2.37$

$\text{Mean of data set 2}=\frac{1+1+1+1+1+2+2+2+2+2+2+2+2+3+3+3+4+4}{18}$

$\text{Mean of data set 2}=\frac{38}{18}$

$\text{Mean of data set 2}=2.11$

We can see that mean of data set 1 is greater than mean of data set 2, therefore, 1st statement is true.

2. The mean of data set 1 is equal to the mean of data set 2.

Since mean of data set 1 is greater than mean of data set 2, therefore, 2nd statement is false.

3. The median of data set 1 is greater than the median of data set 2.

Since data set 1 has 19 data points, so median of data set 1 will be value of 10th data set, that is 2.

Our data set 2 has 18 data points, so median of data set 2 will be the average of 9th and 10th data points.

$\text{Median of data set 2}=\frac{2+2}{2}$

$\text{Median of data set 2}=\frac{4}{2}=2$

Since median of data set 2 is also 2, therefore, 3rd statement is not true.

4. The median of data set 1 is equal to the median of data set 2.

Since both data set's median is 2, therefore, 4th statement is true.

5. The standard deviation of data set 1 is smaller than the standard deviation of data set 2.

Using online SD calculator we get SD of data set 1 is 1.422 and SD of data set 2 is 0.936. Since 1.422 is greater than 0.936, therefore, 5th statement is false.

6. The data sets have the same interquartile range.

$Q_1\text{ of data set 1}=1$

$Q_3\text{ of data set 1}=3$

$\text{IQR of data set 1}=3-1=2$

$Q_1\text{ of data set 2}=1$

$Q_3\text{ of data set 2}=3$

$\text{IQR of data set 2}=3-1=2$

Since both data set's IQR is 2, therefore, 6th statement is true.

3 0

3 years ago

Read 2 more answers

Music Jeremy spent $33 on 3 CDs .At this a rate how much would 5 CDs cost

kvasek [131]

Question: Jeremy spent $33 on 3 CDs .At this a rate how much would 5 CDs cost?

Answer: I think the answer is 55$.

Hope this helps. c;

8 0

2 years ago

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A restaurant offered cooking classes on 24 of the 30 days in November. What decimal is equivalent to the fraction of days in Nov

zvonat [6]

Assuming they mean the fraction is 24/30 the answer is 0.8 (24÷30 is the equation to use)

3 0

2 years ago

Find the midpoint of the line segment whose endpoints are (2.6, 5.1) and (3, 4.7).

Tresset [83]

$(2.6, 5.1) \Rightarrow x_1=2.6,y_1=5.1
\\(3,4.7)\Rightarrow x_2=3,y_2=4.7
\\
\\x= \frac{x_1+x_2}{2}= \frac{2.6+3}{2}=2.8
\\
\\y= \frac{y_1+y_2}{2}= \frac{5.1+4.7}{2}=4.9
\\
\\M(2.8,4.9)
$

5 0

2 years ago

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What is 3248x9853 plezzzzzzzzzzz

DochEvi [55]

Answer: 32002544

Step-by-step explanation:

6 0

2 years ago