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anzhelika [568]
3 years ago
10

Show that each number is a rational number by expressing it as a ratio of two integers

Mathematics
1 answer:
kykrilka [37]3 years ago
8 0
The answer will be c 
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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
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The Martin family's truck gets an average of 33 miles per gallon. Predict how many miles they can drive using 3 gallons of gas.
igomit [66]

The Martin family can drive 99 miles using 3 gallons of gas

3 0
3 years ago
Please help, need asap
Debora [2.8K]

Answer:

Choice 2

Step-by-step explanation:

8 0
3 years ago
Explain why we use rulers instead of hands to measure things.
Snezhnost [94]
We use rulers obviously because the length of rulers are about 4 more times longer than hands. Hope this helps you :]
3 0
3 years ago
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the pairs of polynomials to their products.
andreyandreev [35.5K]

The products of the polynomials are:

  • (xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6
  • (2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²
  • (x - y) * (x + 3y) = x² + 2xy + 3y²
  • (xy + 3x + 2) * (xy – 9)  = x²y² - 7xy + 3x²y - 27x  - 18
  • (x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 7xy - 6
  • (x + 3y) * (x – 3y) = x² - 9y²

<h3>How to evaluate the products?</h3>

To do this, we multiply each pair of polynomial as follows:

<u>Pair 1: (xy + 9y + 2) and (xy – 3)</u>

(xy + 9y + 2) * (xy - 3)

Expand

(xy + 9y + 2) * (xy - 3) = x²y² - 3xy + 9xy² - 27y + 2xy - 6

Evaluate the like terms

(xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6

<u>Pair 2: (2xy + x + y) and (3xy² - y)</u>

(2xy + x + y) * (3xy² - y)

Expand

(2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²

<u>Pair 3: (x – y) and (x + 3y) </u>

(x - y) * (x + 3y)

Expand

(x - y) * (x + 3y) = x² + 3xy - yx + 3y²

Evaluate the like terms

(x - y) * (x + 3y) = x² + 2xy + 3y²

<u>Pair 4: (xy + 3x + 2) and (xy – 9) </u>

(xy + 3x + 2) * (xy – 9)

Expand

(xy + 3x + 2) * (xy – 9)  = x²y² - 9xy + 3x²y - 27x + 2xy - 18

Evaluate the like terms

(xy + 3x + 2) * (xy – 9)  = x²y² - 7xy + 3x²y - 27x  - 18

<u>Pair 5: (x² + 3xy - 2) and (xy + 3) </u>

(x² + 3xy - 2) * (xy + 3)

Expand

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 9xy - 2xy - 6

Evaluate the like terms

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 7xy - 6

<u>Pair 6: (x + 3y) and (x – 3y)</u>

(x + 3y) * (x – 3y)

Apply the difference of two squares

(x + 3y) * (x – 3y) = x² - 9y²

Read more about polynomials at:

brainly.com/question/4142886

#SPJ1

5 0
2 years ago
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