Which of the following describes the parabola with the equation y = 4x^2- 12x + 9?

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

Sienna shares half of a pizza equally among herself and 3 friends. What fraction of the whole pizza will each friend get? *

zhenek [66]

1/8

1/2 = 4/8
(4/8) / 4 = 1/8

6 0

2 years ago

There are five nickels, five dimes and five quarters in your pocket. You randomly pick three coins and place them on the counter

Goshia [24]

Answer:

The question is incomplete, this is the complete question.;

There are five nickels, five dimes and five quarters in your pocket. You randomly pick three coins and place them on the counter the first coin is a nickel, the second is a dime and the third is a quarter.find the probability of this occurring.

The answer to the question is;

the probability of this occurring is 1/27

Step-by-step explanation:

Let n(N) =5 ( the number of nickels)

n(D) =5 ( the number of dimes) and

n(Q) = 5 ( the number of quarters)

P(N)= 5/15=1/3 (prob of picking a nickel)

P(D) =5/15=1/3 (prob of picking a dime)

P(Q) = 5/15= 1/3 (prob of picking a quatre)

The probability of picking the three= P(N)×P(D)×P(Q)

= 1/3×1/3×1/3

= 1/27

7 0

3 years ago

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50Á, b

Gnesinka [82]

5580 if i did my math right thats the answer

4 0

2 years ago

Read 2 more answers

A plane flies 35 km in the direction n 30° w, then flies 60 km in the direction n 60° e. how far is the plane from its original

Kipish [7]

The distance of plane from the starting point is 69.46 km.

Given that the plane first flies 35 km in the direction N30W and then 60 km in the direction N60E.

We have to find the distance of plane from starting point.

We have to use pythagoras theorem in this which says that the square of hypotenuse is equal to sum of squares of the base and perpendicular.

$H^{2} =P^{2} +B^{2}$