1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andrews [41]
3 years ago
10

There are two mystery numbers. The sum of 7 times the first number and 5 times the second number is -11. The sum of 10 times the

first number and 8 times the second number is -20. What are the two numbers?
Mathematics
1 answer:
AlekseyPX3 years ago
8 0
First is 2, second is -5
You might be interested in
Two soccer teams play 8 games in their season. The number of goals each team scored per game is listed below: Team X: 11, 3, 0,
Gre4nikov [31]

Answer:

C. Team Y’s scores have a lower mean value.

Step-by-step explanation:

We are given that Two soccer teams play 8 games in their season. The number of goals each team scored per game is listed below:

Team X: 11, 3, 0, 0, 2, 0, 6, 4

Team Y: 4, 2, 0, 3, 2, 1, 6, 4

Firstly, we will calculate the mean, median, range and inter-quartile range for Team X;

Mean of Team X data is given by the following formula;

        Mean, \bar X =  \frac{\sum X}{n}

                       =  \frac{11+ 3+ 0+ 0+ 2+ 0+ 6+ 4}{8}  =  \frac{26}{8}  = 3.25

So, the mean of Team X's scores is 3.25.

Now, for calculating the median; we have to arrange the data in ascending order and then observe that the number of observations (n) in the data is even or odd.

Team X: 0, 0, 0, 2, 3, 4, 6, 11

  • If n is odd, then the formula for calculating median is given by;

                         Median  =  (\frac{n+1}{2} )^{th} \text{ obs.}

  • If n is even, then the formula for calculating median is given by;

                         Median  =  \frac{(\frac{n}{2})^{th} \text{ obs.} +(\frac{n}{2}+1)^{th} \text{ obs.}  }{2}

Here, the number of observations is even, i.e. n = 8.

So, Median =  \frac{(\frac{n}{2})^{th} \text{ obs.} +(\frac{n}{2}+1)^{th} \text{ obs.}  }{2}

                   =  \frac{(\frac{8}{2})^{th} \text{ obs.} +(\frac{8}{2}+1)^{th} \text{ obs.}  }{2}

                   =  \frac{(4)^{th} \text{ obs.} +(5)^{th} \text{ obs.}  }{2}

                   =  \frac{2+3}{2}  = 2.5

So, the median of Team X's score is 2.5.

Now, the range is calculated as the difference between the highest and the lowest value in our data.

               Range = Highest value - Lowest value

                           = 11 - 0 = 11

So, the range of Team X's score is 11.

Now, the inter-quartile range of the data is given by;

        Inter-quartile range = Q_3-Q_1

Q_1=(\frac{n+1}{4} )^{th} \text{ obs.}

     =  (\frac{8+1}{4} )^{th} \text{ obs.}

     =  (2.25 )^{th} \text{ obs.}

Q_1 = 2^{nd} \text{ obs.} + 0.25[ 3^{rd} \text{ obs.} -2^{nd} \text{ obs.} ]

     =  0 + 0.25[0 - 0] = 0

Q_3=3(\frac{n+1}{4} )^{th} \text{ obs.}

     =  3(\frac{8+1}{4} )^{th} \text{ obs.}

     =  (6.75 )^{th} \text{ obs.}

Q_3 = 6^{th} \text{ obs.} + 0.75[ 7^{th} \text{ obs.} -6^{th} \text{ obs.} ]

     =  4 + 0.75[6 - 4] = 5.5

So, the inter-quartile range of Team X's score is (5.5 - 0) = 5.5.

<u>Now, we will calculate the mean, median, range and inter-quartile range for Team Y;</u>

Mean of Team Y data is given by the following formula;

        Mean, \bar Y =  \frac{\sum Y}{n}

                       =  \frac{4+ 2+ 0+ 3+ 2+ 1+ 6+ 4}{8}  =  \frac{22}{8}  = 2.75

So, the mean of Team Y's scores is 2.75.

Now, for calculating the median; we have to arrange the data in ascending order and then observe that the number of observations (n) in the data is even or odd.

Team Y: 0, 1, 2, 2, 3, 4, 4, 6

  • If n is odd, then the formula for calculating median is given by;

                         Median  =  (\frac{n+1}{2} )^{th} \text{ obs.}

  • If n is even, then the formula for calculating median is given by;

                         Median  =  \frac{(\frac{n}{2})^{th} \text{ obs.} +(\frac{n}{2}+1)^{th} \text{ obs.}  }{2}

Here, the number of observations is even, i.e. n = 8.

So, Median =  \frac{(\frac{n}{2})^{th} \text{ obs.} +(\frac{n}{2}+1)^{th} \text{ obs.}  }{2}

                   =  \frac{(\frac{8}{2})^{th} \text{ obs.} +(\frac{8}{2}+1)^{th} \text{ obs.}  }{2}

                   =  \frac{(4)^{th} \text{ obs.} +(5)^{th} \text{ obs.}  }{2}

                   =  \frac{2+3}{2}  = 2.5

So, the median of Team Y's score is 2.5.

Now, the range is calculated as the difference between the highest and the lowest value in our data.

               Range = Highest value - Lowest value

                           = 6 - 0 = 6

So, the range of Team Y's score is 6.

Now, the inter-quartile range of the data is given by;

        Inter-quartile range = Q_3-Q_1

Q_1=(\frac{n+1}{4} )^{th} \text{ obs.}

     =  (\frac{8+1}{4} )^{th} \text{ obs.}

     =  (2.25 )^{th} \text{ obs.}

Q_1 = 2^{nd} \text{ obs.} + 0.25[ 3^{rd} \text{ obs.} -2^{nd} \text{ obs.} ]

     =  1 + 0.25[2 - 1] = 1.25

Q_3=3(\frac{n+1}{4} )^{th} \text{ obs.}

     =  3(\frac{8+1}{4} )^{th} \text{ obs.}

     =  (6.75 )^{th} \text{ obs.}

Q_3 = 6^{th} \text{ obs.} + 0.75[ 7^{th} \text{ obs.} -6^{th} \text{ obs.} ]

     =  4 + 0.75[4 - 4] = 4

So, the inter-quartile range of Team Y's score is (4 - 1.25) = 2.75.

Hence, the correct statement is:

C. Team Y’s scores have a lower mean value.

4 0
3 years ago
Make Q the subject of the formula A = Q2 - 2a.
son4ous [18]

Answer:

\huge\boxed{Q = \sqrt{A+2a}}

Step-by-step explanation:

A = Q^2 -2a

Adding 2a to both sides

Q^2 = A+2a

Taking sqrt on both sides

Q = \sqrt{A+2a}

8 0
3 years ago
The measure of the missing angle is ?
Cerrena [4.2K]
X = 97

Working on other question.
3 0
3 years ago
The coordinate below represents a town. Curtis’s house is at (-4, -6) and Jean’s house is at (-4, 3).Plot the points where Curti
Fiesta28 [93]

It would take Curtis 45 minutes to ride his bike to Jean's house.

7 0
3 years ago
What is the solution of the system of linear equations below?
Kipish [7]

Answer:

A is the correct answer

Step-by-step explanation:

To get the fastest answer for these kind of questions, you just have to apply (0, -2) into either one of the 2 equations:

2 * 0 - 6 * (-2) = 12

0 - (-12) =12

0 + 12 = 12  (TRUE)

So the solution will be (0, -2)

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is the answer to this problem
    13·1 answer
  • Using V = lwh , find an expression in factored form for the volume of this prism. Explain the general steps you used to arrive a
    11·2 answers
  • A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 29 ft/s. Its height
    12·1 answer
  • Please do them both​
    11·1 answer
  • Please help!!
    7·1 answer
  • Is 12 a prime or composite number? And why?.
    5·2 answers
  • PLEASE HELP ME QUICK DUDES!!
    11·1 answer
  • Sydney is building a doghouse. The house will be 3 and one-half feet tall. How
    7·2 answers
  • Help!!!<br> I will mark the person who answers with an actual answer brainliest<br> Due soon
    10·2 answers
  • If log x+y/5 = 1/2(log x + log y) the find the value of x/y + y/x ?​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!