MATHEMATICS COLLEGE

Answer the following true or false. Justify your answer.(a) If A is a subset of B, and x∈B, then x∈A.
(b) The set {(x,y) ∈ R2 | x > 0 and x < 0} is empty.
(c) If A and B are square matrices, then AB is also square.
(d) A and B are subsets of a set S, then A∩B and A∪B are also subsets of S.
(e) For a matrix A, we define A^2 = AA.

Answers

Answer 1

Answer:

Answer:

a) False

b) True

c) True

d) True

e) True

Step-by-step explanation:

a) Consider the sets $B=\{1,2,3,4,5,6\}$ and $A=\{4,5,6\}$ . Observe that A is a subset of B and $1\in B$ but $1\notin A$

b) Any number different of 0 can be positive and negative simultaneusly. Then doesn't exist $x\in\mathbb{R}$ such that $x<0 and x>0$ . Then the set $\{(x,y) \in \mathbb{R}^2 | x > 0\; \text{and}\; x < 0}$ is empty.

c) If the multiplication AB is defined and A and B are square matrices with A of size nxn, then B is the size nxn and the matrix AB is the size nxn.

d) Let A and B subsets of a set S. Since each element of A and B are in S then each element of $A\cup B$ is in S. Also, if $x\in A\cap B$ , the $x\in A\subset S$ and $x\in B\subset S$ then $x\in S$ . This shows that $A\cap B \subset S$ .

e) By definition AA=A^2

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The data set shows the number of practice free throws players in a basketball competition made and the number of free throws they made in a timed competition.Practice throws 312 614 2 710 8Free throws 10 22 9 35 4 11 28 20A. Use technology to find the equation AND coefficient of determination for each type of regression model. Use the number of practice throws for the input variable and the number of free throws for the output variable. Round all decimal values to three places. Equation of regression modelCoefficient of determinationLinear model Quadratic model Exponential model B. EXPLAIN, using the information you found above, which model best fits the data set. How did you come to your conclusion?Note: write exponents like this x^2 if you need to.

Answers

Let

x -----> number of practice throws

y -----> the number of free throws

Part A

Linear Model

Using a Linear Regression Calculator

we have

ŷ = 2.352X - 0.852

see the attached figure

Remember that

With linear regression, the coefficient of determination is equal to the square of the correlation between the x and y variables

the coefficient r=0.919

Quadratic model

Using a Quadratic regression Calculator

we have

y=0.073x^2+1.205x+2.555

correlation coefficient r=0.925 ------> strong correlation

see the attached figure

Exponential model

Using an Exponential Regression Calculator

we have

y=4.229(1.17)^x

Correlation:r=0.913

see the attached figure

Part B

The model that best fits the data is the Quadratic model because its value of r is greater than the linear model and greater than the exponential model

suppose a ladder 20 feet long is placed against a vertical wall 20 feet high. How far would the top of the ladder move down the wall by pulling out the bottom of the ladder by 5 feet?

Answers

the ladder would now be 15 feet long

Solve the following equation for the given variable 3(x+6)=-9

Answers

Answer:

x = -9

Step-by-step explanation:

3(x+6)=-9

Divide each side by 3

3/3 *(x+6)=-9/3

x+6 = -3

Subtract 6 from each side

x+6-6 = -3-6

x = -9

Answer:

Step-by-step explanation:

so... 3(x+6)=-9

at 1st you do 3*x which is 3x then 3*6=18

all together is (3x+18)=-9

then get rid of brackets 3x+18=-9

after that take away 18 from both sides 3x+18=-9

-18 -18

which is 3x = -27

then you divide 3 in the both side

its going to be 3x = -27

3/3=1x or x then -27/3 = -9

so x = -9

Which of the following solutions are correct?

Answers

Answer:

A and C are the answer

Step-by-step explanation:

hope it helps bye!!

Select the scenario below that demonstrates sampling bias. Select the correct answer below: a) Justin wants to estimate the ethnic background distribution of residents of his town. He collects data from 1000 randomly selected town residents by using a random number generator.
b) To estimate the mean salary of professors at her university, Patricia collects data by recording the salaries of all professors included in 12 randomly selected departments.
c) Elizabeth wants to estimate the mean height of students at her school. She collects data by selecting a random group of students within her classroom.
d) To estimate the mean grade point average of students at her school, Annie collects data by recording the grade point average of every 25th student on the list of students after randomly selecting first student.

Answers

Answer:

(C) Elizabeth wants to estimate the mean height of students at her school. She collects data by selecting a random group of students within her classroom.

Step-by-step explanation:

In option C, the sample is an example of convenience sampling, It is not representative of the population of student being studied.

Convenience sampling is a type of non-probability sampling method in which the sample is taken from the part of the population easy to reach.

The sample are not chosen at random thereby undermining the ability to generalize the results from the sample to the entire population under study.

Which equation is a function?O A. X = -2
O B. Y= 2x – 9
O C. y² = x - 2
O D. x² + y² = 9

Answers

the answer is B -- no matter the x factor y should be single

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A fish tank has a base, B, with an area, in square inches, modeled by B(x) = 2x^2 + 6x + 4. The height, H, in inches, is modeled by H(x) = x + 3. Find the equation that models the fish tank’s volume, V, in cubic inches.A. V(x) = 2x^2 + 7x + 7B. V(x) = 2x^2 + 5x + 1C. V(x) = 2x^3 + 12x^2 + 22x + 12D. V(x) = 2x^3 + 8x^2 + 10x + 4

I BET YOU CANT SOLVE THIS...