true - A statement that can be proven formally from the axioms

(10+x)-y=10+(x-y)

Removing the parentheses since there is nothing to distribute, we have:
10 + x - y = 10 + x - y
This is true!

3 is a factor of 18 true or false

3 is a factor of 18 true or false
We go to our math engine and type in [URL='https://www.mathcelebrity.com/factoriz.php?num=18&pl=Show+Factorization']factors of 18[/URL] and we see that 3 is a factor of 18, so our answer is [B]TRUE.[/B]

30 people are selected randomly from a certain town. If their mean age is 60.5 and ? = 4.6, find a 9

30 people are selected randomly from a certain town. If their mean age is 60.5 and ? = 4.6, find a
95% confidence interval for the true mean age, ?, of everyone in the town.

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 poin

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?
Let's call the 5 point questions m for multiple choice. Let's call the 2 point questions t for true-false. We have two equations:
[LIST=1]
[*]m + t = 38
[*]5m + 2t = 100
[/LIST]
Rearrange (1) to solve for m - subtract t from each side:
3. m = 38 - t
Now, substitute (3) into (2)
5(38 - t) + 2t = 100
190 - 5t + 2t = 100
Combine like terms:
190 - 3t = 100
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=190-3t%3D100&pl=Solve']equation solver[/URL], we get [B]t = 30[/B].
Plugging t = 30 into (1), we get:
30 + t = 38
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=m%2B30%3D38&pl=Solve']equation solver[/URL] again, we get [B]m = 8[/B].
Check our work for (1)
8 + 30 = 38 <-- Check
Check our work for (2)
5(8) + 2(30) ? 100
40 + 60 ? 100
100 = 100 <-- Check
You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+38&term2=5m+%2B+2t+%3D+100&pl=Cramers+Method']simultaneous equations calculator[/URL]

A test has three true-false questions. Find the total number of ways you can answer the three questi

A test has three true-false questions. Find the total number of ways you can answer the three questions
We can either choose T or F. So we have:
Question 1: 2 choies
Question 2: 2 choices
Question 3: 2 choices
2 * 2 * 2 = [B]8 choices
[/B]
[LIST=1]
[*][B]TTT[/B]
[*][B]TTF[/B]
[*][B]TFT[/B]
[*][B]FTT[/B]
[*][B]FTF[/B]
[*][B]FFT[/B]
[*][B]TFF[/B]
[*][B]FFF[/B]
[/LIST]

A test has twenty questions worth 100 points . The test consist of true/false questions worth 3 poin

A test has twenty questions worth 100 points . The test consist of true/false questions worth 3 points each and multiple choice questions worth 11 points each . How many multiple choice questions are on the test?
Set up equations where t = true false and m = multiple choice:
[LIST=1]
[*]t + m = 20
[*]3t + 11m = 100
[/LIST]
Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=t+%2B+m+%3D+20&term2=3t+%2B+11m+%3D+100&pl=Cramers+Method']simultaneous equation calculator[/URL]:
[B]t = 15, m = 5[/B]

A test has twenty questions worth 100 points total. the test consists of true/false questions worth

A test has twenty questions worth 100 points total. the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many true/false questions are on the test?
Let m be the number of multiple choice questions and t be the number of true/false questions. We're given:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We can solve this system of equations 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the following answers:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]
Check our work in equation 1:
5 + 15 ? 20
[I]20 = 20[/I]
Check our work in equation 2:
11(5) + 3(15) ? 100
55 + 45 ? 100
[I]100 = 100[/I]

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 poin

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
Let the number of true/false questions be t. Let the number of multiple choice questions be m. We're given two equations:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We have a set of simultaneous equations. We can solve this using 3 methods:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we pick, we get the same answer:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]

A U ? = A

A U ? = A
Let x ? [I]S[/I], where [I]S[/I] is the universal set.
First we show that if A ? Ø ? A.
Let x ? A ? Ø.
Then x ? A or x ? Ø. by definition of the empty set, x cannot be an element in Ø.
So by assumption, x ? A ? Ø, x must be in A.
So A ? Ø ? A.
Next, we show that A ? A ? Ø.
This is true because the set resulting from the union of two sets contains both of the sets forms the union
Since A ? Ø ? A and A ? A ? Ø, we have that A ? Ø = A.

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants an

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants and recorded their vital statistics. Of the trapped elephants, 12 were female. If that rate holds true for the entire population of 180 elephants, how many female elephants are on the wildlife reserve?
Set up a proportion of female to trapped elephants:
12/60 = f/180
Using our [URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=f&den1=60&den2=180&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that f = [B]36[/B]

A young dad, who was a star football player in college, set up a miniature football field for his fi

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true?
The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway.
Imagine a third post midway between the two goal posts. It has the same height as the two goalposts.
From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

All squares are rectangles and all rectangles are parallelograms, therefore all squares are parallel

All squares are rectangles and all rectangles are parallelograms, therefore all squares are parallelograms. Is this true?
[B]Yes.[/B]
This is similar to A implies B and B implies C so A implies C also known as transitive property

are all integers whole numbers true or false

are all integers whole numbers true or false
[B]False
[/B]
[LIST]
[*]All whole numbers are integers but not all integers are whole numbers.
[*]Whole numbers are positive integers. Which means negative integers are not whole numbers
[*]-1 for instance is an integer, but not a whole number
[/LIST]

Assume that you make random guesses for 5 true-or-false questions

Assume that you make random guesses for 5 true-or-false questions.
(a) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form)
(b) What is the probability of getting the correct answer in the 5th question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form)
(c) If event A is “Getting the correct answer in the 5th question” and event B is “The first four answers are all wrong”. Are event A and event B independent? Please explain.
(a) Correct Answer on each one is 1/2 or 0.5. Since all are independent events, we have:
(1/2)^5 = [B]1/32[/B]
(b) We have [B]1/2[/B]
(1/2)^4 * 1/2/((1/2)^4)
c) [B]Independent since you could have gotten correct or wrong on any of the 4 and the probability does not change[/B]

C is the midpoint of BD then BC congruent CD

C is the midpoint of BD then BC congruent CD
[URL='https://www.mathcelebrity.com/proofs.php?num=cisthemidpointofbd&pl=Prove']True using this proof[/URL]

Congruence Modulo n

Given a possible congruence relation a ≡ b (mod n), this determines if the relation holds true (b is congruent to c modulo n).

cscx-cotx*cosx=sinx

cscx-cotx*cosx=sinx
A few transformations we can make based on trig identities:
[LIST]
[*]csc(x) = 1/sin(x)
[*]cot(x) = cos(x)/sin(x)
[/LIST]
So we have:
1/sin(x) - cos(x)/sin(x) * cos(x) = sin(x)
(1 - cos^2(x))/sin(x) = sin(x)
1 - cos^2(x) = sin^2(x)
This is [B]true[/B] from the identity:
sin^2(x) - cos^2(x) = 1

cscx/secx =cotx

cscx/secx =cotx
This is [B]true[/B]
Remember that:
csc(x) = 1/sin(x)
sec(x) = 1/cos(x)
So we have:
1/sin(x)/1/cos(x)
cos(x)/sin(x)
cot(x)

Determine if the statement below is True or False

Determine if the statement below is True or False
If B ? A, then A ? B = B
Is this statement True or False?
[B]True:[/B] If B ? A, then B ? A
So A ? B is the similar elements of both. B contains itself as a subset.
So this is [U]true[/U]

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b
We have a logarithmic property that states:
ln(a) - ln(b) = ln (a / b)
We're given a < b, so (a / b) < 1
Therefore:
ln (a / b) < 0
And since ln(a) - ln(b) = ln (a / b)
Then Ln(a) - Ln(b) < 0
So this is [B]TRUE[/B]

Determine whether the statement is true or false. If y = e^2, then y’ = 2e

Determine whether the statement is true or false. If y = e^2, then y’ = 2e
e^2 is a constant, and the derivative of a constant is 0. So y' = 0
So this is [B]FALSE[/B]

Determine whether the statement is true or false. You can always divide by e^x

Determine whether the statement is true or false. You can always divide by e^x
[B]True. As x --> infinity, 1/e^x approaches 0 but never touches it.[/B]

Does (6,5) make the equation y = x true

Does (6,5) make the equation y = x true
x =6 and y = 5, so we have:
5 = 6 which is [B]false. So no[/B], it does not make the equation True.

If (a - b)/b = 3/7, which of the following must also be true?

If (a - b)/b = 3/7, which of the following must also be true?
A) a/b = -4/7
B) a/b = 10/7
C) (a + b)/b = 10/7
D) (a - 2b)/b = -11/7
We can rewrite (a - b)/b as:
a/b - b/b = 3/7
Since b/b = 1, we have:
a/b - 1 = 3/7
Since -1 = -7/7, we have:
a/b - 7/7 = 3/7
Add 7/7 to each side:
a/b - 7/7 + 7/7 = 3/7 + 7/7
Cancel the 7/7 on the left side, we get:
[B]a/b = 10/7 or Answer B[/B]

If all A's are B's, then all B's are A's. Is this true?

If all A's are B's, then all B's are A's. Is this true?
[B]No.[/B]
Example:
All dogs are mammals, but not all mammals are dogs.
All squares are rectangles, but not all rectangles are squares.

If n is odd, then 3n + 2 is odd

Look at the Contrapositive: If n is even, then 3n + 2 is even...
Suppose that the conclusion is false, i.e., that n is even.
Then n = 2k for some integer k.
Then we have:
3n + 2 = 3(2k) + 2
3n + 2 = 6k + 2
3n + 2 = 2(3k + 1).
Thus 3n + 2 is even, because it equals 2j for an integer j = 3k + 1.
So 3n + 2 is not odd.
We have shown that ¬(n is odd) ? ¬(3n + 2 is odd),
therefore, the contrapositive (3n + 2 is odd) ? (n is odd) is also true.

if p=2x is even, then p^2 is also even

if p=2x is even, then p^2 is also even
p^2 = 2 * 2 * x^2
p^2 = 4x^2
This is [B]true [/B]because:
[LIST]
[*]If x is even, then x^2 is even since two evens multiplied by each other is even and 4x^2 is even
[*]If x is odd, the x^2 is odd, but 4 times the odd number is always even since even times odd is even
[/LIST]

if two angles are supplementary and congruent then they are right angles

if two angles are supplementary and congruent then they are right angles
Let the first angle be x. Let the second angle be y.
Supplementary angles means their sum is 180:
x + y = 180
We're given both angles are congruent, meaning equal. So we set x = y:
y + y = 180
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/B]

In simple linear regression the slope and the correlation coefficient will have the same signs True

In simple linear regression the slope and the correlation coefficient will have the same signs
True
False
[B]FALSE[/B] - Only if they are normalized

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
At least means greater than or equal to, so we have:
[B]3x + 4y >= 76[/B]

Madeline’s science quiz consists of 10 questions, all of which are true or false. How many different

Madeline’s science quiz consists of 10 questions, all of which are true or false. How many different choices for answering the 10 questions are possible?
2 ways of answering each True or False Question ^ (10 different ways to answer each question)
2^10 = [B]1,024 ways[/B]

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the pho

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test, [U][B]the Type I error is[/B][/U]:
a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher [B]b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same [/B] [I]A Type I error is when you reject the null hypothesis when it is in fact true[/I]

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher [B]b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same [/B] [I]A Type I error is when you reject the null hypothesis when it is in fact true[/I]

Prove 0! = 1

Prove 0! = 1
Let n be a whole number, where n! represents the product of n and all integers below it through 1.
The factorial formula for n is:
n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1
Written in partially expanded form, n! is:
n! = n * (n - 1)!
[U]Substitute n = 1 into this expression:[/U]
n! = n * (n - 1)!
1! = 1 * (1 - 1)!
1! = 1 * (0)!
For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! <> 1 which contradicts the equation above

Six is the principal square root of 36

Six is the principal square root of 36
The two square roots of 36 are:
[LIST]
[*]+6
[*]-6
[/LIST]
The positive square root is known as the principal square root, therefore, this is [B]true[/B].

Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the

Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then.
(a) Which of the following is the hypothesis to be conducted?
A. H0: p = 0.122, H1 p > 0.122
B. H0: p = 0.122, H1 p <> 0.122
C. H0: p = 0.122, H1 p < 0.122
(b) Which of the following is a Type I error?
A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage.
c) Which of the following is a Type II error?
A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
(a) [B]C H0: p = 0.122, H1: p < 0.122[/B]
because a null hypothesis should take the opposite of what is being assumed. So the assumption is that nothing has changed while the hypothesis is that the rate has decreased.
(b) [B]C.[/B] The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. Type I Error is rejecting the null hypothesis when it is true
c) [B]C.[/B] The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% Type II Error is accepting the null hypothesis when it is false.

The average of 16 and x is 21. Find x.

The average of 16 and x is 21. Find x.
The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have:
(16 + x)/2 = 21
Cross multiply:
16 + x = 21*2
16 + x = 42
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2Bx%3D42&pl=Solve']we type this expression into the search engine[/URL] and get [B]x = 26[/B].
Check our work by restating our answer:
The average of 16 and 26 is 21. TRUE.

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognit

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the bran. How many adults must he survey in order to be 90% confident that his estimate is within seven percentage points of the true population percentage?
[IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5
1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5
margin of error (E) = 0.07
At 90% confidence level the t is,
alpha = 1 - 90%
alpha = 1 - 0.90
alpha = 0.10
alpha / 2 = 0.10 / 2 = 0.05
Zalpha/2 = Z0.05 = 1.645
sample size = n = (Z[IMG]https://ci4.googleusercontent.com/proxy/mwhpkw3aM19oMNA4tbO_0OdMXEHt9juW214BnNpz4kjXubiVJgwolO7CLbmWXXoSVjDPE_T0CGeUxNungBjN=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Calpha[/IMG] / 2 / E )2 * [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] * (1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] )
= (1.645 / 0.07)^2 *0.5*0.5
23.5^2 * 0.5 * 0.5
552.25 * 0.5 * 0.5
= 138.06
[B]sample size = 138[/B]
[I]He must survey 138 adults in order to be 90% confident that his estimate is within seven percentage points of the true population percentage.[/I]

The circle has an arc measure of 180 degrees

The circle has an arc measure of 180 degrees - True or False.
False. A Circle has an arc measure of 360 degrees.
A few vital facts about arcs measures, also called central angles:
[LIST=1]
[*]An arc measure [I]< [/I]180° is a minor arc.
[*]An arc measure [I]> [/I]180° is a major arc.
[*]An arc measure [I]= [/I]180° is a semicircle.
[*]An arc measure [I]= 36[/I]0° is a circle.
[/LIST]

The coefficient of determination is found by taking the square root of the coefficient of correlatio

The coefficient of determination is found by taking the square root of the coefficient of correlation. True or False
[B]FALSE[/B] - It is found by squaring the coefficient of correlation

The negative of the sum of C and D is equal to the difference of the negative of C and D

The negative of the sum of C and D is equal to the difference of the negative of C and D
The negative of the sum of C and D means -1 times the sum of C and D
-(C + D)
Distribute the negative sign:
-C - D
the difference of the negative of C and D means we subtract D from negative C
-C - D
So this statement is [B]true[/B] since -C - D = -C - D

The set of all letters in the word true is

The set of all letters in the word true is:
We have [B]{t, r, u, e}[/B]

The square of a number is always nonnegative.

The square of a number is always nonnegative.
This is true, and here is why:
Suppose you have a positive number n.
n^2 = n * n
A positive times a positive is a positive
Suppose you have a negative number -n
(-n)^2 = -n * -n = n^2
A negative times a negative is a positive.

There are 10 true or false questions on a test. You do not know the answer to 4 of the questions, so

There are 10 true or false questions on a test. You do not know the answer to 4 of the questions, so you guess. What is the probability that you will get all 4 answers right?
Probability you guess right is 1/2 or 0.5.
Since each event is independent of the other events, we multiply 1/2 4 times:
1/2 * 1/2 * 1/2 * 1/2 = [B]1/16[/B]

True False Equations

Determines if a set of addition and subtraction of numbers on each side of an equation are equivalent.
Also known as true or false equations

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance

True or False
(a) The normal distribution curve is always symmetric to its mean.
(b) If the variance from a data set is zero, then all the observations in this data set are identical.
(c) P(A AND A^{c})=1, where A^{c} is the complement of A.
(d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis.
(e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.
[B](a) True, it's a bell curve symmetric about the mean
(b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical
(c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space.
(d) False, we have sufficient evidence to reject H0.
(e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

True or False: The standard deviation of the chi-square distribution is twice the mean.

True or False: The standard deviation of the chi-square distribution is twice the mean.
[B]False[/B], the variance is twice the mean. Mean is k, Variance is 2k

Unknown Number

Determines the unknown number needed to make an equation true.

Which of the following descriptions of null hypothesis are correct? (Select all that apply) a. A nu

Which of the following descriptions of null hypothesis are correct? (Select all that apply)
a. A null hypothesis is a hypothesis tested in significance testing.
b. The parameter of a null hypothesis is commonly 0.
c. The aim of all research is to prove the null hypothesis is true
d. Researchers can reject the null hypothesis if the P-value is above 0.05
[B]a. A null hypothesis is a hypothesis tested in significance testing.
[/B]
[I]b. is false because a parameter can be anything we choose it to be
c. is false because our aim is to disprove or fail to reject the null hypothesis
d. is false since a p-value [U]below[/U] 0.05 is often the rejection level.[/I]

Which of the following is NOT TRUE about the distribution for averages?

Which of the following is NOT TRUE about the distribution for averages?
a. The mean, median, and mode are equal.
b. The area under the curve is one.
c. The curve never touches the x-axis.
d. The curve is skewed to the right.
Answer is d, the curve is skewed to the right
For a normal distribution:
[LIST]
[*] The area under the curve for a standard normal distribution equals 1
[*] Mean media mode are equal
[*] Never touches the x-axis since in theory, all events have some probability of occuring
[/LIST]

You choose an alpha level of .01 and then analyze your data.

(a) What is the probability that

You choose an alpha level of .01 and then analyze your data.
(a) What is the probability that you will make a Type I error given that the null hypothesis is true?
(b) What is the probability that you will make a Type I error given that the null hypothesis is false.
[B](a) 0.01. Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B]
[B](b) Impossible Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B]

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the

You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the rest of the money to buy shirts. Find the inequality.
Let j be the number of jeans. Let s be the number of shirts. We are given:
[LIST]
[*]Mom told you to buy one pair of jeans. So we have $80 to start with - $29 for 1 pair of jeans = $51 left over
[/LIST]
Now, since shirts cost $12 each, and our total number of shirts we can buy is s, our inequality is [B]12s <= 51[/B].
We want to find the s that makes this inequality true.
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12s%3C%3D51&pl=Show+Interval+Notation']Run this statement through our calculator[/URL], and we get s <= 4.25. But, we need s to be an integer, so we have s <= 4.

___is the probability of a Type II error; and ___ is the probability of correctly rejecting a false

___is the probability of a Type II error; and ___ is the probability of correctly rejecting a false null hypothesis.
a. 1 - ?; ?
b. ?; 1 - ?;
c. ?; ?;
d. ?; ?
[B]b. ?; 1 - ?;[/B]
[LIST]
[*]H0 is true = Correct Decision 1 - ? Confidence Level = Size of a Test ? = Type I Error
[*]Ho is false = Type II Error ? = Correct Decision 1 - ? = Power of a Test
[/LIST]