MATHEMATICS
HIGH SCHOOL

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

Answer: Commutative property of multiplication is shown above. This is because no matter how you put them, the answer will still be 140.

Answer:

Answer:

B) Commutative property of multiplication

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COLLEGE

hompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 125 millimeters, and a variance of 49. If a random sample of 41 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 2.2 millimeters? Round your answer to four decimal places.

Answer:

So since we want the probability that "the sample mean would differ from the population mean by greater than 2.2 millimeters". Then we use the complement rule and we got

P=1-0.9558=0.0442

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:

Where and

And let represent the sample mean, the distribution for the sample mean is given by:

On this case

Solution to the problem

We can begin the problem finding this probability

We can use the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability on this way:

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

So since we want the probability that "the sample mean would differ from the population mean by greater than 2.2 millimeters". Then we use the complement rule and we got:

P=1-0.9558=0.0442

MIDDLE SCHOOL

What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)?

6x(x − 4) − 16x^2 − (9x − 1)

=6x^2 - 24x - 16x^2 - 9x + 1

= -10x^2 - 33x + 1

hope it helps

=6x^2 - 24x - 16x^2 - 9x + 1

= -10x^2 - 33x + 1

hope it helps

MIDDLE SCHOOL

What is 45 to 180 in simplest form

1/4's equivalent in lowest terms is 1/4.

HIGH SCHOOL

A card is drawn from a standard deck of 52 playing cards. Find the probability if the card is... A) an ace or heart

B) an even number or a spade

C) a red queen or black face card

D) a face card or a heart

A standard deck of 52 playing cards includes 13 of each of the 4 suits :

clubs , diamonds, hearts and spades.

Of these, the clubs and spades are black, and the hearts and diamonds are red.

Each of the 4 suits contains a King, a Queen, and a Jack (The face cards).

The Sample Space is the set of all possible outcomes in an experiment. Thus, the sample space in our problem is the set containing each of the 52 cards.

The number of this set, is denoted by n(S), and it is equal to 52.

If E is a certain event, then P(E)=n(E)/n(S).

A) E: an ace or heart, what is P(E)?

The event E can occur if any of the 13 hearts is drawn, or if any of the clubs ace , diamonds ace, or spades ace is drawn.

Thus, n(E)=13+3=16. That is, P(E)=n(E)/n(S)=16/52=0.308

B) E: an even number or a spade. P(E)=?

Event E can occur as follows:

Any spade is drawn, that is 13 cards. Or, any of the cards 2, 4, 6, 8, 10 of one of the clubs , diamonds, or hearts is drawn.

Thus, n(E)=13+5*3=13+15=28.

This means that P(E)=n(E)/n(S)=28/52=0.538

C) E: a red queen or black face card. P(E)=?

There are a total of 2*3=6 black face cards, and 2 red queens. This means that

n(E)=6+2=8.

Thus, P(E)=n(E)/n(S)=8/52=0.154

D) E: a face card or a heart. P(E)=?

There are a total of 13 heart cards, and 3*3=9 non heart, face cards.

Thus, n(E)=13+9=22.

This means that, P(E)=n(E)/n(S)=22/52=0.423

Answers:

A) 0.308

B) 0.538

C) 0.154

D) 0.423

clubs , diamonds, hearts and spades.

Of these, the clubs and spades are black, and the hearts and diamonds are red.

Each of the 4 suits contains a King, a Queen, and a Jack (The face cards).

The Sample Space is the set of all possible outcomes in an experiment. Thus, the sample space in our problem is the set containing each of the 52 cards.

The number of this set, is denoted by n(S), and it is equal to 52.

If E is a certain event, then P(E)=n(E)/n(S).

A) E: an ace or heart, what is P(E)?

The event E can occur if any of the 13 hearts is drawn, or if any of the clubs ace , diamonds ace, or spades ace is drawn.

Thus, n(E)=13+3=16. That is, P(E)=n(E)/n(S)=16/52=0.308

B) E: an even number or a spade. P(E)=?

Event E can occur as follows:

Any spade is drawn, that is 13 cards. Or, any of the cards 2, 4, 6, 8, 10 of one of the clubs , diamonds, or hearts is drawn.

Thus, n(E)=13+5*3=13+15=28.

This means that P(E)=n(E)/n(S)=28/52=0.538

C) E: a red queen or black face card. P(E)=?

There are a total of 2*3=6 black face cards, and 2 red queens. This means that

n(E)=6+2=8.

Thus, P(E)=n(E)/n(S)=8/52=0.154

D) E: a face card or a heart. P(E)=?

There are a total of 13 heart cards, and 3*3=9 non heart, face cards.

Thus, n(E)=13+9=22.

This means that, P(E)=n(E)/n(S)=22/52=0.423

Answers:

A) 0.308

B) 0.538

C) 0.154

D) 0.423

COLLEGE

A mixture contains 1/16 pound sand and 7/8 pound compost. At that rate, what amount of sand is needed if the mixture contains 1 pound of compost? A.

1/14

pound

B.

8/24

pound

C.

14 pounds

D.

15/16

pound

Answer:

A. ¹/₁₄ lb

Step-by-step explanation:

¹/₁₆ lb sand goes with ⅞ lb compost.

For 1 lb compost, the mass of sand needed is:

1 lb compost × (¹/₁₆ lb sand)/(⅞ lb compost).

We must evaluate the fraction (¹/₁₆)/(⅞).

Invert the denominator and multiply

(¹/₁₆)/(⅞) = ¹/₁₆ × ⁸/₇ Cancel the 8s

= ½ × ⅐ Multiply numerators and denominators

= ¹/₁₄

For 1 lb of compost, the mass of sand needed is ¹/₁₄ lb.

COLLEGE

A college administration has conducted a study of 224 randomly selected students to determine the relationship between satisfaction with academic advisement and academic success. They obtained the following information: Of the 79 students on academic probation, 42 are not satisfied with advisement; however, only 21 of the students not on academic probation are dissatisfied with advisement. What is the probability that a student selected at random is not onis not on academic probation and is not satisfied with advisement?

The probability that a student is not on probation is (224 - 79)/224 = 145/224.

The probability that a student who is not on probation is not satisfied with advisement is 21/145.

The required probability is therefore given by:

The answer is 3/32.

The probability that a student who is not on probation is not satisfied with advisement is 21/145.

The required probability is therefore given by:

The answer is 3/32.

MIDDLE SCHOOL

The system of equations is inconsistent. What are the missing values?

y=2/3x+3

y=__/__x+5

Y=2/3x+3

y=(z/t)x+5

so subsitute and solve

3/2x+3=(z/t)x+5

subtract 5 from both sides

3/2x-2=(z/t)x

divide both sides by x

3/2-2/x=z/t

so combine

3/2-2/x

3/2 times x/x-2/x times 2/2=3x/2x-4/2x=(3x-4)/2x

the values are (3x-4)/2x

y=(z/t)x+5

so subsitute and solve

3/2x+3=(z/t)x+5

subtract 5 from both sides

3/2x-2=(z/t)x

divide both sides by x

3/2-2/x=z/t

so combine

3/2-2/x

3/2 times x/x-2/x times 2/2=3x/2x-4/2x=(3x-4)/2x

the values are (3x-4)/2x

MIDDLE SCHOOL

A bag contains eleven red marbles, seven blue marbles, nine green marbles, and thirteen yellow marbles. Which of the following statements is not true? The theoretical probability of selecting a red marble from the bag is 27.5%. The odds of selecting a yellow marble from the bag are 13 to 27. The theoretical probability of selecting a blue or green marble from the bag is . The odds of selecting a red or blue marble are .

Disclaimer: The options were not given correctly so they are added here:

a. The theoretical probability of selecting a red marble from the bag is 27.5%.

b. The odds of selecting a yellow marble from the bag are 13 to 27.

c. The theoretical probability of selecting a blue or green marble from the bag is 2/3.

d. The odds of selecting a red or blue marble are 9/11.

Among the given statements, c. The theoretical probability of selecting a blue or green marble from the bag is 2/3. which is not true.

What is the probability of an event?The probability of an event is the fractional value determining how likely is that event to take place. If the event is denoted by A, the number of outcomes favoring the event A is n and the total number of outcomes is S, then the probability of the event A is given as:

P(A) = n/S.

What are the odds of a given event?When a given event suppose A, has a Probability of occurring = P(A) and Probability of not happening = 1 - P(A).

When we calculate the odds in favor of event A, the value is given by the ratio, P(A):(1 - P(A)).

When we calculate the odds against the event A, the value is given by the ratio, (1 - P(A)):P(A).

How do we solve the given question?We are informed that a bag contains eleven red marbles, seven blue marbles, nine green marbles, and thirteen yellow marbles.

Let the event of selecting a red marble from the bag be R.

Number of outcomes favoring R = 11 (number of red marbles)

Total number of outcomes = 40 (number of marbles in the bag)

∴ The probability of the event R is P(R) = 11/40

1 - P(R) = 1 - 11/40 = 29/40

Let the event of selecting a blue marble from the bag be B.

Number of outcomes favoring B = 7 (number of blue marbles)

Total number of outcomes = 40 (number of marbles in the bag)

∴ The probability of the event B is P(B) = 7/40

1 - P(B) = 1 - 7/40 = 33/40

Let the event of selecting a green marble from the bag be G.

Number of outcomes favoring G = 9 (number of green marbles)

Total number of outcomes = 40 (number of marbles in the bag)

∴ The probability of the event G is P(G) = 9/40

1 - P(G) = 1 - 9/40 = 31/40

Let the event of selecting a yellow marble from the bag be Y.

Number of outcomes favoring Y = 13 (number of yellow marbles)

Total number of outcomes = 40 (number of marbles in the bag)

∴ The probability of the event Y is P(Y) = 13/40

1 - P(y) = 1 - 13/40 = 27/40

Now, we analyze all the options, to check for the ones which are not true.

a. The theoretical probability of selecting a red marble from the bag is 27.5%.

The probability of selecting a red marble P(R) = 11/40 =11/40 * 100% = 27.5%, which is the same we are looking for.

∴ The statement is true.

b. The odds of selecting a yellow marble from the bag are 13 to 27.

The odds of selecting a yellow marble (odds in favor) = P(Y)/(1 - P(Y)) = 13/27 or 13 to 27, which is the value we are looking for.

∴ The statement is true.

c. The theoretical probability of selecting a blue or green marble from the bag is 2/3.

The probability of selecting a blue or green marble from the bag = P(B) + P(G) = 7/40 + 9/40 = 16/40 = 2/5, which is not the value we are looking for.

∴ The statement is not true.

d. The odds of selecting a red or blue marble are 9/11.

The probability of selecting a red or blue marble from the bag

P(R+B) = P(R) + P(B) = 11/40 + 7/40 = 18/40 = 9/20.

1 - P(R+B) = 1 - 9/20 = 11/20

∴ Odds of selecting a red or blue marble (odds in favor)

= P(R+B)/(1 - P(R+B)) = (9/20)/(11/20) = 9/11, which is the value we are looking for.

∴ The statement is true.

So, among the given statements, c. The theoretical probability of selecting a blue or green marble from the bag is 2/3. which is not true.

Learn more about the odds in favor and against at

brainly.com/question/14350753

#SPJ2

Answer: In total there are 40 marbles because 11+7+9+13=40

There are 7 Blue marbles, so

P(blue)=7/40

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COLLEGE

Six groups of students sell 162 balloons at the school carnival there are 3 students in each group if each student sells the same number of balloons how many. Balloons dose each student sell ?

Each student sells 9 balloons because 162 balloons divided by 6 groups of students is 27, and 27 divided by 3 students is 9 balloons.

They all sell nine each.