Work with a partner. Supercooling is the process of lowering the temperature
of a liquid or a gas below its freezing point without it becoming a solid. Water
can be supercooled to 86°F below its normal freezing point (32°F) and still
not freeze.

a. Let x represent the temperature of water. Which inequality represents the
temperature at which water can be a liquid or a gas? Explain your reasoning.

Answer:

  [-2, 2/5] ∪ [2, ∞)

Step-by-step explanation:

You want the solution to the inequality 7x³ -20x +11 ≥ 2x³ +2x² +3.

The inequality can be rewritten to a comparison with zero by subtracting the right-side expression.

  7x³ -20x +11 -(2x³ +2x² +3) ≥ 0

  5x³ -2x² -20x +8 ≥ 0 . . . . . . . simplify

  x²(5x -2) -4(5x -2) ≥ 0 . . . . . . factor pairs of terms

  (x² -4)(5x -2) ≥ 0 . . . . . . . . . . remove common factor

  (x -2)(5x -2)(x +2) ≥ 0 . . . . . factor difference of squares

The values of x that make this product equal to zero are

  x -2 = 0   ⇒   x = 2

  5x -2 = 0   ⇒   x = 2/5

  x +2 = 0   ⇒   x = -2

These x-intercepts divide the domain into 4 intervals where we need to check the sign.

From left to right:

(-∞, -2)

  Using x = -3, we find the product to be ...

  (-3 -2)(5(-3) -2)(-3 +2) = (-5)(-17)(-1) = -85, less than 0

[-2, 2/5]

  Using x = 0, we find the product to be ...

  (0 -2)(5·0 -2)(0 +2) = (-2)(-2)(2) = 8, part of the solution

(2/5, 2)

  Using x = 1, we find the product to be ...

  (1 -2)(5·1 -2)(1 +2) = (-1)(3)(3) = -9, less than 0

[2, ∞)

  Using x = 3, we find the product to be ...

  (3 -2)(5·3 -2)(3 +2) = (1)(13)(5) = 65, part of the solution

The solution to the inequality is [-2, 2/5] ∪ [2, ∞).

__

Additional comment

The function we're comparing to zero is a cubic with a positive leading coefficient. That means the general shape of its graph is /, negative on the left and positive on the right.

The graph changes sign at each of the zeros, so we already know the curve is positive between the left two x-intercepts, and to the right of the rightmost x-intercept. We just need to define the intervals so the zeros themselves are included in the solution set.

Answer:

12x^2.y^2 + 2xy - 2

Step-by-step explanation:

I put the dot so you don't get confused thinking it is 2y. Tell me if I misinterpreted the question

Answer:

C≈31.9

Step-by-step explanation:

By identifying all possible outcomes and the probability of each outcome the negotiation used here is Game theory.

The study of mathematical models of strategic interactions between rational beings is known as game theory and it has uses in computer science, logic, systems science, and all branches of social science.

The most well-known application of game theory is The Prisoner's Dilemma for instance take two offenders who were detained following an arrest as an example. The prosecution lacks concrete proof to prove their guilt. Officials, however, take the inmates out of their isolation cells and question each one separately in order to extract a confession.

The area of mathematics known as "game theory" is concerned with the analysis of such games. Classical game theory and combinatorial game theory are the two primary subfields of game theory. Traditional game theory examines games where participants can move, wager, or strategize all at once.

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Answer: $22.40

Step-by-step explanation:

30% of 32, or 0.3(32) is equal to 9.6. Then you have to subtract that amount, which is 32 - 9.6, which then gets us to 22.40.

Multipluy the equations i think...

Can 'r' be 0? No, because a cylinder wouldn't exist otherwise. Because a radius on Earth cannot be endlessly vast, the highest limit would be constrained. But it is hard to say what is excessive, so I'd probably just say that the domain is r > 0.

What do you mean by a domain?

The set of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this set. The collection of values that the function assumes is known as its range. Following the insertion of an x value, the function outputs this set of values. The domains of f(x)=x2 and g(x)=1/x, respectively, are all real numbers with the exception of x=0.

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The measure of angle QOB is  75°.

What is right angle?

90 degrees is the angle of a right.

The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol stands for a right angle.

Given:

Point O is the incenter of triangle ABC.

Lines are drawn from the points of the triangle to point O.

Lines are drawn from point O to the sides of the triangle to form right angles and line segments OQ, OR, and OS.

Angle OBC is 15 degrees. Angle OCR is 30 degrees.

OBC= 15

OCR =30

In OBQ

OBQ + QOB + OQB = 180

OBQ= OBC=15

OQB= 90

So,

QOB = 180- OBQ- OQB

= 180-15 -90

= 75

Hence, the measure of angle QOB is  75°.

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The answer is (a) Zimbardo did not use a control group.

The stanford prison experiment was a two week simulation of a prison environment that examined the effect of situational variables on participants reactions and behaviors.

The Stanford prison experiment, one of the most famous and compelling psychological studies of all time.

The major flaw in the research design of the Stanford prison experiment was that the Zimbardo did not use a control group.

A control group is used to establish a cause-and-effect relationship by isolating the effect of an independent variable. A control group was necessary to study a particular variable in prison. He had no alternative group to compare to measure the results of the experiment.

A control group in an experiment does not receive the treatment. Instead, it serves as a comparison group for the treatments.

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Answer:

(x+6)(x-)

Step-by-step explanation:

The factors by applying distributive property out the greatest common factor is 20(3 - 2y).

For the stated equation;

= 60 − 40 y

Do the prime factorization of the both numbers-

60 = 2×2×3×5

40 = 2×2×2×5

Thus, the greatest common factor from both numbers is-

2×2×5 = 20

Taking 20 common from both terms in equation-

Using distribute property;

= 20(3 - 2y)

Thus, factors by applying distributive property out the greatest common factor is 20(3 - 2y).

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Answer:

[tex]\textsf{D)} \quad 27x^3+33x^2-x -8[/tex]

Step-by-step explanation:

Given expression:

[tex](9x+8)(3x^2+x-1)[/tex]

Distribute the parentheses:

[tex]\implies 9x \cdot 3x^2+9x \cdot x+ 9x \cdot (-1) + 8 \cdot 3x^2 + 8 \cdot x +8 \cdot(-1)[/tex]

Simplify:

[tex]\implies 27x^3+9x^2-9x + 24x^2 + 8x -8[/tex]

Collect like terms:

[tex]\implies 27x^3+9x^2+ 24x^2-9x + 8x -8[/tex]

Combine like terms:

[tex]\implies 27x^3+33x^2-x -8[/tex]

Answer:

d= 24 + 9a

Step-by-step explanation:

– 9a – 12 = 12 – d

by collecting like terms

–9a +d = 12 +12

–9a +d = 24

d= 24 + 9a

Answer:

Step-by-step explanation:

-9a-12=12-d

d=9a+24

The purpose of accounts receivable confirmations is to obtain third-party verification of the account's balance and to determine how frequently misstatements take place.

Here,

Only a small portion of the entire population is often subject to accounts receivable confirmation. The confirmation's goals are to gain external confirmation of the account's balance and to get a sense of how frequently misstatements in the accounts occur.

The majority of errors revealed by discrepancies on the confirmation replies won't be significant; however, discrepancies must be examined individually and collectively to establish their impact on the total balance of accounts receivable.

Even while the discrepancies between individuals may not be significant, they could point to a significant issue with the internal controls over accounts receivable when applied to the entire population.

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The equation that can be solve to know the amount of tights needed is c = 20p.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the teacher orders 20 tights for the dance class and she buys as many as p tights as there are students.

The equation will be illustrated thus:

Let total amount be c

c = 20 × p

c = 20p

The equation is c = 20p.

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Complete question

A teacher orders 20 tights for the dance class. She buys as many as p tights as there are students. What equation can solve the amount of tights needed?

Answer:

This equation represents Plan 1, since it shows that the cost to join the plan is $30 and the cost for each bowling visit is $3.

Step-by-step explanation:

Answer: 3x + 30

Step-by-step explanation: the $3 fee depends on how many times joey goes bowling so it will be 3x + the flat $30 per month

In 609638400 ways eight men and five women can stand in a line so that no two women stand next to each other.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. There is no alternative way to organize the components of set A, as you can see.

In contrast to combination, where the order of the parts is irrelevant, permutation calls for a specific arrangement of the elements in many ways.

We genuinely wonder how the timetables of trains, buses, and airlines are set up in accordance with the convenience of the general population. Of course, the permutation is quite useful in planning the departure and arrival timetables for these.

How to solve?

For 8 men in a line: 8! = 40320  

In order to separate 2 women, we have to choose 5 out of 9

C(9,5) = 9! / 5!4! = 126

Random place 5 women in the 5 chosen places: 5! = 120

Total ways= 40320 * 126 * 120 = 609638400

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With any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, considering that n is 40:

n = 40 as a positive integer

Probability of not choosing any of the six ideal numbers in a lottery:

C(34 , 6)/C(40 , 6)

The likelihood of choosing none of the six correct integers in a lottery:

1344904/3838380

Probability of not winning a lottery with any of the six correct integers:

0.35

Therefore, with any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.

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Correct question:
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)

a) 0.40

b) 0.48

c) 0.56

d) 0.64

e) 0.35

The probability that the coin will come up heads on the fourth try is 1/2.

Given,

If a fair coin were tossed three times and each time it landed on its head.

We have to find the probability that it will come up heads on the fourth try;

Here,

Coming up short in the first three of four attempts.

The probability will not depend on the first three occurrences in the fourth try.

Consequently, the likelihood of winning the fourth time will be as follows:

Desired outputs as a percentage of overall output

=> 1 / 2

Hence,

The probability of the coming head in the fourth time is 1/2 because the coming head in the fourth time is independent of the coming head in the first three times.

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Answer: $16 dollars

Step-by-step explanation: 40% of 40 is 16 so you save $16. Game would now cost $24.

Jo's sum is easy   = (100)(101)/2  =  50 * 101   =  5050

Given,

In the question:

Jo adds up all the positive integers from 1 to 100. Kate does a similar thing with the first 100 positive integers.

She first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values.

To find the what is the positive difference between jo's sum and Kate's sum?

Now, According to the question:

Kate  would first start with 5  [ since 1 - 4 ]  are rounded to 0

Starting with 5 thru 14  she will have ten 10s

15 - 24   she will have  ten 20s

25 - 34 she will have  ten 30s

.

.

.

.

.

85 - 94 she will have ten 90s

95 - 100   she will have six 100s

So.....her sum is

10  [10  + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90]  + 6 [100]

10  [ (10) (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ] + 6[100]  

10 (10)  [  sum of the first nine positive integers ] + 6 [ 100]

100  [  (9)(10) / 2 ]  + 6[100]  

100 [ 45]  + 6[100]

100 [ 45 + 6 ]  

100 [ 51 ]

5100

Hence, The positive difference is 5100 - 5050  =  50

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Answer: 9

Step-by-step explanation:

Answer:

78 in²   (Choice B)

Step-by-step explanation:

Since they have exploded the 3-D cuboid into 2-D, it is easier to compute

Looking at the 2-D version you can see 4 rectangles each 3" x 5"

At the bottom on each side are 2 squares each 3" x 3"

Area of a rectangle = l x w

In this case, area of each rectangle = 3 x 5 = 15

Since there are 4 rectangles, total area of these four = 4 x 15 = 60 in²

Each square is area 3" x 3" = 9"

Since there are 2 such squares, total area of these two = 9 x 2 = 18in²

Total area of the 2-D blowup which is the same as the Surface Area of the prism = 60 in² +  18in² = 78 in²

In Coralbank $ 1,359,468.19 and In Bank of Munich $ 1,240,088.97

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

Given:

Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.

So, After 15 years

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P[tex](1 + r/n)^{nt[/tex]

A = 500,000.00[tex](1 + 0.03/1)^{(1)(15)[/tex]

A = 500,000.00[tex](1 + 0.03)^{(15)[/tex]

A = $778,983.71

and, for Another $500,000

A = P[tex](1 + r/n)^{nt[/tex]

A = 500,000.00 [tex](1 + 0.00/1)^{(1)(15)[/tex]

A = 500,000.00 [tex](1 + 0.01/1)^{(1)(15)[/tex]

A = $580,484.48

Total he Invests= $ 1,359,468.19

and, Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.

Then solve the equation for A

r = R/100

r = 2/100

r = 0.02 rate per year,

Then solve the equation for A

A = P[tex](1 + r/n)^{nt[/tex]

A = 250,000.00[tex](1 + 0.02/1)^{(1)(15)[/tex]

A = 250,000.00 [tex](1 + 0.02)^{(15)[/tex]

A = $336,467.08

and, for Another $750,000 .

A = P[tex](1 + r/n)^{nt[/tex]

A = 750,000.00[tex](1 + 0.0125/1)^{(1)(15)[/tex]

A = 750,000.00 [tex](1 + 0.0125)^{(15)[/tex]

A = $903,621.89

Total he Invests= $ 1,240,088.97

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Answer:09.8990

Step-by-step explanation: take one and add

The probability that the marksman will hit the target 13 times is 0.279.

Here, we are given that the probability that a marksman will hit a target each time he shoots is 0.89.

Thus, the probability that he will not hit the target = 1 - 0.89 = 0.11

Here, we can use the concept of binomial distribution to find the probability.

There are a total number of 15 trials, thus, n = 15

Success ⇒ marksman hits the target

Probability of success ⇒ p = 0.89

Failure ⇒ marksman fails to hit the target

Probability of failure ⇒ q = 0.11

Number of successful outcomes required ⇒ x = 13

Now, according to the formula for calculating binomial probability-

P(x) = [tex]nCx *p^{x} *q^{n-x}[/tex]

P(x) = [tex]15!/(13!*2!) *(0.89)^{13} *(0.11)^{2}[/tex]

P(x) = (15*14/2) (0.2198) (0.0121)

P(x) = 105* 0.0026

P(x) = 0.279

Thus, the probability that the marksman will hit the target 13 times is 0.279.

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Answer:

276 inches

Step-by-step explanation:

︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎

It belongs to isometric sampling or systematic sampling in every fifth adult entering an airport is checked for extra security screening.

What is systematic sampling?

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.

Security workers at an airport randomly choose one of the first 50 people to pass through a checkpoint for extra security screening.

After that person, they choose every 50th person who passes through for extra screening as well

By the topic

The sampling interval is 50, which is periodic.

It belongs to isometric sampling or systematic sampling.

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[tex]\frac{10 +3b}{a} =x[/tex]

By manipulating equations, we can solve for different variables.

Error

The error in the equation is in the factoring. In the second line, the x is factored out of the expression; however, this cannot be factored. Factoring is like dividing. When you factor x out you divide the terms by x. Since there is not an x in 3b, x cannot be factored out.

A correct version of factoring looks like:

Correction

Now, we can go back to the beginning and solve for x correctly using the properties of equality. First, rewrite the equation.

Then, add 3b to both sides.

Finally, divide by a.

This is the final, correct equation solved for x.