Which is the better value?

A. 6 ounces of hot Cheetos for $2.16
B. 10 ounces of hot Cheetos for $2.70

The minimum recommended temperature for the cold temperature run (\#7) is 15 degrees below room temperature.

The cold temperature run, marked as \#7, requires a specific temperature range to ensure optimal performance and safety. The minimum recommended temperature for this run is 15 degrees below room temperature.

Running at temperatures below room temperature allows for a more controlled environment that mimics colder conditions, which can be beneficial for various purposes such as testing equipment, evaluating performance, or assessing durability in colder climates. It helps identify potential issues or limitations that may arise in colder environments.

Setting the minimum recommended temperature at 15 degrees below room temperature provides a sufficient cold environment without excessively low temperatures that could pose risks or potential damage.

This temperature range strikes a balance between achieving the desired cold conditions for testing purposes while ensuring the safety and integrity of the equipment or system being evaluated.

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The marginal profit is a constant value of $27 per unit produced.

First, let's establish the revenue function. The revenue (R) is the product of the number of units sold (x) and the price per unit ($47). So, R(x) = 47x.

Next, let's find the profit function (P). Profit is the difference between revenue and cost: P(x) = R(x) - C(x). Plugging in the given functions, we get P(x) = (47x) - (160 + 20x + 6).

Now, to find the marginal profit P'(x), we need to take the derivative of the profit function with respect to x:

P'(x) = d/dx[(47x) - (160 + 20x + 6)]
P'(x) = 47 - 20

Therefore, the marginal profit P'(x) = 27. This means that, for each additional unit produced, the profit increases by $27.

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See below for the solution to the inverse function and the rational equation

Create functions f(x) and g(x)

The functions are given as:

f(x) = x + a/b

g(x) = cx − d

Let a = 4 and b = 2.

So, we have:

f(x) = x + 4/2

Rewrite as:

y = x + 2

Swap x and y

x = y + 2

Make y the subject

y = x - 2

So, we have:

g(x) = x - 2

So, the functions are:

f(x) = x + a/b ⇒ f(x) = x + 4/2

g(x) = cx − d ⇒ g(x) = x - 2

Show that the functions are inverse functions

In (a), we have:

f(x) = x + 4/2

g(x)= x - 2

If the functions are inverse functions, then:

f(g(x)) = x

We have:

f(x) = x + 4/2

This gives

f(g(x)) = g(x) + 4/2

This gives

f(g(x)) = x - 2 + 4/2

Evaluate

f(g(x)) = x

Evaluate g(f(x))

In (a), we have:

f(x) = x + 4/2

g(x)= x - 2

We have:

g(x)= x - 2

This gives

g(f(x)) = f(x) - 2

This gives

g(f(x)) = x + 4/2 - 2

Evaluate

g(f(x)) = x

Graph the functions

See attachment for the graph

The table of values is:

x    f(x)    g(x)

0    2     -2

1     3      -1

2    4       0

3    5      1

4    6      2

Create the equations

The form of the equations is given as:

\(a\sqrt{x + b} + c= d\)

So, we have:

\(\sqrt{4x + 5} + 1 = 0\) --- has extraneous solution

\(2\sqrt{3x - 1} + 2 = 8\) --- has no extraneous solution

The equation solution

Equation 1 with extraneous solution

\(\sqrt{4x + 5} + 1 = 0\)

Subtract 1 from both sides

\(\sqrt{4x + 5} = -1\)

Square both sides

4x + 5 = 1

Evaluate the like terms

4x = -4

Divide by 4

x = -1

Substitute x = -1 in \(\sqrt{4x + 5} + 1 = 0\) to check

\(\sqrt{4(-1) + 5} + 1 = 0\)

\(\sqrt{-4 + 5} + 1 = 0\)

\(\sqrt{1} + 1 = 0\)

Evaluate the root

\(1 + 1 = 0\)

\(2= 0\) --- false

Equation 2 without extraneous solution

\(2\sqrt{3x - 1} + 2 = 8\)

Subtract 2 from both sides

\(2\sqrt{3x - 1} = 6\)

Divide by 2

\(\sqrt{3x - 1} = 3\)

Square both sides

3x - 1 = 9

Evaluate the like terms

3x = 10

Divide by 3

x = 10/3

Substitute x = x = 10/3 in \(2\sqrt{3x - 1} + 2 = 8\) to check

\(2\sqrt{3 * \frac{10}{3} - 1} + 2 = 8\)

\(2\sqrt{10 - 1} + 2 = 8\)

\(2\sqrt{9} + 2 = 8\)

Evaluate the root

\(2*3 + 2 = 8\)

\(8 = 8\) --- true

Why the equations have (or do not have) an extraneous solution

The first equation has an extraneous solution because the solution is false for the original equation and the second does not have an extraneous solution because the solution is true for the original equation

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The mean cost of repairing the defective copiers is $500, indicating the average expense incurred by the company for repairs. The standard deviation of $433.01 represents the spread or variability of the repair costs around the mean. These calculations provide insights into the expected cost and the degree of uncertainty associated with the repair expenses for the randomly selected copiers.

To calculate the mean and standard deviation of the cost of repairing the defective copiers, we need to consider the probabilities associated with selecting different numbers of defective copiers.

Total number of copiers (N) = 10

Number of defective copiers (D) = 4

1. Mean Calculation:

The mean cost (μ) can be calculated by multiplying the probability of selecting a particular number of defective copiers by the cost of repairing each defective copier, and then summing up the results.

The probability of selecting 0 defective copiers is (6/10)*(5/9)*(4/8)*(3/7)*(2/6) = 0.1429.

The probability of selecting 1 defective copier is (4/10)*(6/9)*(5/8)*(4/7)*(3/6) = 0.2857.

The probability of selecting 2 defective copiers is (4/10)*(3/9)*(6/8)*(5/7)*(4/6) = 0.2857.

The probability of selecting 3 defective copiers is (4/10)*(3/9)*(2/8)*(6/7)*(5/6) = 0.1429.

The probability of selecting 4 defective copiers is (4/10)*(3/9)*(2/8)*(1/7)*(6/6) = 0.0476.

The mean cost is calculated as:

μ = (0.1429 * 0) + (0.2857 * $250) + (0.2857 * $500) + (0.1429 * $750) + (0.0476 * $1,000)

  = $500

2. Standard Deviation Calculation:

The standard deviation (σ) can be calculated by taking the square root of the sum of the squared differences between the cost and the mean, multiplied by the probabilities.

The standard deviation is calculated as:

σ = sqrt((0.1429 * (0 - $500)^2) + (0.2857 * ($250 - $500)^2) + (0.2857 * ($500 - $500)^2) + (0.1429 * ($750 - $500)^2) + (0.0476 * ($1,000 - $500)^2))

  = $433.01

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 In conclusion, the Poisson distribution was successfully applied by Student (1907) to the study of errors in counting yeast cells or blood corpuscles with a haemacytometer. It is possible to calculate an approximate 95% confidence interval for each estimated count, as well as to compare observed and expected counts.

The Poisson distribution was first applied to the study of errors made in counting yeast cells or blood corpuscles with a haemacytometer by Student (1907). The study involved the preparation of four different concentrations of a mixture of yeast cells, water, and gelatin spread on a glass. Counts were made on 400 squares and the data summarized in the following table.

An approximate 95% confidence interval for each estimate can be calculated using the Poisson distribution. For each of the four concentrations, the lower bound of the confidence interval is given by the formula x - 1.96*sqrt(x) and the upper bound is given by the formula x + 1.96*sqrt(x), where x is the observed count for that concentration.

It is also possible to compare the observed counts with the expected counts for each concentration. The expected count for each concentration is given by the formula λ = n*p, where n is the number of squares and p is the probability of an event occurring in a single square. The expected counts can be compared to the observed counts to determine whether they are in agreement with the Poisson distribution.

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The solution to the given system of equations is a = 0, b = 2, and c = -3.

1. Start by rearranging the second equation to solve for b in terms of c:

  b - c = 5

  b = c + 5

2. Substitute the value of b from step 1 into the first equation:

  a - (c + 5) + c = -6

  a - c - 5 + c = -6

  a - 5 = -6

3. Simplify the equation from step 2 and solve for a:

  a - 5 = -6

  a = -6 + 5

  a = -1

4. Substitute the values of a and b into the third equation:

  2(-1) - 2c = 4

  -2 - 2c = 4

5. Solve the equation from step 4 for c:

  -2c = 4 + 2

  -2c = 6

  c = 6 / -2

  c = -3

6. Substitute the value of c into the equation from step 1 to solve for b:

  b = c + 5

  b = -3 + 5

  b = 2

7. Substitute the values of a and c into the first equation to verify the solution:

  a - b + c = -6

  -1 - 2 + (-3) = -6

  -6 = -6

8. Therefore, the solution to the given system of equations is a = 0, b = 2, and c = -3.

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Answer:

(x+8)(x+8)

Step-by-step explanation:

Assuming x2 is x^2

(x+8)(x+8) = x^2 + 16x + 64

Continuation

The Zeros Would Be

x = -8

Answer:

25 boxes.

Step-by-step explanation:

Because we know that 5 boxes of pasta cost $13 and we want to find the total number of boxes that can be bought with $65, we can set up a proportion:

\(\frac{5_{boxes} }{13.00}=\frac{x_{boxes} }{65}\\ 13x=325\\ x=25\)

The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Answer:

A Scalene

B Isosceles

C Equilateral

Explanation: Interior angles are all different To see why this is so, imagine two angles are the same. The triangle would then be an Isosceles triangle, which has two sides the same length. Similarly, if all three angles are the same, it would be an equilateral triangle and all three sides would be the same length.

Step-by-step explanation:

A parenthesis is used when the number next to it is NOT part of the solution set

   like :   all numbers up to but not including 3 .    

  Parens are always next to  infinity  when it is part of the solution set .

  A bracket is used when the number next to it is included in the solution set.

Answer:

6

Step-by-step explanation:

-6 + (12)

○ First you remove the brackets

○ Then you will get -6 + 12

○ Negative Positive (-+) equals Negative

○ You will put will subtract the bigger number by the smaller number

i.e 12-6

○ You will get your answer as 6

Given that 25% of students solved at least two tasks and there were 32 students who wrote the test, we can prove that there was at least one task that no more than 12 students solved.

There was at least one task that no more than 12 students solved, we can use a proof by contradiction.

Assume that all five tasks were solved by more than 12 students. This means that for each task, there were at least 13 students who solved it. Since there are five tasks in total, this implies that there were at least 5 * 13 = 65 students who solved the tasks.

However, we are given that only 25% of students solved at least two tasks. If we let the number of students who solved at least two tasks be S, then we can write the equation:

S = 0.25 * 32

Simplifying, we find that S = 8.

Now, let's consider the remaining students who did not solve at least two tasks. The maximum number of students who did not solve at least two tasks is 32 - S = 32 - 8 = 24.

If all five tasks were solved by more than 12 students, then the total number of students who solved the tasks would be at least 65. However, the maximum number of students who could have solved the tasks is 8 (those who solved at least two tasks) + 24 (those who did not solve at least two tasks) = 32.

This contradiction shows that our initial assumption is false. Therefore, there must be at least one task that no more than 12 students solved.

Hence, we have proven that there was at least one task that no more than 12 students solved if 32 students wrote the test.

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The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The perimeter of a rectangle is 40 cm. The length is 14 cm.

Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.

Fran says she can find the width using the equation 2x + 28 = 40.

now, we get,

1. Divide both sides by 2

 2(x+14) = 40

 x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

 2x + 28 = 40

 2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

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Answer:

heres your answe 2√30

Answer:

Simplification of Square Root of 120

⇒ √120 = 2√30.

Step-by-step explanation:

The expected value of the die roll is 2.47.  Finding the value of kProbability is the measure of the likelihood of an event taking place. The sum of the probability of all events occurring must equal one, otherwise, the set of events would be incomplete, which is not possible.

Therefore, we have 0.28 + k + 0.15 + 0.3 = 1 where k is the probability of getting 2 on the die.Solving for k:k = 1 - 0.28 - 0.15 - 0.3k = 0.27Therefore, the value of k is 0.27. b. Calculating the expected valueThe expected value of the die roll is the sum of each score multiplied by its probability of occurrence. This is also called the mean of the probability distribution, given by: E(X) = ΣxP(x)where X is the random variable and P(x) is the probability of X being equal to x.Using the given table of probabilities:E(X) = 1(0.28) + 2(0.27) + 3(0.15) + 4(0.3)E(X) = 0.28 + 0.54 + 0.45 + 1.2E(X) = 2.47Therefore, the expected value of the die roll is 2.47.

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Answer:

14km

Step-by-step explanation:

The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.

According to the statement

we have given that the 3 integers are in an arithmetic progression and their product is prime.

And we have to find the sum of their squares.

So, let the three integers which is A, B, C.

And according to the arithmetic progression the

A = x and B = x-d, C = x-2d. here d is the common difference and x is a 1st term.

So, there product is prime

then

(x) (x-d) (x-2d) = c -(1)

And

their sum of square is

(x)^2 + (x-d)^2 + (x-2d)^2 - (2)

So, The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.

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Answer:

____________

is it 1700 miles ?

Answer:

The answer is 43.52 you're welcome

On a unit circle, the terminal point of theta is (sqrt 3/2, 1/2). theta if 0° is 30 degrees.

The measurement of an angle is expressed in terms of degrees. Radians and degrees are the two most often used units for measuring angles. In actual geometry, the angle is always measured in degrees. Degree is denoted by the sign °. (degree symbol). One full rotation is equal to 360 degrees (sometimes written as 360°), which is the measurement of a complete angle in degrees. The unit of measurement for angles is the degree. Since radians are the SI unit for measuring angles, it is not a SI unit. In geometry, we typically use a protractor to measure angles in degrees. In most cases, a protractor is utilized in schools to measure angles in order to address various mathematical issues.

Given

x = √3/2

y = 1/2

theta = arctan(y/x)

theta = arctan(1/2÷√3/2)

theta = arctan(1/2 * 2/√3)

theta = arctan(1/√3)

theta = 30°

On a unit circle, the terminal point of theta is (sqrt 3/2, 1/2). theta if 0° is 30 degrees.

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Answer:

x < 2

Step-by-step explanation:

Given

5 + 2x < 9 ( subtract 5 from both sides )

2x < 4 ( divide both sides by 2 )

x < 2

The approximate percentage of lightbulb replacement requests numbering between 56 and 59 is 34%.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% of data falls within two standard deviations of the mean, and about 99.7% of the data falls within three standard deviations of the mean.

In this scenario, the mean of the number of daily requests is 56 and the standard deviation is 3. So, the range from 1 standard deviation below the mean to 1 standard deviation above the mean would be from 56-3=53 to 56+3=59.

Since the question asks for the approximate percentage of requests numbering between 56 and 59, we can use the 68% figure from the empirical rule to estimate that roughly 68/2 = 34% of the requests fall in this range.

Therefore, we can estimate that approximately 34% of the requests for fluorescent lightbulb replacements at the university's main campus fall between 56 and 59 daily requests.

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Cluster sampling method subdivides the population into categories sharing similar characteristics and then selects a sample from each​ subdivision

In the probability sampling technique known as cluster sampling, you split a population into groups, such as districts or schools, and then randomly choose a sample from among these groups. As far as possible, each cluster ought to be a miniature representation of the community as a whole.

Cluster sampling is also referred to as multi-stage sampling since additional items are collected from the sample clusters that were chosen in the first step.

When studying large, dispersed populations, cluster sampling is most effective since interviewing every individual would be expensive, time-consuming, and sometimes impossible. By using cluster sampling, it is possible to create smaller, more comparable clusters that represent the population being studied.

Cluster sampling is method of sampling in which samples re subdivided into categories sharing similar characteristics and then selects a sample from each​ subdivision. These groups are called clusters.

For equal sample sizes cluster sampling provide less precision than,simple random sampling and stratified sampling. On the other hand when travel costs between clusters are high, cluster sampling is more cost-effective than the other methods.

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Answer:

9

Step-by-step explanation:

RST = 90

90 - (22 + 41) = 27.

3x = 27

27/3 = 9

x = 9

Answer:

is there a photo of a scatter plot?

Step-by-step explanation:

Answer:

\(\sf 9.6\:hours \:\: or \:\: 576\: minutes\)

Explanation:

\(\sf Time \ taken : \dfrac{Distance}{Speed}\)

Here given:

Applying formula,

\(\sf Time \ Taken = \dfrac{48}{5} = 9.6 \ hours = 576 \ minutes\)

Answer:

a=4 and b = 0

Step-by-step explanation:

Given : \(\dfrac{\sqrt 3 -1}{\sqrt 3+1}+\dfrac{\sqrt 3+1}{\sqrt 3-1}=a+\sqrt 3 b\)

To find, The value of a and b

Solution,

Solving LHS of the given equation,

\(\dfrac{(\sqrt 3-1)^2+(\sqrt3+1)^2}{(\sqrt 3+1)(\sqrt 3-1)}=a+\sqrt 3 b\)

Since,

\((a-b)^2=a^2+b^2-2ab\\\\(a+b)^2=a^2+b^2+2ab\\\\(a-b)(a+b)=a^2+b^2\)

So,

\(\dfrac{3+1-2\sqrt 3+3+1+2\sqrt 3}{3-1}=a+\sqrt 3 b\\\\4=a+\sqrt 3 b\)

or

\(4+0=a+\sqrt 3 b\)

On comparing we get :

a = 4 and b = 0