1 is the only number that's neither prime nor composite-right?

A beverage company has decided to manufacture a new juice with mixed flavors, which is prepared from orange and pineapple. The vitamin contents are 5% of vitamin A and 2% of vitamin C in the orange flavor, while pineapple flavor contains 8% of vitamin C.

The company's policies are to add at least 20 L of orange flavor to the new juice and limit the vitamin C content to no more than 5%. The cost of orange flavor is $1000 per liter, while the cost of pineapple flavor is $400 per liter.To satisfy a minimum demand of 100 L of juice, we must determine the optimal amount of each flavor to use.A) A linear programming model is needed for the company to solve this problem (Minimize production cost of the new juice)B) Use a graphic solution for this problem.The objective function of the optimization problem can be given as:min C = 1000x + 400yThe constraints that the company has are,20x + 0y ≥ 100x + y ≤ 5x ≥ 0 and y ≥ 0The feasible region can be identified by graphing the inequality constraints on a graph paper. Using a graphical method, we can find the feasible region, and by finding the intersection points, we can determine the optimal solution.The graph is shown below; The optimal solution is achieved by 20L of orange flavor and 80L of pineapple flavor, as indicated by the intersection point of the lines. The optimal cost of producing 100 L of juice would be; C = 1000(20) + 400(80) = $36,000.C) If the company decides that the juice should have a vitamin C content of no more than 7%, it would alter the problem's constraints. The new constraint would be:x + y ≤ 7Dividing the equation by 100, we obtain;x/100 + y/100 ≤ 0.07The objective function and the additional constraint are combined to create a new linear programming model, which is solved graphically as follows: The feasible region changes as a result of the addition of the new constraint, and the optimal solution is now achieved by 20L of orange flavor and 60L of pineapple flavor. The optimal cost of producing 100 L of juice is $28,000.

In conclusion, the optimal amount of each flavor that should be used to satisfy a minimum demand of 100 L of juice is 20L of orange flavor and 80L of pineapple flavor with a cost of $36,000. If the company decides that the juice should have a vitamin C content of no more than 7%, the optimal amount of each flavor is 20L of orange flavor and 60L of pineapple flavor, with a cost of $28,000.

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Answer:

4/13

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

Nyla owns 13 films in total, out of which 9 are romance films. To solve for how many films are not romance, we can subtract the number of romance films from the total amount of films:

This means that the remaining 4 films are not romance films.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In this case, the number of favorable outcomes is the number of non-romance films (4) and the total number of possible outcomes is the total number of films (13).

4 ÷ 13 = \(\frac{4}{13}\)

Therefore, the probability that Nyla chooses a non-romance film at random is \(\frac{4}{13}\). This fraction is already in its simplest form.

Answer:

C

Step-by-step explanation:

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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Among the options given in the question, the following are the properties of the linear correlation coefficient:

The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

If r=−​1, then a perfect negative linear relation exists between the two variables.

Properties of linear correlation coefficient:

Linear correlation coefficient is a value calculated from given data and used to measure the strength of linear relationship between two variables, for instant between x and y variables.

The sign of this coefficient (r) indicates the direction linear relationship will take between x and y. Below are some properties of the linear correlation coefficient:

Now, the properties of the linear correlation coefficient among the given ones in the question are:

b. The linear correlation coefficient is always between−1 and 1. That​ is,−1≤r≤1.

d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.

f. If r=−​1, then a perfect negative linear relation exists between the two variables.

Hence, options b, d and f are correct.

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y equals x times 5 is the answer because 2 times 5 is 10 and so on and so forth hope this helps :D

Answer:

8, 0

Step-by-step explanation:

Answer:

1. ATC=UAG, so ATC is UAG in mRNA form.

2. UAG=AUC, so UAG is AUC in tRNA form.

3. UAG mRNA is isoleucine.

Answer:

y=

Step-by-step explanation:

Perpendicular means opposite reciprocal of the slope. This means that the slope would change from 2/5 to 5/2 and add a negative, so it is -5/2.

y=-5/2x+b

2=-5/2 (2) +b

7=b

y=-5/2x+7

Step-by-step explanation:

There are choices when it comes to color (3). Then there is the choice between a boy dog or a girl dog (2). Multiply the number of colors by the number of genders. (6)

When choosing a dog from random, you can either choose:

Brown/M

Brown/F

Black/M

Black/F

Yellow/M

Yellow/F

(This list is called the Sample Space, a list of all possible outcomes)

Because the text says that all types of dogs are found in even numbers, it would not matter if there was 6, 12, 18, ... amount of dogs.

When looking at this sample space, you can see that the chance of choosing a Yellow/F dog, is 1 in 6.

Answer:x=-7

Step-by-step explanation:X equals negative 7

Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.

A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.

The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.

By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.

Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.

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Answer:

6

Step-by-step explanation:

3x + 12 = 5x add like terms

12 = 2x divide both sides by 2

6 = x

Answer:

Step-by-step explanation:

5x = 3x + 12

2x = 12

x = 6

5(6) = 30 degrees

3(6) + 12= 18 + 12 = 30 degrees

The difference between your monthly allowance and your friend's monthly allowance. The monthly allowance for you and your friends is $35 and $28.

Given that,

The tape diagram illustrates the difference between your monthly allowance and your friend's monthly allowance. The entire monthly allowance is $63.

We have to find what does each allowance cost.

The 9 parts represent $63  so each part represent

$63/9

7

Then,

The monthly allowance is

$7×5=$35

The monthly allowance for your friends is

$7×4=$28

Therefore, The monthly allowance for you and your friends is $35 and $28.

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Answer:

sry, i am doing this for points

Answer:

2,5 ,17,65.

Step-by-step explanation:

The sequence is x*4-3

I hope this helps!

Knowledge workers use specialized information systems, called kwss, to create information in their area of expertise. The statement is:  b. true

Knowledge workers, such as researchers, analysts, and professionals in various fields, rely on specialized information systems to perform their tasks efficiently. These systems, often referred to as kwss (knowledge work support systems), are designed to facilitate the creation, organization, and dissemination of information within a specific domain or area of expertise.

For example, a scientist may utilize a specialized information system to store and analyze research data, collaborate with colleagues, and publish findings. Similarly, a financial analyst may rely on a kwss to access market data, perform complex calculations, and generate reports.

These specialized information systems typically offer features tailored to the needs of knowledge workers, such as advanced search capabilities, data visualization tools, collaboration functionalities, and workflow management options. They enable knowledge workers to access relevant information quickly, organize and structure their work, and ultimately create valuable insights and solutions in their respective fields.

In summary, knowledge workers do indeed utilize specialized information systems, known as kwss, to support their work and enhance their productivity and effectiveness in generating information within their area of expertise.

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The  equation in logarithmic form is log₄(64) = 3

Given the equation is:

64 = 4³

The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function a y = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).

Convert the exponential equation to a logarithmic equation using the logarithm base (10)of the right side (0.01) equals the exponent (−2).

A popular method for changing a mathematical equation from one form to another is to transform it from exponential to log form. The exponential form an x = N is translated into the logarithmic form

Log aⁿ= x.The exponent of x, which is equal to N, has the exponential form a to it is converted to the logarithm of a number N to the base of a, which is equal to x.

log₄(64) = 3

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The two binomials for the expression x(x − 8) − 9(x − 8) are (x - 8) and (x - 9).

What are the binomials expression ?

The expression x(x − 8) − 9(x − 8) can be simplified as follows:

x(x − 8) − 9(x − 8) = x² - 8x - 9x + 72

= x² - 17x + 72

To find the two binomials, we need to factor the expression \(x^2 - 17x + 72\). We can do this by finding two numbers that multiply to 72 and add to -17. Those numbers are -8 and -9. Therefore, we can write:

\(x^2 - 17x + 72 = (x - 8)(x - 9)\)

Hence, the two binomials for the expression x(x − 8) − 9(x − 8) are (x - 8) and (x - 9).

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Answer:

9

Step-by-step explanation:

9+9=18

18-9=9

Answer: - 6 & - 3

Step-by-step explanation:

This 1) First start off by listing the multiplication partners of 18:

1*18

2*9

3*6

2) Now take away add the two partners of every multiplication partner you have like this:

1+18= 19

2+9=11

3+6= 9

3) Determine which one is equal to 9 but multiplies to 18 as you can see 3*6 is the option however in the problem you have to have -9 so here are some rules:

2 negatives times each other will equal a positive number

2 negatives plus each other will equal a negative number

4) From this information you can conclude that you can use -6 & -3 because:

-6*-3 = 18

(-6) + (-3) = -9

The measurements can be explained as low accuracy and high precision.

Accuracy is how close or far off a given set of measurements are to their true value.

Precision is how close or dispersed the measurements are to each other.

Given,

His height = 5 feet 3 inches

Friend measures you three times and gets these results =5 ft 10 in, 5 ft 9.5 in and 5 ft 10.5 in

Here, the measurements are closely dispersed but the measurements are far from actual measurement.

Hence, the measurements can be explained as low accuracy and high precision.

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Properties of determinants are Reflection Property, Reliable scales Property, Scalar Multiple Property, Switching Property and All-zero Property.

1. Reflection Property: The determinant remains unchanged when its columns turn into rows and vice versa. The reflection property is what is used to describe this.

2. If every element in a row (or column) is zero, the determinant is zero, according to the all-zero property.

3. Reliable scales (Repetition) Property: If every element in a row or column is proportional to or identical to every element in another row, the determinant is zero (or column).

4. When any two of the determinant's rows (or columns) are exchanged, the sign of the determinant changes.

5. Scalar Multiple Property: If all of a determinant's components in a row (or column) are multiplied by a non-zero constant, the determinant is multiplied by that constant.

6. Factor Property: If a determinant Δ becomes zero when we put x = α, then (x – α) is a factor of Δ.

Hence this is all about determinants problems.

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Check the picture below.

Answer: X= 15

Step-by-step explanation:

Answer:

4(x+3)

Step-by-step explanation:

Answer:

52°

Step-by-step explanation:

\(6x - 8= 4x + 12 \\ (exterior \: alternate \: \angle s) \\ \\ 6x - 4x = 12 + 8 \\ \\ 2x = 20 \\ \\ x = \frac{20}{2} \\ \\ x = 10 \\ \\ 4x + 12 = 4 \times 10 + 12 \\ \\4x + 12 = 40 + 12 \\ \\ 4x + 12 = 52 \degree\)

Answer:

61 vehicles per 1 acre

Step-by-step explanation:

Simply divide 559 by 9

There are three main parts to a division problem: the dividend, the divisor, and the quotient. The dividend is the number that will be divided. The divisor is the number of “people” that the number is being divided among. The quotient is the answer.

Answer: We can write the piecewise defined function for the monthly cost C(x) as follows:

C(x) =

45.75 - 9.55, if x ≤ 500

45.75 - 9.55 + 0.35(x - 500), if x > 500

Explanation:

For the first 500 minutes, the monthly cost is a flat rate of $45.75 for the plan fee and $9.55 for taxes, so the total cost is simply the sum of these two amounts: C(x) = 45.75 + 9.55 = 55.30, for x ≤ 500.

For any additional minutes beyond the 500-min limit, there is an additional charge of $0.35 per minute, so the cost increases linearly with the number of extra minutes used. The expression (x - 500) represents the number of minutes beyond the limit, so we multiply this by the rate of $0.35 per minute and add this amount to the base cost of $55.30, giving the piecewise expression:

C(x) =

55.30, if x ≤ 500

55.30 + 0.35(x - 500), if x > 500

Therefore, the piecewise defined function for the monthly cost C(x) is:

C(x) =

45.75 - 9.55, if x ≤ 500

45.75 - 9.55 + 0.35(x - 500), if x > 500

Note: The two expressions are equivalent, but the second expression is simplified by combining the constants.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

10 - 2 + 3- 7 = 5

Answer:

5........................

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.