The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:


f(x) = 0.25x2 − 8x + 600


The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:

x g(x)

6 862.2

8 856.8

10 855

12 856.8

14 862.2


Based on the given information, determine which company has a lower minimum and find the minimum value.

A- g(x) at (10, 855)

B- f(x) at (16, 536)

C- g(x) at (16, 536)

D- f(x) at (10, 855)

Answer:

Andre would have more

Step-by-step explanation:

100 + (5x4) = 120

10 + (20x4) = 90

Answer:

Andre will have more in their savings account

Step-by-step explanation:

andre starts out with 100 and adds 5 each week

100-105-110-115-120

S. 1. 2. 3. 4

Elena starts with 10 and adds 20 each week

10-30-50-70-90

S. 1. 2. 3. 4

(A)120>90(E)

If the partial derivative is equal to zero for all values of x then it indicates that the function is constant.

What is a partial derivative?

In differential calculus, partial derivative is defined as the rate of change of multivariable functions concerning change in just one of its variables.

Consider the restriction of f to a line y=c,

then

\( \frac{∂f}{∂x}(x \: c) = fx(f \: c) = 0\)

Pick 2 points a and b, then by mean value theorem there is x0, such that

\(fx(x \: c) = \frac{f(b \: c) - f(a \: c)}{b - a} = 0\)

\(⟹f(b \: c) - f( \: a \: c) = 0⟹f(b \: c) = f(a \: c)⟹f(x \: c) = const.\)

We can show the same way that f(c,y)=const.

Combining f(x,c)=const and f(c,y)=const to get f(x, y)=const.

Hence, If the partial derivative is equal to zero for all values of x then it indicates that the function is constant.

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The length and width of the plot that will maximize the area is 60 meters by 120 meters. The largest area that can be enclosed is 7200 square meters.

To maximize the area of the rectangular plot, Farmer Ed must use 9000 meters of fencing to enclose three sides of the plot. The fourth side, which borders the river, does not need to be fenced. To find the length and width of the plot that will maximize the area, the 9000 meters of fencing must be divided into two sides of equal length, with the remaining fencing used for the third side. This results in a length of 120 meters and a width of 60 meters, which maximizes the area of the plot. The largest area that can be enclosed is 7200 square meters.

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Answer:

Hey there!

\(\sqrt{5}= 2.24\\\sqrt{32}= 5.66\\\sqrt{70}=8.37\)

Let me know if this helps :)

Answer:

7.74 yd²

Step-by-step explanation:

Answer:

7.74 yd²

Step-by-step explanation:

The shaded area can be calculated by subtracting the area of the circle from the area of the square.

Given:

Area of the square = side length × side length

                               = 6 × 6

                               = 36 yd²

Area of the circle = πr²

                             = 3.14 × 3²

                             = 28.26 yd²

Shaded area = area of square - area of circle

                      = 36 - 28.26

                      = 7.74 yd²

A system of n number of linear equations in n unknowns has an many number of solutions if the coefficients of matrix is unique. The assertion is always accurate. The given statement is always true.

From the question, the given statement is:

A system of n linear equations in n unknowns has an endless number of solutions if the matrix of coefficients is unique. The assertion is always accurate.

The given statement is always true.

Consider the system of equations Ax = b. If A is single, there is no A-inverse. As a result, there is no one approach to solve the system. Then, there are still two options:

We can't tell which condition is right only examining the matrix [A b]. There exists an endless number of solutions if [A b] is equal to A's rank.

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The function that represents the balance after t years is ,

FV = $470( 1.011)^4t

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

FV = Future value

P = Present value

R = interest rate

m = number of compounding

N = number of years

here, we have,

given that,

P = Present value= $470.

R = interest rate = 4.4%/4 =

m = number of compounding =4

N = number of years = t

FV = $470( 1.011)^4t

Hence,  The solution is, a function to represent the balance A in the account after t years is, FV = $470( 1.011)^4t

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Answer:

y = -1/2x+4

Step-by-step explanation:

y = 2x-1

This equation is in slope intercept form  y = mx+b  where m is the slope

m=2

A line perpendicular will have a slope that is the negative reciprocal

m = -1/2

Using the slope intercept form

y = mx+b

y = -1/2x+b

and the point given (2,3)

3 = -1/2(2)+b

3 = -1+b

4 =b

y = -1/2x+4  is the equation of a line that is perpendicular to the original line and contains (2,3)

Answer:

(f∘g)(12) = 24

Step-by-step explanation:

We are given the functions f(x)=4x+8 and \(g(x)=\sqrt{x+4}\). We want to find (f∘g)(12).

(f∘g)(12) means that we first find the value of g(12), and then plug that value into f(x).

First, we find g(12). To do this, substitute x as 12.

\(g(12) = \sqrt{12 + 4}\)

Add 12 and 4 together under the radical.

\(g(12) = \sqrt{16}\)

Take the square root of 16.

g(12) = 4

Now, substitute 4 as x in f(x) = 4x + 8.

f(4) = 4(4) + 8

Multiply.

f(4) = 16 + 8

Add 16 and 8 together.

f(4) = 24

f(4) has the same value as (f∘g)(12), since 4 is the value of (g)(12), and then the value of g(12) was plugged in as x in f(x).

Therefore, (f∘g)(12) is 24.

By applying repeated and independent measures concepts, it can be concluded that there are 11 individuals participated in the repeated-measures research study and 12 individuals participated in the independent-measures research study (option D).

In a repeated-measures research study, the degree of freedom (df) is calculated by subtracting 1 from the number of individuals in the study (n). Therefore, if df = 10, then the number of individuals in the study is 10 + 1 = 11.

Whilst, in an independent-measures research study, the degree of freedom (df) is calculated by subtracting 2 from the number of individuals in the study (n). Therefore, if df = 10, then the number of individuals in the study is 10 + 2 = 12.

Therefore, it can be concluded that there are 11 individuals participated in the repeated-measures research study and 12 individuals participated in the independent-measures research study (option D).

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Answer:

Slope is .18

Step-by-step explanation

Find two points along the line.

Calculate slope using \(\frac{y2-y1}{x2-x1}\).

I used the points (1985, .21) and (1990, .30).

Check the picture below.

z =  -2.114, test statistic used to test the claim that fewer than 90% of the company employees opted to work from home at least one day a week at the 5% significance level.

A result of a statistical test of a hypothesis is a number known as the test statistic. It displays how closely the distribution predicted by your observed data fit the null hypothesis of that statistical test.

The p value of your findings, which aids in determining whether to accept or reject your null hypothesis, is calculated using the test statistic.

P = \(\frac{x}{n}\)

= \(\frac{36}{41}\)

1 - P₀ = 1 - 0.95 = 0.05

Test statistic= z

=P - P₀ / {√P₀ * (1 - P₀)/ n}

=0.8780 - 0.95 /√(0.95 * 0.05) / 41

z = -2.114

Test statistic used to claim that is, z = -2.114 .

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Step-by-step explanation:

Refer to attachment.

Hope it helps.

1. rhombus - figure (f)

2. quadrilateral - figure (h)

3. trapezoid - figure (e)

4. square - figure (c)

5. isosceles trapezoid - figure (a)

6. kite - figure (g)

7. rectangle - figure (b)

8. parallelogram - figure (d)

"It is polygon that has four sides, four vertices and four angles."

"It is a quadrilateral whose opposite sides are parallel and equal in length."

"It is a quadrilateral whose all angles measure 90° and opposite sides are parallel and equal in length."

"It is a quadrilateral whose all angles measure 90° and all sides are equal in length."

"It is a quadrilateral whose all sides are equal in length."

"It is a quadrilateral that has two pairs of adjacent sides that are equal in length."

"It is a quadrilateral whose one pair of opposite sides is parallel."

"It is a trapezoid in which the non-parallel sides are equal in measure."

For given question,

We need to match the quadrilateral to its most precise name.

1. rhombus - figure (f)

2. quadrilateral - figure (h)

3. trapezoid - figure (e)

4. square - figure (c)

5. isosceles trapezoid - figure (a)

6. kite - figure (g)

7. rectangle - figure (b)

8. parallelogram - figure (d)

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1)13/4: Rational (a fraction)

2)√17: Irrational (square root of a non-perfect square)

3)3π: Irrational (product of a rational number and an irrational number)

4)0.1 (1 bar): Rational (repeating decimal)

5)-√2: Irrational (negative square root of a non-perfect square)

6)√24: Irrational (square root of a non-perfect square)

7) -√49: Rational (negative square root of a perfect square)

1)13/4: Rational - This number is a fraction, and any number that can be expressed as a fraction is considered rational. In this case, 13/4 can be simplified to 3.25, which is a rational number.

2)√17: Irrational - The square root of 17 cannot be expressed as a simple fraction or terminating decimal. It is an irrational number, meaning it cannot be expressed as a ratio of two integers.

3)3π: Irrational - π (pi) is an irrational number, and when multiplied by a rational number like 3, the result is still an irrational number. Therefore, 3π is an irrational number.

4)0.1 (1 bar): Rational - This number is a repeating decimal, indicated by the bar over the 1. Although it does not have a finite representation, it can be expressed as the fraction 1/9, which makes it rational.

5)-√2: Irrational - Similar to √17, the square root of 2 is also an irrational number. Multiplying it by -1 does not change its nature, so -√2 remains an irrational number.

6)√24: Irrational - The square root of 24 is an irrational number because it cannot be expressed as a simple fraction or terminating decimal. It can be simplified to √(4 × 6), which further simplifies to 2√6, where √6 is an irrational number.

7)-√49: Rational - The square root of 49 is 7, which is a rational number. Multiplying it by -1 does not change its nature, so -√49 remains a rational number.

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The complete question is :

Select whether the following numbers are rational or irrational.

1. 13/4

2. \sqrt{17}

3. 3 π

4. 0.1 (1 bar)

5. - \sqrt{2}

6. \sqrt{24}

7. - \sqrt{49

Answer:

It is the total cost of housing and plane tickets for four years.

Step-by-step explanation:

Mark's costs for tuition, technology fee, and books are all per semester, s. ($2,600 + $150 + $310)s = $,060s

The cost for housing and plane tickets are a once a year cost. Mark pays these amounts once a year for four years.4($5,600 + $289) = $23,556

Therefore, the constant in the expression is $23,556, and it is the total cost for housing and plane tickets for four years.

The confidence interval for a proportion should be constructed since the variable of interest is a person's opinion, which is a qualitative variable.

A trait that cannot be quantified is referred to as a categorical variable (also known as a qualitative variable).

Nominal or ordinal categorical variables are also acceptable.

Since the variable of interest is a person's opinion, which is a qualitative variable, the confidence interval for a proportion should be built.

Statistical Variables Qualitative variables also referred to as categorical variables are variables without a built-in sense of hierarchy.

As a result, they are quantified using a nominal scale.

For instance, a qualitative variable is a name as well as hair color (Black, Brown, Gray, Red, Yellow).

Therefore, the confidence interval for a proportion should be constructed since the variable of interest is a person's opinion, which is a qualitative variable.

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ANSWER

k = 7

EXPLANATION

The unknown variable in this equation is k,

To find its value, first, we have to combine like terms. This means that on the left side of the equation, we have to combine the coefficients of k,

And then, divide both sides by 6,

Hence, the value of k is 7.

The correct statement among the given options is A. "Research cannot use both qualitative and quantitative methods in a study."

This statement is not correct because research can indeed use both qualitative and quantitative methods in a study. Qualitative research focuses on collecting and analyzing non-numerical data such as observations, interviews, and textual analysis to understand phenomena in depth. On the other hand, quantitative research involves collecting and analyzing numerical data to derive statistical conclusions and make generalizations.

Many research studies employ a mixed methods approach, which combines both qualitative and quantitative methods, to provide a comprehensive understanding of the research topic. By using both qualitative and quantitative data, researchers can gather rich insights and statistical evidence, allowing for a more comprehensive analysis and interpretation of their findings.

Therefore, option A is the statement that is not correct concerning qualitative and quantitative research.

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Using Pythagorean's theorem we can see that the measure of the other leg of the right triangle is 17.89 cm

By Pythagorean's theorem, we know that the sum of the squares of the legs is equal to the square of the hypotenuse.

Then if the other leg has a length x, we can write the equation:

\(x^2 + 2^2 = 18^2\)

Solving for x we get:

\(x = \sqrt{(18^2 - 2^2)}\)

Solving that square root we will get:

x = 17.89 cm

That is the measure of the other leg of the right triangle.

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The value of the postfix expression 6 3 2 4 + - * is 18, which falls between 15 and 100. Therefore, the correct answer is d) Something between 15 and 100.

Here is the step-by-step  of how to evaluate the postfix expression:

1. Start with the first two numbers, 6 and 3, and the first operator, *. Multiply 6 and 3 to get 18.
2. Move on to the next two numbers, 2 and 4, and the next operator, +. Add 2 and 4 to get 6.
3. Now you have 18 and 6, and the last operator, -. Subtract 6 from 18 to get 12.
4. The final result is 12.

Therefore, the value of the postfix expression 6 3 2 4 + - * is 12, which falls between 15 and 100. The correct answer is d) Something between 15 and 100.

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Answer:

0.01041666666

Step-by-step explanation:

The probability of rolling a prime number is 50% since there are 6 sides on the cube and 3 of them contain a prime number.

The probability of rolling a number greater than 2 is 75% since there are 6 sides on the cube and 4 of them contain a number greater than 2.

Answer: X=22

Step-by-step explanation:

Answer:

d. x=2

Step-by-step explanation:

i hope this helps :)

Answer:x=2

Step-by-step explanation:

Answer:

radius ≈ 19.2

Step-by-step explanation:

CV is the perpendicular bisector of the chord ST , so SV = 15

CS is the radius of the circle

using Pythagoras' identity in right triangle CVS

CS² = CV² + SV² = 12² + 15² = 144 + 225 = 369 ( square root both sides )

CS = \(\sqrt{369}\) ≈ 19.2 ( to 1 decimal place )

The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.

There could be only two terms, but there could be one hundred, a thousand, or a million.

Here are always an integer number of terms in a summation.

As per the given,

Length of the trench on the first day = 18/20 meters

Length of the trench on the second day = 9/20

Total length of the trench = 18/20 + 9/20

Take LCM as 20

⇒ (18 + 9)/20 = 27/20

⇒ 1.35 which is closest among the given option by 1 1/2 meters.

Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".

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Answer:

Irrational Number

Step-by-step explanation:

Answer:

"The sum of a rational number and an irrational number is irrational."

Step-by-step explanation:

By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats.

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9