a case of fruit weighs 53 kilogram and another weighs 47 kilograms how much weight must be removed from the first case and placed in the second is that they both equal

a . 2 kilograms
b . 4 kilograms
c . 6 kilograms
d . 8 kilograms ​

the partial derivative fy(x, y) is:

fy(x, y) = ln(5x – 3y) + y * (1/(5x – 3y)) * (-3) = ln(5x – 3y) - 3y/(5x – 3y)

To summarize: fx(x, y) = 5y/(5x – 3y)

fy(x, y) = ln(5x – 3y) - 3y/(5x – 3y)

To find the partial derivatives of the function f(x, y) = y ln(5x – 3y), we differentiate with respect to x and y separately.

The partial derivative with respect to x, denoted as ∂f/∂x or fx(x, y), is obtained by treating y as a constant and differentiating the function with respect to x:

fx(x, y) = ∂f/∂x = y * d/dx(ln(5x – 3y))

To differentiate ln(5x – 3y) with respect to x, we can use the chain rule:

d/dx(ln(5x – 3y)) = (1/(5x – 3y)) * d/dx(5x – 3y) = (1/(5x – 3y)) * 5

Therefore, the partial derivative fx(x, y) is:

fx(x, y) = y * (1/(5x – 3y)) * 5 = 5y/(5x – 3y)

Now, let's find the partial derivative with respect to y, denoted as ∂f/∂y or fy(x, y), by treating x as a constant and differentiating the function with respect to y:

fy(x, y) = ∂f/∂y = ln(5x – 3y) + y * d/dy(ln(5x – 3y))

To differentiate ln(5x – 3y) with respect to y, we again use the chain rule:

d/dy(ln(5x – 3y)) = (1/(5x – 3y)) * d/dy(5x – 3y) = (1/(5x – 3y)) * (-3)

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Answer:

x=17

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

2x - 4 = 30

2x = 30 + 4

2x = 34

x = 34/2

◆ x = 17

This is a Right answer

Answer:

B. 3× 2/4

______________

Answer:

From greatest to least

One and five-sixth rounded to 2

One and StartFraction 7 over 29 rounded to 1

0.16 rounded to 0

Step-by-step explanation:

1+7/29=29+7/29

=36/29

=1.24

Approximately

=1

1+5/6=6+5/6

=11/6

=1.83

Approximately

=2

0.16

Approximately =0

From greatest to least

One and five-sixth rounded to 2

One and StartFraction 7 over 29 rounded to 1

0.16 rounded to 0

Answer:

8-5 times R

Step-by-step explanation:

you subtract 8-5 to get that answer and then you do less than twice the number r i think this is correct hope it helps :)

An essential concept in mathematics and can be applied to a variety of fields such as physics, economics, and engineering.

The slope of a line in a Cartesian plane is a numerical representation of its steepness and inclination relative to the x-axis.

The slope of a straight line refers to the rise or fall of the y-coordinate as it moves from left to right along the x-axis.

There are a few different ways to interpret the slope of a line, but generally it can be thought of as the rate at which the dependent variable changes with respect to the independent variable.
When the slope is positive, the line rises from left to right, indicating that the dependent variable is increasing as the independent variable increases.

In other words, there is a direct relationship between the two variables.

Conversely, when the slope is negative, the line falls from left to right, indicating that the dependent variable is decreasing as the independent variable increases.

This means that there is an inverse relationship between the two variables.
The magnitude of the slope can also provide information about the relationship between the variables.

If the slope is close to zero, then the relationship between the two variables is weak or nonexistent.

However, if the slope is large in magnitude (i.e. close to 1 or -1), then there is a strong relationship between the variables.

A slope of zero indicates that there is no change in the dependent variable as the independent variable changes, while a slope of undefined means that the line is vertical and has no slope.
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Answer:

I do not quiet know

but u can u show the passage it came form

1. Objective Function and Constraints:

Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

2. Using Excel Solver, find the optimal allocation of funds.

3. The maximum value of the objective function is reported by Excel Solver.

We have,

Objective Function and Constraints:

Let:

x1 = amount spent on food

x2 = amount spent on shelter

x3 = amount spent on entertainment

Objective Function:

Maximize: 2x1 + 3x2 + 5x3 (since each dollar spent on food has a satisfaction value of 2, each dollar spent on shelter has a satisfaction value of 3, and each dollar spent on entertainment has a satisfaction value of 5)

Constraints:

Subject to:

x1 + x2 + x3 ≤ $1,500 (maximum disposable income)

x1 + x2 ≤ $1,100 (amount spent on food and shelter combined must not exceed $1,100)

x2 ≤ $800 (amount spent on shelter alone must not exceed $800)

x3 ≤ $400 (entertainment cannot exceed $400)

Using Excel Solver:

In Excel, set up a spreadsheet with the following columns:

Column A: Variable names (x1, x2, x3)

Column B: Objective function coefficients (2, 3, 5)

Column C: Constraints coefficients (1, 1, 1) for the first constraint (maximum disposable income)

Column D: Constraints coefficients (1, 1, 0) for the second constraint (amount spent on food and shelter combined)

Column E: Constraints coefficients (0, 1, 0) for the third constraint (amount spent on shelter alone)

Column F: Constraints coefficients (0, 0, 1) for the fourth constraint (entertainment limit)

Column G: Right-hand side values ($1,500, $1,100, $800, $400)

Apply the Excel Solver tool with the objective function and constraints to find the optimal allocation of funds.

Once the Excel Solver completes, it will report the maximum value of the objective function, which represents the optimal satisfaction value achieved within the given budget constraints.

Thus,

Objective Function and Constraints: Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

Using Excel Solver, find the optimal allocation of funds.

The maximum value of the objective function is reported by Excel Solver.

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Given:

Height of the tree

To find the height of the tree, we use ratio/proportion.

So, we let x be the height of the tree and use the formula:

Height of man/length of man's shadow = x/length of the tree's shadow

Therefore ,the height of the tree is 20 ft.

Interval scales in marketing research possess the characteristics of ordinal scales, but with the additional feature of equal intervals between points to indicate relative amounts. They allow for quantitative comparisons and analysis, although they may have an arbitrary zero point, making calculations involving ratios or proportions inappropriate.

Scales that have the characteristics of ordinal scales, along with equal intervals between points to indicate relative amounts and may include an arbitrary zero point, are known as interval scales.

Interval scales are commonly used in marketing research and other fields where quantitative measurements are required. They possess the properties of ordinal scales, which means that the data can be ranked or ordered based on the values. In addition to that, interval scales have the feature of equal intervals between points, indicating the relative amount or difference between the values.

Unlike ordinal scales, which only provide information about the order or rank of the data, interval scales allow for meaningful comparisons of the magnitude or distance between the values. The intervals between adjacent points on the scale are consistent throughout the measurement range. This property enables researchers to analyze and interpret the data in a more precise and quantitative manner.

An important characteristic of interval scales is the presence of an arbitrary zero point. Unlike ratio scales, where the zero point represents the absence of the measured attribute, interval scales do not have a true zero point. Instead, the zero point is chosen arbitrarily as a reference or starting point. This means that calculations involving ratios or proportions are not meaningful with interval scales, as the zero point does not hold any inherent value or significance.

Examples of interval scales in marketing research can include rating scales, such as a 5-point Likert scale measuring customer satisfaction or a 10-point scale assessing brand preference. These scales allow respondents to provide their opinions or perceptions using equal intervals between the response options, facilitating comparative analysis and interpretation of the data.

In summary, interval scales in marketing research possess the characteristics of ordinal scales, but with the additional feature of equal intervals between points to indicate relative amounts. They allow for quantitative comparisons and analysis, although they may have an arbitrary zero point, making calculations involving ratios or proportions inappropriate.

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1. The radius of the track, in feet, is 420.04 ft.

2. The circumference of a circle with a diameter of 28 cm, using a pi of 22/7 is 88 cm.

3. The area of the circle with a diameter of 36 inches, using π = 3.14, is C. 1,017.36 in².

1. Radius = circumference divided by (2 multiplied by pi).

r = c / (2 * π)

π = 3.14

Circumference = 0.5 miles

1 mile = 5,280 ft

Circumference in feet = 2,640 ft (5,280 x 0.5)

r = 2,640/(2 x 3.14)

r = 2,640/6.28

r = 420.04 ft

2. Diameter = 28 cm

Pi = 22/7

Therefore, Circumference = Diameter x π

= 28 x 22/7

= 88 cm.

3. Diameter = 36 inches

π = 3.14

Area = piR²

R = 1/2 diameter

= 18 inches

Area = 3.14 x 18²

= 3.14 x 324

= 1,017.36 in²

OR:

= A= 1/4πd²

= 1/4 x 3.14 x 36²

=  1/4 x 3.14 x 1,296

= 1,017.36 in²

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Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

Answer:

113.04 square inches

Step-by-step explanation:

The diameter of the circle is 12 inches, so the radius is (1/2) * 12 = 6 inches. The area of this circle is approximately 3.14(6^2) = 3.14 * 36 = 113.04 square inches.

Answer:

15 : 8

Step-by-step explanation:

5 3/4:3 1/15

23/4:46/15

doing crisscrossed multiplication

23×15:46×4

345:184

15:8 is your answer.;

Therefore, the length of each side are \(32cm, 44cm,56cm\).

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

The perimeter of a triangle is \(132\) cm and the lengths of its side are in the ratio \(8:11:14\)

So, the length of each side would be

\(8x+11x+14x=132\\\\33x=132\\\\x=\frac{132}{33}\\\\x=4\)

Now,

\(8x=8(4)\\\\=32\\\\\\11x=11(4)\\\\=44\\\\\\14x=14(4)\\\\=56\)

Hence, the length of each side are \(32cm, 44cm,56cm\).

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So, y = (1/2)(x + 8) is the equation of the linear function.

To write the equation of a linear function with a given x-intercept and y-intercept, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

In this case, we are given that the x-intercept is (-8, 0) and the y-intercept is (0, 4). We can use the coordinates of the x-intercept as (x1, y1) and the slope of the line as m to write the equation:

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

This is the equation of the linear function.

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y - y1 = m(x - x1)

y - 0 = m(x - (-8))

y = m(x + 8)

We can then substitute the y-intercept into this equation to find the value of m:

4 = m(0 + 8)

4 = 8m

m = 1/2

Substituting the value of m back into the equation, we get:

y = (1/2)(x + 8)

Answer:

20 percent

Step-by-step explanation:

Add 300 to 1200 to get 1500 and then divide 300/1500 to get 20

The percent of the school population, who wore their school colors is; 20%

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that 1,200 students wore their school colors of green and white.

Also, we are given he that 300 students did not wear school colours green and white.

Thus, the total number of students = 1200 + 300 = 1500

Therefore, The percent of the school population, who wore their school colors is;

= (1200/1500) × 100%

= 20%

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Answer:

\(H^{-1}(x)=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

Step-by-step explanation:

Given function:

\(H(x)=\left(\dfrac{2}{3}\right)^x-\dfrac{4}{9}\)

The domain of the given function is unrestricted:  (-∞, ∞).

As aˣ > 0, the range of the given function is restricted:  (-⁴/₉, ∞).

The inverse of a function is its reflection in the line y = x.

To find the inverse of a function, replace x with y:

\(\implies x=\left(\dfrac{2}{3}\right)^y-\dfrac{4}{9}\)

Rearrange the equation to make y the subject.

Add 4/9 to both sides:

\(\implies x+\dfrac{4}{9}=\left(\dfrac{2}{3}\right)^y-\dfrac{4}{9}+\dfrac{4}{9}\)

\(\implies x+\dfrac{4}{9}=\left(\dfrac{2}{3}\right)^y\)

Take natural logs of both sides:

\(\implies \ln\left(x+\dfrac{4}{9}\right)=\ln \left(\dfrac{2}{3}\right)^y\)

\(\textsf{Apply the power law}: \quad \ln x^n=n \ln x\)

\(\implies \ln\left(x+\dfrac{4}{9}\right)=y\ln \left(\dfrac{2}{3}\right)\)

Divide both sides by ln(2/3):

\(\implies y=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

Replace y with H⁻¹(x):

\(\implies H^{-1}(x)=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

The range of the original function is the domain of the inverse of the function.

Therefore, the domain of the inverse function is  (-⁴/₉, ∞).

The required inverse function of the given function is given as H⁻¹(x) = log[x + 4/9] / log[2/3].

Given that,
A function H(x) = (2/3)ˣ - 4/9, the inverse of the given function is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
H(x) = y
y = (2/3)ˣ - 4/9
y + 4/9 = (2/3)ˣ
log[y + 4/9] = x log[2/3]
Now. invert x and y
log[x + 4/9] = ylog[2/3]
y = log[x + 4/9] / log[2/3]
Now, put y = H⁻¹[x]
H⁻¹(x) = log[x + 4/9] / log[2/3]

Thus, the required inverse function of the given function is given as H⁻¹(x) = log[x + 4/9] / log[2/3].

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Answer:

4...    hope this will help

Step-by-step explanation:

Answer:

it is 4 i am late so i am sure thing will not help and i am sorry but maybe to the ones who need it now uhhhhhh here it is 4 have a nice long life

Step-by-step explanation:

The probability of a core of the two odd number be 1/4.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The outcome of one die has no bearing on the outcome of the other since the two dice are independent.

In this instance, a complex event's probability is calculated by adding its component simple event probabilities.

Three odd and three even results occur from each roll of the dice. So, the probability of getting an odd number exists \($\frac{3}{6}=\frac{1}{2}$\)

The probability that this happens with both dice exists \($\frac{1}{2} \cdot \frac{1}{2}=\frac{1}{4}$\)

It is relatively simple to list the "excellent" possibilities in this situation because there are a total of 36 outcomes (all numbers from 1 to 6 for one die and the same for the other die). The positive results are

(1, 1), (1, 3), (1, 5)

(3, 1), (3, 3), (3, 5)

(5, 1), (5, 3), (5, 5)

And in fact, 9 good outcomes over 36 total outcomes means

\($\frac{9}{36}=\frac{1}{4}$$\)

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Answer:

decimal form

x = 6.5

exact form

x = 13/2

mixed number form

x = 6 1/2

For the given quadratic equation 6x² – 2x + 1 = 0, the value of x will be 1/6+i√5/6 and 1/6-i√5/6.

Any equation of the form \(\rm ax^2+bx+c=0\)  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation. The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic equation.

It is given that the quadratic equation is,

6x² – 2x + 1 = 0

Apply arithmetic operations in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

\(x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:6\cdot \:1}}{2\cdot \:6} \\\\\ \\\ x_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{5}i}{2\cdot \:6} \\\\\\\ x_1=\frac{-\left(-2\right)+2\sqrt{5}i}{2\cdot \:6},\:x_2=\frac{-\left(-2\right)-2\sqrt{5}i}{2\cdot \:6}\\\ \\\\x=\frac{1}{6}+i\frac{\sqrt{5}}{6},\:x=\frac{1}{6}-i\frac{\sqrt{5}}{6}\)

Thus, for the given quadratic equation 6x² – 2x + 1 = 0, the value of x will be 1/6+i√5/6 and 1/6-i√5/6.

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Answer:

29(!£6287&7&(&

Step-by-step explanation:

That's it ty

Answer

4 = ax - 14

18 = ax

x = 18/a or 4

Step-by-step explanation:

According to the triangle, the line of reflection is at the point (0,3)

To start, let's plot the given triangle XYZ on a coordinate plane using the provided vertices X(-2, 4), Y(-9, 3), Z(-10, 7). Once you have plotted the triangle, you can draw the line of reflection that will produce the image of Y'(9, 3).

Here are the steps you can follow to find the line of reflection:

Draw a perpendicular bisector of YY'. This is the line that passes through the midpoint of segment YY' and is perpendicular to it. To find the midpoint of YY', you can use the midpoint formula:

Midpoint of YY' = [(-9 + 9)/2, (3 + 3)/2] = [0, 3]

Draw a line passing through the midpoint of YY' and vertex X. This line will be perpendicular to YY' since it is a perpendicular bisector. To find the equation of this line, we can use the point-slope form:

Slope of line = (3 - 4)/(0 - (-2)) = 1/2

Equation of line: y - 3 = 1/2(x - 0) or y = 1/2x + 3

Extend this line to the other side of YY'. This extended line will be the line of reflection that produces the image of Y'.

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9514 1404 393

Answer:

   35%

Step-by-step explanation:

The percentage increase is found from ...

  % increase = ((new value)/(old value) -1) × 100%

  = (1026/760 -1) × 100%

  = (1.35 -1) × 100% = 0.35 × 100%

  % increase = 35%

Therefore, the average number of customers waiting in the queue (Lq) is approximately 4.17.

To predict the average number of customers waiting in the queue (Lq) in an M/D/1 queuing model, we can use Little's Law, which states that Lq = λ * Wq, where λ is the arrival rate and Wq is the average time a customer spends waiting in the queue.

In this case:

Arrival rate (λ) = 5 customers per minute

Service time (D) = 10 seconds = 10/60 = 1/6 minutes

To calculate the average time a customer spends waiting in the queue (Wq), we need to use the formula Wq = Ls / λ, where Ls is the average number of customers in the system.

In an M/D/1 queuing model, Ls can be calculated using the formula Ls = (λ²) / (μ * (μ - λ)), where μ is the service rate.

Since the service time is deterministic and given by D = 1/6 minutes, the service rate (μ) is the reciprocal of the service time: μ = 1/D = 6 customers per minute.

Now we can calculate Ls:

Ls = (λ²) / (μ * (μ - λ))

= (5²) / (6 * (6 - 5))

= 25 / 6

≈ 4.17

Finally, we can calculate Lq:

Lq = λ * Wq

= λ * (Ls / λ)

= Ls

≈ 4.17

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Four siblings whose ages are consecutive odd integers. If the sum of their ages is 112 then The eldest sibling is 31, followed by siblings 29, 27, and 25.

What is consecutive integers ?

Consecutive means in order.  Integers are a collection of whole integers and their antipodes, such as -3, -2, 1, 0, 1, 2, 3, etc.

Let x = the 1st sibling

Let x -2 = the second sibling

Let x -4 = the third sibling

Let x-6 = the fourth sibling.

If you add the four siblings together they equal 112

(x) +(x-2)+(x-4)+(x-6) = 112  Combine like terms

4x - 12 = 112

add 12 from both sides

4x - 12 + 12 = 112 + 12

4x = 124

divide 4 both side :

x = 31

The eldest sibling is 31, followed by siblings 29, 27 and 25

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A p-value of 0.23 in the context of a clinical trial testing a vaccine's effectiveness suggests that the observed reduction in the percentage of individuals catching the virus, when comparing the vaccine group to the control group, is not statistically significant at conventional levels of significance (such as 0.05 or 0.01).

The p-value represents the probability of obtaining the observed data, or data more extreme, under the assumption that the null hypothesis is true.

In this case, the null hypothesis would typically state that there is no difference in the percentage of virus cases between the vaccine and control groups. A p-value of 0.23 indicates that there is a 23% chance of observing the reported reduction in cases or an even more substantial reduction if the null hypothesis were true.

Therefore, based solely on the p-value of 0.23, the best interpretation is that the observed reduction in virus cases could plausibly be due to random variation or chance, rather than a true effect of the vaccine. However, it is important to consider other factors, such as the study design, sample size, and clinical significance of the observed reduction, before drawing final conclusions about the vaccine's effectiveness.

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