Find the minimum value of c=x+y subject to the following constraints 2x+y>=20, 2x+3y>=0, x>=0, y>=0

Answer:

Step-by-step explanation:

Part A:

Let's use the information given in the problem to create the inequalities:

Each batch of chicken soup takes 3 hours to prepare, so the total preparation time for c batches of chicken soup is 3c hours.

Each batch of beef barley takes 3.5 hours to prepare, so the total preparation time for b batches of beef barley soup is 3.5b hours.

Each batch of chicken soup takes 4 hours to package, so the total packaging time for c batches of chicken soup is 4c hours.

Each batch of beef barley takes 2 hours to package, so the total packaging time for b batches of beef barley soup is 2b hours.

There are 5 preparation workers who work 40 hours per week, so the total preparation time available is 5 workers x 40 hours/worker = 200 hours.

There are 6 packaging workers who work 40 hours per week, so the total packaging time available is 6 workers x 40 hours/worker = 240 hours.

To create the system of inequalities, we need to make sure that the total preparation and packaging times for both types of soup do not exceed the available time. Therefore:

3c + 3.5b ≤ 200 (total preparation time ≤ available preparation time)

4c + 2b ≤ 240 (total packaging time ≤ available packaging time)

Also, we have the non-negativity constraints:

c ≥ 0 (number of batches of chicken soup is non-negative)

b ≥ 0 (number of batches of beef barley soup is non-negative)

Therefore, the system of inequalities is:

3c + 3.5b ≤ 200

4c + 2b ≤ 240

c ≥ 0

b ≥ 0

Part B:

To find two possible combinations of batches of chicken soup and beef barley soup that could be made in one week based on the constraints, we can try different values for c and b that satisfy the inequalities from Part A. Here are two possible combinations:

Combination 1: c = 40, b = 0

Total preparation time: 3c + 3.5b = 3(40) + 3.5(0) = 120

Total packaging time: 4c + 2b = 4(40) + 2(0) = 160

Both inequalities are satisfied, and c and b are non-negative.

Therefore, in one week, the company can make 40 batches of chicken soup and 0 batches of beef barley soup.

Combination 2: c = 30, b = 20

Total preparation time: 3c + 3.5b = 3(30) + 3.5(20) = 135

Total packaging time: 4c + 2b = 4(30) + 2(20) = 160

Both inequalities are satisfied, and c and b are non-negative.

Therefore, in one week, the company can make 30 batches of chicken soup and 20 batches of beef barley soup.

Expanded form of 804082 is 8 x 100000 + 0 x 10000 + 4 x 1000 + 0 x 100 + 8 x 10 + 2 x 1.

To write the number 804082 in expanded form, we need to break it down into its component parts based on place value.

Expanded form 1:

804082 = 8 x 100000 + 0 x 10000 + 4 x 1000 + 0 x 100 + 8 x 10 + 2 x 1

In this expanded form, we can see that the digit 8 is in the hundred thousands place, the digit 0 is in the ten thousands place, the digit 4 is in the thousands place, the digit 0 is in the hundreds place, the digit 8 is in the tens place, and the digit 2 is in the ones place.

Expanded form 2:

804082 = 8 x [tex]10^{5}[/tex] + 0 x [tex]10^{4}[/tex] + 4 x [tex]10^{3}[/tex] + 0 x [tex]10^{2}[/tex] + 8 x [tex]10^{1}[/tex] + 2 x [tex]10^{0}[/tex]

In this expanded form, we can see that each digit in the number is multiplied by its corresponding power of 10 based on its position in the number.

Both forms give us the same result, but they express the number in different ways based on the place value of each digit.

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An r value of 0 in a correlation analysis indicates that there is no linear relationship between the two quantities being analyzed.

This means that there is no correlation between the two variables, and any observed pattern or association between them is likely due to chance. In other words, the values of one variable do not predict the values of the other variable. However, it is important to note that a correlation analysis only measures linear relationships, and there may still be other types of relationships between the variables that are not captured by the r value.

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The percentage of values and the z-scores are listed below

Here, we have

Between z = 0.53 and 2.67

This is represented as

Percentage = (0.53 < z < 2.67)

Using a graphing calculator, we have

Percentage = 29.43%

Next, we have

To the right of z = 1.61

This is represented as

Percentage = x > 1.61

Using a graphing calculator, we have

Percentage = 5.40%

Here, we have

Percentage = 35% to the left of the z-score

This means that

P(z < z) = 0.35

Using a graphing calculator, we have

z =  -0.385

Next, we have

Percentage = 18% to the right of the z-score

This means that

P(z > z) = 0.18

Using a graphing calculator, we have

z =  0.915

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Answer:

5.6 miles

Second answer option

Step-by-step explanation:

From the tables we see that 1 mile ≈ 1.61 km

Therefore 1 km ≈ 1/1.61 mile

9 km ≈ 9 x 1/1.61 ≈ 9/1.61 ≈ 5.592341 miles

Rounded to first decimal(tenth) that would be 5.6 miles

This is the second answer option

Answer:

y = -5x + 4.

Step-by-step explanation:

Slope-intercept formula: y = mx (m is slope) + B (y-intercept)

Plug in it:

y = 5x + 4.

Slope Formula:

[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Differentiation

Derivative Rule [Product Rule]:
[tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Let's identify what the problem initially gives us:

This means that they give us the derivative of each respective curve at x = 2, since the definition of a derivative is the slope of the tangent line.

We are also given that some function [tex]\displaystyle r(x)[/tex] is equal to [tex]\displaystyle p(x)q(x)[/tex], where the functions are multiplied by each other.

We are then asked to find [tex]\displaystyle r'(2)[/tex], which is the derivative of the [tex]\displaystyle r(x)[/tex] function at x = 2.

In order to find the derivative of [tex]\displaystyle r(x)[/tex], we will need to use the Product Rule, which states how to find a derivative of 2 functions being multiplied by each other. Note the equation given under "General Formulas and Concepts":

[tex]\displaystyle \begin{aligned}r(x) & = p(x)q(x) \\r'(x) & = \boxed{ p'(x)q(x) + p(x)q'(x) }\\\end{aligned}[/tex]

∴ the derivative of [tex]\displaystyle r(x)[/tex] is equal to [tex]\displaystyle \boxed{ r'(x) = p'(x)q(x) + p(x)q'(x) }[/tex]

To find the derivative evaluated at x = 2, we substitute in x = 2 into our derivative:

[tex]\displaystyle\begin{aligned}r'(x) & = p'(x)q(x) + p(x)q'(x) \\r'(2) & = p'(2)q(2) + p(2)q'(2) \\\end{aligned}[/tex]

This is where the graphs and their tangent lines come into play.

To find [tex]\displaystyle q(2)[/tex] and [tex]\displaystyle p(2)[/tex], we simply refer to the [tex]\displaystyle y = q(x)[/tex] and [tex]\displaystyle y = p(x)[/tex] graphs, respectively:

[tex]\displaystyle \begin{aligned}\implies r'(2) & = p'(2)(-1) + 3q'(2) \\& = \boxed{ -p'(2) + 3q'(2) }\end{aligned}[/tex]

We have now simplified our derivative equation [tex]\displaystyle r'(2)[/tex] to be:

[tex]\displaystyle\begin{aligned}r'(x) & = p'(x)q(x) + p(x)q'(x) \\r'(2) & = p'(2)q(2) + p(2)q'(2) \\& = -p'(2) + 3q'(2) \\\end{aligned}[/tex]

To find [tex]\displaystyle p'(2)[/tex] and [tex]\displaystyle q'(2)[/tex], we refer to the tangent lines of the graphs [tex]\displaystyle y = p(x)[/tex] and [tex]\displaystyle y = q(x)[/tex], respectively. We will have to find their slopes (by the definition of a derivative) using the Slope Formula:

[tex]\displaystyle\begin{aligned}\therefore r'(2) & = -p'(2) + 3q'(2) \\ r'(2) & = -2 + 3 \bigg( \frac{-1}{3} \bigg) \\& = -2 - 1 \\& = \boxed{ -3 }\end{aligned}[/tex]

[tex]\displaystyle \therefore \boxed{ r'(2) = -3 }[/tex]

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Topic: Calculus

Unit: Derivatives

When excluding stoppages, the speed of a bus is 54 km/h, and including stoppages, it is 36 km/h. the bus stop is 20 minutes per hour

We have to Calculate the distance traveled by bus in 1 hour excluding stoppages and calculate the distance traveled by bus in 1 hour including stoppages. Then we have to calculate the time taken to cover that difference between the distances and convert the calculated time into minutes.

Given data:

The speed of a bus while excluding stoppages = 54 km/h.

the speed of the bus while including stoppages = 36 km/hr.

From the given data we can say that:

The Distance traveled by bus in 1 hour, excluding stoppages is = 54 km.

The Distance traveled by bus in 1 hour, including stoppages, is = 36 km.

Distance traveled = Distance traveled by bus in 1 hour excluding stoppages – distance traveled by bus in 1 hour including stoppages

= 54km − 36km = 18km

The bus covers 18 km less due to stoppages.

the time taken to cover18 km, = distance traveled / speed of the bus

= 18km / 54km/hour

= 1 / 3 hour

Time taken in minutes = ( 1 / 3×60 )minutes

=20minutes

Therefore, the bus stops per hour for 20 minutes.

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Answer:

it is 19 brainliest please

Step-by-step explanation:

Answer: 84 square inches.

Step-by-step explanation:

Side A of shaded: 5+3+3 = 11

Side B of shaded: 3+3+3= 9

11x9= 99

99-(3x5{normal rectangle area})= 84

If A girl is 5 cm taller than her mother and 8 cm less than her dad, the height of the girl's dad is 122 cm.

Let's assume that the height of the girl's mother is x cm. Then, according to the given information, the height of the girl would be (x + 5) cm and the height of her dad would be (x + 5 + 8) cm or (x + 13) cm.

Now, we know that the total height of the three individuals is 3.45 m or 345 cm (since 1 m = 100 cm). Therefore, we can write an equation as follows:

x + (x + 5) + (x + 13) = 345

Simplifying the equation, we get:

3x + 18 = 345

Subtracting 18 from both sides, we get:

3x = 327

Dividing both sides by 3, we get:

x = 109

Therefore, the height of the girl's mother is 109 cm, the height of the girl is (109 + 5) cm or 114 cm, and the height of the girl's dad is (109 + 13) cm or 122 cm.

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The measure of m∠2 is given as 130

Since ∠1 and ∠4 are supplementary, their sum equals 180°:

m∠4 = 180° - m∠1

m∠4 = 180° - 50°

m∠4 = 130°

Now, we need to find m∠2. Since lines m and n cross, forming vertical angles, m∠1 is vertical to m∠3 and m∠2 is vertical to m∠4. Vertical angles are equal, so:

m∠2 = m∠4

m∠2 = 130°

Thus, m∠2 is 130°.

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Option a. The graph that would correctly display the data that we have jere would be: a bar graph titled favorite topping with the x-axis labeled topping and the y-axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44.

The correct graph to display this type of categorical data is a bar graph. The correct option should show the data with the correct number of customers for each topping as it is listed in the question we have :

Sprinkles: 17

Nuts: 12

Hot Fudge: 27

Chocolate Chips: 44

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Answer:

  an = 1/2n² -1/2n -2

Step-by-step explanation:

You want a formula for the n-th term of the quadratic sequence -2, -1, 1, 4.

Using x = 1, 2, 3 and y = -2, -1, 1 we can write equations for the coefficients a, b, c of the quadratic expression ax² +bx +c.

  a(1²) +b(1) +c = -2

  a(2²) +b(2) +c = -1

  a(3²) +b(3) +c = 1

Subtracting the first equation from the other two, we get ...

  3a +b = 1

  8a +2b = 3

Subtracting twice the first from the second of these, we get ...

  (8a +2b) -2(3a +b) = (3) -2(1)

  2a = 1

  a = 1/2

Then b can be found from ...

  b = 1 -3a = 1 - 3/2 = -1/2

And c can be found from ...

  -2 -b -a = c = -2 -(-1/2) -(1/2) = -2

The formula is ...

  an = 1/2n² -1/2n -2

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Additional comment

For systems of equations, the solver used in the second attachment works well. It tells us (a, b, c) = (1/2, -1/2, -2) as we found above.

Alternate solution

The first differences of the given terms are ...

  1, 2, 3

And their differences are ...

  1, 1

The coefficient of n² is half this second-difference value: 1/2.

If you subtract 1/2n² from the given terms, you get ...

  -5/2, -3, -7/2, -4

This arithmetic sequence has the formula ...

  a1 +d(n -1)

  -5/2 +(-1/2)(n -1) = -1/2n -2

Adding this to the term we subtracted gives ...

  an = 1/2n² -1/2n -2 . . . . . as above

Answer:

The answer to your problem is, 12 1/2

Step-by-step explanation:

As shown to the problem we would need to add

4 1/2 + 2 7/12

Lets make them equivalent denominators:

1/2 & 7/12

= 24

1/2 = 12/24

7/12 = 14/24

Then make the new problem into;

4 12/24 + 7 14/24

= 12 1/2

Thus the answer to your problem is, 12 1/2

The statistical measures are: Min: 6 Q1: 7 Med: 11.5 Q3: 13 Max: 15.

The box and whiskers plot is given below.

To create a box and whiskers plot, we have to first derive the statistical measures of the data set given, which is the five number summary that include, the mina nd max values, the median, and the quartiles.

Given the data set, 6, 7, 7, 8, 10, 13, 13, 13, 15, 15, the five number summary which are the statistical measures are:

Minimum: 6 (lowest value)

First Quartile: 7 (middle of the first half of the data)

Median: 11.5 (center of the data set)

Third Quartile: 13 (middle of the second half of the data)

Maximum: 15 (largest value).

The box and whiskers plot of the data set, 6, 7, 7, 8, 10, 13, 13, 13, 15, 15, is shown in the diagram attached below.

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Answer: -3

Step-by-step explanation:

by puggin in 1 to the equation, you get 1^2 + k + 2 = 0, which equals 3 + k; to solve, bring 3 to the other side to get k = -3.

The commission made by Jarrod and total sales done by Jewelry store is equals to  $15.90 and $514.10 respectively.

Percent of commission rate earned = 3%

Amount of Jewelry sold last week = $530

Commission Jarrod made last week

= multiply the amount of his sales by the commission rate.

⇒ Commission Jarrod made last week = 3% of $530

⇒ Commission Jarrod made last week = 0.03 x $530

⇒ Commission Jarrod made last week = $15.90

Jarrod made $15.90 in commission last week.

The jewelry store made from Jarrod's sales

=  subtract the commission from the total amount of sales.

⇒Store's profit = $530 - $15.90

⇒ Store's profit = $514.10

The jewelry store made $514.10 from Jarrod's sales last week.

Therefore, the amount of commission and sales made by jewelry store is equal to $15.90 and $514.10 respectively.

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Answer: yes he can transport them all

Step-by-step explanation: yes.

If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.

This means that we are 90% confident that the true population mean of points scored by all students at the high school falls within this range based on the sample of 30 students who played the game for an hour.
A random sample of 30 students at a high school was allowed to play a popular cell phone game for an hour, yielding an average score of 375 with a standard deviation of 100. The 90% confidence interval is 375 ± 31. The statement that best summarizes the meaning of this confidence interval is: If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.

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The calculated height of the​ lighthouse, h will be yards

From the question, we have the following parameters that can be used in our computation:

Similar triangles of shadows and house

This means that

Ratio = Division or ratio of corresponding sides

So, we have

h : 9 = 18 : 6

So, we have the following representation

h/9 = 18/6

This gives

h = 9 * 18/6

By calculation, we have

height = 27 yards

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Answer: The total area of the table top is given by the product of its length and width:

Area of table top = length × width

= (5x - 2)(x + 2)

The width of the section not covered by the glass is (x - 3) metre, which means that the width covered by the glass is (width of table top) - (width of section not covered):

Width covered by glass = (width of table top) - (width of section not covered)

= (x + 2) - (x - 3)

= 5

Therefore, the area of the table top not covered by the glass is:

Area not covered by glass = (length of table top) × (width not covered by glass)

= (5x - 2)(5)

= 25x - 10 square metres

Hence, the area of the table top that is not covered by the glass is 25x - 10 square metres.

Step-by-step explanation:

Therefore, when x is 13, y is 52 if y varies directly with x.

In mathematics, an equation is a statement that two expressions are equal. It is usually written using an equal sign (=). Equations can contain variables, which are usually represented by letters, and the goal is often to solve the equation for the value(s) of the variable(s) that make the equation true.

Here,

If y varies directly with x, then we can write the relationship between y and x using the equation:

y = kx

where k is the constant of proportionality. To solve for k, we can use the given information that when x is 7, y is 28:

28 = k(7)

Solving for k, we get:

k = 4

Now that we know k, we can use the equation to find y when x is 13:

y = 4(13)

y = 52

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Answer: $4.16

Step-by-step explanation:

20% of 63.20 = 12.64
63.20 + 12.64 = 75.84

80.00 - 75.84 = 4.16

Answer:  =[tex]\frac{a}{4(a+2)}[/tex]

Step-by-step explanation:

Let's find common denominator of the the other side first

we have:

2a-4= 2(a-2)

2a²-8 = 2(a²-4) = 2(a-2)(a+2)

a²+2a = a(a+2)

common denominator is 2a(a-2)(a+2)

combine right side:

[tex]\frac{a^{2}(a+2)-a(a^{2}+4)-4(a-2) }{2a(a-2)(a+2}[/tex]

combine like terms on top:

[tex]\frac{a^{3}+2a^{2}-a^{3}-4a-4a+8 }{2a(a-2)(a+2}[/tex]

[tex]\frac{2a^{2}-8x+8 }{2a(a-2)(a+2}[/tex]

lets put the whole problem together.

[tex]\frac{a-2}{4(a^{2}+4a+4) }[/tex]  / [tex]\frac{2a^{2}-8x+8 }{2a(a-2)(a+2}[/tex]

When dividing fractions, keep the first, change the sign, flip the 2nd fraction

   [tex]\frac{a-2}{4(a^{2}+4a+4) }[/tex]  * [tex]\frac{2a(a-2)(a+2}{2(a^{2}-4x+4) }[/tex]         simplify more and then reduce

[tex]\frac{a-2}{4(a+2)(a+2) }[/tex] * [tex]\frac{2a(a-2)(a+2}{2(a-2)(a-2) }[/tex]

=[tex]\frac{a}{4(a+2)}[/tex]

Answer:

585.14

Step-by-step explanation:

3677=2πr

r=3677÷44/7

=585.14

Answer:49.4g

Step-by-step explanation:

After considering the given data we conclude that the total amount of trace element collected by Abdoulaye is 4 grams.

Formula for volume of a cylinder
[tex]V = \pi r^2 h[/tex]
Here,
Radius = 13.4 / 2 = 6.7 cm
Height = 10.3
Then
V = 3.14 × (6.7)² × 10.3
V = 1,451.8 cubic centimeters
Volume of cylinder is approximately 1,451.8 cubic centimeters.

In the event a water sample shows  0.034 grams  of some trace element for every cubic centimeter of water, then the amount of trace element in the sample can be evaluated by multiplying the volume of the sample by the concentration of the trace element in the water sample.
1.451.8 × 0.034 = 49.36 grams
Then , approximately 49.36 grams of trace element has Abdoulaye collected rounding the value to the nearest tenth which is 4 grams.

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Answer: 23

Step-by-step explanation:

     The range of the data set is the same thing as subtracting the smallest value from the largest value.

     Here, our smallest value is 8 and our largest value is 31.

                 31 - 8 = 23

     This data set has a range of 23.

The probability of a bluebird egg taking more than 14 days to hatch, based on the data provided, is 6/7 or approximately 0.86.

Probability is a measure of the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In this case, the event we are interested in is the probability of a bluebird egg taking more than 14 days to hatch. We can calculate this probability by dividing the number of eggs that took more than 14 days to hatch by the total number of eggs.

According to the data provided, there were 6 eggs that took more than 14 days to hatch, out of a total of 7 eggs. Therefore, the probability of a bluebird egg taking more than 14 days to hatch, based on this data, is 6/7 or approximately 0.86.

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