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Answer: The first box (the 450 g box for $4.69)

===========================================================

Explanation:

To get the unit cost, we'll divide each price by the weight

The first box has a unit cost of (4.69)/450 = 0.010422 approximately which rounds to 0.01; so this unit cost is approximately $0.01 per gram or 1 cent per gram.

For the second box, its unit cost is (6.49)/600 = 0.0108167 approximately. When we round to the nearest cent, we get the same unit cost as before. Without rounding, we see that the first box has a slightly lower unit cost. Therefore box 1 is the better buy.

Alternate optimal solutions exist when the Allowable Increase values for changing cells are zero. The correct answer is option C.

In linear programming, an alternate optimal solution occurs when there are multiple solutions that all have the same optimal value for the objective function. One way to identify an alternate optimal solution is by looking at the Allowable Increase values for the changing cells in the sensitivity report. If the Allowable Increase value is zero, it means that increasing the value of that changing cell will not change the optimal solution. This indicates that there are alternate optimal solutions.

In contrast, options A, B, and D are not correct because they do not accurately describe the conditions for an alternate optimal solution. The reduced cost, ratio of objective coefficient to constraint coefficient, and final value of changing cells are all important factors in linear programming, but they are not directly related to the existence of alternate optimal solutions.

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The number of cheese produced in 2006 is 7.8 thousand

The number of cheese produced in 2014 is 9.8 thousand

The given equation that models the growth of cheese is known as an exponential equation. An exponential equation is a non-linear equation.

The given exponential equation is y = 7.1(1.03)^x

Where:

Number of cheese produced in 2006 = 7.1(1.03)^3 = 7.8 thousand

Where x = 2006 - 2003 = 3

Number of cheese produced in 2014 = 7.1(1.03)^11 = 9.8 thousand

Where x = 2014 - 2003 = 11

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Answer:

12 miles

Step-by-step explanation:

3 miles per 30 minutes

2 hours is made of 4 30 minutes, so 3 x 4 = 12

Answer:

The answer is 12 miles

Step-by-step explanation:

30 minutes is half an hour.

If 30 minutes is half an hour then, 2 hours is 120 minutes.

3 miles in this problem is 30 minutes, so 120 divided by 30 is 4 and 4x3 is 12.

x = ± π/2 + 2kπ    with k ∈ Z is the solution of fundamental identities

What is fundamental identities?

An equation is referred to as an identity if it has one or more variables and holds true for any replacement value of each variable that is specified on both sides of the equation.

 y = cscx

  y³ - y² - y + 1 = 0   has a root for y = 1

=  y³ - y² - y + 1  

= ( y² - 1 ) ( y - 1 )

= ( y + 1 ) ( y - 1 )²

   cscx = ± 1

  sinx = ± 1

or

  x = ± π/2 + 2kπ    with k ∈ Z

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The answer is 0.7166. The Poisson distribution can be used to model the arrival of customers. If the mean number of customers per hour is 2, then the mean number of customers per minute is 2/60 = 1/30.

Let X be the number of customers that arrive in the next 10 minutes. Then X follows a Poisson distribution with parameter λ = (1/30) * 10 = 1/3.

The probability that no one will arrive in the next 10 minutes is given by P(X = 0), which can be computed as:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-1/3) ≈ 0.7166

Therefore, the answer is 0.7166.

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Answer:

Option C 100

Step-by-step explanation:

BRAINLIST please

Answer:

Well here we have, r = 10m

And Area= πr²

And thus we can solve i by using the value of pie and radius in the area formlae.

Now we have:

π10² = area of the circle

100π = Area of the circle,

Thus, its option C

Answer:

-108 is the answer to the question..

Answer:

​-108

Step-by-step explanation:

The correct option is A. The median is the best measure of center for quantitative data unless there is an outlier in the sample.

The best measure of center for this data set would be the median. The median represents the middle value when the data is sorted in ascending or descending order. In this case, the median would be the value that separates the lower and upper halves of the data.

The reason the median is the best measure of center in this scenario is because there is an outlier in the data set. Outliers are values that significantly deviate from the rest of the data and can have a disproportionate impact on the mean. In this case, the value of 45 stands out as significantly larger than the other values.

If the mean were used as the measure of center, it would be heavily influenced by the outlier and might not accurately represent the central tendency of the majority of the data. The mean is sensitive to extreme values, and in the presence of outliers, it can be skewed towards those outliers, resulting in a misleading representation of the data.

The mode, which represents the most frequently occurring value, is not suitable in this case as there are no repeated values in the data set.

Regarding the true statement, the correct option is A. The median is the best measure of center for quantitative data unless there is an outlier in the sample. This statement aligns with the reasoning mentioned above.

In summary, the median is the best measure of center for this data set because it is not influenced by outliers and provides a more representative value for the central tendency of the data, especially in the presence of extreme values.

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Step-by-step explanation:

∆COT is congruent with ∆NPA

by rule A.S.S (angles, sides, sides)

Answer:

△COT≅△NPA by SSA

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the volume of a cone, we need to use the formula:

Volume = (1/3) * π * r^2 * h,

where π is the mathematical constant pi (approximately 3.14159), r is the radius of the base of the cone, and h is the height of the cone.

Given that the diameter of the cone is 12 m, we can find the radius by dividing the diameter by 2:

radius = diameter / 2 = 12 m / 2 = 6 m.

Now we can substitute the values into the volume formula:

Volume = (1/3) * π * (6 m)^2 * 5 m.

Calculating the volume:

Volume = (1/3) * 3.14159 * (6 m)^2 * 5 m

= (1/3) * 3.14159 * 36 m^2 * 5 m

= 3.14159 * 6 * 5 m^3

= 94.24778 m^3.

Therefore, the volume of the cone is approximately 94.25 cubic meters.

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

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Answer:

the scale factor is times 0.5

Explanation:

20 plus 10 is 30. Half of 20 is 10 so that is 0.5

It is also like that for the others

Answer:

17

Step-by-step explanation:

The correct sum of the polynomial is \(\rm 6x^3 + 3x - 6\).

We have to determine

The correct sum of the polynomials.

Sum of the polynomials is just a matter of combining like terms, with some order of operations.

Then,

The correct sum of the polynomial is;

\(\rm (4x^3 - 2x - 9) + (2x^3 + 5x + 3) \\\\ 4x^3 - 2x - 9 + 2x^3 + 5x + 3\\\\ 6x^3 + 3x - 6\)

Hence, the correct sum of the polynomial is \(\rm 6x^3 + 3x - 6\).

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Answer:

Use sine for this:

we have

sin 30 =perpendicular/hypotenuse

1/2=x/19

doing crisscrossed multiplication

19/2=x

x=9.5

The unit m/s represents the speed of light. Therefore, the units of the right-hand side of the equation prove that the speed of light is represented in the equation.

The equation mentioned in the question is as follows; The SI units of magnetic permeability and permittivity of free space are Henry/meter and farad/meter respectively. In order to prove that the units given by the right-hand side of the equation are m/s, we need to perform the following steps: Substitute the values of magnetic permeability and permittivity of free space in the equation. Let's substitute µ0 and ε0 values in the above equation, we get; In order to perform this step, we need to know the units of each component in the equation. A unit of force is Newton, and a unit of charge is Coulomb. A magnetic field has the unit Tesla. Let's find out the units of the right-hand side component of the above equation. We can now rearrange the equation to make it simpler.!)

The unit m/s represents the speed of light. Therefore, the units of the right-hand side of the equation prove that the speed of light is represented in the equation.

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The solution to the equation is x = -1.00 and x = 1.00.To summarize, the solution to the equation x²-1 using a graphing calculator is

x = -1.00 and x = 1.00.

Given equation is x²-1.To solve the equation using a graphing calculator, follow the steps below.Step 1: Enter the equation into the calculator. Press the "y=" key on the calculator and enter the equation. In this case, it is x²-1. Step 2: Graph the equation.Press the "graph" button on the calculator to graph the equation. Step 3: Find the x-intercepts. Look at the graph and find where the graph intersects the x-axis.

These points are called the x-intercepts. In this case, the x-intercepts are at approximately -1 and 1. Step 4: Round the answer.Rounding the answer to two decimal places gives -1.00 and 1.00. Therefore, the solution to the equation is

x = -1.00 and x = 1.00.

To summarize, the solution to the equation x²-1 using a graphing calculator is

x = -1.00 and x = 1.00.

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Given the probabilities P(A) = 0.7, P(Ac) = 0.3, P(B|A) = 0.4, and P(B|Ac) = 0.8, the joint probabilities can be calculated as follows: P(A and B) = 0.28, P(A and Bc) = 0.42, P(Ac and B) = 0.12, and P(Ac and Bc) = 0.18.

The joint probability P(A and B) represents the probability of events A and B occurring simultaneously. It can be calculated using the formula P(A and B) = P(A) * P(B|A). Given that P(A) = 0.7 and P(B|A) = 0.4, we can multiply these probabilities to obtain P(A and B) = 0.7 * 0.4 = 0.28.

It can be calculated as P(A and Bc) = P(A) * P(Bc|A). Since the complement of event B is denoted as Bc, and P(Bc|A) = 1 - P(B|A), we can calculate P(A and Bc) as P(A) * (1 - P(B|A)) = 0.7 * (1 - 0.4) = 0.42.

Finally, P(Ac and Bc) represents the probability of both event A and event B not occurring. It can be calculated as P(Ac and Bc) = P(Ac) * P(Bc|Ac). Using P(Ac) = 0.3 and P(Bc|Ac) = 1 - P(B|Ac), we can calculate P(Ac and Bc) as P(Ac) * (1 - P(B|Ac)) = 0.3 * (1 - 0.8) = 0.18.

Therefore, the joint probabilities are: P(A and B) = 0.28, P(A and Bc) = 0.42, P(Ac and B) = 0.24, and P(Ac and Bc) = 0.18.

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide.

Then

a² will go with the y part of the equation

Also, since the focus is 8 units below the center, then c = 8

since the vertex is 17 units above, then a = 17

The equation b² = a² – c² gives me

b²=17²-8²-----> b²=225

the equation is

y²/a²+x²/b²=1------> y²/289+x²/225=1

the answer is

y²/289+x²/225=1

The other answer is correct, but on edge the answer is in this form: y^2/17^2 + x^2/15^2 = 1 which is answer choice D.)

Answer:

6.7

x 2.5

2 x 6 =53

Step-by-step explanation:

Answer:

1. 16.75

2. 12

3. 1.4

4. 1

5. 11

6. 3

7. 0.35

Mary will have to take a sample of 30 to 40 students to treat observations as independent.

According to the central limit theorem, one condition for performing a hypothesis test is that the observations are independent. Mary is going to take a sample from a population of 500 students.

According to the requirement of the central limit theorem, when performing a hypothesis test, the observations should be independent. In order to treat observations as independent, Mary will have to take a sample without replacement.

For a sample to be independent, each of the students in the population should have an equal chance of being selected. Since the total population of students is 500, Mary should pick any number of students that will represent the entire population.Usually, a sample size of about 30 to 40 students is enough to represent the entire population.

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Answer:

Step-by-step explanation:

6(2x+ 10) = x - 61

12x + 60 = x - 61

11x + 60 = -61

11x = -121

x = -11

6y= -11 - 61

6y = -72

y = -12

(-11, -12)

y=2x+10

Swap sides so that all variable terms are on the left hand side.

2x+10=y

Subtract 10 from both sides.

2x=y−10

Divide both sides by 2.

2

2x

​  

=  

2

y−10

​  

Dividing by 2 undoes the multiplication by 2.

x=  

2

y−10

​  

Divide y−10 by 2.

x=  

2

y

​  

−5

SOLVE FOR Y

y=2(x+5)  

6y=x−61

Swap sides so that all variable terms are on the left hand side.

x−61=6y

Add 61 to both sides.

x=6y+61

SOLVE FOR Y

y=  

6

x−61

​  

The stability of the nonzero equilibria found in Problem 2 can be determined by analyzing the phase portrait of the autonomous equation (4).

If the phase portrait shows that any slight deviation from the equilibrium point results in the population returning to the equilibrium point, then the equilibrium is stable.

On the other hand, if any slight deviation from the equilibrium point causes the population to diverge further from the equilibrium point, then the equilibrium is unstable.

To analyze the phase portrait, we need to first find the Jacobian matrix of the autonomous equation (4) evaluated at the nonzero equilibria. Then, we can determine the eigenvalues of the Jacobian matrix and use them to classify the stability of the equilibria.

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Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer:

Step-by-step explanation:

20% of 207.77 = 41.554

1% of 207.77 = 2.0777

21% of 207.77 = 41.554+2.007=43.6317

207.77+43.6317 = 251.4017

Round to 2 decimal places because its money = 251.40

Answer:

False

Step-by-step explanation:

Answer:

False

The proper term would be dodecagon.

At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

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