how do you write the ratio for 30 blue cars out of 42 cars?

Answer:

area=22/7×13=40.85=41 is the nearest whole number

a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

a. The extreme points of the feasible region are the vertices of the polygon formed by the intersection of the constraint lines. In this case, the extreme points are (0,0), (5,0), (3.75, 3.75), (3.5,4.5), and (0,8).

b. To find the optimal solution and the objective function value, we evaluate the objective function at each extreme point and choose the point that maximizes the objective function. In this case, the point (3.5, 4.5) maximizes the objective function with a value of 59.5. Therefore, the optimal solution is x = 3.5 and y = 4.5, and the objective function value is 59.5.

c. The slack variables represent the surplus or slack in each constraint. We calculate the slack variables by subtracting the actual value of the left-hand side of each constraint from the right-hand side. In this case, the values of the slack variables are s1 = 0 (indicating no slack in the first constraint), s2 = 2 (indicating a surplus of 2 in the second constraint), and s3 = 0 (indicating no slack in the third constraint).

Therefore, the correct option is:

a. (0,0), (5,0), (3.75, 3.75), (3.5,4.5), (0,8);

b. x = 3.5, y = 4.5, OFV = 59.5;

c. s1 = 0, s2 = 2, s3 = 0.

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It will take the company 20.3 years to have a financial worth of $11.4

The estimate of profit is given as;

Profit = $0.6 million per year

This means that the engineers based their estimate per year

Hence, the unit of time is year

To do this, we make use of any variable of our choice.

In this case, we let x represents the variable of the amount of time.

In (a), we have:

Profit = $0.6 million per year

So, the expected financial status is 0.6x

This is the amount taken as loan by the engineers.

So, the financial status at the beginning is 1.8

Using the expressions above, we have the yearly worth to be:

y = 0.6x - 1.8

When the financial status is $11.4 million, we have:

0.6x - 1.8 = 11.4

Evaluate the like terms

0.6x = 12.2

Divide both sides by 0.6

x = 20.3

Hence, it will take the company 20.3 years to have a financial worth of $11.4

See attachment for the graph of y = 0.6x - 1.8

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Answer:

2 decimal places

Step-by-step explanation:

just simple count the number of decimal points on both sides

Answer:

Step-by-step explanation:

The initial quantity is the quantity at t = 0 time:

Or simply in this kind of equations consider the coefficient as the initial quantity.

Answer:

I am going to give this to someone and see if they can help!

Step-by-step explanation:

The unit price of a loaf of bread at each store Whole Foods is 0.2495, Safeway is $0.265 and Trader Joe's is $0.249.

The unit price of a loaf of bread at each store:

Store Price Unit Price

Whole Foods $4.99 $0.2495

Safeway $3.99 $0.265

Trader Joe's $2.99 $0.249

To calculate the unit price, we divide the price of the loaf of bread by the number of slices in the loaf. The following table shows the number of slices in a loaf of bread at each store:

Store Number of Slices

Whole Foods 24

Safeway 20

Trader Joe's 21

Therefore, the unit price of a loaf of bread at each store is as follows:

Store Price Unit Price

Whole Foods $4.99 $0.2495 (24 slices)

Safeway $3.99 $0.265 (20 slices)

Trader Joe's $2.99 $0.249 (21 slices)

As you can see, the unit price of a loaf of bread is lowest at Trader Joe's. Therefore, Camillo should buy his loaf of bread at Trader Joe's.

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Answer:

6.13

Step-by-step explanation:

This diagram shown is a right triangle;

USing the SOH CAH TOA idenity

Adjacent = x

Hypotenuse = 8

Angle of elevation = 40 degrees

cos theta = adj/hyp

cos 40 = x/8

x = 8cos40

x = 6.13

Hence the value of x to the nearest hundredth is 6.13

Answer: We can work out the normal speed of the truck between the two camera areas to decide how the specialists knew the transporter surpassed as far as possible.

Step-by-step explanation: The time distinction between the two camera readings is 5 minutes, or 5/60 = 1/12 hour

The truck voyages 8 miles between the two camera areas.

We partition the distance when to get the typical speed: 8 miles/ (1/12 hour) = 96 miles each hour.

Since the roadway speed limit is 65 miles each hour, clearly the transporter was surpassing as far as possible, which makes sense of why they got a speeding ticket.

Because of the information from the traffic light cameras and the determined typical speed, it was resolved that the transporter surpassed as far as possible, which brought about the issuance of the speeding ticket.

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We can determine the truck's speed on the roadway at a particular time using the information provided.

The truck covered an 8-mile route between the first and second cameras between 9:10 and 9:15 am. Five minutes have passed between the two camera readings.

We can apply the following formula to determine the truck's average speed over this period:

Total Distance x Total Time = Average Speed

Since there are 60 minutes in an hour, the total distance is 8 miles and the total time is 5 minutes, which can be translated to hours by dividing by 60.

Average Speed = 8 miles / (5 minutes / 60 minutes per hour)

            = 8 miles / (5/60) hours

            = 8 miles / (1/12) hours

            = 8 miles * 12 hours

            = 96 miles per hour

As a result, the vehicle was traveling 96 miles per hour on the highway at that moment. This is why the truck driver was issued a speeding ticket because it is above the 65 mph limit.

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Answer: 10 times

Step-by-step explanation:

The new coordinates of Rita's tent after rotating 90° clockwise and dilating by a scale factor of 3 centered at the origin are (3y, -3x).

Scale factor is a numerical value used to represent the proportional change between two similar objects. This value is often used to compare the size of objects in different measurements, such as inches to millimeters or feet to meters. Furthermore, the scale factor can be used to find the area, volume, or surface area of an object, as the measurements are proportional to the scale factor. This is especially useful when objects are enlarged or reduced, as it allows for the accurate calculation of the changed measurements.

To find the new coordinates of Rita's tent, the first step is to rotate the tent 90° clockwise about the origin. This means that in the coordinate plane, the tent will be moved along the positive x-axis 90° in the clockwise direction, resulting in the new coordinates (y, -x).

The next step is to dilate the tent by a scale factor of 3, centered at the origin. This means that the coordinates of the tent will be multiplied by a factor of 3. The new coordinates would then be (3y, -3x).

Therefore, the new coordinates of Rita's tent after rotating 90° clockwise and dilating by a scale factor of 3 centered at the origin are (3y, -3x).

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Check the picture below.

The important to select the appropriate value of alpha based on the characteristics of the data and the goals of the forecasting model.

The statement "for a time series for simple exponential smoothing, a larger alpha is smoother than a shorter period" is true.

In simple exponential smoothing, the forecast for the next period is based on the previous forecast and the difference between the actual value and the previous forecast. The smoothing parameter alpha controls the weight given to the most recent observation compared to the previous forecasts.
A larger alpha places more weight on the most recent observation, resulting in a forecast that is more responsive to recent changes in the data. As a result, the forecast will exhibit less volatility or variability, making it smoother. This means that a larger alpha will lead to a more stable forecast with less fluctuation around the trend.
On the other hand, a smaller alpha places less weight on the most recent observation, resulting in a forecast that is less responsive to recent changes in the data.

As a result, the forecast will be more volatile or variable, making it less smooth. This means that a smaller alpha will lead to a forecast that is more susceptible to fluctuations around the trend.
In summary, the choice of alpha is a trade-off between stability and responsiveness to changes in the data. A larger alpha will lead to a smoother forecast, while a smaller alpha will lead to a more volatile forecast.

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The sum of the series converges to 7 / (1 + 2z), and the domain for which it converges is -1/2 < z < 1/2.

To find the sum of the given geometric series\(7−14z+28z^2−56z^3+\)⋯, we need to first identify the first term (a) and the common ratio (r).
Step 1: Identify the first term (a)
The first term is 7.
Step 2: Identify the common ratio (r)
Observe the series and find the ratio between consecutive terms:
-14z / 7 = -2z
\(28z^2 / -14z = -2z\)
\(-56z^3 / 28z^2 = -2z\)
The common ratio is -2z.
Step 3: Determine the convergence of the series
A geometric series converges when the absolute value of the common ratio (|r|) is less than 1:
| -2z | < 1
To solve for the domain of z, we need to find the values for which this inequality holds:
-1 < -2z < 1
Divide all parts of the inequality by -2, and remember to reverse the inequality signs when dividing by a negative number:
1/2 > z > -1/2
Step 4: Find the sum of the converging series
For a converging geometric series, the sum can be calculated using the formula:
sum = a / (1 - r)
Plug in the values of a and r:
sum = 7 / (1 - (-2z))

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A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.

A slant asymptote exists of the form y = mx + b where m ≠ 0.

Vertical lines go up and down and are in the form of x = a, where a stands for the common x-coordinate of all locations, whereas horizontal lines go left to right and take the shape of y = b, where b stands for the y-intercept.

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's domain, the graph can never cross it. There may be multiple vertical asymptotes for a given function. All common factors are cancelled in the denominator, D(x).

A horizontal asymptote exists of the form y = k where x→∞ or x→ -∞ if the value of the one/both of the limits lim ₓ→∞ f(x) and lim ₓ→ -∞ f(x).

A vertical asymptote exists of the form x = k where y→∞ or y→ -∞.

A slant asymptote exists of the form y = mx + b where m ≠ 0.

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Answer:

Future Value = $ 12528.15

Step-by-step explanation:

The depreciation is applied to the car annually. The value of the car after depreciation in "n" no. of years can be given by the following formula:

\(Future\ Value = (Present\ Value)(1-depreciation\ rate)^n\\\)

where,

Future Value = ?

Present Value = $ 24000

Depreciation Rate = 15% = 0.15

n = no. of years = 4

Therefore,

\(Future\ Value = (\$ 24000)(1-0.15)^4\)

Future Value = $ 12528.15

Answer:

B. y=50x

Step-by-step explanation:

We can see the y intercept is 0 because the line starts at 0.

To find the slope, we can look at the first point. It is at (1, 50).

Slope=rise/run or change in y/change in x=50/1=50.

Answer:

No, It will not taste the same

Step-by-step explanation:

12 cups of pineapple juice should be mixed with 15 cups of Orange juice

Using probability distribution, we can distribute the cottages as the follows along the road.

An experiment's potential outcomes are broken down into a probability distribution, which indicates the relative possibility of each one happening. For the purpose of describing a probability distribution, there are two key functions.

They are the cumulative distribution function and the probability density function, sometimes known as the probability mass function.

As the distance between each cottage and its neighbour is 1, 2, 3, 4, ... 25, or 26 miles, the entire length of the road that these distances occupy must equal 27 miles. The road links the six cottages, which explains why.

The cottages 1and 2 are separated by a mile, according to one conceivable distribution.

Similarly,

Two miles separate cottages 3 and 4.

Three miles separate cottages 5 and 6.

There are 4 miles between Cottages 1 and 3.

There are 5 miles between cottages 2 and 4.

There are 6 miles between cottages 3 and 5.

There are 7 miles between cottages 4 and 6.

Twenty-five miles separate cottages 1 and 6.

There are 26 miles between cottages 2 and 5.

By flipping the order of the cottage distances, a second potential distribution can be created. Which is:

There are 26 miles between cottages 2 and 5.

Twenty-five miles separate cottages 1 and 6.

There are 7 miles between cottages 4 and 6.

There are 6 miles between cottages 3 and 5.

There are 5 miles between cottages 2 and 4.

There are 4 miles between Cottages 1 and 3.

Three miles separate cottages 5 and 6.

Two miles separate cottages 3 and 4.

Two cottages 1 and 2 are one mile apart.

These two show that there are numerous ways to arrange the distances between the cottages while still adhering to the requirement that the distances must add to 27 miles, while there may be other alternative distributions.

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These two demonstrate that there are a variety of distributions for the distances between the cottages that still adhere to the requirement that the distances sum up to 27 miles.

The probability distribution of the possible results of an experiment shows the relative likelihood of each one occurring. There are two essential functions for defining a probability distribution.

They are the probability density function, also called the probability mass function, and the cumulative distribution function.

The total length of the road that these distances fill must be 27 miles because the distance between each cottage and its neighbor is 1, 2, 3, 4,... 25, or 26 miles. The six houses are connected by a road, which explains why.

According to one possible distribution, the distance between cottages 1 and 2 is one mile.

Similarly,

Cottages 3 and 4 are separated by two kilometers.

Cottages 5 and 6 are separated by three kilometers.

The distance between Cottages 1 and 3 is 4 kilometers.

The distance between houses 2 and 4 is 5 miles.

The distance between cottages 3 and 5 is six kilometers.

The distance between cottages 4 and 6 is seven kilometers.

The distance between houses 1 and 6 is 25 miles.

The distance between houses 2 and 5 is 26 miles.

It is possible to generate a second potential distribution by flipping the order of the cottage distances. That is:

The distance between houses 2 and 5 is 26 miles.

The distance between houses 1 and 6 is 25 miles.

The distance between cottages 4 and 6 is seven kilometers.

The distance between cottages 3 and 5 is six kilometers.

The distance between houses 2 and 4 is 5 miles.

The distance between Cottages 1 and 3 is 4 kilometers.

Cottages 5 and 6 are separated by three kilometers.

Cottages 3 and 4 are separated by two kilometers.

Two cottages 1 and 2 are one mile apart.

These two demonstrate that there are a variety of distributions for the distances between the cottages that still adhere to the requirement that the distances sum up to 27 miles.

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The number of centimeters in the length of ab is 12 cm.

A polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

An inscribed circle is a circle that is contained within a polygon such that the circle touches all sides of the polygon. If the radius of the inscribed circle is 6 cm, then the diameter of the circle is 12 cm.

The diameter of a circle divides the circle into two equal parts, called semicircles. If we draw a line segment from one end of a diameter to the opposite vertex of the polygon, the length of that line segment is the same as the diameter of the inscribed circle. In this case, the length of line segment $\overline{ab}$ is 12 cm.

The number of centimeters in the length of ab is 12 cm.

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Therefore, the dimensions of the rectangle that will maximize the area of the garden are: Length = 9 ft; Width = 18 ft.

To maximize the area of the garden, we need to find the dimensions of the rectangle that will maximize the product of its length and width. Let's assume the length of the rectangle is x ft. In that case, the width of the rectangle would be (36 - 2x) ft, since we need to subtract twice the length from the total fencing to account for the two sides of the rectangle.

Now, the area of the rectangle is given by the formula: Area = length * width.

Substituting the expressions for length and width, we have:

Area = x * (36 - 2x)

To find the dimensions that maximize the area, we can take the derivative of the area function with respect to x and set it equal to zero.

d(Area)/dx = 36 - 4x

Setting this derivative equal to zero and solving for x:

36 - 4x = 0

4x = 36

x = 9

So, the length of the rectangle is 9 ft. Substituting this value into the expression for the width, we have:

Width = 36 - 2x

= 36 - 2(9)

= 36 - 18

= 18 ft

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Answer:

Step-by-step explanation:

(h + 6) - 2    Here we find the sum of h and 6, and from that sum we subtract 2.

This simplifies to h + 4.

Answer:

h+4

Step-by-step explanation:

h+6-2=h+4

Answer:

-1

Step-by-step explanation:

When the line is slanting down it means its negative.

The range of the data in the 4th of July parade is greater than the range of the data in the New Years's Day parade.

A dataset's range, which reflects the gap among its greatest and lowest values, is measured statistically. By deducting lowest value from the greatest value, it is computed. If range of total data is wider in Fourth of July parade than it is in the New Year's Day parade, then highest and lowest figures in Fourth of July parade will be further apart than highest and lowest values in New Year's Day parade.

For example, if highest value in 4th of July parade is 100 and lowest value is 10, then total range is 100 - 20 = 80. If the highest value in the New Year's Day parade is 60 and the lowest value is 20, then the range is 60 - 20 = 40. Thus, here range of the data in 4th of July parade is greater than range of the data in the New Year's Day parade.

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If the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces, then the sample space would not change.

It would still contain the same six possible outcomes. However, the probability of rolling an odd number would change to 4/7, as the face with the 3 would come up twice as often.

The sample space for this experiment is {1,1,1,2,2,3}, which is all the possible outcomes when the die is rolled. The probability of rolling an odd number is 2/3, as there are two faces with a 1 and one face with a 3.

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Answer:

21x + 12

Step-by-step explanation:

Distribute

3(7x) = 21x 3(4) = 12

21x + 12

So that’s the answer cuz like terms cannot b combined with numbers

Hey there!

\(\bold{3(7x+4)}\\\bold{DISTRIBUTE\downarrow}\\\bold{3(7x)+3(4)}\\\bold{3(7x)=21x}\\\bold{3(4)=12}\\\bold{= 21x +12}\\\boxed{\boxed{\bold{Answer:21x+12}}}\huge\checkmark\)

Good luck on your assignment and enjoy your assignment day!

~\(\frak{Amphitrite1040:)}\)