My guys pls help new you got me right I’m giving brainliest:)

The optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

To solve this linear programming problem using the Simplex method, we first need to convert it into standard form by introducing slack variables.

Our problem can be rewritten as follows:

Minimize w = 9x1 + 6x2

Subject to:

x1 + 2x2 + x3 = 5

2x1 + 2x2 + x4 = 8

x1 + 2x2 + 2x3 = 6

where x1, x2, x3, and x4 are all non-negative variables.

Next, we set up the initial simplex tableau:

Basic Variables x1 x2 x3 x4 RHS

x3 1 2 1 0 5

x4 2 2 0 1 8

x5 1 2 2 0 6

z -9 -6 0 0 0

The last row represents the coefficients of the objective function. The negative values in the z-row indicate that we are minimizing the objective function.

To find the pivot column, we look for the most negative coefficient in the z-row. In this case, the most negative coefficient is -9, which corresponds to x1. Therefore, x1 is our entering variable.

To find the pivot row, we calculate the ratios of the RHS values to the coefficients of the entering variable in each row. The smallest positive ratio corresponds to the pivot row. In this case, the ratios are:

Row 1: 5/1 = 5

Row 2: 8/2 = 4

Row 3: 6/1 = 6

The smallest positive ratio is 4, which corresponds to row 2. Therefore, x4 is our exiting variable.

To perform the pivot operation, we divide row 2 by 2 to make the coefficient of x1 equal to 1:

Basic Variables x1 x2 x3 x4 RHS

x3 0 1 1 -1 1

x1 1 1 0 1/2 4

x5 0 1 2 -1 2

z 0 -3 9 9/2 -18

We repeat the process until all coefficients in the z-row are non-negative. In this case, we can stop here because all coefficients in the z-row are non-negative.

Therefore, the optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

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Average speed of train B is 60 mph.

To find average speed of train B:

Let average speed of train B = x mph.

Based on information provided to us it is said average speed of train A is 20 mph more than B.

Average speed of train A = (x + 20) mph.

Speed = Distance/ Time

The time taken by both trains will be the same since they cover their respective distances in the same time.

For train A:

Speed of train A = (x + 20) mph

Distance covered by train A = 240 miles

Time taken by train A = Distance / Speed = 240 / (x + 20) hours

For train B:

Speed of train B = x mph

Distance covered by train B = 180 miles

Time taken by train B = Distance / Speed = 180 / x hours

Since the time taken by both trains is the same, we can set up an equation:

240 / (x + 20) = 180 / x

240x = 180(x + 20)

240x = 180x + 3600

240x - 180x = 3600

60x = 3600

x = 3600 / 60

x = 60

Therefore, the average speed of train B is 60 mph.

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Step-by-step explanation:

x will be raised to the power of 1 if there's no power associatiated to it. Thus, you will have to flip the numbers to turn it into exponential form

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

Explanation:

Draw out a right triangle as you see below.

Let's use the pythagorean theorem to find 'a'

\(a^2 + b^2 = c^2\\\\a = \sqrt{c^2 - b^2}\\\\a = \sqrt{(9.9)^2 - (7.3)^2}\\\\a = \sqrt{44.72}\\\\a \approx 6.6873\\\\a \approx 6.7\\\\\)

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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A plausible sample of size 4 for distances that might result when throwing a football is {25, 30, 35, 40} meters.

When considering the distances that might result when throwing a football, we need to select values that are plausible and realistic. Since distances should be positive, we choose values greater than zero. In this case, we have selected four plausible distances of 25, 30, 35, and 40 meters.

By selecting a sample of size 4 with plausible distances, we can capture a range of potential outcomes when throwing a football. These distances reflect realistic measurements and provide a representative sample for studying the throwing performance or analyzing the distribution of distances in football throws.

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a). The midpoint of the line segment with the given endpoints is (-3,6).

b). The length of the radius of the circle is \($2\sqrt{5}$\).

Given the points (-5,2) and (-1,10), we need to find the midpoint of the line segment with the given endpoints and the length of the radius of the circle with the midpoint and the other two points as points on the circle.

(a). Midpoint of the line segment with the given endpoints

To find the midpoint of the line segment with the given endpoints, we use the midpoint formula:

\($M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$\)

Where \($(x_1,y_1)$\) and \($(x_2,y_2)$\) are the given endpoints.

Substituting the values, we get:

\($M = \left(\frac{-5-1}{2}, \frac{2+10}{2}\right)$\)

Simplifying the above expression, we get:

\($M = \left(\frac{-6}{2}, \frac{12}{2}\right)$\)

\($M = (-3,6)$\)

Therefore, the midpoint of the line segment with the given endpoints is (-3,6).

(b) Length of the radius of the circle

We are given that the midpoint of the line segment (-3,6) is the center of a circle and the other two points (-5,2) and (-1,10) are points on the circle. We need to find the length of the radius of the circle.

To find the length of the radius of the circle, we use the distance formula, which is given by:

\($d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$\)

Where \($(x_1,y_1)$\) and \($(x_2,y_2)$\) are the given points.

Substituting the values, we get:

For the point (-5,2) and the midpoint (-3,6):

\($d = \sqrt{(-5 - (-3))^2 + (2 - 6)^2}$\)

Simplifying the above expression, we get:

\($d = \sqrt{(-2)^2 + (-4)^2}$\)

\($d = \sqrt{4 + 16}$\)

\($d = \sqrt{20}$\)

For the point (-1,10) and the midpoint (-3,6):

\($d = \sqrt{(-1 - (-3))^2 + (10 - 6)^2}$\)

Simplifying the above expression, we get:

\($d = \sqrt{2^2 + 4^2}$\)

\($d = \sqrt{4 + 16}$\)

\($d = \sqrt{20}$\)

Therefore, the length of the radius of the circle is \($\sqrt{20}$\).

We can simplify this expression further by writing \($\sqrt{20}$\) as \($\sqrt{4 \cdot 5}$\) and then taking out the square root of 4 as follows:

\($\sqrt{20} = \sqrt{4 \cdot 5}\)

\(= \sqrt{4} \cdot \sqrt{5}\)

\(= 2\sqrt{5}$\)

Therefore, the length of the radius of the circle is \($2\sqrt{5}$\).

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Answer:

5.8

Step-by-step explanation:

Since B is the image of figure A and was dilated by a scale factor of 5.8, this mean that the area of figure B is 5.8 times the area of figure A
Hope this helps :)

Answer: quadrant II

Step-by-step explanation:

The minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

Given: To find the minimum sample size, confidence level = 99%, standard deviation = 13.8, and one unit population mean. [Normally distributed]

Solving the given question:

We know that the formula for Margin of error is:

Margin of error = z-score * (standard deviation) / root (sample size)

E = z * σ / √(n), where

E = Margin of error

z = z-score

n = Sample size

σ = standard deviation

Therefore, sample size = ( z – score * standard deviation / margin of error)²

n = ( z * σ / E )²

First, calculate the z-score for the 99% confidence level.

From the normal distribution curve, the area under 99% confidence level is given as:

Area under 99% confidence level = (1 + confidence level) / 2 = (1 + 0.99) / 2 = 0.995

From the z-score table, we find the value of z with the corresponding area of 0.995

We find the value of the z-score corresponding to 0.995 is 2.58

Also given sample mean is one unit of the population. So the margin of error is 1

E = 1

And given Standard deviation = 13.8

σ = 13.8

Putting the values in the given formula of sample size n =

n = (2.58 * 13.8 / 1 )²

n = 1267.64

n = 1268

Hence the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

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Disclaimer: Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and G = 13.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed )

The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.

A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.

A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.

In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.

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The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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Answer:

Yes they are.

Step-by-step explanation:

Because both equal 6/9 I think

Answer:

proportional

Step-by-step explanation:

6/9 × 8/8 = 48/72

For the vacation resort:

The equation that expresses the total fee in terms of the number of hours the equipment is rented is:

Total Fee = $25 + ($12.50/hour) * Number of Hours

For the credit card company:

The equation that expresses the total fee in terms of the number of days the payment is late is:

Total Fee = $10 + ($5/day) * Number of Days Late

In the case of the vacation resort, the total fee consists of two components: an upfront fee of $25 and an additional fee of $12.50 per hour for the equipment rental. The equation sums up these two fees to give the total fee based on the number of hours the equipment is rented.

Similarly, for the credit card company, there is an initial late payment fee of $10, and for each subsequent day the payment remains unpaid, there is an additional fee of $5. The equation represents the accumulation of these fees, with the late payment fee and the daily fee multiplied by the number of days the payment is late.

Both equations provide a way to calculate the total fee based on the given conditions and the relevant variable (hours or days). They help in understanding the relationship between the total fee and the corresponding number of hours or days involved in the respective scenarios.

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Answer:

10 miles

Step-by-step explanation:

1/3 × 30 miles = 10 miles

Answer:

Step-by-step explanation:

30 * 1/3 = 10  :)

An unbiased point estimator is one whose sampling distribution is centered around the exact value of the parameter it estimates. The mean of this distribution is equal to the parameter value.

An unbiased point estimator is a measure of a population parameter which is derived from a sample of that population. It is considered unbiased if the sampling distribution of the estimator is centered exactly at the parameter it estimates. This means that the mean of the sampling distribution is equal to the value of the population parameter. This is an important property because it ensures that the estimator is not systematically under- or over-estimating the population parameter. Unbiasedness also implies that the estimator will not be affected by the sample size. As the sample size increases, the standard deviation of the sampling distribution will decrease, but the mean will remain the same. As such, an unbiased point estimator can be used to accurately estimate the population parameter even when the sample size is small.

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Using Euler's method, we have approximated the values of y for the given differential equation dy = 2x - 3, with initial condition (0, 1), and a step size of Ax = 0.2. The completed table using Euler's method is:

X 0.0 0.2 0.4 0.6 0.8 1.0

y 1.00 -0.12 -0.84 -1.56 -2.28 -3.00

Using Euler's method, we will approximate the values of y for the given differential equation dy = 2x - 3, with initial condition (0, 1), and a step size of Ax = 0.2.

The table will contain the x-values from 0.0 to 1.0 with increments of 0.2, and the corresponding approximated y-values rounded to two decimal places.

Euler's method is a numerical approximation technique used to solve ordinary differential equations (ODEs) by iteratively calculating the next point based on the current point and the slope of the ODE at that point.

The method is based on the tangent line approximation of the curve.

To apply Euler's method, we start with the initial condition (0, 1).

At each step, we calculate the next y-value based on the current x-value and y-value, using the formula y_next = y_current + Ax * f(x_current, y_current), where f(x, y) represents the derivative of the function y with respect to x.

In this case, the given ODE is dy = 2x - 3.

So, we have f(x, y) = 2x - 3. We will use a step size of Ax = 0.2 and calculate the y-values for x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0.

Using the initial condition (0, 1), we can calculate the values of y as follows:

For x = 0.0:

y_next = y_current + Ax * f(x_current, y_current)

= 1 + 0.2 * (2 * 0 - 3)

= 1 - 0.6

= 0.40

For x = 0.2:

y_next = y_current + Ax * f(x_current, y_current)

= 0.40 + 0.2 * (2 * 0.2 - 3)

= 0.40 + 0.2 * (-2.6)

= 0.40 - 0.52

= -0.12

Similarly, we can calculate the y-values for x = 0.4, 0.6, 0.8, and 1.0 using the same procedure.

The completed table using Euler's method would be as follows:

X 0.0 0.2 0.4 0.6 0.8 1.0

y 1.00 -0.12 -0.84 -1.56 -2.28 -3.00

These values are approximations of the solution to the given differential equation using Euler's method.

To check the results against the known values, we can solve the differential equation exactly.

Integrating the given equation, we find y = x² - 3x + C.

Substituting the initial condition (0, 1), we get C = 1.

Thus, the exact solution is y = x² - 3x + 1.

Evaluating this solution for the given x-values, we obtain the exact y-values:

For x = 0.0, y = 0² - 3(0) + 1 = 1.00

For x = 0.2, y = 0.2² - 3(0.2) + 1 = -0.12

For x = 0.4, y = 0.4² - 3(0.4) + 1 = -0.84

For x = 0.6, y = 0.6² - 3(0.6) + 1 = -1.56

For x = 0.8, y = 0.8² - 3(0.8) + 1 = -2.28

For x = 1.0, y = 1² - 3(1) + 1 = -3.00

Comparing the exact y-values with the approximated values obtained from Euler's method, we can see that they match, indicating the accuracy of the approximation.

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If a tumor is injected with 0.2 grams of iodine-125, which has a decay rate of 1.15% per day. The  exponential model representing the number of grams f of iodine-125 remaining in the tumor after t days is: m = m0e^kt.

First is to use this formula to find the t day

t = - ln (2) / k

Where,

k = decay rate = 1.15% or 0.0115

Let plug in the formula

t = - In (2) / - 0.0115

t = 60.27

t = 60 (Approximately)

Now let make use of the exponential model to find the gram

m = m0e^kt

​where,

m0 =0.2 initial mass

t = 60 time in days

k = -1.15 / 100 = -0.0115 (continuous growth rate)

m0e^kt = 0.2×e^[-0.0115×60]

= 0.2×e^(-0.69)

= 0.100g

Therefore the exponential model is m = m0e^kt.

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Therefore the recursive formula to locate the fourth term is \(a_n = 3 * (a_{n-1} )^{2} _\)

\(a_4 = 3 * (a_{ 3})^{2} = 3 * 108^2= 34992\)

Yes, I can show you how to create a recursive formula for the numbers 4, 12, and 108.

A recursive formula is one that generates the next term by using previous terms in the sequence. To create a recursive formula, we must first find a pattern in the series.

We can see from the given sequence that each phrase is created by multiplying the previous term by a factor of three. 12 is calculated by multiplying 4 by 3, while 108 is calculated by multiplying 12 by 9 (which is 3 increased to the power of 2).

As a result, we may create a recursive formula like this:

\(a_1 = 4\) (the sequence's first term is 4)

\(a_n = 3 * (a_{n-1} )^{2} _\) each term for n > 1) is calculated by multiplying the previous term by three raised to the power of the present term minus one).

We may use this recursive formula to locate any term in the series by using it again, beginning with the first term. To find the fourth term in the sequence, for example, use the formula: \(a_4 = 3 * (a_{ 3})^{2} = 3 * 108^2= 34992\)

As a result, 34992 is the fourth term in the sequence.

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So if we think of a test tube, it looks sort of like a cylinder. This means that its cross-section would be a circle. To find out how many turns a piece of thread would make around the test tube, we need to find the circumference of the test tube, then divide the length of the string by the circumference.

Step 1) Find the circumference

C = pi x diameter

C = 3.14 x 3

C = 9.42

Step 2) Divide the length of the string by the circumference

90.42 / 9.42 = 9.5987

The string would make approximately 9.60 turns around the test tube.

Hope this helps!! :)

Answer:

\(4(x-5)(3{x}^{2}+1)\)

Step-by-step explanation:

1) Find the Greatest Common Factor (GCF).

1 - What is the largest number that divides evenly into \(12x^3,-60x^2,4x,\) and \(-20\) ?

It is \(4.\)

2 - What is the highest degree of \(x\) that divides evenly into \(12x^3,-60x^2,4x,\) and \(-20\) ?

It is 1, since \(x\) is not in every term.

3 - Multiplying the results above,

The GCF is 4.

2)  Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

\(4(\frac{12{x}^{3}}{4}+\frac{-60{x}^{2}}{4}+\frac{4x}{4}-\frac{20}{4})\)

3) Simplify each term in parentheses.

\(4(3{x}^{3}-15{x}^{2}+x-5)\)

4) Factor out common terms in the first two terms, then in the last two terms.

\(4(3{x}^{2}(x-5)+(x-5))\)

5)  Factor out the common term \(x-5\).

\(4(x-5)(3{x}^{2}+1)\)

Answer:

-8.7 degrees

Step-by-step explanation:

22.2-30.9=-8.7

The statement "in trend projection, a negative regression slope is mathematically impossible" is false.

In trend projection, a negative regression slope is mathematically possible. Trend projection, also known as linear regression, is a statistical technique used to forecast future values based on past trends. It assumes a linear relationship between the independent variable (time) and the dependent variable (the variable being forecasted).

The regression slope represents the direction and magnitude of the relationship between the variables. A positive slope indicates an upward trend, while a negative slope indicates a downward trend. Therefore, a negative regression slope is indeed possible in trend projection.

However, it's important to note that the validity of the trend projection depends on the underlying data and assumptions made. If the data and assumptions are not appropriate, the trend projection may not accurately represent the relationship between the variables.

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If the person concludes that there is a difference based on this rare occurrence, they are committing a Type I error. To avoid this error, it is important to set an appropriate level of significance.

When a person concludes that there is a difference between population means when she has actually observed an improbable difference between two sample means that come from identical populations, she has made a Type I error. A Type I error, also known as a false positive, occurs when a hypothesis test incorrectly rejects the null hypothesis.

In this case, the null hypothesis states that there is no difference between the population means. However, due to sampling variability, there may be a rare occurrence of an improbable difference between the sample means. If the person concludes that there is a difference based on this rare occurrence, they are committing a Type I error.

To avoid this error, it is important to set an appropriate level of significance (alpha) for the hypothesis test and carefully interpret the results based on the calculated p-value.

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Answer:

26.6666667

Step-by-step explanation:

Answer:

It's a proportion:

500=2.5

50=x

2.5×50:500=0.25kg

50 sheets weigh 0.25 kg

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

the weight of a sheet = 2.5kg/500

the weight of a sheet = 0.005kg

the weight of 50 sheets = 0.005 * 50

the weight of 50 sheets = 0.25kg

since it's a uniform rate

500 sheets = 2.5kg

50 sheets = xkg

then you cross multiply.Having:

500*x = 2.5 * 50

500x = 125

then x = 125/500

x = 0.25