Find \( i_{1}, i_{2}, i_{3} \)

Answer:

  x = -6

Step-by-step explanation:

You want the x-coordinate of point X(x, 7) such that line WX is parallel to line UV when the points are U(1, -9), V(5, 7), W(-8, -1).

It works fairly nicely to graph the given points. This lets you see that line UV has a rise/run of 4/1. You can find the desired point by drawing a line through W with the same slope. It crosses the horizontal line y=7 at x = -6.

The point of interest is X(-6, 7), where x = -6.

The slope of UV is ...

  m = (y2 -y1)/(x2 -x1)

  m = (7 -(-9))/(5 -1) = 16/4 = 4

Then the point-slope equation of the line through W is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -(-1) = 4(x -(-8)

Solving for x gives ...

  (y +1)/4 -8 = x

  (7 +1)/4 -8 = x = -6 . . . . . . . for point (x, 7)

The x-coordinate of point X is -6.

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The probability of picking a white ball from Box 2 after a ball is moved from Box 1 is 5/10, or 50%.

To explain this, we must first calculate the probability of picking a white ball from Box 1 and then moving that ball to Box 2.  Box 1 has 4 red balls and 6 white balls, so the probability of picking a white ball from Box 1 is 6/10, or 60%.

Now, since the ball is moved to Box 2, the ratio of red balls to white balls changes from 7:3 to 8:3. Therefore, the probability of picking a white ball from Box 2 is now 3/11, or 27.27%.

To calculate the final probability, we must use conditional probability. The probability of picking a white ball from Box 2 given that a ball is moved from Box 1 is equal to the probability of picking a white ball from Box 1 multiplied by the probability of picking a white ball from Box 2. This gives us the answer of 6/10 x 3/11 = 5/10 = 50%.

In conclusion, the probability of picking a white ball from Box 2 after that ball is moved from Box 1 is 5/10, or 50%.

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Answer:

19

Step-by-step explanation:

Answer:

Total amount spent for meal = $16.65

Step-by-step explanation:

Given:

Amount spent on dinner = $20

Tip = 20%

Find:

Total amount spent for meal

Computation:

Total amount spent for meal = Amount spent on dinner / (1+tip)

Total amount spent for meal = 20 / 1.2

Total amount spent for meal = 16.666

Total amount spent for meal = $16.65

Answer:

x=-1½

Step-by-step explanation:

1/3^x=27^x+2

3^-x=3^3x+6

-x=3x+6

-6=3x+x

-6=4x

x=-1½

The quadratic solution of the linear system of equations y = x2 + 5x - 3 is y = (x+3)(x-1).

1. Rewrite the equation as y = x2 + 5x - 3

2. Factor the equation by grouping the terms: y = (x+3)(x-1).

3. Set each factor equal to 0 and solve for x: x+3 = 0 and x-1 = 0

4. Solve each equation: x = -3 and x = 1

5. Substitute the values of x into the original equation to find the corresponding values of y:

y = (-3+3)(-3-1) = (-3)(-4) = 12

y = (1+3)(1-1) = (4)(0) = 0

Therefore, the solution of the linear quadratic system of equations y = x2 + 5x - 3 is y = (x+3)(x-1).

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It is safe to say that it is nearly impossible for devices to be produced at zero production costs.

It is highly unlikely that any devices will be produced if the production cost is R0,00 (assuming R refers to South African Rand). There are various factors involved in the production of devices, including the cost of materials and labor, research and development, marketing, and distribution costs.

Even if we disregard the cost of materials and labor, there are still other production expenses that cannot be escaped, like facility costs, machinery, and intellectual property rights. Furthermore, marketing and distribution costs add considerable expenses.

Therefore, it is safe to say that it is nearly impossible for devices to be produced at zero production costs. Even if a device could somehow be developed without incurring any initial costs, other costs incurred during the device's production, such as power costs, facility rent, and salaries, would have to be covered. Therefore the reality is that there is always a cost involved in producing any device, and that cost must be factored in for any real-world production.

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Step-by-step explanation:

Just use the equation y-y1=m(x-x1)

Where you plug in (-8,5) at your and x1. Then you do the Algebra.

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

The mean yield for the three temperatures are equal.

Temperature is a unit used to express how hot or cold something is. It can be expressed using the Celsius or Fahrenheit scales, among others. Temperature shows which way heat energy will naturally flow, i.e., from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Given:

Number of groups \(k=3\)

Number of observation in group 50°C, \(n_{1} =5\)

Number of observation in group 60°C, \(n_{2} =5\)

Number of observation in group 70°C, \(n_{3} =5\)

Total number of observation \(N=15\)

Null hypothesis \(H_{0}\) :

The mean yield for the three temperatures are equal.

Alternative hypothesis \(H_{1}\) : The mean yield for the three temperatures are not equal.

Now, Sum of the squares of between groups:

⇒∑  \(n_{i} (X_{i} -X)^{2}\)

Here, \(X_{i}\) is the mean of the jth group, \(X\) is the overall mean and \(n_{1}\) is the sample size of the jth group.

\(X=\frac{X_{1} +X_{2}+...+X_{i} }{i}\)

\(X_{1} =34+24+36+39+32=165\\X_{2} =30=31+34+23+27=145\\X_{3} =23+28+28+30+31=140\)

\(X_{i} =\frac{X_{i} }{n_{i} }\)

⇒ \(X_{1} =\frac{165}{5} =33\)

⇒ \(X_{2} =\frac{145}{5} =29\)

⇒ \(X_{3} =\frac{140}{5} =30\)

\(=n_{1} (X_{i} -X)^{2}+n_{2} (X_{2} -X)^{2}+n_{3} (X_{3} -X)^{2}\)

SSB= 5 × \((33-30)^{2}\)+ 5 × \((29-30)^{2}\) + 5 × \((28-30)^{2}\)

      = 5 × \(3^{2}\) + 5 × \(1^{2}\) + 5 × \(2^{2}\)

      = 5 × 9 + 5 × 1 + 5 × 4

      = 45 + 5 + 20

      = 70

Now, Sum of difference between each element and grand mean squared (SST)

⇒ \((34-30)^{2} +(34-30)^{2}+(36-30)^{2} +...+(31-30)^{2}\)

⇒ 306

Now, SSE = SST - SSB

= 306 - 70 = 236

Therefore,

Source of         Sum of                 Degrees of                   Mean

variation         squares             freedom                    square

Between      \(SSB=70\)           \(df_{1} =k-1=2\)            \(MSB=\frac{SSB}{df_{1} } =\frac{70}{2} =35\)          

groups

Error    \(SSE=236\)        \(df_{2} =N-k=12\) \(MSE= \frac{SSE}{df_{2} } =\frac{236}{2} =19.67\)                                          

Total                \(306\)

Given .05 level of significance. i.e, \(F(0.05,2,12)=3.8853\) tabulated value.

As \(1.7794 < 3.8853\), tabulated value is higher than calculated value.

So, the null hypothesis is accepted.

Hence, the mean yield for the three temperatures is equal.

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Answer:

5 minutes per mile

Step-by-step explanation:

15 divided by 3 = 5

The soccer team and the football team will have to share the field again after 30 days.

To find the number of days until the soccer team and the football team have to share the field again, we need to find the least common multiple (LCM) of 3 and 10.

The LCM is the smallest number that is divisible by both 3 and 10. In this case, the LCM of 3 and 10 is 30.

Therefore, after 30 days, the soccer team and the football team will have their practice sessions on the same day and will need to share the field again.

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[1] 11

    This is basic addition.

-14 + 25 = 11

[2] 186 in²

    We will break the shape up into two different pieces. See attached.

    The area of a rectangle can be found with A = L * W.

A = L * W

A = (27 in) * (3 in) = 81 in²

-

A = L * W

A = (15 in) * (7 in) = 105 in²

    Now, we will add the two parts together.

81 in² + 105 in² = 186 in²

Considering supplementary angles, we have that the measures of x and y are given as follows:

We also have that x and y have different measures, hence the student is incorrect, and x and 40º are complementary.

Supplementary angles are angles whose measures add to 180º.

The three internal angles of a triangle are supplementary, hence we can find x as follows:

90 + 40 + x = 180

130 + x = 180

x = 50º.

Angles x, y and 50º are also supplementary, hence:

x + y + 50 = 180

50 + y + 50 = 180

y = 80º.

The angles with measures x and 40º are complementary, as they add to 90º.

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Answer:

sum up to 130 but not equal

Step-by-step explanation:

A large sample size and low variability increase the likelihood of rejecting the null hypothesis, while a small sample size and high variability decrease the likelihood of rejecting the null hypothesis.

When a sample is selected from a population and a treatment is administered, it is important to determine if the treatment had a significant effect on the sample. This is done by comparing the sample mean to the original population mean and testing if the difference is statistically significant.

If there is a 3-point difference between the sample mean and the original population mean, the likelihood of rejecting the null hypothesis depends on the characteristics of the sample. In particular, the size of the sample and the variability of the data can influence the likelihood of rejecting the null hypothesis.

If the sample size is large and the data is relatively homogeneous (low variability), then even a small difference between the sample mean and the population mean may be statistically significant. This is because a larger sample size allows for more precision in estimating the population mean and reduces the effect of random sampling error.

On the other hand, if the sample size is small and the data is highly variable, a larger difference between the sample mean and the population mean may be required to reject the null hypothesis. This is because a small sample size and high variability increase the uncertainty in estimating the population mean and make it more difficult to detect small differences.

In summary, when there is a 3-point difference between the sample mean and the original population mean, the likelihood of rejecting the null hypothesis depends on the sample characteristics, specifically the size of the sample and the variability of the data.

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We can use the shell approach to get the solid's volume that results from rotating a plane region around the line x. A cylindrical shell's height times its circumference are integrated using the shell method.

What are the steps to use this method?

Here are the steps to find the volume using the shell method:

1. Determine the limits of integration for the x-coordinate. These limits represent the x-values of the region that is being revolved.

2. Express the radius of each cylindrical shell as a function of x. This can be done by finding the distance from the x-axis to the line x for each x-value within the region.

3. Determine the height of each cylindrical shell. This is equal to the difference between the upper and lower y-values of the region at each x-value.

4. Set up the integral using the formula for the volume of a cylindrical shell:

  \(V = ∫ [2π(radius)(height)] dx\)
 
  Integrate the expression with respect to x over the determined limits of integration.

5. Evaluate the integral to find the volume of the solid generated.

Remember to include the terms "shell method," "volume," "solid," "plane region," and "line x" in your answer.

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To find the volume of the solid generated by revolving a plane region about the line x, we can use the shell method. The shell method involves integrating the product of the circumference of a shell and its height over the desired interval.

Here's how you can use the shell method to find the volume step-by-step:
1. First, identify the plane region that needs to be revolved around the line x. This region should be bounded by a curve or curves.
2. Determine the limits of integration, which define the interval over which the region will be revolved around the line x.
3. Choose a vertical shell within the region. The shell should be an infinitesimally thin strip that is parallel to the line x and perpendicular to the axis of rotation.
4. Calculate the circumference of the shell. This can be done by multiplying the height of the shell (which corresponds to the change in x) by 2π.
5. Calculate the height of the shell. This can be determined by finding the difference between the upper and lower curves at a particular x-value.
6. Multiply the circumference and height of the shell together to obtain the volume of that shell.
7. Integrate the volumes of all the shells over the interval using the limits of integration determined earlier.
8. Simplify and evaluate the integral to find the final volume of the solid.

Remember to adjust the integral if the region is rotated around a line other than the x-axis.
It's important to note that without the specific equation or region you're working with, I can't provide an example calculation. However, if you provide the equation or region, I'll be happy to walk you through the steps.

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For this combination can be used , the answer would be  639450 ways

What is combination?

In arithmetic, a combination may be a choice of things from a group that has distinct members, such the order of choice doesn't matter.

Main body:

Given, the total number of members in the chorus are 30.

Also, it is given that 6 members from the chorus have to be

chosen for a special performance.

The number of ways of choosing r people out of given n people

is given by the expression

nCr

= n!/r!(n-r)!

So the number of ways of choosing 6 members out of 30 are

³⁰C₆

=  30!/24!6!

= 639450 ways

But since only the expression to represent the number of ways

was asked not the exact number of ways we can leave the

answer as ³⁰C₆ .

Hence total number of ways is 639450 ways.

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To solve a 3×3 augmented matrix use the method of elementary row operations.

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

An augmented matrix for a system of equations is a matrix of numbers where each column contains all the coefficients for a single variable and each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign).

The system of equations are - x - 2y + 3z = 7, 2x + y + z = 4, -3x + 2y -2z = -10

Here is the augmented matrix for this system.

\(\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-3 & 2 & -2 & -10\end{array}\right]\)

This matrix can be solved using the method of elementary row operations.

Interchange Two Rows. With this operation interchange all the entries in row  i and row j. The notation used here is Ri ↔ Rj.

\(\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-3 & 2 & -2 & -10\end{array}\right] \stackrel{R_1 \leftrightarrow R_3}{\rightarrow}\left[\begin{array}{rrr|r}-3 & 2 & -2 & -10 \\2 & 1 & 1 & 4 \\1 & -2 & 3 & 7\end{array}\right]\)

Multiply a Row by a Constant. In this operation multiply row i by a constant c and the notation will be cRi.

\(\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-3 & 2 & -2 & -10\end{array}\right] \stackrel{-4 R_3}{\rightarrow}\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\12 & -8 & 8 & 40\end{array}\right]\)

Add a Multiple of a Row to Another Row.

Row i will be replaced in this procedure with row i times a constant c plus row j. Ri + cRi → Rj is the notation for this operation. This procedure involves taking an input from row i multiplying it by c, adding the equivalent value from row j, and then returning the result to row i.

\(\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-3 & 2 & -2 & -10\end{array}\right] \begin{gathered}R_3-4 R_1 \rightarrow R_3 \\\rightarrow\end{gathered}\left[\begin{array}{rrr|r}1 & -2 & 3 & 7 \\2 & 1 & 1 & 4 \\-7 & 10 & -14 & -38\end{array}\right]\)

Let’s go through the individual computation to make sure you followed this.

-3 - 4(1) = -7

2 - 4(-2) = 10

-2 - 4(3) = -14

-10 - 4(7) = -38

Therefore, the matrix is solved using row operations.

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Answer:

The y intercept is (0,-1)

Step-by-step explanation:

To find the y intercept, let x = 0

y = -x^2 -6x-1

y = -0^2-6(0) -1

y = -1

The y intercept is (0,-1)

To create a sign chart for the polynomial function F(x) = -(x+5)(x-2)(2x-4)(x-4)², we will examine the intervals defined by the critical points and the zeros of the function.

1. Determine the critical points  -

  - The critical points occur where the factors of the polynomial change sign.

  - The critical points are x = -5, x = 2, x = 4, and x = 4 (repeated).

2. Select test points within each interval  -

  - To evaluate the sign of the polynomial at each interval, we choose test points.

  - Common choices for test points include values less than the smallest critical point, between critical points, and greater than the largest critical point.

  - Let's choose test points  -  x = -6, x = 0, x = 3, and x = 5.

3. Evaluate the sign of the polynomial at each test point

  - Plug in the test points into the polynomial and determine the sign of the expression.

The sign chart for F(x) = -(x+5)(x-2)(2x-4)(x-4)² would look like this

Intervals              Test Point         Sign

-∞ to -5                  -6                    -

-5 to 2                   0                       +

2 to 4                    3                      -

4 to ∞                    5                      +

Note  - The signs in the "Sign" column indicate whether the polynomial is positive (+) or negative (-) in each interval. See the attached sign chart.

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Since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

If every term of the sequence is either greater than or equal to (≥) some number M or less than or equal to (≤) some number N (finite numbers), then the sequence is said to be bounded.

Otherwise, the sequence is said to be unbounded. And, if a sequence has a convergent subsequence, then the sequence is called bounded.

Let’s look at the example to answer the question.

Example of an unbounded sequence that has a convergent subsequence:

Let {an} = 1, 2, 3, 4, 5, 6, 7, …It is an unbounded sequence since there is no number that can be defined as M or N, that will make every term of the sequence less than or equal to (≤) or greater than or equal to (≥) this number (M or N).

However, {an} = 1, 2, 3, 4, 5, 6, 7, … has a convergent subsequence which is {an} = 1, 2, 3, 4, 5, 6, 7, … itself.

And, since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

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Answer:

14

Step-by-step explanation:

You multiply the negatives and then you get the positive.

Answer:

3/10 of the total distance to her grandmother's house was traveled on Sunday

Step-by-step explanation:

Carly's family traveled distance of Saturday = \(\frac{3}{10}\)

Remaining distance =\(1-\frac{3}{10}=\frac{7}{10}\)

They traveled 3/7 of the remaining distance on Sunday.

So, Distance traveled on Sunday =\(\frac{3}{7}(\frac{7}{10})\)

Distance traveled on Sunday =\(\frac{3}{10}\)

Fraction of the total distance to her grandmother's house was traveled on Sunday =\(\frac{3}{10}\)

Hence 3/10 of the total distance to her grandmother's house was traveled on Sunday

Answer:

there are 8 pieces total

The average angular velocity during the dive is 10.78 rad/sec.

Given,

displacement of the diver = 10.4m

as the diver falls freely then the acceleration will be g=9.8 \(m/s^2\)

To find average angular velocity during dive use formula,

\(\omega=\frac{\theta}{t}\)

where, θ=angular displacement and t= time taken to reach water

the diver makes 2.5 revolutions, here 1 revolution is 2π radians then total angular displacement is

θ=2.5* 2π=15.7 radian

To find time taken, use formula \(s=ut+\frac{1}{2}gt^2\)

here u=initial velocity=0

s=displacement of diver=10.4m

\(10.4=0+\frac{1}{2}9.8t^2\\\\10.4=4.9t^2\\\\2.122=t^2\\\\t=1.456 s\)

angular velocity, \(\omega=\frac{15.7}{1.456}=10.78\ rad/sec\)

Thus, the average angular velocity during the dive is 10.78 rad/sec.

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Answer:

if your looking for z it is 5/8k+2.375

Step-by-step explanation:

Answer:

Step-by-step explanation:

Please, include the instructions.

I'm assuming you want to solve this system of linear equations for z and w, assuming that k is an unknown constant.

Use the method of elimination by addition and subtraction.  To eiiminate w, multiply all four terms of the first equation by 10, obtaining:

10 z + 10w - 30 = 10k

6z   - 10 w        = 80

Then 16z - 30 - 80 = 10k, or

16z  -110 = 10k,  Simplifying this, we get:

      10(k + 11)  

z = ---------------

            16

Substituting this expression for z into the first equation, we get:

(10/16)(k + 11) + w - 3 = k.  We must solve this for w:

-(10/16)(k + 11) + w - 3 = k), or

-(10/16)(k + 11) - w + 3 = -k

Then -(10/16)(k + 11) + 3 + k = w

and so the solution, in terms of the unknown constant k, is

      10(k + 11)  

(     --------------,  -(10/16)(k + 11) + 3 + k   )

            16

Answer:

1/36

Step-by-step explanation:

hope this helps:0

Answer:

1/6

Step-by-step explanation:

with a six sided dice a possible outcome writing a two out of six is one

1.  The present value of the fuel oil cost for heat is approximately $30,167.62.

2. The Savings to Investment Ratio (SIR) for the cooling tower replacement is approximately 2.2143.

3. The Return on Investment (ROI) for the solar electric system is 25%.

To calculate the Present Value (PV) of the fuel oil cost for heat, we can use the formula for present value of a series of cash flows:

PV = CF / (1 + r)ⁿ

Where:

CF = Annual cost

r = Annual interest rate

n = Number of years

In this case, the annual cost is $80,000, the annual interest rate is 5% (or 0.05), and the estimated useful life is 20 years. The escalation rate is not needed for this calculation.

PV = $80,000 / (1 + 0.05)²⁰

PV = $80,000 / (1.05)²⁰

PV = $80,000 / 2.65329770517

PV ≈ $30,167.62

Therefore, the present value of the fuel oil cost for heat is approximately $30,167.62.

The Savings to Investment Ratio (SIR) can be calculated using the following formula:

SIR = (LCC of Present System - LCC of New System) / Cost of New Equipment

Given:

LCC of Present System = $85,000

LCC of New System = $54,000

Cost of New Equipment = $14,000

SIR = ($85,000 - $54,000) / $14,000

SIR = $31,000 / $14,000

SIR ≈ 2.2143

Therefore, the Savings to Investment Ratio (SIR) for the cooling tower replacement is approximately 2.2143.

The ROI (Return on Investment) can be calculated using the following formula:

ROI = (Net Profit / Cost of Investment) ×100

Given:

Cost of Investment = $10,000

Net Profit = Annual savings in electricity costs = $2,500

ROI = ($2,500 / $10,000) × 100

ROI = 0.25 × 100

ROI = 25%

Therefore, the Return on Investment (ROI) for the solar electric system is 25%.

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If the length of AC equals 50, the length of the midsegment DE is 25.