In woodshop class, you must cut several pieces of wood to within 3/16 inch of the teacher's specifications. Let (s-x) represent the difference between the specification s and the measured length x of a cut piece.

(a)Write an absolute value inequality that describes the values of x that are within the specifications.

(b) The length of one piece of wood is specified to be s=5 1/8 inches. Describe the acceptable lengths for this piece.

Answer:

The probability that the balls are the same color is [tex]\frac{175-7x}{250}[/tex] where x is the number of blue balls in the second urn

Step-by-step explanation:

Let's call x the number of blue balls in the second urn. Since there are 25 ball in this urn, the number of red balls would be 25 - x.

Now, we're looking for the probability that the balls are the same color, this means, that both balls are either blue OR red. (since we're using "or", this gives us the clue that we will sum up both probabilities.

1) P(both balls are the same color) = P(both balls are blue) + P( both balls are red).

2) Now we will find what is the probability that both balls are blue (this will be a multiplication since we need that ball 1 is blue AND ball 2 is blue:

P(both balls are blue) = P(ball 1 is blue) x P(ball 2 is blue)

P(both balls are blue) = [tex](\frac{3}{10} )(\frac{x}{25} )[/tex] = [tex]\frac{3x}{250}[/tex]

3) To find what is the probability that both balls are red, the process is similar than when both are blue.

P(both balls are red) = P(ball 1 is red) x P(ball 2 is red)

P(both balls are red) = [tex](\frac{7}{10} )(\frac{25-x}{25} )[/tex]= [tex]\frac{175-7x}{250}[/tex]

4) Going back to 1) and substituting:

P(both balls are the same color) = [tex]\frac{3x}{250} +\frac{175-7x}{250} \\ \\ = \frac{3x-7x+175}{250} \\ \\=\frac{175-4x}{250}[/tex]

Final answer:

The probability that the balls are the same color is 17/40.

Explanation:

The probability that the balls are the same color is 17/40.

To calculate this, we need to find the probabilities of both balls being red and both balls being blue and then add them together.

Probability of both balls being red: (7/10) * (26/35) = 182/350

Probability of both balls being blue: (3/10) * (9/35) = 27/350

Finally, add the two probabilities: 182/350 + 27/350 = 209/350 = 17/40

Could not do the 2nd one, but will update if I figure it out

To analyze each graph and determine the scenario it models, first, understand the variables on the axes. Label the x- and y-axis with the appropriate quantity and unit of measure. Finally, label each tick mark with the correct intervals based on the scale of the graph.

In order to analyze each graph and determine the scenario it models, we need to understand the information represented on the axes. The x-axis typically represents the independent variable, while the y-axis represents the dependent variable. For example, in a graph showing time on the x-axis and distance on the y-axis, we can determine if the scenario is representing a moving object and measure the time intervals along the x-axis and the distance intervals along the y-axis.

Once we understand the variables represented on the axes, we can label them accordingly. For instance, if the x-axis represents time, we would label it as 'Time (seconds)' or 'Time (minutes)', depending on the unit of measure. Similarly, if the y-axis represents distance, we would label it as 'Distance (meters)' or 'Distance (kilometers)', again depending on the unit of measure.

We would then label each tick mark with the correct intervals based on the scale of the graph. For example, if the x-axis represents time and each tick mark represents 1 second, we would label each tick mark as '1s', '2s', '3s', etc. The same applies to the y-axis based on the unit of measure.

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Answer:

Phyllis will get $33280.

Jim will get $8320.

Step-by-step explanation:

Jim Murray and Phyllis Lowe received a total of $52,000 from a deceased relative's estate. They decided to put $10,400 in a trust for their nephew and divide the remainder.

The remainder = [tex]52000-10400=41600[/tex] dollars

Phyllis received 4/5 of the remainder; = [tex]0.8 \times41600=33280[/tex] dollars

Jim received 1/5 ; =[tex]0.2\times41600=8320[/tex] dollars

So, Phyllis will get $33280.

Jim will get $8320.

Phyllis received $18,720, which was 45% of the remaining estate, while Jim received $6,240, which was 15% of the remaining estate.

Jim Murray and Phyllis Lowe received a total of $52,000 from a deceased relative's estate. They first put $10,400 in a trust for their nephew. This leaves $52,000 - $10,400 = $41,600 remaining to divide between Jim and Phyllis. Phyllis received 45% of the remainder and Jim received 15% of the remainder.

To find out how much Phyllis received, calculate 45% of $41,600, which is $41,600 x 0.45 = $18,720. To find out how much Jim received, calculate 15% of $41,600, which is $41,600 x 0.15 = $6,240. Therefore, Phyllis received $18,720 and Jim received $6,240 from the remaining estate after the trust was funded.

Answer:

Asset B generate most benefit.

Step-by-step explanation:

Correlation shows the strength of relation between two variables.

Greater the correlation coefficient greater the strength between two variables.

Since here It is given that Correlation Coefficient between risk reduction and Asset B is higher (i.e. 60%) than the Correlation Coefficient between risk reduction and Asset A (i.e. 40%).

Thus, Asset B generate most benefit.

For risk reduction in a 2-asset portfolio, a lower correlation coefficient would be most beneficial, specifically one closer to -1. This is due to the fact that negative correlation allows for diversification, where one asset rises as the other falls, reducing overall volatility and risk.

In terms of reducing risk for a 2-asset portfolio, a lower correlation coefficient would generate the most benefit. This means two assets that tend not to move in the same direction at the same time. In other words, a negative correlation between Asset A and Asset B would be most beneficial for risk diversification. If Asset A goes up when Asset B goes down, and vice versa, these movements could cancel out and reduce the overall volatility of the portfolio.

Correlation coefficients range from -1 to +1. A coefficient of +1 indicates that the two assets move perfectly together, i.e., they have a perfect positive correlation. A coefficient of -1 means that the two assets move perfectly oppositely, i.e., they have a perfect negative correlation. A coefficient near zero indicates little or no correlation between the assets.

Therefore, the most useful correlation coefficient for risk reduction would be the one closer to -1. This is because the negative correlation coefficients allow for diversification – one asset zigging while the other is zagging – and this helps to provide a safety net against significant loss in the portfolio.

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Answer:

This statement is an example of - statistical inference

Step-by-step explanation:.

A political pollster states: "Fifty-seven percent of all voters approve of the President."

This statement is an example of - statistical inference

Statistical inference is defined as the process of drawing conclusions about populations by using data analysis.

There are two types of statistical inference - statistical estimation and statistical hypothesis testing.

Answer:

15

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Combine like terms: 5x + 3x = 8x

Divide both sides by 8: 8x/4; 32/8

Solve for x: x = 4

Plug it in: DE = 5(4) = 20

Check: 5(4) + 3(4) = 32; 20 + 12 = 32

Answer:

[tex]c = \cfrac{\pi}{3}[/tex]

Step-by-step explanation:

We can see in the first figure that area enclosed between the curves is a triangle like shape that is between the x= 0 axis and the two cosine curves, whose top vertex is the point (0,1) . We can calculate its area by integration, but first we must find the intersection between cos(x) and cos (x-c)

We can check easily that the intersection between these curves will always be [tex]x= \cfrac{c}{2}[/tex] because cos is an even function.

[tex]\cos\Big(\cfrac{c}{2}-c\, \Big) = \cos\Big(-\cfrac{c}{2}\, \Big) = \cos\Big( \cfrac{c}{2}\, \Big)[/tex]

Where the last step is justified because cosine is an even function.

now, to find the area we will integrate the difference between these functions as follows:

[tex]A= \int\limits^{\frac{c}{2}}_0 {\cos(x) - \cos(x-c)} \, dx \\\\A=  \Big[ \sin(x) - sin (x-c) \,  \Big]^{c/2 }_0\\ \\A= \sin(c/2) - \sin (-c/2) - \big( sin (0) - sin (-c)  \big) \\\\A= 2 \sin (c/2) - \sin (c)[/tex]

Where we have used the property that sine is an odd function.

Now we must find the area for the other region, which is shown on the bottom right in the second figure.

Now, we have to find for which value of x will the cos(x-c) intersect the y=0 axis. We can see tho that as the function cos(x-c) is just the cosine function displaced to the right by c units, its root will shift aswell. Therefore we see that when [tex]x= \cfrac{\pi}{2} + c[/tex] we will have that: [tex]\cos(x-c) = 0[/tex]

Now, to find the second area, (let's call it B) we integrate the difference between the top and bottom curves, in this case  y= 0 and y= cos(x-c) up until [tex]x= \pi[/tex]

[tex]B=\int\limits^{\pi}_{\pi/2+c} {0-\cos(x-c)} \, dx \\\\B=  \Big[ - \sin(x-c)\Big]^\pi_{\pi/2+c}\\\\B=  \sin(\pi/2)-\sin(\pi-c)[/tex]

And finally we set A = B:

[tex]2 \sin (c/2) - sin (c) = 1 - \sin(c)\\\\2 \sin (c/2)= 1\\\\ \sin (c/2) = \cfrac{1}{2} \implies  c/2 = \pi /6 \\\\\implies c = \cfrac{\pi}{3}[/tex]

This problem involves finding the value of 'c' such that two areas under different curves are equal. This requires setting up and solving two integral equations, which involves knowledge of trigonometric functions and calculus. This is a challenging problem.

The question asks for the value of c when the first region enclosed by the curves y = cos(x), y = cos(x - c), and x = 0 has equal area to the second region enclosed by the curves y = cos(x - c), x = π, and y = 0. To solve this, you need knowledge about trigonometric functions and properties. This is less about probability and more about areas under curves and integral calculus.

Generally, if you're asked to find areas under curves, the area between the x-axis (in this case, y=0) and the curve from x=a to x=b is given by the definite integral ∫ from a to b of f(x) dx, where f(x) is the equation of the curve. If you have not studied calculus, you might struggle with this problem because it essentially asks you to set up and solve two different integral equations and then to equate those two areas in order to solve for c.

Please seek additional help in setting up and solving these integrals if you need it. This is a challenging problem!

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Answer:

The answer is E. Impossible to determine

Step-by-step explanation:

Normally, you would find the Confidence interval of a normal sample by using

X(-+) Z* Sigma/n

Where x is the mean, sigma the standard deviation n the size of the sample and z the value  determined by your confidence interval size of 95%

.However, this approximation of a confidence interval may only be used for a sample if the number of observations is at least 30 or above.  When we have less observations than 30 we must use the standard deviation of the populations. But we only have a sample standard deviation so its not adequate or possible to determine CI the true mean of the population with such a small sample size.

Answer:

The answer to your question is letter: c) √106 units

Step-by-step explanation:

data

B (5, 3)

D (-4 , -2)

Formula

d = √((x2-x1)² + (y2-y1)²)

dBD = √(-4-5)² + (-2-3)²)

dBD = √(-9)² + (-5)²

dBD = √81 +25

dBD = √106 units

Answer:

  42 minutes

Step-by-step explanation:

time = distance / speed

time = (7/8 mi)/((1 1/4 mi)/(60 min)) = 60×(4/5)(7/8) min = 42 min

Answer:

Step-by-step explanation:

72/6=13

Answer:

Each person picked 12 bananas.

Step-by-step explanation:

Given,

Total numbers of banana = 72,

The number of persons = 6,

If each person picks equal number of bananas,

Then,

[tex]\text{Total bananas picked by each person}=\frac{\text{Total bananas}}{\text{Total persons}}[/tex]

[tex]=\frac{72}{6}[/tex]

= 12

Answer:

100 blocks.

Step-by-step explanation:

Let x represent number of blocks built by Gage.

We have been given that Colton was 5 times as fast at building the castle than Gage, so number of blocks built by Colton would be [tex]5x[/tex].

We are also told that it takes 120 blocks to build the castle. Since Colton and Gage were building a castle together, so number of blocks built by both will be equal to 120.

[tex]x+5x=120[/tex]

[tex]6x=120[/tex]

[tex]\frac{6x}{6}=\frac{120}{6}[/tex]

[tex]x=20[/tex]

Number of blocks built by Colton: [tex]5x=5\cdot 20=100[/tex].

Therefore, Colton had build 100 blocks.

Answer:

i) There are 40320 possible orders

ii) There are 336 possible orders for the first 3 positions.

Step-by-step explanation:

Given: The number of finalists = 8

The number of boys = 3

The number of girls = 5

To find the number of sample point the sample space S for the number of possible orders, we need to find factorial of 8!

The number of possible orders = 8!

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

= 40320

ii) From all 8 finalist, we need to choose first 3 position. Here the order is important. So we use permutation.

nPr =[tex]\frac{n!}{(n - r)!}[/tex]

Here n = 8 and r = 3

Plug in n =8 and r = 3 in the above formula, we get

8P3 = [tex]\frac{8!}{(8 - 3)!}[/tex]

= [tex]\frac{8!}{5!} \\= \frac{1.2.3.4.5.6.7.8}{1.2.3.4.5}[/tex]

= 6.7.8

= 336

So there are 336 possible orders for the first 3 positions.

Answer:

x=8

Step-by-step explanation:

6. an odd-degree polynomial function.

   f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

Step by step explanation;

6. The graph represent an odd-degree polynomial function.

The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;

f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

Answer:

End behavior: [tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]  and [tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]

The function has odd-degree.

The number of real zeros in 5.

Step-by-step explanation:

From the given graph it is clear that the graph approaches towards negative infinite as x approaches towards negative infinite.

[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]

The graph approaches towards positive infinite as x approaches towards positive infinite.

[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]

For even-degree the polynomial has same end behavior.

For odd-degree the polynomial has different end behavior.

Since the given functions has different end behavior, therefore the graph represents an odd-degree polynomial function.  

If the graph of a function intersects the x-axis at a point then it is a zero of the function.

If the graph of a function touch the x-axis at a point and return then it is a zero of the function with multiplicity 2. It means, the function has 2 equal zeros.

The graph intersect the x -axis at 3 points and it touch the x-axis at origin. So, the number of zeros is

[tex]N=3+2=5[/tex]

The number of real zeros is 5.

Answer:

  8

Step-by-step explanation:

The coordinates of Preston's house are ...

  2J -E = P = 2(-5, 3) -(3, -2) = (-13, 8)

The y-coordinate of P is 8.

Answer: True.

Step-by-step explanation:

Let [tex]\mu[/tex] be the population mean.

Given : Null hypothesis = [tex]H_0:\mu=160[/tex]

Alternative hypothesis =[tex]H_1:\mu<160[/tex]

Since , the alternative hypothesis is left-tailed, then the test is a left-tailed test.

The sample mean ([tex]\overlien{x}[/tex]) of the 80 students who were weighed was found to be 142 pounds and the p-value was 0.03.

We know that p-value gives that probability that if the null hypothesis is true, than the sample mean ([tex]\overlien{x}[/tex]) will be at least as small as the actual mean ([tex]\mu[/tex]).

It means that if the mean of all students’ weight is 160 lbs, then there would be only a 3% chance that a randomly selected group of 80 students would have a mean weight of less than 142 lbs.

Hence, the answer is "True".

Final answer:

The statement is true; a p-value of 0.03 indicates a 3% chance of observing a sample mean weight of 142 lbs or less if the true mean weight of all college students is 160 lbs, suggesting strong evidence against the null hypothesis.

Explanation:

The statement provided is true: if the null hypothesis is true (that college students' average weight is 160 lbs), there would only be a 3% chance that a random sample of 80 students would have a mean weight of 142 lbs or less. This small p-value (0.03) typically indicates strong evidence against the null hypothesis, suggesting that the average weight of college students is indeed less than the average American.

In other words, a p-value is the probability that we observe a sample statistic as extreme as the one measured (or more extreme) given that the null hypothesis is true. Taking another example to illustrate the concept: if the null hypothesis assumes no difference in the average height between male and female students, and we observe a sample where the difference is 4 inches with a p-value of 0.04, this means there's a 4% chance we would see at least this large a difference if in reality there was no difference at all.

Hey!

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Question #1:

= 6n^2 - 2n - 3 + 5n^2 - 9n - 6

= 6n^2 + (-2n) + (-3) + 5n^2 + (-9n) + (-6)

= (6n^2 + 5n^2) + (-2n + -9n) + (-3 + -6)

= (11n^2) + (-11n) + (-9)

Answer: 11n² + (-11n) + (-9)

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Question #2:

= 8c^2 - c + 3 + 2c^2 - c + 2

= 8c^2 + (-c) + 3 + 2c^2 + (-c) + 2

= (8c^2 + 2c^2) + (-c + -c) + (3 + 2)

= (10c^2) + (-2c) + (5)

Answer: 10c² + (-2c) + 5

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Hope This Helped! Good Luck!

Answer:

1. 11n^2-11n-9

2. 10c^2-2c+5

Step-by-step explanation:

1. 6n^2+5n^2 = 11n^2

-2n-9n = -11n

-3-6=-9

2. 8c^2+2c^2 = 10c^2

-c-c= -2c

3+2=5

Answer:

264cm2

Step-by-step explanation:

the length of line in green = 5 cm

the length of line in yellow = 3 cm

the length of line in red = 6 cm

the length of line in white = 16 cm

the total area = 100 + 12 + 12 + 20 + 24 + 96 = 264 cm2

The area of the composite figure is 262 cm².

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is side².

We have,

The composite figure has:

- 3 squares of 10 cm, 4 cm, and 6 cm.

- 1 rectangle of 3cm x 10 cm

- 1 trapezium of two paralel sides (10 cm and 6 cm) and height of 7 cm.

- 1 rectangle with 4cm x 6cm.

Now,

Area of the squares.

= 10² + 4² + 6²

= 100 + 16 + 36

= 100 + 52

= 152 cm²

Area of the rectangle.

= 3 x 10

= 30 cm²

Area of trapezium.

= 1/2 x (10 + 6) x 7

= 1/2 x 16 x 7

= 56 cm²

Area of the rectangle.

= 4 x 6

= 24 cm²

Now,

Area of the composite figure.

= 152 + 30 + 56 + 24

= 262 cm²

Thus,

262 cm² is the area.

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Answer:

D

Step-by-step explanation:

[tex]4=r cos \theta\\-4=r sin \theta\\square ~and~add\\16+16=r^2(cos^2 \theta+sin^2\theta)\\r^2=32\\ r=4\sqrt{2} \\divide \\tan \theta=-1\\as x is positive ,y is negative ,so \theta lies in 4th quadrant.\\tan \theta=-1=-tan 45=tan(360-45)=tan 315\\\theta=315°\\\\co-ordinates~ are~(r,theta) ~or~(-r,\theta+ -180°)\\hence ~co-ordinates~are(4\sqrt{2} ,315°),(-4\sqrt{2} ,135°)[/tex]

Answer:

25 seconds

Step-by-step explanation:

Hi there!

In order to answer this question, first we need to know how many bolts per second are produced by each machine, this can be known by dividing the number of bolts by the time it takes.

For machine A:

[tex]A = \frac{120 bolts}{40 s}= 3 \frac{bolts}{s}[/tex]

For machine B:

[tex]B = \frac{100 bolts}{20 s}= 5 \frac{bolts}{s}[/tex]

So, if the two machines run simultaneously, we will have a rate of prodcution of bolts equal to the sum of both:

[tex]A+B=(3+5)\frac{bolts}{s}=8\frac{bolts}{s}[/tex]

Now, we need to know how much time it will take to producee 200 bolts, to find this out we need to divide the amount of bolts by the production rate:

[tex]t = \frac{bolts}{ProductionRate}= \frac{200 bolts}{8 \frac{bolts}{s} }[/tex]

The bolts unit cancell each other and we are left with seconds

[tex]t = \frac{200}{8} s = 25 s[/tex]

So it will take 25 seconds to produce 200 bolts with machine A and B running simultaneously.

Greetings!

Answer:

25 seconds.

Step-by-step explanation:

We have been given that Machine A produces bolts at a uniform rate of 120 every 40 seconds.

Bolts made by Machine A in one second would be [tex]\frac{120}{40}=3[/tex] bolts.

Machine B produces bolts at a uniform rate of 100 every 20 seconds.

Bolts made by Machine B in one second would be [tex]\frac{100}{20}=5[/tex] bolts.

The speed of making bolts in one second of both machines running simultaneously would be [tex]3+5=8[/tex] bolts per second.

[tex]\text{Time taken by both Machines to make 200 bolts}=\frac{200\text{ bolts}}{8\frac{\text{bolts}}{\text{Sec}}}[/tex]

[tex]\text{Time taken by both Machines to make 200 bolts}=\frac{200\text{ bolts}}{8}*\frac{\text{Sec}}{\text{bolts}}[/tex]

[tex]\text{Time taken by both Machines to make 200 bolts}=25\text{ Sec}[/tex]

Therefore, the both machines will take 25 seconds to make 200 bolts.

The component of A that is parallel to B can be found using the equation A_parallel to B = (A.B)/|B|. Therefore, the component of A parallel to B is A_parallel to B = Scalar product / |B|

The component of A that is parallel to B can be found using the equation:

Aparallel to B = (A.B)/|B|

where A.B is the dot product of vectors A and B and |B| is the magnitude of vector B.

Since the scalar product is equal to the magnitude of B times the component of A parallel to B, we can rewrite the equation as:

Scalar product = |B| * Aparallel to B

Therefore, the component of A parallel to B is:

Aparallel to B = Scalar product / |B|

Answer:

The answer to your question is: 165 in

Step-by-step explanation:

Data

1 cm --------------- 60 inches

If 1 side of the courtyard measures 2.75, what is the actual size of that side?

We can solve this problem with a rule of three

                     1 cm --------------------  60 inches

                    2.75 ---------------------    x

          [tex]\frac{2.75(60)}{1}[/tex]

= 165 inches

Answer:

Tension in each half of the clothesline is 25 kg

Step-by-step explanation:

When the middle of the line is pulled down  a right triangle is formed in each half of the rope whose legs measure 0.1 m and 5 m respectively.

Since the rope has an insignificant sag, the measure of the hypotenuse of the triangle is approximately equal to that of the longer leg.

The value of the rope tension is equal to the value of the force applied divided by the sine value of the angle of the rope with the horizontal.

So,

[tex]Sin (a)=\frac{0.1}{5} = 0.02[/tex]

T=[tex]\frac{0.5 kg}{0.02}=25kg[/tex]

Answer: d 6000 bytes

Step-by-step explanation: The web server will acknowledge 6000 bytes of information after receiving 4 packets of data from the PC. This is because 1 packet of data has a size of 1500 bytes. In a situation where the web server receives 4 of these, it is 1500 multiplied by 4 which is 6000 bytes. The window size of 6000 is there to try distract you from calculating the answer correctly, it serves as a misguidance.

The byte of information that the web server acknowledge is 6000 bytes.

From the information given, were told that the web server is utilizing a window size of 6,000 bytes when sending data and a packet size of 1,500 bytes.

The byte of information that'll be received will be:

= 1500 × 4

= 6000 bytes

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A square has all 4 sides equal, so divide the amount of fence available by 4 to get the length of one side of the square

600/4 = 150

Now since the creek is being used for one side, add one side of the square to the other side to get a rectagle 150 by 300 feet.

Area = 150 x 300 = 45,000 square feet.

The maximum possible area of the pasture is;

A_max = 45000 ft²

Available fencing; Perimeter = 600 feet

Number of sides to fence; 3 sides of rectangle

Perimeter of rectangle; P = 2L + 2W

But we are told one of the edges is the creek.

Thus, New perimeter = L + 2W

thus, we have;  L + 2W = 600

L = 600 - 2W

Let's put 600 - 2W for L in the area equation to get;

A = (600 - 2W)W

A = 600W - 2W²

Thus;

dA/dW = 600 - 4W

At dA/dW = 0, we have;

600 - 4W = 0

4W = 600

W = 600/4

W = 150 ft

Let's put 150 for W in L = 600 - 2W

L = 600 - 2(150)

L = 600 - 300

L = 300 ft

 Therefore, Maximum possible area of pasture = 300 × 150 = 45000 ft²

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The question revolves around basic algebra and setting up an equality equation based on the given information. In this case, from the facts given, we can state Mai's earnings (x) in terms of Noah's earnings plus an additional amount (y), resulting in the equation x = w + y.

The subject of this problem is algebra, specifically involving variables and the concept of equality. In this problem, Noah earned an amount we will denote as w dollars over the summer. Mai, on the other hand, earned x dollars, and it's said that this is an amount of y dollars more than Noah did.

We can express Mai's earnings in terms of Noah's earnings by adding the extra amount to what Noah earned, which gives us the following equality equation:

x = w + y

This equation means that Mai's earnings (x) are equal to the sum of Noah's earnings (w) and the additional amount (y).

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let's bear in mind that B is the midpoint and thus it cuts a segment into two equal halves.

[tex]\bf \underset{\leftarrow \qquad \textit{\large 10x-6}\qquad \to }{\boxed{A}\stackrel{4x+2}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\underline{4x+2}}{\rule[0.35em]{10em}{0.25pt}\boxed{C}}} \\\\\\ AC=AB+BC\implies 10x-6=(4x+2)+(4x+2)\implies 10x-6=8x+4 \\\\\\ 2x-6=4\implies 2x=10\implies x=\cfrac{10}{2}\implies x= 5 \\\\[-0.35em] ~\dotfill\\\\ AC=(4x+2)+(4x+2)\implies AC=[4(5)+2]+[4(5)+2] \\\\\\ AC=22+22\implies AC=44[/tex]

This is a geometry problem, specifically involving the calculation of lengths using the properties of midpoints. A midpoint divides a line into two equal lengths. The problem is solved by equating the length of AB to half of AC to determine the value of x, which is then substituted back into the equation for AC to find its length.

The solution to your problem involves understanding that Point B is the midpoint of AC. A midpoint essentially divides a line into two equal lengths. Therefore, AB is equal to BC which can also be referred to as (AC/2). If AB = 4x+2 and AC = 10x-6, then to solve for the value of x, you would need to equate (4x+2) to (10x-6)/2. After solving this equation, the value of x can then be substituted back into the equation of AC to get the length of AC.

https://brainly.com/question/28224145

#SPJ3

Answer:

Equation of tangent of curve at x = 36:    

1)[tex]y = \frac{x}{12} + 3[/tex] 

2[tex]y = \frac{-x}{12} - 3[/tex]     

Step-by-step explanation:

We are given the following information:

[tex]y = \sqrt{x}[/tex]

Value of curve when x =  36:

[tex]y = \sqrt{36} = \pm 6[/tex]

Thus, [tex]y = \pm6[/tex], when x = 6.

Slope of curve, m =

[tex]\frac{dy}{dx} =\frac{d(\sqrt{x})}{dx}=\frac{1}{2\sqrt{x}}[/tex]

At x = 36,

slope of curve =

[tex]\frac{1}{2\times \sqrt{36}}\\\\m=\frac{1}{12},\frac{-1}{12}[/tex]

Equation of tangent of curve at x = 36:

[tex](y-y_1) = m(x-x_1)[/tex]

[tex]= (y-(\pm 6)) = (\pm\frac{1}{12} )(x - 36)[/tex]

Thus, equation of tangents are:

1)

[tex](y-6) = \frac{1}{12}(x-36)\\12(y-6) = x-36\\y = \frac{x}{12} + 3[/tex]

Comparing to [tex]y = mx + c[/tex], we get [tex]m = \frac{1}{12}[/tex] and [tex]c =3[/tex]

2)

[tex](y+6) = \frac{-1}{12}(x-36)\\12(y+6) = -x+36\\y = \frac{-x}{12} - 3[/tex]

Comparing to [tex]y = mx + c[/tex], we get [tex]m = \frac{-1}{12}[/tex] and [tex]c =-3[/tex]

Final answer:

The equation of the tangent line at x = 36 for the curve y = sqrt(x) is y = 1/12x + 3, found by using the slope of 1/12 and solving for the y-intercept c, which is 3.

m = 1/12

c = 3

Explanation:

To find the equation of the tangent line at x = 36 for the curve y = sqrt(x), we first identified that y = 6 when x = 36 and computed the slope of the curve, which is 1/12 at x = 36.

Using the slope-intercept form of a line, y = mx + c, where m is the slope, and c is the y-intercept, we can substitute m = 1/12 and the point (36, 6) to solve for c.
Substituting into the slope-intercept equation gives us 6 = (1/12)\(36) + c.

Solving for c, we find that the y-intercept c = 3.

Thus, the equation of the tangent line is y = 1/12x + 3.

Answer:

Step-by-step explanation:

Let "e" and "a" represent the speeds of Elvira and Aletheia, respectively. Then the total distance they cover is ...

  distance = speed × time

  (1/2)e + (2/3)a = 3.1

And the relationship between their speeds is ...

  e - a = 0.6

__

To solve this system, we can double the first equation and subtract the second to get ...

  2(1/2e +2/3a) -(e -a) = 2(3.1) -(0.6)

 7/3a = 5.6 . . . . . . . . . . simplify

  a = (3/7)(5.6) = 2.4 . . . multiply by 3/7

  e = a +0.6 = 3.0 . . . . . Elvira's speed is 0.6 mph more than Aletheia's

Elvira's walking speed is 3.0 miles per hour; Aletheia's is 2.4 miles per hour.