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The foot will be moving at a rate of 2.373 ft/s away from the wall when the top is 13 feet above the ground.

From the question, we have the following;

Hypotenuse=17 foot

Height(y)=13 feet

Base(x)=(17^2-13^2)^1/2

        =120^1/2 or sqrt(120)

The ladder against the wall is a right angle triangle, so we have:

x^2+y^2=17^2

x^2+y^2=289

Top slips down at 2ft/s

dy/dt=-2 ft/s, where height (y)=13ft

The foot will be moving horizontally(x), along the x axis, to find how fast the foot will be moving, we find dx/dt

Now, we take the derivative with respect to time:

=x^2+y^2=17^2

=2x(dx/dt)+2y(dy/dt)=0

Substitute the known values, y=13, x=sqrt(120), z=17, dy/dt=-2 ft/s

2(sqrt(120))(dx/dt)+2(13)(-2)=0

2(sqrt(120))(dx/dt)-52=0

We solve for dx/dt:

dx/dt=52/(2sqrt(120))

dx/dt=52/21.9089

dx/dt=2.373 ft/s

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Answer:

1 4/5

Step-by-step explanation:

Step-by-step explanation:

we have

2x + 3y = 6

4x + 6y = 12

do you see it right away ? both equations describe the same function or line.

the second equation is just the first equation with everything multiplied by 2. but because that happened on both sides of the equation, the equation itself is not changed.

we could divide equation 2 by 2 again, or multiply it further by e.g. 15 (as always on both sides of the equation) or, or, or ...

it would not change the information defined by the equation, and the corresponding line would still be the same.

so, both equations represent the same line.

that means both lines are covering each other perfectly (as they are identical), and so we have infinitely many intersections or solutions.

The marketing section of a business plan is completed once the market has been analyzed, and goals and objectives have been established.

The marketing section of a business plan is a crucial component that outlines the strategies and tactics to reach the target market effectively. It encompasses various aspects, including market research, target audience identification, competitive analysis, marketing goals, positioning, and promotional strategies. Before completing this section, thorough market analysis is conducted to understand the industry landscape, customer needs, market trends, and competitive dynamics. Once this analysis is complete, the business can establish clear goals and objectives based on their understanding of the market and their desired positioning. These goals can include market share targets, revenue projections, customer acquisition goals, or brand awareness objectives. The marketing section also outlines the marketing mix, including product or service offerings, pricing strategies, distribution channels, and promotional activities. By completing the marketing section, the business can articulate its marketing strategies and plans, which will guide its efforts to attract and retain customers, differentiate itself from competitors, and achieve its overall business objectives.

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The sequence of transformations that maps quadrilateral ABCD to A'B'C'D' is:

- Translation - Two units to the right and two units down.

- Reflection over the x-axis.

- Translation.

We have,

To map quadrilateral ABCD to A'B'C'D', we can use a sequence of transformations.

Translation:

We can translate point A to A' by moving it two units to the right and two units down. So, A' = (-1, 3) + (2, -2) = (1, 1).

Similarly, we translate points B, C, and D:

B' = (1, 3) + (2, -2) = (3, 1)

C' = (2, 3) + (2, -2) = (4, 1)

D' = (1, 4) + (2, -2) = (3, 2)

After the translation, we have quadrilateral A'B'C'D' with vertices A' (1, 1), B' (3, 1), C' (4, 1), and D' (3, 2).

Reflection:

Next, we can reflect quadrilateral A'B'C'D' over the x-axis. This will change the signs of the y-coordinates of the vertices.

So, the reflected coordinates are:

A'' = (1, -1)

B'' = (3, -1)

C'' = (4, -1)

D'' = (3, -2)

Translation:

Finally, we can translate quadrilateral A''B''C''D'' two units to the left and two units up. This gives us the final transformed quadrilateral.

A''' = (1, -1) + (-2, 2) = (-1, 1)

B''' = (3, -1) + (-2, 2) = (1, 1)

C''' = (4, -1) + (-2, 2) = (2, 1)

D''' = (3, -2) + (-2, 2) = (1, 0)

Therefore, the sequence of transformations that maps quadrilateral ABCD to A'B'C'D' is:

Translation: Two units to the right and two units down.

Reflection over the x-axis.

Translation: Two units to the left and two units up.

The final transformed quadrilateral A'''B'''C'''D''' is:

A''' (-1, 1)

B''' (1, 1)

C''' (2, 1)

D''' (1, 0).

Thus,

Translate A (-1, 3) to A' (1, 1), reflect over the x-axis, and translate A'' (1, -1) to A''' (-1, 1).

Repeat for the other vertices to obtain the transformed quadrilateral A'''B'''C'''D''' with vertices A''' (-1, 1), B''' (1, 1), C''' (2, 1), and D''' (1, 0).

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The cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.

Let's call the number of miniature cycles given away "x". The number of bumper stickers given away would then be 5000 - x.

The cost of the cycles is 0.62x, and the cost of the bumper stickers is 0.52 (5000 - x).

So we can write an equation to represent the total cost:

0.62x + 0.52 (5000 - x) = 2798

Expanding the second term:

0.62x + 2600 - 0.52x = 2798

Combining like terms:

0.10x = 198

Finally, solving for x:

x = 1980

So the cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.

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The 95% confidence interval for the population mean weight of bags of sugar produced by the company is [35.76, 38.24] ounces

(a) The margin of error (in ounces) is computed using the given data and 95% confidence level.

Given that a sample of 121 bags of sugar produced by Domain sugar producers showed an average of 2 pounds and 5 ounces with a standard deviation of 7 ounces.

The margin of error (in ounces) is calculated as follows;

Margin of error (in ounces) = Critical value (z*) x

Standard Error of Mean

Standard Error of Mean = Standard deviation / √n

where n = sample size

z* for 95% confidence level = 1.96Margin of error (in ounces) = 1.96 x 7 / √121 = 1.24 ounces

Therefore, the margin of error (in ounces) is 1.24.

This means that the population mean lies between 2 pounds, 5 ounces + 1.24 and 2 pounds, 5 ounces - 1.24 with 95% confidence level.

(b) 95% confidence interval for the population mean weight of bags of sugar produced by the company (in ounces) is computed using the given data.

Margin of error (in ounces) is calculated as 1.24 in part a.

The formula for calculating the 95% confidence interval is given as follows:

Confidence Interval = (sample mean) ± margin of error

Using the given data,

Sample mean = 2 pounds and 5 ounces = 37 ounces.

Confidence Interval = 37 ± 1.24 ounces≈ [35.76, 38.24] ounces

Therefore, the 95% confidence interval for the population mean weight of bags of sugar produced by the company is [35.76, 38.24] ounces.

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Answer:

parallel

Step-by-step explanation:

all horizontal lines are parallel

Answer:Parallel and all horizontal lines are parallel

Step-by-step explanation:

Answer:

1. a) x b)1

2. a)x^3 b) 3

3. a) 3x^7 b) 7

Step-by-step explanation:

The correct answer is option O: 5 V.

To determine the average voltage (Vavg) given a peak-to-peak voltage (Vpp) of 10 V, we need to consider the relationship between Vavg and Vpp in an alternating current (AC) waveform.

The average voltage of an AC waveform is related to its peak-to-peak voltage by the formula: Vavg = 0.5 * Vpp.

Applying this formula to the given Vpp of 10 V, we can calculate the Vavg as follows: Vavg = 0.5 * 10 V = 5 V.

The average voltage is equal to half of the peak-to-peak voltage, resulting in an average voltage of 5 V for a Vpp of 10 V.

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Answer:

7

Step-by-step explanation:

\(f(-2)=(-2)^2+3=4+3=7\)

Answer:1)Distance covered by cyclist=3.75 miles.

Time =0.3 hours.

Speed= Distance ÷Time

Speed =3.75÷0.3=12.5 miles per hour.

2) Speed = 12.5 miles per hour, Distance = 4.5 miles .

Time = Distance ÷Speed.

Time = 4.5÷12.5=0.36 hours.

Time taken to cover 4.5 miles is 0.36 hours.

Answer: 0.36

Step-by-step explanation:

4.5 divided by 12.5

4.5 divided by 12.5 =

= 0.36

Answer:

11/15

Step-by-step explanation:

Answer:

- 11 / 15

Step-by-step explanation:

x = - 2

y = - 1 / 5

1 / 3 + x . z

= 1 / 3 + ( - 2 ) . ( - 1 / 5 )

= 1 / 3 + ( - 2 . - 1 ) / 5

= 1 / 3 + 2 / 5

1 / 3

= ( 1 / 3 ) x ( 5 / 5 )

= ( 1 x 5 ) / ( 3 x 5 )

= 5 / 15

2 / 5

= ( 2 / 5 ) x ( 3 / 3 )

= ( 2 x 3 ) / ( 5 x 3 )

= 6 / 15

1 / 3 + 2 / 5

= 5 / 15 + 6 / 15

= ( 5 + 6 ) / 15

= 11 / 15

The 99% confidence interval for the mean operative time for this performance is approximately 133.929 to 142.271 minutes.

What is Mean?

In statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is commonly referred to as the arithmetic mean. To calculate the mean, you add all the values ​​in the set and divide the sum by the number of values.

We can use the sample data provided to construct a confidence interval for the mean operation time. Here are the steps to calculate a 99% confidence interval:

Determine the sample size (n), which is 129 operations.

Determine the sample mean (x), which is 138.1 minutes.

Find the sample standard deviation (s), which is 23.3 minutes.

Select a confidence level. In this case, it is 99%, which corresponds to a significance level (α) of 0.01.

Determine the critical value based on the confidence level and sample size. Since the sample size is large (n > 30), we can use the Z-distribution. For a 99% confidence level, the critical value is 2.576.

Calculate the standard error (SE) using the formula: SE = s / sqrt(n).

SE = 23.3/sqrt(129).

Calculate the margins of error (ME) using the formula: ME = critical value * SE.

ME = 2.576 * (23.3 / sqrt(129)).

Construct a confidence interval by adding and subtracting the margin of error from the sample mean:

Confidence interval = x ± ME.

Enter the values:

Confidence interval = 138.1 ± (2.576 * (23.3 / sqrt(129))).

Calculating the expression in parentheses:

(2.576 * (23.3 / sqrt (129))) ≈ 4.171.

Therefore, the 99% confidence interval for the mean operation time is:

Confidence Interval = 138.1 ± 4.171.

Lower bound: 138.1 - 4.171 ≈ 133.929.

Upper bound: 138.1 + 4.171 ≈ 142.271.

Thus, the 99% confidence interval for the mean operative time for this performance is approximately 133.929 to 142.271 minutes.

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By looking at the point where the lines intersect, we can see that the solution of the system is (-1, 1).

When we have a system of equations, one way of solving it is by graphing both equations in the same coordinate axis, and then finding the points where the two graphs intercept.

Here we can see two graphs of lines (so we have a system of linear equations), and we can see that they intercept at the point (-1, 1), which means that the solution of the system is that point.

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The solution for the inequalities is x > - 1 OR x < -1.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given  : 5x - 29 > -34 OR 2x + 31 < 29.

to solve the equations,

5x - 29 > -34 OR 2x + 31 < 29.

For 5x - 29 > -34

On adding both sides by 29.

5x > - 34 + 29 .

5x > -5

On dividing both sides by 5.

x > - 1 .

For 2x + 31 < 29.

On subtracting both sides by 31

2x < 29 -31

2x < - 2

On dividing both sides by 2.

x < -1

So , x > - 1 OR x < -1 .

Therefore, option A is correct.

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He took 7.616 hours for victory at the speed of 131.3009 and cover 1000 miles.

What is distance?

The distance between two sites is the length of the route. The metre is the SI unit for distance.

What is speed?

The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.

What is time?

The amount of time that something happens, goes through a process, or remains the same.

Speed= 131.3009 mph

Total distance= 1000 miles

Speed = distance/ time

time= distance/ speed

time= 1000/131.3009

(nearest thousandth means round off upto 3 decimal places)

time= 7.616 hours

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If we have an equation in the form y = kx + c where k is a constant then y and x are directly proportional with a constant of proportionality k. In this case, k = 1/2.

To determine whether the equation 2y - 5 = x which represents a direct proportion.

Here we want to check if there is a constant ratio between the variables y and x.

In the given equation,

we have the expression 2y - 5 on the left side, which represents a combination of y and a constant term (-5), and x on the right side. The equation can be rearranged to isolate y,

2y = x + 5

Now, we are dividing both sides of the equation by 2,

y = (x + 5) / 2

Now,we can see that y is equal to (x + 5) divided by 2 which means y is directly proportional to x with a constant of proportionality of 1/2.

Therefore, if we have an equation in the form y = kx + c where k is a constant then y and x are directly proportional with a constant of proportionality k. In this case, k = 1/2.

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Answer:

8 cm

Step-by-step explanation:

When you combine the two figures, you 'block off ' two 4 cm segments at the joint ..... so the combined figure is 8 cm less

To calculate the percent change in renewable energy investment in the US from 2005 to 2018, you can use the following formula:

Percent change = ((Final value - Initial value) / Initial value) * 100%

In this case, the initial value is $11.4 billion in 2005 and the final value is $46.5 billion in 2018. Plugging these values into the formula, we get:

Percent change = (($46.5 billion - $11.4 billion) / $11.4 billion) * 100%

= ($35.1 billion / $11.4 billion) * 100%

= 3.085 * 100%

= 308.5%

So, the percent change in renewable energy investment in the US from 2005 to 2018 was 308.5%, a substantial increase over the 13-year period.

Factor using the difference of cubes and set each factor equal to  0

. i believe

x  = −  4,2  +  2i√3,2  −  2i√3

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An equation is formed of two equal expressions. The value of x that can make the given equation true is -4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of x that can make the given equation true can be found as shown below,

x³ = -64

Take cube root on both sides of the equation,

∛x³ = ∛-64

Write 64 in terms of its factors,

∛x³ = ∛(-4 × -4 × -4)

x = -4

Hence, the value of x that can make the given equation true is -4.

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The test batch can be chosen in 2,002 ways. So, the correct option is D.

The problem involves combinations, which is the number of ways to choose 5 batteries from a set of 14.

The formula for combinations is:

C(n, k) = n! / (k! * (n-k)!)

Where n is the total number of items, k is the number of items chosen, and ! denotes the factorial. In this case, n = 14 and k = 5.

Plugging in the values:

C(14, 5) = 14! / (5! * (14-5)!) C(14, 5) = 14! / (5! * 9!) C(14, 5) = 87,178,291,200 / (120 * 362,880) C(14, 5) = 87,178,291,200 / 43,545,600 C(14, 5) = 2,002

Hence, based on the options given, the answer is D.

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Given equation is,

Where, n is the number of years since 1990.

To find the average programmer’s salary in 2010.

Let us find the number of years between 1990 and 2010.

So, n=20

Substitute n=20 in the above equation we get,

Hence, the average programmer’s salary in 2010 is $102,000.

Hence, the correct option is A.

There are 15,504 ways to randomly select a team of 5 people from a group of 20 people

If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:

C(20, n) = 20! / (n! * (20 - n)!)

where C(20, n) represents the number of ways to select n people from a group of 20 people.

For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:

C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504

Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.

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Answer:

what equation   ?

The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.

The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.

Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.

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After answering the given query, we can state that  In light of this, Q is a equation point that is coplanar with J, K, L, and M but not collinear with JK and IM.(-4, 13, -5).

In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. Through a mathematical statement, algebraic equations show that two mathematical expressions are equal. For instance, the equal sign separates the numbers 3x plus 5 and 14 in the equation 3x + 5 = 14. To comprehend the relationship between the two lines written on the opposing edges of a letter, use a mathematical formula. The logo and the specific program tend to correspond most of the time. An illustration would be 2x - 4 = 2.

JK = <6 - (-4), -3 - 3> = <10, -6>

JM = <3 - (-4), 3 - 3> = <7, 0>

JK x JM = 10, -6, and 0 for n

10(x - (-4)) - 6(y - 3) + 0(z - 3) = 0

10x - 6y - 30 = 0

5x - 3y - 15 = 0

JL = <-4 - (-4), -5 - 3> = <0, -8>

x=-4 + 0t, y=3 - 8t, and z=-5 + 0t

5(-4 + 0t) - 3(3 - 8t) - 15 = 0

-24t - 30 = 0

t =-5/4

x = -4 + 0(-5/4) = -4

y = 3 - 8(-5/4) = 13

z = -5 + 0(-5/4) = -5

Therefore, position Q is (-4, 13, -5).

In light of this, Q is a point that is coplanar with J, K, L, and M but not collinear with JK and IM.(-4, 13, -5).

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Answer:

0.489 yards per second

Step-by-step explanation:

Answer: 120

Step-by-step explanation: if f(2) then F(2)= 5(2)12 so we multiply 5x2=

10x12=

120 Answer