A spring exerts a force of 1000 pounds when stretched five feet from its equilibrium
position. How much work is needed to stretch the spring six feet from its equilibrium position?

Answer:

D. 32%

Step-by-step explanation:

In an exponential function, exponential growth is modeled by f(x) = a(1 + [rate])ˣ. In this function, the initial value a, which is 2.3, is multiplied by 1.32 x times, so 1.32 represents the actual growth happening.

This means that to find the actual rate of exponential growth, you’d have to set 1.32 equal to (1 + [rate]). If (1 + [rate]) = 1.32, then the rate = .32, and because rates are written as percentages, we change .32 to 32%.

Step-by-step explanation:

55/12

hope this helps:)

The roots are located at (2,0) and (4,0)

In short, the roots are x = 2 and x = 4

The term "x intercept" is another way of saying "root". Both describe the location where the graph crosses the x axis.

Answer:

(2,0) and (4,0)

Step-by-step explanation:

Hello!

The roots of the parabola are the coordinates where the graph intersects the x-axis (y = 0).

As you can see, the vertex of the graph is above the x-axis, and opens down, meaning that there are two roots for the graph.

Points of intersection:

Therefore, the coordinates of the roots are (2,0) and (4,0).

Answer:

190 children and 150 adults

Step-by-step explanation:

1. 1.25x + 2y = 537.5

2. x + y = 340

Here, x represents the children and y represents the adults.

Again, the first equation represent the cost of tickets, while the second represents the number of people.

From the above equation, we can solve for x and y

From equation 2,

x + y = 340

x = 340 - y

Substitute for x in equation 1

1.25x + 2y = 537.5

Then,

1.25(340 - y) + 2y = 537.5

Expand the bracket

425 - 1.25y + 2y = 537.5

Collect like terms

-1.25y + 2y = 537.5 - 425

0.75y = 112.5

y = 150.

To get the value of x, substitute for y in equation 2

x + y = 340

x + 150 = 340

x = 340 - 150

x = 190

Therefore,

There were 190 children and 150 adults at the pool that day

Answer:

Thanks and have a good day.

Answer:

Step-by-step explanation:

Explanation in image

When two biased dice are rolled, the probability of obtaining a sum of 6 is 5/18 or approximately 0.2778. There are five possible ways to roll a sum of 6.

When two dice are thrown and each of them is biased, a four is obtained four times as often as any of the other numbers. In this problem, we have to find out the probability of getting a sum of 6 when the dice are rolled. The probability of rolling a sum of 6 is obtained by summing the probabilities of all the ways of rolling a sum of 6.

There are five ways to roll a sum of 6, and we have to compute the probability of each one. The first way is to roll a 2 on one die and a 4 on the other die. The probability of rolling a 2 on one die is 1/6, and the probability of rolling a 4 on the other die is 4/6.

So the probability of getting a sum of 6 is 1/6 × 4/6 = 4/36 = 1/9. The second way is to roll a 4 on one die and a 2 on the other die. The probability of rolling a 4 on one die is 4/6, and the probability of rolling a 2 on the other die is 1/6.

So the probability of getting a sum of 6 is 4/6 × 1/6 = 4/36 = 1/9. The third way is to roll a 3 on one die and a 3 on the other die. The probability of rolling a 3 on one die is 1/6, and the probability of rolling a 3 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. The fourth way is to roll a 5 on one die and a 1 on the other die. The probability of rolling a 5 on one die is 1/6, and the probability of rolling a 1 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. The fifth way is to roll a 1 on-one die and a 5 on the other die. The probability of rolling a 1 on one die is 1/6, and the probability of rolling a 5 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. Therefore, the total probability of rolling a sum of 6 is 1/9 + 1/9 + 1/36 + 1/36 + 1/36 = 5/18, which is approximately 0.2778.

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The statement suggests that there is likely to be an interaction between nitrogen (N) and phosphorus (P), which are two fertilizer ingredients used to achieve optimum levels in plant growth. However, without further context or specific details, it is uncertain to determine the nature and extent of this interaction.

In agriculture and plant nutrition, both nitrogen and phosphorus are essential elements for plant growth and development. They play crucial roles in various physiological processes and are often supplied through fertilizers to optimize crop yields. The interaction between nitrogen and phosphorus can have significant implications for plant growth and nutrient utilization.

The ratio of nitrogen to phosphorus in the soil can affect nutrient uptake, plant growth, and overall productivity. Different plant species and soil conditions may exhibit varying responses to the interaction between these two fertilizer ingredients. Factors such as soil type, pH, organic matter content, and crop-specific nutrient requirements further contribute to the complexity of this interaction. To fully understand and assess the interaction between nitrogen and phosphorus, detailed research and experimentation specific to the particular context are necessary.

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Option B is correct.

Given that   Function G(F(x)) = (x - 5)3 + x - 5 ;

Lets take a function G(x) = x3 + x as (i) and check that it will produce the above equation or not.

Now suppose that the value of the function F(x) = x-5 as (ii) , using this value we will check that whether it support the value for g(x) or not.

Put the value of  function  f(x) in the equation number i , it will be like this :

G(f(x)) = f(x)3 + f(x)

we know that the value of f(x) from (ii)

Therefore, G(f(x)) will be :

G(f(x)) =  (x - 5)3 + x - 5, this will satisfy the above equation which means our supposition was correct. Hence the correct ans is B

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We have that because the central angle is 90°, the sector represents 1/4 of a circle with a radius of 10 yd.

So, length of the safety rail is given by:

Where:

r = 10 yd

pi = 3.14

Substitute, we have:

The Answer is 15.7 yd

Next, area of the deck is given by:

Substitute the values:

The answer is 78.5 yd^2

use sin

sin(50) = x/6

sin(50) x 6 = x

x = ~4.5963

For the figure shown in the image having TV as the midsegment, the length of TV is 40

When the comparable triangles' angles are congruent and their respective sides are proportionate, this is referred to as similar triangles in geometry.

In light of this, if the triangle's corresponding angles are congruent, then the side should be proportionate.

For the given figure, the proportionate sides are

UV and TV, UW and WX

Calculating for s

UV / TV = UW / WX

1 / (-2s + 42) = 2 / (3s + 77)

cross multiplying

3s + 77= 2(-2s + 42)

3s + 77= -4s + 84

collecting like terms

3s + 4s = 84 - 77

7s = 7

s = 1

solving for TV

= -2s + 42

= -2 * 1 + 42

= 40

the value of TV is 40

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The value of solutions are,

(f/g) (t) = (t - 5) / (t - 3)

And, (f/g) (- 4) = 9/7

We have to given that,

Functions are,

f (t) = t - 5

And, g (t) = t - 3

Hence, Simplify the function as,

(f/g) (t) = f (t) / g (t)

(f/g) (t) = (t - 5) / (t - 3)

At t = - 4;

(f/g) (t) = (t - 5) / (t - 3)

(f/g) (- 4) = (- 4 - 5) / (- 4 - 3)

(f/g) (- 4) = - 9/- 7

(f/g) (- 4) = 9/7

Thus, We get;

(f/g) (t) = (t - 5) / (t - 3)

And, (f/g) (- 4) = 9/7

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Answer:

\( \frac{151}{20} \)

Step-by-step explanation:

x - 4/5 = 6 3/4

6 × 4 + 3/4 = 27/4

x - 4/5 = 27/4

x = 27/4 + 4/5

x = 151/20

Answer:

38 degree

Step-by-step explanation:

all the angles of a triangle are 180 . a supplementary angle is 105 degree... first subtract 180 - 105 (A), because it is a supplementary angle , so 75 degrees then do 180 - ( 67 + 75 ) that is 38 = x

1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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Answer:

y = (1/3)x + 7

Step-by-step explanation:

The general structure form of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.

The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.

m = 1/3

x = -3

y = 6

y = mx + b                                  <----- Slope-intercept form

6 = (-3)(1/3) + b                           <----- Insert values

6 = -1 + b                                    <----- Multiply -3 and 1/3

7 = b                                           <----- Add 1 to both sides

Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.

y = (1/3)x + 7

The indefinite integral of 2 * √(x + ²) dx is (4/3) * (x + ²)^(3/2) + 17x + C.

7. The indefinite integral of e¹ dt multiplied by (1 - e¹)² is -(1/3) * (1 - e¹)³ + C, where C is the constant of integration.

To solve this integral, we can use the power rule for integration, which states that ∫xⁿ dx = (1/(n+1)) * x^(n+1) + C. Applying this rule, we have:

∫(e¹ dt) * (1 - e¹)² = -(1/3) * (1 - e¹)³ + C.

Therefore, the indefinite integral of e¹ dt multiplied by (1 - e¹)² is -(1/3) * (1 - e¹)³ + C.

8. The indefinite integral of 2 * √(x + ²) dx is (4/3) * (x + ²)^(3/2) + 17x + C, where C is the constant of integration.

To solve this integral, we can use the power rule for integration and apply it to the term √(x + ²). Using the power rule, we integrate (x + ²)^(1/2) as follows:

∫(2 * √(x + ²) dx) = (4/3) * (x + ²)^(3/2) + C.

Additionally, we integrate the term 17x as (17/2) * x² + C using the power rule.

Combining both results, we obtain the indefinite integral of 2 * √(x + ²) dx as (4/3) * (x + ²)^(3/2) + 17x + C.

Therefore, the indefinite integral of 2 * √(x + ²) dx is (4/3) * (x + ²)^(3/2) + 17x + C.

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The answer is ∫sin(3x)dx = x·sin(3x) + (1/6)·cos(3x)·x^2 - (1/18)·sin(3x)·x^2 + C

where C is the constant of integration.

To use integration by parts on the indefinite integral of sin(3x) dx, we need to choose appropriate functions for f and g' such that we can simplify the integration by applying the integration by parts formula.

Let's choose f(x) = sin(3x) and g'(x) = dx. This choice leads to the following:

f'(x) = 3cos(3x)

g(x) = x

Now, we can apply the integration by parts formula:

∫sin(3x)dx = x·sin(3x) - ∫(3cos(3x)·x)dx

To simplify the integral on the right-hand side, we can again apply integration by parts with f(x) = 3cos(3x) and g'(x) = x:

f'(x) = -9sin(3x)

g(x) = (1/2)x^2

Using the integration by parts formula again, we get:

∫sin(3x)dx = x·sin(3x) + (1/6)·cos(3x)·x^2 - (1/18)·sin(3x)·x^2 + C

where C is the constant of integration.

Therefore,

∫sin(3x)dx = x·sin(3x) + (1/6)·cos(3x)·x^2 - (1/18)·sin(3x)·x^2 + C

where C is the constant of integration.

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The geometric sequence is 9 + 2 + 20 = 29.

The smallest number the third term in the geometric sequence can be is 29.

This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,

the third term of the geometric sequence is 9 + 2 + 20 = 29.

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Answer: 34.8

Step-by-step explanation:

After 30 minutes, the amount of salt remaining in the tank is 18.75 kg. This is because the brine entering the tank contains 0.03 kg of salt per liter of water, and 25 liters of brine are entering the tank every minute.

Thus, in 30 minutes, 750 liters of brine will have entered the tank, bringing with it 22.5 kg of salt. Since the tank initially contained 20 kg of salt, the amount of salt remaining after 30 minutes is 18.75 kg.

The theory behind the amount of salt remaining in the tank after a given amount of time is based on the idea that the amount of salt entering the tank is equal to the amount of salt leaving the tank. The amount of salt entering the tank is determined by the concentration of salt in the brine solution and the rate at which the brine enters the tank. The amount of salt leaving the tank is determined by the same rate at which the brine enters the tank.

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lets take

x+y=100 firstly.

then x=100-y equation (i)

Now,

x-y=10

Putting value of x from equation(i)

100-y-y=10

-2y=10-100

-2y=-90

therefore, y=45

Now,

putting value of y in equation(i)

we get

x=100-45

ie x=55

hence, x=55 & y=45

Answer:

The solution is (55, 45).

Step-by-step explanation:

Solve the system of linear equations

x + y = 100

x - y = 10

through elimination by addition / subtraction.

Combining these two equations temporarily eliminates y, leaving us with 2x = 110.  Then x = 55.

Substituting 55 for x in the first equation, we get:

55 + y = 100.  Subtracting 55 from both sides leaves us with y = 45.

The solution is (55, 45).

Answer:

97.9

Step-by-step explanation:

Pythagorean Theorem: 75^2+63^2=AB^2

5625+3969=AB^2

9594=AB^2

AB=97.9

Answer:

150ft²

Step-by-step explanation:

Front facing rectangle: lw=6*5=30

Back facing rectangle: lw=6*5=30

Top facing rectangle: lw=2*6=12

Bottom facing triangle: lw=10*6=60

Trapezoid: (h(a+b))/2=(3(2+10))/2=3(12)/2=36/2=18

Total surface area = 30+30+12+60+18=150ft²

10 y plus 9 y minus 6 y plus 6 y

=> 10y + 9y - 6y + 6y
= 10y + 9y - 0 = 19y

Answer:

When we say 'as many as' or 'no more than', we mean 'less than or equal to' which means that a could be less than b or equal to b. But, when we say 'at least', we mean 'greater than or equal to'. Here a could be greater than b or equal to b.

9514 1404 393

Answer:

  A  y = 2x + 5

Step-by-step explanation:

The cost per dog is the slope of the cost equation, 2. The equation can be written in point-slope form as ...

  y -7 = 2(x -1) . . . . using the point (1, 7)

Simplified, this is ...

  y = 2x -2 +7

  y = 2x +5 . . . . matches choice A

Answer:

4.8

Step-by-step explanation: