if the work required to stretch a spring 1 ft beyond its natural length is 15 ft-lb, how much work is needed to stretch it 9 in. beyond its natural length?

Answer:

Reasonable

Step-by-step explanation:

The comparison 3.84 > 3.8 is reasonable.

In this comparison, 3.84 is a larger number than 3.8, so it makes sense to say that 3.84 is greater than 3.8. When comparing decimal numbers, we can simply compare the values to the right of the decimal point. In this case, both 3.84 and 3.8 have two digits to the right of the decimal point, so we can compare those digits directly. Since 4 is greater than 8, it follows that 3.84 is greater than 3.8.

The comparison is reasonable because it is based on a correct understanding of the relative sizes of the numbers involved.

The values in the table are 7, 11, 15, and 19.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We are assuming the table to be:

x             value

2            2x2 + 3 = 7

4           4x2 + 3 = 11

6           6x2 + 3 = 15

8           8x2 + 3 = 19

Thus,

The values in the table are 7, 11, 15, and 19.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ9

By evaluating both equations in x = 8 we will see that the hawk will be closer to the ground.

We know that the height of the hawk is modeled by:

y=−20x+350

And the height of the eagle is modeled by:

y=−10x+400

Now we need to evaluate both equations in x = 8.

hawk:

y = -20*8 + 350 = 190

For the Eagle:

y = -10*8 + 400 = 320

We can see that the hawk is closer to the ground.

Learn more about evaluating equations at:

https://brainly.com/question/4344214

#SPJ1

The values of a and b in the exponential function f(x) = [tex]ab^x[/tex] can be found by using the two given points and solving a system of two equation.

To find the values of a and b in the exponential function f(x) = [tex]ab^x[/tex] given that it passes through the points (0, 11) and (3, 1375), we can use the supplied positions where a and b must be solved.

Let's start with the point (0, 11). Plugging x = 0 and y = 11 into the equation, we have:

11 = [tex]a * b^0[/tex]

Since [tex]b^0[/tex] = 1 for any value of b, we have:

11 = a * 1

So a = 11.

Next, let's use the point (3, 1375) to find b. Plugging x = 3 and y = 1375 into the equation, we have:

1375 = [tex]11 * b^3[/tex]

Dividing both sides of the equation by 11, we have:

125 = [tex]b^3[/tex]

By combining the cube roots of the two sides, we obtain:

b = 5

So the values of a and b are a = 11 and b = 5. The exponential function that passes through the points (0, 11) and (3, 1375) is f(x) = [tex]11 * 5^x[/tex].

Learn more about exponential function here:

https://brainly.com/question/12260956

#SPJ4

The complete question is:

an exponential function f(x) = [tex]ab^x[/tex] passes through the points (0, 11) and (3, 1375). Find the values of a and b?

If Lin walks at a speed of 2. 5 miles per hour. Andre walks at a speed of 3 miles per hour. It will take 4 hours until Lin and Andre meet on the path.

Lin and Andre are walking toward each other on a 22-mile trail, so they will meet when the sum of the distances they have walked is equal to 22 miles. Let's call the time they walk until they meet "t".

During this time, Lin will have walked a distance of 2.5t miles, and Andre will have walked a distance of 3t miles. The sum of these distances is equal to 22 miles, so we can set up the equation:

2.5t + 3t = 22

Combining like terms, we get:

5.5t = 22

Dividing both sides by 5.5, we get:

t = 4

So it will take Lin and Andre 4 hours to meet on the path.

Note that we could have also solved this problem by using the formula:

time = distance / speed

For Lin, the time to cover the 22-mile distance would be:

time = distance / speed = 22 / 2.5 = 8.8 hours

For Andre, the time to cover the 22-mile distance would be:

time = distance / speed = 22 / 3 = 7.33 hours

Since they are walking towards each other, we can add their times to get the time it takes for them to meet:

time = 8.8 + 7.33 = 16.13 hours

However, we can see that this answer is not correct, as it is greater than the time it would take for either of them to cover the entire distance. This is because the time it takes for them to meet is less than the sum of their individual travel times, due to them moving towards each other.

So we go back to our original equation and solve for "t" to get the correct answer of 4 hours.

To learn more about time click on,

https://brainly.com/question/14283343

#SPJ4

Answer: Since triangle QRS and triangle TUV are both triangles, we can use the fact that the sum of the interior angles in a triangle is 180 degrees.

In triangle QRS, the measure of angle Q is 117 degrees and the measure of angle R is 180 - 117 = 63 degrees. The measure of angle S is 180 - 63 = 117 degrees, since the angles in a triangle add up to 180 degrees.

In triangle TUV, the measure of angle T is 180 - 30 = 150 degrees and the measure of angle U is 30 degrees. The measure of angle V is 180 - 150 = 30 degrees, since the angles in a triangle add up to 180 degrees.

The measures of LQ and LS can be found using the fact that the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

The measure of LQ is equal to the sum of the measures of angles R and T:

LQ = 63 + 150 = 213 degrees

The measure of LS is equal to the sum of the measures of angles Q and U:

LS = 117 + 30 = 147 degrees

So the measure of LQ is 213 degrees and the measure of LS is 147 degrees.

Step-by-step explanation:

Rounded to the nearest minute, the answer is 12 minutes.

The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.

The radius of the Ferris wheel is half its diameter, which is 20/2 = 10 meters. When the Ferris wheel makes a full revolution, a person riding it will pass the loading platform twice: once on the way up and once on the way down. The highest point reached by the Ferris wheel is at the top, which is 10 + 1 = 11 meters above the ground.

To find out how many minutes of the ride are spent higher than 19 meters above the ground, we need to figure out at which times the rider is at or above this height. Let's call h(t) the height of the rider at time t. We know that h(t) is a sinusoidal function with a period of 10 minutes, an amplitude of 10 meters, and a vertical shift of 11 meters. In other words, we can write:

h(t) = 10 sin(2πt/10) + 11

To find out when h(t) is greater than 19, we solve the inequality:

10 sin(2πt/10) + 11 > 19

Subtracting 11 from both sides, we get:

10 sin(2πt/10) > 8

Dividing by 10, we get:

sin(2πt/10) > 0.8

The sine function is greater than 0.8 at two times in each period: once when it is increasing from 0.8 to 1, and once when it is decreasing from 1 to 0.8. We can find these times by solving the equations:

sin(2πt/10) = 0.8

sin(2πt/10) = -0.8

Using a calculator, we find that these equations have solutions at:

t = 1.167, 8.833, 3.5, 6.5

These times represent the four moments during the 10-minute period when the rider is at or above 19 meters. The first and fourth of these moments occur in the first half of the period, and the second and third occur in the second half.

Therefore, the total time spent higher than 19 meters is:

(8.833 - 1.167) + (6.5 - 3.5) = 11.6667 minutes

Rounded to the nearest minute, the answer is 12 minutes.

To know more about time visit:

https://brainly.com/question/28050940

#SPJ1

The experimental probability of selecting the name Alex would be  40 % or 2 / 5

The experimental probability of selecting the name Alex can be found by the formula :

= Number of times Alex is drawn / Number of total draws x 100 %

Number of times Alex is drawn = 4 times

Number of total draws = 10 draws

The experimental probability of selecting Alex would therefore be :

= 4 / 10 x 100 %

= 0. 4 x 100 %

= 40 % or 2 / 5

Find out more on experimental probability at https://brainly.com/question/14395891

#SPJ1

The multiply of 45 and 23 is = 1035  we calculate this by simple multiplication method.

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

And here we have 2 number 1st is 45 and 2nd is 23 so here we will multiply

    4  5

 x  2 3

----------------

  1 3 5

  9 0 x

---------------

1 0 3 5

--------------

final ans is 1035

know more about multiply click here;

https://brainly.com/question/620034

#SPJ4

The area of the shaded region in each of the following figures are the same, that is, 94.5cm²

(i) Area of the shaded region in the first figure:

= (Area of the square with side 21m) - (Area of the circle with diameter 21m)

we know the diameter of the circle is 21 cm, therefore we can say that the radius of the circle is 10.5 cm

we need to find the area of the shaded region = (21 × 21)

([tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex]) cm² = 441 - 346.5

= 94.5cm²

(ii) Area of the shaded region in the second figure:

(Area of the square with side 21 cm) - (4×Area of the sector)

= (21 - 21) - (4×[tex]\frac{90}{360}[/tex]×[tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex])

(21 - 21) = (4 - [tex]\frac{1}{4}[/tex]×[tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex])

= (441−346.5) cm²

=94.5 cm²

To learn more about area, click here:

brainly.com/question/1631786

#SPJ4

Answer:

Step-by-step explanation:

5x - 10 - 4 = 6

5x - 14 = 6

5x = 20

x = 4

Option C is the solution

The complete tables for the given equations is:-

For y = 3x

X   Y

1     3

2    6

3    9

For y = -2x + 5

X   Y

1    3

2   1

3   -1

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The given two equations are;-

y = 3x

y = -2x +5

The different points passing through the line y =3x are:-

X   Y

1     3

2    6

3    9

The different points passing through the line y =-2x + 5 are:-

X   Y

1    3

2   1

3   -1

The graph of the points and the line as is attached with the answer below.

To know more about an equation follow

https://brainly.com/question/25798491

#SPJ9

Answer: 22 units²

Step-by-step explanation:

Just count the squares, its faster than breaking this into individual quadrilaterals.

22 squares, so the Area is 22 units²

The ordered pair of the inequality will be (9,-3).

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that inequality is given as y ≤ 1/3x−6.

The ordered pair can be calculated as:-

y ≤ 1/3x−6

Substitute the value of x equal to 9 and get the value of y,

y ≤ 1/3(9) - 6

y ≤ 3 - 6

y ≤ -3

Hence, the ordered pair will be (9,-3).

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ9

According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:

[tex]P = P_0 * 2^{t/t_d)}[/tex]

where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.

To find the time it will take for the population to increase to 3 times its original population size, we can set [tex]P = 3P_0[/tex] and solve for t:

[tex]3P_0 = P_0 * 2^{t/t_d}[/tex]

Dividing both sides by [tex]P_0[/tex] gives:

[tex]3 = 2^{t/t_d}[/tex]

Taking the logarithm of both sides (using any base) gives:

[tex]log(3) = log(2^{t/t_d} )[/tex]

Using the logarithmic identity

[tex]log(a^b) = b*log(a),[/tex]

we can rewrite this as:

[tex]log(3) = (t/t_d)*log(2)[/tex]

Solving for t, we get:

[tex]t = t_d * (log(3)/log(2))[/tex]

Substituting [tex]t_d[/tex] = 6 hours (given in the problem), we get:

[tex]t = 6 * (log(3)/log(2)) hours[/tex]

Simplifying using the change of base formula

[tex](log(a)/log(b) = log_b(a))[/tex], we get:

[tex]t = 6 * log_2(3)[/tex] hours

Therefore, the answer is (f) None of the above.

For more question on exponentially click on

https://brainly.com/question/29166359

#SPJ4

Correct question should be

Click on image for question

Answer:

Step-by-step explanation:

The total cost for Nayeli to enter the amusement park is $40. If she goes on 9 rides, the cost for the rides would be 9 * $2 = $18. Therefore, the total cost for Nayeli to enter the park and go on 9 rides would be $40 + $18 = $58.

To find the total cost if she goes on r rides, we can use the formula:

Total cost = $40 + r * $2

So, if Nayeli goes on r rides, she would have to pay $40 + r * $2 in total.

To calculate the total cost, multiply the number of rides by the cost per ride and add it to the admission price.

To calculate the total amount Nayeli would have to pay if she goes on 9 rides, we need to first calculate the cost of admission. The admission price is $40. Then, we multiply the number of rides (9) by the cost per ride ($2) and add it to the admission price to get the total cost.
Total cost = Admission price + (Number of rides x Cost per ride) = $40 + (9 x $2) = $40 + $18 = $58.
If Nayeli goes on 'r' rides, we can use the same formula to calculate the total cost. The total cost would be the admission price ($40) plus the product of the number of rides ('r') and the cost per ride ($2). Total cost = $40 + (r x $2) = $40 + $2r.

https://brainly.com/question/32471258

#SPJ2

Answer:

y = -2x + 8

When x = 4, Mark has no more money , so when x is greater than 4, Mark is in debt or is not able to give his sister any more money.

Step-by-step explanation:

Answer:

C) 187 1/2 miles

Step-by-step explanation:

We can start by using the formula for converting between scale measure and actual measure:

actual measure = scale measure * (actual distance / scale distance)

Here, the scale measure is 3/4 inch and the scale distance is 1 1/2 inches, so:

actual measure = (3/4) * (n / 250)

Rearranging the equation, we can isolate n:

n = (actual measure * 250) / (3/4)

Substituting in the actual measure of 3/4 inch, we find:

n = (3/4 * 250) / (3/4) = 250 miles

So the answer is C) 187 1/2 miles.

The error that Louise made in her model is that "the small arrows should all end in the same place as the large one.

What is error model?

Error modelling is used to describe the variability in how well a parameter describes the data.

The error that Louise made in her model is that "the small arrows should all end in the same place as the large one.

" The model as described shows four small arrows going from 4 to 8, 8 to 12, 12 to 16, and 16 to 20, respectively, and one large arrow going from 0 to 20. Since the expression is 20 divided by 4, the model should show four equal parts from 0 to 20, and each part should have a length of 5.

The arrows should start at the beginning of each part and end at the end of each part, resulting in four equal segments.

To know more about error visit,

https://brainly.com/question/14467769

#SPJ1

Watershed can expect an average profit of $10.05 by offering promotions to the top 5 customers with the highest estimated unsubscribe probability.

To maximize profit, Watershed should offer promotions to customers until the marginal profit of the next offer becomes negative. The marginal profit is the difference between the expected value of retaining a customer and the cost of the promotion:

Marginal profit = [tex](0.7 * $60) - $15 = $33[/tex]

Therefore, Watershed should offer promotions to customers until the estimated unsubscribe probability drops below the point where the expected profit of retention becomes less than $33.

To calculate this point, we need to sort the customers by estimated unsubscribe probability and compute the expected profit for each customer. Let [tex]p_i[/tex] be the estimated unsubscribe probability for customer i, and let [tex]R_i[/tex] be the expected profit if we offer them a promotion:

[tex]R_i = 0.7 * $60 - $15 = $33[/tex]

If customer i unsubscribes, then the profit is -$15. Otherwise, the profit is $60 - $15 = $45. Thus, the expected profit is:

[tex]E(R_i) = (1 - p_i) * $45 - p_i * $15[/tex]

If we order the customers by decreasing [tex]p_i[/tex], we can compute the expected profit of retaining the top n customers:

[tex]E(profit_n) = ∑_{i=1}^n E(R_i)[/tex]

Watershed should offer promotions to customers until the marginal profit of the next offer becomes negative, which means that:

[tex]E(R_{n+1})[/tex] < 33

Substituting the expression for [tex]E(R_i)[/tex], we get:

[tex](1 - p_{n+1}) * $45 - p_{n+1} * $15[/tex] < 33

Simplifying, we get:

[tex]p_{n+1} >[/tex] 0.6

Therefore, Watershed should offer promotions to customers until the estimated unsubscribe probability drops below 0.6. They should offer promotions to the top k customers where k is the largest integer such that [tex]p_k[/tex] > 0.6.

To compute the average profit from offering promotions to the top k customers, we can use the formula for [tex]E(profit_n)[/tex] and substitute k for n:

[tex]profit_k = ∑_{i=1}^k E(R_i)[/tex]

Substituting the expression for [tex]E(R_i)[/tex], we get:

[tex]profit_k = ∑_{i=1}^k [(1 - p_i) * $45 - p_i * $15][/tex]

Using the data provided, we can compute the estimated unsubscribe probability for each customer and sort them in descending order:

Customer Unsubscribe Probability

1                              1                 0.92

2                              1                0.85

3                              1                0.75

4                              0               0.68

5                              0               0.61

6                              0               0.54

7                              0               0.47

8                              0               0.39

9                              0               0.32

10                              0             0.25

We can see that the estimated unsubscribe probability drops below 0.6 after the top 5 customers. Therefore, Watershed should offer promotions to the top 5 customers.

Using the formula for [tex]profit_k[/tex], we get:

[tex]profit_5 = (1-0.92)$45-0.92$15 + (1-0.85)$45-0.85$15 + (1-0.75)*$45-0.\\profit_5 = (1-0.92)$45-0.92$15 + (1-0.85)$45-0.85$15 + (1-0.75)$45-0.75$15 + (1-0.68)$45-0.68$15 + (1-0.61)$45-0.61$15\\= $10.05[/tex]

Therefore, Watershed can expect an average profit of $10.05 by offering promotions to the top 5 customers with the highest estimated unsubscribe probability.

To know more about probability:

https://brainly.com/question/12844710

#SPJ4

The x-axis represents the distance traveled (in miles).

Considering that the x-axis shows the distance travelled (in miles) and the y-axis represents the amount of gas left in the tank (in gallons), the x-intercept would represent the point at which Brianna's gas tank is empty, and she would need to refill her tank to continue traveling. In other words, the x-intercept is the distance Brianna can travel before running out of gas, assuming her car's fuel efficiency remains constant and she does not refill her tank.

Two key lines known as the x and y axes are the building blocks of a graph.

To learn more about x-axis here:

https://brainly.com/question/2491015

#SPJ4

PLEASE GIVE BRAINLIEST

thank you and have a good day :)

Answer:

3 ounces per 12 cups

Step-by-step explanation:

you multiply the left side by 6 on both numerator and denominator

1/2 per 2 = X per 12

1/2 * 6 = 6/2 or 3

2 * 6 = 12

3 per 12 = x per 12

the rate is 3 ounces per 12 cups

i hope this helps

Answer:

[tex]-22.8[/tex]

Step-by-step explanation:

[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]

The column for x = 5 should be used if the probability is 0.75 in the binomial distribution table.

The binomial distribution table is a table of values that shows the probability of getting a certain number of successes (x) in a certain number of trials (n). In this case, the probability is 0.75, so we need to look for the column that has a value of 0.75. We can see that this column corresponds to x = 5, so that is the column we should use.

The column for x = 5 should be used if the probability is 0.75 in the binomial distribution table.

the complete question is :

on the table for the binomial distribution, if you have a probability of 0.75, which vertical column for x do you use?

Table :

n x P(x)

5 0 0.23730

5 1 0.39615

5 2 0.26335

5 3 0.08789

5 4 0.01801

5 5 0.00152

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

Part A:

The graph of g(x) = |x - 7| is a V-shaped graph that opens upward, with a vertex at x = 7 and y = 0. The graph of the function is symmetrical about the vertical line x = 7. The domain of the function is all real numbers, and the range is all non-negative real numbers, including zero.

Part B:

The transformation from f(x) to h(x) is a vertical shift upward by 2 units. The vertex of the parent function f(x) = |x| is at (0, 0), and the vertex of the transformed function h(x) = |x| + 2 is at (0, 2). The range of the parent function f(x) is all non-negative real numbers, including zero. The range of the transformed function h(x) is all non-negative real numbers greater than or equal to 2. The transformation shifts the entire graph of the parent function upward, increasing the y-values of all points on the graph by 2 units.

The equivalent expression for  8b-4b is 4b.

In algebra, like terms are the terms that contain the same variable which is raised to the same power. In this only numerical coefficients may vary.

Given 8b-4b. b=5

We have to combine the like terms to get an equivalent expressions.

Like terms containing variables with same power.

When combining like terms, we have to add or subtract their coefficients.

Coefficients are the numbers which are placed with variable.

Then, 8b-4b=4b.

When b=5⇒4*5=20

Hence, the equivalent expression for  8b-4b is 4b.

Complete question:

Write an equivalent expression by combining the like terms 8b-4b. Find the value of expressions when b=5.

Learn more about like terms here:

https://brainly.com/question/29085383

#SPJ9

Answer:

6°

Step-by-step explanation:

Two angles are called complementary if the sum of their measures equals to 90°:

The complementary angle of 84° = 90° - 84°

                                                       = 6°

Answer:   6

Step-by-step explanation:

The complementary angle means the sum of two angles equal to 90. Let x be the other angle.

x + 84 = 90

       x = 6

Based on the information in the graph, it can be stated that the median test score of period 2 was less than the median test score of period 1.

The median is identified by locating the value that lies in the middle, in the case of a whisker plot, the median corresponds to the value shown by the vertical line.

The median for period 1: 84

The median for period 2: 82

Based on this information, it can be stated that the median test score of period 2 was less than the median test score of period 1.

Learn more about the median in https://brainly.com/question/28060453

#SPJ1

Answer:

$10 / hour

Step-by-step explanation:

$40 ÷ 4 hours = 10/hour

Answer:  Part A: Zach is paid $10 per hour

Part B: The equation would be p = 10h

Step-by-step explanation: Part A :Zach worked 4 hours and was paid $40. The question asks How much is Zach's paid per hour? Per hour means to find the unit rate and in order to find the unit rate in this case, you have to divide the $40 by the 4 to get how much Zach got per hour.

1.$40/4=10

Therefore, Zach is paid $10 per hour.

Part B: In the question it says Which equation shows the relationship between , h, the number of hours worked. The number of hours Zach worked was 4 hours. So, h = 4. Then for the next part of the problem, and p the amount paid.  We know that Zach got paid $40. So p = 40. Now that we know our numbers, we could put the equation together.

1. P = 10h is the same as $40 = 10 x 4.

There's the answer, Hope it helps! Have a nice day!

The true proportion of all American adults who would report having earned money by selling something online in the previous year lies between 0.178 and 0.221.

A confidence interval is computed from the sample data and provides a range of values within which the true population parameter is expected to lie. The confidence level is the probability that the confidence interval contains the population parameter.

Using this critical value, we can construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year. To do this, we use the formula:

confidence interval = sample proportion ± z* (standard error)

The sample proportion is the number of adults who reported earning money by selling something online (914) divided by the total sample size (4579), which gives us a proportion of 0.1997.

The standard error is calculated as:

standard error = √ [(sample proportion)(1 - sample proportion) / sample size]

Substituting the values, we get:

standard error = √ [(0.1997)(1 - 0.1997) / 4579] = 0.009

Plugging in the values, we get:

confidence interval = 0.1997 ± 2.33(0.009)

This gives us a confidence interval of 0.178 to 0.221.

To know more about Confidence interval here.

https://brainly.com/question/24131141

#SPJ4