find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→5 x2 − 25 x2 − 5x

Answer is: manager can be 95% confident that the true proportion of time spent mowing is between 0.452 and 0.548

We can use the normal approximation to the binomial distribution to estimate the confidence interval for the true proportion of time spent mowing.

The sample proportion of time spent mowing is:

p = 200/400 = 0.5

The standard error of the sample proportion is:

SE = sqrt(p(1-p)/n) = sqrt(0.5 * 0.5 / 400) = 0.025

To find the 95% confidence interval for the true proportion of time spent mowing, we can use the formula:

p ± z*SE

where z* is the critical value from the standard normal distribution corresponding to a 95% confidence level, which is approximately 1.96.

So the 95% confidence interval for the true proportion of time spent mowing is:

0.5 ± 1.96*0.025 = (0.452, 0.548)

Therefore, the manager can be 95% confident that the true proportion of time spent mowing is between 0.452 and 0.548.

To know more about ratio-proportions:

https://brainly.com/question/12024093

#SPJ11

The derivative of the function at s=0 is approximately 258.

The derivative of the function[tex]r=[5(e4s-e-45)]/e45[/tex]is:

[tex]r' = 5[(4e4s + 45e-45)e45 - e45(4e4s - e-45)(e45)]/e902[/tex]

Plugging in s=0, we get:

[tex]r' = 5[(4 + 45)e45 - (4 - 1)(e45)]/e902[/tex]

[tex]r' = 5[49e45 - 3e45]/e902[/tex]

[tex]r' = 5(46e45)/e902[/tex]

r' ≈ 258

Therefore, the derivative of the function at s=0 is approximately 258.

To know more about derivative, refer here:

https://brainly.com/question/30365299

#SPJ11

The surface area of the pyramid is 310.00 square centimeters.

To find the surface area of the pyramid, we need to find the area of each of its faces and add them up.

First, let's find the area of the base of the pyramid;

Area of base = (side length)² = 7² = 49 cm²

Now, we find the area of each triangular face. To do this, we need to find the length of the slant height (l), which is the hypotenuse of a right triangle with one leg equal to half the base and the other leg equal to the height of  pyramid.

Half of the base = 7/2 = 3.5 cm

Using Pythagorean theorem, we find the slant height;

l² = (3.5)² + (15)²

l² = 122.25 + 225

l² = 347.25

l = √(347.25) ≈ 18.64 cm

Now we find the area of each triangular face;

Area of face = (1/2) x base x height = (1/2) x 7 x 18.64 ≈ 65.24 cm²

Finally, we can find the total surface area by adding up the areas of all four faces;

Total surface area = 4 x (area of face) + (area of base)

Total surface area = 4 x 65.24 + 49

Total surface area = 261.00 + 49

Total surface area = 310.00 cm²

Therefore, the surface area of the pyramid is 310.00 cm².

To know more about surface area here

https://brainly.com/question/29101132

#SPJ1

The number of adult tickets purchased that day was 36 if the charge is $3.25 for each adult and $1.50 for each student and 400 people paid $1237

Let the number of adults be x

the number of students be y

Total people = 400

x + y = 400

Total receipts = $1,237

Cost of an adult ticket = $3.25

Cost of a student ticket = $1.50

Cost of x adults tickets = 3.25x

Cost of y student tickets = 1.50y

3.25x + 1.50y = 1237

Multiply the first equation by 1.50

1.50x + 1.50y = 600

Subtract the second and above equation

1.75x = 637

x = 364

364 + y = 400

y = 36

Thus, the number of adult tickets purchased is 36.

Learn more about Equations:

https://brainly.com/question/28871326

#SPJ4

An equation representing the statement that 282828 is 121212 less than kkk is kkk = 282828 + 121212.

An equation is a mathematical statement showing that two or more mathematical or algebraic expressions share equality or equivalence.

Equations are represented using the equal symbol (=).

Unlike equations, mathematical expressions do not use the equal symbol.

282828 = kkk - 121212

kkk = 282828 + 121212

Thus, one way of representing the statement that that 282828 is 121212 less than kkk is by forming an equation like kkk = 282828 + 121212.

Learn more about equations at https://brainly.com/question/2972832.

#SPJ1

The radius of the circle is 10 inches.

A sector is a part of a given circle which is made from two radii and an arc. It's area can be determined by;

area of a sector = θ/360*πr^2

where θ is the measure of its central angle, and r is its radius.

Then from the given question, we have;

area of a sector = θ/360*πr^2

162 = 180/360 *3.14*r^2

      = 1.57r^2

r^2 = 162/1.57

     = 103.1847

So that;

r = (103.1847)^1/2

 = 10.16

The radius of the circle is approximately 10 inches.

Learn more about area of a sector at https://brainly.com/question/22761976

#SPJ1

The interquartile range (IQR) of the given data set {3, 8, 11, 11, 12, 13, 15} is 5.

To find the interquartile range (IQR) of a data set, follow these steps:

Order the data set in ascending order: 3, 8, 11, 11, 12, 13, 15.

Find the first quartile (Q1): This is the median of the lower half of the data set. In this case, the lower half is {3, 8, 11}. Since there is an odd number of data points, the median is the middle value, which is 8.

Find the third quartile (Q3): This is the median of the upper half of the data set. In this case, the upper half is {12, 13, 15}. The median of this set is 13.

Calculate the interquartile range (IQR): The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). In this case, IQR = Q3 - Q1 = 13 - 8 = 5.

Therefore, the interquartile range (IQR) of the given data set {3, 8, 11, 11, 12, 13, 15} is 5.

Learn more about the interquartile range (IQR) for a given data set.

brainly.com/question/31190938

#SPJ11

To find the volume of the cylinder, we need to use the formula:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

If we have a cylinder with radius r and height h, and another cylinder with the same radius r but double the height (2h), the volume of the second cylinder is:

V' = πr^2(2h) = 2πr^2h

So, to answer the questions:

The volume of the cylinder is V = π(5 cm)^2(8 cm) = 100π cubic cm, which is approximately 314.16 cubic cm rounded to two decimal places.

The volume of the cylinder with the same radius and double the height is V' = 2π(5 cm)^2(8 cm) = 200π cubic cm, which is approximately 628.32 cubic cm rounded to two decimal place

The given question is in Spanish, English translation of given question is below.

The perimeter of a rectangle is 54 inches. its length is twice as wide. find the length and width of the rectangle find the area of ​​the rectangle.

The width of the rectangle is 9 inches, the length of the rectangle is 18 inches, and the area of the rectangle is 162 square inches.

Let us assume the width of the rectangle w and the length l.

Given, the perimeter of the rectangle is 54 inches:

We know that

Perimeter = 2(length + width) = 54

2(l + w) = 54

Given, length is twice as width i.e. l=2w

2(2w + w) = 54

2(3w) = 52

6w = 54

w = 54/6

w = 9

l = 2(9)

l = 18

We know that

Area = length x width

Area = 18 x 9

= 162

Therefore, the width of the rectangle is 9 inches, the length of the rectangle is 18 inches, and the area of the rectangle is 162 square inches.

Learn more about area of rectangle here

https://brainly.com/question/15218510

#SPJ4

The union set of A and B is A∪B={1, 2, 3, 4, 5, 6, 7, 9}.

Given that, A={x|x is an odd number greater than 0 and less than 10} and B={2, 3, 4, 5, 6}.

Here, set A={1, 3, 5, 7, 9}

Now, A∪B = {1, 3, 5, 7, 9}∪{2, 3, 4, 5, 6}

= {1, 2, 3, 4, 5, 6, 7, 9}

Therefore, the union set of A and B is A∪B={1, 2, 3, 4, 5, 6, 7, 9}.

Learn more about the set here:

https://brainly.com/question/18877138.

#SPJ1

To use the GCF and distributive property to find the sum of 22 + 33, we first need to identify the GCF of both numbers, which is 11.

We can then write each number as a product using the GCF as a factor: 22 = 11 x 2 and 33 = 11 x 3. Next, we can apply the distributive property by multiplying the GCF by the sum of the other factors in each number: 11 x (2 + 3).

Finally, we can simplify the expression by adding the sum of the other factors, which is 5: 11 x 5 = 55. Therefore, the sum of 22 + 33 using the GCF and distributive property is 55.

In summary, to find the sum of 22 + 33 using the GCF and distributive property, we first identify the GCF as 11 and write each number as a product using the GCF as a factor.

We then apply the distributive property by multiplying the GCF by the sum of the other factors in each number. Finally, we simplify the expression by adding the sum of the other factors and arrive at the answer of 55. This method can be helpful when working with larger numbers or more complex expressions.

To know more about distributive property click on below link:

https://brainly.com/question/6276874#

#SPJ11

Answer:

The answer to your problem is, 39

Step-by-step explanation:

In order to find the area of the triangle use the formula down below:

A = [tex]\frac{h_{b} b}{2}[/tex]

Base = 13

Height = 6

Replace them equals:

= [tex]\frac{6*13}{2}[/tex] = 39

Thus the answer to your problem is, 39

The mean absolute deviation (MAD) of the data in the pictograph is equals to the one basketball.

We have a data in the pictograph. In mathematics, a pictograph is a pictorial representation of data using images, icons. It is also known as a pictogram. We have a pictograph, in which the vertical axis is labeled Baskets made and the horizontal axis is labeled Student. Here, one basketball picture equals two baskets. Mean absolute deviation (MAD) is a statistical measure of the average absolute distance between each data value and the mean of a data set. It is a parameter or statistic that measures the spread, or variation, in data.

Mean is defined as the sum of data values divided by number of values.

Sum of data values = 4 + 4×2 + 3×2 + 5×2

= 28

So, mean = 28/4 = 7

Now, | 4 - 7| + |8 - 7| + |6 -7 | + | 10 - 7|

= 3 + 1 + 1 + 3 = 8

So,, mean absolute deviation (MAD) of the data = 8/7 = 1.1 ~ 1. Hence, required value is 1.

For more information about mean absolute deviations, visit :

https://brainly.com/question/26462759

#SPJ4

Complete question :

Find the mean absolute deviation (MAD) of the data in the pictograph below. Baskets

The key says one basketball picture equals two baskets. The key says one basketball picture equals two baskets. A picture graph labeled Baskets each student made. The vertical axis is labeled Baskets made. The horizontal axis is labeled Student. The names from left to right on the horizontal axis are Reynaldo, Marcelle, Allie, and Fernando. There are two basketball pictures above Reynaldo. There are four basketball pictures above Marcelle. There are three basketball pictures above Allie. There are five basketball pictures above Fernando

in the given triangle, using SOH CAH TOA, the value of x is 16.48

From the question, we are to determine the value of x in the given diagram

In the given diagram,

We are given a right triangle.

70° is the included angle

6 is the adjacent

and x is the opposite

Using SOH CAH TOA,

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

Then, we can write that

tan (angle) = Opposite / Adjacent

Then,

tan (70°) = x/6

x = 6 × tan(70°)

x = 16.48

Hence, the value of x is 16.48

Learn more on Trigonometry here: https://brainly.com/question/20734777

#SPJ1

The limit of the given function as t approaches 0 is undefined.

To find the limit of the given function,[tex]lim (e^(5t) - 1) / (t × sin(t))[/tex] as t approaches 0, follow these steps:

Observe the given function

[tex]lim (e^(5t) - 1) / (t × sin(t)) as t → 0[/tex]

Apply L'Hopital's Rule, since the limit is of the form 0/0 as t approaches 0.

Differentiate the numerator and denominator with respect to t.

Numerator: [tex]d(e^(5t) - 1)/dt = 5e^(5t)[/tex]

Denominator: [tex]d(t × sin(t))/dt = sin(t) + t × cos(t)[/tex]

Rewrite the function with the new numerator and denominator.

lim [tex](5e^(5t)) / (sin(t) + t × cos(t)) as t → 0[/tex]

Evaluate the limit as t approaches 0.

[tex](5e^(5 × 0)) / (sin(0) + 0 × cos(0)) = 5 / 0[/tex]

Since the denominator is still 0, the limit does not exist.

for such more question on limit

https://brainly.com/question/12017456

#SPJ11

Therefore, it will take 3 years for Rs. 6350 to amount to Rs. 8255 at 10% per annum. Therefore, the rate of interest is 32.6% per annum if the loan is returned in 1 1/2 years.

Interest is the amount of money that a lender charges a borrower for the use of money or assets. It is typically expressed as a percentage of the amount borrowed or invested, and is paid by the borrower to the lender as compensation for the use of the money. There are two main types of interest: simple interest and compound interest. Simple interest is calculated based on the initial amount borrowed or invested, and is paid out at regular intervals over a fixed period of time. Compound interest, on the other hand, is calculated based on the initial amount plus any accumulated interest, and is paid out at the end of the investment period.

Here,

Using the formula for simple interest:

Simple Interest = (Principal x Rate x Time) / 100

where Principal is the initial amount, Rate is the interest rate per annum, and Time is the duration of the loan in years. To find the time it takes for Rs. 6350 to amount to Rs. 8255 at 10% per annum, we can set up the equation:

8255 - 6350 = (6350 x 10 x Time) / 100

Simplifying the equation, we get:

1905 = 635 x Time

Time = 1905 / 635

Time = 3 years

To find the interest rate if the loan is returned in 1 1/2 years, we can rearrange the formula for simple interest as:

Rate = (100 x Simple Interest) / (Principal x Time)

Plugging in the values, we get:

Rate = (100 x (8255 - 6350)) / (6350 x 1.5)

Rate = 3105 / 9525

Rate = 0.326 or 32.6%

To know more about interest,

https://brainly.com/question/28792777

#SPJ1

[tex](\text{x}+2)^{1/2}-5 = -2\\\\\sqrt{\text{x}+2}-5 = -2\\\\\sqrt{\text{x}+2} = -2+5\\\\\sqrt{\text{x}+2} = 3\\\\(\sqrt{\text{x}+2})^2 = 3^2\\\\\text{x}+2= 9\\\\\text{x}= 9-2\\\\\text{x}= 7\\\\[/tex]

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

Check:

[tex](\text{x}+2)^{1/2}-5 = -2\\\\\sqrt{\text{x}+2}-5 = -2\\\\\sqrt{7+2}-5 = -2\\\\\sqrt{9}-5 = -2\\\\3-5 = -2\\\\-2 = -2 \ \ \ \checkmark\\\\[/tex]

The answer is confirmed.

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

The difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they would vote for this candidate was approximately 0.025.

We are given a confidence interval of (-0.014, 0.064) for the true difference in proportions of likely voters who would vote for the political candidate before and after the debate. This means that we can be 95% confident that the true difference in proportions falls within this interval.

To find the difference in sample proportions, we need to subtract the pre-debate proportion from the post-debate proportion. Let's call the pre-debate proportion "p1" and the post-debate proportion "p2".

We are not given the sample proportions directly, but we can use the midpoint of the confidence interval as an estimate for the true difference in proportions. The midpoint is (-0.014 + 0.064)/2 = 0.025.

So, we can estimate the difference in sample proportions as:

p2 - p1 = 0.025

This means that the post-debate proportion was 0.025 higher than the pre-debate proportion, on average. Note that we don't know the actual values of p1 and p2, just their difference.

Learn more about confidence interval: https://brainly.com/question/20309162

#SPJ11

The top two officers hand out approximately 56.86% of the good driving citations.

The given good traffic citations are = 14, 8, 10, 4, and 15.

Among the above citations, the top two officers get top 2 values for their good driving. The top two values are 14 and 15.

Lets add those top two good traffic citations and divide it by the total number of citations to find out the percentage the top two officers hand out.

Total number of citations = 14 + 8 + 10 + 4 + 15 = 51

Citations get by top two officers = 14 + 15 = 29

percentage handout by top two officers = 29 / 51 = 0.5686.

To convert the obtained value in to peercentage multiply it by 100.

so, 0.5686 x 100 = 56.86%

From the above analysis, we can conclude that the 56.86% of the citations could be hand out by the top two officers.

To know more about percentage,

https://brainly.com/question/24877689

#SPJ1

Answer:15)5760.1 6)78. 17)582.4 18)112

Step-by-step explanation:

The calculated value of x is 8 and the perimeter is 80 units

From the question, we have the following parameters that can be used in our computation:

The figure

If the lines that appear to be tangent are tangent, then we have the following equation

x = 26 - 18

Evaluate the like terms

x = 8

The perimeter is the sum of the side lengths

So, we have

Perimeter = 26 + 18 + 14 + 14 + x

This gives

Perimeter = 26 + 18 + 14 + 14 + 8

Evaluate

Perimeter = 80

Hence, the perimeter is 80 units

Read more about perimeter at

https://brainly.com/question/19819849

#SPJ1

The scientific notation 5.3*10‐⁵ in standard notation gives 0.000053

From the question, we have the following parameters that can be used in our computation:

Write 5.3*10‐⁵ in standard notation.

The above number is written in scientific notation

The standard notation of a number a * 10ⁿ is represented as

a000 where the 0's are in n places

Using the above as a guide, we have the following:

5.3 * 10‐⁵ = 0.000053

Hence, 5.3*10‐⁵ in standard notation is 0.000053

Read more about scientific notation at

https://brainly.com/question/1767229

#SPJ1

To find the area of a parallelogram, multiply the base length by the height. Therefore, the area of the parallelogram is 8 cm * 24 cm = 192 cm².

To find the area of a parallelogram, you can use the formula A = base × height. In this case, the given measurements are 8 cm for the base, 9 cm for the height, and 24 cm for one of the sides of the parallelogram.

First, identify the base and height of the parallelogram. In this case, the base is 8 cm and the height is 9 cm.

Next, substitute the values into the formula for the area of a parallelogram: A = base × height.

A = 8 cm × 9 cm

Multiply the base and height:

A = 72 cm²

Therefore, the area of the parallelogram is 72 square centimeters. It's important to note that the area is not drawn to scale, so the measurements given are solely used for calculation purposes.

Learn more about formula

brainly.com/question/28647690

#SPJ11

Answer:

$450

Step-by-step explanation:

Let's use the variables C, I, and F to represent the number of chocolate fudge bars, ice cream sandwiches, and frozen fruit bars, respectively, that you will sell.

The cost of each chocolate fudge bar is $0.75, the cost of each ice cream sandwich is $0.85, and the cost of each frozen fruit bar is $0.50. Therefore, the total cost of the frozen treats that you buy will be:

Total cost = 0.75C + 0.85I + 0.50F

We want to make sure that this total cost is no more than $450. Therefore, we can write the following inequality:

0.75C + 0.85I + 0.50F ≤ 450

This inequality represents the number of chocolate fudge bars, C, the number of ice-cream sandwiches, I, and the number of frozen fruit bars, F, that will cost you no more than $450.

About the equation used to estimate the height E of the tramway t seconds after it left the station, we first need to calculate the rate of elevation gain per second.

Elevation difference: 5632 feet (Range Peak) - 4692 feet (tramway station) = 940 feet
Time: 4 minutes * 60 seconds/minute = 240 seconds

Rate of elevation gain: 940 feet / 240 seconds = 3.9167 feet/second (approximately 3.9 feet/second)

Now, we can write the equation to estimate the height E of the tramway t seconds after it left the station:

E = initial elevation + (rate of elevation gain * t)
E = 4692 + 3.9t

So, the correct equation is: E = 4692 + 3.9t

Learn more about Wyler Aerial Tramway at https://brainly.com/question/18666885

#SPJ11

Answer: B

Step-by-step explanation:

The distance from the place Tyler meets his neighbor to his home is 450 meters.

Tyler's speed is 1.2 meters per second.

Part A:

To find the distance from the place Tyler meets his neighbor to his home, we need to find the distance when x=0, since it's the time they meet. Plug x=0 into the equation y=450-72x:

y = 450 - 72(0)

y = 450

The distance from the place Tyler meets his neighbor to his home is 450 meters.

Part B:

To find the speed of Tyler, we need to find the rate at which the distance is decreasing. This can be found by taking the derivative of the distance function with respect to time:

dy/dx = -72

Since the derivative is constant, Tyler's speed is constant, and it is 72 meters per minute. To convert it to meters per second, we need to multiply by the conversion factor (1 minute = 60 seconds):

Speed = 72 m/min * (1 min / 60 s)

Thus, the speed = 1.2 m/s

Tyler's speed is 1.2 meters per second.

Read more about speed here:

https://brainly.com/question/13943409

#SPJ1

The statements that  gives the best reasons that ben’s rent payment is an essential (fixed) expense is he agreed to pay the same amount every month. The correct answer is D.

In personal finance, an essential expense is a regular expenditure that is necessary for maintaining a basic standard of living. These expenses are typically fixed, meaning that they do not fluctuate from month to month, and are difficult or impossible to eliminate without sacrificing basic needs like food, housing, or healthcare.

Since, this is his rent, the amount of money that he is legally bound to pay every month in order to keep on living in that location.

He has an agreement with his landlord to pay $215 each month and thus he has to do it.

Essential expenses are often considered a top priority in budgeting because they are critical to maintaining health, safety, and overall well-being. In the given scenario, Ben's rent payment is an essential expense because it is a fixed expense that is necessary for maintaining his housing, which is a basic need. The correct answer is D.

Learn more about essential expense at https://brainly.com/question/30804860

#SPJ11

Answer:

1.2

Step-by-step explanation:

based on your description the top sides are corresponding pairs, the bottom sides are corresponding sides, the left sides are corresponding sides, and the right sides are corresponding sides between the 2 polygons.

the dilation (scaling) is happening for all points on the polygon with the same scaling factor.

so, we only need to find the scaling factor f between one of these corresponding pairs.

8×f = 9.6

f = 9.6/8 = 1.2

Answer: The answer is 1.2

Step-by-step explanation:

Just trust me.

It would take approximately one minute and a half (or 1.6 minutes) to reach 100 jumping jacks at this rate.

What was the activity?

The dependent variable is the number of jumping jacks completed in a specific time period. In this case, the number of jumping jacks completed in one minute is the dependent variable.

The independent variable is the time in minutes. This means that the number of jumping jacks completed is influenced by the time spent doing the activity.

The relationship between the dependent variable (number of jumping jacks completed) and the independent variable (time in minutes) is directly proportional, with a ratio of approximately 63 jumping jacks per minute. This means that for every one minute spent doing jumping jacks, approximately 63 jumping jacks can be completed.

To calculate how much of the activity would be completed if this rate was maintained for 12 minutes, we can multiply the rate (63 jumping jacks per minute) by the time (12 minutes), which gives us 756 jumping jacks.

To find out how long it would take to reach 100 jumping jacks, we can set up a ratio:

63 jumping jacks / 1 minute = 100 jumping jacks / x minutes

We can solve for x by cross-multiplying:

63x = 100

x = 100 / 63

x ≈ 1.6

Learn more about dependent variable

brainly.com/question/31878363