G technical mathematics with calculus volume 10 find the derivative of the function y = sqrt(x^2+1) using limits definition

Answer:

4,17,13,7

Step-by-step explanation:

i got it right :)

To assist Hugo in organizing patron pet ownership into a two-way frequency table, calculations were made to determine the number of patrons with both a dog and a cat, leading to a complete frequency table illustrating pet ownership among 41 patrons.

Hugo, the veterinarian, is attempting to organize patron pet ownership information into a two-way frequency table. First, let's establish the total number of patrons which is 41. Since 20 patrons do not have a dog, it implies that 41 - 20 = 21 patrons have a dog. Of the 41 patrons, we know that 17 have a cat. Also, 7 patrons have neither a dog nor a cat. To create the two-way frequency table, we need to figure out how many patrons have both a dog and a cat.

To find the number of patrons with both pets, we add the number of patrons without pets to those with dogs and then subtract from the total number of patrons, which gives us 41 - 20 + 7 = 28. However, since this number includes all dog owners, we need to subtract those who only have dogs and no cats, which gives us 28 - (41 - 17) = 28 - 24 = 4 patrons with both a dog and a cat.

With these calculations, we can now fill out the two-way frequency table:

Patron\PetDogNo DogTotalCat41317No Cat17724Total212041

Note: The sum of the numbers for dog owners and non-dog owners must equal the total number of patrons, and the same applies for cat ownership.

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Julie studied for 3 1 3 hours during the 4 days before her last math test. If she studied for the same amount of time each day, how much time did she spend studying each day?

Solution:

Julie studied for 3 [tex]\frac{1}{3}[/tex] hrs in 4 days

Let us first find how many minutes Julie studied in 4 days

In 1 hour, there are 60 minutes

Julie studied for 3 complete hours and one-third of the hour.

So, Number of minutes in 3 hours is 3*60=180hrs

and, Number of minutes in one-third of an hour=[tex]\frac{1}{3} *60[/tex]

=[tex]\frac{60}{3}[/tex]=20minutes

So, time spent by Julie in studying in 4 days is 3[tex]\frac{1}{3}[/tex] hours

or, Julie studied for 180+20 minutes in 4 days

Adding 180 and 20

Julie studied for 200 minutes during the 4 days

To find time she spend studying each day, we must divide total time spent in studies by number of days

Time she spend studying each day= [tex]\frac{200}{4}[/tex] minutes

Dividing 200 by 4, we get

Time she spend studying each day=50 minutes

Answer:

time she spend studying each day=50 minutes

Answer:

sally makes more

Step-by-step explanation:

john makes 20 per 2 hours

20/2= 10

sally makes 50$ per 4 hours

50/4= 12.5

so Sally makes more

the / is division

Answer:

Option C. [tex]7.\frac{\sqrt{74}}{74}[/tex]

Step-by-step explanation:

At the end of one swipe the tip of one blade is at (-5, 7). We have to find sine value of this function.

As shown in the figure coordinates of the tip of the wiper blade are (-5, 7)

So [tex]sin a = \frac{Height}{Hypotenuse}[/tex]

Here Height of the triangle = 7

and Hypotenuse = x = [tex]\sqrt{(-5)^{2}+7^{2}}=\sqrt{25+49}=\sqrt{74}[/tex]

By putting these values in the expression

[tex]sina=\frac{7}{x}=\frac{7}{\sqrt{74}}=7.\frac{\sqrt{74}}{74}[/tex]

Answer is option C.[tex]7.\frac{\sqrt{74}}{74}[/tex]

B) The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.

Answer with explanation:

The Description about the Histogram is

Vertical Axis = 0-14

Horizontal Axis      Bar Height

0-49                            2

50-99                            6

100-149                         12

150-199                            5

200-249                          1

Plotting the Histogram

→Class interval 150-199 has frequency =5, and class interval 50-99, has frequency equal to 6.

→The curve is not uniform on both sides.

→The interval in which mean , median lies has 6+2=8 frequency on the left of that interval , and 5+1=6, values on the right of class interval [100-149].We can conclude that,the histogram is left Skewed.

→But when we join ,mid points of histogram,the curve obtained resembles with a normal distribution curve called bell curve.It is not exactly bell shaped,as not uniform on both sides explained above.

Option C: Approximately bell Shaped

The time take him to grade 35 essays is, 5.6 hours.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A teacher grades 25 students essays in 4 hours.

And, To find the time take him to grade 35 essays.

Now, Let us assume that,

Time take him to grade 35 essays is, x

Hence, We get;

25 / 4 = 35 / x

Solve for x;

x = 35 × 4 / 25

x = 5.6 hours

Thus, the time take him to grade 35 essays is, 5.6 hours.

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Answer:

Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees. Supplementary and complementary angles do not have to be adjacent

Step-by-step explanation:

To compare the maximum values of function, which is a discrete function with given values, we find that C ) It is 3 units lower for f ( x ) than g ( x )

To compare the maximum values of functions f(x) and g(x), we first analyze each function separately. The quadratic function f(x) = -4x2 + 5x has a vertex form which reveals its maximum value at x = 1/3, and since g(x) is a discrete function defined by its values at certain points, we look directly at the given values to find its maximum.

Function g(x) reaches its maximum at g(2) = 8. Comparing this to f(x), whose vertex form shows that its maximum is f(1/3), we need to compute f(1/3) = -4(1/3)2 + 5(1/3) to find its specific value. After calculation, f(1/3) is found to be higher than 8, which is the maximum of g(x).

Thus,

g ( x ) maximum value = 8

f ( x ) maximum value = 5

g ( x ) max - f ( x ) max = 8 - 5 = 3

Complete Question:

Functions f(x) and g(x) are described as follows:

f(x) = -4x2 + 5

x g(x)

0 0

1 4

2 8

3 4

4 0

Which statement best compares the maximum value of the two functions? A. It is equal for both functions. B. It is 3 units higher for f(x) than g(x). C. It is 3 units lower for f(x) than g(x). D. It is 4 units lower for f(x) than g(x).

Answer=(4,5)

Step-by-step explanation: