if f(x) = 7x2 − x3, what is the rate of change of f '(x) at (2, 20)?

The dimensions of the rectangular field are L = 2x - 1 m and W = x + 3 m.

Let's call the length of the field L and the width of the field W. Then we have:

Area = Length * Width

(2x² + 5x - 3) m² = L * W

To find the dimensions, we need to factor the expression for the area.

Area = 2x² + 5x - 3

Area = 2x² + 6x - x - 3

Area = 2x(x + 3) - (x + 3)

Area = (2x - 1)(x + 3)

We can now see that the expression for the area is the same as (2x^2 + 5x - 3), so:

Area = (2x - 1)(x + 3) m²

Therefore, the dimensions of the rectangular field are L = 2x - 1 m and W = x + 3 m.

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Option D is correct. 73.9 percent of the workforce between the ages of 25 and 65 has achieved post-secondary educational credentials in Canada.

According to the most recent data from Statistics Canada, approximately 73.9 percent of the workforce between the ages of 25 and 65 has achieved post-secondary educational credentials in Canada. This data shows a significant increase in the number of Canadians who have pursued higher education in recent years, reflecting a trend towards increased investment in education and training as a means of achieving higher levels of skills and knowledge.

This high percentage of workers with post-secondary credentials is a positive indicator of the strength of Canada's economy, as it demonstrates a well-educated and highly skilled workforce. This, in turn, attracts investment and contributes to the growth of industries, creating new job opportunities and fostering economic prosperity.

Furthermore, the attainment of post-secondary education is associated with higher earnings and improved job prospects, both of which contribute to greater overall financial security and stability. As such, the high percentage of the workforce with post-secondary credentials in Canada is a testament to the country's commitment to education and the pursuit of economic and personal success.

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To determine the total weight of the coins to within 0.1% uncertainty, we need to weigh 100 coins.

We can use the formula for the standard deviation of the mean to determine the number of coins needed to be weighed. The formula is given by -

σ mean = σ/√N

Where σ is the standard deviation of the coins and N is the number of coins weighed.

We are given that the standard deviation of the coins is 1%, we have,

σ mean = 1%/√N

We want to determine the number of coins N such that σ mean = 0.1%. So, 0.1% = 1%/√N

Dividing both sides by 0.1% we get,

√N = 1%/0.1% = 10

Taking the square of both sides,

N = [tex]10^2[/tex] = 100

Therefore, to determine the total weight of the coins to within 0.1% uncertainty, we need to weigh 100 coins.

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The probability that a student has a GPA under 2.0 given that he has skipped many classes is 8/11.

From the table we see that,

The student who have a GPA under 2.0 = 80

The student who has skipped many classes = 80 + 25 + 5

The student who has skipped many classes = 110

Hence, the probability that a student has a GPA under 2.0 given that he has skipped many classes = The student who have a GPA under 2.0/The student who has skipped many classes

The probability that a student has a GPA under 2.0 given that he has skipped many classes = 80/110

The probability that a student has a GPA under 2.0 given that he has skipped many classes = 8/11

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The complete question is:

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.

What is the probability that a student has a GPA under 2.0 given that he has skipped many classes?

A. 0.080

B. 0.281

C. 0.285

D. 0.314

E. 0.727

The probability that a standard normal random variable will take a value less than 1.05 is approximately 0.8528.

Probability is a mathematical concept that quantifies the likelihood or chance of an event occurring. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To find the probability that a standard normal random variable is less than a certain value, use a standard normal table or use a calculator with a cumulative distribution function (CDF) for the standard normal distribution.

Look up that value in the standard normal table and find the corresponding cumulative probability.

Hence, p(z < 1.05) = 0.8528.

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The change in demand is $15 per barrel.

Given is that the price of oil increases from 20 to 5 per barrel.

So we can write the change in demand as -

$20 per barrel - $5 per barrel

$15 per barrel

Therefore, the change in demand is $15 per barrel.

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Nicole's daily salary is $116.67.

The formula for Hourly pay is defined as:

Hour Pay = Month Salary ÷ Hours Per Month.

The formula for Dialy pay is defined as:

Daily Pay = Hour Pay x Hours Per Day.

let $x be Nicole's daily salary. From the given information x can be determined as:

24% of x=28

24*1/100*x=28

Multiplying 100 on both sides.

24*1/100*x*100=28*100

24*x=28*100

Divide 24 into both sides.

24*x/24=28*100/24

By solving we get x value:

x=116.67

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Answer:

Let y be the total number of dogs

dogs on leash = y/5

dogs not on leash = y-y/5

= 4y/5

The expression to represent how many dogs were not on a leash is 4x / 5, using both subtraction and multiplication.

An expression is combination of variables, numbers and operators.

If 1/5 of the dogs were on a leash, then the remaining 4/5 of the dogs were not on a leash.

To find the number of dogs that were not on a leash, we can multiply the total number of dogs (x) by 4/5:

Number of dogs not on a leash = x * 4/5

We can also express this using subtraction:

Number of dogs not on a leash = x - (x * 1/5)

Simplifying the expression on the right side:

Number of dogs not on a leash = x - x/5

Combining like terms:

Number of dogs not on a leash = (5x - x) / 5

= 4x / 5

Therefore, the expression to represent how many dogs were not on a leash is 4x / 5, using both subtraction and multiplication.

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(a) The average velocity for the first half of the swim: v1 = L / t1.

(b) The average velocity for the second half of the swim: v2 = L / t2.

(c) The average velocity for the round trip is given by:  v = 2L / (t1 + t2).

(d) The average speed for the round trip is the magnitude of the average velocity: s = |v| = 2L / (t1 + t2).

Let's assume the length of the pool is L and

The time for the athlete to swim to the other end is t1,

And the time for her to swim back is t2.

(a) The average velocity for the first half of the swim (from one end to the other end) is given by:

the distance travelled divided by the time taken:

=> v1 = L / t1.

(b) The average velocity for the second half of the swim (from the other end back to the starting position) is given by

v2 = L / t2.

(c) The average velocity for the round trip is given by:

the total distance traveled divided by the total time taken:

=> v = 2L / (t1 + t2).

(d) The average speed for the round trip is the magnitude of the average velocity:

s = |v| = 2L / (t1 + t2).

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The drawing's scale factor, if The scale of the drawing was 9 inches = 6 feet, is 3/4.

What is the scale factor?

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an object.

Given,

orter made a scale drawing of a campsite. The scale of the drawing was 8 inches = 6 feet.

The scale of the drawing was 8 inches = 6 feet,

The original value = 6 feet,

The value on paper = 8 inches,

Calculate the scale factor as shown below,

Scale factor = The original value / The value on paper

Scale factor = 6 / 8

Scale factor = 3 / 4

Therefore, The drawing's scale factor, if The scale of the drawing was 9 inches = 6 feet, is 3/4.

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Answer:

a) 11m

b)4.1cm

Step-by-step explanation:

if 1 cm = 2m

hence,

5.5cm = (5.5 x 2) = 11m

if 2m = 1cm

hence,

8.2 = (8.2 ÷ 2) = 4.1cm

The collection of all feasible inputs and outputs for a function, respectively, is its domain and range.

A function's domain is its collection of inputs. The collection of outputs for a function is known as range. For example, when specifying domain and range, interval notation is used to describe groups of numbers. There are two types of intervals: open and closed.

The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.

By using values enclosed in brackets to define a group of numbers, interval notation can be used to express the domain and range. In interval notation, we use a square bracket to denote that the endpoint is included in the set and a parenthesis to denote that the endpoint is either excluded from the set or that the interval is unbounded.

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The drums of sealant will be needed if each drum covers 150 sa yd are 5.

The total area of the four driveways is 84.8 sq yd + 124.1 sq yd + 98.9 sq yd + 344.7 sq yd = 652.5 sq yd.

So, the number of drums of sealant needed is given by the total area divided by the area covered by each drum:

652.5 sq yd / 150 sq yd/drum = 4.35 drums (rounded up to the nearest whole number, 5 drums will be needed).

Therefore, 5 drums of sealant will be needed if each drum covers 150 sa yd.

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Answer:

13 people wouldn't have electricity

Step-by-step explanation:

Ratio of people with electricity to people without electricity is 8,000,000,000 : 1,000,000,000 or 8:1

8:1 = 100:x  We need to find x.  To do this, divide 100 by 8.

100/8 = 12.5

Then multiply the other side of the ratio (1) by that number.

12.5 · 1 = 12.5

Out of 100 people in a village 12.5 of them don't have electricity.  (You can't have half of a person so you round it to 13.)

As the given interval is a half-open interval, it is a closed interval. So, the extreme value theorem is not applicable and the correct option is B) The domain of f is not a closed and bounded interval.

We are given f(x) = x sinx

Let us first take x in f(x).

In the question, the domain of f(x) is [0, ∞) which means x ∈ [0, ∞).

Hence, the range of x is also [0, ∞)

Now, let us take sinx.

The range of sin x is [-1, 1] for all x ∈ R.

For x ∈ [0, ∞), the range of sinx will remain. [-1, 1]

Hence, we can conclude that the range of f(x) is (-∞, ∞) and its domain is [0, ∞)

Therefore, it can be concluded that the domain of f is not a closed and bounded interval.

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The area and perimeter of the given parallelogram are

30√30 cm² and 56 cm respectively.

Given is a parallelogram as shown in the image attached.

From the Pythagoras theorem, we can write that -

h² = 13² - 7²

h² = 169 - 49

h² = 120

h = √120

h = 2√30                                                                      .... Eq { 1 }

Now, we can write the parallelogram as -

A = b x h

A = 15 x 2√30

A = 30√30 cm²

We can write the perimeter as -

P = 15 x 2 + 13 x 2

P = 30 + 26

P = 56 cm

Therefore, the area and perimeter of the given parallelogram are

30√30 cm² and 56 cm respectively.

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The response to the above question regarding the dot plot is as follows:

Dot plot is is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles.

The plot groups the data as little as possible and the identity of an individual observation is not lost. A dot plot uses dots to show where the data values (or scores) in a distribution are.

According to this question, a teacher puts all her students' quiz on the dot plot above. Based on the dot plot graph, the corresponding answers to the above attached questions is as illustrated in the main answer part.

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We got 1 blue and 4 green packs. The solution has been obtained by using the linear equation.

What is a linear equation?

A linear equation has the degree of one that is highest. It follows that a linear equation with an exponent greater than one cannot have any variables. This equation results in a straight line on the graph.

Let the pack of blue cards be 'x' and pack of green cards be 'y'.

We are given that the blue cards came in packs of 5 and the green cards came in packs of 6 and in total we had 29 cards.

So, from this we get

5x + 6y = 29   ...(1)

Also, it is given that we have total of 5 packs,

So,

x + y = 5   ...(2)

From (2), we get

x = 5 - y

Substituting this value in (1), we get,

⇒5(5-y) + 6y = 29

⇒25 - 5y + 6y = 29

⇒25 + y = 29

⇒y = 4

So, x = 5-4 = 1

Hence, we got 1 blue and 4 green packs.

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The position s(t) of the ant at time t is s(t) = 3/(t²+31)^1/2 + 15 - 3/√31

The velocity of an ant moving along the t-axis is given as

                         v(t) = - 3t/(31 + t^2)^3/2

Now, the distance travelled by the ant at time t is :

                         s(t) = -∫3t/(31 + t^2)^3/2 dt

Put t = √31 tanθ

     dt = √31 sec²θ dθ

                         s(t) = -∫3t/(31 + t^2)^3/2 dt

                               = -∫(3√31 tanθ/(31 + 31 tan²θ)^3/2) √31 sec²θ dθ

                               = -93∫ tanθsec²θ/(31 sec²θ)^3/2  dθ

                               = -3/√31∫ tanθ sec²θ/sec³θ  dθ

                               = -3/√31∫ tanθ / secθ  dθ

                               = -3/√31∫ sinθ  dθ

                               = (3/√31) cosθ  + c

we took t = √31 tanθ or tanθ= t/√31

So, cosθ = (31/t²+31)^1/2

                   ∴  s(t)  = (3/√31) (31/t²+31)^1/2  + c

                       s(t)  = 3/(t²+31)^1/2  + c

At t = 0, s = 15

So, s(0) = 3/(0²+31)^1/2  + c

       15 = 3/√31 + c

         c = 15 - 3/√31

Hence, s(t) at time t is s(t) = 3/(t²+31)^1/2 + 15 - 3/√31

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Answer:

(-32c+3)/15

Step-by-step explanation:

(c+1)/5-7c/3 =

= (3×(c+1) -5×7c)/15 =

= (3c+3-35c)/15 =

=( -32c+3)/15

The lowest energy  and highest energy conformations of 1-chloropropane is as follow

Cl-CH2-CH2-CH3.

For better visualize different conformations of a given molecule,

A drawing convention is convenient to use called the Newman projection.

In a Newman projection,

we look lengthwise down a specific bond of interest – the carbon-carbon bond in ethane.

We depicted the front atom as a dot, and the ‘back’ atom as a larger circle.

the C-C bond in this way, the angle formed between a C-H bond on the front carbon and a C-H bond on the back carbon

carbon is referred to as a dihedral angle.

1-chloropropane. molecular formula  is C3H7Cl

The lowest energy  and highest energy conformations of 1-chloropropane is as follow

Cl-CH2-CH2-CH3.

Cl would be the largest substituent for Carbon 1, and CH3 would be the largest substituent for Carbon 2,

so I would put them opposite from each other on the projection.

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Answer:

Step-by-step explanation:

(F - 32)0.56 = 4

F - 32 = 4/0.56

F = 39.1⁰ F

The point be (9, -4) and slope = -2/3 the slope of the equation of line be y = -2x/3 +2

What is meant by slope of the line?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. While there has been no net change in the x coordinate, there has been no net change in the y coordinate.

The slope is m and the y-intercept is b in the slope-intercept version of the equation (y=mx+b). We can also change some equations to be written in slope-intercept form.

Let the equation be y - (-4) = (-2/3)(x - 9)

y + 4 = -2 x/3 + 6

simplifying the equation, we get

y = -2x/3 + 6 - 4

Therefore, the slope of the equation be y = -2x/3 +2

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What is the point of . (9, -4); slope = -2/3

The required values of x = 8 units and z = 15 units for the given polygon.

A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.

The two polygons shown are similar.

As we know that two similar polygons with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

So QP/WX = PS/WZ

⇒ x/12 = 6/9

⇒ x = 72/9

⇒ x = 8 units

Now, RS/YZ = PS/WZ

⇒ 10/z = 6/9

⇒ z = 90/6

⇒ z = 15 units

Thus, the required values of x = 8 units and z = 15 units.

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Answer:

38feet 4.4 inches. .. ..........

The definition of percent helps you write fraction and decimal equivalents by understanding that "per cent" means "per hundred".

For example, if you are asked to write the fraction and decimal equivalent of 25%, you would divide 25 by 100 to get the fractional equivalent of ¼, and divide 25 by 100 to get the decimal equivalent of 0.25.

The decimal equivalent of a fraction or percentage is the numerical value expressed in decimal form. For example, the decimal equivalent of 1/2 is 0.5 and the decimal equivalent of 25% is 0.25. Decimal equivalents are useful for calculations and can be used to convert fractions and percentages into decimal form.

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PICTURE 1: the value of h is 8√2 units

PICTURE 2: the angle measures of the triangle are 30,60,90

PICTURE 3: x = 5√2 units

PICTURE 4: x = 5√3 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

PICTURE 1

sin 45° = 8/h

h =  8/sin 45°

h = 8√2 units

PICTURE 2

We have a 90° there already (the box)

Let the unknown angles be x and y respectively

sin x = 6/12

sinx = 1/2

x = arcsin (1/2)

x = 30°

y = 90 - 30 = 60°

Thus, the angle measures of the triangle are 30,60,90

PICTURE 3

sin 45 = x/10

x = 10 sin 45

x = 5√2 units

PICTURE 4

tan 30 = x/15

x = 15 tan 30

x = 5√3 units

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The errors in the equations are given as follows:

a. We should multiply the constants 4 and 3, not add them, hence the result would be 12a^7.

b. The exponent one was forgotten, hence the correct result is of x^(6 + 1 + 3) = x^10.

c. The terms have different bases, hence the exponents cannot be added.

When two terms with the same base and different exponents are multiplied, we must keep the bases and then add the exponents.

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