NO LINKS!! Please help me with this one​

The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

Given that, [tex]\frac{d}{dx}(e^x) =e^x[/tex].

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Differentiate using the Exponential Rule which states that [tex]\frac{d}{dx}(a^x)[/tex] is [tex]a^xln(a)[/tex] where [tex]a=e.e^x[/tex]

So, now [tex]\frac{d}{dx}(e^x) =e^x[/tex]

The differentiation of [tex]e^x[/tex] is [tex]\frac{d}{dx}(e^x) =e^x[/tex]. Hence, proved,

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The required length of the pieces is given as 20 ft, 16ft, and 14ft.

Given that,
An electrician cuts a 50 ft piece of wire into 3 pieces. The first piece is 4 ft longer than the second piece and the third piece is 2 feet shorter than the second piece. How long are the pieces is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
according to the question,
Length of the first, second, and third  be x, y and z,
According to the question,
x + y + z = 50 - - - - - - - - (1)
x = y + 4
z = y - 2
put x and z in equation 1
y + 4 + y + y - 2 = 50
3y = 50-2
y = 48/3
y = 16 ft
Now,
x = 16 + 4 = 20 ft
z = 16 - 2 = 14 ft

Thus, the required length of the pieces is given as 20 ft, 16ft, and 14ft.

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Answer:

7.8

Step-by-step explanation:

Switch 8 and 7, it round to 8 and end in tenths.

Answer:

7.8

Step-by-step explanation:

7.8 rounds to 8, because 8 is greater than 5, and then we end in the tenths place.

Answer:

3

Step-by-step explanation:

Using the Quotient Rule, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .

In the given question,

We have to differentiate the given function with respect to x.

The given function is [tex]y=\frac{x^4+1}{3x^4+4}[/tex]

We have differentiate with respect to x.

The given function is in fraction format. So solving the given expression we use Quotient Rule

According to Quotient Rule

"A method for recognizing issues where one function is divided by another is the quotient rule."

The formula of Quotient Rule is

[tex]\frac{d}{dx}[\frac{f(x)}{g(x)}]=\frac{g(x)f'(x)-g'(x)f(x)}{(g(x))^2}[/tex]....................(1)

As we see in our function then f(x) = x[tex]^4+[/tex]1 and g(x) = 3x[tex]^4+[/tex]4

Before solving the function we find the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex]

Now solving the f(x) for f'(x) with respect to x.

f(x) = x[tex]^4+[/tex]1

[tex]\frac{d}{dx}f(x)=\frac{d}{dx}(x^4+1)[/tex]

[tex]f'(x)=\frac{d}{dx}x^4+\frac{d}{dx}1[/tex]

We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.

So [tex]f'(x)=4x^{(4-1)}+0[/tex]

[tex]f'(x)=4x^3[/tex]

Now solving the g(x) for g'(x) with respect to x.

g(x) = 3x[tex]^4+[/tex]4

[tex]\frac{d}{dx}g(x)=\frac{d}{dx}(3x^4+4)[/tex]

[tex]g'(x)=3\frac{d}{dx}x^4+\frac{d}{dx}4[/tex]

We know that the differentiation of [tex]x^n=nx^{n-1}[/tex] and differentiation of constant value is zero.

[tex]g'(x)=3(4x^{(4-1)})+0[/tex]

[tex]g'(x)=3(4x^{3})[/tex]

[tex]g'(x)=12x^{3}[/tex]

Now finding the value of (g(x))[tex]^2.[/tex]

g(x) = 3x[tex]^4+[/tex]4

[tex](g(x))^4=(3x^4+4)^2[/tex]

Now using the formula of [tex](a+b)^2=a^2+2ab+b^2[/tex].

Now solving

[tex](g(x))^4=(3x^4)^2+2\times(3x^4)\times4+(4)^2[/tex]

Simplifying

[tex](g(x))^4=9x^8+24x^4+16[/tex]

Now putting the value of f'(x), g'(x) and (g(x))[tex]^2.[/tex] in the equation (1)

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4+4)(4x^3)-(12x^3)(x^4+1)}{9x^8+24x^4+16}[/tex]

Simplifying

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(3x^4(4x^3)+4(4x^3))-((12x^3)x^4+1(12x^3))}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{(4+3)}+16x^3)-(12x^{(3+4)}+12x^3)}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{(12x^{7}+16x^3)-(12x^{7}+12x^3)}{9x^8+24x^4+16}[/tex]

Now solving the bracket

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{12x^{7}+16x^3-12x^{7}-12x^3}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{16x^3-12x^3}{9x^8+24x^4+16}[/tex]

[tex]\frac{d}{dx}[\frac{x^4+1}{3x^4+4}]=\frac{4x^3}{9x^8+24x^4+16}[/tex]

Hence, the differentiate the function with respect to x is [tex]\frac{4x^3}{9x^8+24x^4+16}[/tex] .

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Answer: 1) C- the survey participants should be randomly selected

2) C- how interested would you be in purchasing a blue car?
3) C- the stadiums front gate

Step-by-step explanation: I took the quick check.

Answer:

1. c

2. d

3. c

Step-by-step explanation:

The total number of students going on a trip is 375 students.

Given that,

The entire third through fifth graders are taking a field trip to Coney Island. There are 125 pupils each grade. The cafeteria should provide lunches.

We have to find how many students will be travelling on the trip.

So,

In Grade 3 we have 125 students.

In Grade 4 we have 125 students.

In Grade 5 we have 125 students.

So,

Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5

= 125 + 125 + 125 = 375.

Therefore, The total number of students going on a trip is 375 students.

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Eve's data is a random sampling since she picked the participants randomly.

A simple random sample is a subset of a population chosen at random. This sampling strategy gives each person of the population an exact equal chance of being chosen, reducing the likelihood of selection bias.

To be considered a truly random sample, every subject in your target demographic must have an equal chance of being chosen. Conducting a study to estimate the length of time college students workout at your campus each week is an example of breaking this assumption.

In this case, Eve needed to collect the eye color of 50 random people for a high school statistics project and she felt more comfortable collecting the data from 20 arbitrary classmates, 12 arbitrary neighbors, and 18 arbitrary members of her bible study group. In this case, she picked them randomly. In Adam's case, it doesn't necessarily have to be strangers.

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The estimation of 719 x 26 is 14,000

Making a number simpler so that its value stays near to its original state is known as rounding. Although less exact, the outcome of rounding off a number is simpler to utilise.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

Estimation of 719 x 26

Now, Round off nearest hundred for 719 which is 700

i.e., Round 719 = 700

Now, Round off nearest hundred for 26 which is 20

i.e., Round 26 = 20

Hence, the estimation is 700 x 20 = 14,000.

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The liquid that Richard used in the punch is 1 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Richard made punch for a party. He used 1/2 cup of pineapple juice, 1/2 cup of ginger ale, and 1/4 cup of white grape juice.

The total fraction will be:

= 1/2 + 1/2 + 1/4

= 1 1/4 cups.

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The probability of picking a shirt that is red or striped is 2/3.

Given, that a drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green.

We have to find the probability of picking a shirt that is red or striped,

P(R ∪ S) = P(R) + P(S) - P(R∩S)

where, R be the event that the shirt is red.

and S be the even that the shirt is striped.

P(R) = 5/12 (as, there are 5 red shirts)

P(S) = 5/12 (as, there are 5 striped shirts)

P(R∩S) = 2/12 (as, there are 5 striped red shirts)

P(R ∪ S) = 5/12 + 5/12 - 2/12

P(R ∪ S) = 8/12

P(R ∪ S) = 2/3

The probability of picking a shirt that is red or striped is 2/3.

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If the p-value is 0.023 from a hypothesis test is compared to a significance level of 0.05, the conclusion which we would make is: A) accept the null hypothesis.

A p-value is also referred to as the probability value and it can be defined as a probability which arises when the null hypothesis (H₀) is true of obtaining a sample result that is at least as unlikely as what is originally observed.

In Mathematics, the following rules are applicable to both a p-value and a hypothesis test:

In this context, we can logically deduce that the null hypothesis would be accepted because the p-value (0.023) is greater than a significance level of 0.05 and not statistically significant.

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The measure of side AC in the triangle is 2.7 m

From the question, we are to determine the measure of AC

From the given information, we have that ΔADC is similar to ΔCDB

Thus,

We can write that

|DC| / |DB| = |AC| / |CB|

From the diagram,

|DC| = 5.5 m

|DB| = 6.3 m

|AC| = h

|CB| = 3.1 m

Then,

5.5 / 6.3 = h / 3.1

∴ h = (5.5 × 3.1) / 6.3

h = 17.05 / 6.3

h = 2.70635 m

h ≈ 2.7 m

Hence,

The length of AC is 2.7 m

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By performing some simple mathematical operations, the answers to all the subparts are:

So, the answers after multiplication are:

Therefore, by performing some simple mathematical operations, the answers to all the subparts are:

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Using mathematical operations, the amount that would be saved by buying 3 dresses instead of buying per piece is $3.40.

The mathematical operations include the following basic operations: addition, subtraction, division, and multiplication.

Mathematical operations determine the results of mathematical expressions and problems.

Cost of a dress = $6.20

Cost of 3 dresses = $15.20

Cost per dress if 3 dresses were bought = $5.067

Amount saved for buying 3 dresses instead of one = $3.40 ($6.20 x 3 - $15.20)

Thus, mathematically, the customer would save $3.40 by buying 3 dresses for $15.20 instead of buying at $6.20 per unit.

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In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).

Graphing the polygon and reflection in a graph:

A polygon is a 2 - dimensional shape, that is formed by three or more straight edges. To graph, a polygon, plot the given points on the plane and connect the vertices using straight lines, without crossing any lines.

To reflect the image in the line y = x, switch the values of x to y and y to x. After switching the points, join the formed points and draw the reflected image.

Here we have

A(2, -1),  B(-1, 2),  C(2, 3),  D(4,2)

After switching the values of x to y and y to x the resultant points are

A'(-1, 2),  B'(2, -1),  C'(3, 2),  D'(2,4)

In the given picture the polygon ABCD is the formed polygon (in red color) and the reflection of the polygon is A'B'C'D' (in green color).

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Answer:

It is A

Step-by-step explanation:

I have brainly tutor and had that exact question

The average rate of change of f(x) on the interval  30 ≤ x ≤ 60 is r = 1/5.

For a function f(x), we define the average rate of change over an interval:

a ≤x ≤b is given by:

( f(b) - f(a))/(b - a)

In this case we have the function defined by the table and the interval:

30 ≤ x ≤ 60

On the table we can see:

f(60) = 19

f(30) = 13

Then the average rate of change is:

r = (19 - 13)/(60 - 30) = 6/30 = 1/5

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The equation to model the situation is given below. And the months will the populations of the towns be​ equal will be 12.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A town's populace is 43,200. Around 125 individuals move out of the town every month. Every month, 175 individuals on the normal move into town. A close by the town has a populace of 45,900. It has nobody moving in and a normal of 175 individuals moving away consistently.

Let y be the total population and x be the number of months. Then the equations are given as,

y = (175 - 125)x + 43200

y = 50x + 43200           ...1

y = -175x + 45900        ...2

From equations 1 and 2, then we have

50x + 43200 = - 175x + 45900

50x + 175x = 45900 - 43200

225x = 2700

x = 2700 / 225

x = 12

The months will the populations of the towns be​ equal will be 12.

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The sum of first 50 terms of the sequence a(n) = 3n + 2 is  3925

In this question, we have been given a sequence a(n) = 3n + 2

We need to find the sum of the first 50 terms of the sequence

a(1) = 3 + 2

      = 5

a(2) = 6 + 2

      = 8

a(3) = 9 + 2

      = 11

a(4) = 12 + 2

      = 14

...

Given sequence is arithmetic sequence with common difference d = 3 and the first term a = 5

Using the formula for the sum of first n terms of AP

Sum of n terms of A.P. = n/2[2a + (n - 1)d]

For n = 50

S(50) = (50/2) * [2(5) + (50 - 1)3]

S(50) = 25 * [10 + (49 * 3)]

S(50) = 25 * 157

S(50) = 3925

Therefore, the sum of first 50 terms of the sequence a(n) = 3n + 2 is  3925

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The solution to the system graphed is (2, 0).

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.

Usually, data that changes over time is represented by a line graph.

Given:

From the graph we have two line red and purple.

The intersecting point for both line is (2, 0).

Hence, the solution to the system graphed is (2, 0).

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The surface area of the cone is  282.6 [tex]in^2[/tex].

What is surface area of cone?

  The region that a cone's surface occupies in three dimensions is known as the surface area of a cone. The whole area a cone's surface covers is known as the cone's surface area. The overall surface area will include the cone's lateral and base surfaces. A three-dimensional solid construction with a circular base is referred to as a cone. A cone can be thought of as a collection of irregularly shaped circular discs that have been stacked on top of one another while maintaining a constant ratio between the radii of the adjacent discs. It is the total of the cone's lateral area and base area.

Here the given ,

=> Height h= 12in

=> Radius r = 5 in

Using surface area of cone formula,

=> Surface area SA = [tex]\pi[/tex]r(r+ [tex]\sqrt{r^2+h^2}[/tex]) square unit.

=> surface area SA = 3.14*5(5+[tex]\sqrt{12^2+5^2}[/tex])

=> surface area SA = 15.7(5+[tex]\sqrt{144+25}[/tex])=15.7(5+13)

=> surface area SA = 15.7*18=282.6 [tex]in^2[/tex]

Therefore surface area of the cone 282.6 [tex]in^2[/tex].

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Answer:

15 more appetizers

Step-by-step explanation:

A restaurant has 60 menu items. Of these menu items, main dishes outnumber appetizers by a ratio of 4:1. How many more appetizers would the restaurant have to add to the menu to bring the ratio to 2:1?

at a ratio of 4e:1a and having 60e: there are (60/4=15) 15 appetizers

at a ratio of 2e:1a and having 60e: there are (60/2=30) 30 appetizers

Because they already have 15 appetizers, they will need:

30 appetizers - 15 appetizers  = 15 more appetizers

The five number from the box plot is presented as follows:

A box and whisker plot shows five things of a distribution, listed as follows:

The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.

The data set's maximum value.

These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.

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Answer: 4/5 or 0.8

Step-by-step explanation:

[tex]1\frac{1}{4}[/tex] * [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{1}[/tex] = 1

[tex]1\frac{1}{4}[/tex] is also equal to 1.25.

1.25 * 0.8 = 1

Answer:

4/5

Step-by-step explanation:

because 4 is half of a half two fourths are a half and 4/4 are 1 whole

The exact value of Cosθ is -1/√10 .

In the question ,

it is given that ,

the value of tanθ = 3/1 ,

that means the perpendicular = 3x

and the base of the triangle is = 1x,

So ,By Pythagoras Theorem

hypotnuse² = perpendicular² + base²

hypotnuse² = (3x)² + (1x)²

hypotnuse² = 9x² + 1x²

hypotnuse² = 10x²

hypotnuse = (√10)x

So , Cosθ = base / hypotnuse

Cosθ = 1x/(√10)x

Cosθ = 1/√10

Since , [tex]\theta[/tex] lies in the second quadrant ,

and in second quadrant Cos is negative ,

So , Cosθ = -1/√10

Therefore , The exact value of Cosθ is  -1/√10  .

The given question is incomplete , the complete question is

If Tanθ = 3 , θ lies in the second quadrant. Use a Pythagorean identity to find the exact value of Cosθ ?

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The solution set for the inequality is (-3, 3)

Here we have the absolute value inequality

|2x| - 6  < 0

To solve this, we need to isolate the variable, which in this case is x.

Adding 6 in both sides we get:

|2x| -6 + 6 < 0 + 6

|2x| < 6

This can be decomposed in the inequality:

-6 < 2x < 6

Now to competely solve the inequality, we will divide both sides by 2, so we get:

-6/2 < 2x/2 < 6/2

-3 < x < 3

So the solution set is (-3, 3)

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The equation for the representation of the given situation will be

y = x - 0.54x, and the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative.

An equation is a statement that says that the value of two mathematical expressions is equal.

Given that, a cinema sends out a coupon for ​54% off the price of a ticket.

The equation for this situation will be y = x - 0.54x,

And the line of this equation will always lie in the first quadrant because values of x and y in the first quadrant are always positive, and here x and y are prices which can't be negative.

Hence,  the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative and The equation for the representation of the given situation will be

y = x - 0.54x

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The completion of the inventory table is as follows:

A = $48

B = $264

C = $420

D = $304.

The above inventory table is completed using some of the inventory methods including:

FIFO (First-in, First-out) assumes that the physical flow of goods sold follows the chronological order of acquisition.

LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.

The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.

Specification Identification does not base allocating the costs of goods sold and ending inventory on any assumptions. Instead, it uses specific costs.

                                     Units    Unit Cost    Total Cost

Jan. 1      Beg. Inventory   8        $6.00            $48 ($6 x 8)

Apri. 11    Purchases        24       $11.00          $264 ($11 x 24)

May 17    Purchases        30      $14.00          $420 ($14 x 30)

Dec. 5    Purchases         19      $16.00          $304 ($16 x 19)

Total                                 81                         $1,036

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Answer: x < 3

Explanation: Once you reach step 3, you divide -2 on both sides. -2x cancels out, and -6 divided by -2 is 3