lim x^lnx

x→0+

The **limit **of xlnx when x is tending towards zero is **zero**.

**What is limit in mathematics?**

In mathematics, a **limit **is the value that a function (or sequence) approaches as the input (or index) approaches a particular value. Without **limits**, it is impossible to perform calculus or mathematical analysis; **limits **are also necessary to compute continuity, derivatives, and integrals.

Given limit is:

[tex]\lim_{x \to 0} x lnX[/tex]

Considering f = x, and g = ln x

The **limit **of f and g are both zero or both ±∞, and the limit f′/g′ exists, then the **limit **f/g equals it.

The wrong in the expression x lnx is we are individually defining f and g doesn't meet the hypothesis. so, we write it as

[tex]\frac{lnx}{1/x}[/tex]

We now use L' Hospital rule with f(x) = lnx, g(x) = 1/x as

The **limits **

[tex]\lim_{x \to 0^+} lnx= - \infty[/tex], and

[tex]\lim_{x \to 0^+} \frac{1}{x}[/tex]

The **limits **[tex]\lim_{x \to 0^+} \frac{f'(x)}{g'(x)}[/tex] exists as:

[tex]\lim_{x \to 0^+} \frac{1/x}{-1/x^2} = \lim_{x \to 0^+} -x = 0[/tex]

Hence the answer is 0.

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Emily is a sales representative. She receives 7% commission on all sales. At the end of the year she receives a bonus of 5% of her commission. If Emily's sales for the year total $412,454, calculate: 1) 7% Commission on Sales 2) 5% Bonus on Commission 3) Total Gross Pay for the year 4) Monthly Income

start by calculating the 7% of all the sales

[tex]\begin{gathered} \text{Comission}=(0.07)\cdot412,454 \\ \text{comission}=28,871.78 \end{gathered}[/tex]Calculate the bonus from the comission

[tex]\begin{gathered} \text{Bonus}=(28,871.78)\cdot(0.05) \\ \text{Bonus}=1,443.59 \end{gathered}[/tex]The total gross pay will be the addition between the comission and bonus

[tex]\begin{gathered} G.\text{ Income=28,871.78+1,443.59} \\ G\text{. income=30,315.37} \end{gathered}[/tex]The monthly income will be the division between 12 months of the year

[tex]\begin{gathered} \text{Monthly income} \\ \frac{30,315.37}{12}=2526.28 \end{gathered}[/tex]Suppose that a population has a mean of 200 and a standard deviation of 26. a. Compute the standard error of the sample mean for a sample size of 10.

Given:

Mean = 200

Standard deviation = 26

a) Find the standard error for a sample size of 10:

[tex]E=\frac{\sigma}{\sqrt{N}}[/tex]Substitute the values:

[tex]E=\frac{26}{\sqrt{10}}=8.22[/tex]**Answer:** 8.22

The lines shown below are parallel. If the green line has a slope of 5, what isthe slope of the red line?.O A.OB. 55O C.C. -//OD. -5(1)→

The slope of the red line is 5. **The correct answer is option B. 5**

Two parallel lines, always have the same slope. Since the green and red line are parallels and the green line has slope 5, the slope of the red line is also 5.

Name The Transformations Y=(x+3)^2-5

**Answer: move three units to the left, and 5 units down would be the answer to it **

**Step-by-step explanation: hope i helped**

2. Suppose you traveled from Saturn to Jupiter, and then from Jupiter to Mars. What would be the total distance in scientific notation

We have that approximately, the distance from Saturn to Jupiter is:

[tex]4.56x_{}10^8\text{ miles}[/tex]and the distance from Jupiter to Mars approximately is:

[tex]3.42x10^8\text{miles}[/tex]then, the total distance traveled would be the sum of these two quantities:

[tex](4.56x10^8)+(3.42x10^8)=7.98x10^8[/tex]**therefore the total distance is 7.98x10^8 miles**

write an email as if

you wanted to set up

an interview with

someone

**Answer:Dear Mikey,**

**I saw your progress on how to serve the best food and we wanted to see if you could help us or join our company if you want.**

**Call 923-456-2483**

**Sincerely Johns Bagel Company**

**Step-by-step explanation:**

how do you do order of operations with negitive signs

Let's use some examples where we have order of operations and also there are negative numbers and signs involved:

Let's evaluate the following:

(-4) x 5 + (-6)

So order of operations tells us to first take care of the multiplications and after that, deal with the additions or subtractions.

So the multiplication goes first here:

(-4) times 5 =** - 20**

Recall that a positive number times a negative number gives alwasy a negative number. So negative times positive gives the negative sign to the multiplication, and then, once the sign is taken care of, you multiply the numbers (4 x 5 = 20)

Next, we do the indicated addition

-20 + (-6) = -20 - 6 = -26

weher again we use the property that the + times the - inside the parenthesis gives a minus. ad we finalize by doing -20 - 6 = **-26** (combining of two negative numbers).

Another example:

(8 + (-5)) x (-8)

So we first work on solving what is inside the first parenthesis :

8 + (-5) this is 8 - 5 (as we did before, the plus outside the parenthesis where -5 is, results in a minus sign as it multiplies the "-" that is shown ahead of 5.

So, inside this parenthesis we get: 8 - 5 = 3

Now we are left to multiply 3 times (-8)

This is a product of a positive number (3) times a negative number (-8). Again, do the rule for product of the signs (positive times negative equals negative) , ad then the product of the numbers: 3 x 8 = 24

so the answer is ** - 24**

Another example:

(-9) x ((-10)+ 10)

We need to start by solving the operation indicated inside the parenthesis:

(-10) + 10 This is the same as: - 10 + 10 = 0

Now, whenwe use this result in the full expression, we get:

(-9) x 0 =** 0 ** SInce any number multiplied times zero is zero.

Please help Me I really need this !!!

**Step-by-step explanation:**

Original Equation:

[tex]x^2+5=0[/tex]

Subtract 5 from both sides

[tex]x^2 = -5[/tex]

Take the square root of both sides

[tex]x=\pm\sqrt{-5}[/tex]

Simplify

[tex]x=\pm i\sqrt{5}[/tex]

Thus we have **two** **non-real solutions**, and **zero real solutions**. This implies that the graph will **never** cross the x-axis when graphing the function out, because it has **no real solutions**.

Which of the following lines best fits the data shown in the scatter plot? 10 9 8 7 6 1 2 3 4 5 6 7 8 9 x Line a A С Line c Line b B. D None of the lines fit the data well

Scatter drawing plot

Two-eighths of the movies in Beth's collection are

action movies. Another of the movies are come

What fraction of Beth's movies are either action

movies or comedies?

The answer is ..

A computer has the shape of a rectangular solid. Find the volume of the computer, with dimensions of 3 inches by 3 inches by 3.6 inches. The volume of the computer is. (simplify your answer. type a whole number or a decimal.)

To find the volume of the computer, we just have to multiply each coordinate.

[tex]\begin{gathered} V=3in\times3in\times3.6in \\ V=32.4in^3 \end{gathered}[/tex]Hence, the volume is 32.4 cubic inches.Select the correct answer from the drop-down menu.Find the solution set for the system of equations.

Given:

9x+5y=28

5x+9y=56

Required:

To calculate the solution of the system

Explanation:

Rearrange like terms to the same side of the equation

[tex]\begin{gathered} 5x=28-9x \\ \\ 5x+9y=56 \\ \\ y=\frac{28-9x}{5} \\ \\ 5x+9y=56 \\ \\ substitute\text{ in the equation } \\ \\ 5x+9\times\frac{28-9x}{5}=56 \\ \\ x=\frac{-1}{2} \end{gathered}[/tex][tex]\begin{gathered} substitute\text{ value in y} \\ \\ y=\frac{28-9\times(\frac{-1}{2}}{5} \\ \\ y=\frac{13}{2} \end{gathered}[/tex]**Required answer:**

Option B

Select all equations that represent this tape diagram.

The** equations** that represent the diagram given are 7 + 8h = 167, 8h = 160

To find the** equation** that represent the situation, we should simply count the number h present in the diagram, add it to 7 and equate the entire length to 167 which is the length of the tube.

This can be represented** mathematically** as

[tex]7 + h + h + h + h + h + h + h + h = 167[/tex]

we can simplify this further as

[tex]7 + h + h + h + h + h + h + h + h = 167\\7 + 8h = 167\\[/tex]

This can also be simplified as

[tex]7 + 8h = 167\\8h = 167 - 7\\8h = 160[/tex]

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Polygon BCDE ≅ polygon RSTU. Find the value of X and the value of Y

By comparing both polygons, we can tell that they are not the same polygon, since one of the sides has length 11 in one trapezoid and 12 in the other. So, this polygons are similar. We notice that the variables X and Y are part of the angles. In polygons that are similar, the measure of the homologous angles are equal. By homologous we mean angles that are located at the same place in both figures. To determine the homologous angles, we should have both figures drawn in the same orientation. To do so, we will flip the trapezoid on the left, so its orientation matches the one fromt the right. I picture of this flipping would be

From this picture, by comparing it to the other polygon, we determine that the angle EDC is homologous to the angle UTS. So, their measure should be the same. So, we get the following equation

[tex]2y\text{ - 37 = }y+2[/tex]By adding 37 on both sides and subtracting y on both sides, we get

[tex]2y\text{-y = +2 +37 = 39}[/tex]This implies that y = 39°.

By doing the same procedure, we find that the angles URS and CBE are homologous. So their measures are equal and we get the equation

[tex]51\text{ = }2x+13[/tex]Then, by subtracting 13 on both sides

[tex]2x\text{ = 51-13 = 38}[/tex]If we divide both sides by 2 we get

[tex]x=\frac{38}{2}=19[/tex]So x = 19°.

Solving a word problem using a system of linear equations

In order to determine the weighs of the boxes, name x as the larger box and y as the smaller one.

Then, based on the given situation, you can write the following equations:

**3x + 2y = 86**

**8x + 4y = 209**

Solve the previous system of equations as follow:

Multiply the first equation by -2 and add the result to the second equation:

**(3x + 2y = 86)(-2)**

**-6x - 4y = -172**

** 8x + 4y = 209**

**-6x - 4y = -172**

** 2x = 37**

Solve the previous equation for x by dividing by 2 both sides:

**x = 37/2**

**x = 18.5**

Next, replace the previous value of x into any of the equations of the system, for instance, into the first equation, and solve for y:

**3x + 2y = 86**

**3(18.5) + 2y = 86**

**55.5 + 2y = 86**

**2y = 86 - 55.5**

**2y = 30.5**

**y = 30.5/2**

**y = 15.25**

**Hence, the weighs of the boxes are:**

**larger box = 18.5 kg**

**smaller box = 15.25 kg**

Sarah needed to get her computer fixed. She took it to the repair store.

The technician at the store worked on the computer for 4.25 hours and

charged her $54 for parts. The total was $585.25. Write and solve an

equation which can be used to determine x, the cost of the labor per

hour.

The **equation** which is **helpful **to **determine **x, the cost of the **labor **per hour is 4.25x + 54 = 585.25.

Determine the **known quantities **and designate the **unknown quantity **as a variable while trying to **set up **or construct a **linear** **equation **to fit a real-world **application**.

Given that,

x is the **labor cost **per hour.

The **technician worked **on the computer for 4.25 hours.

Total **labor cost **= 4.25x

The total **parts cost **= $54

The total **charged cost **= total **parts cost **+ total **labor cost**

585.25 = 54 + 4.25x

4.25x + 54 = 585.25

Hence "The **equation** which is **helpful **to **determine **x, the cost of the **labor **per hour is 4.25x + 54 = 585.25".

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True or false?

When prices increase supply decreases.

**Answer:**

The answer to your question is:

**False.**

**Step-by-step explanation:**

If prices **increase**, then no one would want to **buy the product**. No one would come.

Therefore, the correct answer is;

**When prices increase, supply decreases.**

If OA-OB-OC and if AOB = 9x + 20, BOC = 7x - 6 and AOC = 142 find BOC

The **angle BOC **has a measure of 50 degrees

From the question, the given parameters about the **angles** are:

The above parameters implies that

AOC = AOB + BOC

Next, we substitute the **angle measurements **in the above equation

So, we have

142 = 9x + 20 + 7x - 6

Evaluate the like terms

So, we have the following equation

142 = 16x + 14

Evaluate the **like terms** again

So, we have the following equation

16x = 128

Divide both sides by 16

x = 8

Substitute x = 8 in BOC = 7x - 6

BOC = 7 x 8 - 6

Evaluate

BOC = 50

Hence, the measure of the **angle **is 50 degrees

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What is the x-coordinate for point A? TO B (9.9) Sixta- 9 8 7 6 5 4 3 2. 1 A (9.3) 1 0 1 2 3 4 5 6 7 8 9 10

EXPLANATION

The coordinate for point A is x=9

Rashida was given 48 problems for homework. she has worked out 7/12 of them. how many more left unsolved

**Answer:**

she has left 28 unsolved problem or whatever it is

**Step-by-step explanation:**

48:12=4

4x7=27

order the following number from smallest to largest. 25, 10, -15, 0, -5

**Answer:**

-15, -5, 0, 10, 25

**Step-by-step explanation:**

**Answer:-**

**15, -5, 0, 10, 25 **

**Least -> greatest **

**Step-by-step explanation:**

PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!

YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!

1) [tex]VX=ZX, \angle XVY=\angle XZW[/tex] (given)

2) [tex]\angle X=\angle X[/tex] (reflexive property)

3) [tex]\triangle VXY \equiv \triangle ZXW[/tex] (ASA)

What is the perimeter of the figure shown below which is not drawn to scale

The perimeter of a figure is found adding the length of all its sides.

In this case, the perimeter is:

P = (x + 6) + (3x - 2) + (x- 3) + (x+ 2) + (x) + (x + 5)

P = (x +3x + x +x + x + x) + (6 - 2 -3 +2 + 5)

**P = 8x + 8**

An architect notices that the scale on a blueprint he is using has been torn off. However, he sees that a 12.5-ft. wall that has been built is 5 in. long on the blueprint. What is the scale for this blueprint?

A. 1 in. : 2.5 ft.

B. 1 in. : 25 ft.

C. 1 in. : 62 ft.

D. 1 in. : 62.5 ft.

**Answer it is c because when you multiply 12 x 5 you get 60 right so round up to the nearest number 62 an u can't subtract or divide you won't get a or b**

A random sample of 89 observations produced a mean x = 25.4 and a standard deviation s = 2.4.a. Find a 95% confidence interval for u.b. Find a 90% confidence interval for H.c. Find a 99% confidence interval for u.a. The 95% confidence interval is O.(Use integers or decimals for any numbers in the expression. Round to two decimal places as needed.)

The formula for the confidence interval is;

Where:

[tex]undefined[/tex]Given:

The mean is 25.4, the sample size n is 89, the standard deviation s is 2.4.

a. **For the 95% confidence interval, the z-score for a 95% interval is 1.96.**

Therefore, the 95% confidence interval is;

[tex]\begin{gathered} CI=25.4-1.96\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+1.96\frac{2.4}{\sqrt[]{89}} \\ CI=24.90<\operatorname{mean}<25.90 \end{gathered}[/tex]**Answer: (24.90, 25.90)**

b.** For the 90% confidence interval, the z-score for a 90% interval is 1.645.**

Therefore, the 90% confidence interval is;

[tex]\begin{gathered} CI=25.4-1.645\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+1.645\frac{2.4}{\sqrt[]{89}} \\ CI=24.98<\operatorname{mean}<25.82 \end{gathered}[/tex]**Answer: (24.98, 25.82)**

c. **For the 99% confidence interval, the z-score for a 99% interval is 2.576.**

Therefore, the 99% confidence interval is;

[tex]\begin{gathered} CI=25.4-2.576\frac{2.4}{\sqrt[]{89}}<\operatorname{mean}<25.4+2.576\frac{2.4}{\sqrt[]{89}} \\ CI=24.74<\operatorname{mean}<26.06 \end{gathered}[/tex]**Answer: (24.74, 26.06)**

The graph of g(x) shown below has the same shape as the graph of f(x)=x2 but it is shifted right by 5 units write the equation for g(x)please help me!! :(

f(x)= x^2

To shift 5 units to the right subtract 5 to x .

**g(x)= (x-5)^2 **

What is the answer to this question?

**Answer:**

C. (5, 5)

**Step-by-step explanation:**

To do this, you take each coordinate and perform the function that is shown in the translation.

So for (x-2, y+3),

you are going to take the x value of the coordinate you are given:

(**7**,2) and subtract 2, and then take the y value of (7,**2**) and add 3.

(7 - 2, 2 + 3)

Then solve this:

(5, 5)

The length of a rectangle is double its width. If the rectangle has a perimeter of 138cm, find its length (in cm).

**Answer:**

length = 46cm

**Step-by-step explanation:**

p = 2l + 2w

when l = 2w, substitute in to equation:

138 = 2(2w) + 2w

138 = 4w + 2w

138 = 6w

divide both sides by 6:

138/6 = 6w/6

so **width = 23cm **

and we know that length = 2 width so:

length = 23cm × 2

**length = 46cm **

Determine which expression is equivalent to the expression 5 over 4 times g minus 3 minus 7 over 12 times g minus the expression one over 3 times g plus 15. negative 1 over 3 times g plus negative 18 negative 4 over 12 times g plus negative 12 4 over 12 times g plus negative 18 16 over 12 times g plus negative 12 (BEST ANSWER WILL GET BRAINLIST)

The **expression** that is **equivalent** to the expression illustrated is 1/12g - 18.

It should be noted that an **expression** is used to show the relationship between the variables.

The **expression** will be illustrated as:.

= 5/4g - 3 - 7/12g - (1/3g + 15)

= 5/4g - 3 - 7/12g - 1/3g - 15

= 5/4g - 7/12g - 1/3g - 3 - 15

= 15/12g - 7/12g - 4/12g - 18

= 1/12g - 18

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write the missing power of 10 in the exponential form…….*0.006=0.6

**Answer:**

10 to the second power

[tex]10^2[/tex]**Explanation:**

Let the **unknown value be x**

The **given expression** can be rewritten as:

**Express as a fraction;**

**Cross multiply**

**Hence the required unknown number in the exponential power of 10 is 10^2**

The monthly mortgage payment on the Flynn's home is $634.8. Additionally, they pay $1,785.13 in annual real estate taxes and $726 per year in homeowner's insurance.What is the total amount of their entire monthly payment?State your answer in terms of dollars, rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.
Abhasra made a trip to the town hall and back. On the trip there she drove 60 mph and on the return trip she went 75 mph . How long did the trip there take if the return trip took four hours ?HELP ASAP PLEEASE!!
Select the correct operator for the following exponential expression.(-2)^4 ? 2^4 A. C. =
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