Lateral surface area of a cylinder with a radius of 3 and a height of 8

Answer:

The answer is [tex]y^{'} =e^{\frac{1}{x} } (2x-1)[/tex]

Step-by-step explanation:

First of all, we have product of 2 functions [tex]e^{1/x}[/tex] and [tex]x^{2}[/tex]

[tex]y^{'} =u\frac{dv}{dx}+v\frac{du}{dx}[/tex]

Let [tex]u=e^{1/x}[/tex] and [tex]v=x^{2}[/tex]

using chain rule for [tex]u[/tex], [tex]\frac{du}{dx}=-\frac{1}{x^2}[/tex]

and [tex]\frac{dv}{dx}=2x[/tex]

Therefore,

[tex]y^{'} =u\frac{dv}{dx}+v\frac{du}{dx}=e^{1/x}(2x)+x^{2} (-\frac{1}{x^2})=e^{1/x}(2x-1)[/tex]

Final answer:

To solve for A and B, we translated the word problem into two algebraic equations and then solved the system of equations step-by-step to find that A equals 200 and B equals 250.

Explanation:

We are given two equations based on the relationship between 30% of number A and 20% of number B, and vice versa. Let's translate the words into algebraic expressions where A and B represent the numbers we need to find:

0.30A = 0.20B + 10 (Equation 1)

0.30B = 0.20A + 35 (Equation 2)

Now let's solve this system of equations step-by-step:

Multiply both sides of Equation 1 by 10 to clear out decimals: 3A = 2B + 100.

Multiply both sides of Equation 2 by 10 as well: 3B = 2A + 350.

Rearrange Equation 1 to get A on its own: A = (2B + 100) / 3.

Substitute the expression for A from step 3 into Equation 2: 3B = 2((2B + 100) / 3) + 350.

Multiply through by 3 to clear the fraction: 9B = 4B + 200 + 1050.

Simplify to find B: 5B = 1250, so B = 250.

Substitute B back into the equation from step 3 to find A: A = (2(250) + 100) / 3, so A = 200.

Therefore, the numbers we are looking for are A = 200 and B = 250.

Answer:

Li Jing's formula i.e.  [tex]\boxed{g_n=-5\cdot \:5^{n-1}}[/tex]  is right.

Step-by-step explanation:

Considering the sequence

[tex]-5,\:-25,\:-125,\:-625,...[/tex]

A geometric sequence has a constant ratio r and is defined by

[tex]g_n=g_0\cdot r^{n-1}[/tex]

[tex]\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{g_{n+1}}{g_n}[/tex]

[tex]\frac{-25}{-5}=5,\:\quad \frac{-125}{-25}=5,\:\quad \frac{-625}{-125}=5[/tex]

[tex]\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}[/tex]

[tex]r=5[/tex]

So, the sequence is geometric.

as

[tex]\mathrm{The\:first\:element\:of\:the\:sequence\:is}[/tex]

[tex]g_1=-5[/tex]

[tex]r=5[/tex]

so

[tex]g_n=g_1\cdot r^{n-1}[/tex]

[tex]\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:[/tex]

[tex]g_n=-5\cdot \:5^{n-1}[/tex]

Therefore, Li Jing's formula i.e.  [tex]\boxed{g_n=-5\cdot \:5^{n-1}}[/tex]  is right.

Answer:

Step-by-step explanation:

Given set of data is 0, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6

First finding Mean

Answer:

Mean: 3.5

Median: 3.5

Range: 6

Interquartile range: 1

Step-by-step explanation:

Answer:

16mt + 30 mt

Step-by-step explanation:

your welcome!

Answer:

6. 19

Step-by-step explanation:

Answer:

6.19

Step-by-step explanation:

85.75-32.95=52.8

58.99-52.8=6.19

Answer: 0.15

Step-by-step explanation:

7 (0.42)/ 20

Answer:

see below

Step-by-step explanation:

So when you have mixed numbers, you have to turn them into regular fractions. How you change them into regular fractions is multiplying the whole number by the denominator (the bottom number in the fraction) and then adding that number to the numerator (the top number in the fraction). So, for example you have

3[tex]\frac{2}{3}[/tex]

3 x 3 = 9

9 + 2 = 11

so, 3[tex]\frac{2}{3}[/tex] = [tex]\frac{11}{3}[/tex]

After you change the mixed fractions that you have into normal fractions, then you can normally subtract the two fractions. If they have the same denominator, then you just subtract the numerators like normal numbers and leave the denominators alone.

[tex]\frac{11}{3}[/tex] - [tex]\frac{2}{3}[/tex] = [tex]\frac{9}{3}[/tex]

If there are different denominators, then you have to multiply one or more fractions by any number so that both fractions have the same denominator.

For example,

[tex]\frac{11}{3}[/tex] - [tex]\frac{7}{6}[/tex]

you have to multiply [tex]\frac{11}{3}[/tex] by two, so that the denominator will equal six. This is the only way that you will be able to add or subtract the two fractions.

2([tex]\frac{11}{3}[/tex]) = [tex]\frac{22}{6}[/tex]

[tex]\frac{22}{6}[/tex] - [tex]\frac{7}{6}[/tex] = [tex]\frac{22-7}{6}[/tex] = [tex]\frac{15}{6}[/tex]

Then, if you are asked to, this fraction can be simplified if you divide both the denominator and the numerator by [tex]\frac{3}{3}[/tex], so

[tex]\frac{15}{6}[/tex] divided by [tex]\frac{3}{3}[/tex] is equal to [tex]\frac{5}{2}[/tex].

This works because [tex]\frac{3}{3}[/tex] = 1.

Answer:

The mean/average is 5.8

Step-by-step explanation:

The mean is the average

Step 1:  Find the average

4 + 8 + 3 + 9 + 5

29 / 5

5.8

Answer:  The mean/average is 5.8

Answer: Aly , Marvin, Hank

Step-by-step explanation:

Aly has the lowest with 20, Marvin has 30, and hank has 50. it says least to mostly likely to win

The question pertains to probabilities. It has been determined that the most probable event is either Hank winning or Marvin winning, and it's least likely for Aly to win.

The question is regarding the probability of three individuals, Marvin Martian, Aly Alien, and Hank Human, finding a hidden spaceship first. We know the probabilities of Marvin and Aly finding it first but the probability of Hank finding it is not given.

However, from the properties of probability, we know that the sum of the probabilities for all possible outcomes is 1. Therefore, if we add the probabilities of Marvin and Aly finding the spaceship first, we get 0.30(30%) + 0.2(20%) = 0.5(50%). We then subtract this from 1 to get Hank's probability, which is, therefore, 1 - 0.5 = 0.5(50%).

So, in order from least to most likely: Aly wins (0.2 or 20%), then Hank and Marvin are equally likely to win (0.5 or 50% each).

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Answer:

Step-by-step explanation: 288

Answer:

See explaination

Step-by-step explanation:

Multiply 9670 by 0.1, you get 967

Multiply 9670 by 0.01, you get 96.7

Answer:

x > -4

Step-by-step explanation:

Step 1:  To combine like terms means to add the same variable numbers together.

-6x + 5 - 4x < 45

-10x + 5 < 45

Step 2:  Subtract 5 from both sides

-10x + 5 - 5 < 45 - 5

-10x < 40

Step 3:  Divide both sides by -10

-10x / -10 < 40 / -10

Since you divided by a negative, you need to reverse/flip the sign.

x > -4

Answer:  x > -4

Steps to solve:

-6x + 5 – 4x < 45

~Combine Like Terms

(-6x - 4x) + 5 < 45

~Simplify

-10x + 5 < 45

~Subtract 5 to both sides

-10x + 5 - 5 < 45 - 5

~Simplify

-10x < 40

~Divide -10 to both sides and switch the symbol since we're dividing a negative number

-10x/-10 > 40 / -10

~Simplify

x > -4

Best of Luck!

Answer:

4 & 8 = Corresponding Angles | 6 & 7 = Linear Pair | 1 & 3 = Vertical Angles | 2 & 8 = Alternate Interior Angles

Step-by-step explanation:

Answer:

398,000 is your answer.

Step-by-step explanation:

you round up at the 1000s place

The number 397,864 rounded to the nearest thousand is 398,000.

Explanation:

Rounding 397,864 to the nearest thousand means finding the closest whole number that is a multiple of 1,000. The thousands place digit is 7, so we look at the digit to the right of it, which is 8. Since 8 is greater than 5, we round up the thousands place digit to 8, and the rest of the digits become zeros. Therefore, 397,864 rounded to the nearest thousand is 398,000.

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Question 1

The given system of equations is:

[tex]y = {x}^{2} + 5x + 6 \\ y = 3x + 6[/tex]

Equate the two equations:

[tex] {x}^{2} + 5x + 6 = 3x + 6[/tex]

Rewrite in standard form:

[tex] {x}^{2} + 5x - 3x + 6 - 6 = 0[/tex]

[tex] {x}^{2} + 2x = 0[/tex]

[tex]x(x + 2) = 0[/tex]

[tex]x = 0 \: or \: x = - 2[/tex]

When we put x=0, in y=3x +6, we get:

[tex]y = 3(0) + 6 = 6[/tex]

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

[tex]y = 3( - 2) + 6 = 0[/tex]

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

[tex]f(x) = {x}^{6} - {x}^{4} [/tex]

Let us put x=-x,

[tex]f( - x) = {( - x)}^{6} - {( - x)}^{4} [/tex]

This gives:

[tex]f( - x) = {x}^{6} - {x}^{4} [/tex]

We can observe that:

[tex]f(x) = f( - x)[/tex]

This is the property of an even function.

Question 3:

The given function is

[tex]f(x) = {x}^{2} + 3x - 2[/tex]

The average rate of change of f(x) from x=a to x=b is given as:

[tex] \frac{f(b) - f(a)}{b - a} [/tex]

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

[tex] = \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11[/tex]

The average rate of change is 11

The distance around the pool is 43.96 m.

Solution:

The distance across the circle is diameter.

The distance around the circle is circumference.

The value of π = 3.14

Diameter of the circle = 14 m

Circumference of the circle = πd

                                              = 3.14 × 14 m

Circumference of the circle = 43.96 m

The distance around the pool is 43.96 m.

Answer:

0.7=7/10

this is the fraction in the simplest form

Step-by-step explanation:

Answer:

0.31

Step-by-step explanation:

one hundredth is 0.01 and 3 tenths would be 0.3 so just add those two together :)

Answer:

11 digits

Step-by-step explanation:

x-xxx-xxx-xxxx

Counting these x's they would be 11. (if living in U.S.A)

The area code has 3 numbers. The first section has 3. Last section has 4. 6+4=10

There are 10 digits in a phone number.

Answer:

Step-by-step explanation:

rational number

Answer:

40%

Step-by-step explanation:

so first we can calculate what percentage of 40 24 is

we can do that with 24/40 which equals 0.6, or 60 percent

100-60

that means that there was a 40 percent decrease.

Answer:

x>-4

Step-by-step explanation:

-6x + 5 – 4x < 45

Combine like terms

-10x + 5 < 45

Subtract 5 from each side

-10x + 5 – 5 < 45-5

-10x< 40

Divide each side by -10, remembering to flip the inequality

-10x/-10 >40/-10

x >-4

Answer: The last option

Step-by-step explanation:

3/4÷1/8=6

This is the answer because this is the only equation that gives a true answer all the others give an incorrect answer.

Answer:

look at pic

Step-by-step explanation:

The expression representing the cost of food for one person is $x + $7.

For the expression that represents the cost of food for one person if two friends bought a $14 pizza, and each person bought their own drink at $2x (where x is the number of drinks).

To find the cost for one person, we start with the total cost expression $2x + $14. Since there are two friends, we divide this total cost by 2. The expression for the cost of food for one person is $x + $7. This represents the individual cost of one person's drink at $2x, divided by 2, plus half of the pizza cost, which is $14 divided by 2, resulting in $7.

Answer:

[tex]y =8x+9[/tex]

Step-by-step explanation:

The points are (6,39) and (-5,-49)

We need to find the equation of this line.

The slope is given by:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

[tex]m = \frac{ - 49 - 39}{ - 5 - 6} [/tex]

[tex]m = \frac{ - 88}{ - 11} [/tex]

[tex]m = 8[/tex]

We use the formula:

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the point (6,39) and m=8 to get:

[tex]y - 39 = 8(x - 6)[/tex]

We expand to obtain:

[tex]y - 39=8x-48[/tex]

[tex]y =8x-48 + 39[/tex]

[tex]y =8x + 9[/tex]

To find the equation of the line passing through two points, we can use the point-slope form of a linear equation:

[tex]\[y - y_1 = m(x - x_1)\][/tex]

Where:

- [tex]\( (x_1, y_1) \)[/tex] is one point on the line.

- [tex]\( m \)[/tex] is the slope of the line.

First, let's find the slope (\(m\)) using the two given points:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Given points:

[tex]\( (x_1, y_1) = (6, 39) \)\( (x_2, y_2) = (-5, -49) \)\[ m = \frac{-49 - 39}{-5 - 6} \]\[ m = \frac{-88}{-11} \]\[ m = 8 \][/tex]

Now, we have the slope (\(m\)). We can choose either of the two given points and plug them into the point-slope form. Let's use \( (6, 39) \):

[tex]\[ y - 39 = 8(x - 6) \][/tex]

Now, we can simplify this equation to get it into slope-intercept form (\(y = mx + b\)):

[tex]\[ y - 39 = 8x - 48 \]\[ y = 8x - 48 + 39 \]\[ y = 8x - 9 \][/tex]

So, the equation of the line passing through the points (6, 39) and (-5, -49) is [tex]\( y = 8x - 9 \).[/tex]

Answer:

Step-by-step explain

Find the horizontal asymptote for f(x)=(3x^2-1)/(2x-1) :

A rational function will have a horizontal asymptote of y=0 if the degree of the numerator is less than the degree of the denominator. It will have a horizontal asymptote of y=a_n/b_n if the degree of the numerator is the same as the degree of the denominator (where a_n,b_n are the leading coefficients of the numerator and denominator respectively when both are in standard form.)

If a rational function has a numerator of greater degree than the denominator, there will be no horizontal asymptote. However, if the degrees are 1 apart, there will be an oblique (slant) asymptote.

For the given function, there is no horizontal asymptote.

We can find the slant asymptote by using long division:

(3x^2-1)/(2x-1)=(2x-1)(3/2x+3/4-(1/4)/(2x-1))

The slant asymptote is y=3/2x+3/4

Answer:

y = 3/2.

Step-by-step explanation:

This is  the ratio of the coefficients of the terms in x of highest degree of the function:

y  = 3/2.

Answer: The volume is 126 yards

Step-by-step explanation:

Answer:

the answer is 128

Step-by-step explanation:

first, i did 6x7 and got 42

then, i muutiplied 42 and 3 and got 128

thank me

Answer:

y = 6x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 6 and c = - 7, thus

y = 6x - 7 ← equation of line

Final answer:

The equation of the line with a slope of 6 and y-intercept of -7 is y = 6x - 7.

Explanation:

The equation of a line in slope-intercept form is y = mx + b, where m represents the slope and b is the y-intercept. In this case, we are given a slope (m) of 6 and a y-intercept (b) of -7. Thus, by substituting these values into the slope-intercept formula, we get the equation of the line as y = 6x - 7.