Write an equation that represents the volume V as a function of the height h

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:

Generally equation of a line is given as

y=mx+c

Then given the point (x, y)=(0,2)

Therefore x=0 and y=2

y=mx+c

2=m×0+c

2=0+c

Then, c=2

Then intercept is 2

Also given the point (x, y)=(3,4)

x=3 and y=4 and c=2

y=mx+c

4=m×3+2

4=3m+2

4-2=3m

2=3m

Then, m=2/3

Then, the slope of the graph is 2/3

y=mx+c

Now, m=2/3 and c=2

The general equation of the line becomes

y=2/3x+2

Multiply through by 3

3y=2x+6

Then this is the equation of the line

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:  4:5

Step-by-step explanation:

oranges=4

apples=5

4 oranges to 5 apples

Answer:

5 apples to 4 oranges

Step-by-step explanation:

ratios are easy

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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Answer:

y = 8

Step-by-step explanation:

remove the constant, 6:

3y=24

divide both by 3. leave x by itself

3y/3=24/3

y = 8

do these steps and you can do these easily

The solution to the equation 3y + 6 = 30 is y = 8.

To solve the equation 3y + 6 = 30 and find the value of y, we need to isolate the variable y on one side of the equation by performing various operations. Here are the steps to solve the equation:

Step 1: Begin with the given equation:

3y + 6 = 30

Step 2: Subtract 6 from both sides of the equation to move the constant term to the other side:

3y + 6 - 6 = 30 - 6

3y = 24

Step 3: Divide both sides of the equation by 3 to isolate the variable y:

(3y)/3 = 24/3

y = 8

Step 4: Verify the solution by substituting the value of y back into the original equation:

3(8) + 6 = 30

24 + 6 = 30

30 = 30

Since the equation is true, we can conclude that the solution to the equation 3y + 6 = 30 is y = 8. By performing the necessary operations, we successfully isolated the variable y and found its value that satisfies the original equation.

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Answer:

20

Step-by-step explanation:

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:

11 weeks

Step-by-step explanation:

She bought the watch for $149

And paid $50 immediately.

She has $149-$50 left, which gives $99

If she pays $9 each week,

In two weeks, she would be paid $9+$9=$18

In three weeks $9+$9+$9=$27 then it will take her 99/9 weeks to pay off the watch

99/9

It will take her $11 to pay off the watch

Answer:

Option C is correct.

Step-by-step explanation:

The rule of dilation implies that when a figure is dilated by a scale factor of 1/2, the length of the sides of the image can be obtained by multiplying the sides of the original figure/object by 1/2.

For example, if the length of a side of a segment is 6 and is dilated by a scale factor of 1/2. The length of the image segment will be 6/2 or 3/2. i.e. the original length 6 of the segment is multiplied by 1/2 to get the image segment 3/2.

Other important thing to consider is when the scale factor to be multiplied is less than 1, than the image will be smaller, but if the scale factor to be multiplied is greater than 1, than the image will be larger.

Now, coming towards the question and lets dilate the sides of the figure A by a scale factor of 1/2.

        i.e. 5/2= 2.5

        i.e. 2/2 = 1

        i.e. 4/2 = 2

        i.e. 1/2 = 0.5

Therefore, option C is correct.

Answer:

Step-by-step explanation:

Sunflower can u please come answer my question next it says

HELP ASAP WILL GIVE BRAINLIEST PLEASE IM DESPERATE!!!!!!!

The probability that both are country music is 2/87.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that,

Number of CDs = 30

Number of country music CDs = 5

Now , at first when 1st CD is selected

Probability (1st), P(1st) = 5/30 = 1/6

After selecting 1st CD,

Total CDs left will be 29

Number of country music CD= 4

So, for 2nd CD selection,

Probability (2nd), P(2nd) = 4/291

Hence the required probability,

P(1st∩2nd) = P(1st) x P(2nd)

                  = 1/6 x 4/29

                  = 2/87

Hence,the probability that both are country music is 2/87.

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Answer:

Step-by-step explanation:

One equivalent expression is 7^6:  7 is used as a multiplicand 7 times.

Another equivalent expression would be (7^2)(7^5).  Note that 2 and 5 add up to 7.

[tex]\text{Hey there!}[/tex]

[tex]\mathsf{7\times7\times7\times7\times7\times7= \ ?}\\\mathsf{49\times49\times49= \ \ ?}\\\mathsf{2,401\times49= 11,649}\\\\\\\\\boxed{\boxed{\mathsf{Answer\ \#1: 11,649}}}\checkmark[/tex]

[tex]\mathsf{Since\, we\ have\ SIX\ 7\, \we \ can\ have\ 7\ raised\ to\ the\ 6^{th}\ power}[/tex][tex]\mathsf{.\ Because, they all equal to\ 7\times7\times7\times7\times7\times7}[/tex]

[tex]\boxed{\boxed{\mathsf{Answer\#2: 7^6}}}[/tex]

[tex]\mathsf{Thus\ your\ answers\ are\downarrow}\\\\\bullet\ \boxed{\mathsf{Answer \ \#1: 11,649}}]\checkmark\\\\\bullet\ \boxed{\mathsf{Answer\ \#2: 7^6}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

Answer:1/2

Simplified

Step-by-step explanation:

Greatest Common Divisor (GCD) =2

Divide by GCD =

2 ÷ 2

4 ÷ 2

Greatest Common Divisor (GCD) =2

Divide by GCD =

2 ÷ 2

4 ÷ 2

Simplified =

1/2

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:

5/6

Step-by-step explanation:

Answer: 8x³ - 7x² - 6x + 5

Step-by-step explanation:

8x³ - 7x² - 6x + 5 is a cubic expression.

The variable is x

The variable x has highest power as 3.

8x³ - 7x² - 6x + 5 is a polynomial.

-7x + 4 is a linear expression because highest power of the variable x is 1.

7x² - 5x + 6 is a quadratic expression because the highest power of the variable x is 2.

9x^4 + 8x^3 - 6x^2 - 2x + 11 is a polynomial with the highest power of the variable being 4.

The expression that represents a cubic expression is 8x³ − 7x² − 6x + 5, as it contains the highest power of x raised to 3, making it a cubic polynomial.

A cubic expression is a type of polynomial with the highest degree term being raised to the power of 3. In mathematical terms, it is represented as f(x) = ax^3 + bx^2 + cx + d, where 'a' is the coefficient of the cubic term, 'b' is the coefficient of the quadratic term, 'c' is the coefficient of the linear term, and 'd' is the constant term.

Among the options provided:

- −7x + 14 is a linear expression as it contains only a single degree term (degree 1).

- 7x² − 5x + 6 is a quadratic expression as it contains a term with x^2 (degree 2).

- 8x³ − 7x² − 6x + 5 is indeed a cubic expression as it contains a term with x^3 (degree 3).

- 9x⁴ + 8x³ − 6x² − 2x + 11 is a quartic expression with the highest power of x being 4 (degree 4).

Therefore, the expression that represents a cubic expression is 8x³ − 7x² − 6x + 5, as it has the highest power of x equal to 3. Cubic expressions often appear in various mathematical and scientific contexts, including physics, engineering, and economics, and are characterized by their distinctive "S"-shaped curves on graphs.

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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.

(f + g)(x) is x² + 4x - 4

Step-by-step explanation:

Step 1:

Given f(x) = 4x + 1, g(x) = x² - 5. Find (f+g)(x)

(f + g)(x) = f(x) + g(x) = 4x + 1 + x² - 5 = x² + 4x - 4

[tex]( {t}^{9} ) {}^{ - 8} \\ = t {}^{9 \times ( - 8)} \\ = {t}^{ - 72} [/tex]

Final answer:

The expression simplifies to [tex]1/t^72[/tex] by using exponent rules to multiply the exponents and then applying the rule for negative exponents.

Explanation:

To simplify the expression [tex](t^9)^-8[/tex] , you need to use the exponent rules.

Specifically, when you have a power raised to another power, you multiply the exponents.

Here, you have the base t raised to the 9th power, and then that result is raised to the -8th power.

The rule is: [tex](a^m)^n = a^(m*n).[/tex]

Applying this rule here gives us:

[tex]= (t^9)^-8[/tex]

[tex]= t^(9*-8)[/tex]

[tex]= t^-72.[/tex]

Since we are dealing with a negative exponent, the rule for negative exponents says that [tex]a^-n = 1/a^n.[/tex]

Therefore, our final simplified expression is [tex]1/t^72.[/tex]

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:

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:

4 pounds

Step-by-step explanation:

8.64(4) is 34.56+55.44=90

Answer:

Amy bought 4 pounds of coffee.

Step-by-step explanation:

To begin, subtract what she has left, $55.44, from what she began with with, $90. That equation looks like: 90 - 55.44 = 34.56

Now divide $34.56 by the cost of each pound of coffee, $8.64. That equation looks like: 34.56 ÷ 8.64 = 4

So your answer is 4. Amy bought 4 pounds of coffee.

The perimeter of the given shape is 63.50 units and its area is 170.625 square units.

Step-by-step explanation:

Step 1:

First, we need to determine the distance between each of the points in the shape ABCDEFGH.

There are vertical lines and horizontal lines. The distances between vertical lines are found by calculating the difference in y values while for horizontal lines, the distances are found by calculating the difference between the x values.

Step 2:

Distance of line AB, 15 - 4.5 = 10.5,

Distance of line BC, 14 - 8 = 6,

Distance of line CD, 15 - 10 = 5,

Distance of line DE, 8 - 3 = 5,

Distance of line EF, 15 - 10 = 5,

Distance of line FG, 3 - (-2.25) = 5.25,

Distance of line GH, 15 - 4.5 = 10.5 and

Distance of line AH, 14 - (-2.25) = 16.25.

Step 3;

The area of ABCDEFGH = The area of ABGH - the area of CDEF.

The area of ABGH = Length × Width = AH × AB = 16.25 × 10.5 = 170.625 square units.

The area of CDEF = Length × Width = CD × DE = 5 × 5 = 25 square units.

The area of ABCDEFGH = 170.625 - 25 = 145.625 square units.

Step 4:

The perimeter of shape ABCDEFGH is just the sum of all its lines.

Perimeter of ABCDEFGH = 10.5 + 6 + 5 + 5 + 5 + 5.25 + 10.5 + 16.25 = 63.50 units.

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]

Answer:

12

Step-by-step explanation:

3r = 36

3r/3 = 36/3

r = 12

Answer:

[tex]r = 12[/tex]

Step-by-step explanation:

[tex]3r = 36 \\ \frac{3r}{3} = \frac{36}{3} \\ r = 12[/tex]

Answer:

y = 5x + 3

x = 5y + 3

5y + 3 = x

5y = x - 3

y = x/5 - 3/5

f^-1(x) = x/5 - 3/5

Step-by-step explanation:

Answer: B) highly

Step-by-step explanation:

Answer: B. highly

Step-by-step explanation:

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.

Answer:

obtuse

Step-by-step explanation:

Answer:

Obtuse Angle

Step-by-step explanation:

Obtuse Angle:

An obtuse angle is greater than 90 and less than 180, therefore it's a obtuse angle.

Answer:  If you are using a calculator, simply enter 64÷320×100 which will give you 20 as the answer.

Step-by-step explanation: Hope it helps:)

and tryna mark a child brainlest ;)

Answer:

20%

Step-by-step explanation:

64/320=0.2

0.2*100=20%