Find the derivative of the following function. S = t^23 ln|t| Which rule of differentiation will be most helpful in beginning this problem? A. The chain rule B. The product rule C. The sum or difference rule D. The constant rule E. The power rule The expression in |t| appears as a subexpression of the given function. What is the derivative of this expression? d/dt (ln|t|) = t/|t|^2 Find the derivative of the given function ds/dt =

The equation for the table is r = -3s + 15,

when s = 0, r = 15 and when s = 9, r = -12

the formula for Δr in terms of Δs is Δr = -3Δs.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given value of r is varying at a constant rate with respect to s,

given table for r and s

s(independent quantity)            r(dependent quantity)

1                                                           12

3                                                           6

9                                                           ?

12                                                          -21

since both quantities vary at a constant rate so it is the condition of a linear equation,

y = mx + c

where m is the slope or the rate of change,

let s₁ = 1, s₂ = 3 and r₁ =  12, r₂ = 6

coordinates for graphs (1, 12) and (3, 6)

the equation is a form of s and r is

r = ms + c (because s is independent and r is dependent)

A: formula for Δr in terms of Δs is

Δr = mΔs

m = Δr/Δs = (6 - 12)/(3 - 1)

m = -3

Δr = -3Δs

the equation will be,

r = -3s + c

when s = 1 r = 12

12  = -3(1) + c

c = 15

the formula for r in terms of s  is,

r = -6s + 15

B: the value of r when s = 0

r = -3(0) + 15

r = 15

and when s = 9

r = -3(9) + 15

r = -12

C: true and false;

i.  The graph that represents s in terms of r is linear: True

ii.  r is proportional to s: False, no r is not proportional to s because the relation between r and s has a constant

iii. Δr is proportional to Δs: True because the relation is Δr = -3Δs.

iv. The graph of r in terms of s is a straight line that passes through the origin (0, 0): False, because when s = 0 r = 15, so the graph does not pass from the origin.

Hence equation for r and s is: r = -3s + 15

when s = 9, r = -12 and when s = 0, r = 15

and Δr = -3Δs.

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Answer:

To find the number of cats Carly can feed, divide the total weight of cat food by the weight of cat food used per cat.

2.85 lbs ÷ 0.19 lbs/cat = 15 cats

Therefore, Carly can feed 15 cats.

Answer:

$9.20 per toy or $9.20/1

Step-by-step explanation:

$46/5 hours=9.2

Answer:

Step-by-step explanation:

Let, width = x

length = x+4

perimeter, 2(x+4+x) = 40

4x+8 = 40

4x = 32

x = 8

so, (x+4) = 8+4 = 12

so, the area would be,

= 12 * 8 = 96 in²

The largest possible value of [tex]$k$[/tex] is [tex]$k=3^{11}$[/tex].

Let [tex]$a_1, a_2, \ldots, a_k$[/tex] be the [tex]$k$[/tex] consecutive positive integers, such that [tex]$a_1 + a_2 + \ldots + a_k = 3^{11}$[/tex]. The average of these [tex]$k$[/tex] numbers is [tex]$\frac{a_1 + a_k}{2} = \frac{3^{11}}{k}$[/tex], which is an integer if and only if [tex]$k$[/tex] divides [tex]$3^{11}$[/tex].

The largest divisor of  [tex]$3^{11}$[/tex] is  [tex]$3^{11}$[/tex] itself, so the largest possible value of [tex]$k$[/tex] is [tex]$k=3^{11}$[/tex].

However, [tex]$k$[/tex] must also be an integer greater than 0, so the largest possible value of [tex]$k$[/tex] for which [tex]$3^{11}$[/tex] is expressible as the sum of [tex]$k$[/tex] consecutive positive integers is [tex]$3^{11} - 1 = 177147$[/tex].

This problem is about finding the largest number of consecutive positive integers whose sum is equal to a given number. In this case, the given number is [tex]$3^{11}$[/tex].

By using the formula for the sum of consecutive integers, the average of the numbers is calculated, and the requirement for this average to be an integer is used to find the largest possible value of [tex]$k$[/tex], which represents the number of consecutive positive integers. The solution shows that the largest possible value of [tex]$k$[/tex] is [tex]$177147$[/tex].

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Answer: -4,9 I AM PRETTY SURE FROM ALL OF MY RESEARCH SIORRY IF I AM WRONG I WISH YOU GOODLUCK

Step-by-step explanation:

Answer:

(3, -7)

Step-by-step explanation:

If you choose 3 as one of your x-coordinates, you simply need to solve for y to get -7 as your y-coordinate:

[tex]3x+y=2\\3(3)+y=2\\9+y=2\\y=-7[/tex]

Answer I think Ann is 36 and Denny is 12 Im not for sure but thats what i got

Step-by-step explanation:

The answer of the questions:

a) The surface is an ellipsoid,

(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and

(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,

What is an ellipsoid?

An Ellipsoid is a closed surface on which all plane cross sections are either ellipses or circles. An ellipsoid is symmetrical about three mutually perpendicular axes that intersect at the center.

(a)

x = k:

Trace: Circle in the x-z plane

Identification: Circle

y = k:

Trace: Circle in the y-z plane

Identification: Circle

z = k:

Trace: Circle in the x-y plane

Identification: Circle

The surface is an ellipsoid, which is a 3-dimensional surface that is the result of stretching or compressing a sphere along different axes.

(b)

If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, but it is rotated so that its axis is the x-axis.

(c)

If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore, and its shape cannot be determined from the equation alone.

This is because the equation contains a linear term (2y) that makes it non-quadratic.

To find the shape of the surface, a more in-depth analysis would be required.

Hence, the answer of the questions:

a) The surface is an ellipsoid,

(b) If the equation is changed to x² - y² + z² = 4, the graph is still an ellipsoid, and

(c) If the equation is changed to x² + y² + 2y - z² = 3, the graph is not an ellipsoid anymore,

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The derivative of a composite function is given by the chain rule: the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.

d(fog(x))/dx = df/d(g(x)) * d(g(x))/dx

The fifth derivative of fog(x) can be calculated by taking the derivative five times:

d^5(fog(x))/dx^5 = d^5f/d(g(x))^5 * (dg(x)/dx)^5 + 5 * d^4f/d(g(x))^4 * d^2g(x)/dx^2 * (dg(x)/dx)^3 + 10 * d^3f/d(g(x))^3 * (dg(x)/dx)^2 * (d^2g(x)/dx^2)^2 + 10 * d^2f/d(g(x))^2 * (dg(x)/dx) * (d^3g(x)/dx^3) + 5 * df/d(g(x)) * (d^4g(x)/dx^4)

Since g'(x) is constant, dg(x)/dx is also constant, and its derivative is 0. Therefore, all the terms with derivatives of g(x) higher than 1 are 0, leaving us with:

d^5(fog(x))/dx^5 = 5 * d^2f/d(g(x))^2 * (dg(x)/dx)^2 * d^2g(x)/dx^2 + 5 * df/d(g(x)) * d^4g(x)/dx^4

Since g'(x) is constant, dg(x)/dx and d^2g(x)/dx^2 are also constant, and can be replaced by their values. Therefore, the fifth derivative of fog(x) depends only on the second and fourth derivatives of f.

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The total amount of money in the bag is M = $ 2.98

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as M

Now , the value of M is

Let the total amount of money in the bag be M

The number of coins in the bag = 50 coins

The number of pennies = 12 % of coins

So , the number of pennies = ( 12/100 ) x 50 = 6 pennies

The number of dimes in the bag = 44 % of the coins

The number of dimes in the bag = ( 44/100 ) x 50 = 22 dimes

The number of nickels = 8 + number of pennies = 8 + 6

The number of nickels = 14 nickels

The remaining number of coins are quarters

On simplifying the equation , we get

So , the number of quarters = 50 - 6 - 22 - 14 = 8 quarters

And , the value of 6 pennies = $ 0.06

The value of 22 dimes = $ 0.22

The value of 14 nickels = $ 0.70

The value of 8 quarters = $ 2.00

Therefore , the total amount in the bag = $ 2.00 + $ 0.70 + $ 0.22 + $ 0.06

The total amount of money in the bag = $ 2.98

Hence , the total money in the bag is $ 2.98

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The area of the lawn in the Wilson family's back yard is 4400 square feet.

The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet.

Let us assume that A₁ be the area of the reactangular plot.

Using the formula for the area of rectangle,

A₁ = 100 × 80

A₁ = 8000 sq. ft.

The family planted a garden with a length and width of 60 feet.

This means, the shape of the garden must be square.

Using the formula for the area of square,

A₂ = 60 × 60

A₂ = 3600 sq. ft.

The family planted a lawn in the remaining area of the back yard, as shown.

Let us assume that A represents the area of the lawn in the Wilson family's back yard.

A = A₁ - A₂

A = 8000 - 3600

A = 4400 sq. ft.

Therefore, the required area is: 4400 sq.ft.

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The distance between X and B is 67.5 feet for the given triangle.

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

As per the given figure, we have two similar triangles, as below:

ΔXAB and ΔXCD are similar,

So AB/CD = BX/DX

45/63 = BX/(BX+BD)

45/63 = BX/(BX+27)

45(BX+27) = 63BX

63BX - 45BX = 1215

18BX = 1215

BX = 67.5

Thus, the distance between X and B is 67.5 feet.

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Answer:

Form W-2 is completed by an employer and contains important information that you need to complete your tax return. It reports your total wages for the year and the amount of federal, state, and other taxes withheld from your paycheck.

Form 1040 is used by U.S. taxpayers to file an annual income tax return.

Head of household offers wider tax brackets, a bigger standard deduction and faster eligibility for other write-offs.

Step-by-step explanation:

with no missing powers, meaning including any "stepping down" values, anyhow, let's do so

[tex]3x^3-70\implies \boxed{\begin{array}{llll} 3x^3+0x^2+0x^1 + 0x^0 - 7 \\\\\\ 3x^3+0x^2+0x^1 - 7 \end{array}}[/tex]

now, notice, the others were there all along, however their coefficient is 0, thus anything times 0 goes poof, however they were there all along.

some folks like to use the 1st form there, I usually use the 2nd form, but both are acceptable.

The given assertion states that the length of BD in its simplest radical version is 7/√2.

A triangle is indeed a 3-sided shape that is occasionally (though not frequently) referred to as the trigon. There are three edges and three angles in every triangle, some of which could be the same.

Since BD is an altitude of the right triangle ABC, we can use the Pythagorean Theorem to find the length of BD. First, let's determine the size of AC:

AC² = AD * DC = 7 * 5 = 35

When we square the two edges, we obtain:

AC = √35

Now, we can use the fact that BD is an altitude to write:

BD = (AC * AD) / hypotenuse

where hypotenuse is the length of BC.

Using the Pythagorean Theorem, we can find the length of BC:

BC² = AC² + AB²

Since triangle ABC is a right triangle, we have AB = BC, so we can write:

BC² = AC² + BC²

Simplifying, we get:

BC² / AC² = 2

When we square the two edges, we obtain:

BC / AC = √2

Multiplying both sides by AC, we get:

BC = AC * √2 = √35 * √2 = √70

Now, we can substitute the values of AC, AD, and BC into the formula for BD:

BD = (AC * AD) / BC = (√35 * 7) / √70 = 7 / √2

Therefore, the length of BD in simplest radical form is 7 / √2.

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Therefore , The negative linear equation result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.

A straightforward regression graph is created using the equation y=mx+b. The y-intercept is m, and the slope is B. Despite the fact that the line before it contains independent parts, it is repeatedly alluded to as a "mathematical formula combining many factors." Only two factors are present in bivariate linear equations. There are no known solutions to application issues concerning linear equations. Y=mx+b.

Here,

Let H be the number of hot coffee drinks sold yesterday, and I be the number of iced coffee drinks sold yesterday. We know that:

H + I = 100 (since a total of 100 cups were sold)

We also know that the average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00. Therefore, the total revenue from hot coffee drinks is:

3.50H

And the total revenue from iced coffee drinks is:

2.00I

To find the difference in revenue between the hot and iced coffee drinks sold yesterday, we need to subtract the revenue from iced coffee drinks from the revenue from hot coffee drinks:

3.50H - 2.00I

We want this expression to equal zero, so we can set it equal to zero and solve for H:

3.50H - 2.00I = 0

3.50H = 2.00I

H = (2/3.50)I

H ≈ 0.57I

Since H + I = 100, we can substitute 0.57I for H in the equation:

0.57I + I = 100

1.57I = 100

I ≈ 63.7

Rounding to the nearest whole number, we get:

I = 64

Therefore, H = 100 - I = 36

So the difference in revenue between the hot and iced coffee drinks sold yesterday is:

3.50H - 2.00I = 3.50(36) - 2.00(64) = $72 - $128 = -$56

The negative result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.

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The complete question is "Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero

A local coffee shop sells iced and hot coffee drinks. Yesterday, the shop sold a total of 100 cups of coffee. The average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00.

What is the difference in revenue between the hot and iced coffee drinks sold yesterday?"

Answer: x = 4

Step-by-step explanation:

Translating the problem into mathematical terms:

Let's call the number x. Then the problem can be written as:

5 * (2x - 3) - (x + 8) = 13

Expanding the left side of the equation:

5 * 2x - 5 * 3 - x - 8 = 13

Simplifying the left side of the equation:

10x - 23 - x - 8 = 13

Combining like terms:

9x - 31 = 13

Adding 31 to both sides of the equation:

9x = 44

Dividing both sides of the equation by 9:

x = 4.88888...

Since x has to be a whole number, we round down to the nearest whole number:

x = 4

Therefore, the number that satisfies the equation is 4.

Answer:

86.4 ft^2

Step-by-step explanation:

Respuesta:

x = 47

Explicación paso a paso:

Necesitamos resolver x en este problema.

[tex]x+4x=235[/tex]

Combinar los términos x juntos
[tex]5x=235[/tex]

Divide 5 en ambos lados

[tex]x=47[/tex]

Nuestra respuesta es 47

Answer: 4/3

Step-by-step explanation:

Look at the points (0,-4) (3,0)

Formula: y2-y1/x2-x1

Substitute: 0-(-4)/3-0 = 4/3

Please make me brainliest, I would also add you as friend if you make me brainliest!

Let's consider what the question asks for:

--> slope of line

The slope of the line is calculated by:

  [tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

  --> where:

      [tex](x_1,y_1)-- > \text{any one point on the line}\\\\(x_2,y_2)-- > \text{another point on the line}[/tex]

Let's find our points

  [tex](x_1,y_1)-- > (3,0)\\\\(x_2,y_2)-- > (0,-4)[/tex]

Let's plug these points into our equation:

 [tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-4-0}{0-3}=\dfrac{-4}{-3} =\dfrac{4}{3}[/tex]

Answer: 4/3

Answer:

1 to 7.99 miles

Step-by-step explanation:

According to the given histogram, Maria logged runs for 1 to 7.99 miles, and the number of runs for each mile range is also given. Therefore, the range of the number of miles Maria jogged is 1 to 7.99 miles.

Note that the histogram shows that there were no recorded runs for exactly 8 miles, so the range does not include 8.

87 is the test score is 1.2 standard deviations above the mean.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15.

We need to find the test score is 1.2 standard deviations above the mean

1.2 standard deviations is 1.2×15 =18

So 105-18=87

87 is the score that is 1.2 standard deviations from the mean.

Hence, 87 is the test score is 1.2 standard deviations above the mean.

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The perimeter of the figure is given by the sum of the perimeter of rectangle and a semicircle P = 20.28

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the perimeter of the figure be represented as P

Let the width of the rectangle W = 4

So , the radius of the circle = 4 / 2 = 2

Now , the length of the rectangle = 5

And , the perimeter of the figure = 5 + 5 + 4 + ( perimeter of semicircle )

where the perimeter of semicircle = πr

On simplifying , we get

The perimeter of the figure P = 14 + 2π

The perimeter of the figure P = 14 + 6.28

The perimeter of the figure P = 20.28

Hence , the perimeter of the figure is 20.28

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The number of pea is 6. By using formulas of mean, median and mode.

A dataset's mean (also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. It is frequently referred to as the "average" and is the most widely used measure of central tendency.

Taking pea counts into account,

A pod of peas contains 4, 5, 6, 7 or 8 peas.

Number of pods: 2, 10, 18, 6, and 14

The mode is the number that corresponds to the highest frequency.

The frequency of each number in the list is 1.

Mode is not possible with the information provided.

The middle value, after sorting the numbers in ascending or descending order, is the median if all of the numbers are odd.

The median of the given numbers is.

Replace the values in the formula to get the mean value.

Mean = 4+5+6+7+8/5 = 30/5 = 6

Consequently, based on the quantity of peas provided, the values of the following measure are as follows:

It is impossible to use Peas in a Pod mode.

The median number of peas in a pod is 6.

the typical quantity of peas is 6.

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Answer:

Step-by-step explanation:

Using the Pythagorean Theorem, we know the hypotenuse is 2[tex]\sqrt{26}[/tex]

sin = Opp/hyp ----> [tex]\frac{5}{2\sqrt26}[/tex]

csc = hyp/opp -----> [tex]\frac{2\sqrt{26} }{5}[/tex]

cot = adj/opp -------> [tex]\frac{7}{5}[/tex]

The Inferential statistics is given below.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given is to discuss the statistical inference.

Therefore, the Inferential statistics is given above.

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Answer: Let X be the number of tables that ordered chips and salsa. Then, 7X tables did not order chips and salsa. So, X + 7X = 108, which simplifies to 8X = 108. Dividing both sides by 8, we have X = 13.5.

Since X must be a whole number, we round down to get X = 13 tables ordered chips and salsa.

Step-by-step explanation: