I have this calculus problem that I’m having trouble with. I’m not allowed to use the power rule. I need to use the formula s’(t) = (s(t+h) - s(t))/h. Please help

Answer:

It's the third choice.

Step-by-step explanation:

IF y varies inversely as x then y = k/x   where k is a constant,

and k = xy    

For the 3rd choice

-1 * -2/7 = 2/7

4 * 1/14 = 2/7 and

6 * 1/21 = 2/7

so, this is inverse variation.

The piecewise function for the price of n gallons of diesel at Buc-ee’s would be = $1.00

The price paid for 3 gallons or less = $2.68 per gallon

That is, $2.68 =/< 3 gallons

Therefore $x= 1 gallon

Make X the subject of formula;

X = 2.68/3

X= $0.89

The price paid for 4 gallons or less = $2.41 per gallon

That is, $2.41 per =/< 4 gallons

Therefore $y = 1 gallon

Make y the subject of formula;

y = 2.41/4

y = $0.60

From the both outcomes, it can be concluded that the n gallons of diesel at Buc-ee’s would be approximately $1.00.

Learn more about cost price here:

https://brainly.com/question/25109150

#SPJ1

The expected value of the game to the player is $5.95, and if they play 1000 times, they would expect to lose $5950.

The expected value of the game to the player is the average amount of money they can expect to win or lose in the long run. To calculate the expected value, we must multiply the probability of winning (1/38) by the amount of money won ($210) and subtract the probability of losing (37/38) by the amount of money paid to play ($6). This gives us an expected value of (1/38) x ($210) - (37/38) x ($6) = $5.95. If you played the game 1000 times, you would expect to lose $5950 in total, as the expected value of each game is -$5.95. This means that, on average, you would lose $5.95 for every game you play. Multiplying this amount by 1000 gives us our expected total loss of $5950.

The calculation for the expected value of the game and the total expected loss for playing it 1000 times is as follows:

Expected value = (1/38) x ($210) - (37/38) x ($6)

= ($5.526) - ($5.684)

= -$0.158

Therefore, the expected value of each game is -$0.158, which means that on average, a player can expect to lose $0.158 for every game played.

Total expected loss for playing 1000 times = (-$0.158) x 1000

= -$158

Therefore, if the game is played 1000 times, the total expected loss is -$158

Learn more about expected value here

https://brainly.com/question/18523098

#SPJ1

The value of the tax for the meal is $1.05.

The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a standard sales tax is imposed, collected by the shop, and paid to the government.

Depending on the regulations in that country, a business may be responsible for sales taxes in that jurisdiction if it has a presence there, which can be a physical site, an employee, or an associate.

Given the  cost of the meal = $15.00

and rate of tax = 7%

converting the rate of tax into decimal form,

rate of tax = 7% = 7/100

rate of tax = 0.07

amount of tax = cost x rate of tax

amount of tax = 15 x 0.07

amount of tax = $1.05

Hence the amount of tax is $1.05.

Learn more about sales tax;

https://brainly.com/question/29442509

#SPJ1

Answer:

A chi-square goodness-of-fit test

Step-by-step explanation:

GOF test is used to determine if the data meets the expected values.

A chi-square goodness-of-fit test procedure should be used to test whether or not the shuffle feature is working correctly.

What is a distribution?

A distribution includes an algebraic function that calculates the likelihood that long-been-considered outcomes will occur. In the perspective of its population space as well as event probability, it is a schematic representation of random phenomena.

To ascertain regardless of whether the observed sample frequency deviates noticeably from those given in the null hypothesis, should use the chi-square goodness of fit test.

He notes the number of tracks in each classification after listening to 100 songs selected at random while his player is in shuffle mode. One can determine out whether the quality of fit is "good enough" and draw the conclusion that the population matches the distribution by applying the chi-square goodness of fit test.

Learn more about distribution, Here:

https://brainly.com/question/29062095

#SPJ5

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

11.5

Step-by-step explanation:

It would be number 3

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

A line segment that measures 92 millimeters in length can be drawn using scale.

Given that,

A line segment has to be drawn which has a measure of length 92 millimeters.

We know that,

10 millimeters = 1 centimeter

1 millimeter = 1/10 centimeters

92 millimeters = 92/10 = 9.2 centimeters

So it is enough to draw a line segment of length 9.2 centimeters.

In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.

In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.

So draw a line segment starting from 0 to 9.2.

Hence the line segment is drawn with scale.

Learn more about Line Segments here :

https://brainly.com/question/9477630

#SPJ1

The volume of the circular cylinder be,

⇒ 62.8 mm³

Given that,

For a circular cylinder,

Height = 5 mm

Radius = 2 mm

Then we have to find the volume of this circular cylinder

Since we know that,

The right circular cylinder is a cylinder with circular bases that are parallel to each other. It's a three-dimensional form. The axis of the cylinder connects the centers of the cylinder's two bases.

This is the most frequent sort of cylinder encountered in daily life. The oblique cylinder, on the other hand, does not have parallel bases and resembles a skewed construction.

volume of circular cylinder = πr²h

Here we have,

r = 2 mm

h = 5 mm

Now put the values into the formula we get,

Volume = π x 2² x 5

             = 62.8 mm³

To learn more about volume visit:

https://brainly.com/question/16860802

#SPJ1

The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

Read more on proportional relationship:

https://brainly.com/question/12242745

#SPJ1

Answer:

1.65

Step-by-step explanation:

equation will be 12(f−0.55)=13.20

12f−6.6=13.20

12f = 19.8

f = 19.8/12 = 1.65

So, each can of soup at full price is $1.65.

The solution is, the correct option is, A.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The translation of a sin function can be modeled by the form: P(t)=Asin(Bx+C)+D

Where:

A = the curve's amplitude (highest and lowest points)

The period = (2[pi])/ |B|

The phase shift (horizontal shift) = (-C)/B

D = vertical shift

By looking at the function we are given: P(t)=30sin(2[pi]t)+100,

We can see that the amplitude (the curve's highest and lowest points) = 30.

The phase shift (C) or in this case 't' = 0 (so there is no horizontal shift)

The period = 1

And D (the vertical shift) = 100

To learn more on function click:

brainly.com/question/21145944

#SPJ9

Answer:

-4920.75 or 18

Step-by-step explanation:

I'm not quite sure if this is correct because I got two diffrent soultions for a.

In a1=3 I got a=3

In a8= -6561 I got a= -820.125

So i plugged my two solutions in to find a6

I got

18

or

-4920.75

That doesn't really seem correct, but I tried!!

Answer:

No solution

Step-by-step explanation:

2x-5y-2z= -2

6x-15y-6z=20

2x-2y-5z = 4

3rd eq - 1st eq

3y - 3z = 6

2nd eq - 3 × 1st eq

0 = 26

This is a false statement. Therefore, there is no solution.

Answer: No solution

Explanation:

On the first day, the shop owner sampled 12 slip of paper which gives him / her a number of YES and NO

According to the analysis,

the total number of YES = 8

The total number of NO = 4

This implies that 8 shoppers were happy

Therefore, Proportion = Number of happy shoppers / over total number of sampled shoppers

Proportion = 8 / 12

Proportion = 2/3

In percentage = 2/3 x 100%

= 0.6667 x 100%

= 66.67%

This implies that 66.67 % of the shoppers were happy

Second day, the owner of the shop founds that 25% of the 12 selected slips were marked yes.

This implies that

25% of the total slip selecetd will result to the number of slips marked yes

25/100 x 12

0.25 x 12

= 3

Therefore, the number of happy shoppers were 3

Firstly, This is not the over all proportion because there is a deviation from the first analysis made. The selected 12 slips in the first day indicates that 8 happy shoppers were selected and 4 shoppers were marked No

The other day, shows that 3 happy shoppers were marked YES and 9 shoppers were marked NO.

I would advice the shop owner to gather more data

Answer:

-60...make me brainlistt

Step-by-step explanation:

The total number of fish in the lake would be = 60 fishes

The total of a data set is the addition of the various components that makes up a data set which gives a particular value.

On the first day the number of fish that was marked by the fisher man = 50 fishes.

On the second day the total amount of fishes that was caught = 80 fishes

The number of fishes that where among the 80 fishes that are marked= 20

Therefore the total amount of fishes in the lake = 80 - 20

= 60 fishes.

Learn more about addition here:

https://brainly.com/question/25421984

#SPJ1

Answer:

i think it's b4

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + y + z = 97 eq1

x - z = 9 eq2

y = 2z eq3

Since y is already defined in eq3, we can substitute eq3 into eq1.

x + 2z + z = 97

x + 3z = 97 new eq1

Now, we have only 2 equations to work with that have two variables.

x + 3z = 97 new eq1

x - z = 9 eq2

Subtract eq2 from new eq1 to eliminate the x terms.

4z = 88

z = 22

Next, substitute this value of z into eq3 to solve for y.

y = 2(22)

y = 44

Finally, we can substitute the values of y and z into eq1 to solve for x.

x = 97 - 44 - 22

x = 31

The three numbers are 22, 31, and 44.

Answer:

  3 in

Step-by-step explanation:

Apparently, we are to assume that the height and width are proportional:

  height/width = (6 in)/(8 in) = (new height)/(4 in)

Multiplying by 4 in will tell us the new height:

  new height = (4 in)(6/8) = 3 in

The reduced frame will be 3 inches tall.

Answer:

Step-by-step explanation:

6

\(m=6n^2+1\hspace{5em}L=\sqrt{m-7} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{L=\sqrt{(6n^2+1)-7}} \implies L=\sqrt{6n^2 -6} \\\\[-0.35em] ~\dotfill\\\\ \textit{when n = 2, what is "L"?}\qquad L=\sqrt{6(2)^2 -6} \\\\\\ L=\sqrt{6(4)-6}\implies \boxed{L=\sqrt{18}} \\\\[-0.35em] ~\dotfill\\\\ \textit{when L = 6, what is "n"?}\qquad 6=\sqrt{6n^2 -6}\implies 6^2=6n^2 -6 \\\\\\ 36=6n^2-6\implies 42=6n^2\implies \cfrac{42}{6}=n^2\implies 7=n^2\implies \boxed{\sqrt{7}=n}\)

Answer:

See below

Step-by-step explanation:

\(\dfrac{d}{dx} (\tan^3 x) = 3\sec^4 x - 3\sec^2 x\)

Recall

\(\dfrac{d}{dx}\tan x=\sec^2\)

Using the chain rule

\(\dfrac{dy}{dx}= \dfrac{dy}{du} \dfrac{du}{dx}\)

such that \(u = \tan x\)

we can get a general formulation for

\(y = \tan^n x\)

Considering the power rule

\(\boxed{\dfrac{d}{dx} x^n = nx^{n-1}}\)

we have

\(\dfrac{dy}{dx} =n u^{n-1} \sec^2 x \implies \dfrac{dy}{dx} =n \tan^{n-1} \sec^2 x\)

therefore,

\(\dfrac{d}{dx}\tan^3 x=3\tan^2x \sec^2x\)

Now, once

\(\sec^2 x - 1= \tan^2x\)

we have

\(3\tan^2x \sec^2x = 3(\sec^2 x - 1) \sec^2x = 3\sec^4x-3\sec^2x\)

Hence, we showed

\(\dfrac{d}{dx} (\tan^3 x) = 3\sec^4 x - 3\sec^2 x\)

================================================

For the integration,

\($\int \sec^4 x\, dx $\)

considering the previous part, we will use the identity

\(\boxed{\sec^2 x - 1= \tan^2x}\)

thus

\($\int\sec^4x\,dx=\int \sec^2 x(\tan^2x+1)\,dx = \int \sec^2 x \tan^2x+\sec^2 x\,dx$\)

and

\($\int \sec^2 x \tan^2x+\sec^2 x\,dx = \int \sec^2 x \tan^2x\,dx + \int \sec^2 x\,dx $\)

Considering \(u = \tan x\)

and then \(du=\sec^2x\ dx\)

we have

\($\int u^2 \, du = \dfrac{u^3}{3}+C$\)

Therefore,

\($\int \sec^2 x \tan^2x\,dx + \int \sec^2 x\,dx = \dfrac{\tan^3 x}{3}+\tan x + C$\)

\($\boxed{\int \sec^4 x\, dx = \dfrac{\tan^3 x}{3}+\tan x + C }$\)

Answer:

Step-by-step explanation:

The distributive property tells us that the term in the inside the parentheses will by multiply by the term on the outside of the parentheses first.  Example:

3(x + 5) means that (x + 5) + (x + 5) + (x + 5) = 3x + 15

So 7(x + 5) - x = 42 ; without the distributive property you would have to write what is inside the parentheses seven times then complete solving the problem

7( x + 5) -x = 42

(x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) - x = 42   by definition

(x + x + x + x + x + x + x) + (5 + 5 + 5 + 5 + 5 + 5 +5) -x = 42  (x + 5) Associative and Commutative

7x + 35 - x = 42      Addition

6x + 35 = 42           Associative and Commutative

6x = 7                     Subtraction

x =7/6                     Division

Now with the Distributive property

7(x + 5) - x = 42

7·x + 7 · 5 - x = 42        Distributive property

7x + 35 - x = 42           Multiplication

6x + 35 = 42                Associative and Commutative

6x =  7                          Subtraction

x = 7/6                          Division