Find the missing side length

Answer:

75 square feet

Step-by-step explanation:

The aquarium is designed to hold 62.5cubic feet

Since the aquarium has a square base, assume the aquaruim is a square prism

Let X be the lenght

Let y be the height

x^2.y = 62.5

y = 62.5x^2

The area of each side of the aquarium is xy. Since there are four sides, the total area of the side= 4xy

The area of the bottom of the aquarium = x^2

Total surface area = 4xy + x^2

Put y = 62.5/x^2 into the total surface area equation

A = 4x(62.5/x^2) + x^2

A= 250/x + x^2

Differentiate A with respect to x

dA/dx = -250(x^-2) + 2x

dA/dx = 0

0 = 2x - 250x^-2

2x = 250x^-2

2x =250/ x^2

2x^3 = 250

x^3 = 250/2

x^3 = 125

x = cbrt (125)

x = 5

Put x= 5 into A = x^2 + 250x^-1

A= 5^2 + 250(5^-1)

A= 25 + 250/5

A = 25 + 50

A = 75 square feet

The surface area of a solid object can be determine by measuring the total area that surface of the object cover.

The minimum possible exterior surface area of the aquarium is [tex]75 \:\rm feet^2[/tex].

Given:

The aquarium designed hold [tex]62.5 \:\rm feet^3[/tex].

Let assume the aquarium is square prism.

Let [tex]x[/tex] is height and [tex]y[/tex] is length.

The aquarium designed hold [tex]62.5 \:\rm feet^3[/tex]. Write the system equation.

[tex]x^2y=62.5\\y=\frac{62.5}{x^2}[/tex]

The area of four side of aquarium is as follows,

[tex]\rm A_1=4xy[/tex]

The bottom area of aquarium is as follows,

[tex]A_2=x^2[/tex]

The total area is as follows,

[tex]A=A_1+A_2\\A=4xy+x^2[/tex]

Put [tex]y=\frac{62.5}{x^2}[/tex] in above expression.

[tex]A=4x(\frac{65.2}{x^2} )+x^2\\A=\frac{250}{x}+x^2[/tex]

Differentiate [tex]A[/tex] with respect to [tex]x[/tex].

[tex]\frac{dA}{dx}=-250(x^{-2})+2x[/tex]

For the minimum possible exterior surface area [tex]\frac{dA}{dx} =0[/tex].

[tex]0=2x-250x^{-2}\\2x=250x^{-2}\\2x^3=250\\x^3=\frac{250}{2}\\x^3=125\\x=5[/tex]

Substitute [tex]x=5[/tex] to find the area.

[tex]A=5^2+250\times 5^{-1}\\A=25+\frac{250}{5}\\A=75\:\rm feet^2[/tex]

Thus, the minimum possible exterior surface area of the aquarium is [tex]75 \:\rm feet^2[/tex].

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The [tex]a_n[/tex] reprsents the nth term where n is some positive whole number {1,2,3,...}

The [tex]a_{n-1}[/tex] represents the term just before the nth term. For example, if n = 22 then [tex]a_{n} = a_{22}[/tex] and [tex]a_{n-1} = a_{21}[/tex]

The +5 at the end means we add 5 to the previous term just before the nth term to get the nth term. In other words, the rule is "add 5 to each term to get the next term".

To get the 9th term [tex]a_{9}[/tex], we need to find the terms before this one because the recursive sequence builds up. The 9th term depends on the 8th term, which depends on the 7th term, and so on. The countdown stops until you reach the first term.

-------

[tex]a_{1} = 3[/tex] (given)

[tex]a_{2} = 8[/tex] (given)

[tex]a_{3} = 13[/tex] (given)

[tex]a_{4} = 18[/tex] (given)

[tex]a_{5} = 23[/tex] (given)

[tex]a_{6} = a_{5}+5 = 23+5 = 28[/tex] (add 5 to the prior term)

[tex]a_{7} = a_{6}+5 = 28+5 = 33[/tex]

[tex]a_{8} = a_{7}+5 = 33+5 = 38[/tex]

[tex]a_{9} = a_{8}+5 = 38+5 = 43[/tex]

So the 9th term is [tex]a_{9} = 43[/tex]

Answer: c. H0: p = 0.16; Ha: p ≠ 0.16

Step-by-step explanation:

We know that ,

Null hypothesis is a statement about the population parameter([tex]\mu , p, \sigma....[/tex]) and contains equality (=),≤ or  ≥ signs.

Alternative hypothesis is also statement about the population parameter([tex]\mu , p, \sigma....[/tex]) but against null hypothesis and contains signs < , > or ≠.

In the given situation , the parameter is p (population proportion).

A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16.

i.e. the point estimate of the population proportion(p) of the young adults who reported smoking at least twice a week or more is 0.16.

Now, the hypotheses to be tested for this study would be :

[tex]H_0: p=0.16\\\\ H_a: p\neq0.16[/tex]

Hence, the correct answer is  c. H0: p = 0.16; Ha: p ≠ 0.16

Answer:

B

Step-by-step explanation:

There is a vertical asymptote at x=3. It is not defined and therefore not included in the domain.

All other numbers are included in the domain.

Answer:

A. 960

Step-by-step explanation:

Multiply each heart rate by 24 (hours in a day)

Subtract the human's daily heart rate from the elephant's.

30 x 24 = 720

70 x 24 = 1680

1680 - 720 = 960

Answer:

It’s A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Nelson grows tomatoes and sells them at a nearby farmers roadside stand.

Let x = number of tomatoes sold

Let m = amount of money made for selling x tomatoes.

He sells them for $2.50 each. This means that he sells x tomatoes for 2.5×x = $2.5x

The farmer charges him $15 a day to use the stand. This means that he pays a constant amount of $15 each day.

Amount of money that Nelson will make will be total amount made in selling x tomatoes minus the constant amount being paid for rent. It becomes

m = 2.5x - 15 This is the general form. In the factored form, it will be

m = 2.5(x+6)

its B. on ed :)  

Hope this helps

Answer:

Step-by-step explanation:

1) 5x(x-2)-2x^2 for x =2

= 5(-2)(-2-2) -2(2)^2

= -10(-4) -2(4)

= 40 - 8

= 36

2) 2x^2 - 5 + 8 for x = 3

= 2(3)^2 - 5(3) + 8

= 2(9) -  15 + 8

= 18 -  15 + 8

= 3 + 8

= 11

Answer:

1. 32.

2. 11.

Step-by-step explanation:

1.   5x(x-2)-2x^2 for x=-2:

= 5(-2)( -2-2)-2(-2)^2

=  -10*-4 - 2*4

= 40-8

= 32.

2. 2x^2-5x+8 for x=3:

= 2(3)^2 -5(3)+8

=  18 - 15 + 8

= 11.

Answer:

P(No blue)=7/9=0.778

Step-by-step explanation:

The sample space of an experiment is "the set of all possible outcomes of that experiment".

The Complement Rule states "that the sum of the probabilities of an event and its complement must equal 1". So for example if A is an event and A' their complement we have this:

[tex]P(A)+P(A')=1[/tex]

[tex]P(A')=1-P(A)[/tex]

The probability of an event is "a number describing the chance that the event will happen".

For this problem we need to find first the sample space and is given by:

[tex]\Omega = [6white,8Black,4Blue][/tex] for a total of 18 socks.

[tex]n(\Omega)=8[/tex]

We can use the definition of probability of an event, and we find the probability that the randomly select sock would be blue we  have:

[tex]P_{blue}=\frac{Favorable outcomes}{Total outcomes}=\frac{4}{18}=\frac{2}{9}[/tex]

And then using the complement rule if we want the probability that the randomly selected sock would be NOT blue we have:

[tex]P'_{blue}=1-P_{blue}=1-\frac{2}{9}=7/9=0.778[/tex]

Answer:

x intercept = 15 # of cars to detail if no SUVs

y intercept =  10 # of SUVs to detail if no cars

Hope this helps!

The x-intercept and the y-intercept for the equation 30x + 45y = 450 are 15 and 10 respectively, The x-intercept denotes the number of cars if there is no SUV serviced and the y-intercept represents the number of SUVs if there is no car.

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.

Given:

Awesome autos car detail charges $30 for a full-service detail on SUVs,

The equation 30x + 45y = 450 represents the amount that must be earned each hour to cover expenses,

From this equation, we can determine that the autos car detail charges $45 for a full-service detail on car,

Find the x-intercept as shown below,

30x + 45 × 0 = 450   (For x-intercept y = 0)

30x = 450

x = 450 / 30

x = 15

Find the y-intercept as shown below

30 × 0 + 45y = 450   (For y-intercept x = 0)

45y = 450

y = 10

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Answer:

d) Good, the interval is related to the variable of interest and the population mean analyzed.

Step-by-step explanation:

1) Data given

[tex]\bar x = 23[/tex] represent the mean

[tex]ME=2[/tex] represent the margin of error

[tex]confidence=95\%=0.05[/tex]

The confidence interval for the mean is given by the following formula:

[tex]\bar x \pm ME = 23\pm 3=(21,25)[/tex]

Where the margin of error is given by [tex]ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

Based on the interval obtained we can say that "we have 95% of confidence that the mean winter snowfall would be between 21 and 25"

2) Analyze the possible options

a) Wrong, we are not analyzing the individual winters, the interval is related to the population mean.

b) Wrong, the confidence interval can't be interpreted as a chance that are not related to the population mean of interest.

c) Wrong, the confidence interval is not related to the individual days of winter.

d) Good, the interval is related to the variable of interest and the population mean analyzed.

e) Wrong, the confidence interval is not related to specific events, is related to the population mean.

Viewers should interpret the news by considering the confidence interval and understanding the statements.

The viewers should interpret this news as follows:

a. The statement that during 95 of the past 100 winters, the region got between 21" and 25" of snow is valid.

This is because the average winter snowfall of 23" falls within this range with a margin of error of 2".

b. The statement that there's a 95% chance the region will get between 21" and 25" of snow this winter is not correct.

The confidence interval (21" to 25") represents the range of values in which the true average snowfall is likely to fall, not the probability of the upcoming winter's snowfall falling within that range.

c. The statement that there will be between 21" and 25" of snow on the ground for 95% of the winter days is not supported by the given information.

The confidence interval pertains to the average winter snowfall, not individual daily observations.

d. The statement that residents can be 95% sure that the area's average snowfall is between 21" and 25" is valid.

The confidence interval provides a range of values within which the true average is likely to fall.

e. The statement that residents can be 95% confident that the average snowfall during the past century was between 21" and 25" per winter is valid.

The confidence interval represents the range of likely values for the true average.

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Answer:

A company declares a​ 5% stock dividend.

The debit to retained earnings is an amount equal to - the market value of the shares, that are to be issued.

We can say that a retained earnings balance is increased when we are using a credit and this is decreased when we make a debit.

A retained earnings is the total amount of money left, after all the expenses and dividends are paid by the company.

A 5% stock dividend represents a distribution of extra shares, 5% of existing ones, to shareholders. The debit to retained earnings is equal to 5% of the total market value of the previously existing shares.

When a company declares a 5% stock dividend, this means that the company is distributing additional shares of its stock to the existing shareholders. The quantity of these additional shares is equal to 5% of the shares that each shareholder currently owns. The debit to retained earnings is an amount equal to the total market value of these additional shares, which is determined by multiplying the declared dividend rate (5%) by the total market value of circulating shares prior to the issuance of dividend.

For instance, if a company has 1000 shares with a market value of $10 each, it would issue additional 50 shares (5% of 1000 shares). Therefore, the debit to retained earnings would be $500 (50 shares * $10/share).

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Answer:

Part 1) The perimeter of triangle ABC is 24 units

Part 2) [tex]y=97\°[/tex]

Step-by-step explanation:

Part 1)

we know that

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

The perimeter of triangle ABC is equal to

[tex]P=AB+BC+AC[/tex]

Applying the Midpoint Theorem

Find the measure of AB

[tex]AB=\frac{XZ}{2}[/tex]

substitute given value

[tex]AB=\frac{18}{2}=9\ units[/tex]

Find the measure of BC

[tex]BC=\frac{XY}{2}[/tex]

[tex]XY=2AY[/tex]

substitute given value

[tex]XY=2(7)=14\ units[/tex]

[tex]BC=\frac{14}{2}=7\ units[/tex]

Find the measure of AC

[tex]AC=\frac{YZ}{2}[/tex]

[tex]YZ=2BZ[/tex]

substitute given value

[tex]YZ=2(8)=16\ units[/tex]

[tex]AC=\frac{16}{2}=8\ units[/tex]

Find the perimeter  of triangle ABC

[tex]P=9+7+8=24\ units[/tex]

Part 2)

step 1

Find the measure of angle z

Remember that the sum of the interior angles in a triangle must be equal to 180 degrees

[tex]55\°+42\°+z=180\°\\97\°+z=180\°\\z=180\°-97\°\\z=83\°[/tex]

step 2

Find the measure of angle y

we know that

[tex]y+z=180\°[/tex] ----> by supplementary angles (form a linear pair)

substitute the value of z

[tex]y+83\°=180\°[/tex]

[tex]y=180\°-83\°=97\°[/tex]

Answer:

The average volume of air in the lungs during one cycle is 0.53176 liters.

Step-by-step explanation:

Given : The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated by the model [tex]V=0.1729t+0.1522t^2- 0.0374t^3[/tex], where t is the time in seconds.

To find : The average volume of air in the lungs during one cycle ?

Solution :

The volume V of air in the lungs during a five-second respiratory cycle is [tex]V=0.1729t+0.1522t^2- 0.0374t^3[/tex]

Then the average volume of air in the lungs during one cycle [0,5] is

[tex]V_a=\frac{1}{b-a}\int\limits^a_b {V(t)} \, dt[/tex]

[tex]V_a=\frac{1}{5-0}\int\limits^0_5 {0.1729t+0.1522t^2- 0.0374t^3} \, dt[/tex]

[tex]V_a=\frac{1}{5}[\frac{0.1729t^2}{2}+\frac{0.1522t^3}{3}- \frac{0.0374t^4}{4}}]^5_0[/tex]

[tex]V_a=\frac{1}{5}[0.08645t^2+0.05073t^3- 0.00935t^4]^5_0[/tex]

[tex]V_a=\frac{1}{5}[0.08645(5)^2+0.05073(5)^3- 0.00935(5)^4-0.08645(0)^2+0.05073(0)^3- 0.00935(0)^4][/tex]

[tex]V_a=\frac{1}{5}[2.1613+6.3413-5.8438][/tex]

[tex]V_a=\frac{1}{5}[2.6588][/tex]

[tex]V_a=0.53176\ l[/tex]

The average volume of air in the lungs during one cycle is 0.53176 liters.

Final answer:

To find the average volume of air in the lungs during one cycle, calculate the definite integral of V(t) over the interval t = 0 to t = 5 seconds.

Explanation:

The average volume of air in the lungs during one cycle can be approximated by finding the average value of the function V(t) over the interval t = 0 to t = 5 seconds. To do this, we need to find the definite integral of V(t) over the given interval:

∫[0,5] V(t) dt

After calculating the integral, divide the result by the length of the interval (5 seconds) to find the average volume of air in the lungs during one cycle.

Answer:

124.8 %

Step-by-step explanation:

Given,

Initial percentage of working students = 14.1%,

Final percentage of working students = 31.7%,

Thus, the percentage increase = [tex]\frac{\text{Final percentage-initial percentage}}{\text{Initial percentage}}\times 100[/tex]

[tex]=\frac{31.7 - 14.1}{14.1}\times 100[/tex]

[tex]=\frac{17.6}{14.1}\times 100[/tex]

[tex]=\frac{1760}{14.1}[/tex]

≈ 124.8 %

Final answer:

To find the original percentage of working students before an increase of 14.1%, subtract 14.1% from the new percentage of 31.7%, which gives us 17.6% as the original percentage.

Explanation:

The student is asking to find the original percentage of working students before a 14.1% increase resulted in a new percentage of 31.7%. To determine the original percentage, we need to subtract the increase from the final percentage. Here's the calculation:

Final percentage = Original percentage + Increase

31.7% = Original percentage + 14.1%

To find the original percentage, we subtract 14.1% from 31.7%:

Original percentage = 31.7% - 14.1% = 17.6%

Rounded to the nearest tenth of a percent, the original percentage of working students was 17.6%.

Answer: The speed of the current is 3 miles per hour.

The speed of the boat in still water is 10 miles per hour

Step-by-step explanation:

Let the speed of the boat be x miles per hour

Let the speed of the current be y miles per hour

Speed = distance / time

If the boat moves 39 miles downstream in 3 hours, then, the speed is

39/3= 13 miles per hour

Let us assume that it moved it moved in the same direction with the current hence, it moved in still water

The total speed would be x + y. Therefore

x + y = 13 - - - - - - -1

If the boat moves 21 miles upstream in 3 hours, the the speed is

21/ 3 = 7 miles per hour

It is assumed that it moved in the opposite direction to the current.

The total speed would be x - y. Therefore

x - y = 7 - - - - - - -2

Adding equation 1 and equation 2, it becomes

2x = 20

x = 20/2 = 10 miles per hour

y = 13 - x

y = 13 - 10 = 3 miles per hour

Answer:

4.18 hours

Step-by-step explanation:

Since the plane needs 2 hours to cover the las 990 miles at the end of the flight, and in the last half hour it flies with a speed of 190mph, meaning it covers a distance of 190 / 2 = 95 miles in this last half hours.

That means for the other 1.5 hours, its cruising speed is

[tex] v_c = \frac{990 - 95}{1.5} = 596.7 mph[/tex]

Beside the first and last half hour of the trip (which covers 190 miles), the cruising distance must be

d = 2090 - 190 = 1900 miles

The cruising time is therefore

[tex]t_c = \frac{d}{v_c} = \frac{1900}{596.7} = 3.18 hours[/tex]

Hence the total time for the entire flight is

3.18 + 1 = 4.18 hours

In 4.18 hours is the entire flight.

Given

A plane flies at 190 mph for the first and last half hours of a flight.

It flies at a higher constant speed for the rest of the flight.

The route is 2090 miles.

The plane is 990 miles from the destination 2 hours before the end of the flight.

The plane needs 2 hours to cover the last 990 miles at the end of the flight, and in the last half hour it flies with a speed of 190mph,

Then,

The distance covered by plane in last half hour is;

[tex]\rm Distance=\dfrac{190}{2}\\\\Distance=95 \ miles[/tex]

The velocity is;

[tex]\rm Velocity = \dfrac{Distance }{Time}\\\\Velocity=\dfrac{900-95}{1.5}\\\\Velocity=\dfrac{805}{1.5}\\\\Velocity=596.7[/tex]

The first and last half hour of the trip (which covers 190 miles), the cruising distance must be;

Distance = 2090 - 190 = 1900 miles

Therefore,

The cruising time is;

[tex]\rm Time =\dfrac{Distance}{Velocity}\\\\Time=\dfrac{1900}{596.7}\\\\Time=3.18 \ hours[/tex]

The total time for the entire flight is

= 3.18 + 1 = 4.18 hours

Hence, in 4.18 hours is the entire flight.

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Answer:

The number of leaves are 10648

Step-by-step explanation:

By the given information,

number of leaves be= z

height of tree= y

hours of sunlight= x

by the given conditions,

[tex]z = (k)(y)(x^{3})[/tex]

,where k is portionality constant.

now, z=6048, y=7 and x=6,

evaluating value of k using above conditions,

k=4

thus, using this value of k,

[tex]z=(4)(2)(11^{3})[/tex]

z= 10648.

The number of leaves on a tree of 2 yards tall receiving 11 hours of sunlight is predicted to be approximately 8712 based on the given relation.

The number of leaves z on a tree varies directly with the height of the tree y in yards and directly with the cube of the hours x of direct sunlight that the tree receives. Let's represent this relationship as z = kyx³ , where k is a constant of proportionality.

From the information provided, we know that a tree that is 7 yards tall and receives 6 hours of direct sunlight has 6048 leaves. Therefore, we can substitute these values into the equation and solve for k. Thus, if we replace z = 6048, y = 7, and x = 6, we find that k is approximately equal to 3.

With k approximately equal to 3, we can then predict the number of leaves on a tree that is 2 yards tall and receives 11 hours of sunlight. If we replace k = 3, y = 2, and x = 11 into our equation, we find that the predicted number of leaves is approximately 8712.

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Answer: Our required probability is 45.05%.

Step-by-step explanation:

Since we have given that

                         Males                  Females               total

Left handed       6.3                         4.95                     11.25%

Right handed     43.7                       45.05                  88.75%

Total                   50%                        50%                   100%

Since 12.6% of 50% are males are left handed = 6.3%

So, 9.9% of 50% are females are left handed = 4.95%

So, Females who are right handed would be

[tex]50\%-4.95\%\\\\=45.05\%[/tex]

Hence, our required probability is 45.05%.

To calculate the probability that the selected person is a female, given the person is right-handed, we need to use conditional probability. The exact probability cannot be calculated without the percentage of females in the population. However, it is known that the probability is less than or equal to 11.25%.

To find the probability that the selected person is a female, given that the person is right-handed, we need to use conditional probability. Let's denote the events A and B as follows: A: Selected person is a female, B: Selected person is right-handed.

The probability of event A (P(A)) can be calculated as the product of the probability of event B given event A (P(B|A)) and the probability of event A without any condition (P(A)) divided by the probability of event B (P(B)).

In this case, P(A) refers to the probability of selecting a female, P(B|A) refers to the probability of being right-handed given the person is female, and P(B) refers to the probability of being right-handed.

First, let's calculate the probability of being right-handed (P(B)). Since 90% of people are right-handed, P(B) = 0.9.

Next, let's calculate the probability of being right-handed given the person is female (P(B|A)). Since 9.9% of females are left-handed, the probability of being right-handed is 1 - 0.099 = 0.901.

Finally, let's calculate the probability of selecting a female (P(A)). Since the percentage of females in the population is not provided, we cannot calculate the exact probability. We can only say that it is less than or equal to the total percentage of left-handed people, which is 11.25%.

Therefore, the probability that the selected person is a female, given that the person is right-handed, can be defined as: P(A|B) = (P(B|A) * P(A)) / P(B) = (0.901 * P(A)) / 0.9 = 0.901 * P(A).

Since we don't have the exact value of P(A), we cannot calculate the exact probability. However, we know that it is less than or equal to 11.25%.

Answer: m<YSH = 35°  

               m<YIH = 20°

              m<SAI =  71°

               m<PAY = 8°

                    PY =  i don' t know

and P.S these answers may all be wrong sorry but hope it helps. :)

Answer:

Step-by-step explanation:

Answer:

Light intensity = L =1

Step-by-step explanation:

The given function is:

[tex]P = \frac{120L}{L^{2}+L+1 }[/tex]                    (Equation.1)

Taking derivative of the whole equation:

[tex]\frac{dP}{dL}[/tex] =[tex]\frac{d}{dL}[/tex] [tex](\frac{120L}{L^{2}+L+1 } )[/tex]

[tex]\frac{dP}{dL}[/tex] =120 [tex]\frac{1 (L^{2}+L+1) - (\frac{d}{dL}L^{2} +\frac{d}{dL} L+\frac{d}{dL}1)L}{(L^{2}+L+1)^{2} }[/tex]

[tex]\frac{dP}{dL}[/tex] =[tex]\frac{120 (L^{2}-1)}{L^{2}+L+1 }[/tex]

[tex]\frac{dP}{dL}[/tex] =[tex]\frac{120 (L+1)(L-1)}{L^{2}+L+1 }[/tex]

For first derivative test, there is a maxima. for that , we need to take:

L+1 =0 and L-1 =0

we get:

L= -1

or L=1

Since light intensity cannot be negative so, L=1

put this in equation 1:

[tex]P(1) = \frac{120}{1^{2}+1+1 }[/tex]

P = [tex]\frac{120}{3}[/tex]

P= 40  which is the maximum value of P (At L=1)

To find the light intensity that maximizes photosynthesis, you must differentiate the function P = 120I/(I^2 + I + 1) with respect to I, equate it to zero and solve for I. Then, use these values to examine the second derivative and verify whether these are local maxima or minima.

To find the light intensity (I) that maximizes photosynthesis rate (P), we should analyze the function P = 120I/(I2 + I + 1) using calculus concepts. This type of problem is looking for a maximum value, so we need to find where the derivative of the function equals zero.

First, differentiate the function P regarding I, using quotient rule: P' = (120(I² + I + 1) - 120I (2I + 1))/ (I² + I + 1)² = 0.

Then, solve this equation for I to find the values for which the rate of change of P with respect to I is zero. These are the points where P is at a maximum or a minimum. Finally, check the second derivative of the function P on these values to determine whether these correspond to a local maximum, a local minimum, or a saddle point.

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Answer:

inverse of f(x) is g(x)

Step-by-step explanation:

f(x) = (x+9)/4

g(x) = 4x-9

f^-1(x) = g(x)

Let y = (x+9)/4

4y = x + 9 (make x the subject)

x = 4y - 9

f^-1(x) = 4x - 9

= g(x) (shown)

Answer:

Below.

Step-by-step explanation:

If f(x) is the inverse then f(g(x)) = x.

f(g(x)) =  ((4x - 9) + 9) / 4

= 4x/4

= x.

So it is true.

It can also be shown that g(f(x)) = x.

The amount increased 4% from last year.

Step-by-step explanation:

Given,

Average cost last year = $625

Average cost this year = $650

Increase amount = Average cost last year - Average cost this year

Increase amount = 650 - 625 = $25

Percent increase = [tex]\frac{Increase\ amount}{Average\ cost\ last\ year}*100[/tex]

[tex]Percent\ increase=\frac{25}{625}*100\\Percent\ increase=\frac{2500}{625}\\Percent\ increase=4\%[/tex]

The amount increased 4% from last year.

Keywords: percentages, subtraction

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Answer:

  30 miles

Step-by-step explanation:

Let d represent the distance to the island. The relation between time, speed, and distance is ...

  time = distance/speed

so the total time for the round trip is ...

  d/15 +d/10 = 5

Multiplying by 30, we get

  2d +3d = 150

  d = 150/5 = 30

The island was 30 miles from the harbor.

To solve this problem we use the equation Speed = Distance/Time for both legs of the trip to form an equation and solve for the distance. Through these calculations, we find the distance from the harbor to the island to be 30 miles.

This problem can be solved by understanding the relationship of speed, distance, and time, often expressed as Speed = Distance/Time. First, let's define the time it took to go to the island and back. From the problem, we know that the total time was 5 hours but the speeds were different, so the time spent on each leg of the trip was different. We'll define the time it took to get to the island as two hours. Therefore, the return trip took 5-t hours. Solving for Distance To calculate the distance, we use the speed of each leg of the trip multiplied by the time of that leg. So, Distance = 15t = 10(5-t). We can solve this equation for t, finding that t equals to 2 hours. Inserting t back into Distance = 15t gives us a distance of 30mph to the island. This means it is 30 miles from the harbor to the island.

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Answer:

  c.  an algorithm

Step-by-step explanation:

Most math problems are best solved using an algorithm. Certainly, converting numbers from one form to another is easily done that way.

_____

The integer part is the whole-number quotient of the division. The fractional part is the remainder divided by the denominator:

  39/8 = 32/8 + 7/8 = 4 7/8

Answer:

8

Step-by-step explanation:

Only the innermost 8 1-inch cubes would have no red paint on any face.

The 4 inch cube is divided into 1 inch cubes, and the number of cubes that do not have red on any face is calculated. There are no 1 inch cubes that do not have red on any face.

To find the number of 1 inch cubes that do not have red on any face, we need to consider the number of cubes that have red on at least one face. Since the complete outside of the 4 inch cube is painted red, each face of the cube has a 4x4 square painted red. Therefore, the area of each face is 16 square inches.

Dividing the 4 inch cube into 1 inch cubes, we have a total of 64 smaller cubes (4x4x4 = 64). Each smaller cube has 6 faces.

So, the total area of all the faces of the smaller cubes is 64 x 6 = 384 square inches. Since each face of the smaller cubes has an area of 1 square inch, the number of cubes that have red on at least one face is 384/1 = 384 cubes.

Therefore, the number of 1 inch cubes that do not have red on any face is 64 - 384 = -320. However, since negative numbers do not make sense in this context, we can conclude that there are no 1 inch cubes that do not have red on any face.

Final answer:

To find the original selling price of the ski set, work backward from the sale price by adding the markdowns back to it. Start by assigning a variable to represent the original selling price and use the given markdown amounts to calculate the original price. The original selling price of the ski set is $387.50.

Explanation:

A sporting goods store manager was selling a ski set for a certain price. The manager offered markdowns, making the one-day sale price of the ski set $325. To find the original selling price of the ski set, we will work backwards from the sale price by adding the markdowns back to it.

Step-by-step process:

Let x be the original selling price.

Given markdowns, if the sale price after markdowns is $325, then x - $30 - $20 - $12.50 = $325.

Solving for x, we get x = $387.50.

Answer:

  -tan(73°)

Step-by-step explanation:

The reference angle is the smallest angle between the terminal ray and the x-axis. Here, the terminal ray is in the 4th quadrant, so the reference angle will be ...

  ref∠ = 360° -287° = 73°

In the 4th quadrant, the tangent is negative, so we have ...

  tan(287°) = -tan(73°)

Answer:

0.273

Step-by-step explanation:

Let the number of insured pieces of luggage be i and u be the number of uninsured pieces of luggage, therefore,

i + u = 27

Now,

probability that exactly one of the damaged pieces of luggage is insured = (iC1)(uC3)/(27C4)

probability that none of the damaged pieces are insured = (uC4)/(27C4)

and,

(iC1)(uC3)/(27C4) = 2 (uC4)/(27C4)

=> u − 2i = 3

By solving, i + u = 27 and  u − 2i = 3

i = 8 and u = 19

and,

(8C2)(19C2)/(27C4) = 0.273

Answer:

Step-by-step explanation: