how many four-digit numbers greater than $2999$ can be formed such that the product of the middle two digits exceeds $5$?

Answers

Answer 1

A total of 4970 four-digit numbers that are greater than 2999 can be created so that the middle two digits' product is greater than 5.

Combinations are mathematical operations that count the number of possible combinations for a set of elements when the order of the selection is irrelevant. One can choose the components of combinations in any order. Here, we have to find four-digit number combinations.

The digit in the thousands place should be greater than 2 so that the four-digit number be will greater than 2999. So the possible numbers are 3, 4, 5, 6, 7, 8, and 9.  Therefore, this occurs in 7 ways.

The digit in the one's place can be any number from 0 to 9. Therefore, this occurs in 10 ways.  

For the middle two digits, the combinations are given by,

If the hundreds digit is 1 then, the tens digit can be 6, 7, 8, and 9. This occurs in 4 ways.

If the hundreds digit is 2 and the tens digit can be from 3 to 9. This occurs in 7 ways.

If the hundreds digit is 3 and the tens digit can be from 2 to 9. This occurs in 8 ways.

If the hundreds digit is 4 and the tens digit can be from 2 to 9. This occurs in 8 ways.

If the hundreds digit is 5 and the tens digit can be from 2 to 9. This occurs in 8 ways.

If the hundreds digit is 6 and the tens digit can be from 1 to 9. This occurs in 9 ways.

If the hundreds digit is 7 and the tens digit can be from 1 to 9. This occurs in 9 ways.

If the hundreds digit is 8 and the tens digit can be from 1 to 9. This occurs in 9 ways.

If the hundreds digit is 9 and the tens digit can be from 1 to 9. This occurs in 9 ways.

The total ways for the middle two digits are 4+7+8+8+8+9+9+9+9=71 ways.

Therefore, the total number of four-digit numbers greater than 2999 is  7×10×71=4970.

The answer is 4970.

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Related Questions

The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is cubic inches when its base area is square inches and its height is inches. What is the volume of a pyramid with a base area of square inches and a height of inches?.

Answers

The volume of a pyramid is 60 inches.

Given that,

A pyramid's volume varies in tandem with both its base area and height. When a pyramid's base is square inches and its height is inches, its volume is cubic inches.

V1 = 35 cubic inches

A1 = 15 square inches

h1 = 7 inches

A2 = 36 inches

h2 = 5 inches

To find  : What is V2

The following formula is used to determine a pyramid's volume:

V = (Base Area × Height)/3

V2 = (36 square inches multiplied by 5)/3

V2 = 60 cubic inches

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chegg how many cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected?

Answers

26 cards must be selected from a standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.

We have given that standard deck of 52 cards.

And we have to find the number of cards must be selected from a deck to get at least four hearts, four diamonds and five clubs.

So four hearts + four diamonds + five clubs = 13 cards

The worst case, we may select all the spade i.e 13 cards before any heart, diamond and club.

So the guarantee that at least four hearts, four diamonds and five clubs are selected, 13 + 13 = 26

Therefore 26 cards must be selected from standard deck of 52 cards to guarantee that at least four hearts, four diamonds and five clubs are selected.

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Which of the following is TRUE about the slope of a line? *
A. The slope of a vertical line is zero.
B. The slope of a vertical line is undefined.
C. The slope of a line is always positive. D. The slope of a horizontal line is negative.​

Answers

Answer:

Step-by-step explanation:

The answer is B.

The slope of a verticle line is "undefined" by nature. As it is infinite

The relationship between a company’s profit, y, and the number of units sold, x, is represented by the equation 6x − 9y = 12. rewrite the equation to give the profit in terms of the number of units sold.

Answers

After solving the equation in terms of y will be y = (2/3)x - 4/3.

What is an equation?

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

The given equation is,

6x - 9y = 12

Then, the equation in terms of y will be,

9y = 6x - 12

Divide the above equation by 3,

3y = 2x - 4

y = (2/3)x - 4/3

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What is the length of side bc of the triangle? enter your answer in the box. Units.

Answers

The length of the side  BC Iis equal to 28 units which we get by using congruency.

What is congruency?

In other words, if the lengths of the sides and angles are the same for two shapes, they are congruent (the same in shape and size). When two triangles are congruent, it is frequently useful to know.

* In triangle ABC

∵ Angles B and C comes to be congruent

∴ m∠B = m∠C

* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length

∴ AB = AC

∵ AB = 4x - 7

∵ AC = 2x + 7

∴ 4x - 7 = 2x + 7 ⇒ collect same terms

∴ 4x - 2x = 7 + 7

∴ 2x = 14 ⇒ divide both the sides by 2

∴ x = 14 ÷ 2 = 7

* Now we can find the length of side BC

∵ The length of side BC = 4x ⇒ substituting the value of x

∴ The length of side BC = 4 × 7 = 28 units

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Correct Question

What is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vertex A lies above side B C. Angle B and angle C are marked congruent. The length of side A C is labeled as 2 x plus 7. The length of side A B is labeled as 4 x minus 7. The length of side B C is labeled as 4 x.

The table represents some points on the graph of linear function f.
x = -2, 1, 5, 10
f(x) = -224, 64, 448, 928

Which function represents f`? Please show your work.
A. f(x) = 32(3x - 1)
B. f(x) = -32(x - 3)
C. f(x) = -2(32x - 3)
D. f(x) = 16(2x - 1)

Answers

The function representing the points relation is f(x) = 32(3x - 1)

What is function?

A function is defined as a relation between a set of inputs having one output each.

Given a table, represents some points on the graph of linear function f.

x = -2, 1, 5, 10

f(x) = -224, 64, 448, 928

From option A)

f(x) = 32(3x - 1)

Put x = -2

= 32(-2x3-1)

= 32x(-7) = -224

Hence, The function representing the points relation is f(x) = 32(3x - 1)

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Darren bought 53.11 pounds of fruit for a class party. The class ate 0.6 pounds of the fruit. How much fruit is left?

Answers

This is pretty simple just do this:
53.11-0.6=52.51
There ya go :)

If x = 6 and y = -4, evaluate the following expression: 20 - 5y + 2x​

Answers

answer:

20-5y+2x=52

step-by-step explanation:

plug in the values of x & y into the expression and calculate using the order of operations to get the answer. hope that helps!

Answer: 52

Step-by-step explanation:

1. plug in x and y into the expression : 20 - 5(-4) +2(6)

2. multiply the numbers in the parenthesis:  20 + 20 + 12
3. add all the numbers together (simplify): 52

167. for the training adaptation of maximum strength, what is the recommended number of repetitions per set?

Answers

Each strength training exercise should be performed for 2 to 6 sets with no more than 6 repetitions. To encourage the greatest outcomes, the training intensity for each set should be 85% or greater.

What is percent?

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). %, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

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Given: -6x < 36. Choose the solution set. {x | x < -6} {x | x > 6} {x | x > -6} {x | x < 6}.

Answers

The correct answer is this inequality {x | x > -6}

What does a math inequality look like?

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

Given that:

-6x < 36

we multiply -1 on both the sides

6x > -36

divide 6 on both the side

x > -6

Hence the correct answer is this inequality {x | x > -6}.

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Is joni correct? explain. joni is not correct, because $230 is just the interest she will earn; she will have $430 total. joni is not correct; $230 will be her balance after 1 year. after 3 years, she will have $290. joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. she will have $231.53. joni is correct. she correctly applied the i = p · r · t formula, and will have $230.

Answers

Joni is mistaken because she applied the compounding rate formula rather than just the simple interest rate equation, which is incorrect. $231.53 will belong to her.

Explain the term compounded annually?The equation A=P(1+r)t can be used to calculate the amount A you would have after t years if you deposit P dollars together in savings account including an annual interest rate of r and also the interest is compounded annually.

The $200 was deposited by Joni into an account that earned interest at a 5% annual compound rate.

Joni calculated and she'll have a final balance of $230 after three years.

The steps are as following,

P = 200, r = 5, t = 3I = 200*0.05* 3I = 3030 + 200 = 230

Because Joni employed the simple interest rate method instead of the compound interest rates formula, she is mistaken $231.53 will belong to her.

The yearly compound interest rate if 5% is stated above.

As a result, she ought to have used the compound interest calculation when calculating.

A = P(1 + r/n)∧(nt)

Amount then becomes:

A = 200(1 + 0.05)³

A = $231.53.

Thus, final amount will be obtained as  $231.53.

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The complete question is-

Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230. Her work is shown below. Step 1: P = 200, r = 5, t = 3 Step 2: I = 200 ∙ 0.05 ∙ 3 Step 3: I = 30 Step 4: 30 + 200 = 230 Is Joni correct? Explain. Joni is not correct, because $230 is just the interest she will earn; she will have $430 total. Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290. Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53. Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.

Given the diagram below, if Z is the incenter of WXY, WYX =86, and WXZ=33. Find each measure.​

Answers

Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

The values of each measure:

m∠WYZ = 43

m∠WXY = 33

m∠YWX = 61

m∠ZWX = 30.5

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Z is the incenter of WXY.

m∠WYX = 86

This means,

m∠WYZ = m∠XYZ = x

m∠WYZ + m∠XYZ = m∠WYX

2x = 86

x = 43

m∠WXZ = 33.

m∠WXZ = m∠WXY

Now,

The triangle WXY.

m∠YWX + m∠WXY + m∠WYX = 180

m∠YWX + 33 + 86 = 180

m∠YWX = 180 - 119

m∠YWX = 61

m∠ZWX = 61/2 = 30.5

Thus,

The values of each measure:

m∠WYZ = 43

m∠WXY = 33

m∠YWX = 61

m∠ZWX = 30.5

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Remember
to estimate first
by rounding and multiplying
to find where the first digit
goes in the quotient.
1. 1,593/13

Answers

Answer:

Step-by-step explanation:

1593/13

122.538

answer: 122.5

what is the ratio of 500 students and 10 classrooms

Answers

Answer:

FOR EVERY 1 CLASSROOMS THERE ARE 50 STUDENTS, SO 50 STUDENTS IN EACH CLASSROOM the ration would be 50:1

Step-by-step explanation:

Answer:

I think its 50:1

Step-by-step explanation:

NEED HELP. ASAP For the bleacher section, what is the minimum number of games a fan needs to attend to make purchasing a season ticket a less expensive option than single-game tickets?

Seating Area

Single-Game Ticket

Season Ticket

Main box

$50

$3240

Bleachers

$12

$810

Left field reserve

$20

$1377

Answers

The best way is to pick the one you think has a higher chance

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f-1(x) go through?.

Answers

The positions through which the equation of f^-1(x) travels are: (4, 1), (6, 4)

What are equations?

A mathematical statement called an equation is comprised of two expressions joined together with the equal sign.

A formula would just be 3x - 5 = 16, for instance.

When this equation is solved, we observe that the value of the variable x is 7.

So, (1, 4) and (4, 6) are points through which the equation of f(x) goes.

If the f (x) equation contains (x, y).

Therefore, the f^-1(x) equation is as follows: (y, x).

Here, the f (x) equation passes through the following points: (1, 4) and (4, 6).

So, (4, 1) and (6, 4) are the points through which the equation of f^-1(x)  goes through.

Therefore, the positions through which the equation of f^-1(x) travels are:

(4, 1), (6, 4)

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Correct question:
If the equation of f(x) goes through (1,4) and (4,6), what points does f^-1(x) go through?

question if x, y, and z are integers and xy z is an odd integer, is x an even integer? (1) xy xz is an even integer. (2) y xz is an odd integer.

Answers

xy + xz is an even integer & x is even and y + xz is an odd integer &  either (x-1) is even or (y-z) is even .

1. xy + xz is an even integer - SUFFICIENT

Given:

xy + z is odd ...(i)

xy + xz is even ...(ii)

subtracting (ii) from (i)

we get xz - z, which should be odd (* since odd - even = odd)

=> z(x-1) is odd

=> both z and (x-1) is odd

=> since (x-1) is odd, x must be even.

2. y + xz is an odd integer -INSUFFICIENT

Given:

xy + z is odd ...(i)

y + xz is odd ...(ii)

subtracting (ii) from (i)

we get xy + z - y - xz

= (x-1)(y-z) , which should be even

=> either (x-1) is even or (y-z) is even ....insufficient to determine

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you draw a card from a standard deck of 52 cards, replace it, and draw another card. find each probability. (enter your probabilities as fractions.)

Answers

The probabilities when choosing a card of the respective color are

1/26, 1/8, 3/169, 1/676

What are probability and examples?

The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

How do I solve probability?

Multiply the total number of possible outcomes by the total number of occurrences. Divide the entire number of ways the event can occur by the total number of potential outcomes after determining the probability event and its related consequences.

The probabilities are:-

p= (1/13)*(1/2)=1/26

p=(1/2)*(1/4)=1/8

p=(1/13)*(3/13)=3/169

p=(1/52)*(1/13)=1/676

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between 149714971497 and 150015001500, amerigo vespucci embarked on two voyages to the new world. according to vespucci’s letters, the first voyage lasted 434343 days longer than the second voyage, and the two voyages combined lasted a total of 1{,}0031,0031, comma, 003 days. how many days did the second voyage last?

Answers

The number of days that the second voyage last's is 480 days.

Given,

The discrepancy in the length of the two excursions, we are asked to determine how many days the second voyage lasted.

We initially assign variables in order to overcome this issue. Let the duration of the first cruise be f days and the duration of the second expedition be s days.

We are aware that the first journey lasted 43 days longer than the second.

In mathematics, f = 43 plus s. (I)

The cumulative duration of the two journeys was 1003 days. Mathematically:

f + s = 1003........(ii) (ii)

We transform I into ii

43 + s + s = 1003

43 +2s = 1003

2s = 1003 - 43

2s = 960

s = 960/2 = 480 days

That is,

The second voyage lasted about 480 days

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HELP PLEASE!!!! URGENT!!

Answers

Seen your post like 5 times lol I’ll help you in the other one

Which mixed number is represented on the number line?



4
5
4
5

Answers

You need to attach the number line if you want people to answer.

a newborn weighing 5 lb (2250 g) needs to eat 3 oz (90 ml) of formula every 3 hours. to meet this goal, how many ounces of formula per day will the parent need to feed the newborn? record your answer using a whole number.

Answers

it would be 72.94 ounces of formula per day will the parent need to feed the newborn

In this problem, the infant is fed for every 3 hours.

Then, the frequency of feeding for a day would be: (24hours/day) / 3(hours/times)= 6 times/ day.

The volume of feeding for a day that the infant need would be:  = 473.68ml/day

The number of milk for every fed would be: (473.68ml/day)/ (6 times/day)=  72.94 ml/times

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Write this number in word form 84,052

Answers

84,052 = Eighty four thousand fifty two

Answer:

eighty-four thousand fifty-two

Step-by-step explanation:

the way i think about it is writing it as the sum of the digits together.  

80000+4000+50+2

eighty-four thousand fifty-two

Can I get 10 comments in 10 minutes

Answers

Answer: Welp, here it is.

Step-by-step explanation:

I clicked the keyboard :)

hhhhhhhhhhhhhhhhhhhhhhhhh

use the appropriate normal distribution to approximate the resulting binomial distributions. a fair coin is tossed 130 times. what is the probability of obtaining between 70 and 82 tails, inclusive? a) 0.2137 b) 0.1908 c) 0.2154 d) 0.1880 e) 0.2166 f) none of the above.

Answers

The probability of obtaining between 70 and 82 tails is 0.2137, that is, option A.

Here, we are given that a fair coin is tossed 130 times.

Thus,

number of trials ⇒ n = 130

p = P(getting tails in a single toss) = 0.5

mean of a binomial distribution = np

= 130*0.5

= 65

variance = np(1-p)

= 65*0.5

= 32.5

standard deviation = sqrt(variance)

= sqrt(32.5)

= 5.7

Now, x = number of tails

X follows a normal distribution with mean 65 and variance 5.7

P(70 < x < 82)

= P( 69.5 < X < 82.5)  [applying continuity correction]

= P[(69.5-65)/5.7 < Z < (82.5-65)/5.7)]

= P(0.79 < Z < 3.07)

= P(Z < 3.07) - P(Z < 0.79)

= 0.9989- 0.7852

= 0.2137

Thus, the probability of obtaining between 70 and 82 tails is 0.2137, hence, option A. .

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nine new employees, two of whom are married to each other, are to be assigned nine desks that are lined up in a row. if the assignment of employees to desks is made randomly, what is the probability that the married couple will have adjacent desks? (round your answer to the nearest tenth of a percent.)

Answers

The probability that the married couple will have adjacent desks is 0.22.

Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.

Thus, by Fundamental Principle of Counting, the number of possible arrangements where the married coupe has adjacent desks is 80640.

= 8 x 7! x 2

= 80640

Ans the total number of possible arrangements is 362880.

= 9!

= 362880

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

probability = 80640/362880

probability = 0.22

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a person stands on a scale in an elevator. as the elevator starts, the scale has a constant reading of 590 n. as the elevator later stops, the scale reading is 386 n. assume the magnitude of the acceleration is the same during starting and stopping.

Answers

Assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.

What is the magnitude?

The magnitude or size of a mathematical object determines whether it is larger or smaller than other objects of the same kind in mathematics.

Formally speaking, the magnitude of an object is the visible outcome of an ordering—of the class of objects to which it belongs.

So, the weight of the person will be:

The scale measures the passenger's normal upward force as it is applied by the floor.

When moving upward, the most force is generated (when starting an upward trip or ending a downward trip).

When there is a downhill acceleration, the normal force is at its lowest.

For any such circumstance:

∑F y​ =ma y  becomes for starting  +591N−mg=+ma and for stopping      +391N−mg=−ma.

Where a stands for the acceleration's magnitude.

To get rid of a and find mg, add these two simultaneous equations:

+591N−mg+391N−mg=0

OR

982N–2mg=0

Fg​ = mg = 982N/2​ = 491N

Therefore, assuming the weight and magnitude of the person, we can conclude that the weight of the person is 491N.

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Complete question:
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.

What two numbers multiplies to negative 480 and adds to negative 28?​

Answers

Answer:

-40 ,12

Step-by-step explanation:

you will have to look for the factors of 480 that satisfy this condition and for this case , they're -40 and 12

Find the value of x in the trapezoid below. Type only the numerical answer.

Answers

The value x of the trapezoid is 3 units.

How to find the side of a trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides .

The midsegment of a trapezoid is the segment connecting the midpoints of the two non-parallel sides.

The midsegment of a trapezoid is parallel to each base, and its measure is half the sum of the lengths of the bases.

Therefore,

29 = 1 / 2 × (23 + 11x + 2)

29 = 1 / 2 × (25 + 11x)

cross multiply

29 × 2 = 25 + 11x

58 = 25 + 11x

58 - 25 = 11x

33 = 11x

divide both sides by 11

x = 33 / 11

x = 3

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Find the 54th term of the arithmetic sequence -2, -8, -14,

Answers

Answer:

-2n+4

-2×54+4

-108+4

-104

Other Questions
Work with a partner. Supercooling is the process of lowering the temperatureof a liquid or a gas below its freezing point without it becoming a solid. Watercan be supercooled to 86F below its normal freezing point (32F) and stillnot freeze.a. Let x represent the temperature of water. Which inequality represents thetemperature at which water can be a liquid or a gas? Explain your reasoning. The length of the rectangle is 5 cm less than twice its width.the area of the rectangle is 42 cm^2. What is the width of the rectangle help mee please no wrong answer thank uu The government has many obligations to provide services to its tax-paying citizens. If you were in Congress, howwould you balance the need for the government to spend money on necessary things with a prudent approach to controlling the debt and the deficit? Use examples in your answer. determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point o. there are 20 common, naturally occuring amino acids. modify the given ompies of compund 1 to draw the stuctures of 2 and 3 athan's Mom stands beside him while he brushes his teeth, allowing him to complete the tasks alone but prompting him if he skips steps or performs them incorrectly. Nathan is learning to brush his teeth viaA. Backward ChainingB. Forward ChainingC. Total Task Chainingc what 4 are important to consider when identifying the purpose of a speech? Which description is true of parenthetical phrases or clauses?ResponsesA. They contain the subjectB. They separate subjects and verbsC. They are nonessentialD. They are necessary microscopic examination of cerebrospinal fluid reveals gram-positive rods. what is the organism? group of answer choices streptococcus listeria naegleria haemophilus neisseria The area of the Okhotsk Sea is 1.583 10^6 km^2. The area of the Indian Ocean is 7.3556 10^7 km^2. Find the total area. Write the final answer in scientific notation with the correct number of significant digits. 8.9386 10^13 km2 8.939 10^13 km2 7.5139 10^7 km2 7.514 10^7 km2 insurance that protects the lender in the event that the borrower does not repay the mortgage is called: Write a short paragraph that explains the central idea of the article. Use at least two details from the article to support your response.Breaking down World War II in graphics is the text i need a short paragraph (1 point) 5 dice of different colors are rolled, and the number coming up on each die is recorded. how many different outcomes are possible? During the meeting, kristof asked, "where is the product typically bought by customers in the international market segments?" what element of the marketing mix is he addressing?. a process whereby an infant begins to draw apart from the symbiotic bond with mother and develop autonomous functioning is known as the nurse is caring for clients on a neurological intensive care unit. which client should be assessed first? question 6 options: the client recovering from a motor vehicle accident (mva) diagnosed with increased intracranial pressure whose glasgow coma scale (gcs) went from 11 to 14 the quadriplegic client diagnosed with a c-6 sci who has bradycardia, hypotension, and hyperflexia the client with a brainstem herniation whose big tow moves toward the top surface of the foot and the other toes fan out after the sole of the foot has been firmly stroked the 20-year-old client diagnosed with west nile virus who has a temperature of 101.2f and generalized body aches The table shows information about themasses of some dogs.a) Work out the minimum number of dogsthat could have a mass of more than 26 kgb) Work out the maximum number of dogsthat could have a mass of more than 26 kgMass, x (kg)0x1010x2020x3030x40Frequency48115 in the gi tract, a food bolus is converted into a semiliquid mass of partly digested food and digesteive secretions known as a cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 132 inches. find the dimensions of the package of maximum volume that can be sent. (the cross section is circular.)