URGENT !!!!


A greengrocer has 38 lb of carrots when he opens on Monday morning. During the dayhe gets a delivery of 60 lb of carrots and sells 29 lb of the carrots. How many pounds ofcarrots are left when he closes on Monday evening?

Answers

Answer 1

He has 69 lb of carrots left when he closes


Related Questions

write the statement for 4p = 8​

Answers

Answer:

See below

Step-by-step explanation:

The statement that can be written for 4p = 8 is:

=> Four times a certain number equals eight.

A parallelogram has coordinates A(1, 1), B(5, 4), C(7, 1), and D(3, -2). What are the coordinates of parallelogram A′B′C′D′ after a 180° rotation about the origin and a translation 5 units to the right and 1 unit down? I need Help

Answers

Hey there! I'm happy to help!

First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).

Let's convert this below

A: (1,1)⇒(-1,-1)

B: (5,4)⇒(-5,-4)

C: (7,1)⇒(-7,-1)

D: (3,-2)⇒(-3,2)

Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.

A: (-1,-1)⇒(4,-2)

B: (-5,-4)⇒(0,-5)

C: (-7,-1)⇒(-2,-2)

D: (-3,2)⇒(2,1)

Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)

Now you know how to find the coordinates of translated figures! Have a wonderful day! :D

2. The half life of uranium-232 is 68.9 years. a) If you have a 100 gram sample, how much would be left after 250 years? b) If you have a 100 gram sample, how long would it take for there to be 12.5 grams remaining?

Answers

Step-by-step explanation:

The amount left is:

A = A₀ (½)^(t/T)

where A₀ is the initial amount,

t is the amount of time,

and T is the half life.

a) A = 100 g (½)^(250 yr / 68.9 yr)

A = 8.09 g

b) 12.5 g = 100 g (½)^(t / 68.9 yr)

0.125 = (½)^(t / 68.9 yr)

3 = t / 68.9 yr

t = 206.7 yr

In the diagram AB=AD and

Answers

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS congruence theorem, if two triangles have 2 corresponding sides that are equal, and also have one included corresponding angle that are equal to each other in both triangles, both triangles are regarded as congruent.

Given ∆ABC and ∆ADC in the question above, we are told that segment AB ≅ AD, and also <BAC ≅ <DAC, the additional information that is necessary to prove that ∆ABC and ∆ADC are congruent, according to the SAS theorem, is segment AC ≅ segment AE.

This will satisfy the requirements of the SAS theorem for considering 2 triangles to be equal or congruent.

Con proceso por favor

Answers

Answer:se

Step-by-step explanation:

Classify the triangle with angles measuring 1130, 47°, and 20°.
A. Straight
B. Right
C. Acute
D. Obtuse

Answers

Answer:

D. Obtuse

Step-by-step explanation:

Answer:

You typed that incorrectly.  That first angle should be 113 degrees.

It would be an obtuse triangle.

Step-by-step explanation:

45% of 80.374 is a number between

Answers

Answer:

36.1683

Step-by-step explanation:

45*80.374/100=

A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 11 students, he found the average time was 4.52 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.1 level of significance. Assume normality. (can you please show how to do this without a calculator or excel i just dont want answer but want to know how to do it).
a) What are the appropriate null and alternative hypotheses?
A) H0: μ = 5 versus Ha: μ < 5
B) H0: μ = 5 versus Ha: μ ≠ 5
C) H0: x = 5 versus Ha: x ≠ 5
D) H0: μ = 5 versus Ha: μ > 5
b) What is the test statistic? Give your answer to four decimal places.
c) What is the P-value for the test? Give your answer to four decimal places.
d) What is the appropriate conclusion?
A) Fail to reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
B) Reject the claim that the mean time is 5 minutes because the P-value is larger than 0.01.
C) Reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.
D) Fail to reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.01.

Answers

Answer:

A) Null Hypothesis;H0: μ = 5

Alternative Hypothesis;Ha: μ ≠ 5

B) test statistic = -2.1226

C) p-value = 0.0598

D) Option A is correct

Step-by-step explanation:

We are given;

x = 4.52 minutes

s = 0.75 minutes

μ = 5 minutes

n = 11

degree of freedom = n - 1 = 11 - 1 = 10

A) The hypotheses are;

Null Hypothesis;H0: μ = 5

Alternative Hypothesis;Ha: μ ≠ 5

B) t-statistic = (x - μ)/(s/√n)

(4.52 - 5)/(0.75/√11) = -2.1226

C) From the t-score calculator results attached, the p-value is approximately 0.0598.

D) The P-value of 0.0598 is is greater than the significance level of 0.01, thus we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant. So option A is correct.

rectangular field has a total perimeter of 128 feet. The width is
A
24 feet less than the length. What are the dimensions of the field?

Answers

Answer:

The length is 44 feetThe width is 20 feet

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

Perimeter = 128 feet

The width is 24 feet less than the length is written as

w = l - 24

128 = 2l + 2( l - 24)

128 = 2l + 2l - 48

Group like terms

4l = 176

Divide both sides by 4

l = 44

The length is 44 feet

Substitute l = 44 into w = l - 24

w = 44 - 24

w = 20

The width is 20 feet

Hope this helps you

less than 0 but greater than (−5)

Answers

Answer:

-5 < x < 0

Step-by-step explanation:

A cylinder has a volume of 200 mm3 and a height of 17 mm.

a) The volume formula for a cylinder is v = pie r squareℎ. Isolate for the variable r in this formula.

b) Using the equation where you isolated for r in part a, find the radius of the cylinder. Round your answer to the nearest hundredth. (1 mark)​

Answers

Answer:

The radius of the cylinder is 1.93mm.

Step-by-step explanation:

1) Formula to find the missing radius : V= pi r^2 (h)

( V= volume, pi=3.14 r=radius, h= height)

2) Plug all the give variables into the formula: 200=pi r^2 (17)

3) Multiply pi with 17 and then round it to the nearest hundredth which you get  53.401707511 -> 53.41, now your equation is: 200= 53.41 r^2

4) Next you want to isolate the r^2 by dividing both sides by 53.41

200/53.41= 53.41r^2/53.41 ( 3.74461711 round to the nearest hundredth --> 3.74)  ---> 3.74=r^2

5) Now you have to square both sides to get rid of that exponent  : squared 3.74 = squared r^2

6) Your equation would be 1.933907961 = r, round that whole decimal to the nearest hundredth and you will get 1.93 ( 19.3 = r)

7) So the radius of the cylinder given the volume is 200 mm^3 and a height of 17 mm is 1.93 mm.

what is the surface area of a cylinder height is 4 cm and diameter is 5 cm

Answers

Answer:

20cm it's is the answers

Step-by-step explanation:

5*4=20

Integrate the following: ∫[tex]5x^4dx[/tex]

A. [tex]x^5+C[/tex]
B. [tex]x^5[/tex]
C. [tex]5x^5+C[/tex]
D. [tex]5x^5[/tex]

Answers

Answer:

A. [tex]x^5+C[/tex]

Step-by-step explanation:

This is a great question! The first thing we want to do here is to take the constant out of the expression, in this case 5. Doing so we would receive the following expression -

[tex]5\cdot \int \:x^4dx[/tex]

We can then apply the power rule " [tex]\int x^adx=\frac{x^{a+1}}{a+1}[/tex] ", where a = exponent ( in this case 4 ),

[tex]5\cdot \frac{x^{4+1}}{4+1}[/tex]

From now onward just simplify the expression as one would normally, and afterward add a constant ( C ) to the solution -

[tex]5\cdot \frac{x^{4+1}}{4+1}\\[/tex] - Add the exponents,

[tex]5\cdot \frac{x^{5}}{5}[/tex] - 5 & 5 cancel each other out,

[tex]x^5[/tex] - And now adding the constant we see that our solution is option a!

Answer:

Answer A

Step-by-step explanation:

Use the property of integrals. You now have [tex]5 x\int\limits\,x^{4}dx[/tex] where the first x next to the 5 stands for multiplication. Let's evaluate it. We get [tex]5 (\frac{x^{5} }{5})[/tex]. From here, we can simplify this into [tex]x^{5}[/tex]. Add the constant of integration, which will give you the answer of [tex]x^{5} + C[/tex].

need some help thxx ;)

Answers

Answer:

DEA

Step-by-step explanation:

The area of the region under the curve of the function f(x)=5x+7 on the interval [1,b] is 88 square units, where b>1. What is the value of b.

Answers

Answer:

[tex]\displaystyle b = 5[/tex]

General Formulas and Concepts:

Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^b_1 {5x + 7} \, dx = 88[/tex]

Step 2: Solve

[Integral] Rewrite [Integration Property - Addition/Subtraction]:               [tex]\displaystyle \int\limits^b_1 {5x} \, dx + \int\limits^b_1 {7} \, dx = 88[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]:               [tex]\displaystyle 5 \int\limits^b_1 {x} \, dx + 7 \int\limits^b_1 {} \, dx = 88[/tex][Integrals] Integration Rule [Reverse Power Rule]:                                     [tex]\displaystyle 5 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^b_1 + 7(x) \bigg| \limits^b_1 = 88[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           [tex]\displaystyle 5 \bigg( \frac{b^2}{2} - \frac{1}{2} \bigg) + 7(b - 1) = 88[/tex]Simplify:                                                                                                         [tex]\displaystyle \frac{5b^2}{2} - \frac{5}{2} + 7b - 7 = 88[/tex]Isolate:                                                                                                           [tex]\displaystyle \frac{5b^2}{2} + 7b = \frac{195}{2}[/tex]Solve:                                                                                                             [tex]\displaystyle b = \frac{-39}{5} ,\ 5[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:5

Step-by-step explanation:

got it right

Please tell me if I'm right or wrong! No work needed! Brainliest will be given!

Answers

Answer:

The first one is correct

The second one is also correct

The third is also correct

Congrats!

Answer:

1) [tex]\boxed{Option \ B}[/tex]

2) [tex]\boxed{Option \ B}[/tex]

3) [tex]\boxed{Option \ B}[/tex]

You're totally correct, Man! :)

Step-by-step explanation:

Question 1:

[tex](6b^2-4b+3)-(9b^2-3b+6)\\Resolving \ the\ brackets\\6b^2-4b+3-9b^2+3b-6\\Combining \ like \ terms\\6b^2-9b^2-4b+3b+3-6\\-3b^3-b-3[/tex]

Question 2:

[tex](b+6)(b-3)\\Using \ FOIL\\b^2-3b+6b-18\\b^2+3b-18[/tex]

Question 3:

[tex](4x-3)(6x-1)\\Using \ FOIL\\24x^2-4x-18x+3\\24x^2-22x+3[/tex]

6th grade math , help me please :)

Answers

Answer:B

Step-by-step explanation:

f(x) = x + 2
g(x) = x - 4
(fg)(x) =

Answers

Answer:

Step-by-step explanation:pleased to help u....

Line B passes through the points (5, 10) and (0, 0). What is the slope of the line perpendicular to line B?

Answers

Answer:

The line that is perpendicular to B has a slope of -1/2

Step-by-step explanation:

First find the slope of line B

m = ( y2-y1)/(x2-x1)

    = (10-0)/(5-0)

    = 10/5

    = 2

Lines that are perpendicular have slopes that multiply to -1

m * 2 = -1

m = -1/2

The line that is perpendicular to B has a slope of -1/2

Answer:

-1/2x

Step-by-step explanation:

Hey there! :)

Well to find the slope of line B we'll use the following formula.

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

We'll use the points (0,0) and (5,10),

10 - 0 = 10

5 - 0 = 5

Slope = 2x

The slopes of 2 perpendicular lines are reciprocals of each other,

meaning if the slope of line B is 2x then its perpendicular lines slope is -1/2x.

Hope this helps :)

68. A hexagon has two sides each of length 3x inches. It has three sides each of length 2x inches. The sixth side has a length of 15 inches. If the perimeter of the hexagon is 135 inches, what is the value of x?


E.4
F.5
G. l0
H. 15

Answers

Answer:

G 10

Step-by-step explanation:

2*3x+3*2x+15=135 inches

6x+6x=120 inches

12x=120 inches

x= 10 inches

Please answer soon. Include Statement and Reason if possible.
Given: ΔABC, AC = BC, AB = 3
CD ⊥ AB, CD = √3
Find: AC

Answers

Answer:  AC = sqrt(21)/2

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

Explanation:

Triangle CDA is congruent to triangle CDB. We can use the HL (hypotenuse leg) congruence theorem to prove this. This only works because we have two right triangles.

Since CDA and CDB are congruent, this means their corresponding pieces are the same length. Specifically AD = DB, so

AD+DB = AB

AD+AD = 3

2*AD = 3

AD = 3/2 = 1.5

For triangle CDA, we have AD = 3/2 = 1.5 and CD = sqrt(3). We can use the pythagorean theorem to find the missing side AC

a^2 + b^2 = c^2

(AD)^2 + (CD)^2 = (AC)^2

(3/2)^2 + (sqrt(3))^2 = (AC)^2

9/4 + 3 = (AC)^2

(AC)^2 = 9/4 + 3

(AC)^2 = 9/4 + 12/4

(AC)^2 = 21/4

AC = sqrt(21/4)

AC = sqrt(21)/sqrt(4)

AC = sqrt(21)/2

This is the same as writing (1/2)*sqrt(21) or 0.5*sqrt(21)

4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7​

Answers

Answer:

[tex]1 \frac{1}{4} [/tex]

Step-by-step explanation:

[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]

To divide by a fraction, multiply the reciprocal of that fraction

[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]

Reduce the number with the G.C.F 7

[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]

Reduce the numbers with the G.C.F 17

[tex] \frac{5}{6} \times \frac{3}{2} [/tex]

Reduce the numbers with the G.C.F 3

[tex] \frac{5}{2} \times \frac{1}{2} [/tex]

Multiply the fraction

[tex] \frac{5}{4} [/tex]

In mixed fraction:

[tex]1 \frac{1}{4} [/tex]

Hope this helps..

Good luck on your assignment...

The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.

Answers

Answer:

We have the measure of both angles as  55 degrees and 35 degrees

Step-by-step explanation:

We know that there are three angles in a right-angled triangle. One of which is 90. FOr now, the other two are unknown, so we would designate them to be x and y.

We now set up an equation using the information we are given about the problem.

From this statement "The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle." we can set up the following equation:

x =2y -15 -------- equation 1

similarly, we know that the sum of angles in a triangle = 180 degrees. Hence, we can use this to set up another equation as follows:

x + y + 90 = 180

x+ y = 90 ------------- equation 2

we can now solve the two equations simultaneously as

x -2y =-15

x+ y = 90

from this, we have that

x = 55 and y = 35

We have the measure of both angles as  55 degrees and 35 degrees

[PLEASE HELPP] write an equation that represents the area Bruce covered (y) in terms of the number of tiles he used, x?

Answers

Answer:

y=(x/6)

Step-by-step explanation

divide every input by 6 to get the output

NEED HELP ASAP!!
What is the equation of the line that is parallel to the
given line and has an x-intercept of -3?
O y = x + 3
O y = ?X + 2
Oy=-3x + 3
y=-3x+2

Answers

Answer:

B

Step-by-step explanation:

The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

We have a graph.

So, slope of line in graph is

= (-1-1)/ (0.-3)

= -2/ (-3)

= 2/3

and, we know that two parallel line have same slope.

so, the slope of parallel line is 2/3 and the x intercept is -3.

So, the Equation line is y= 2/3 x  + b

0 = 2/3 (-3) +b

b= 2

Thus, the required equation is y= 2/3x + 2.

Learn more about Slope here:

https://brainly.com/question/2863474

#SPJ5

√9m^2n^2 + 2√m^2n^2 - 3mn

Answers

Answer:

I think it is

Step-by-step explanation:

Answer:

5n√2m^ - 3mn

Step-by-step explanation:

Six identical coins are tossed. How many possible arrangements of the coins include three heads and three tails?​

Answers

Answer:

The possible arrangement= 18 ways

Step-by-step explanation:

Six identical coin are tossed.

Coin has only a tail and a head.

In how many possible ways can the arrangement be 3 head and 3 tail.

The possible arrangement= (3! * 3!)/2

The reason for dividing by two because coin has two face.

The possible arrangement= (3! * 3!)/2

The possible arrangement=( 6*6)/2

The possible arrangement= 36/2

The possible arrangement= 18 ways

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x3 + 3x2 − 72x

Answers

Answer:

x = -6 and x = 4

Step-by-step explanation:

In math, the critical points of a function are the points where the derivative equals zero.

So, first we will find the derivative of the function. The derivative is:

[tex]f'(x)=3x^2 +6x-72[/tex]

Now, we are going to make the derivative equal zero and find the answers of the equation.

[tex]3x^2 +6x-72=0\\3(x^2 +2x-24)=0\\3(x+6)(x-4)=0\\[/tex]

So we have that the critical points are the answers to this equation:

[tex]x+6= 0 \\x= - 6[/tex]

and

[tex]x-4=0\\x=4[/tex]

Thus, the critical points are x=-6 and x=4

Using it's concept, it is found that the critical numbers of the function are:

x = -6 and x = 4.

The critical numbers of a function f(x) are the values of x for which it's derivative is zero, that is:

[tex]f^{\prime}(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = x^3 + 3x^2 - 72x[/tex]

The derivative is:

[tex]f^{\prime}(x) = 3x^2 + 6x - 72[/tex]

[tex]f^{\prime}(x) = 3(x^2 + 2x - 24)[/tex]

Then:

[tex]f^{\prime}(x) = 0[/tex]

[tex]3(x^2 + 2x - 24) = 0[/tex]

[tex]x^2 + 2x - 24 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 1, b = 2, c = -24[/tex], which we have to solve.

[tex]\Delta = 2^2 - 4(1)(-24) = 100[/tex]

[tex]x_{1} = \frac{-2 + \sqrt{100}}{2} = 4[/tex]

[tex]x_{2} = \frac{-2 - \sqrt{100}}{2} = -6[/tex]

The critical numbers of the function are x = 4 and x = -6.

A similar problem is given at https://brainly.com/question/16944025

What is the equation perpendicular to -x+y= 7 and passes through (-1,1)

Answers

Answer:

Step-by-step explanation:

First , let us rewrite the given equation into y= mx+b format

.y= -x +7

Slope is -1

Slope of the line perpendicular to the given equation is -(-1) ie., 1

Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b

1 = -1 +b

2 = b

Equation of the line perpendicular to the given equation and passing through (-1,1) is

y=x +2

what is the slope of the line with the equation y= -2x - 1? A -2 B -1 C 2 D 1

Answers

Answer:

The answer is "A'' -2 because anything next to the letter x is the slope

Step-by-step explanation:

The equation to slops is y=mx+b

m= slope

b= y intercept

Slope = -2

Y intercept = ( 0 , -1)

Step-by-step explanation:

Hope this helps. Your answer would be A

Other Questions
Durante las vacaciones, fuimos a ________ de dos horas por el parque. una extranjera una postal un local un recorrido Which best describes a neutralizationreaction?A) a reaction between an acid and a baseB) a reaction between two acidsC) a reaction between a base and a saltD) a reaction between two salts Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds out he is off course and 160 miles from island B. What bearing should he turn to, so he is heading to island B? The slope of the line below is 5/7 Write a point-slope equation of the lineusing the coordinates of the labeled point.O A. y+2 --$(x+6)O B. y-6--(x-2)O C. y+6 -- (x + 2)O D, y-2 - (x - 6) Find the missing angle measures in the given rhombus. If there were a collaborative discussion based on Fast Food Nation, participants would discuss ideas from the book. Consider these statements from a discussion of ideas from Fast Food Nation. Then, determine whether each is a fact or an opinion. please help me with this problem What is the coefficient of the second term in the expression 12x+xy-7y? FIRST GETS BRAINLLEST What is the perimeter of the track, in meters? Use = 3.14 and round to the nearest hundredth of a meter. Nine less than five times a number is three more than twice the number? Pecans sell for 7.95 per round. How much will 3.2 pounds cost? NEED STEP BY STEP EXPLANATION. Why is [tex]a^{2}*a^{-6}* a^{6}=a^{5}[/tex] correct? Which of the following options have the same value as 15 percent of 20? Jess works for a corporation as a research psychologist. The corporation recently revised its policies to require that researchers not provide informed consent to participants. The American Psychological Association (APA) would _____ 12 miles below sea level Write the molecular equation and net ionic equation for the reaction of hydroiodic acid and potassium hydroxide. Include phases (states). Enter the formula for water as H2O . Bill shops in a candy store where chocolate bars are $1 and lollipops are $0.50 He can spend at most $5 and he wants to buy at least 3 more lollipops than chocolate bars. Which of the following graphs represent the possible candy combinations? Explain three ways in which the humansperm cell is adapted to its function. Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.Required:a. What percentage of time is Judy idle? b. How much time, on average, does a student spend waiting in line? c. How long is the (waiting) line on average? d. What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? Adult men have heights that a normally distributed with a mean of 69.5 inches and a standard deviation of 2.4 inches. Adult women have heights that a normally distributed with a mean of 63.8 inches and a standard deviation of 2.6 inches. Between a man with a height of 74 inches and a women with a height of 70 inches, who is more unusually tall within his or her respective sex ?