The courtyard outside East Middle School is in the shape of a rectangle and half-circle.
What is the approximate area of the courtyard?

The Courtyard Outside East Middle School Is In The Shape Of A Rectangle And Half-circle.What Is The Approximate

Answers

Answer 1

Answer:

The correct option is the third one counting from the top. (5892 m^2)

Step-by-step explanation:

First, we need to remember that:

For a rectangle of length L and width W, the area is:

A = L*W

For a circle of diameter D, the area is:

A = pi*(D/2)^2

Where pi = 3.14

In the image, we can see a rectangle and half a circle, the total area of the image will be equal to the area of the rectangle plus the area of the half circle.

In the image, we can see a rectangle of length L = 100m and width W = 50m

Then the area of the rectangle is:

A = 100m*50m = 5000m^2

And we can see that for the half-circle the diameter is D = 50m

Note that the area of a half-circle is half of the area of a complete circle, then the area of that half-circle is:

A = (1/2)*(3.14*(50m/2)^2) = 981.25 m^2

If we add these two areas we get:

Total area =  5000m^2 + 981.25 m^2 = 5981.25 m^2

If we round it up, we get:

Total area = 5982 m^2

The correct option is the third one counting from the top.


Related Questions

The two-way frequency table contains data about students' preferred exercise.



Enjoys swimming Enjoys cycling Row totals

Likes running 28 62 90

Does not like running 46 64 110

Column totals 74 126 200


What is the joint relative frequency of students who do not like to run but enjoy cycling?

64%

55%

32%

23%

Answers

The joint relative frequency for those students who don't like to run, but however enjoy cycling, is C. 32%.

How to find the joint frequency ?

The joint frequency for students who like cycling, but do not like running, can be found by the formula :
= Number of students who enjoy cycling but don't enjoy running / Number of students in total

Number of students who enjoy cycling but don't enjoy running = 64

Number of students in total = 200

The joint frequency is :

= 64 / 200 x 100%

= 0.32 x 100 %

= 32 %

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You buy 9 granola bars for a camping trip. Each bar costs $0.95. What
is the total cost of 9 granola bars before tax?

Answers

Answer:

Step-by-step explanation: 9 multiplied by .95 = $8.55 before tax

A circle with center w is shown in the figure below.

Answers

Radius = TW

Diameter = TX

Chord = UV

The length of TX is 6 units.

What is a circle?

A circle is a two-dimensional figure with a radius and circumference of 2 x pi x r.

The area of a circle is given as πr².

We have,

From the figure:

Diameter = TX

Radius = TW or WX or WY

Chord = UV

WY = 3 units

TX = TW + WX = 3 + 3 = 6 units.

Thus,

TX is 6 units.

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If x varies directly as y, find x when y = 8 a) x = 6 when y = 32 b) x = 14 when y = -2

Answers

a) The value of x is 42.6 when k =16/3 is directly proportional to y.

b) The value of x is -56 when k is -7  is directly proportional to y.

What kind of variation is one where x and y are directly proportional?

If x = ky for some constant k can be used to indicate the relationship between the variables y and x, then we may say that y varies directly with y or that x is directly proportional to y.

x varies directly as y

x α y

x = ky

a) x=6 ; y = 32

x = ky

6 = k(32)

k = 16/3

if y = 8

then,

x = (16/3) * 8

= 128/3

x = 42.6

Hence, the value of x is 42.6 when k =16/3 is directly proportional to y.

b) x= 14 and y = -2

x = ky

14 = k(-2)

k = -7

if y = 8

then,

x = ky

x= (-7) 8

x = -56

Hence, the value of x is -56 when k is -7  is directly proportional to y.

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a duck flew at 18 miles per hour for 3 hours than at 15 miles per hour for 2 ours how far did the duck fly in all

Answers

The distance the duck fly in all is 99 miles

How to determine how far the duck fly in all

From the question, we have the following parameters that can be used in our computation:

Distance 1: 18 miles per hour for 3 hoursDistance 2: 15 miles per hour for 2 hours

The distance covered in all can be calculated as

Distance = The sum of the product of speed and time

Substitute the known values in the above equation, so, we have the following representation

Distance = 18 * 3 + 15 * 2

Evaluate the products

This gives

Distance = 54 + 45

Evaluate the sum

Distance = 99 miles

Hence, the distance is 99 miles

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Find the Derivative of 1/x+2

Answers

Answer: 2x+1

                  x

Step-by-step explanation:

Alex biked a 48-mile trail in 4 hours. For the first half of the time, he biked twice as fast as he did the second half of the time. What speed did Alex bike the first half?

Answers

Alex's speed in the first half of the time is 12 miles per hour

How t find the speed of biking

Information from the problem include:

For the first half of the time, Alex biked a 48-mile trail in 4 hours.

he biked twice as fast as he did the second half of the time.

Average speed is calculated using the ratio of distance to time spent

this is represented by the formula

= distance / time

The speed for the first half is  solved as below

= 48 mile / 4 hours

= 12 mile / hours

= 12 mph

speed for the first half is 12 mph

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Does anyone know the answer for this?

Answers

The Venn diagram has been drawn and the product of LCM and GCF are the same as 24 x 36.

What is a Venn diagram?

A Venn diagram is a pictorial representation of data represented in a circle.

The intersection parts of the circle represent the commonality of both sets.

As per the given, 24 and 36

The factors of 24 are as 2³ × 3

The factors of 36 are as 2² × 3²

The common factors 2² × 3

The LCM of 24 and 36 is 72 and the GCF is 12.

LCM x GCF = 24 x 12

72 x 12 = 24 x 12

864 = 864

Hence "After drawing a Venn diagram, it was discovered that the LCM and GCF product equals 24 x 36.".

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Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
f ''(x) = 2x + 4ex

Answers

After integration, the required function f is (2x³ - sin (x) + Cx + D).

What is the integration of 'xⁿ' and 'sin (x)'?

[tex]\int {x^{n} } \, dx = \frac{x^{n+1} }{n+1} + C\\\\\\\int {sinx} \, dx = -cosx + C[/tex]

Given, f''(x) = 12x + sin x

Therefore,

[tex]\int {f''(x)} \, dx \\\\=\int {f'(x)} \, dx \\\\\\= \int{12x + sin x} \, dx + C\\\\= 6x^{2} - cosx + C\\[/tex]

Again, f'(x) = 6x - cos (x) + C

Therefore,

[tex]\int {f'(x)} \, dx\\ \\=\int {f(x)} \, dx \\\\= \int {6x^{2} - cosx + C } \, dx \\\\= 2x^{3} - sinx + Cx + D[/tex]

Therefore, the required function is (2x³ - sin (x) + Cx + D).

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If (x+2) is a factor of

Answers

Answer: a=3 and b=1

Step-by-step explanation:

Let p(x)=x 2 +ax+2b

If x+2 is a factor of p(x)

Then by factor theorem

p(−2)=0

⇒(−2)

2

+a(−2)+2b=0

⇒4−2a+2b=0

⇒a−b=2   ---(i)

Also given that a+b=4    ---(ii)

Adiing (i) and (ii) we get

2a=6

⇒a=3

putting a=3 in (i) we get

a−b=2

⇒3−b=2

⇒b=1

Therefore we get a=3 and b=1

a persons weight varies directly with gravity if a person weights 180 pounds on earth they will weigh only 30 pounds on the moon if harsh weights 54 pounds on earth how much would he weight on the moon

Answers

The weight of harsh on the moon if he weighs 54 pounds on earth is 9 pounds

How to calculate direct variation?

Weight varies directly with gravity

Let

Weight of a person = w

Gravity = g

So,

w = k × g

Where,

k = constant of proportionality

If w = 180 pounds and g = 30 pounds

w = k × g

180 = k × 30

180 = 30k

divide both sides by 30

k = 180/30

k = 6

If w = 54 pounds g = ?

w = k × g

54 = 6 × g

54 = 6g

divide both sides by 6

g = 54/6

g = 9 pounds

Therefore, harsh weighs 9 pounds on the moon.

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Convert the measurement. 28.4 grams ≈ ounces

Answers

Answer: 1.0017805194 ounces

Step-by-step explanation:

To change 28.4 g to oz divide the mass in grams by 28.349523125. The 28.4 grams to ounces formula is [oz] = [28.4] / 28.349523125. Thus, we get (all results rounded to 2 decimals):

28.4 g to oz = about 1 oz

28.4 g to ounces =  about 1 ounces

28.4 grams to ounces = about  1 oz

Twenty-eight point four grams to ounces equal 1 international avoirdupois ounces, the unit used to measure grocery products (mass) in retail stores in the United States for example.

HOPE THIS HELPS 189328 :)!

5x^2-13+6=0
i need helppp

Answers

Answer:

answer is 2.5

Step-by-step explanation:

Question 12 options:
Nick determines the remainder of

, using the remainder theorem.

How does she proceed to the correct answer?

Fill in the blanks from the work bank below: (do not enter spaces)

x = 1 x = -1 x = 0 -23 -19 -15 -29

Nick evaluates the numerator of the rational expression when

. He concludes that the remainder of the division is

Answers

The input value for the expression is 1 and the remainder is -15.

What is the remainder theorem?

The Remainder Theorem begins with an unnamed polynomial p(x), where "p(x)" simply means "some polynomial p with variable x". The Theorem then discusses dividing that polynomial by some linear factor x a, where an is simply a number.

Given polynomial is 5x⁴⁵ - 3x¹⁷ +2x⁴ - 19 and is divided by x + 1. Find the value of the polynomial at 1 and then calculate the remainder by synthetic solution.

F(x) = 5x⁴⁵ - 3x¹⁷ +2x⁴ - 19

F(1) = 5 - 3 + 2 - 19

F(1) = -19 + 4

F(1) = -15

The remainder will be calculated by synthetic calculation,

1 __5 ___-3___2_____-19

 |

 | ______5___ 2______4          

      5         2      4          -15

The remainder of the given expression is -15.

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Write an equation for the line through the given point with the given slope in slope-intercept form. (10, –9); m = –2

Please explain.

Answers

Considering the definition of a line, the equation of the line that passes through the point (10, -9) and has a slope of -2 is y= -2x +11.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this case

In this case, you know:

The line has a slope of -2.The line passes through the point (10, -9).

Substituting the value of the slope m and the value of the point y=mx+b, the value of the ordinate to the origin b is obtained as follow:

-9= -2×10 + b

-9= -20 + b

-9 + 20= b

11= b

Finally, the equation of the line is y= -2x +11.

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Here we show that function defined on an interval value property cannot have (a; b) and satisfying the intermediate removable or (a) jump discontinuity. Suppose has & jump discontinuity at Xo € (a,b) and lim f (x) lim f (x) xx0 {ix0 Choose 0 such that lim f (x) < 0 < lim f (x) and 0 + f(xo) xI*o Xx0 In Exercise & we showed there is interval [xo 0,.Xo) such that f(x) < 0 if Xe [xo 6,xo): Likewise, there an interval (xo, Xo + 6] such that f(x) > 0 if xe(xo, Xo + 6]. Conclude that does not satisly the intermediate value property on [xo 6,xXo + 6]. (6) Suppose has a removable discontinuity at Xo € (a,b) and a = lim f(x) < f(xo) Show that there is an interval [xo = 6,Xo) such that f(x)< a+[f(xo) - &] if x e[xo 6,Xo]: Conclude that f does not satisfy the intermediate value property

Answers

f cannot have a jump discontinuity at [tex]$x_0 \in(a, b)$[/tex] and  [tex]$$ \lim _{x \uparrow x_0} f(x) < \lim _{x \mid x_0} f(x) .$$[/tex]

f cannot have a removable discontinuity at [tex]$$x_0 \in(a, b) $$[/tex] and [tex]\alpha=\lim _{x \rightarrow x_0} f(x) < f\left(x_0\right)[/tex]

Let f be a function defined on (a, b) satisfies intermediate value property.

Claim: f ca not have removable on jump discontinuity.

Suppose f has a jump discontinuity at [tex]$x_0 \in(a, b)$[/tex]

We take [tex]$\theta$[/tex] such that

[tex]$$\lim _{x \rightarrow x_0} f(x) < \theta < \lim _{x \downarrow x_0} f(x) \text { and } \theta \neq f\left(x_0\right)$$[/tex]

Now there exist [tex]$\delta > 0$[/tex] such that [tex]$f(x) < \theta$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0\right)$[/tex] and [tex]$f(x) > \theta$[/tex] for all [tex]$x \in\left(x_0, x_0+\delta\right]$[/tex]

Now [tex]$f\left(x_0-\delta\right)[/tex][tex]< \theta < f\left(x_0+\delta\right)$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0+\delta\right] \backslash\left\{x_2\right\}$[/tex] and [tex]$f\left(x_0\right) \neq \theta$[/tex].

Therefore the point [tex]$\theta$[/tex] has no preimage under f

that is, there does not exists [tex]$y \in\left[x_0-\delta, x_0+\delta\right][/tex] for which

[tex]$$f(y)=\theta[/tex] because [tex]\left\{\begin{array}{l}y=x_0 \Rightarrow f(y) \neq \theta \\y > x_0 \Rightarrow f(y) > \theta \\y < x_0 \Rightarrow f(y) < \theta\end{array}\right.$$[/tex]

Therefore f does not satisfies intermediate value property on [tex]$\left[x_0-\delta, x_0+\delta\right]$[/tex],

Hence f does not satisfies IVP on (a, b) which is not possible because we assume f satisfies IVP on (a, b),

Therefore f can not have a jump discontinuity.

Suppose f has a removable point of discontinuity at [tex]$x_0 \in(a, b)$[/tex],

Let [tex]$\alpha=\lim _{\alpha \rightarrow x_0} f(x)$[/tex],

Let [tex]\alpha < f\left(x_0\right)$[/tex] so [tex]$f\left(x_0\right)-\alpha > 0$[/tex].

Now [tex]$\lim _{x \rightarrow x_0} f(x)=\alpha$[/tex] then [tex]\exists$ \delta > 0$[/tex] such that

[tex]$$\begin{aligned}& |f(x)-\alpha| < \frac{f\left(x_0\right)-\alpha}{2} \text { for all } x \in\left\{x_0-\delta, x_0-\alpha\right]-\left\{x_0\right\} \\& \Rightarrow \quad f(x) < \alpha+\frac{f\left(x_0\right)-\alpha}{2} \text { for all } x \in\left[x_0-\delta, x_0+\delta\right]-\left\{x_0\right\}\end{aligned}$$[/tex]

So [tex]$f(x) < \frac{f\left(x_0\right)+\alpha}{2}$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0\right]-\left\{x_0\right\}$[/tex]

Now [tex]$f\left(x_0\right) > \alpha$[/tex].

And  [tex]$f(x) < \frac{f\left(x_0\right)+\alpha}{2} < f\left(x_0\right)$[/tex] for all [tex]$x \in\left[\left(x_0 \delta, x_0\right)\right.$[/tex]

Let [tex]$\mu=\frac{f\left(x_0\right)+\alpha}{2}$[/tex].

Then there does not exist [tex]$e \in\left[x_0-\delta, c\right]$[/tex] such that [tex]$f(c)=\mu$[/tex]

Because for [tex]$e=x_0 \quad f(e) > \mu$[/tex]

                for [tex]$c < x_0 \quad f(c) < \mu$[/tex].

Therefore f does not satisfy IVP on [tex]$\left[x_0-\delta_1 x_0\right]$[/tex] which contradict our hypothesis,

therefore [tex]$\alpha \geqslant f\left(x_0\right)$[/tex]

Let [tex]$\alpha > f\left(x_0\right)$[/tex]. so [tex]$\alpha-f\left(x_0\right) > 0$[/tex]

[tex]$\lim _{x \rightarrow x_0} f(x)=\alpha$[/tex]

Then [tex]\exists $ \varepsilon > 0$[/tex] such that

[tex]$|f(x)-\alpha| < \frac{\alpha-f\left(x_0\right)}{2}$[/tex] for all [tex]$\left.x \in\left[x_0-\varepsilon_0 x_0+\varepsilon\right]\right\}\left\{x_i\right\}$[/tex]

[tex]$\Rightarrow f(x) > \alpha-\frac{\alpha-f\left(x_0\right)}{2}$[/tex] for all [tex]$x \in\left[x_0-\varepsilon_1, x_0+\varepsilon\right] \backslash\left\{x_0\right\}$[/tex]

[tex]$\Rightarrow f(x) > \frac{\alpha+f\left(x_0\right)}{2}$[/tex] for all [tex]$x \in\left[x_0-\varepsilon_1, x_0\right)$[/tex]

Now [tex]$f\left(x_0\right) < \alpha$[/tex]

The [tex]$f(x) > \frac{f\left(x_0\right)+\alpha}{2} > f\left(x_0\right)$[/tex].

So [tex]$f\left(x_0\right) < \frac{f\left(x_0\right)+\alpha}{2} < f(x)$[/tex] for all [tex]$x \in\left[x_0 \varepsilon, \varepsilon_0\right)$[/tex]

Let [tex]$\eta=\frac{f\left(x_e\right)+\alpha}{2}$[/tex]

Then there does not exist [tex]$d \in\left[x_0-\varepsilon, x_0\right]$[/tex] such that [tex]$f(d)=\xi$[/tex].

Because if [tex]$d=x_0, f(d)=f\left(x_0\right) < \eta$[/tex] if [tex]$d E\left[x_0-\varepsilon, x_0\right)$[/tex]

Then [tex]$f(d) > \eta$[/tex]

Therefore f does not satisfies IVP on [tex]$\left[x_0-\varepsilon, x_0\right]$[/tex] which contradict olio hypothesis.

Therefore [tex]$\alpha \leq f\left(x_0\right)$[/tex] (b) From (a) and (b) it follows [tex]$\alpha=f\left(x_0\right)=\lim _{x \rightarrow x_0} f(x)$[/tex]. Therefore f can not have a removable discontinuous

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Staci pays $32.70 for 5 cell phone cases. Each case costs the same amount. How much does each case cost?

Part A
Which expression represents the problem?
$32.70 × 5
$32.70 ÷ 5
$32.70 + 5
$32.70 – 5
Part B
Evaluate the expression from Part A.

$ ( ??? )

Answers

Answer:

$32.70 ÷ 5

Each case is $6.54.

Step-by-step explanation:

$3270 for 5 cases, meaning you would split $32.70 into 5.

$32.70 ÷ 5 phone cases = $6.54

This also means each case is $6.54. To prove this, multiply by 5.

i literally don’t know

Answers

∠U is congruent ∠S because all right angles are congruent.

Define congruent.

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent, or to be in the relation of congruence. When two sides and their included angle in one triangle are equal to two sides and their included angle in another, two triangles are said to be congruent. This concept of congruence appears to be based on the idea of a "rigid body," which may be moved without affecting the internal relationships between its components.

Given

∠U ≅ ∠S

All right angles are congruent.

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on their next training run, pepe averaged a speed of 2/3 of a mile in 5 minutes, while paula averaged 1/4 of a mile in 2 minutes. if pepe and paula each ran at their individual pace for 60 minutes, how many total miles did they cumulatively run?

Answers

Answer:

15.5

Step-by-step explanation:

Pepe= 2/3 x 12 = 8

Paula= 1/4 x 30 = 7.5


8+7.5=15.5

Find the area of a circle with radius 6 ft.

Answers

Answer:

The area of the circle is 113.04 square feet.

Step-by-step explanation:

Given;Radius (r) = 6 ftπ = 3.14Formula;A = πr²

A = 3.14 × (6)² ft

A = 3.14 × 36 ft

A = 113.04 square feet.

Thus, The area of the circle is 113.04 square feet.

Answer:

28.274 square feet

Step-by-step explanation:

Multiply the radius by pi

Which of the following represents members of the domain of the graphed function?

See attached picture

Responses

{-4, 2, 3}
{-4, 0, 1}
{1, 2, 3, 4}
{1, 2, 3, 5}

Answers

The {-4, 0, 1} represents members of the domain of the graphed function.

What is the domain of the function?

A function is a mathematical object that accepts input, appears to apply a rule to it, and returns the result.

A function can be thought of as a machine that requires in a number, performs some operation(s), and then outputs the result.

The domain of a function is the collection of all its inputs. Its codomain is the set of possible outputs.

The range refers to the outputs which are actually used.

Domain: {-4, 0, 1}.

Simply list the domain as -4 < x < 2, which would imply ALL values between -4 and 2 inclusive.    

Yes, this is a function. No x-values repeat, and it passes the Diagonal Line Test for functions.

Hence, the {-4, 0, 1} represents members of the domain of the graphed function.

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Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. Select the correct answer below and fill in the answer box to complete your choice. O A. According to the Divergence Test, the series converges because lim ak = k- 00 (Simplify your answer.) OB. According to the Divergence Test, the series diverges because lim ax = kos (Simplify your answer.) OC. The Divergence Test is inconclusive because lim ak (Simplify your answer.) OD. The Divergence Test is inconclusive because lim ak does not exist.

Answers

The Divergence Test is inconclusive because lim ak = ∞

The Divergence Test is used to determine whether a given infinite series converges or diverges.

In order to use the Divergence Test, we must examine the limit of the terms of the series as n approaches infinity.

In the given series, the limit of the terms as n approaches infinity is not defined. Therefore, the Divergence Test is inconclusive.

The Divergence Test is inconclusive because lim ak = ∞

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What are the values of u and v?
u = ?°
v = ?°

Answers

v=58
u=94

You have to multiple 43 by 2 you would get 86 so now you would have to subtract that from 180 and would get 94

You have to subtract 64 from 180 and you would get 116 so now you would have to divide it by 2 and you would get 58

10. ANEW ACAR. Solve for x and CR. *
X=
Given: ANEW ACAR
NE = 11
EW = 12
I
AR = 4y - 12
CA = 4x + 3
NW = x + y

Answers

Applying the definition of congruent triangles, the values of x and y are:

x = 2; y = 6

Length of CR = 8 units.

How to Find  the Sides of Congruent Triangles?

If two triangles are congruent to each other, based on the CPCTC, all their corresponding angles, and their corresponding sides will be equal to each other.

Given that triangles NEW and CAR are congruent to each other, therefore:

NE = CA

NW = CR

EW = AR

Given the following measures:

NE = 11

EW = 12

AR = 4y - 12

CA = 4x + 3

NW = x + y

Therefore:

NE = CA

11 = 4x + 3

Solve for x:

11 - 3 = 4x

8 = 4x

8/4 = x

x = 2

EW = AR

12 = 4y - 12

12 + 12 = 4y

24 = 4y

24/4 = y

y = 6

NW = CR = x + y

Plug in the values of x and y:

CR = 2 + 6

CR = 8 units.

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what does
QR=
PR=
M

Answers

We need to use Right Angled Triangle Properties.

PR≈15 and QR≈12 is the length of the sides.

What is a Right Angled Triangle?

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of its angles is a right angle (90o). Triangle PQR is a right triangle in the illustration, and its components are its base, height, and hypotenuse. Here, QR is the base, PQ is the height, and PR is the hypotenuse. The essential side of a right triangle is its hypotenuse, which is also its largest side and sits across from the triangle's right angle.

In a right triangle we have: (Hypotenuse)2 = (Base)2 + (Altitude)2

Area of a right triangle = (1/2 × base × height) square units.

Calculation:

PR is the Hypotenuse of the Triangle.

PQ=9

Angle ∡PQR=37° and Angle ∡RPQ=53°

So Sin(theta)=opposite side/Hypotenuse

⇒Sin(37°)=9/Hypotenuse

⇒Hypotenuse=9/0.6018

⇒Hypotenuse=14.955

PR⇒14.955

We know that (Hypotenuse)2 = (Base)2 + (Altitude)2

⇒(14.955)2=(9)2+(QR)2

QR=11.9438

PR≈15 and QR≈12

We need to use Right Angled Triangle Properties.

PR≈15 and QR≈12 is the length of the sides.

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The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15
minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.
Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84
shoppers per hour make a purchase and each of these shoppers spends an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers,
on average, are waiting in the checkout line to make a purchase at the Good Deals Store

Answers

Note that at any time during business hours, about 7 shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store. This is solved using Little Law.

What is littles Law?

Little's Law asserts that the long-term average number of individuals in a stable system, L, is equal to the long-term average effective arrival rate,λ, multiplied by the average duration a customer spends in the system, W.

To compute,

First, let's make sure that all the variables use the same time unit.

Thus, if there are 84 shoppers who are making a purchase per house, then there will be: 84/60 minutes

= 1.4

This means that  λ (rate) = 1.4 and the average time (W) is 5 minutes

Using Little's Law which states that the queuing formula is:

L = λW

Where L = Average number of factors in the system (in this case, people on the queue)λ = Average arrival and departure rate; andW = lead time that a factor spends in the system

Note that:

λ = 1.4 (computed)

W = 5 mintues (given)

Hence, the Average number of people in queue per time is:

L = 1.4 x 5

L = 7 shoppers.

Thus, it is correct to state that at any time during work hours, about 7 shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store.

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Full Question:

If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for an average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N=rT. This relationship is known as Little's law.

The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.

Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?

The square of a number is equal to 72 more than the number. Find all such numbers.

Answers

Answer:

You just need to think about this a little. There is a number, that you don't know, x, and if you square it ([tex]x^2[/tex]), that value will be equal to 72 more than the unknown number itself, so you put that into an equation.

Step-by-step explanation:

[tex]x^2=x+72\\x^2-x-72=0\\[/tex]

Apply quadratic formula (you can look it up)

[tex]x_1=\frac{-(-1)+\sqrt{(-1)^2+(-4*1*-72} )}{2(1)} \\\\x_2=\frac{-(-1)-\sqrt{(-1)^2+(-4*1*-72} )}{2(1)} \\\\[/tex]

There are two answers to the quadratic formula.

The rest should be easy.

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The expoential function given by f(x) = e^x called the (a. natural logarithmic, natural exponential, c. 1 to 1 exponential, d. 1 to 1 algebraic, e. transcendental algebraic) function and the base e is called the (a. algebraic, b. 1 to 1, c. natural, d. rational, e. transcendental)

Answers

Answer:

natural exponential

natural

quizlet

Answer:

b. natural exponential

c. natural

Step-by-step explanation:

Given function:

[tex]f(x)=e^x[/tex]

The given exponential function is called the:

natural exponential function

The base e is called the:

natural base

The number "e" occurs naturally in math and the physical sciences.

It is the base rate of growth shared by all continually growing processes, and so is called the natural base.

It is an irrational number and named after the 18th century Swiss mathematician, Leonhard Euler, and so is often referred to as "Euler's number".

Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are 17576 ways to perform steps 1-3, and there are 10000 ways to perform the remaining steps. Thus, the number of license plates is 175760000 (b) How many license plates could begin with A and end in 0? and the number of ways to place the 0 in the In this case, the number of ways to place the A in Step 1 is 1 final step is 1 . Thus, the answer is 676000 (c) How many license plates could begin with BWC? In this case, the number of ways to perform steps 1-3 is ___ Thus, the answer is ___(d) How many license plates are possible in which all the letters and digits are distinct? (e) How many license plates could begin with AB and have all letters and digits distinct? Enter an exact number

Answers

the total number of license plate is 17576000 and In this the number ways to place 'A' in step 1 is = '1'1, and the number of steps '0' in final steps id '1' thus the total answer is 67600

What is permutation and combination?

In mathematics, there are two alternative methods for dividing up a collection of items into subsets: combinations and permutations. Any order may be used by a combination to list the subset's elements. An ordered list of a subset's components is called a permutation.

There are [tex]26^3[/tex] = 17576, ways to perform step 1-3, and there are [tex]10^3[/tex] = 1000, ways to perform remaining steps .

the total number of license plate is 17576000

In this the number ways to place 'A' in step 1 is = '1'1, and the number of steps '0' in final steps id '1'

thus the total answer is 67600

26 X 25 X 24 X 10 X 9 X 8 = 11232000

24 X 10 X 9 X 8 = 17280

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Sample Response: First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller.

Which did you include in your answer?
Check all that apply.
Write the ratios as fractions.
Find a common denominator.
Compare the numerators to see that 4:10 is the smaller ratio.

Answers

In the aforementioned scenario, the choice you must include in your response is to find a common denominator.

In the simplest terms, what is fraction?

One can refer to a fraction as being in its lowest term or in its simple form when the numerator and denominator are known to have no common factors besides 1. In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in daily speech.

The common denominator will be between 10 and 20, and there is a common numerator as well. The common denominator will be 20 because both can divide it and 10 is less than 20.

Finding a common denominator is the solution you should choose in the scenario mentioned above.

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