What percentage of the guesst at this hotel called for room service yesterday?

Answer:

1. Express the width of the rectangle in terms of the length X.

width = 500 - X

2. Express the surface area of the rectangle in terms of X.

area = -X² + 500X

3. What value of X gives the maximum surface area?

maximum surface area results from the rectangle being a square, so 1,000 ÷ 4 = 250

X = 250 ft

4. What is the maximum surface area?

maximum surface area = X² = 250² = 62,500 ft²

Step-by-step explanation:

since the perimeter = 1,000

1,000 = 2X + 2W

500 = X + W

W = 500 - X

area = X · W = X · (500 - X) = 500X - X² or -X² + 500X

The area of a shape is the amount of space it occupies.

The length is represented as x.

Let the width be y.

So, we have:

[tex]\mathbf{Perimeter =2(x + y)}[/tex]

This gives

[tex]\mathbf{2(x + y) = 1000}[/tex]

Divide both sides by 2

[tex]\mathbf{x + y = 500}[/tex]

Make y the subject

[tex]\mathbf{y = 500 -x}[/tex]

So, the width in terms of x is 500 - x

The surface area is calculated as:

[tex]\mathbf{A = xy}[/tex]

Substitute [tex]\mathbf{y = 500 -x}[/tex]

[tex]\mathbf{A = x(500 - x)}[/tex]

So, the surface area in terms of x is x(500 - x)

Expand [tex]\mathbf{A = x(500 - x)}[/tex]

[tex]\mathbf{A = 500x - x^2}[/tex]

Differentiate

[tex]\mathbf{A' = 500- 2x}[/tex]

Equate to 0

[tex]\mathbf{500- 2x = 0}[/tex]

Rewrite as:

[tex]\mathbf{2x = 500}[/tex]

Divide both sides by 2

[tex]\mathbf{x = 250}[/tex]

So, the value of x that gives maximum surface area is 250

Substitute 250 for x in [tex]\mathbf{A = x(500 - x)}[/tex]

[tex]\mathbf{A = 250 \times (500 - 250)}[/tex]

[tex]\mathbf{A = 250 \times 250}[/tex]

[tex]\mathbf{A = 62500}[/tex]

Hence, the maximum area is 62500

Read more about areas at:

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Answer:

-20i^2 + 22i - 6

Step-by-step explanation:

(3 - 5i)(-2 + 4i) = -6 + 10i + 12i - 20i^2 = -20i^2 + 22i - 6

if you want to go further,

-20i^2 + 22i - 6 = -2(10i^2 - 11i + 3)

Answer:

14+22i

Step-by-step explanation:

Edge Verified

Hello!

the answer is 83/100!

Hopefully this helps ^^

Answer:

it is not the same

Step-by-step explanation:

16x4=64 & 48x8=394

Answer:

a. E(X) = 0.333 minutes

b. [tex]\mathbf{\sigma_x =0.333 \ minutes}[/tex]

c.  0.9986

Step-by-step explanation:

a.

To find the mean time between counts

Let X be the random variable that illustrates the time between the successive log-ons, then X is exponential with the rate [tex]\lambda = 3[/tex] log-ons per minute.

i.e.

[tex]E(X) = \dfrac{1}{\lambda}[/tex]

[tex]E(X) = \dfrac{1}{3}[/tex]

E(X) = 0.333 minutes

b. Since X is attributed to an exponential distribution, The standard deviation between counts is:

[tex]\sigma_x = \dfrac{1}{3}[/tex]

[tex]\mathbf{\sigma_x =0.333 \ minutes}[/tex]

c.

Given that;

The average number of count per minute = 3

The value of X such that P(X < x) = 0.95 can be calculated as;

[tex]\int \limits ^x_0 \lambda e^{-\lambda t}= 0.95[/tex]

[tex]3\int \limits ^x_0 \lambda e^{3 t}= 0.95[/tex]

[tex]\bigg [ -e^{3t}\bigg ]^x_0 = 0.95[/tex]

[tex]e^{3t} = 1-0.95[/tex]

-3x = ㏑ (0.05)

-3x = - 2.9957

x = -2.9957/ -3

x = 0.9986

The value of x = 0.9986

Answer:

a) 3

b)3

c) 8.9872

Step-by-step explanation:

a) According to the question, mean is 3.

b) Since it is an exponential distribution, standard deviation equals to mean. Therefore, the answer is 3.

c) P[x<X]=0.95

f(x)= λ*e^(-λ*x)

∫f(x)dx, 0 to x

mean = 1/λ =3. So, λ= 1/3.

∫(1/3)*e^(-x/3)dx= 1/3*e^(-x/3)/(-1/3)=-e^(-x/3) 0 to x

-e^(-x/3)+1 = 0.95

-e^(-x/3)=-0.05

x/3=ln(0.05)

x=ln(0.05)*3= 8.9872

Your equation for the first point will be y=x+50

Explanation...

The x is zero so we just only put x. The y is 50 so we input a 50 giving us y=x+50.

Your equation for the second point will be y=2x+100.

Explanation...

Your slope is 2 so we input that and the y intercept is 100 giving us the equation y=2x+100.

Your equation for the third point will be y=4x+150

Explanation...

Your slope is 4 so we input that. Your y intercept is 150 so we input that. It gives us the equation y=4x+150.

Answer:

50 days?

Step-by-step explanation:

Answer:

i think it is 2 because

10 divide by 5 = 2

1 x 2 = 2

2 days

u must use the formula

so, the answer is 10 units²

Answer:

The distance from Earth to Mars is 8×10¹¹ m.

Step-by-step explanation:

Given that,

The speed of light is 3×10⁸ m/s. The sun is approximately 230,000,000,000 m from Mars. If the sun is approximately 1.5 x 10¹¹ meters from Earth, what is the approximate distance from Earth to Mars.

The sun is approximately 2.3 × 10¹¹ m from Mars.

The sun is approximately 1.5 x 10¹¹ m from Earth.

The distance between from Earth to Mars is :

d = 2.3 × 10¹¹ m - 1.5 x 10¹¹ m

= 8×10¹¹ m

Hence, the distance from Earth to Mars is 8×10¹¹ m.

Answer:

B

Step-by-step explanation:

7+ 8+ 9= 24

24 x 3= 72

Answer:

The three integers whose three times the sum of three consecutive integers is 72 will be: 7, 8, 9

Step-by-step explanation:

Let x, y, and z be the three consecutive integers

The sum of x, y, and z will be: x+y+z

The three times the sum of three consecutive integers is 72.

so the equation becomes:

3(x+y+z)=72

Now, putting x = 7, y=8 and z=9 in the L.H.S equation to check

3(x+y+z)

⇒ 3(7+8+9)

⇒ 3(24)

⇒ 72

Therefore, it is clear that the three integers whose three times the sum of three consecutive integers is 72 will be: 7, 8, 9

Answer: The answer is 4

Step-by-step explanation: and FYI nobody is -2 years old

Answer:

50

I've attached the drawing of my number line to show my thinking.  Download to turn it in if you need to.

Have a beautiful day, and stay safe.

Answer:

285.00

Step-by-step explanation:

Because you change 57 to a decimal (57.0) then you multiply.

57.0×2.3=285.00

today is my birthday wish me a happy birthday

The correct answer is the graph in the top right corner because it is a constant function. The bottom left graph is also considered a function but is an absolute function. So both are technically correct.

Answer:

Step-by-step explanation:

Find the slope and then the equation of line.

(x₁ , y₁) = (2 , 2)   & (x₂, y₂) = (6 , 10)

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

        [tex]= \frac{10 - 2}{6 - 2}\\\\= \frac{8}{4}\\\\= 2[/tex]

m = 2

Equation of the line: y - y₁  = m(x - x₁)

              y - 2 = 2 (x - 2)

              y - 2 = 2x - 4

                   y = 2x - 4 + 2

                  y = 2x - 2  --------------(I)

(a, 8)  

Plug in x = a & y = 8 in (I)

8  = 2a - 2

8 + 2 = 2a

10   = 2a

a = 10/2

a = 5

(4 , b)

Plug in x = 4 & y = b in (I)

b = 2*4 - 2

b = 8 - 2

b = 6

Answer:

dog peas

Step-by-step explanation:

donkey peas

Answer:

False

I hope this helps!

Answer: Children tickets cost 7.50

Adult tickets cost 12.50

Step-by-step explanation:

Let a represent adult tickets

Let c represent child tickets

On the first day she sells 6 adult tickets and 5 children tickets for total of 112.50. This can be written as:

6a + 5c = 112.50 ...... equation i

On the second day she sells 8 adult tickets and 4 children tickets for the total 130. This can be written as:

8a + 4c = 130 ....... equation ii

6a + 5c = 112.50 ...... equation i

8a + 4c = 130 ....... equation ii

Multiply equation i by 4

Multiply equation ii by 5

24a + 20c = 450 ........ equation iii

40a + 20c = 650 ......... equation iv

Subtract iii from iv

16a = 200

a = 200/16

a = 12.50

Adult tickets cost 12.50

From equation ii,

8a + 4c = 130

8(12.50) + 4c = 130

100 + 4c = 130

4c = 130 - 100

4c = 30

c = 30/4

c = 7.50

Children tickets cost 7.50

Using the concept of elimination, the cost of adult and children tickets are $12.5 and $7.5 respectively

Let :

Creating a system of equation thus :

6a + 5c = 112.50 - - - (1)

8a + 4c = 130 - - - - (2)

Multiply (1) by 4 and (2) by 5

24a + 20c = 450 - - - - (3)

40a + 20c = 650 - - - - (4)

Subtract

-16a = - 200

Divide both sides by - 16

a = 12.5

From (2) :

8(12.5) + 4c = 130

100 + 4c = 130

4c = 130 - 100

4c = 30

c = 7.5

Hence, the cost of adult and children tickets are $12.5 and $7.5

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Answer:

10

Step-by-step explanation:

40/4= 10

Answer:

A.

Step-by-step explanation:

$15 rental fee added to the 12.75 per hour. you have to multiply the 12.75 times the amount of hours rented, which we don't know yet so that's variable x. then he has only $45 to spend so it has to be equal to or less than that.

Answer:

the total Hight would be 42 meters

Step-by-step explanation:

Answer:

b. Kolmogorov–Smirnov test

Step-by-step explanation:

The Kolmogorov–Smirnov test is also known as KS test. It is statistical non-parametric test used to test and compare cumulative distributions between two sets of data.

It is used to test whether the distribution scores are deviated from the comparable normal distribution or if the data are normally distributed.

Answer:

Cool

Step-by-step explanation:

Do you mean a 30 foot cable is being cut into pieces that are 7 1/2 feet long, how many pieces is it cut into?

Answer:

goodluck

Step-by-step explanation:

Answer:

the probability that more than 3 of them will have more than one ounce of mustard is 0.05975

Step-by-step explanation:

Given te data in the question;

let x rep the quantity of mustard on a hotdog ( in oz)

so

X → N ( u = 0.9, α² = 0.01 )

now P( more than one ounces of mustard on a hotdog) will be

P( X>1 ) = P( Z > ((1-0.9)/(√0.01)) ) = P( Z > 1 ) = 1 - P( Z < 1 )

= 1 - 0.84134 = 0.15866

Also let Y rep the number of hotdogs that have more than one ounces of mustard, so

Y → Bin( n = 10, p = 0.15866 )

P( y = y ) = (¹⁰ _y) ( 0.15855)⁰ ( 1 - 0.15866 )^10-y, y = 0,1,2,3......, 10

so required probability = P(Y > 3) = 1 - P(Y ≤ 3)

= 1 - P(Y=0) - P(Y=1) - P(Y=2) - P(Y=3)

=1 -  (¹⁰ ₀) ( 0.15855)⁰ (1 - 0.15855)¹⁰⁻⁰ - (¹⁰ ₁) ( 0.15855)¹ (1 - 0.15855)¹⁰⁻¹ - (¹⁰ ₂) ( 0.15855)² (1 - 0.15855)¹⁰⁻² - (¹⁰ ₃) ( 0.15855)³ (1 - 0.15855)¹⁰⁻³

= 0.05975

Therefore the probability that more than 3 of them will have more than one ounce of mustard is 0.05975

Answer:

*20 Songs and 2 Movies

*8 Songs and 6 movies

Step-by-step explanation:

Answer:

The given polynomial is p(x)=x  

4

−2x  

3

+3x  

2

−ax+3a−7

Given that, the polynomial p(x) when divided by (x+1) leaves remainder 19

Therefore, p(−1)=19 (By Remainder theorem)

=>(−1)  

4

−2×(−1)  

3

+3(−1)  

2

−(−1)a+3a−7=19

=>1+2+3+a+3a−7=19

=>4a−1=19

=>4a=20

=>a=5

The value of a is 5

Now,

p(x)=x  

4

−2x  

3

+3x  

2

−5x+3×5−7

       =x  

4

−2x  

3

+3x  

2

−5x+15−7

       =x  

4

−2x  

3

+3x  

2

−5x+8

Remainder when the polynomial is divided by (x+2)

              =p(−2)    (By Remainder Theorem)

              =−2  

4

−2(−2)  

3

+3(−2)  

2

−5(−2)+8

              =16+16+12+10+8

              =62

Thus, the remainder of the polynomial p(x) when divided by (x+2) is 62

Step-by-step explanation:

The remainder when P(x) is divided by (x-3) is 8

The quotient-remainder theorem says that when any integer n is divided by any positive integer d, the result is a quotient q and a nonnegative remainder r that is smaller than d.

Given here, P(x)=x⁴ - 2x³ - 3x² + 4

Now we know from the polynomial remainder theorem that the remainder on dividing by (x-a) is f(a)

Thus P(3)=8

Hence, The remainder is 8

Learn more about the remainder theorem here:

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Answer:

4 would be $55.00 and 8 would be $75.00