Three guests check into a hotel room. The manager says the bill is $30, so each guest pays $10. Later the manager realizes the bill should only have been $25. To rectify this, he gives the bellhop $5 as five one-dollar bills to return to the guests.

On the way to the guests' room to refund the money, the bellhop realizes that he cannot equally divide the five one-dollar bills among the three guests. As the guests aren't aware of the total of the revised bill, the bellhop decides to just give each guest $1 back and keep $2 as a tip for himself, and proceeds to do so.

As each guest got $1 back, each guest only paid $9, bringing the total paid to $27. The bellhop kept $2, which when added to the $27, comes to $29. So if the guests originally handed over $30, what happened to the remaining $1?​

Answers

Answer 1

Answer:

the manager has it

Step-by-step explanation:

this sounds more like a riddle than a math question

Answer 2

Answer:

This was so confusing and I had to use like 3 sheets of paper

Step-by-step explanation:

$25 + $2 + $1 + $1 + $1 = $30.

So the manager has it, the point is to change the numbers so your brain gets confused.


Related Questions

If 2^x=3^y=12^z then prove it 2/x = 1/z -1/y.​

Answers

SOLUTION:

[tex] \begin{array}{l} 2^x = 3^y = 12^z \\ 2^x = 3^y = 2^{2z} \cdot 3^z \\ \Rightarrow 3 = 2^{\frac{x}{y}} \\ \Rightarrow 2^x = 2^{2z} \cdot 2^{\frac{xz}{y}} \\ \Rightarrow x = 2z + \frac{xz}{y} \\ \Rightarrow xy = 2zy + xz \\ \Rightarrow 2zy = xy - xz \\ \text{Dividing both sides by }xyz,\text{ we get:} \\ \dfrac{2}{x} = \dfrac{1}{z} - \dfrac{1}{y} \end{array} [/tex]

Identify the errors made in the finding the inverse of y= x^2 +12x
X= y^2+12x
Y^2= x- 12x
Y^2 = -11x
Y=√11x, for x greater than or equal to 0

Answers

9514 1404 393

Answer:

  y was not substituted for every x

Step-by-step explanation:

To find the inverse of ...

  y = f(x)

you need to solve ...

  x = f(y)

Here, f(x) = x^2 +12x, so f(y) = y^2 +12y

This is not the expression we see on the right of ...

  x = y^2 +12x

Apparently y was not properly substituted into f(x).

Where r is the radius of the cone's base and h is the height of the cone. Find the approximate volume of a
cone when r is 4 inches and his 3 inches.



Use volume of cone formula

Answers

Answer:

The volume of this cone is V = 50 (~50.27)

(I'm assuming that 'his' is height?)

Answer: 50

Step-by-step explanation:

(15)(16)/a=(3)(4)(5)

Answers

Answer:

a = 4

Step-by-step explanation:

(15)(16)/ a = (3)(4)(5)

15 * 16 = 240

240/ a = (3)(4)(5)

240/a = 60

240/60 = a

a = 4

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

a = 4

Step-by-step explanation:

(15)(16)/a = (3)(4)(5)

Step 1. Solve for (3)(4)(5)

(15)(16)/a = 60

Step 2. Multiply (15)(16)

240/a = 60

Step 3. Solve for a

a = 240/60

a = 4

Consider the following three expressions. To be the same what would P, Q, and R have to be

Answers

Step-by-step explanation:

Px^2+6x+1=x^2+x^2+Qx+1

P=2 and Q=6

Next, 3x^2-5-(x^2-6x+R/2)=2x^2+6x+1

2x^2-5-R/2+6x=x^2+6x+1

-5-R/2=6, R=-22

The lengths of the sides of a triangle arc 3, 4, and 5. If Theta is the measure of the smallest angle of the triangle, what is the
value of tah theta?
(A)4/3
(B)5/4
(C)3/4
(D)3/5

Answers

Answer:

C

Step-by-step explanation:

Since they are pythagorian triplets, ABC is a right angled triangle at the angle between the arc 3 and arc 4. Theta is the angle opposite to 3 and hence tan(theta)=3/4

Write an equation that expresses the following relationship.
w varies directly with u and inversely with the square of d
In your equation, use k as the constant of proportionality.

Answers

Answer:

w = [tex]\frac{ku}{d^{2} }[/tex]

Step-by-step explanation:

An equation that expresses the given relationship is ud²=1.

Given that, w varies directly with u and inversely with the square of d.

We need to write an equation that expresses the following relationship.

What is directly and inversely varies?

Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant.

Now, w∝u⇒w=ku

and w∝1/d²⇒w=k/d²

⇒wd²=k

⇒w=wd²u

ud²=1

Therefore, an equation that expresses the given relationship is ud²=1.

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Why do interest rates on loans tend to be higher in a strong economy than in a weak one?

Answers

In a weak economy there is less demand for credit, so the price drops.

find lub and glb of the following set E={0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,.....}​

Answers

The lub is 0.23[tex]\mathbf{\overline{43}}[/tex], while the glb is 0.2

The given set is presented as follows;

E = {0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,...}

The least upper bound, lub, of a set, E, is known as the supremum of the set which is the number B such that all x ∈ E are of the value x  ≤ B, while there all y ∈ E has a x ∈ E such that t < x

Therefore;

The supremum, lub of the given set is 0.23[tex]\overline{43}[/tex]

The greatest lower bound, glb, b, also known as the infimum, is defined as follows;

b is the greatest lower bound if for all xE then x ≥ b

Given that b < t, then where x ∈ E, there exist a x < t

The glb of the given set is 0.2

Learn more about lub, supremum, glb, infimum, here;

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F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23

Answers

Answer:

∠ H ≈ 23°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus

∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )

can anyone show me this in verbal form?

Answers

Answer:

2 * (x + 2) = 50

Step-by-step explanation:

Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.

been stuck on this for a few days now, help on even one would be greatly appreciated!!!

Answers

Answer:

-5-9i

Step-by-step explanation:

-1-8i-4-i

-1-4-8i-i

-5-9i

Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the distribution of the population is normally distributed. 150 150 180 170
a. State the null and alternative hypotheses.
b. Using a critical value, test the hypothesis at the 10% level of significance.
c. Using a p-value, test the hypothesis at the 10% level of significance.
d. Using a confidence interval, test the hypothesis at the 10% level of significance.
e. Could a Type II error have been committed in this hypothesis test?

Answers

Answer:

a; H0: u= 140 Ha: u ≠ 140 two tailed test.

b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or

3 > t ( ∝/2) (n-1) =2.353    

c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05  therefore reject H0.

d. Again reject H0 as 140 < 150.163

e. A type II error has not been committed as H0 is rejected.

Step-by-step explanation:

We formulate the null and alternative hypotheses as

a; H0: u= 140 Ha: u ≠ 140 two tailed test.

For a two tailed test the significance level ∝= 0.1 the critical region is given by

t ≤ t ( ∝/2) (n-1) and t > t ( ∝/2) (n-1)

So the critical region will be

t≤ t ( ∝/2) (n-1) =2.353

where

t= x` - u / s/ √n

Sr. No X X²

1 150 22500

2 150 22500

3 180 32400

4 170 28900

∑ 650 106,300

X`= ∑x/n = 650/4= 162.5

s²= 1/n-1 (x-x`)²= 1/n-1 [ ∑x² -(∑x)²/n ]

= 1/3[106,300 -650²/4] = 225

s= 15

Putting the values in the above equation

t= 162.5- 140/ 15/ √4

t= 3

So calculated value of t= 3

b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or

3 > t ( ∝/2) (n-1) =2.353    

c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05  therefore reject H0.

d. a 90% confidence interval based on the calculated values will be

x`± 1.645 (s)/ √n

Putting the values

162.5 ±1.645 ( 15/2)

162.5 ±12.3375

174.84 , 150.163

d. Again reject H0 as 140 < 150.163

e. A type II error has not been committed as H0 is rejected.

solve the equation.
g - 16 = 8
g =

Answers

Answer:

24

Step-by-step explanation:

24-16=8

The solution to the equation is g = 24.

To solve the equation g - 16 = 8 and find the value of g.

we need to isolate the variable g on one side of the equation.

Starting with the given equation:

g - 16 = 8

To isolate g, we can add 16 to both sides of the equation:

g - 16 + 16 = 8 + 16

g = 24

Therefore, the solution to the equation is g = 24.

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Which of the following is -32(5x-7)(x+8)/-4(x+8)(5x-7) simplified? A.8/(x+8) B.8 C.4 D.4/(5x-7)

Answers

Answer:

work is shown and pictured

Please help me answer the question

Answers

Answer:

fourth option

Step-by-step explanation:

Common difference is given by difference of two consecutive term

d = nth term - (n-1)th term

______________________________________

for all the  series lets take second term as nth term

and first term as (n-1)th term

_________________________________________

for first series

n th term = -3 1/2 = -3.5

(n-1)th term = -5

therefore

d= -3.5 -(-5) = -3.5 +5 = 1.5

______________________________________

for second series

n th term = 4 1/2 = 4.5

(n-1)th term = 2 1/2 = 2.5

therefore

d= 4.5 -(2.5) =2

_________________________

for third series

n th term = 3

(n-1)th term =1.5

therefore

d= 3 - 1.5 = 1.5

__________________________________

for fourth series

n th term = -1.5

(n-1)th term = -4

therefore

d= -1.5 -(-4) = -1.5 + 4 = 2.5 = 2 1/2

___________________________________

Thus, based on above solution option four has common difference of 2 1/2

What is the 50th term of the arithmetic sequence having u(subscript)1 = -2 and d = 5

Answers

Answer:

243

Step-by-step explanation:

The general term for this arithmetic sequence is:

a(n) = -2 + 5(n - 1).

Then a(50) = -2 + 5(49) =   243

what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10

Answers

Answer=16. Hope this helps

Answer:18.5

Step-by-step explanation:

10+8=18

18*5=90

90/4

22.5-4=18.5

find the surface area of the prism HURRY

Answers

Answer:

Does the answer help you?

How many feet are in 26 miles, 1, 155 feet? Enter only the number. Do not include units
The solution is

Answers

Answer:

137, 280 feet

Step-by-step explanation:

There are 5,280 feet in a mile.

26 * 5,280 = 137,280

There are 137, 280 feet in 26 miles.

There are 137,280 feet in 26 miles.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We know that there are 5,280 feet in a mile.

So, the solution would be;

26 x 5,280 = 137,280

Thus, There are 137,280 feet in 26 miles.

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find the value and express it in standard form : 5×10^8×2×10^11​ please answer​

Answers

5×10⁸×2×10¹¹=5×1,00,000,000×2×1,00,000,000,000=5,00,000,000×2,00,000,000,000=100,000,000,000,000,000,000=1E20

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A student says that a coordinate grid under a dilation with the center at the origin and scale factor 2 does not change the grid. The image is still a coordinate grid. How do you​ respond?

Answers

Answer:

Dilation changes (x,y) values not the grid or coordinate plane. Basically, dilating a graph or a coordinate grid means the original coordinates you may have had will be changed with the dilation.  For example, a triangle plotted had its original area of 26 dilated to an area of 58.

Integers are sometimes whole numbers

true or false

Answers

Answer:

True

Step-by-step explanation:

Integers are always whole numbers

negative, 0, positive:: whole numbers

40pts and a brainliest to the person who answers this question with detailed explanations and steps to solve shown.

Find y. Give your answer in the simplest form.​

Answers

Answer:

y = 7 sqrt(2)

Step-by-step explanation:

Since this is a triangle, we can use trig functions

sin theta = opp/ hyp

sin 45 = 7/y

y sin 45 = 7

y = 7/ sin 45

y = 7 / (1/sqrt(2) )

y = 7 sqrt(2)

Answer:

the answer is y = 7 sqrt (2)

Step-by-step explanation:

[tex]\sf{}[/tex]

♛┈⛧┈┈•༶♛┈⛧┈┈•༶

Graph the function f(x) = 1/2(2)^x

Answers

Answer; Down

Step-by-step explanation:The graph of the squaring function has the shape of a parabola that opens up. Its vertex is at (0,0). The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2).

1km make how many cm​

Answers

Answer:

100000

Step-by-step explanation:

Proceed as in Example 4 in Section 6.1 and find a power series solution y = [infinity] n = 0 cnxn of the given linear first-order differential equation. (Give your answer in terms of c0.) y' = xy

Answers

Let y be a solution to the given differential equation,

[tex]y' = xy[/tex]

where

[tex]\displaystyle y = \sum_{n=0}^\infty c_n x^n \\\\ y' = \sum_{n=0}^\infty nc_nx^{n-1} = \sum_{n=1}^\infty nc_nx^{n-1} = \sum_{n=0}^\infty (n+1)c_{n+1}x^n[/tex]

Substituting these series into the DE gives

[tex]\displaystyle \sum_{n=0}^\infty (n+1)c_{n+1}x^n = x\sum_{n=0}^\infty c_nx^n \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=0}^\infty c_nx^{n+1} \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty \bigg((n+1)c_{n+1}-c_{n-1}\bigg)x^n = 0[/tex]

Then the coefficients [tex]c_n[/tex] in the series solution are governed by the recurrence,

[tex]\begin{cases}c_0 = c_0 \\ c_1 = 0 \\ (n+1)c_{n+1}-c_{n-1} = 0&\text{for }n\ge1\end{cases}[/tex]

We have

[tex](n+1)c_{n+1}-c_{n-1} = 0 \implies nc_n - c_{n-2} = 0 \implies c_n = \dfrac{c_{n-2}}n[/tex]

so it follows that [tex]c_1=c_3=c_5=\cdots = 0[/tex], while

[tex]c_0 = \dfrac{c_0}1 = \dfrac{c_0}{2^0\times0!} \\\\ c_2 = \dfrac{c_0}2 = \dfrac{c_0}{2^1\times1!}\\\\ c_4 = \dfrac{c_2}4 = \dfrac{c_0}{2\times4} = \dfrac{c_0}{2^2\times2!}\\\\ c_6 = \dfrac{c_4}6 = \dfrac{c_0}{2\times4\times6} = \dfrac{c_0}{2^3\times3!}[/tex]

and so on, with the general n-th coefficient being

[tex]c_n = \begin{cases}0&\text{if }n\text{ is odd} \\ \dfrac{c_0}{2^{n/2}\left(\frac n2\right)!} &\text{if }n\text{ is even}\end{cases}[/tex]

Then the power series solution is

[tex]\displaystyle y(x) = c_0 \sum_{n=0}^\infty \frac{x^n}{2^{n/2}\left(\frac n2\right)!} = c_0 \sum_{n=0}^\infty \frac1{\left(\frac n2\right)!} \left(\frac x{\sqrt2}\right)^n[/tex]

but this doesn't tell the whole story because it doesn't capture the odd-index-is-zero case.

More concisely: let n = 2k for integers k ≥ 0. Then

[tex]\displaystyle y(x) = c_0 \sum_{k=0}^\infty \frac{x^{2k}}{2^k k!} = c_0 \sum_{k=0}^\infty \frac1{k!} \left(\frac{x^2}2\right)^k[/tex]

and as a bonus, it's easier to get an exact solution for this DE,

[tex]y(x) = c_0e^{x^2/2}[/tex]

find the factors of f(x), given that x = -2 is zero. f(x) = x³ + x² - 14x - 24​

Answers

Answer:

x=-3 and x=4

Step-by-step explanation:

Since x=-2 is a zero of the function, we can find the other two factors by dividing f(x) by (x+2) using long division to obtain the other two roots. The quadratic obtained is x^2-x-12. Now factorising this quadratic will result in (x-4)(x+3)=0, x=-3 and 4 are the other rrots

The factorization of the function f(x) = x³ + x² - 14x - 24​ will be (x + 2), (x + 3), and (x - 4).

What is factorization?

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The function is given below.

f(x) = x³ + x² - 14x - 24​

Factorize the function, then we have

f(x) = x³ + x² - 14x - 24​

f(x) = x³ + x² - 14x - 24

f(x) = x³ + 2x² - x² - 2x - 12x - 24

f(x) = x²(x + 2) - x(x + 2) - 12(x + 2)

f(x) = (x + 2)(x² - x - 12)

f(x) =(x + 2)(x² - 4x + 3x - 12)

f(x) = (x + 2)[x(x - 4) + 3(x - 4)]

f(x) = (x + 2)(x + 3)(x - 4)

The factorization of the function f(x) = x³ + x² - 14x - 24​ will be (x + 2), (x + 3), and (x - 4).

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logx-log(x-l)^2=2log(x-1)​

Answers

Answer:

  x = 1.00995066776

  x = 2.52925492433

Step-by-step explanation:

This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...

  [tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]

The attached graph shows zeros at

  x = 1.00995066776 and 2.52925492433

_____

Comment on the equation

Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068

Comment on the answer refinement

We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.

Draw the perpendicular bisector of the given line segment a.9.4 cm b. 8.6cm c. 10 cm ​

Answers

Answer:

Please do it by your shelf because if we measure it and send you may not be able to do by online .So, please do it by by yourself using your scale .

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