three guards were protecting an orchard. A third met the guards,one after the other,To each guard he gave half of the apples he has at the time and two extra . Eventually he escaped with just one apple. How many apples did the thief take? Fellow up questions for extension. What if he had 2 left? 3 left? 4 left?​

Answers

Answer 1

Answer:

The thief stole 36 apples originally.

Step-by-step explanation:

The thief left the orchard with 1 apple.

which means:

​∴  before meeting the 3rd watchman, he must have had ​=6 apples.

​∴  before meeting the 2nd watchman, he must have had ​=16 apples.

​∴  before meeting the 1st watchman, he must have had ​=36 apples.

​(1+2)×2

​(6+2)×2

​(16+2)×2

​​

So, the thief stole 36 apples originally.

Answer 2

Answer:

The thief took 36 apples.

Step-by-step explanation:

This problem can be solved from end to beginning.

The thief ends up with a single apple. This happed after he gave half of the apples he had and two extra apples.

Thus, adding two apples 1+2=3 and doubling the result, the thief had 3*2=6 apples when he met the last guard.

Before that, he gave 2 apples to the second guard, thus he had 6+2=8 apples. Doubling it 8*2=16 is the number of apples he had when met the second guard.

Doing this again, 16+2=18. 18*2=36.

The thief took 36 apples.

Gave 18+2=20 to the first guard. He had 36-20=16 now.

Gave 8+2=10 to the second guard. He had 16-10=6 now.

Gave 3+2=5 to the third guard and got away with just one apple


Related Questions

What is the result of 60-15? Use the model to find the answer. A 4 B 5 C 12 D 20​

Answers

Answer:

its a).4

Step-by-step explanation: 60 divided by 15= 4 you can use a calculator to check if im right if you dont trust me

The answer would be 4 if the number expression is 60 ÷ 15 after using the arithmetic operation, option (A) 4 is correct.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

The number expression is:

60 ÷ 15

Using model:

= (15 + 15 + 15 + 15) ÷ 15

= 1 + 1  + 1 + 1

= 4

Thus, the answer would be 4 if the number expression is 60 ÷ 15 after using the arithmetic operation, option (A) 4 is correct.

Learn more about the arithmetic operation here:

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ANSWER ASAP AS MANY AS YOU CAN ITS FOR FINALS
Name the relationship complementary,
linear pair, vertical, zen, strate interior corresponding, or alternate conio 1) 2) 3) 4)​

Answers

1. Complementary
2. Alternate exterior
3. Linear pair
4. Alternate interior

can you understand ........

answer this!! will mark brainliest! 20 points

Answers

Answer:

Step-by-step explanation:

is the first choice, no other terms have anything in common with the number

399 or variable w

time. weight
8. 0.04
9. 0.07
10. 0.14
11. 0.25
12. 0.49

what is the average rate of change in weight of the plankton from week 8 to week 12?

A) 0.0265
B)0.0375
C)0.055
D)0.1125​

Answers

Answer:D

Because 0.49/12 -0.04/8 = 0.1125

Please help I will mark brainliest

Answers

Answer:

a)(2x+1)² - 3

4x² + 4x + 1 - 3

4x² + 4x - 2

4(-2)² + 4(-2) - 2

16 - 8 - 2

6 (final answer)

b) 4(3)² + 4(3) - 2

36 + 12 - 2

46 ( final answer)

c) 2(x²-3) + 1

2x² - 6 + 1

2(3)² - 5

18 - 5

13(final answer)

How long will it take to pay off 47,538 with only 4,782 per month?

Please HELPPPP

Answers

Answer:

9.9 months not counting mortgage or any other factors

Step-by-step explanation:

Box 1:
Dimensions: x by 3x by x
Area of base =x(3) = 3r?
Dimensions: x by 4x-1 by x
Area of base = x(4x-1) = 41²-x

Answers

Answer:

1. monomial

2. binomial

Step-by-step explanation:

Box 1's volume will be a monomial

Box 's volume will be a binomial

Merry Christmas please help

Answers

-3,2,3,7

Happy holidays! Hope you have a great Christmas!

Answer:

All Of The Number At The Top

Step-by-step explanation:

Like Said, The Tables Functions f

So, Basically It's A Challenge,

All Of The Numbers In Row X From Above Table

I Hope You Found This Answer Helpful

Good Day

You'll Get 100% Don't Stress It✨

By: LocalLesMara

In 1992, Jason bought a gallon of gas for $1.15. Yesterday, he bought a gallon of gas for $2.12. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.
A.
84.3%
B.
45.8%
C.
54.2%
D.
15.7%

Answers

I think it is b hope this helps

pleassssssssse hellpp

Answers

Answer:

c

Step-by-step explanation:

In preparation for the school play, the number of adult tickets sold by the ticket office was 5 less than twice the number of children's tickets. They sold 95 adult tickets. Write an equation you can use to find how many children's tickets were sold.

Answers

Answer:

3

Step-by-step explanation:

i think 5-2

PLEASE HELP if you help you like to play among us
Subtracting a number is the same as adding its opposite.

Use this understanding to complete each of the equations below.
CLEAR CHECK

Answers

Answer:

-5 - (-7) = -5 + -7

= 2

-5 - 7 = -5 + -7

= -12

What is the present value of ₱30,000 due in 27 months at 3% compounded annually?

Answers

Answer:

32,063.06

Step-by-step explanation:

the formula for compound interest: [tex]A = P(1+\frac{r}{n})^{nt\\}[/tex]

so to use this you are essentially solving for a.

p is the principle (or initial) amount deposited.

r is the rate (in percent)

n is the number of time periods compounded (like annually, monthly, weekly, or daily)

t is the time period (in years)

In this instance the formula looks like: [tex]A = 30,000(1+\frac{0.03}{1})^{1*2.25}[/tex]

You then solve for A using the formula. It is important to remember to use the order of operations

259 students enrolled in a freshman level chemistry class by the end of semester 6 times the number of students passed as failed find the number of students who passed and the number of students who failed​

Answers

Answer:picture?

Step-by-step explanation:

Given ΔABC, m∠C = 90° , m∠ ABC = 30° , AL ∠ Bisector CL = 6ft. Find LB (Feet)
WILL GIVE BRAINLIEST!!

Answers

Answer:

The Answer is 12 feet

Step-by-step explanation:

This is my second account lol I just wanted to give Angie the brainliest!

Answer:

10 feet

Step-by-step explanation:

Item 12
The graph represents the height y, in feet, above the ground of a water balloon x seconds after it is dropped from a window.



Which statement is true?

Select each correct answer.




The maximum height of the water balloon occurs at x = 0.

The water balloon is in the air for 2 s.

The water balloon hits the ground in 64 s.

The water balloon rises above 64 ft before falling toward the ground.

The maximum height of the water balloon is 64 ft.

Answers

Answer:

O The maximum height of the water balloon occurs at x = 0.    

O The water balloon is in the air for 2 s.    

O The maximum height of the water balloon is 64 ft.

Step-by-step explanation:

Firstly, by simply looking at the x axis on the graph (time), you will see that it starts at 0 and the 64 ft maximum height is aligned with the starting point of 0 seconds.  

The graph also shows (x axis) the 'time' represented, and as the height rapidly decreases the graph eventually reaches the 2 second mark, going no further and no lower.  

Finally, the graph shows (y axis) the peak of the water balloon's height is 64 ft, as it is the highest number reached while the water balloon was airborne.

The following statement is True.

The maximum height of the water balloon occurs at x = 0.The water balloon is in the air for 2 s.The maximum height of the water balloon is 64 ft.

A true statement to be chosen from the following.

What is a graph?

The graph is a demonstration of curves  that gives the relationship between the x and y-axis.

From the graph, the following points are to be noted.
The water balloon is at 64 ft at x = 0.
The water balloon takes 2 sec to reach y = 0.
The water balloon has a maximum height of x = 0.

Thus, points 1,2, and 5 are true.


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Help me please asap on a time limt

Answers

Answer: 51 grams

Step-by-step explanation:

Plug in 60 for t and calculate

A local insurance agent visits the high school and tells the students that his insurance company will give students a 7% discount on liability insurance, PIP. comprehensive insurance, and collision insurance for three years if they take a defensive driving course. Maria spends $1,437.00 on her auto insurance annually.

Answers

The question is vague, but I'll try and help.

Answer:

She saves $100.59 a year.

Step-by-step explanation:

Saving 7% of $1,437.00 each year.

7% of $1,437.00 (0.07 x $1,437.00) = $100.59

If it asks how much she saves over a certain number of years, just multiply 100.59 times how many years it asks for. Hope this helps.

The required, if Maria takes the defensive driving course and receives the 7% discount on her auto insurance, she will save a total of $301.77 over three years.

What is the investment?

Investment is defined as when an individual spends money on something that returns him or her higher money than the money they invested.

Here,
If Maria spends $1,437.00 on her auto insurance annually and she takes the defensive driving course, she will get a 7% discount on her liability insurance, PIP, comprehensive insurance, and collision insurance for three years.

To calculate the amount of the discount, we first need to find 7% of $1,437.00:

Discount = 0.07 × $1,437.00 = $100.59

So, the amount of the discount that Maria will receive annually is $100.59.

To find the total savings over three years, we multiply the annual discount by three:

Total savings = $100.59 × 3 = $301.77

Therefore, if Maria takes the defensive driving course and receives the 7% discount on her auto insurance, she will save a total of $301.77 over three years.

Learn more about investments here:

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hange each decimal or mixed decimal to a percent.
a. 0.73
b. 0.023
c. 0.176
d. 2.415

Answers

The answer is d.2.415

Answer:

a. 73 percent

b. 2.3 percent

c. 17.6 percent

d. 241.5 percent

Step-by-step explanation:

Brian borrows $7,400 from Ed, who charges him 12% simple interest each year. How much will Brian pay Ed, if he repays after 5 years?

Answers

Answer:

$11,840

Step-by-step explanation:

Answer:

$11,840

Step-by-step explanation:

TRUST ME

Solve for the complimentary angle b

Answers

Answer:

b = 38

Step-by-step explanation:

The two angles form a 90 degree angle so they add to 90

b+52 = 90

Subtract 52 from each side

b+52-52 =90-52

b = 38

Answer:

38

Step-by-step explanation:

90-52=38

and the little box indicates it's a right angle which is 90 degrees

This my homework and I'm bad at math if you can take the time please help me out f(x)= (x-5)to the power of 2 +12

I need the vertex
Axis of symmetry
Domain
Range

Answers

Answer:

Vertex: (5,12)

Axis of Symmetry: x=5

Domain: (-infinity, +infinity)

Range: [12, +infinity)

Step-by-step explanation:

Determine the total surface area of each right triangle-based prism

Answers

Answer:

small prism: 630 m²large prism: 2520 m²

Step-by-step explanation:

The total surface area of the prism is the sum of the base area and the lateral area. The base area is made up of two right triangles, so will be the product of the triangle leg dimensions. The lateral area is made up of three rectangles whose width is that of the prism and whose equivalent length is the perimeter of the triangle base.

For the smaller prism, the area is ...

  (20 m)(21 m) +(3 m)(20 m + 21 m + 29 m) = 420 m² +210 m² = 630 m²

The larger prism is similar, with a scale factor of 2, so its area will be 2² = 4 times that of the smaller prism:

  4×630 m² = 2520 m²

__

In summary, the total surface area of each prism is ...

small prism: 630 m²large prism: 2520 m²

1/13 times 1/2.54 show your work

Answers

Answer:

0.03028467595

Step-by-step explanation:

calculator?

Basic Computation: Testing M1 2 M2 A random sample of 49 measurements from a population with population standard deviation 3 had a sample mean of 10. An independent random sample of 64 measurements from a second population with population standard deviation 4 had a sample mean of 12. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements What distribution does the sample test statistic follow

Answers

Answer:

The sample statistics follows a standard normal distribution since the sample size are large enough.

Step-by-step explanation:

Given that:

First population:

Sample size [tex]n_1[/tex] = 49

Population standard deviation [tex]\sigma_1[/tex]  = 3

Sample mean [tex]\overline x _1[/tex]= 10

Second population:

Sample size [tex]n_2[/tex] = 64

Population standard deviation [tex]\sigma_2[/tex]= 4

Sample mean [tex]\overline x_2[/tex]= 12

The sample statistics follows a standard normal distribution since the sample size are large enough.

The null and alternative hypotheses can be computed as:

[tex]\mathbf{H_o:\mu_1=\mu_2}[/tex]

[tex]\mathbf{H_1:\mu_1\ne\mu_2}[/tex]

Level of significance  = 0.01

Using the  Z-test statistics;

[tex]Z = \dfrac{\overline x_1 - \overline x_2}{\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}}[/tex]

[tex]Z = \dfrac{10- 12}{\sqrt{\dfrac{3^2}{49} + \dfrac{4^2}{64}}}[/tex]

[tex]Z = \dfrac{-2}{\sqrt{\dfrac{9}{49} + \dfrac{16}{64}}}[/tex]

[tex]Z = \dfrac{-2}{\sqrt{0.18367 +0.25}}[/tex]

[tex]Z = \dfrac{-2}{\sqrt{0.43367}}[/tex]

[tex]Z = \dfrac{-2}{0.658536}[/tex]

Z = - 3.037

Z [tex]\simeq[/tex] - 3.04

The P-value = 2P (z < -3.04)

From the z tables

= 2 × (0.00118)

= 0.00236

Thus, since P-value is less than the level of significance, we fail to reject the null hypotheses [tex]H_o[/tex]

Can you please answer number 23. And number 24.
Please please show me how to do it and tell me the answers

Answers

Answer:24 is 34miles per hour

Step-by-step explanation:

Answer:

1st

A pound is defined as exactly 0.45359237 kilograms.

so 50 x 0.45359237 = 22.679619 Kilograms

2. 55km to miles = 34.16

for an approximate result, divide the length value by 1.609

Step-by-step explanation:

Find the value of x.



Group of answer choices

77

34

69

146

Answers

Answer:

69

Step-by-step explanation:

Use the 3x-2 and take it out

A store manager purchases a DVD for $15. He marks it up to $21.75 in order to make a profit. What is the percent of increase?

Answers

Percent of increase: 100 * (final - initial)/initial, final = 21.75, initial = 15

(21.75-15)/15 = 0.45 * 100
There is a 45% increase

What is the perimeter of the triangle?



a
84 in
b
94 in
c
74 in
d
64 in

Answers

Answer:

The answer is C

Step-by-step explanation:

We alsreadyknow that 37 and 12 is the 2 given lines.  and  The last line is not 37 but pretty close making C the answer.

Answer:

D) 64 In

Step-by-step explanation:

P=12+37+64

A polygon is graphed on a coordinate plane, with a vertex located at
a point represented by (x,y).
The polygon is dilated with a scale factor, a , with the origin as the
center of dilation. The dilated image of the polygon is larger than
the polygon.
Which statement is true?

Answers

Answer:

a is greater than 1

Step-by-step explanation:

Let the two polygons be represented as  A and B.

Where A is the original polygon and B is the image of A

Such that

Polygon A has vertex (x,y) and scale factor = a

From the question, we understand that polygon B is bigger than A

When the dilated image (polygon B) is bigger than the original image (polygon A), then the scale factor is greater than 1.

Take for instance.

One of the coordinate point of polygon A is (2,4)

The corresponding coordinate point of polygon B will be greater than (2,4) because a is greater than 1.

Take a as 2:

The corresponding point on Polygon B would be 2 * (2,4) = (4,8)

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