As a gift for your hard-earned victory in defense of the kingdom, the king gives you a reward. One penny with the promise to double it every day for the next 25 days. What would a reasonable range be in this situation? How many pennies will you have on the 25th day?
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Answer: 9/56

Step-by-step explanation:

Answer:

x = (2√6)/3

Step-by-step explanation:

Reference angle = 30°

Hypotenuse = x

Adjacent = √2

Thus, applying trigonometric ratio, we have:

Cos(30) = adj/hyp = √2/x

x*cos(30) = √2

x = √2/cos(30)

x = √2/(√3/2) (cos 30 = √3/2)

x = √2 × 2/√3

x = (2√2)/√3

Rationalize

x = (2√2 × √3)/(√3 × √3)

x = (2√6)/3

Answer:

2.6, 2 3/5, 2 6/10

Step-by-step explanation:

2.6 as a fraction is 2 3/5. When you read the decimal 2.6, it is read as ''2 and 6 tenths. '' This can also be written as a mixed number of 2 6/10.

9514 1404 393

Answer:

  (5, 3 2/3)

Step-by-step explanation:

The centroid is the average of the vertex coordinates:

  (A +B +C)/3 = ((2, 3) +(8, 1) +(5, 7))/3 = (2+8+5, 3+1+7)/3 = (5, 3 2/3)

Answer:

46940064

Step-by-step explanation:

1)

The angle of inclination is the angle between the horizontal and the ramp.

Using the sine ratio in the right triangle formed by the ground and the ramp

let x be the angle of inclination, then

sinx = \frac{opposite}{hypotenuse}

hypotenuse

opposite

= \frac{0.7}{4.2}

4.2

0.7

, then

x = sin^{-1}sin

−1

(\frac{0.7}{4.2}

4.2

0.7

) ≈ 10° ( to the nearest degree )

(2)

Again there is a right triangle between the ground and the vertical height of the kite, with hypotenuse being length of string.

let y be the height of the kite and x the horizontal distance, then

sin27° = \frac{opposite}{hypotenuse}

hypotenuse

opposite

= \frac{y}{176}

176

y

( multiply both sides by 176 )

176 × sin27° = y , then

y ≈ 80m ( to the nearest metre ) ← height of kite

and

cos27° = \frac{adjacent}{hypotenuse}

hypotenuse

adjacent

= \frac{x}{176}

176

x

( multiply both sides by 176 )

176 × cos27° = x , then

x ≈ 157m ( to the nearest metre ) ← horizontal distance

Answer:

60 percent

Step-by-step explanation:

Where: 40 is the old value and 64 is the new value. In this case we have a positive change (increase) of 60 percent because the new value is greater than the old value.

Chance of success

0.03841 or 3.84%

Step-by-step explanation:

Answer:

the percent of her saving to the price of the bike is 35%

Answer: R = √(3*r^2)

Step-by-step explanation:

For a cylinder with radius r and height H, the volume is:

V = pi*r^2*H

For a cone of height H, and with a base of radius R, the volume is:

V = (1/3)*pi*R^2*H

In this case, we know that both figures have the same height, and the same volume, then we can write:

pi*r^2*H = (1/3)*pi*R^2*H

Now we can divide by pi in both sides to get:

(pi*r^2*H)/pi = ((1/3)*pi*R^2*H)/pi

r^2*H = (1/3)*R^2*H

Now we can divide both sides by H:

(r^2*H)/H = ((1/3)*R^2*H)/H

r^2 = (1/3)*R^2

Now we want to write R in terms of r.

Then we need to isolate R in the above equation:

r^2 = (1/3)*R^2

3*r^2 = R^2

√(3*r^2) = R

R = √(3*r^2)

Answer:

$16.20

Step-by-step explanation:

Bill: $54.00

Tip: 20%

People: 4

To figure out 10% of the bill, you need to move the decimal point over to the left one place: $5.40

10%: $5.40

5.40 times 2 = $10.80

54.00 + 10.80 = 64.80

Grand Total= $64.80

Since there are 4 people, we need to divide by 4:

64.80 divided by 4 = $16.20

Answer:

a. 5ab                  b. 11x+15y

Answer:

a. 5ab

b. 11x+5y

Step-by-step explanation:

12ab-7ab they have the same variables, so you can just subtract

19x+5y-8x just rearrange it to 19x-8x+5y and subtract 19x and 8x

Answer:

5/11*5/11=25/121

Step-by-step explanation:

There are 6+5 marbles.

Of those, 5 are red.

The chances of drawing a red marble are 5/11

Since you replace the marble you drew, the chances each draw remain 5/11

You cannot draw two red marbles without drawing a red marble on your first draw, so the odds of you making a second draw are 5/11. The odds of that also being red are 5/11… but we only care about that 5/11ths the time

Answer:

The y intercept is positive 1 because that's where the graph crosses the y axis.

Answer:

Horizontal Asymptote of y= -7

Step-by-step explanation:

Answer:

Ok... what's the question

Step-by-step explanation:

Answer:

anwser= 8 she will have 0 left

Step-by-step explanation:

each student gets 8 stickers

:)

Answer:

x is less than or equal to 3

Step-by-step explanation:

The dot is a closed dot, which means that it is something or equal to, and the arrow is pointing down, which means less than. So the sign would be less than or equal to (sorry I don't have that sign on my computer). The dot is on three, so the inequality is x is less than or equal to 3.

Answer:

$7700

Step-by-step explanation:

As the account earns 6% interest, if we find 6% of $5000 we get $300, the interest is simple and given every month, meaning you get $2700 in interest as $300 x 9 months = $2700

$5000 initial + $2700 interest = $7700

EDIT:

It could be that the interest is 6% yearly, which means that yearly you get 6% interest, and the answer is $5225.

6% interest is $300 per year

$300÷12= $25 per month

$25 x 9 months = $225

$5000 initial plus $225 interest = $5225 total

Answer:

4/27=14.8%

Step-by-step explanation:

In order to solve this, we have to see first each option possible, there are 2/3 of possibilities that a random Entrée ends up being Chicken Cutlet or Lasagna, then you have again 2/3 chances to get milk or water, and as you only want fruit the chances are 1/3 that you get that.

In order to calculate if this could happen at random we have to multiply all of the odds:

[tex]Probability: \frac{2}{3} *\frac{2}{3} *\frac{1}{3} \\Probability: \frac{2*2*1}{3*3*3} \\Probability: \frac{4}{27}[/tex]

So we know that for every 27 times you pick a lunch at random, 4 times it will not have the Veggie Wrap, contain milk or water, and will have fruit as the snack.

There are 2/3 of possibilities that a random Entrée ends up being Chicken Cutlet or Lasagna, then you have again 2/3 chances to get milk or water, and as you only want fruit the chances are 1/3 that you get that.

We need to now multiply the odds:

2/3x2/3x1/3

2x2x1/3x3x3

4/27

So we know that for every 27 times you pick a lunch at random, 4 times it will not have the Veggie Wrap, contain milk or water, and will have fruit as the snack.

So now we know it is, %15 rounded but 14.8% not rounded.

Answer:

24 CDs

Step-by-step explanation:

if he dropped half of his CDs then the other half is in the equation. 12×12=24 the 6 is just there to throw you off...

if I get it wrong my bad its 2 am

Answer:

Jason starts with 18 CDs

Step-by-step explanation:

12 x 2 = 24

24 - 6 = 18

Answer:

your answer will be A'B'/AB=3/1=3

Step-by-step explanation:

i hope this helps you

Answer:

3 is the correct answer......

Answer:

a 35

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

These are vertical angles, so both equal 51 degrees. To solve for x, solve the equation (9x + 6) = 51. 51 - 6 is 45. 45 divided by 9 is 5. So x = 5.

Hope it helps!

Answer:

answer is 3 3/20

Answer:

16/15 or 1  1/15

Step-by-step explanation:

4/5 divided by 3/4

Flip 3/4 so it is 4/3

Multiply 4/5 by 4/3

16/15

Answer:

67°

Step-by-step explanation:

Corresponding angles are equal in parallel lines.

Here, ∠acb and ∠aed are corresponding angles for lines bc and de

hence ∠aed = ∠acb = 39

in triangle ade,

x + 74 + 39 = 180 (angle sum property of a triangle)

x = 67°

Answer:39/50

Step-by-step explanation:

Answer:

31.6

Step-by-step explanation:

Answer:

1. Skewed to left (negative)

2. Right skewed (positive)

3. Symmetric

Step-by-step explanation: