Ask question

Ask question

All categories

3 years ago

15

To ensure he never eats the whole cake, Bobby only decides to eat half of what’s left for each serving. If 2/3 of the cake are l

eft initially, and no one else but Bobby eats the cake, how much of the cake will Bobby have eaten by his 5th serving?

1 answer:

siniylev [52]3 years ago

4 0

1st serving: 2/3 * 1/2 = 2/6 or 1/3
2nd serving: 1/3 * 1/2 = 1/6
3rd serving: 1/6 * 1/2 = 1/12
4th serving: 1/12 * 1/2 = 1/24
5th serving: 1/24 * 1/2 = 1/48

1/3 + 1/6 + 1/12 + 1/24 + 1/48
1/3 * 16/16 = 16/48
1/6 * 8/8 = 8/48
1/12 * 4/4 = 4/48
1/24 * 2/2 = 2/48
1/48 * 1/1 = 1/48

16/48 + 8/48 + 4/48 + 2/48 + 1/48 = 31/48

Bobby ate 31/48 of the cake in total.

You might be interested in

What is the unit rate of 144 miles on 4.5 gallons

Vinvika [58]

Miles using 4.5 gallons = 144 miles
Miles using 1 gallon
(144 miles / 4.5 gallons)
32 miles / gallon

3 0

2 years ago

Read 2 more answers

Hi I need to know the slope(m) before 11:00 I know the y-intercept(b) is -3

Alexxandr [17]

Answer:

slope is 2/3

Step-by-step explanation:

y=mx + b where m is the slope

6 0

2 years ago

Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

Ugo [173]

Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ <em>(Approximated)</em>

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ <em>(Approximated)</em>

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

3 years ago

I'll give brainlist for this !!!!!!!!

castortr0y [4]

Answer:

The first error in the bill is +8

because when two opposite signs of number are multiplied so the result is always negative.

so,

2 × -4 = -8

instead of 8 their should be -8.

hope this answer helps you dear...take care!

4 0

2 years ago

35 POINTS!!!!!!!!!!!!!!!!!!!

loris [4]

The answer is C

see attached picture:

4 0

2 years ago