Mist ate 2 slices of cake. Flout ate 1 slice. If Mist ate 2/4 of the cake and all the slices were the same size, what fraction of the cake remained after Mist and Flout had eaten?


Answer 1
Answer: 1/4 remained
2/4 - mist + 1/4 -flout = 3/4
4/4 - 3/4 = 1/4
Answer 2
Answer: one fourths would be left

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Factor each expression by factoring out the common binomial 5a(y + 4) + 8(y + 4)

A right triangle has side lengths a, b , and c as shown below. Use these lengths to find cosx , sinx and tanx. (GIVING BRAINLEST TO BEST ANSWER)​


9514 1404 393


  • cos(x) = a/c
  • sin(x) = b/c
  • tan(x) = b/a

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to help you remember the relationships between triangle sides and trig functions. These abbreviations tell you that ...

  Sin = Opposite/Hypotenuse   ⇒   sin(x) = b/c

  Cos = Adjacent/Hypotenuse   ⇒   cos(x) = a/c

  Tan = Opposite/Adjacent   ⇒   tan(x) = b/a

Hector's school is holding a fitness challenge. Student are encouraged to exercise at least 2 1/2 hours per week. Hector exercises about the same number of hours each week. During a 4-week period, he exercises for 11 1/2 hours. Hector wants to compare his exercise rate with the fitness challenge rate. How many hours per week does Hector exercise?



The answer is 2 7/8

Final answer:

Hector exercises 2.875 hours per week, which is calculated by dividing the total of 11 1/2 hours he exercised during the 4 weeks by 4.


Hector wants to compare his exercise rate with the fitness challenge rate. To find out how many hours per week Hector exercises, we need to divide the total hours he exercised in a 4-week period by the number of weeks.

Hector exercised for 11 1/2 hours during 4 weeks, which is equal to 11.5 hours. Dividing 11.5 hours by 4 weeks gives us:

11.5 hours ÷ 4 weeks = 2.875 hours per week

Thus, Hector exercises 2.875 hours per week, which is slightly more than the 2 1/2 hours (or 2.5 hours) per week recommended by the fitness challenge.

Learn more about Exercise Rate here:



In order to estimate the average electric usage per month, a sample of 81 houses was selected and the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is _________?


Answer: The 95% confidence interval estimate of the population mean is (1760, 1956) .

Step-by-step explanation:

Formula for confidence interval for population mean((\mu)) :

\overline{x}\pm z^*(\sigma)/(√(n))

, where n= Sample size

\overline{x} = sample mean.

z^* = Two-tailed critical z-value

\sigma = population standard deviation.

By considering the given information, we have

n= 81

\sigma=450 kilowatt-hours.

\overline{x}=1858 kilowatt-hours.

By using the z-value table ,

The critical values for 95% confidence interval : z^*=\pm1.960

Now , the 95% confidence interval estimate of the population mean will be :

1858\pm (1.960)(450)/(√(81))\n\n=1858\pm(1.960)(450)/(9)=1858\pm98\n\n=(1858-98,\ 1858+98)\n\n=(1760,\ 1956)

Hence, the 95% confidence interval estimate of the population mean is (1760, 1956) .

Divide 44 in the ratio 2:8:6




Step-by-step explanation:

A cone is inside a cylinder. The cone and the cylinder have the same base and height.The part of the cylinder that is NOT taken up by the cone has twice the volume of the cone. What fraction of the total cylinder is taken up by the cone?

A. 3/2
B. 2/3
C. 1/2
D. 1/3




Step-by-step explanation:


B. 2/3 because I just gesused idk

Please help need help asap!!


5v - 9 = 6
5v = 6 + 9
v = (6 + 9) / 5
v = 3

8v + 7 = 8 (3) + 7 = 31