I have attached 3 different problems, please could you help. Thank you

  1a) 210

  1b) 0.18

  2) 17.7 will fit (> 17)

  3) 515 cm^2

Step-by-step explanation:

1a) The sample of 25 is exactly 1/30 of the population of 750, so the number of orange cakes in the population will be 30 times the number in the sample.

The total number of orange cakes made on Monday is 30·7 = 210.

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1b) The lowest number that will round to 5 is 4.5. The lowest probability that a cake is an orange cake is ...

  4.5/25 = 18/100 = 0.18

The lower bound on the probability that the cake is orange is 0.18.

2) The working shown is partly correct.

The possible error in the box dimension is 1/2 cm, so the box may be as short as 28 -1/2 cm = 27.5 cm.

The possible error in the disc case dimension is 1/2 mm = 0.05 cm, so the case may be as thick as 1.5 +.05 = 1.55 cm.

The minimum number discs that will fit in the case is (27.5 cm)/(1.55 cm) = 17.7. Thus, 17 cases will definitely fit in the box.

3) The shaded area will be the largest when the outside rectangle is the largest and the inside rectangle is the smallest. Errors in dimensions can be as much as 1/2 cm, so the Outside rectangle can be 42.5 cm by 21.5 cm. The inside rectangle can be as small as 27.5 cm by 14.5 cm.

Then the shaded area can be as large as ...

  (42.5)(21.5) -(27.5)(14.5) = 515 . . . . cm^2

it would be 6xy and -16xy.