Sara needs 40 inches of yarn to glue onto each of 25 picture frames. she has a ball of yarn with a total of 950 inches. which of the following explains whether sara has enough yarn to glue onto all 25 picture frames?

a. because 950 ÷ 40 = 24 r10, she has enough yarn for all 25 picture frames.

b. because 950 ÷ 40 = 24 r10, she has enough yarn for only 24 picture frames.

c. because 950 ÷ 40 = 23 r30, she has enough yarn for only 23 picture frames.

d. because 950 ÷ 40 = 23 r30, she has enough yarn for only 24 picture frames.

  C. Because 950 ÷ 40 = 23 R30, she has enough yarn for only 23 picture frames.

Step-by-step explanation:

  950/40 = 23.75 = 23 r 30

Sara has enough for 23 frames.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).