Without actually calculating the logarithm, determine what two integers the value of log(1.37×109) falls between.

Answer: OPTION C.

Step-by-step explanation:

It is essential to consider the following:

Dilation:

• A transformation where the image retains the same shape as the original but differs in size.

• Dilation maintains the order of points.

•  Measurements of angles remain unchanged.

Translation:

• A transformation that keeps the image identical in size and shape to the original.

• Translation preserves the ordering of points.

• The angle measurements do not change.

Consequently, since Square T underwent translation followed by dilation to form Square T'', we conclude that the rationale explaining why they are similar is:

Translations and dilations maintain the order of points; thereby, the corresponding sides of squares T and T″ are proportional.

<span>The outcome = probability of choosing exactly 2, 3, 4, or 5 passing plays. The probability of selecting exactly two passing plays is given by: (8C2)*(9*8)* (15*14*13*12*11*10) /(26*28*.....19) where: 8C2 represents the combinations of choosing two from 8 and probability that the first passing play is selected = 9/26 probability that the second passing play is chosen = 10/25, and so forth you can similarly calculate the other three scenarios and sum them to find the total probability.</span>

D) moved 2 units to the left and 4 units upwards

In the first month, she made a payment of $1451

In the second month, she paid one-third of that, which amounts to:
1451/3 = 483.66

For the third month, she pays one-third of 483.66 as indicated, meaning she takes one-third of the prior month's payment.

483.66/3 = 161.22

In the fourth month, her payment was

161.22/3 = 53.74

Altogether, her total payments amounted to:

$2149.62 - B.

Hope this information is helpful:)

Answer: Initially, he had 27 sweets.

Step-by-step explanation: The most logical approach is to work backwards from what remained after the third day to the start of the first day.

On the third day, he consumed one-third of his sweets and was left with 8. If we let the total sweets on day three be denoted as a, then one-third of a equals what he ate and the two-thirds left equals 8, giving us:

8/a = 2/3

By cross-multiplying, we find:

8 x 3 = 2a

Therefore, 24 = 2a

This leads to a = 12.

Let the sweets on day two be represented as b. If he consumed one-third of b and was left with 12, we have the same structure; hence:

12/b = 2/3

Cross-multiplying gives:

12 x 3 = 2b

So, 36 = 2b, leading to b = 18.

Denote the number of sweets on day one as x. If one-third of x was eaten and 18 remained, we can set up the equation:

18/x = 2/3

Again, cross-multiplying results in:

18 x 3 = 2x

Which simplifies to 54 = 2x, yielding x = 27.

Thus, Tim received 27 sweets at the start.