All categories

2 years ago

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

1 answer:

6 0

First we need to find out what kind of logarithm rule is given, the given is logarithm product rule which states that a log of a product is equal to the sum of the log of the first base and the log of the second base.

By:

= log (1.37 x 10⁹) = log (1.37) + log (10⁹)

= log (1.37) + 9

= 9 + log (1.37)

In the meantime, 1.37 is between 1 and 10 its logarithm will be between 0 and 1. Thus, the value of log (1.37 x 10⁹) falls between 9 and 10 because when you compose a scientific notation you will always have a number among 1 and 10 by 10 to some power. That power tells you the integer part of the logarithm.

You might be interested in

On a road map, the locations A, B and C are collinear. Location C divides the road from location A to B, such that AC:CB = 1:2.

koban [17]

Answer:

C. (-1,-2)

Step-by-step explanation:

Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.

Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Substituting the values of the coordinates, we have

x = (mx₂ + nx₁)/(m + n)

3 = (1 × x₂ + 2 × 5)/(2 + 1)

3 = (x₂ + 10)/3

multiplying through by 3, we have

9 = x₂ + 10

x₂ = 9 - 10

x₂ = -1

y = (my₂ + ny₁)/(m + n)

10 = (1 × y₂ + 2 × 16)/(2 + 1)

10 = (x₂ + 32)/3

multiplying through by 3, we have

30 = y₂ + 32

y₂ = 30 - 32

y₂ = -2

So, the coordinates of B are (-1, -2)

3 0

2 years ago

Alex787 [66]

One possible inequality is:

299m+261j ≥ 1000.

Explanation:

m is the number of cups of milk and j is the number of cups of juice.

Each cup of milk contains 299 mg of calcium. This gives us 299m mg of calcium for m cups of milk drank.

Each cup of juice contains 261 mg of calcium. This gives us 261j mg of calcium for j cups of juice drank.

Together, this would be a total of 299m+261j mg of calcium.

We want to meet or exceed 1000 mg of calcium. This means we could have more than 1000 or equal to 1000; this gives us the inequality symbol "greater than or equal to":

299m+261j ≥ 1000

5 0

2 years ago

Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the ta

Evgen [1.6K]

Answer:

1) He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2) He did not multiply the numerator and denominator by the correct number to equal 1,500.

5) He should have multiplied the numerator and denominator by 75, not 30, because 20 x 75 = 1,500.

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

A falcon flying 55 mph crosses a lake in 1 minute. How long would it take a hummingbird flying 45 mph to cross the same lake?

OverLord2011 [107]

Answer:

1 2/9 minutes

Step-by-step explanation:

55 mph

55 / 60 = 11/12

11/12 of a mile = 1 minute

45 mph

45 / 60 = 3/4

3/4 of a mile = 1 minute

11/12 divided by 3/4

11/12 * 4/3

We can cross-cancel

11/3 * 1/3 = 11/9 = 1 2/9

It takes 1 2/9 minutes for the hummingbird to cross the lake

Hope this helps!

(Please let me know if I did something wrong!)

7 0

2 years ago

Read 2 more answers

For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured

kati45 [8]

The answers are the following:
P(A)=0.75
P(B|A)=0.9
P(B|A′)=0.8
P(C|A∩B)=0.8
P(C|A∩B′)=0.6
P(C|A′∩B)=0.7
P(C|A′∩B′)=0.3

4 0

2 years ago