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2 years ago

3. To which set of numbers does the product of the following numbers belong?

Mathematics

1 answer:

PIT_PIT [208]2 years ago

7 0

Natural number because they are while

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If log2 5 = k, determine an expression for log32 5 in terms of k.

lukranit [14]

Answer:

$log_3_2(5)=\frac{1}{5} k$

Step-by-step explanation:

Let's start by using change of base property:

$log_b(x)=\frac{log_a(x)}{log_a(b)}$

So, for $log_2(5)$

$log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)$

Now, using change of base for $log_3_2(5)$

$log_3_2(5)=\frac{log(5)}{log(32)}$

You can express $32$ as:

$2^5$

Using reduction of power property:

$log_z(x^y)=ylog_z(x)$

$log(32)=log(2^5)=5log(2)$

Therefore:

$log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)$

As you can see the only difference between (1) and (2) is the coefficient $\frac{1}{5}$ :

So:

$\frac{log(5)}{log(2)} =k\\$

$log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k$

6 0

2 years ago

Sophia pays £222 for a plane ticket.

Maurinko [17]

9514 1404 393

Answer:

24.6%

Step-by-step explanation:

The cost of the ticket in euros is ...

£222 × €1.38/(£1) = €306.36

Then the ratio of the tax to the to the total cost is ...

€100/(€306.36 +100) = 100/406.36 ≈ 24.6%

6 0

2 years ago

Please help solve for x

Ludmilka [50]

Answer:

8.49

Step-by-step explanation:

there is a little formula related to the famous formula of Pythagoras.

it says that the height of a triangle is the square root of the product of both segments of the baseline (the segments the height splits the baseline into).

so, x is actuality the height of the triangle.

x = sqrt(3×24) = sqrt(72) = 8.49

7 0

3 years ago

Nancy shot a 24 on 4 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes?

Elden [556K]

Answer:

108

Step-by-step explanation:

"At this rate, ..." means we're to assume Nancy's score is proportional to the number of holes:

score/18 = 24/4

Multiplying by 18, we get ...

score = 18(24/4) = 18(6) = 108

Nancy can expect a score of 108 on 18 holes.

4 0

2 years ago

5. Name three sets of supplementary angles.<br>and<br>and<br>and

jarptica [38.1K]

87 and 93
45 and 135
74 and 106

8 0

2 years ago