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3 years ago

Solve 3 log6 2 + 2 log6 3 − log6 x = 2.

1 answer:

3 0

$D:x \ \textgreater \ 0\\\\3\log_62+2\log_63-\log_6x=2\\-----------------------\\Use:\\\log_ab=c\iff a^c=b\\\log_ab+\log_ac=\log_a(bc)\\\log_ab-\log_ac=\log_a(\frac{b}{c})\\\log_ab^c=c\log_ab\\-----------------------\\\log_62^3+\log_63^2-\log_6x=2\\\\\log_68+\log_69-\log_6x=\log_66^2\\\\\log_6(8\cdot9)-\log_6x=\log_636\\\\\log_672-\log_6x=\log_636\\\\\log_6\frac{72}{x}=\log_636\iff\dfrac{72}{x}=36\\\\\dfrac{x}{72}=\dfrac{1}{36}\ \ \ \ \ |multiply\ both\ sides\ by\ 72\\\\x=\dfrac{72}{36}\\\\\boxed{x=2}\in D$

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A swim meet has 13 contestants signed up for the 100-meter butterfly event. The first heat has 6 swimmers. How many different wa

tino4ka555 [31]

Answer:

6 swimmers in the first heat can be arranged in 1716 different ways.

Step-by-step explanation:

A swim meet has 13 contestants signed up. To calculate the arrangement of first 6 swimmers in first heat we will use combinations because order doesn't matter.

So to select 6 swimmers out of 13 contestants number of different ways

= $^{13}C_{6}$

= $\frac{13!}{(6!)(13-6)!}$

= $\frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!}$

= $\frac{13\times 12\times 11\times 10\times 9\times 8}{6\times 5\times 4\times 3\times 2\times 1}$

= $\frac{1235520}{720}$

= 1716

Therefore, 6 swimmers in the first heat can be arranged in 1716 different ways.

5 0

3 years ago

An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is

Ganezh [65]

Answer:

(a) 0.20

(b) 31%

Step-by-step explanation:

The random variable Y models the amount of time the subject has to wait for the light to flash.

The density curve represents that of an Uniform distribution with parameters a = 1 and b = 5.

So, $Y\sim Unif(1,5)$

(a)

The area under the density curve is always 1.

The length is 5 units.

Compute the height as follows:

$\text{Area under the density curve}=\text{length}\times \text{height}$

$1=5\times\text{height}\\\\\text{height}=\frac{1}{5}\\\\\text{height}=0.20$

Thus, the height of the density curve is 0.20.

(b)

Compute the value of P (Y > 3.75) as follows:

$P(Y>3.75)=\int\limits^{5}_{3.75} {\frac{1}{b-a}} \, dy \\\\=\int\limits^{5}_{3.75} {\frac{1}{5-1}} \, dy\\\\=\frac{1}{4}\times [y]^{5}_{3.75}\\\\=\frac{5-3.75}{4}\\\\=0.3125\\\\\approx 0.31$

Thus, the light will flash more than 3.75 seconds after the subject clicks "Start" 31% of the times.

(c)

Compute the 38th percentile as follows:

$P(Y$

Thus, the 38th percentile is 2.52 seconds.

4 0

3 years ago

Please help I will mark brainliest

Ugo [173]

You don’t even have brainliest...

6 0

3 years ago

How do you convert 10/6 into a mixed number

Westkost [7]

Well, First you want to find out how many times six can go into ten. Since its only once, you immediately get the number 1 as your whole number. Now because you've taken six out of ten you're left with 4/6. The mixed number would be 1 and 4/6 or 1 and 2/3 if you're simplifying

3 0

4 years ago

Read 2 more answers

Simplify the expression in part C, and explain what the number means with regard to the problem.

alexdok [17]

Answer: |55.75 – (-15.8)| = |55.75 + 15.8| = |71.55| = 71.55

Step-by-step explanation: The distance between two positions with longitudes A and B is given by ||A| - |B|| if the two positions are at the same side of the meridian (0 degrees longitude) and |A| + |B| if both positions are at different sides of the meridian.

4 0

3 years ago