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3 years ago

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Which statement compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than fo

r Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.

1 answer:

LUCKY_DIMON [66]3 years ago

7 0

Answer:

a

Step-by-step explanation:

ok'

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Find x?<br> In 3x - In(x - 4) = ln(2x - 1) +ln3

earnstyle [38]

Answer:

$x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

Step-by-step explanation:

Because $3\, x$ is found in the input to a logarithm function in the original equation, it must be true that $3\, x > 0$ . Therefore, $x > 0$ .

Similarly, because $(x - 4)$ and $(2\, x - 1)$ are two other inputs to the logarithm function in the original equation, they should also be positive. Therefore, $x > 4$ .

Let $a$ and $b$ represent two positive numbers (that is: $a > 0$ and $b > 0$ .) The following are two properties of logarithm:

$\displaystyle \ln (a) + \ln(b) = \ln\left(a \cdot b\right)$ .

$\displaystyle \ln (a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ .

Apply these two properties to rewrite the original equation.

Left-hand side of this equation:

$\begin{aligned}&\ln(3\, x) - \ln(x - 4)= \ln\left(\frac{3\, x}{x -4}\right)\end{aligned}$

Right-hand side of this equation:

$\ln(2\, x- 1) + \ln(3) = \ln\left(3 \left(2\, x - 1\right)\right)$ .

Equate these two expressions:

$\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ .

The natural logarithm function $\ln$ is one-to-one for all positive inputs. Therefore, for the equality $\begin{aligned}\ln\left(\frac{3\, x}{x -4}\right) = \ln(3(2\, x - 1))\end{aligned}$ to hold, the two inputs to the logarithm function have to be equal and positive. That is:

$\displaystyle \frac{3\ x}{x - 4} = 3\, (2\, x - 1)$ .

Simplify and solve this equation for $x$ :

$x^2 - 5\, x + 2 = 0$ .

There are two real (but not rational) solutions to this quadratic equation: $\displaystyle \frac{5 + \sqrt{17}}{2}$ and $\displaystyle \frac{5 - \sqrt{17}}{2}$ .

However, the second solution, $\displaystyle \frac{5 - \sqrt{17}}{2}$ , is not suitable. The reason is that if $x = \displaystyle \frac{5 - \sqrt{17}}{2}$ , then $(x - 4)$ , one of the inputs to the logarithm function in the original equation, would be smaller than zero. That is not acceptable because the inputs to logarithm functions should be greater than zero.

The only solution that satisfies the requirements would be $\displaystyle \frac{5 + \sqrt{17}}{2}$ .

Therefore, $x = \displaystyle \frac{5 + \sqrt{17}}{2}$ .

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3 years ago

What is the following quotient?<br><br> Square root of 120/square root of 30

Mekhanik [1.2K]

Answer:

The square root of 120 is 10.9545.

The square root of 30 is 5.47723.

10.9545 divided by 5.47723 is approximately 2.0000073

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3 years ago

Archimedes knew that at 8 am the sunlight reaches the ground at an angle if 43 degrees. The rock besides him is 7 meters tall. H

Alenkasestr [34]

Answer:

Distance between Archimedes and the rock = 7.51 m ≅

Step-by-step explanation:

The sunlight makes an angle of depression of 43 degrees

Hence angle between the rock and the sunlight rays is = 90-43=47 degrees

Distance between Archimedes and the rock = Tan 47 = X/7

X = 7 tan 47 = 7.506580970172 = 7.51m ≅

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3 years ago

A 20-kilogram object falls 2.0 meters to the floor. At what point in its fall

professor190 [17]

Answer:

half way to the floor

Step-by-step explanation:

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3 years ago

Brooke earned $34 for 4 hours of work

zalisa [80]

Rachel earned $34 in 4 hours at her job today. She wants to know how much she could earn tomorrow if she works 10 hours at the same hourly rate. Answer:

Step-by-step explanation:

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2 years ago

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