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3 years ago

Which number line represents the solution set for the inequality 3(8-4x) < 6(x-5) ?

Mathematics

1 answer:

viktelen [127]3 years ago

7 0

Answer:

Second number line(from top to bottom).

Step-by-step explanation:

We are given the following inequality:

$3(8 - 4x) < 6(x - 5)$

It is solved similarly to an equality, so:

$24 - 12x < 6x - 30$

$-18x < -54$

Multiplying by -1, the signal changes from < to >. So

$18x > 54$

$x > \frac{54}{18}$

$x > 3$

Thus the correct answer is given by the second number line.

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3 years ago

One cubic meter of water weighs approximately 2200 pounds. There are 100 cm in one meter. If you have a box-shaped fish tank tha

Diano4ka-milaya [45]

Answer:

158.4 pounds

Step-by-step explanation:

first find the volume of the tank

$V = 30 \times 30 \times 80$

$V = 72000 cm^3$

to convert this to m^3 we know that 1m = 100cm

$V = 72000 cm^3 \times \left(\dfrac{1\,\text{m}}{100\,\text{cm}}\right)^3$

$V = 72000 cm^3 \times \left(\dfrac{1\,\text{m}^3}{100^3\,\text{cm}^3}\right)$

the cm^3 cancel out.

$V = \dfrac{72000}{100^3} m^3$

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by simply converting the side-lengths to meters beforehand can give you this answer directly:

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multiply both sides with 0.072 to find our answer:

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3 years ago

Read 2 more answers

The times to process orders at the service counter of a pharmacy are exponentially distributed with mean 1 0 minutes. If 100 cus

g100num [7]

Answer:

Therefore, the probability that at least half of them need to wait more than 10 minutes is 0.0031.

Step-by-step explanation:

The formula for the probability of an exponential distribution is:

P(x < b) = 1 - e^(b/3)

Using the complement rule, we can determine the probability of a customer having to wait more than 10 minutes, by:

p = P(x > 10)

= 1 - P(x < 10)

= 1 - (1 - e^(-10/10) )

= e⁻¹

= 0.3679

The z-score is the difference in sample size and the population mean, divided by the standard deviation:

z = (p' - p) / √[p(1 - p) / n]

= (0.5 - 0.3679) / √[0.3679(1 - 0.3679) / 100)]

= 2.7393

Therefore, using the probability table, you find that the corresponding probability is:

P(p' ≥ 0.5) = P(z > 2.7393)

P(p' ≥ 0.5) = 0.0031

Therefore, the probability that at least half of them need to wait more than 10 minutes is 0.0031.

8 0

3 years ago