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sashaice [31]
3 years ago
8

If the interval (a, oo) describes all values of x for which the graph of f(x) =

Mathematics
1 answer:
zysi [14]3 years ago
3 0

Answer:

Answer:

a = - 1.1

Step-by-step explanation:

Condition for a single variable function f(x) to be decreasing is f'(x) < 0.

So, in our case, .

Then, differentiating with respect to x on both sides we get,

⇒

⇒

{Dividing both sides with - 1 and hence the inequality sign changes}

⇒

⇒ 8 > - 6x³ {Multiplying both sides with x³}

⇒ 6x³ > - 8 {Interchanging the sides}

⇒

⇒ x > - 1.1

Therefore, a = - 1.1. (Answer)

Step-by-step explanation:

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Find the value of the arc x.
julsineya [31]

Answer:

216°

Step-by-step explanation:

Both chords are the same length, so the left and right arcs are both 72°.  The whole circle is 360°, so:

72° + 72° + x = 360°

x = 216°

7 0
2 years ago
What is 9/18 simplified
White raven [17]
1/2.

divide everything by 9.
7 0
3 years ago
Read 2 more answers
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters tha
uranmaximum [27]

Answer:

0.6826 = 68.26% probability that the first machine produces an acceptable cork.

0.933 = 93.3% probability that the second machine produces an acceptable cork.

The second machine is more likely to produce an acceptable cork.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

What is the probability that the first machine produces an acceptable cork?

The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm, which means that \mu = 3, \sigma = 0.1

Acceptable between 2.9 and 3.1, which means that this probability is the pvalue of Z when X = 3.1 subtracted by the pvalue of Z when X = 2.9.

X = 3.1

Z = \frac{X - \mu}{\sigma}

Z = \frac{3.1 - 3}{0.1}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 2.9

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.9 - 3}{0.1}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability that the first machine produces an acceptable cork.

What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)

For the second machine, we have that \mu = 3.04, \sigma = 0.04. Same probability we have to find out. So

X = 3.1

Z = \frac{X - \mu}{\sigma}

Z = \frac{3.1 - 3.04}{0.04}

Z = 1.5

Z = 1.5 has a pvalue of 0.9332

X = 2.9

Z = \frac{X - \mu}{\sigma}

Z = \frac{2.9 - 3.04}{0.04}

Z = -3.5

Z = -3.5 has a pvalue of 0.0002

0.9332 - 0.0002 = 0.933

0.933 = 93.3% probability that the second machine produces an acceptable cork.

Which machine is more likely to produce an acceptable cork?

Second one has a higer probability, so it is more likely to produce an acceptable cork.

6 0
3 years ago
Rewrite the following mixed number as a decimal. <br><br> 8 1/100
Lemur [1.5K]

Answer:

8.01

Step-by-step explanation:

8\frac{1}{100} is the same as \frac{801}{100}

Divide:

801 ÷ 100 = 8.01

7 0
3 years ago
Read 2 more answers
Suppose that the population of deer in a state is 1,500 and is growing 2% each year. Predict the population after 4 years.
frutty [35]
Required number
= 1500*(1+2%)^4
=1624(cor.to.the nearest integer)
7 0
2 years ago
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