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4 years ago

For some unknown function f(x), we are told that lim x --> 0 ( f(x)-3 ) / 5x = 7

1 answer:

7 0

$\bf \lim\limits_{x\to 0}\ \cfrac{f(x)-3}{5x}=7\\\\
-----------------------------\\\\
 \cfrac{f(x)-3}{5x}=7\implies f(x)-3=35x\implies \boxed{f(x)=35x+3}\\\\
-----------------------------\\\\

\lim\limits_{x\to 0}\ \cfrac{\boxed{35x+3}-3}{5x}\implies \cfrac{35x}{5x}\implies 7$

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Simplify (2-4i) -(3 -6i)

SashulF [63]

$2 - 4i - 3 + 6i = - 1 + 2i$

5 0

2 years ago

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139 millimeters,

FinnZ [79.3K]

Answer:

0.4010 = 40.10% probability that the sample mean would differ from the population mean by more than 0.8 millimeters

Step-by-step explanation:

To solve this question, we need to understan the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 139, \sigma = 6, n = 40, s = \frac{6}{\sqrt{40}} = 0.9487$

Either the sample mean differs by 0.8 mm or less from the population mean, or it differs by more. The sum of these probabilities is decimal 1.

Probability it differs by less than 0.8mm

pvalue of Z when X = 139 + 0.8 = 139.8mm subtracted by the pvalue of Z when X = 139 - 0.8 = 138.2 mm

X = 139.8

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{139.8 - 139}{0.9487}$

$Z = 0.84$

$Z = 0.84$ has a pvalue of 0.7995

X = 138.2

$Z = \frac{X - \mu}{s}$

$Z = \frac{138.2 - 139}{0.9487}$

$Z = -0.84$

$Z = -0.84$ has a pvalue of 0.2005

0.7995 - 0.2005 = 0.5990

What is the probability that the sample mean would differ from the population mean by more than 0.8 millimeters?

p + 0.5990 = 0.4010

0.4010 = 40.10% probability that the sample mean would differ from the population mean by more than 0.8 millimeters

7 0

3 years ago

leaks can write a 500-work essay in a hour. if she writes a essay in 10 minutes, how many words will it contain?

gavmur [86]

Answer:

about 83 words

Step-by-step explanation:

60/6=10

500/6 about 83

7 0

3 years ago

Two cars start from the same point driving in opposite directions. Both cars drive 6miles. One car stops, the other car makes a

dimaraw [331]

Answer:

14.4 mile²

Explanation:

1. By driving 6 miles each, the cars will be 6 miles + 6 miles = 12 miles appart.

2. When one car stops and the other car makes a 90° left-hand turn and drive 8 miles, you can model the situation with a right triangle, where one leg is 12 miles, the other leg is 8 miles, and the hypotenuse is the distance that separates the cars.

Hence, you must use Pythagoras to find that distance.

3. Pythagoras

hypotenuse² = leg₁² + leg₂²

hypotenuse = (12 mile)² + (8 mile)² = 144 mile² + 64 mile² = 208 mile²

$hypotenuse=\sqrt{208mile^2}=14.4mile^2$ , which is rounded to the neartest tenth of a mile.

8 0

3 years ago

Which of the following represents the graph of f(x) = 2(x + 3)?

Yuliya22 [10]

We have that

the correct expression is
y=2^(x+3)

using a graph tool
see the attached figure

the answer is the option C

3 0

4 years ago