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3 years ago

The straight line 2x + 3y = 7 meets the curve

Mathematics

1 answer:

NISA [10]3 years ago

5 0

Step-by-step explanation:

xy + 10 = 0. => y = -10/x.

2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.

When -10/x = -2/3 x + 7/3,

-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.

=> 2x² - 7x - 30 = 0

=> (2x + 5)(x - 6) = 0

=> x = -2.5 or x = 6.

dy/dx = d/dx [-10/x] = 10/x².

When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.

When x = 6, dy/dx = 10 / (6)² = 5/18.

Hence the gradients at the points are 1.6 and 5/18.

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Kamila [148]

Answer:

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Step-by-step explanation:

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3 years ago

The original pulse rates are measure with units of "beats per minute". what are the units of the corresponding z scores? choo

posledela

the complete question is

Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. The original pulse rates are measure with units of "beats per minute". What are the units of the corresponding z scores? Choose the correct choice below.

A. The z scores are measured with units of "beats per minute."

B. The z scores are measured with units of "minutes per beat."

C. The z scores are measured with units of "beats."

D. The z scores are numbers without units of measurement.

we know that

A z-score is the number of standard deviations from the mean a data point is. But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is

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the answer is the option D

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3 years ago

What is it please hurry im timed<br>

lorasvet [3.4K]

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3 years ago

Read 2 more answers

Wade can type 800 words in a quarter of an hour. How many words per minute can Wade type?

Mumz [18]

Answer:

Quarter of an hour = 25 minutes

800 words in 25 minutes.

800 ÷ 25= 32

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3 years ago

A population has mean 187 and standard deviation 32. If a random sample of 64 observations is selected at random from this popul

Zina [86]

Answer:

11.51% probability that the sample average will be less than 182

Step-by-step explanation:

To solve this question, we have to understand 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 $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$