MATHEMATICS COLLEGE

In your own words, describe how to graph the linear equation y = -1/5x + 3. Step by step

Answers

Answer 1

Answer:

Answer:

Steps given below and graph is attached.

Step-by-step explanation:

First Step:

Find out $y-intercept$ by substituting $x=0$

$y=-(1)/(5)* 0+3\n\ny=3\n\nHence\ line\ passes\ through\ (0,3).$

Second Step:

Find out $x-intercept$ by substituting $y=0.$

$0=-(1)/(5)x+3\n\n(1)/(5)x=3\n\nx=15\n\nHence\ line\ passes\ through\ (15,0).$

Third Step:

Draw a line passing through $(0,3)\ and\ (15,0)$ .

Graph is attached.

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Given the function f(x) =-2x^2 + 4x -7 find f(-4)

Answers

Correct the answer is -55

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of and a standard deviation of . (All units are 1000 cells/L.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within standard of the mean, or between and ?
b. What is the approximate percentage of women with platelet counts between and ?

Answers

Answer:

(a) Approximately 95% of women with platelet counts within 2 standard deviations of the mean.

(b) Approximately 99.7% of women have platelet counts between 65.2 and 431.8.

Step-by-step explanation:

The complete question is: The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1. (All units are 1000 cells/mul.) using the empirical rule, find each approximate percentage below.

a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7?

b. What is the approximate percentage of women with platelet counts between 65.2 and 431.8?

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1.

Let X = the blood platelet counts of a group of women

The z-score probability distribution for the normal distribution is given by;

Z = $(X-\mu)/(\sigma)$ ~ N(0,1)

where, $\mu$ = population mean = 248.5

$\sigma$ = standard deviation = 61.1

Now, the empirical rule states that;

68% of the data values lie within 1 standard deviation away from the mean.

95% of the data values lie within 2 standard deviations away from the mean.

99.7% of the data values lie within 3 standard deviations away from the mean.

(a) The approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7 is given by;

As we know that;

P( $\mu-2\sigma$ < X < $\mu+2\sigma$ ) = 0.95

P(248.5 - 2(61.1) < X < 248.5 + 2(61.1)) = 0.95

P(126.3 < X < 370.7) = 0.95

Hence, approximately 95% of women with platelet counts within 2 standard deviations of the mean.

(b) The approximate percentage of women with platelet counts between 65.2 and 431.8 is given by;

Firstly, we will calculate the z-scores for both the counts;

z-score for 65.2 = $(X-\mu)/(\sigma)$

= $(65.2-248.5)/(61.1)$ = -3

z-score for 431.8 = $(X-\mu)/(\sigma)$

= $(431.8-248.5)/(61.1)$ = 3

This means that approximately 99.7% of women have platelet counts between 65.2 and 431.8.

Final answer:

Using the empirical rule, approximately 68% of values fall within 1 standard deviation from the mean in a bell-shaped distribution. For ranges 2 or 3 standard deviations from the mean, the respective approximate percentages are 95% and 99.7%.

Explanation:

The question refers to the Empirical rule, which in statistics, is also known as the Three-sigma rule or the 68-95-99.7 rule. This rule is a shortcut for remembering the proportion of values in a normal distribution that are within a given distance from the mean: 68% are within 1 standard deviation, 95% are within 2 standard deviations, and 99.7% are within 3 standard deviations.

Without given specific values for the mean or standard deviations, we can discuss the problem in a general sense:

For part a, the percentage of women with platelet counts within 1 standard deviation from the mean is approximately 68% under the Empirical rule.
For part b, it depends on how many standard deviations from the mean the range mentioned lies. If it refers to two standard deviations from the mean, then 95% of women would fall into this range, if it refers to three standard deviations, then approximately 99.7% would be the case.

Learn more about Empirical Rule here:

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Is -51/5 rational or irational

Answers

Answer:

Rational

Step-by-step explanation:

Answer:

Step-by-step explanation:

its written as a ratio of two integers, so its a rational number.

PLEASE HELP- 25 points-what is the circumference of the circle. Diameter =9cm

Answers

Answer:

9π cm - exact value

28.26 cm - approximate value

Step-by-step explanation:

C = πd =9π cm - exact value

C=9π≈ 28.26 cm - approximate value

There are 15,958,866 adults in a region. If a polling organization randomly selects 1235 adults without replacement, are the selections independent or dependent? If the selections are dependent, can they be treated as independent for the purposes of calculations? Are the selections independent or dependent?

Answers

Answer:

The selections are dependent.

Yes, they can be treated as independent (less than 5% of the population).

Step-by-step explanation:

Since the selections are made without replacement, each selection affects the outcome of the next selection and, therefore, the selections are dependent.

Although they are dependent, the selections can be treated as independent if the sample size is no more than 5% of the total population. In this case, the sample size is 1235 adults out of a population of 15,958,866 adults. The percentage represented by the sample is:

$P=(12,345)/(15,958.866)*100\n P=0.077\%$

Thus the selections can be treated as independent for the purposes of calculations.

50 POINTS.Tell whether the ordered pairs is a solution of the system of linear inequalities. 4. (8, −2); y −6
8. (1, 3);2x + y −4, 3x − y ≤ 3

Answers

Answer:

4, or it could be 8 but mostly 4

Step-by-step explanation:

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