Find the slope of the line that passes through the points (2,12)and(-2,0)

Answer:

Jamal's answer isn't reasonable because the sum of 183 and 198 is 381, which is way more than 300 and nowhere less than 300.

Step-by-step explanation:

Jamal makes an assertion that the sum of 183 and 198 is less than 300.

We are to check if Jamal's answer is reasonable or not.

183 + 198 = 381 > 300

The sum of the two numbers, 381, is evidently not less than 300, hence, Jamal's answer isn't reasonable because it is downright wrong.

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Answer:

The correct solutions are (6, -2).

Step-by-step explanation:

For the first equation, rearrange to make x the subject.

3x + 4y = 10

Divide the whole equation by 3 to isolate x:

Now substitute this into the second equation:

Subtract 20 from both sides:

20 - 10y = 40

20 - 10y - 20 = 40 - 20

-10y = 20

Divide both sides by 2:

-10y ÷ 10 = 20 ÷ 10

-y = 2 ∴ y = -2

Plug this value back into the first equation:

3x + 4y = 10

3x + 4(-2) = 10

3x + (-8) = 10

3x - 8 = 10

Add 8 to both sides:

3x - 8 + 8 = 10 + 8

3x = 18

Divide both sides by 3:

3x ÷ 3 = 18 ÷ 3

x = 6

Therefore, the correct solutions are (6, -2).

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The value of the given expression will be equal to -3.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The solution to the expression is:-

=  4(  x  +  3  ) (  x + 1  )  /  (  x  +  5  )  (  x  -  5  )

=  4(  3 +  3  ) (  3  + 1  )  /  (  3  +  5  )  (  3  -  5  )

=  (  4  x  6  x  4 )  /  (  8  x   -2  )

=  -3

Therefore the value of the given expression will be equal to -3.

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Answer:

39

Step-by-step explanation:

The median is the middle number

16, 23, 24, 39, 45, 78, 95

There are 7 numbers so the middle number is the 4th number

6, 23, 24,    39    , 45, 78, 95

The median is 39

Answer:

39

Step-by-step explanation:

The median is the number in the middle of a data set.

First, arrange the numbers from least to greatest.

16, 23, 24, 39, 45, 78, 95

Then, cross one number off both sides of the data set until the middle is reached.

16, 23, 24, 39, 45, 78, 95

23, 24, 39, 45, 78

24, 39, 45,

39

The median is 39

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/mu​l.) 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  =    ~ N(0,1)

where, = population mean = 248.5

            = 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( < X < ) = 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 =

                           = = -3

z-score for 431.8 =

                           = = 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.

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