IWhat is the sale price of a stereo that normally sells for $250.00 and is on sale for 10% off?

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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f(x)=x²+20x+40

To complete the square, the same value needs to be added to both sides.

f(x)+?=x²+20x+?+40

Now i make the same thing in different forms ok

To complete the square x²+20x+100=(x+10)² add 100 to the expression

f(x)+?=x²+20x+100+40

Is the same ok you can choose which way you can do

x²+20x+?

write the expression as a product with the factor 2 and x

x²+2x×x10+?

x²+2×x×10+?

Since 10 is part of the middle term, add 10² to the expression

x²+2×x×10+10²

Calculate the product

x²+20x+10²

or evaluate the power

x²+20x+100

f(x) +?=x²+20x+100+40

Since 100 was added to the right - hand side, also add 100 to the left hand side

f(x)+100=x²+20x+100+40

Using a²+2ab+b²=(a+b)², factor the expression

f(x)+100=(x+10)²+40

------------------

x²+20x+100

Write the expression as a product with the factors x and 10

x²+2×x×10+100

Write the number in the exponential form with an exponent of 2

x²+2×x×10+10²

Using a²+2ab+b²=(a+b)² factor the expression

(x+10)²

--------

f(x)+100=(x+10)²+40

Move constant to the right-hand side and change its sign

f(x)=(x+10)²+40-100

Calculate the difference

40-100

Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger

-(100-40)

Subtract the numbers

-60

Answer:f(x)=(x+10)²-60

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Final answer:

To rewrite the function f(x) = x² + 20x + 40 by completing the square, we find half the coefficient of the x term, square it, subtract the constant term in the original equation from this squared result, then rewrite the function as (x+10)^2 - 60.

Explanation:

When you're asked to rewrite the function by completing the square, there are certain steps to follow. We start with the function f(x) = x² + 20x + 40.

1. First, take the coefficient of the x term (in our case, 20) and divide it by 2. This would yield 10.
2. Next, square the result from step 1. That is 10² = 100.
3. Subtract the constant term in the original equation from the squared result i.e. 100 - 40 = 60.
4. Finally, the equation takes this form: f(x) = (x+10)² - 60.

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The zeros of the given functions are shown on the attached picture.

Answer:

let monday be a = 800 (nearest 100)

let tuesday be b = 700 (nearest 100)

a+b = 800 + 700 = 1500

a+b = 1500

Answer: 0.09

Step-by-step explanation: