System AAA \text{\quad}start text, end text System BBB \begin{cases}4x+16y=12\\\\x+2y=-9\end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 4x+16y=12 x+2y=−9 ​ \begin{cases}4x+16y=12\\\\x+4y=3\end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 4x+16y=12 x+4y=3 ​ 1) How can we get System BBB from System AAA?

Answer:

y(t)= 11/3 e^(-t) - 5/2 e^(-2t) -1/6 e^(-4t)

Step-by-step explanation:

We know that , so we have

By using the method of partial fraction we have:

Now we have:

Using linearity of inverse transform we get:

Using the inverse transforms

we have:

Answer:

a. 20.5

Step-by-step explanation:

because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x

therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a

Answer:

The correct answer option is a. 20.5 feet.

Step-by-step explanation:

We are given that the angle of elevation of the ladder is 70° and the height of the ladder is 25 feet from the ground.

We are to find the distance of the building from the base of the ladder.

For this, we will use tan:

x = 20.5 feet

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.

Learn more about Empirical Rule here:

brainly.com/question/35669892

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Answer:

Part 1= Pi * R Squared

Part 2: 50.27

Part 3: 78.54

Part 4: 28.27

Step-by-step explanation:

Part 1: Memorize the formula

Part 2: 8 feet diameter = Pi * 4 squared. 8 feet is the diameter so the radius is 4. 4 squared is 16. 16 * pi = approximately 50.27, but is 50.24 if 3.14 is used as pi.

Part 3: Pi * 5 squared since 10 is diameter. 25 * pi which is close to 78.54, but is 78.5 is 3.14 is used for pi.

Part 4: I subtracted Part 3 from Part 2.

Answer:

There is a 55.97% that a male can find a full time job in his chosen profession.

Step-by-step explanation:

We have these following probabilities:

A 60% probability that a college graduates cannot find a full time job in their chosen profession.

A 40% probability that a college graduates can find a full time job in their chosen profession.

57% of the college graduates who cannot find a job are female

43% of the college graduates who cannot find a job are male

18% of the college graduates who can find a job are female

82% of the college who can find a job are male.

Given a male college graduate, find the probability he can find a full time job in his chosen profession?

The total males are 43% of 60%(Those who cannot find a job) and 82% of 40%(Those who can find a job). So the percentage of males is

Those who are males and find a job in their chosen profession are 82% of 40%. So

There is a 55.97% that a male can find a full time job in his chosen profession.