MATHEMATICS COLLEGE

Which conclusion can be drawn from the data?Question 9 options:

For ten weeks, City A received less rainfall, on average, than City B.

The range between the maximum and minimum values for City B is greater than the range between maximum and minimum values for City A.

During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

The median for City A is less than the median for City B.

Answers

Answer 1

Answer:

During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

Step-by-step explanation:

Given the data :

City A :

Reordered data:

0, 0.2, 0.2, 0.3, 0.4, 1, 1.3, 1.5, 2.5, 3

City B :

Reordered data:

0, 0, 0.1, 0.1, 0.2, 0.3, 0.4, 1, 1, 1

Using a calculator :

Mean Rainfall for City A = 1.04

Mean rainfall for city B = 0.41

Range : maximum - minimum

City A = 3 - 0 = 3

City B = 1 - 0 = 1

Mode (most occurring) :

City A = 0.2

City B = 1

Median :

City A = 0.7

City B = 0.25

The only true conclusion in the options given that can be drawn from the data is that ;During the 10 wk period, the rainfall amount recorded most often for City B was 1 in.

Answer 2

Answer:

Answer:

the Answer is C.

Step-by-step explanation:

I just took the test

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A Ferris wheel has a diameter of 40 feet. What is its circumference?Round to the nearest tenth. Use 3.14 for .

Answers

Answer:125.6 feet

Step-by-step explanation:

diameter=40 feet

π=3.14

Circumference= π x diameter

Circumference=3.14 x 40

Circumference=125.6

An advertising company designs a campaign to introduce a new product to a metropolitan area of population 3 Million people. Let P(t) denote the number of people (in millions) who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one was aware of the product at the beginning of the campaign, and that 50% of the people were aware of the product after 50 days of advertising. The number of people who become aware of the product at time t is:

Answers

Answer:

$P(t)=3,000,000-3,000,000e^(0.0138t)$

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

$P'(t)=K(3,000,000-P(t))$

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

P(0) = 0 and P(50) = 1,500,000

We have and ordinary differential equation of first order that we can write

$P'(t)+KP(t)= 3,000,000K$

The integrating factor is

$e^(Kt)$

Multiplying both sides of the equation by the integrating factor

$e^(Kt)P'(t)+e^(Kt)KP(t)= e^(Kt)3,000,000*K$

Hence

$(e^(Kt)P(t))'=3,000,000Ke^(Kt)$

Integrating both sides

$e^(Kt)P(t)=3,000,000K \int e^(Kt)dt +C$

$e^(Kt)P(t)=3,000,000K((e^(Kt))/(K))+C$

$P(t)=3,000,000+Ce^(-Kt)$

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

$e^(-50K)=(1)/(2)\Rightarrow K=-(log(0.5))/(50)=0.0138$

And the equation that models the number of people (in millions) who become aware of the product by time t is

$P(t)=3,000,000-3,000,000e^(0.0138t)$

A car is traveling at a rate of 48 miles per hour. If the car continues to travel at this same rate, how many hours will it take the car to travel 612 miles?

Answers

Answer:

12.75

Step-by-step explanation:

If you make a proportion: 48/1=612/x

1(612)= 612

612/48

12.75 hours

At a speed of 48 miles per hour, the car will take approximately 12.75 hours to go 612 miles.

What is the distance?

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

A car is traveling at a rate of 48 miles per hour.

To determine the number of hours it will take the car to travel 612 miles at a rate of 48 miles per hour, you can divide the distance traveled by the rate at which the car is traveling:

⇒ distance ÷ rate

⇒ 612 miles / 48 miles/hour

Apply the division operation, and we get

⇒ 12.75 hours

Therefore, it will take the car about 12.75 hours to travel 612 miles at a rate of 48 miles per hour.

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Find the value of x

Answers

Answer:

$x = 70$

Step-by-step explanation:

the sum of the interior angles of a hexagon is 720 degrees. All sides are the same length (congruent) and all interior angles are the same size (congruent). To find the measure of the interior angles, we know that the sum of all the angles is 720 degrees.

Now,

102+146+158+120+124+x=720

or,650+x=720

or,x=70

Therefore The value of X is 70 degree.

no x’s have no value

Sample annual salaries (in thousands of dollars) for employees at a company are listed. 51 53 48 62 34 34 51 53 48 30 62 51 46 (a) Find the sample mean and sample standard deviation. (b) Each employee in the sample is given a $5000 raise. Find the sample mean and sample standard deviation for the revised data set. (c) Each employee in the sample takes a pay cut of $2000 from their original salary. Find the sample mean and the sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)?

Answers

Answer:

Mean increase or decrease (same quantity) according to the quantity of the increment or reduction

As all elements were equally affected the standard deviation will remain the same

Step-by-step explanation:

For the original set of salaries: ( In thousands of $ )

51, 53, 48, 62, 34, 34, 51, 53, 48, 30, 62, 51, 46

Mean = μ₀ = 47,92

Standard deviation = σ = 9,56

If we raise all salaries in the same amount ( 5 000 $ ), the nw set becomes

56,58,53,67,39,39,56,58,53,35,67,56,51

Mean = μ₀´ = 52,92

Standard deviation = σ´ = 9,56

And if we reduce salaries in the same quantity ( 2000 $ ) the set is

49,51,46,60,32,32,49,51,46,28,60,49,44

Mean μ₀´´ = 45,92

Standard deviation σ´´ = 9,56

What we observe

1.-The uniform increase of salaries, increase the mean in the same amount

2.-The uniform reduction of salaries, reduce the mean in the same quantity

3.-The standard deviation in all the sets remains the same.

We can describe the situation as a translation of the set along x-axis (salaries). If we normalized the three curves we will get a taller curve (in the first case) and a smaller one in the second, but the data spread around the mean will be the same

Any uniform change in the data will directly affect the mean value

Uniform changes in values in data set will keep standard deviation constant

Final answer:

The mean salary is affected by each employee's changes in salary, such as raises and pay cuts, but the standard deviation (the spread of salaries) remains the same provided the change is the same for all individuals.

Explanation:

To answer this question, we need to calculate the sample mean and sample standard deviation in each case. The sample mean is the average of the data, while the sample standard deviation is a measure of the amount of variation or dispersion in the data set.

(a) Calculate the sample mean and sample standard deviation of the initial salaries. This involves summing all the salaries and dividing by the total number to get the mean, then calculating the standard deviation using the formula: square root of [sum of (each salary - mean salary)² divided by (total number of salaries - 1)].
(b) When each employee is given a $5000 raise, the mean will increase by 5, while the standard deviation will remain the same because raises do not affect the dispersion of the team's salaries.
(c) Similarly, when each employee takes a pay cut of $2000, the mean salary will decrease by 2, but the standard deviation will again remain the same because pay cuts do not affect the dispersion of the team's salaries.
(d) We can conclude that while the mean is affected by changes in individual salaries (like raises and pay cuts), the standard deviation is not, provided the change is the same for all individuals. Therefore, it shows that while supply changes can affect the central tendency (mean), they do not impact how spread out the salaries are (standard deviation).

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What is the answer to 3(2b-1)

Answers

You need to distribute the 3, so your answer would be 6b-3

You have to distribute the 3 to everything within the parenthesis.

3 • 2b = 6b & 3 • -1 = -3

So, your answer will be 6b-3.

Hope I helped. :)

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