Suppose the value of x varies from x = a to x = b . There are at least two ways of thinking about what percent x changed by. We'll explore two of them here. For each of the following questions, write an expression in terms of a and b to answer the question. Method 1 b is how many times as large as a ? times as large Therefore, b is what percent of a ? % Hence, if x varies from x = a to x = b , x changes by what percent?
Answers
The change in the value of x, as a percentage, is given by:
The percentage change is given by the change multiplied by 100% and divided by the initial value.
In this question, x varies from to
, which means that the initial value is a, and the change is b - a. Then, the percentage chance in the value of x is given by:
A similar problem is given at brainly.com/question/24729807
Answer:
Step-by-step explanation:
i. b is how many times as large as a?
b/a
ii. Therefore, b is what percent of a?
b/a*100
iii. Hence, if x varies from x=a to x = b, x changes by what percent?
(100b)/a-100
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840.54 cm3
1,055.04 cm3
1,456.96 cm3
Answers
Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm
Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³
Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³
cone: height = 12 cm ; radius = 4 cm
Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³
Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³
Answers
Answer:
Step-by-step explanation:
The movement of the minute hand of the clock is circular. This means that a complete movement of the minute hand of the clock is the same as the angle formed at the center of the circle. The sum of the angles at a point is 360 degrees. The minute hand travels 360 degrees in a 60 minutes. It means that the degrees travelled in a minute is
360/60 = 6 degrees
The hour hand travels 360 degrees in 60 minutes. Therefore, the angle that the hour hand travels in 1 minute is
360/6 = 6 degrees
Final answer:
The minute hand of a clock travels 6° in 1 minute. The hour hand travels 0.5° in 1 minute.
Explanation:
To answer this question, we first need to consider what a full rotation is. A complete circle, one full rotation, is 360°. The minute hand of a clock completes one full rotation, or 360°, every hour or 60 minutes.
In 1 minute, the minute hand would have covered 1/60 of a full rotation. To calculate this in degrees, we multiply 360° by 1/60, which gives us 6°. Therefore, the minute hand of a clock travels 6° in one minute.
The hour hand moves more slowly. It takes 12 hours to complete a full rotation or 360°. In 1 minute, the hour hand covers, 360° divided by (12 hours x 60 minutes), which gives us 0.5°. Therefore, the hour hand of a clock moves 0.5° in 1 minute.
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Answers
Answer:
a. Covariance between x and y = – 1.25
b. Correlation coefficient = – 0.07
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Consider the following sample data:
x 10 7 20 15 18
y 22 15 19 14 15
Required:
a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.
b. Calculate the correlation coefficient (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
The explanation to the answer is now given as follows:
Note: See the attached excel file for the calculations of the sum of x and y, means of x and y, deviations of x and y, multiplications of deviations of x and y, and others.
a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
In the attached excel file, we have:
N = Number of observations = 5
Mean of x = Sum of x / N = 70 / 5 = 14
Mean of y = Sum of y / N = 85 / 5 = 17
x - Mean of x = Deviations of x = see the attached excel file for the answer of each observation
y - Mean of y = Deviations of y = see the attached excel file for the answer of each observation
Multiplications of the deviations of x and y = (x - Mean of x) * (y - Mean of y) = see the attached excel file for the answer of each observation
Sum of the multiplications of deviations of x and y = Sum of ((x - Mean of x) * (y - Mean of y)) = –5
Since we are using a sample, we use (N – 1) in our covariance between x and y as follows:
Covariance between x and y = Sum of ((x - Mean of x) * (y - Mean of y)) / (N – 1) = –5 / (5 – 1) = –5 / 4 = –1.25
b. Calculate the correlation coefficient (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
The correlation coefficient can be calculated using the following formula:
Correlation coefficient = Covariance between x and y / (Sum of (x - Mean of x)^2 * Sum of (y - Mean of y)^2)^0.5 ………………… (1)
Where, from the attached excel file;
Covariance between x and y = –5
Sum of (x - Mean of x)^2 = 118
Sum of (y - Mean of y)^2 = 46
Substituting the values into equation (1), we have:
Correlation coefficient = –5 / (118 * 46)^0.5 = –5 / 5,428^0.5 = –5 / 73.6750 = – 0.07
Final answer:
The covariance between two variables can be calculated by first finding the mean of each dataset, subtracting the mean from each data point, multiplying the results for each pair of coordinates, summing these products to obtain the numerator. The denominator is obtained by subtracting one from the number of data points. The covariance is then the numerator divided by the denominator.
Explanation:
The term covariance is one of the key factors for understanding correlation between two variables. To calculate the covariance between the two given variables, we first need to calculate the mean of each set (x and y). After we've gotten the mean, we subtract the mean from each data point and multiply the results for each pair of x and y values. Summing these products will give us the numerator in the covariance calculation. The denominator is calculated by subtracting one from the total number of data points we have (n-1). So, the covariance is the sum we got from the numerator, divided by the denominator. Please don't forget to indicate if the covariance is negative, using a minus sign.
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Answers
if I had enough money, of course I will have change.
Answers
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
Answers
Answer:
The total number of marbles in the bag is 50.
Step-by-step explanation:
Here, we have n trials, without replacement. So the hypergeometric distribution is used.
The mean of the hypergeometric distribution is:
In which n is the number of items in the sample, k is the number of items in the population that are classified a success and N is the size of the population.
15 marbles are drawn:
This means that
A bag contains some number of marbles. It is known that 20 of them are red.
This means that , since a success is drawing a red marble.
Assuming E(X)=6 red, what is the total number of marbles in the bag?
We have to find N when
So
The total number of marbles in the bag is 50.