the most basic distinction between types of data is that some data are quantitative while other data are qualitative. quantitative data generally consists of:
The most basic distinction between types of data is that some data are quantitative while other data are qualitative. Quantitative data consists of numerical information that can be measured or counted, allowing for statistical analysis and objective comparisons. This type of data can be further classified into two subcategories: continuous data and discrete data.
Continuous data represent measurements that can take on any value within a specified range, such as height, weight, temperature, or time. These measurements can be represented using fractions or decimals and are typically collected using precise instruments like rulers or thermometers.
Discrete data, on the other hand, consist of distinct, separate values that can be counted or categorized. Examples of discrete data include the number of students in a class, the number of cars in a parking lot, or the number of books sold in a month. Discrete data is often collected through surveys or counting processes.
In contrast, qualitative data are non-numerical and describe attributes, characteristics, or experiences. This type of data is typically obtained through observation, interviews, or open-ended survey questions. Examples of qualitative data include feelings, opinions, beliefs, or descriptions of events.
In summary, the primary distinction between types of data lies in their nature: quantitative data is numerical and allows for objective measurement, while qualitative data is descriptive and explores subjective aspects. Understanding the difference between these two types of data is essential for conducting accurate and meaningful research.
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true or false? the P(b | a) = P(a and b) / P(b)
True. This is known as Bayes' theorem, which states that the probability of an event A given the occurrence of another event B can be calculated as the probability of both events A and B occurring divided by the probability of event B occurring. It can be written as: P(A | B) = P(B | A) * P(A) / P(B).
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What’s the probability of a dice that is 6 as a fraction
Answer:
1/
Step-by-step explanation:
A standard dice has 6 equally likely outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Each outcome has a probability of 1/6 of occurring on a single roll of the dice, assuming the dice is fair and unbiased.
Since there is only one outcome on a standard dice that is 6, the probability of rolling a 6 is 1/6.
Therefore, the probability of a dice that is 6 as a fraction is 1/6.
The wright brothers named their first powered aircraft the wright flyer. In its first flight, the wright flyer flew 37 meters. In its last flight, the wright flyer flew 223 meters farther than in its first one. How many meters short of a kilometer was the wright flyers last flight?
Answer: 777 Meters
Step-by-step explanation:asa
if event a and event b are independentP(a | b) = 0.35P(b) = 0.5find P(a)
If events A and B are independent, then P(A and B) = P(A) * P(B). Also, from Bayes' theorem we have P(A | B) = P(A and B) / P(B).
Given that P(A | B) = 0.35 and P(B) = 0.5, we can solve for P(A and B) as follows:
P(A and B) = P(A | B) * P(B) = 0.35 * 0.5 = 0.175
Since events A and B are independent, we have P(A and B) = P(A) * P(B). Solving for P(A), we get:
P(A) = P(A and B) / P(B) = 0.175 / 0.5 = 0.35
Therefore, P(A) = 0.35.
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What does PEMDAS stand for?
I'll give you a Brainliest if you answer correctly!
Answer:
PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). It's a helpful mnemonic device to remember the order of operations in arithmetic and algebraic equations. When solving a mathematical expression or equation, it's important to follow PEMDAS to ensure that the solution is accurate and consistent.
Answer:
by Paige Faber, ACDC Peer Advisor. Remember in seventh grade when you were discussing the order of operations in math class and the teacher told you the catchy acronym, “PEMDAS” (parenthesis, exponents, multiplication, division, addition, subtraction) to help you remember?
Step-by-step explanation:
HI
Eduardo’s average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?
Answer:
40(1.25-t)
Step-by-step explanation:
There are 3 components to consider; time, speed and distance
Time and Speed are given.
The distance has to be calculated.
Speed to work = 55 miles per hour
Time to work = 1.25-T
Speed to home = 40 miles per hour
Time to home = 1.25-t
Total Time = T + t = 1.25
Distance for trip to home
Speed = Distance/Time
40 = Total Distance/1.25-t
Total Distance = 40(1.25-t)
Therefore, 40(1.25-t) is the correct answer.
!!
find the inverse of the following matrices by writing them in the form i - d and using the sum-of-powers method on d. check the accuracy of your answer by using the determinant-based formula for the inverse of ~ 2-b)1-2 matrix (see section 3 .3) . (a) .7 - .2 - .4 .8 (b) . 6 .3 .2 .5 (c) .6 0 0 .5
A matrix is a rectangular array of numbers or other mathematical objects arranged in rows and columns.
(a) To find the inverse of the matrix, we write it in the form I - D. Let A be the given matrix.
A =
[0.7 -0.2 -0.4]
[0.8 0.0 0.0]
[0.0 0.0 1.0]
Let D = 0.3A, then we have:
I - D =
[0.7 - 0.3(0.7) - 0.3(-0.2) - 0.3(-0.4)]
[0.8 - 0.3(0.8) - 0.3(0.0) - 0.3(0.0)]
[0.0 - 0.3(0.0) - 0.3(0.0) - 0.3(1.0)]
=
[0.46 0.06 0.12]
[0.56 0.80 0.00]
[0.00 0.00 0.70]
Using the sum-of-powers method, we have:
(I - D)^(-1) =
[1.131 -0.509 -0.343]
[-0.951 1.509 0.000]
[0.000 0.000 1.429]
To check the accuracy of our answer, we can use the determinant-based formula for the inverse:
A^(-1) = (1/det(A)) * adj(A)
where det(A) is the determinant of A, and adj(A) is the adjugate of A. We have:
det(A) = (0.70.01.0) + (-0.20.00.0) + (-0.40.80.0) - (-0.40.0-0.2) - (0.70.80.0) - (-0.20.01.0) = 0.56
adj(A) =
[0.0 0.8 0.0]
[-0.4 0.0 0.28]
[0.28 -0.2 0.0]
So, we have:
A^(-1) = (1/0.56) *
[0.0 0.8 0.0]
[-0.4 0.0 0.28]
[0.28 -0.2 0.0]
=
[1.131 -0.509 -0.343]
[-0.951 1.509 0.000]
[0.000 0.000 1.429]
which is the same as the answer we obtained using the sum-of-powers method.
(b) To find the inverse of the matrix, we write it in the form I - D. Let A be the given matrix.
A =
[0.6 0.3]
[0.2 0.5]
Let D = 0.2A, then we have:
I - D =
[0.52 -0.12]
[-0.08 0.48]
Using the sum-of-powers method, we have:
(I - D)^(-1) =
[2.058 0.514]
[0.343 2.171]
To check the accuracy of our answer, we can use the determinant-based formula for the inverse:
A^(-1) = (1/det(A)) *
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Find the z-score such that: (a) The area under the standard normal curve to its left is 0.5 z = (b) The area under the standard normal curve to its left is 0.9826 z = (c) The area under the standard normal curve to its right is 0.1423 z = (d) The area under the standard normal curve to its right is 0.9394 z =
(a) For an area of 0.5 to the left of the z-score under the standard normal curve, z = 0. This is because the standard normal curve is symmetric, and the area to the left of the mean (which is also the median and mode in this case) is 0.5.
(b) For an area of 0.9826 to the left of the z-score under the standard normal curve, you can look up the corresponding z-score in a standard normal (z) table, or use a calculator or software with an inverse cumulative distribution function. The z-score is approximately z = 2.13.
(c) For an area of 0.1423 to the right of the z-score under the standard normal curve, you first find the area to the left (1 - 0.1423 = 0.8577). Then, look up the corresponding z-score in a standard normal (z) table or use a calculator. The z-score is approximately z = 1.08.
(d) For an area of 0.9394 to the right of the z-score under the standard normal curve, find the area to the left (1 - 0.9394 = 0.0606). Then, look up the corresponding z-score in a standard normal (z) table or use a calculator. The z-score is approximately z = -1.55.
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need to solve by hand1.The yield of a manufacturing process was measured for ten consecutive production lots. The results (in fractional form) are summarized in the table at right. Compute the following sampl
The difference between the highest and lowest yield values.
Range = highest_ yield - lowest_ yield
Based on the information provided, I understand that you have a table with yield data for ten consecutive production lots. To compute the sample statistics, follow these steps:
1. Calculate the sample mean:
Add the yield values from the table and divide by the total number of production lots (10).
Mean = (yield_ 1 + yield_ 2 + ... + yield_ 10) / 10
2. Calculate the sample variance:
Subtract the mean from each yield value, square the result, and sum them. Divide the sum by the number of production lots minus 1 (9).
Variance = [(yield_1 - mean)^2 + (yield_2 - mean)^2 + ... + (yield_10 - mean)^2] / 9
3. Calculate the sample standard deviation:
Take the square root of the variance.
Standard deviation = √(variance)
4. Calculate the range:
Find the difference between the highest and lowest yield values.
Range = highest_yield - lowest_yield
Once you have calculated these sample statistics, you can better understand the yield performance of the manufacturing process and analyze the production data. Remember to use the actual yield values from your table when doing these calculations.
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what are the coordinates of the image point A after a dilation with center (0, 0) and scale factor of 1/4?
The coordinates of the image point A after the dilation is (-1/4, -1/4)
Determining the image of the point A'From the question, we have the following parameters that can be used in our computation:
ABC with vertices at A(-1, -1), B(1, 1), C(0, 1).
The scale factor is given as
Scale factor = 1/4
So, we have
Image = A * Scale factor
Substitute the known values in the above equation, so, we have the following representation
Image = (-1, -1)/4
Evaluate
Image = (-1/4, -1/4)
Hence, the image = (-1/4, -1/4)
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Calculate the area and circumference of a circle with diameter 8cm explain by step by step
Answer:
Area: 201.06 cm^2
Circumference: 50.265 cm
Step-by-step explanation:
Area of a circle: A=πr²
π≅3.1415
A=π(8)²
Area≅201.06 cm²
Circumference of a circle: C=2π²
C=2π(8)
C=50.265 cm
Answer:
Area = 50.27cm² , Circumference = 25.13cm
Step-by-step explanation:
First off, to find the area of a circle the formula is [tex]\pi[/tex]r², and in the equation you gave a diameter, so to get a radius divide the diameter by 2.
So therefore [tex]\pi[/tex]4² is your equation and the answer is 50.27cm²
Now to find the circumference. The formula to find circumference is 2[tex]\pi[/tex]r.
Again if you're given a diameter divide it by 2 to get the radius.
So 2[tex]\pi[/tex]4 is the equation, and the answer is 25.13 cm.
Please let me know if you have any more questions, or need any extra assistance!
unit 7 homework 13 polynomials and factoring
The answers to all parts are shown below.
1. 5a + 3 -4a² + 2a³
writing into standard form of polynomial
2a³- 4a² + 5a +3.
2. 7xy + x³ - y³ -5x²y²
writing into standard form of polynomial
= x³ - y³ - 5x²y² + 7xy
3. The degree of the polynomials are
3x+1 = 1 degree
5x² - 2 degree
10- 0 degree
3x³ -2x² + 10= 3 degree
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A rectangular prism has a width of 5 cm and a height of 8 cm and a depth of 2 cm what is the volume of the prism
Answer:
I'm pretty sure the answer is 80.
Step-by-step explanation:
5 × 8 × 2 = 80
The following frequency table shows the number of fish caught by each of Igor's family members. Number of fish Number of family members 0 0 1 3 2 1 3 0 4 4 What was the minimum number of fish that a family member caught?
The minimum number of fish that a family member caught is 1. Based on the given frequency table, the minimum number of fish that a family member caught can be determined by looking at the lowest "Number of fish" value with a non-zero "Number of family members" value.
Here's a step-by-step explanation:
1. Observe the frequency table:
Number of fish | Number of family members
-----------------------------------------
0 | 0
1 | 3
2 | 1
3 | 0
4 | 4
2. Identify the lowest "Number of fish" value with a non-zero "Number of family members" value. In this case, it's "1 fish" with "3 family members".
Therefore, the minimum number of fish that a family member caught is 1 fish.
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which is the most accurate way to estimate 33% of 71?
Answer:
71 is about 72, and 33% is about 1/3, so 33% of 71 is approximately 1/3 × 72 = 24.
.33 × 71 = 23.43, so the approximation is reasonable
two sides of a triangle are equal in length and double the length of the shortest side. the perimeter of the triangle is 36 inches. x 2x 2
Answer:
Let's use "a" to represent the length of the shortest side. The remaining two sides are equal in length and double the length of the shortest side, thus we may represent them as "2a" according to the issue.
Because the perimeter of a triangle is equal to the sum of its sides' lengths, we may solve the following equation:
a + 2a + 2a = 36
We may simplify the left side of the equation as follows:
5a = 36
When we divide both sides by 5, we get:
a = 7.2
Now that we know the length of the shortest side, we can calculate the lengths of the other two sides:
2a = 14.4
As a result, the triangle's sides are 7.2 inches, 14.4 inches, and 14.4 inches.
To ensure that these lengths match the problem's requirements, we may check that the two larger sides are equal in length and twice the length of the shortest side:
14.4 = 2(7.2)
14.4 = 14.4
As a result, x = 7.2 inches and 2x = 14.4 inches is our solution.
The length of the shortest side is 7.2 inches, and the equal sides are each 14.4 inches (2x).The three sides of the triangle are 7.2 inches, 14.4 inches, and 14.4 inches.
Let's use x to represent the length of the shortest side. According to the problem, the other two sides are equal in length and double the shortest side, so they must be 2x each.
To find the perimeter of the triangle, we add up the lengths of all three sides:
x + 2x + 2x = 5x
We know that the perimeter is 36 inches, so we can set up an equation:
5x = 36
To solve for x, we divide both sides by 5:
x = 7.2
Now that we know the length of the shortest side, we can find the lengths of the other two sides:
2x = 2(7.2) = 14.4
So the three sides of the triangle are 7.2 inches, 14.4 inches, and 14.4 inches.
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3. Solve the equation (x + 3)² = 49
Answer:
x = 4, -10
Step-by-step explanation:
(x + 3)² = 49
[tex]\sqrt{(x + 3){2} }[/tex] = [tex]\sqrt{49}[/tex]
x + 3 = ± 7
x + 3 = 7
x = 4
x + 3 = -7
x = -10
So, the answer is x = 4, -10
express x and y in terms of trigonometric ratios of θ. (express your answer in terms of θ only.)
To express x and y in terms of trigonometric ratios of θ, we need to use the definitions of sine, cosine, and tangent ratios.
Let's assume that θ is an acute angle in a right triangle with hypotenuse of length 1. Then, we have:
sin θ = opposite/hypotenuse = y/1 = y
cos θ = adjacent/hypotenuse = x/1 = x
tan θ = opposite/adjacent = y/x
Therefore, we can express x and y in terms of trigonometric ratios of θ as follows:
x = cos θ
y = sin θ
Alternatively, if we are given the value of one trigonometric ratio and we need to find the others, we can use the Pythagorean identity:
sin^2 θ + cos^2 θ = 1
From this, we can derive:
cos^2 θ = 1 - sin^2 θ
sin^2 θ = 1 - cos^2 θ
And then use the definitions of tangent and cotangent ratios:
tan θ = sin θ/cos θ
cot θ = cos θ/sin θ = 1/tan θ
Hope this helps!
To express x and y in terms of trigonometric ratios of θ, we will use the basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). In a right-angled triangle, we have:
1. sin(θ) = opposite side / hypotenuse
2. cos(θ) = adjacent side / hypotenuse
3. tan(θ) = opposite side / adjacent side
Assuming x is the adjacent side and y is the opposite side in relation to angle θ, and the hypotenuse is denoted by r, we can express x and y in terms of trigonometric ratios of θ as follows:
Step 1: Solve for x using the cosine ratio:
x = r * cos(θ)
Step 2: Solve for y using the sine ratio:
y = r * sin(θ)
So, x and y are expressed in terms of trigonometric ratios of θ as x = r*cos(θ) and y = r*sin(θ).
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Let Ul , U2 , U3 , U4 , U5 be independent, each with uniform distribution on (0,1). Let R
be the distance between the minimum and the maximum of the Ui's. Find
a) E(R);
b) the joint density of the minimum and maximum of the U;'s;
c) P(R> 0.5)
Please do b) and c) and explain in details.
b) To find the joint density of the minimum and maximum of the U_i's, we can use the following approach:
Let M = min(U_1, U_2, U_3, U_4, U_5) and let X = max(U_1, U_2, U_3, U_4, U_5). Then we have:
P(M > m, X < x) = P(U_1 > m, U_2 > m, U_3 > m, U_4 > m, U_5 > m, U_1 < x, U_2 < x, U_3 < x, U_4 < x, U_5 < x)
Since the U_i's are independent and uniformly distributed on (0,1), we have:
P(U_i > m) = 1 - m, for 0 < m < 1
P(U_i < x) = x, for 0 < x < 1
Substituting these expressions, we get:
P(M > m, X < x) = (1 - m)^5 * x^5
Therefore, the joint density of M and X is:
f(M,X) = d^2/dm dx (1-m)^5 * x^5 = 30(1-m)^4 * x^4, for 0 < m < x < 1.
c) To find P(R > 0.5), we need to find the probability that the distance between the minimum and maximum of the U_i's is greater than 0.5. We can use the following approach:
P(R > 0.5) = 1 - P(R <= 0.5)
Now, R <= 0.5 if and only if the difference between the maximum and minimum of the U_i's is less than or equal to 0.5. Therefore, we have:
P(R <= 0.5) = P(X - M <= 0.5)
To find this probability, we can integrate the joint density of M and X over the region where X - M <= 0.5:
P(R <= 0.5) = ∫∫_{x-m<=0.5} f(M,X) dm dx
The region of integration is the triangle with vertices (0,0), (0.5,0.5), and (1,1). We can split this triangle into two regions: the rectangle with vertices (0,0), (0.5,0), (0.5,0.5), and (0,0.5), and the triangle with vertices (0.5,0.5), (1,0.5), and (1,1). Therefore, we have:
P(R <= 0.5) = ∫_{0}^{0.5} ∫_{0}^{m+0.5} 30(1-m)^4 * x^4 dx dm + ∫_{0.5}^{1} ∫_{x-0.5}^{x} 30(1-m)^4 * x^4 dm dx
Evaluating these integrals, we get:
P(R <= 0.5) ≈ 0.5798
Therefore,
P(R > 0.5) = 1 - P(R <= 0.5) ≈ 0.4202.
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49-2/3*34=32-1/6*34 49 - 2/3 x 34=32 - 1/6 x 34
as a teacher assistant you are calculating student greades. one student had the following test scores 85,93.91,81, what is the student's average score?
Answer: 87.5
Step-by-step explanation:
sum of values/number of values
85+93+91+81/4
350/4
87.5
a state politician is interested in knowing how voters in rural areas and cities differ in their opinions about gun control. for his study, 85 rural voters were surveyed, and 21 were found to support gun control. also included in the study were 85 voters from cities, and 57 of these voters were found to support gun control. let population 1 be the voters in rural areas and population 2 be the voters from cities. step 2 of 2: interpret the confidence interval obtained in step 1.
Interpret the Confidence Interval. Based on the information provided, we have the following data: Population 1 (Rural Voters): 85 surveyed, 21 support gun control, Population 2 (City Voters): 85 surveyed, 57 support gun control
Let's assume you've already calculated the confidence interval in Step 1. The confidence interval will show a range within which the true difference in support for gun control between rural and city voters is likely to fall.
To interpret the confidence interval, consider the following example:
Confidence Interval: (X1, X2)
If the entire interval is positive (X1 > 0 and X2 > 0), it indicates that city voters are more likely to support gun control than rural voters, with a certain level of confidence (usually 95% or 99%).
If the entire interval is negative (X1 < 0 and X2 < 0), it indicates that rural voters are more likely to support gun control than city voters, with the same level of confidence.
If the interval contains 0 (X1 < 0 and X2 > 0), it means there is not enough evidence to conclude that there is a significant difference in gun control support between rural and city voters at the chosen confidence level.
Remember to always provide the actual confidence interval values and the chosen confidence level in your interpretation.
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a new cell phone is introduced into the market. it is predicted that sales will grow logistically. the manufacturer estimates that they can sell a maximum of 100 thousand cell phones.after 28 thousand cell phones have been sold, sales are increasing by 10 thousand phones per month.find the differential equation describing the cell phone sales, where y(t) is the number of cell phones (in thousands) sold after t months.
The differential equation describing the cell phone sales is [tex]\frac{{dy}}{{dt}} = 0.5357 \cdot y(t) \cdot \left(1 - \frac{{y(t)}}{{100}}\right)[/tex].
Based on the given information, the cell phone sales growth is logistic, with a carrying capacity of 100 thousand units. When 28 thousand cell phones have been sold, the rate of sales increase is 10 thousand units per month.
The logistic growth differential equation is given by:
[tex]\frac{dy}{dt} = k \cdot y(t) \cdot \left(1 - \frac{y(t)}{M}\right)[/tex]
where dy/dt is the rate of change in sales, y(t) is the number of cell phones sold after t months, k is the growth rate, and M is the carrying capacity.
In this case, y(t) = 28, dy/dt = 10, and M = 100. To find k, we can plug these values into the equation:
10 = [tex]$k \cdot 28 \cdot \left(1 - \frac{28}{100}\right)$[/tex]
Solving for k:
k ≈ 0.5357
Therefore, the differential equation describing the cell phone sales is:
[tex]\frac{{dy}}{{dt}} = 0.5357 \cdot y(t) \cdot \left(1 - \frac{{y(t)}}{{100}}\right)[/tex]
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k^4/(16k^6 5) use the comparison test or limit comparison test to determine whether the following series converges.
To use the comparison test or limit comparison test, we need to find a known series that either diverges or converges and is similar to the given series.
Using the comparison test, we can compare the given series to the series 1/n^2, which is a p-series with p=2 and converges.
To see if our series is smaller or larger than 1/n^2, we can simplify the given series by canceling out k^4 from the numerator and denominator:
k^4 / (16k^6 5) = 1 / (16k^2 5)
Now, we can compare 1 / (16k^2 5) to 1/n^2:
1 / (16k^2 5) < 1/n^2 for all k > 1
Therefore, since our series is smaller than a convergent series, it must also converge.
Alternatively, we can use the limit comparison test by finding the limit of the ratio of the given series to 1/n^2 as n approaches infinity:
lim (n→∞) [k^4/(16k^6 5) / (1/n^2)] = lim (n→∞) (n^2 / (16k^6 5))
This limit is zero for all k > 1, which means the given series and the series 1/n^2 have the same behavior and both converge.
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would a chi-square test based on a 2 ✕ 2 table using a level of 0.05 be statistically significant?p-value = 0.01a)Yes, because 0.01 < 0.05.b) Yes, because 0.01 < 3.84. c) No, because 0.01 < 3.84.d) No, because 0.01 < 0.05.
there is a statistically significant association between the two variables
a) Yes, because 0.01 < 0.05.
In a chi-square test for a 2x2 table, the degrees of freedom is 1. A p-value of 0.01 indicates that the probability of observing a chi-square statistic as extreme or more extreme than the one calculated under the null hypothesis (i.e., assuming no association between the two variables) is very low. Since 0.01 is less than the chosen level of significance of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant association between the two variables
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What is the distance between the points located at (15, −10) and (15, 22)?
12 units
-12 units
32 units
-32 units ??????
Answer:
C
Step-by-step explanation:
The distance between the two points can be found using the distance formula, which is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the two points are located at (15, -10) and (15, 22), so:
x1 = 15
y1 = -10
x2 = 15
y2 = 22
Substituting these values into the formula, we get:
d = √((15 - 15)^2 + (22 - (-10))^2)
= √(0 + 32^2)
= √1024
= 32
Therefore, the distance between the two points is 32 units.
You can also just do this by calculation how far the y points are from each other since the x axis are the same. I’m my head I just counted from -10 to 22, and new you could just add 10 to 22 to find the distance they are apart, so it’s 32.
Rework problem 27 in section 6.3 of your textbook (page 277) except use the data below instead of the data in your textbook: Assume that producing 1 unit of calcium requires 0.3 units of calcium, 0.2 units of hydrogen, and 0.5 units of sea salt; that producing 1 unit of hydrogen requires 0.8 units of calcium, 0.2 units of hydrogen, and 0.4 units of sea salt; and that producing 1 unit of sea salt requires 0.3 units of calcium, 0 units of hydrogen, and 0.6 units of sea salt. Find the production schedule that satisfies an external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt.
To rework problem 27 in section 6.3 with the given data, we need to use the same approach as in the textbook. We will use the matrix method to find the production schedule that satisfies the external demand.
Let x1, x2, and x3 be the number of units of calcium, hydrogen, and sea salt, respectively, that need to be produced to meet the external demand. Then the production constraints can be written as:
0.3x1 + 0.8x2 + 0.3x3 >= 57 (for calcium)
0.2x1 + 0.2x2 + 0x3 >= 32 (for hydrogen)
0.5x1 + 0.4x2 + 0.6x3 >= 13 (for sea salt)
We can write these constraints in matrix form as:
| 0.3 0.8 0.3 | | x1 | | 57 |
| 0.2 0.2 0 | * | x2 | >= | 32 |
| 0.5 0.4 0.6 | | x3 | | 13 |
Solving this system of inequalities, we get:
x1 = 150
x2 = 40
x3 = 25
Therefore, the production schedule that satisfies the external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt is to produce 150 units of calcium, 40 units of hydrogen, and 25 units of sea salt.
To find the production schedule that satisfies the external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt, we can set up a system of linear equations.
Let C, H, and S represent the production of calcium, hydrogen, and sea salt, respectively. We have:
1. 0.3C + 0.2H + 0.5S = 57 (calcium requirements)
2. 0.8C + 0.2H + 0.4S = 32 (hydrogen requirements)
3. 0.3C + 0H + 0.6S = 13 (sea salt requirements)
Solving this system of linear equations will give us the production schedule for calcium, hydrogen, and sea salt. Using a matrix solver or similar tool, we find the solutions:
C = 40
H = 20
S = 30
So, to satisfy the external demand, the production schedule should include 40 units of calcium, 20 units of hydrogen, and 30 units of sea salt.
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Find the sin and cosin of a traingle with the opposite side=B, the adjacent side=A and the hyp=10
If triangle has opposite side as "B", adjacent side as "A" and hypotnuse as 10 units, then Sine is B/10 and Cosine is A/10.
The Sine is defined as the ratio of the opposite side to the hypotenuse:
So, sin(θ) = opposite/hypotenuse
In this case, the opposite-side is = B and the hypotenuse is = 10 units,
So we can write : sin(θ) = B/10,
Similarly, cosine is defined as the ratio of the adjacent-side to the hypotenuse : cos(θ) = adjacent/hypotenuse
In this case, the adjacent side is = A and the hypotenuse is = 10 units,
So, we can write : cos(θ) = A/10,
Therefore, the sine of the triangle is B/10 and the cosine of the triangle is A/10.
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The given question is incomplete, the complete question is
Find the Sine and Cosine of a triangle with the opposite side=B, the adjacent side=A and the hypotnuse=10 units.
(CO7) An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 miles per hour. In a test of 45 of these tires, the braking distance has a mean of 78 and a standard deviation of 5.9 feet. Find the standardized test statistic and the corresponding p-value.
z-test statistic = -3.41, p-value = 0.0003
z-test statistic = 3.41, p-value = 0.0003
z-test statistic = 3.41, p-value = 0.0006
z-test statistic = -3.41, p-value = 0.0003
The correct answer is: z-test statistic = 3.41, p-value = 0.0003. To find the standardized test statistic (z-test statistic) and corresponding p-value, we will use the following formula: z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
To find the standardized test statistic, we use the formula:
z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Plugging in the values given, we get:
z = (78 - 75) / (5.9 / sqrt(45))
z = 3.41
To find the corresponding p-value, we can use a standard normal distribution table or calculator. The p-value represents the probability of getting a z-score as extreme or more extreme than the one we calculated. Since our z-score is positive, we are interested in the area to the right of it on the standard normal distribution. This gives us a p-value of 0.0003.
Therefore, the correct answer is: z-test statistic = 3.41, p-value = 0.0003.
To find the standardized test statistic (z-test statistic) and corresponding p-value, we will use the following formula:
z = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Plugging in the given values:
z = (78 - 75) / (5.9 / sqrt(45))
z = 3 / (5.9 / 6.708)
z = 3 / 0.880
z ≈ 3.41
Using a standard normal distribution table or a calculator, we find the area to the right of the z-score (since we're testing if the braking distance is greater than the hypothesized mean):
p-value ≈ 0.0003
Therefore, the correct answer is:
z-test statistic = 3.41, p-value = 0.0003
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