the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature.
How to find middle angle?
In a right triangle, the middle angle is the angle opposite the hypotenuse. To find this angle using trigonometry, you can use either the sine, cosine, or tangent ratio. Let's say that the two legs of the right triangle are a and b, and the hypotenuse is c. Then, you can use the following trig ratios to find the middle angle:
Sine ratio: sin(theta) = a/c
Cosine ratio: cos(theta) = b/c
Tangent ratio: tan(theta) = a/b
To find the middle angle, you would use the inverse sine, cosine, or tangent function, depending on which ratio you used. For example, if you used the sine ratio, you would take the inverse sine of a/c to find the angle: theta = sin²-1(a/c).
What is the relationship between the sine and cosine of the two non-right angles in a right triangle, and how do they define the ratios sine, cosine, and tangent?
In a right triangle, the two non-right angles are complementary, which means that their sum is 90 degrees. Let's call these angles alpha and beta. The sine and cosine of these angles are defined as follows:
Sine of alpha: sin(alpha) = opposite leg / hypotenuse
Cosine of alpha: cos(alpha) = adjacent leg / hypotenuse
Sine of beta: sin(beta) = adjacent leg / hypotenuse
Cosine of beta: cos(beta) = opposite leg / hypotenuse
Note that the opposite and adjacent legs are relative to the angle being considered. The ratios sine, cosine, and tangent are defined in terms of these ratios:
Sine ratio: sin(theta) = opposite leg / hypotenuse
Cosine ratio: cos(theta) = adjacent leg / hypotenuse
Tangent ratio: tan(theta) = opposite leg / adjacent leg
Therefore, the sine and cosine of the two non-right angles in a right triangle are related to each other by their complementary nature. If you know the value of one of these ratios, you can use it to find the value of the other using the fact that sin(alpha) = cos(beta) and cos(alpha) = sin(beta). This relationship is known as the complementary angle identities.
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Find the total amount and total interest after six months if the interest is compounded every quarter. Principal =₹10 000 Rate of interest =20% per annum.
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000
Step-by-step explanation:
Suppose we select one 2015 Spotify user at random
and record his or her age and whether his or her favorite music genre is pop.
(a) Draw a tree diagram to model this chance process.
(b) Find the probability that the person identifies his or her favorite music genre as pop.
(c) Suppose the chosen person identifies his or her favorite music genre as pop. What’s the probability
that he or she is aged 13–24?
Answer:11
Step-by-step explanation:
design a context-free grammar (cfg) for the following language (20 points). if your grammar has multiple variables, please briefly describe the strings derived by each variable of your grammar (5 points, please see the lecture notes on cfg design for examples). l
L={aibi| 3i=0, j >=0}
Answer: 67
Step-by-step explanation:67 x1
At a party to celebrate a successful school play, the drama club bought 999 large pizzas. Each pizza had sss slices. All together, there were 727272 slices of pizza for the club to share.
Write an equation to describe this situation.
How many slices does each pizza have?
Answer:
Step-by-step explanation:
Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:
999n = 727272
To solve for "n", we divide both sides by 999:
n = 727272/999
Using a calculator or long division, we get:
n ≈ 728.56
Therefore, each pizza has approximately 728 slices.
Suppose Elena has $5 and sells pens for $1.50 each. Her goal is to save $20 to buy a t-shirt. She does not spend any money while she is saving money.
Let p represent the number of pens Elena sells. Write an expression for how much money she saves in total after selling p pens.
Write an equation using your answer from question 1, showing that she saves exactly $20.
Solve the equation you wrote from question 2. What do you notice about your value for p?
What if Elena wants to have some money left over? Write an inequality using your expression from question 1 to show this.
Write down other values for p where Elena would have money left over.
Write an inequality using p, to describe the values of p where she would be able to buy the tshirt and still have money left over.
In conclusion the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc. The equation showing that Elena saves exactly $20 is:
5 + (1.5)p = 20
Why it is?
The expression for how much money Elena saves after selling p pens is:
Total money saved = 5 + (1.5)p
The equation showing that Elena saves exactly $20 is:
5 + (1.5)p = 20
Solving the equation:
5 + (1.5)p = 20
(1.5)p = 15
p = 10
We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.
If Elena wants to have some money left over, we can write the inequality:
5 + (1.5)p > 20
Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.
To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:
5 + (1.5)p > 20
(1.5)p > 15
p > 10
Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.
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an urn contains p black balls, q white balls, and r red balls; and n balls are chosen without replacement. a. find the joint distribution of the numbers of black, white, and red balls in the sample. b. find the joint distribution of the numbers of black and white balls in the sample. c. find the marginal distribution of the number of white balls in the sample.
a. The joint distribution of the numbers of black, white, and red balls in the sample is given by P(x, y, z) = nCx * nCy * nCz / (p + q + r)Cn, where x is the number of black balls, y is the number of white balls, z is the number of red balls, and n is the total number of balls chosen.
b. The joint distribution of the numbers of black and white balls in the sample is given by P(x, y) = nCx * nCy / (p + q)Cn, where x is the number of black balls, y is the number of white balls, and n is the total number of balls chosen.
c. The marginal distribution of the number of white balls in the sample is given by P(y) = nCy / qCn, where y is the number of white balls, and n is the total number of balls chosen.
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In Exercise 5.12 , we were given the following joint probability density function for the random variables Y1 and Y2, which were the proportions of two components in a sample from a mixture of insecticide: f(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhere
Are Y1 and Y2 independent?
The conclude that the Y1 and Y2 are not independent.
The joint probability density function for the random variables Y1 and Y2 for a mixture of insecticide isf(y1,y2)={2,0,0≤y1≤1,0≤y2≤1,0≤y1+y2≤1 elsewhereTo verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Therefore, we need to find the marginal density functions of Y1 and Y2.Probability Density Function:We know that for a given joint probability density function, the probability density function of Y1 is given by integrating over all possible values of Y2, and vice versa.Mathematically,P(Y1)=∫0∫1f(y1,y2)dy2... (1)P(Y2)=∫0∫1f(y1,y2)dy1... (2)Using equation (1) to calculate P(Y1), we get, P(Y1)=∫0∫1f(y1,y2)dy2=∫0∫1(2)dy2=2... (3)Similarly, we can use equation (2) to calculate P(Y2) as follows:P(Y2)=∫0∫1f(y1,y2)dy1=∫0∫1(2)dy1=2... (4)Product of marginal density functions:Now we can find the product of marginal density functions as follows:P(Y1)P(Y2)=2×2=4... (5)Thus, to verify if the Y1 and Y2 are independent, we need to check if f(y1,y2) is equal to the product of the marginal probabilities of Y1 and Y2.Since 2 ≠ 4, Y1 and Y2 are not independent. Hence, we can conclude that the Y1 and Y2 are not independent.
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A manufacturer of paper used for packaging requires a minimum strength of 1400 g/cm2. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour’s production and a strength measurement is recorded for each. The standard deviation of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 140 g/cm2, and the strength measurements are normally
distributed.
a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?
b) If the mean of the population of strength measurements is 1450 g/cm2, what is the
approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400?
The sample mean is 1450g/cm², the standard deviation is 44.3 g/cm² and the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2 is 0.8708
What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?a) The sampling distribution of the sample mean of n = 10 test pieces of paper is approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:
mean of sample mean = mean of population = 1450 g/cm²
standard deviation of sample mean = standard deviation of population / square root of sample size
= 140 g/cm2 / √(10)
= 44.3 g/cm²
Therefore, the sampling distribution of the sample mean is approximately normal with mean 1450 g/cm2 and standard deviation 44.3 g/cm2.
b) To find the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2, we need to standardize the sample mean using the sampling distribution calculated in part (a):
z = (x - mean of sample mean) / standard deviation of sample mean
= (1400 - 1450) / 44.3
= -1.13
Using a standard normal distribution table or calculator, we can find the probability that z is less than -1.13 and subtract that probability from 1 to find the probability that z is greater than -1.13:
P(z > -1.13) = 1 - P(z < -1.13)
= 1 - 0.1292
= 0.8708
Therefore, the approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm² is 0.8708.
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find the volume of a pyramid with a square base, where the area of the base is 4.6 cm 2 4.6 cm 2 and the height of the pyramid is 2.3 cm 2.3 cm. round your answer to the nearest tenth of a cubic centimeter.
The volume of pyramid is 3.5 cm³.
To find the volume of a pyramid with a square base, where the area of the base is 4.6 cm² and the height of the pyramid is 2.3 cm, we can use the following formula:
V = (1/3)B*h
Where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid. Substitute the given values into the formula and solve:
V = (1/3)(4.6)(2.3)V = 3.53 cm³
Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is 3.5 cm³. Therefore, the volume of pyramid is 3.5 cm³.
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solve simultaneously 4x-y=3x+1y 4x+3y=x+6y
(x, y) = (0,0) is the solution of the system of equations.
simultaneous equationSimultaneous equations are a set of two or more equations that contain multiple variables, which must be solved at the same time. The solution to the system of equations is the set of values of the variables that satisfy all of the equations in the system simultaneously.
The given system of equations is:4x - y = 3x + y
4x + 3y = x + 6y
Simplifying the first equation by moving all the y-terms to the left-hand side and all the x-terms to the right-hand side, we get:
4x - 3x = y + y
x = 2y
Substituting this value of x into the second equation, we get:
4(2y) + 3y = (2y) + 6y
8y + 3y = 8y
11y = 0
y = 0
Substituting y = 0 into the equation x = 2y, we get:
x = 2(0)
x = 0
Therefore, the solution to the system of equations is:
x = 0 and y = 0
Hence, (x, y) = (0,0) is the solution of the system of equations.
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Y=3x+3 what is the slope and y intercept
Answer:
y-intercept is (0,3) and the slope is 3
Step-by-step explanation:
Answer: the slope is 3x while 3 is the y-intercept.
Step-by-step explanation:
Someone please help me ASAP!! It’s due today!! Show work please! I will mark brainliest if it’s done correctly
Answer:
D
Step-by-step explanation:
First set up the fraction [tex]\frac{9}{40}[/tex] , and next divide 9 ÷ 40 = 0.225. Lastly, multiply 0.225 × 100 = 22.5%.
Hope this helps.
How much greater is 0.05723 then 0.005?
0.05723 is 0.05223 greater than 0.005.
What is greater than?"Greater than" is a comparison term used to indicate that one quantity or value is larger or more than another quantity or value. It is represented mathematically by the symbol ">".
What is lesser than?"Lesser than" is a comparison term used to indicate that one quantity or value is smaller or less than another quantity or value. It is represented mathematically by the symbol "<".
In the given question,
To find out how much greater 0.05723 is than 0.005, we can subtract 0.005 from 0.05723:0.05723 - 0.005 = 0.05223
Therefore, 0.05723 is 0.05223 greater than 0.005.
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A sports club had 130 members last summer. This summer, due to some renovations, it has 182 members. What is the percent of increase in the number of members?HELP PLSSSSS
Answer:
Step-by-step explanation:
312
Answer:
36.92%
Step-by-step explanation:
180-132=48. Now we have to find 48 of 130 to find the percentage increase. 48 out of 130 = which equals 36.92.
Classify each as Polynomial or Not a Polynomial.
1.) 9x-^3 - 2y
2.) 2x^2 - 4√x
3.) 2x 2/3 - 4y
4.) 20x^2
5.) w/2 + 7
6.) 4y/2x
7.) -20x^2 + y
A researcher randomly chooses 1000 Kentucky families to estimate the proportion of all American families who routinely eat dinner together. What is the population? a) The 1000 Kentucky families b) All Kentucky families c) All American families d) All families around the world
The population in the given scenario of a researcher randomly choosing 1000 Kentucky families to estimate the proportion of all American families who routinely eat dinner together is all American families (option c).
In the given scenario, the population is all American families. The researcher has randomly chosen 1000 families from Kentucky to estimate the proportion of all American families who routinely eat dinner together. The researcher is using the sample of 1000 Kentucky families to make inferences about the population of all American families. By assuming that the sample is representative of the population, the researcher can use statistical methods to estimate the proportion of all American families who routinely eat dinner together. So, option C is the correct answer.
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Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint.
0.82 0.88 0.88 1.06 1.09 1.14 1.30 1.33
1.48 1.50 1.57 1.64 1.64 1.70 1.76 1.83
Determine the z percentile associated with each sample observation. (Round your answers to two decimal places.)
I have the answers below but I don't know how they were computed. z = (X - ?) / ? does not provide the correct value. Can someone provide how the answers below were computer?
z percentile .82 = -1.86
z percentile .88 = -1.32
z percentile .88 = -1.32
z percentile 1.06 = -0.78
z percentile 1.09 = -0.58
z percentile 1.14 = -0.40
z percentile 1.30 = -0.24
z percentile 1.33 = -0.08
z percentile 1.48 = 0.08
z percentile 1.50 = 0.24
z percentile 1.57 = 0.40
z percentile 1.64 = 0.58
z percentile 1.64 = 0.58
z percentile 1.70 = 1.01
z percentile 1.76 = 1.32
z percentile 1.83 = 1.86
The normal probability plot for the following sample deduce by z = (X - mean) / standard deviation as following steps.
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.
The steps to calculate the z-percentiles for the given sample:
Find the mean of the sample:
mean = (0.82 + 0.88 + 0.88 + 1.06 + 1.09 + 1.14 + 1.30 + 1.33 + 1.48 + 1.50 + 1.57 + 1.64 + 1.64 + 1.70 + 1.76 + 1.83) / 16 = 1.235
Find the standard deviation of the sample:
First, find the sum of the squared differences between each observation and the mean:
(0.82 - 1.235)^2 + (0.88 - 1.235)^2 + (0.88 - 1.235)^2 + (1.06 - 1.235)^2 + (1.09 - 1.235)^2 + (1.14 - 1.235)^2 + (1.30 - 1.235)^2 + (1.33 - 1.235)^2 + (1.48 - 1.235)^2 + (1.50 - 1.235)^2 + (1.57 - 1.235)^2 + (1.64 - 1.235)^2 + (1.64 - 1.235)^2 + (1.70 - 1.235)^2 + (1.76 - 1.235)^2 + (1.83 - 1.235)^2 = 2.9878
Next, divide the sum by the sample size minus 1 and take the square root: standard deviation = sqrt(2.9878 / 15) = 0.4323
Use the formula z = (X - mean) / standard deviation to calculate the z-percentile for each observation in the sample.
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To calculate the z-percentile for each observation in the sample.: Find the mean of the sample, Find the standard deviation of the sample and then use the formula z = (X - mean) / standard deviation.
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.
The steps to calculate the z-percentiles for the given sample:
Find the mean of the sample:
mean = (0.82 + 0.88 + 0.88 + 1.06 + 1.09 + 1.14 + 1.30 + 1.33 + 1.48 + 1.50 + 1.57 + 1.64 + 1.64 + 1.70 + 1.76 + 1.83) / 16
mean = 1.235
Find the standard deviation of the sample:
First, find the sum of the squared differences between each observation and the mean:
(0.82 - 1.235)² + (0.88 - 1.235)² + (0.88 - 1.235)² + (1.06 - 1.235)² + (1.09 - 1.235)² + (1.14 - 1.235)² + (1.30 - 1.235)² + (1.33 - 1.235)² + (1.48 - 1.235)² + (1.50 - 1.235)² + (1.57 - 1.235)² + (1.64 - 1.235)² + (1.64 - 1.235)² + (1.70 - 1.235)² + (1.76 - 1.235)² + (1.83 - 1.235)² = 2.9878
Next, divide the sum by the sample size minus 1 and take the square root:
standard deviation = √(2.9878/15)
standard deviation = 0.4323
Use the formula z = (X - mean) / standard deviation to calculate the z-percentile for each observation in the sample.
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Calculate the area and perimeter of this rectangle.
Answer:
Area: 391.92 ft²
Perimeter: 84.4 ft
Step-by-step explanation:
Area of rectangle = L × W
We Take
13.8 × 28.4 = 391.92 ft²
Find the Perimeter of the Rectangle
We Take
28.4 + 13.8 + 28.4 + 13.8 = 84.4 ft
So, Area: 391.92 ft²
Perimeter: 84.4 ft
Answer:
Area = 391.92 square feet
Perimeter = 84.4 feet
Step-by-step explanation:
The area of a rectangle is the product of its width and length.
The perimeter of a rectangle is twice the sum of its width and length.
Given the width of the rectangle is 28.4 feet and its length is 13.8 feet:
[tex]\begin{aligned}\textsf{Area of the rectangle}&=\sf width \times length\\&=28.4 \times 13.8\\&=391.92 \sf \;\;square\;feet\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=\sf 2(width +length)\\&=2(28.4 +13.8)\\&=2(42.2)\\&=84.4 \sf \;\;feet\end{aligned}[/tex]
5my × 5ym = ?
Can you multiply two terms with the same 2 coefficients in different positions like the example above?
Answer:
In the example given, 5my × 5ym, you can simplify it using the commutative property of multiplication as follows:
5my × 5ym = 5 × 5 × m × m × y × y
= 25m²y²
So, the answer is 25m²y².
a random sample of 15 recent college graduates found that starting salaries for attorneys in new york city had a mean of $102,342 and a standard deviation of $21,756. there are no outliers in the sample data set. construct a 95% confidence interval for the average starting salary of all attorneys in the city.
The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a p-value of 1-∝.
So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]
Now, find M as such
[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ
In which is the standard deviation of the population and n is the size of the sample.
[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.
The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.
So the correct answer is:
(91331.94, 113352.06)
Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.
Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.
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Complete Question:
A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices
A). (89869.82, 114814.18)
B). (90292.73, 114391.27)
C). (91331.94, 113352.06)
D). (90371.37, 114312.63)
The volume of this prism is 4950cm3.
The area of the cross-section is 110cm2.
Work out x
Answer:
45cm
Step-by-step explanation:
length × cross section = volume
in this case we call the unknown [tex]x[/tex]
so
[tex]x[/tex] x 110 = 4950
to get [tex]x[/tex] you divide the volume by the cross section
[tex]\frac{4950}{110}[/tex]= [tex]x[/tex]
so [tex]x[/tex] = 45cm
pls help Are the following lines parallel, perpendicular, or neither?
y = 2/3x − 4
y = −3/2x − 7
Responses
Parallel
Perpendicular
Neither
Answer:
Perpendicular.
Step-by-step explanation:
To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form
y = 2/3x - 4 ==> slope = 2/3
y = -3/2x - 7 ==> slope = -3/2
Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.
Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1
(2/3) * (-3/2) = -1
Since the product of the slopes is -1, the two lines are perpendicular.
Therefore, the answer is: perpendicular.
Write and solve an equation to answer the following question. The Smith family rented a recreational vehicle for a seven-day vacation. The cost to rent the recreational vehicle was $80 plus $0.50 per mile. How many miles were driven if the total cost was $1350?
Answer: 2540
Step-by-step explanation: 1350-80=1270. 1270/0.5=2540
Customer five had a $5.00 off coupon, but still has to pay the 4.5% sales tax. How much do they end up paying?
Sure, I can help you with this. To calculate the amount that Customer five will end up paying with their $5.00 off coupon and 4.5% sales tax, we will use the following formula: final amount = original amount - coupon - (original amount * tax rate).
In this case, the original amount is $5.00, the coupon is $5.00, and the tax rate is 4.5%. Plugging these values into the formula, we get:
final amount = 5.00 - 5.00 - (5.00 * 0.045)
final amount = 5.00 - 5.00 - 0.225
final amount = 4.775
Therefore, Customer five will end up paying $4.775 after their coupon and the sales tax.
the national football league (nfl) records a variety of performance data for individuals and teams. to investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 nfl teams for one full season.
The National Football League (NFL) is an American football league that is based in the United States. The NFL records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 NFL teams for one full season.The data collected by the NFL shows that passing has a significant impact on the percentage of games won by a team. Teams that have a higher average number of passing yards per attempt tend to win more games than those with a lower average. Additionally, teams that have a lower number of interceptions thrown per attempt also tend to win more games than those with a higher number of interceptions thrown per attempt.The data also shows that the conference a team plays in does not have a significant impact on the percentage of games won by a team. This means that a team's conference is not a good indicator of its performance.The NFL should continue to record data on passing to help teams improve their performance. Coaches can use this data to identify areas for improvement and develop strategies to help their teams win more games.
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Let A be a set With 12 elements. (a) Find the number of subsets of A. (b) Find the number of subsets of A having one or more elements. (c) Find the number of subsets of A having exactly one element. (d) Find the number of subsets of A having two or more elements. [Hint: Use the answers to parts (b) and (c).]
(a) Total Number of Subsets of A:
In set theory, any set is a subset of itself. Additionally, the empty set is a subset of every set. As a result, there are 2^12 subsets of A.
Number of Subsets of A = 2^12 = 4096
(b) Number of Subsets of A having One or More Elements:
To find the number of subsets of A having one or more elements, we must subtract the empty set from the total number of subsets of A.
∴ Number of Subsets of A having One or More Elements = (2^12) − 1 = 4095
(c) Number of Subsets of A having Exactly One Element:
We can use the formula given below to compute the number of subsets of A having exactly one element. Here, n represents the number of elements in the set.
Formula: nC1 = n
∴ Number of Subsets of A having Exactly One Element = 12C1 = 12
(d) Number of Subsets of A having Two or More Elements:
Using parts (b) and (c), we can obtain the number of subsets of A having two or more elements by subtracting the number of subsets of A having exactly one element from the number of subsets of A having one or more elements.
∴ Number of Subsets of A having Two or More Elements = (2^12) − 1 − 12 = 4083.
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I need help. A explanation and how you got the answer would be amazing. Thx
Answer: What is this equation
Step-by-step explanation:
Evaluate the expression
z + 3x4
A. 27
B. 32
C. 56
D. 1,304
The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.
The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.
z + 3x4 = 15 + 3x4
= 15 + 12
= 27
Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).
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____The given question is incomplete , the complete question is given below:
Evaluate the expression, where z = 15
z + 3x4
A. 27
B. 32
C. 56
D. 1,304
The access code for a car's security system consist of six digits. The first digit cannot be zero and the last digit must be even. How many different codes are available?
If an access code for a car's security system consist of six digits and the first digit cannot be zero and the last digit must be even, then the number of different codes available are 4,500,000
Since the first digit cannot be zero, we have 9 choices for the first digit. For each of these 9 choices, there are 10 possibilities for the second digit (0-9).
Similarly, there are 10 possibilities for the third digit, 10 for the fourth digit, 10 for the fifth digit, and 5 (0, 2, 4, 6, 8) for the last digit.
Therefore, the total number of possible access codes is:
9 x 10 x 10 x 10 x 10 x 5 = 4,500,000
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what is 1 half of 68 ?
Answer:
34
Step-by-step explanation:
1/2 multiplied by 68=34
34 is 1 half of 68 .
Here, we have,
given that,
what is 1 half of 68
we know that,
Half of a number can be found by dividing the number by 2.
i.e. we have to find half of 68,
for that, we need to divide 68 by 2
so, we get,
To find half of 68:
68 / 2 = 34
Therefore, half of 68 is 34.
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