Answer:
linear equations produce straight lines when graphed, and their rate of change remains constant
Nonlinear equations do not produce straight lines when graphed.
To determine whether its linear or nonlinear, you can graph it and see if it produces a straight line, or check if it can be written in the form y= Mx+b
Step-by-step explanation:
3. Consider the following statement: For each positive real number r, if r2 = 18, then r is irrational (a) If you were setting up a proof by contradiction for this statement, what would you assume? Carefully write down all conditions that you would assume. (b) Complete a proof by contradiction for this statement.
(a) To set up a proof by contradiction for the statement "For each positive real number r, if r^2 = 18, then r is irrational," we will assume the opposite of the given statement. Specifically, we would assume that there exists a positive real number r such that r^2 = 18, and r is rational (not irrational).
(b) To complete the proof by contradiction, follow these steps:
1. Assume that there exists a positive real number r such that r^2 = 18, and r is rational.
2. Since r is rational, we can write it as a fraction a/b, where a and b are integers with no common factors other than 1 (i.e., a and b are coprime) and b ≠ 0.
3. We have r^2 = 18, so (a/b)^2 = 18.
4. Squaring both sides, we get a^2 / b^2 = 18.
5. Rearrange the equation: a^2 = 18b^2.
6. Since 18 is an even number, a^2 is also an even number, which implies that a is an even number (let's say a = 2k, where k is an integer).
7. Substitute a with 2k: (2k)^2 = 18b^2, which simplifies to 4k^2 = 18b^2.
8. Divide both sides by 2: 2k^2 = 9b^2.
9. Now, we see that the left side of the equation is an even number (2k^2), which implies that 9b^2 is also an even number. However, 9 is an odd number, so for 9b^2 to be even, b must be even.
10. Both a and b are even, which contradicts our original assumption that a and b are coprime (having no common factors other than 1).
Therefore, our assumption that there exists a positive real number r such that r^2 = 18 and r is rational leads to a contradiction. Thus, the original statement is true: for each positive real number r, if r^2 = 18, then r is irrational.
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How much more interest do vour parents have to pay at the end of the first month because their (i point) rating 15 good rather than excellent?
The more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent is option (D) $19.02.
First, we need to calculate the sales tax on the mobile home purchase:
Sales tax = 4.2% of $89,000 = 0.042 x $89,000 = $3,738
The total cost of the mobile home including sales tax is
Total cost = $89,000 + $3,738 = $92,738
After making a down payment of $3,000, the amount to be financed is:
Amount financed = $92,738 - $3,000 = $89,738
To calculate the interest, we need to know the monthly interest rate. Let's assume the loan term is 30 years, which is 360 months. Then, the monthly interest rate for an excellent credit rating would be:
Monthly interest rate (excellent) = 4.75 / 1200 = 0.00396
And for a good credit score
Monthly interest rate (good) = 5.00 / 1200 = 0.00417
The interest for the first month for an excellent credit rating would be:
Interest (excellent) = $89,738 x 0.00396 = $355.33
And for a good credit rating:
Interest (good) = $89,738 x 0.00417 = $374.43
The difference in interest is:
Difference in interest = $374.43 - $355.33 = $19.02
Therefore, the correct option is (D) $19.02.
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The given question is incomplete, the complete question is:
Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment. How much more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent?
Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40
Options:
A) $29.39
B) $21.10
C) $18.71
D) $19.02
There is a system of two linear equations. The first equation is y=7x+8. The system has infinite solutions. What other equation would complete the system?
If the system has infinite solutions, it means that the two equations are not independent, but rather one equation is a multiple of the other. In other words, the second equation must be a multiple of y = 7x + 8.
One possible equation that completes the system is:
14y = 98x + 112
To check that this equation works, we can substitute y = 7x + 8 into the equation:
14(7x + 8) = 98x + 112
98x + 112 = 98x + 112
As we can see, the equation is true for any value of x, which means that it is satisfied for any value of y that corresponds to y = 7x + 8.
Therefore, the system of equations that has y = 7x + 8 as one of its equations and has infinite solutions is:
y = 7x + 8
14y = 98x + 112
A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?
A future interest in real property typically exists in conjunction with a present interest in that same property at the time the future interest is granted.
What is a future interest?
Future interests are created when a property owner grants an interest in their property that will take effect at a later time, such as after their death or the expiration of a lease.
These interests are typically created in the form of a trust or a will, and they can be used to ensure that property is distributed according to the owner's wishes, to provide for the future needs of family members, or to protect property from creditors or other claims.
Examples of future interests include remainders, reversions, and executory interests.
Complete questin:
A future interest usually exists in conjunction with which of the following real property interests at the time that it is the interest granted?
1) future interest
2) protect property
3) both a and b
4) None of these
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If the dartboard has a diameter of 14 inches and each number occupies 1/20 of the board, how much space does a single number occupy in square inches?
Each number occupies 7.7 inches² of the dartboard.
What is area?In geοmetry, area is the amοunt οf space a flat shape, like a pοlygοn, circle οr ellipse, takes up οn a plane. The area οf a shape is always measured in square units. Tο find the area οf simple shapes like a square οr the area οf a rectangle, yοu οnly need its width, w, and length, l (οr base, b). The area is length times width:
First we need the area of the dartboard
Area = πr²
here r = d/2 = 14/2 = 7
Area of dartboard = πr²
[tex]$ \rm = \frac{22}{7 } \times 7 \times 7[/tex]
= 22 × 7
= 154 inches²
Now, its is said that each number occupies 1/20 of the board,
Then area of each number = 154 × 1/20
= 7.7 inches²
Thus, Each number occupies 7.7 inches² of the dartboard.
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during the summer of 2018, coldstream country club in cincinnati, ohio collected data on 443 rounds of golf played from its white tees. the data for each golfer's score on the twelfth hole are contained in the datafile coldstream12. (round your answers to four decimal places.) (a) construct an empirical discrete probability distribution for the player scores on the twelfth hole.
Given information:
During the summer of 2018, Coldstream Country Club in Cincinnati, Ohio collected data on 443 rounds of golf played from its white tees. The data for each golfer's score on the twelfth hole are contained in the datafile coldstream12. (Round your answers to four decimal places.)
Construct an empirical discrete probability distribution for the player scores on the twelfth hole.
A probability distribution is a tabulation of probabilities for every outcome in a sample space. It is a summary of the probabilities for all possible values of a random variable. In statistics, there are two types of probability distributions: empirical and theoretical.
An empirical distribution is a frequency distribution of observed data. A theoretical distribution is a distribution that is derived from theory.
To construct the empirical probability distribution, we will use the following steps:
Step 1: Calculate the range of the data set, which is the difference between the maximum and minimum values. Range = Maximum value – Minimum value = 8 – 3 = 5.
Step 2: Divide the range by the number of intervals (or classes) desired. In this case, we will use 6 intervals. Interval size = Range / Number of intervals = 5 / 6 = 0.833333333.
Step 3: Determine the lower limit of each interval by subtracting the interval size from the minimum value.
Lower limit of first interval = Minimum value – Interval size = 3 – 0.833333333 = 2.166666667.
Lower limit of second interval = Lower limit of first interval + Interval size = 2.166666667 + 0.833333333 = 2.999999999 ≈ 3.
Lower limit of third interval = Lower limit of second interval + Interval size = 3 + 0.833333333 = 3.833333333.
Lower limit of fourth interval = Lower limit of third interval + Interval size = 3.833333333 + 0.833333333 = 4.666666666.
Lower limit of fifth interval = Lower limit of fourth interval + Interval size = 4.666666666 + 0.833333333 = 5.499999999 ≈ 5.
Lower limit of sixth interval = Lower limit of fifth interval + Interval size = 5 + 0.833333333 = 5.833333333.
Step 4: Count the number of data points that fall in each interval. The table below shows the frequency distribution for the data set.
Interval Lower Limit Upper Limit Frequency Relative Frequency
1 2.166666667 2.999999999 33 0.0745
2 3 3.833333333 93 0.2096
3 3.833333333 4.666666666 74 0.1669
4 4.666666666 5.499999999 56 0.1264
5 5.5 6.333333333 8 0.0180
6 5.833333333 6.666666666 4 0.0090
Total - - 268 1.0000
From the above table, the empirical discrete probability distribution is constructed.
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the probability that a dessert sold at a certain cafe contains chocolate is 86%. the probability that a dessert containing chocolate also contains nuts is 30%. find the probability that a dessert chosen at random contains nuts given that it contains chocolate. round to the nearest tenth of a percent.
The probability that a dessert chosen at random contains nuts given that it contains chocolate is 34.9%.
The likelihood of any event A happening when another event B related to A has already happened is known as conditional probability. This implies that the likelihood of event A relies on event B.
The conditional probability symbol is P(A|B). Conditional probability P(A|B) is crucial for any exam that is part of a competition. The concept of conditional probability P(A|B), formula, and examples with solutions are all covered in this article. The Bayes theorem predicts the likelihood that an event connected to any condition would occur. For the situation of conditional probability, this theorem is taken into account.
Let A : a certain cafe contains chocolates
B: a dessert contains Nuts
P(A) = 86% = 0.86
P(AB) = 30% = 0.3
[tex]P(B|A) =\frac{P(AB)}{P(A)}[/tex]
= 0.3/0.86
= 34.9 %
So the answer is 34.9%
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A rectangular garden plot has a length of 4 meters and a width of 3.5 meters. Jackson wants to put a fence around the garden. He also wants to install landscape fabric over the entire plot to prevent weeds. How much fencing will he need to buy? How much landscape fabric will he need to buy?
Using the formula of area and perimeter of the rectangle, the answers to both subparts are shown:
(A) The fencing required is 15 meters.
(B) The fabric required is 14m².
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).
A rectangle has equal and parallel opposite sides.
Four sides make up a rectangle, which has opposing sides that are parallel and of equal length.
It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees.
An example of a parallelogram with equal angles is a rectangle.
It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.
A square is a rectangle with four equally long sides.
(A) The required fencing:
Perimeter = 2(l+w)
Perimeter = 2(7.5)
Perimeter = 15
The fencing required is 15 meters.
(B) The landscape fabric required:
Area = l*w
Area = 4*3.5
Area = 14m²
The fabric required is 14m².
Therefore, using the formula of area and perimeter of the rectangle, the answers to both subparts are shown:
(A) The fencing required is 15 meters.
(B) The fabric required is 14m².
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assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). a decrease in the student-teacher ratio by 2 will:
the relationship between test scores and the student-teacher ratio can be modeled as a linear function: The right choice is D) lessen test scores by 4.56 for each school locale.
In view of the data in the inquiry, the relationship between test scores and the understudy educator proportion can be numerically composed as follows:
x = 698.9 - 2.28y .................... (1)
Where,
x = test scores
y = understudy educator proportion
The slant of (- 2.28) shows the sum by which x will change at whatever point there is an adjustment of y.
Hence, when there is a reduction in the understudy educator proportion by 2 (for example y = 2), we will have:
Change in x = - 2.28 * 2 = - 4.56
The negative sign thusly shows that the test scores will decrease by 4.56 for each school area. Accordingly, the right choice is D) lessen test scores by 4.56 for each school locale.
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the complete question is:
Assume that the relationship between test scores and the student-teacher ratio can be modeled as a linear function with an intercept of 698.9 and a slope of (-2.28). A decrease in the student teacher ratio by 2 will: A) reduce test scores by 2.28 on average) result in a test score of 698.9C) reduce test scores by 2.56 on average) reduce test scores by 4.56 for every school district.
what is the probability of rolling a sum less than or equal to 7 ? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of rolling a sum of 7 or less on two dice is 11/36. This can be expressed as a decimal number rounded to four decimal places as 0.3056.
We need to look at the possibilities when rolling two dice. Each die has six sides, which means the total number of outcomes when rolling two dice is 36. There are 11 combinations of two dice that produce a sum of 7 or less: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (3,1), (3,2). So, 11/36 can be simplified to 1/4, or 0.3056.
To understand this in a more visual way, you can draw a table and use colored dots to indicate the possible combinations. This will show you that out of 36 total possibilities, 11 of them produce a sum of 7 or less.
In summary, the probability of rolling a sum of 7 or less on two dice is 11/36, which can be expressed as a decimal number rounded to four decimal places as 0.3056.
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Solve for n: 8л = 56
n/8⋅л=56. You’re welcome!
Oliver spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6900 feet.
Oliver initially measures an angle of elevation of 16° to the plane at point A. At some
later time, he measures an angle of elevation of 27° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest tenth of a foot if necessary.
Thus, the distance travelled by the airplane from point A to point B is found as: 1159.93 ft.
Explain about the angle of elevation?The angle from of the horizontal upward to an item is referred to as the angle of elevation. The line of sight of an observer will rise above the horizontal.The angle from horizontal downward to an item is referred to as the "angle of depression." The line of sight of an observer would fall short of the horizontal.Let the distance travelled between A and B be 'x'.
Height h = 6900 feet.
The figure is attached.
Using the tan function:
tan Ф = opposite side/ hypotenuse
In right triangle BCE.
tan 27 = 6900 / y
y = 6900 / tan 27
y = 15281.80
In right triangle ACD
tan 16 = 6900 /(x + y)
x + y = 6900/tan 16
x = 26873.72 - 15281.80
x = 1159.93
Thus, the distance travelled by the airplane from point A to point B is found as: 1159.93 ft.
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Solve (x – 3)2 = 49. Select the values of x. –46, -4, 10, 52.
Answer:
x = 10, -4
Step-by-step explanation:
(x – 3)² = 49
x - 3 = √49
x - 3 = ± 7
x = 10, -4
Looking at options, 10 and -4 is the answer.
now standardize this distance by dividing it by the population standard-deviation (or standard error). in other words, how many population-standard-deviations (or standard-error) away is your sample mean from the population mean?
Population-standard-deviations (or standard-error) away is your sample mean from the population mean is therefore (x - μ) / σ.
In order to standardize the distance, we must divide it by the standard deviation of the population (or standard error).How far the sample mean is from the population mean in terms of population-standard-deviations (or standard-error) can be determined by dividing it by the population standard deviation (or standard error). The equation for the same is as follows:
z = (x - μ) / σ
where,
z = standard score,
x = sample mean,
μ = population mean,
σ = population standard deviation.
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Vincent flipped three coins during a probability experiment. The outcomes of the first 40 trials are shown
Based on the information in the table, in how many of the next 120 trials will the outcome be exactly two of the coins showing heads? in the table.
Answer:
I'm sorry, but I cannot see the table you are referring to. However, I can explain the general approach to solving this type of problem.
When flipping a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads on any one flip is 1/2, and the probability of getting tails is also 1/2.
If Vincent has already flipped the coins 40 times and recorded the outcomes, we can use that information to estimate the probability of getting exactly two heads in the next 120 flips.
One way to do this is to find the proportion of the 40 trials that resulted in exactly two heads. Let's say that out of the 40 trials, 10 of them resulted in exactly two heads. Then the proportion of trials that resulted in two heads is:
10/40 = 1/4
This means that the probability of getting exactly two heads in one trial is 1/4.
To find the expected number of trials out of the next 120 that will result in exactly two heads, we can multiply the probability of getting two heads in one trial by the total number of trials:
(1/4) x 120 = 30
Therefore, we would expect that out of the next 120 trials, approximately 30 of them would result in exactly two heads. However, this is just an estimate based on the information given. The actual number of trials that result in exactly two heads could be more or less than 30 due to random variation.
explain what the p-value means in the given context. a state university wants to increase its retention rate of 4% for graduating students from the previous year. after implementing several new programs during the last two years, the university reevaluates its retention rate and comes up with a p-value of 0.075. using , what can we conclude?
In this context, the p-value represents the probability of observing the data or a more extreme result, assuming that the null hypothesis (the retention rate is still 4%) is true.
In other words, it measures the strength of evidence against the null hypothesis. A small p-value indicates that the observed result is unlikely to have occurred by chance alone, while a large p-value suggests that the null hypothesis cannot be rejected.
In this case, the calculated p-value of 0.075 suggests that there is some evidence to reject the null hypothesis that the retention rate is still 4%.
However, since the p-value is above the conventional threshold of 0.05, we cannot conclude with certainty that the new programs have significantly increased the retention rate. Instead, we can say that there is some indication that the programs may have been effective, but further investigation is needed to determine if this is true.
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Solve for x. Round to the nearest tenth, if necessary.
D
59⁰
7.7
E
Xx
F
Click her
The value of x in the right triangle when calculated is approximately 13.8 units
Calculating the value of x in the triangleGiven the right-angled triangle
The side length x can be calculated using the following sine ratio
So, we have
sin(39) = x/22
To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.
First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.
Then, we can set up the equation:
0.6293 = x/22
To solve for x, we can multiply both sides by 22:
0.6293 * 22 = x
13.8446 = x
Rewrite as
x = 13.8446
Approximate the value of x
x = 13.8
Therefore, x is approximately 13.8 in the triangle
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conditional formulas where the logic would state that if the conditions are met then the tool should exclude the data from analysis. t/f
True, conditional formulas can be used to exclude data from analysis if certain conditions are met. These formulas, often found in spreadsheet software and programming languages, allow you to set specific criteria that must be met in order for the data to be included or excluded from your analysis.
This can be useful in situations where you need to focus on specific subsets of data, or to remove outliers or irrelevant information from your dataset.
By incorporating conditional logic in your formulas, you can ensure that only relevant and useful data is included in your analysis, making it more accurate and efficient. Overall, the use of conditional formulas can greatly enhance your data analysis by providing a flexible and powerful tool to filter and process your data based on specific requirements.
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Which!??! HELPP meee
Answer:
Step-by-step explanation:
Replacing it
Find the exact value of X.
In the given right angled triangle, using Pythagorean theorem, the value of x is 12.73 units.
What is Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the length of the squares on the other two sides add up to the length of the square whose side is the hypotenuse, or the side across from the right angle. This theory can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c:
a² + b² =c²
What is Hypotenuse?The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse.
In the given right angled triangle, using Pythagorean theorem,
x² = (9[tex]\sqrt{2}[/tex] )²+ (9[tex]\sqrt{2}[/tex] )²
x² = 81×2
x = [tex]\sqrt{162}[/tex]
x = 12.73 units
Therefore, the value of x will be 12.73 units.
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HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHelp
Answer:
first box (pies): 3, 6, 9, 12, 15, 18, 33
-> increments of 3
2nd box [cost ($)]: 11, 22, 33, 44, 55, 66, 121
-> increment of 11
Step-by-step explanation:
$44 ÷ 12 pies = $3.67 per 1 pie
3 × $3.67 = $11.01
same process: (number of pies) × $3.67 ≈ COST
Answer:
Step-by-step explanation:
So start off with 66 x 33. That will equal 2,178. Divide 2,178 by 18, like this: 2,178/18. That will equal 121. that will mean that 33 = 121. So 9 = 33 because 9 x 44 = 396 so you will divide that by 12 meaning that 9 equals 33. So now you will multiply 9 and 22 and then divide that answer by 33 making 6 = 22. now divide 22 by 6. That will equal 3.67. So 3.67 is the cost of one pie.
For the boxes above 12 and 44 it will be 16 = 59.
I hope it helped
samantha recently hired a mechanic to do some necessary work. on the final bill, samantha was charged a total of $568. $475 was listed for parts and the rest for labor. if the hourly rate for labor was $31, how many hours of labor was needed to complete the job? (a) first write an equation you can use to answer this question. use x as your variable
Total of 3 hours are needed to complete the job.
The required equation that can be used to answer this question is: 31x = 568 − 475, where x is the number of hours of labor that was needed to complete the job.
Here's how you can solve it:Samantha recently hired a mechanic to do some necessary work. On the final bill, Samantha was charged a total of $568. $475 was listed for parts and the rest for labor.
If the hourly rate for labor was $31, how many hours of labor were needed to complete the job?Solution:Let x be the number of hours of labor needed to complete the job.
Labor cost = $31/hourTotal labor cost = 31x dollars. Total cost of the job = $568.
Cost of parts = $475.
Labor cost = Total cost − Cost of parts.
31x = 568 − 47531x = 93x = 3
Therefore, 3 hours of labor was needed to complete the job.
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how do we ensure trigonometric functions compute values appropriately? what is the value of this expression?
We can ensure trigonometric functions compute values appropriately by validating the results against known values. In order to ensure that the argument is in a short interval surrounding a place where an approximation is highly accurate, one performs a range reduction prior to computing things like a cos or sin.
By comparing the results to established values, we can make sure trigonometric functions compute values correctly. As an example, if we wanted to validate the cosine of 45 degrees, we could compare the result to the known value of 0.707. If the computed value is within a small margin of error of the known value, then we can assume the trigonometric function is computing values appropriately.
In order to calculate functions like cos or sin, one must first perform a range reduction to make sure the input is inside a narrow range surrounding a point where an approximation is highly accurate. It is typically close to zero.
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jennifer needs to estimate the average age of vets in houston. the standard deviation of ages is 22 years. she wants the standard error of her mean to be 3.42 years. how many vets is she going to need to sample to get at least that kind of accuracy? (be sure to round up; you can't survey part of a person)
Jennifer needs to sample at least 151 vets to achieve a standard error of the mean of 3.42 years or less.
The variability or uncertainty of a sample statistic, like the mean or proportion, is measured by standard error. It represents the sample distribution's standard deviation for that statistic. In other words, it calculates the amount by which chance is likely to cause the sample statistic to deviate from the actual population parameter.
The calculation of the standard error is based on the particular statistic being produced as well as the characteristics of the sampled population. For instance, the population's standard deviation is divided by the square root of the sample size to determine the standard error of the mean. If p is the estimated proportion based on the sample, then the standard error of a proportion is determined as (p * (1 - p)) divided by the square root of the sample size.
A population parameter estimate that has a lower standard error is more accurate. Inferential statistics frequently employ the standard error to compute confidence intervals and test population parameter-related hypotheses.
The formula for the standard error of the mean can be used to get the approximate number of veterans Jennifer needs to sample:
[tex]SE = / \sqrt{n}[/tex]
where n: sample size, delta: age standard deviation, and SE: standard error of the mean.
In this instance, we are aware that = 22 years and SE = 3.42 years. As we solve for n, we obtain:
[tex]n = (delta / SE)^2 n = (22 / 3.42)^2 \sn = 150.39[/tex]
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Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if
The distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
Describe Distance?Distance can be calculated using a variety of methods, depending on the context. For example, the distance between two points in a straight line can be calculated using the Pythagorean theorem in two dimensions or the distance formula in three dimensions. In more complex situations, such as when the two points are not in a straight line, distance may be calculated using other mathematical methods or by estimating the distance based on contextual information.
Distance is often used in everyday life to describe how far apart objects or locations are from each other, such as the distance between two cities, the distance from home to work, or the distance between two landmarks. It is also used in many scientific fields to describe the separation between celestial objects, the distances traveled by particles in a chemical reaction, or the distances between neurons in the brain.
We can solve this problem using the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:
a/sin A = b/sin B = c/sin C
Let's label the distance from point A to the boat as a, the distance from point B to the boat as b, and the distance from point C to the opposite bank as c. We are given that AB = 50 meters, angle ABC = 68 degrees, and angle BCA = 73 degrees. We want to find a and b.
First, we can find the measure of angle ACB by using the fact that the sum of angles in a triangle is 180 degrees:
angle ACB = 180 - angle ABC - angle BCA
angle ACB = 180 - 68 - 73
angle ACB = 39 degrees
Next, we can use the Law of Sines to find a and b:
a/sin 68 = c/sin 39
b/sin 73 = c/sin 39
Solving for c in both equations gives:
c = a sin 39 / sin 68
c = b sin 39 / sin 73
We can set these two equations equal to each other and solve for b:
a sin 39 / sin 68 = b sin 39 / sin 73
b = a (sin 39 / sin 73) * (sin 68 / sin 39)
b = a (sin 68 / sin 73)
We know that a + b = 50, so we can substitute the expression for b into this equation:
a + a (sin 68 / sin 73) = 50
Solving for a gives:
a = 50 / (1 + sin 68 / sin 73)
a ≈ 23.3 meters
Substituting this value of a into the expression for b gives:
b ≈ 26.7 meters
So the distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
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The complete question is
Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if angle ABC=68 degree and angle BCA=73 degree. Round to the nearest foot.
The prisms are similar. What is the surface area of Prism B? Prism A is 10 m. Prism B is 6 m. Surface area = 880m2
Answer:
79.92m
Step-by-step explanation:
here you go hope this helps
in california, people use 63 btu of energy per home. this is 30% less than the national average. how many btu does an average american household use?
The national average for energy usage per home in BTU is approximately 90 BTU.
BTU stands for British Thermal Unit, which is the amount of energy required to raise the temperature of one pound of water by one degree Fahrenheit. It is used to quantify the amount of energy consumed by heating or cooling equipment.In California, people use 63 BTU of energy per home, which is 30% less than the national average. Therefore, to calculate the average BTU consumption for American households, we will use the following formula: National average BTU = California BTU / (1 - 30%)
Let's solve for the national average BTU: National average BTU = 63 BTU / (1 - 0.30)
National average BTU = 63 BTU / 0.70National average BTU = 90 BTU
Therefore, the average American household uses 90 BTU of energy per home.
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a bond is worth 100$ and grows in value by 4 percent each year. f(x) =
To represent the value of the bond after x years, we can use the function:f(x) = 100 * (1 + 0.04)^xwhere x is the number of years the bond has been held.The expression (1 + 0.04) represents the growth factor of the bond per year, since the bond grows in value by 4 percent each year. By raising this factor to the power of x, we obtain the cumulative growth of the bond over x years.Multiplying the initial value of the bond, 100$, by the growth factor raised to the power of x, gives us the value of the bond after x years. This is the purpose of the function f(x).
An architect is designing a house. He wants the bedroom to have the dimensions of 10 ft by 6 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume of the bedroom. Solve on paper. Then check your work on Does doubling all three dimensions mean the den will have double the volume of the bedroom? Why or why not? Does doubling all three dimensions mean the den will have double the volume of the bedroom? No If he doubles all three dimensions, the den's volume will be more than double the volume of the bedroom.
Answer:
(2 x 10) x (2 x 6) x (2 x 7) = 3360ft³ <-- the den would be that
The volume:
10 x 6 x 7 = 420ft³ Volume = 8
There are many cylinders with a radius of 6 meters. Let h represent the height in meters and v represent the volume in cubic meters. Write an equation that represents the volume, v , as a function of the height, h
The equation that represents the volume, v, as a function of the height, h is given as: V(h) = 36πh,
where h is the height in meters and V is the volume in cubic meters.
The volume of a cylinder can be calculated using the formula V=πr²h.
Here, we have a number of cylinders with a radius of 6 meters.
Let h represent the height in meters and v represent the volume in cubic meters.
To write an equation that represents the volume, v,
as a function of the height, h,
we can substitute the value of r (radius) with 6m in the formula of the cylinder’s volume,
V = πr²h.
So we get:
V = π(6m)²h
V = 36πh
This equation tells us that the volume of any cylinder with a radius of 6 meters can be expressed as 36πh,
where h is the height of the cylinder.
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