The minimum variance unbiased estimator of the parameter,λ of a poisson population is λ = Σxi/n.
What is variance?Variance is a measure of how spread out a set of data is. In statistics, it is the average of the squared differences from the mean of a set of values. It is calculated by taking the sum of the squared deviations from the mean and dividing it by the number of data points.
According to given information:Let X1, X2, ..., Xn be a random sample from a Poisson distribution with mean λ. The likelihood function is given by:
[tex]L(\lambda | x) = \pi[e^{(-\lambda)} \lambda^{(xi)} / xi!][/tex]
Taking the natural logarithm and differentiating with respect to λ:
ln L(λ | x) = -nλ + ln(λ) Σxi - Σln(xi!)
d/dλ ln L(λ | x) = -n + Σxi/λ
Setting the derivative equal to zero and solving for λ, we get:
λ = Σxi/n
This is the sample mean of the Poisson distribution, which is an unbiased estimator of λ. Moreover, using the Cramer-Rao lower bound, we can show that it is also the minimum variance unbiased estimator of λ.
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a local team has 25 players, 30% of them are left handed. how many playrs are left handed
Step-by-step explanation:
30 % of 25 is
.30 * 25 = ~ 8 left handed ( rounded)
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #3
If the graph of f(x) is changed to [tex]f(x) = 4(\frac{5}{7} )^{x}-2[/tex], the graph of f(x) would be translated down by 2 units.
An equation of the new horizontal asymptote is y = -2.
What is a translation?In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this scenario, we can logically deduce that the graph of the parent function f(x) was translated or shifted downward (vertically) by 2 units.
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1. Determine the slope of a line given the table.
X
y
1
3
56
6
9
9
13
12
The slope of a line given the table is equal to 0.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the slope formula, we have the following;
Slope (m) = (9 - 9)/(3 - 1)
Slope (m) = 0/2
Slope (m) = 0.
Based on the table, the slope is the change in y-axis with respect to the x-axis and it is equal to 0.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
see attached
Step-by-step explanation:
You want the 2-way table filled based on the descriptions of its contents.
TotalThe total number of students surveyed (240) goes in blank 9, where row and column headings are both "Total".
35%The number 35% × 240 = 84 goes in blank 7, the total number interested in athletics.
3/5The number 3/5 × 240 = 144 goes in blank 3, the total number interested in academic clubs.
26The number 26 goes in blank 1, which is in row 1 (interested in academic clubs) and in column 1 (interested in athletics). It is the number interested in both.
DifferencesBlank 2 is the difference between blank 3 and blank 1. It makes the total for the line be correct.
Blank 4 is the difference between blank 7 and blank 1. It makes the total for the column be correct.
Similarly, blanks 8 and 6 are differences that make the row and column totals (respectively) be correct.
Finally, blank 5 is the value that makes its row and column totals be correct. The fact that the one number makes two correct totals gives you a check on that number.
The filled table is shown in the first attachment. The calculations are shown in the second attachment.
Help me with this math if you can.
The actual distance between the two cities is equal to 288 miles.
What is a scale factor?In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
In Geometry, the scale factor of a geometric figure can be calculated by dividing the side lengths of the image by the side lengths of the pre-image:
Scale factor = length of image (new figure)/length of pre-image (actual figure).
Scale:
0.25 inch = 24 miles
0.25/24 = New distance/Actual distance
0.25/24 = 3/Actual distance
Actual distance = (24 × 3)/0.25
Actual distance = 288 miles.
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MEDICO Corporation makes several portable electronic devices used in hospitals. Some of these products require rechargeable batteries that MEDICO purchases from various suppliers. Although they try to find them at the best price, they must also consider the quality. In one case, two suppliers were being considered, and batteries were selected from various purchase dates. A test was run on the time the batteries would last in a certain device before it had to be recharged. The results are given in the table below.
Sample Statistics for Survey of Batteries
Supplier Number of Batteries Used in Test Mean Life Standard Deviation
Power+ 45 24 hours 5.1 hours
Electro 61 22 hours 2.6 hours
a) Set up the null and alternative hypotheses to see if the data supports the conclusion that the rechargeable batteries sold by Power+ last longer.
b) Check the conditions.
c) Calculate the test statistic.
d) Find the p-value.
e) Using α = 0.05, state your conclusion in the context of the problem.
The null hypothesis states that there is no distinction between the mean shelf life of the rechargeable batteries marketed by Power+ and Electro. Whereas, the alternative suggestion maintains that the mean duration of the batteries sold by Power+ stands greater than that of Electro.
The test statistic is 2.24
How to explain the statisticsUtilizing a t-distribution with degrees of freedom akin to the entire sample size minus two (df = n1 + n2 - 2 = 104) alongside the derived test statistic, the p-value can be accessed via calculator or software as 0.014.
As the figure procured from the p-value is lower than the significance level α = 0.05, we invalidate the null positing. The evidence warrants corroborating the allegation that the rechargeable batteries proffered by Power+ remain usable for longer than those provided by Electro.
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1. a || b
2. k || m
3. Not enough information
The correct answer is "not enough information to prove any parallel lines."
What is the special property of two parallel lines?If two lines in a two-dimensional plane are parallel, then the corresponding angles formed by a transversal (a line that intersects both lines) are congruent (i.e., they have the same measure).
Additionally, the alternate interior angles (angles that are on opposite sides of the transversal and inside the pair of parallel lines), as well as the corresponding angles (angles that are in the same position relative to the transversal on the two parallel lines), are also congruent.
In the given diagram, line k is parallel to m, while line a is also parallel to line b but forming a transverse line to line k and line m. Also line k and line m form a transverse line to lines a and b.
So we can conclude that not enough information to prove any parallel lines.
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Liliana's monthly budget is represented by the pie chart below. All amounts
are in dollars.
What percentage of her monthly budget does Liliana spend on car expenses?
A. 11%
B. 13%
C. 16%
D. 6%
Answer:
Step-by-step explanation
The first step is to add up all of the numbers to get the total budget.
Total Budget = 858 + 429 + 924 + 198 + 363 + 528 =3,300
Then to find the percentage for a certain category it is:
[tex]\frac{Budget Category}{Budget Total} times 100%[/tex]
So, 429 / 3300 x 100% = 0.13 x 100% = 13% Car Expense
Answer:
Step-by-step explanation
The first step is to add up all of the numbers to get the total budget.
Total Budget = 858 + 429 + 924 + 198 + 363 + 528 =3,300
Then to find the percentage for a certain category it is:
[tex]\frac{Budget Category}{Budget Total} times 100%[/tex]
So, 429 / 3300 x 100% = 0.13 x 100% = 13% Car Expense
Find the area. ( Hint: First find x . )
Answer:
Step-by-step explanation:
in question no. 17
base=x
perpendicular=9
hipotanus=15
by applying pythagorus
(x)² + (9)² = (15)²
x=√(15)²-(9)²
x= √225-81
x=√144 = 12
now area of triangle = 1/2 ×base×height
= 1/2 × 12 × 9 = 54
area of figure 17 = 54 × 2 = 108
What is escape room answer for a high reward please
Answer:
840, 14
Step-by-step explanation:
(a.) In order to solve a, we first need to solve b since we're essentially dealing with proportions.
(b.) Our proportion to solve for miles per gallon is 350 miles / 25 gallons = x miles / 1 gallon where we solve for x:
[tex]\frac{350}{25}=\frac{x}{1}\\ \\ 25x=350\\\\x=14[/tex]
Thus, the gas mileage is 14 miles per gallon
(a.) Now, we can solve for part a. using the proportion x miles / 60 gallons = 14 miles / 1 gallon:
[tex]\frac{x}{60}=\frac{14}{1}\\ \\ x=840[/tex]
Which is the Which is the completely factored form of 4x2 + 28x + 49?
(x + 7)(4x + 7)
4(x + 7)(x + 7)
(2x + 7)(2x + 7)
2(x + 7)(x + 7)
completely factored form of 4x2 + 28x + 49?
76. Write an equation of
the line that passes
through (3,-2) and
is (a) parallel and
(b) perpendicular to
the line shown.
-2
y
1,3 | 5x
(2,-1)
(1,-4)
The equation of the line that passes through (3,-2) and is (a) parallel to the line is y = 3x - 11 and (b) perpendicular to the line is y = - 1 / 3 x - 2.
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form.
The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptHence, let's find the equation of a line passing through (3, -2) and is parallel to the line shown.
Parallel line have the same slope.
Hence,
m = -4 + 1 / 1 - 2
m = -3 / -1
m = 3
Therefore,
y = 3x + b
-2 = 3(3) + b
b = -2 - 9
b = -11
The equation is y = 3x - 11
Hence, let's find the equation of a line passing through (3, -2) and is perpendicular to the line shown.
The slopes of perpendicular lines are negative reciprocals of one another.
hence,
m = - 1 / 3
Therefore,
y = - 1 / 3 x + b
-2 = - 1 / 3(3) + b
b = -2 + 1
b = -2
Therefore, the equation is y = - 1 / 3 x - 2.
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Consider a football team with a 13
-game schedule. Each game ends with a win (W), a loss (L), or a tie (T). Once the schedule is set, how many ways can the schedule end with 9
wins, 3
losses, and 1
ties?
Answer:
Step-by-step explanation:
To find the answer, we can use the formula for combinations:
nCr = n! / r!(n-r)!
where n is the total number of games, r is the number of losses, and n-r-1 is the number of ties (since we already know there are 9 wins).
Substituting the values, we get:
13C3 * 10C1
= (13! / 3!10!) * (10! / 1!9!)
= (13*12*11 / 3*2*1) * 10
= 2860
Therefore, there are 2860 ways the schedule can end with 9 wins, 3 losses, and 1 tie.
Find the exact value of x.
Applying the Pythagorean theorem, the exact values of x are:
1. x = 13 2. x = 4 3. x = 6 4. x = 8 5. x = 15 6. x = √7
How to Find the Exact Value of x Using the Pythagorean Theorem?If a and b are smaller sides (legs) of a right triangle, and c is the longest side (hypotenuse), the Pythagorean theorem states that:
c = √(a² + b²).
Apply the Pythagorean theorem to find the exact value of x:
1. x = √(12² + 5²)
x = 13
2. x = √(5² - 3²)
x = 4
3. x = √(10² - 8²)
x = 6
4. x = √(17² - 15²)
x = 8
5. x = √(12² + 9²)
x = 15
6. x = √(4² - 3²)
x = √7
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evaluate cos(sin^-1 x0)
Answer:
Pull terms out from under the radical, assuming positive real numbers.
0
Step-by-step explanation:
Rick has earned a total of 581 points on all of his science test. His overall test average mean is 83. How many tests has Rick taken? PLEASE I NEED URGENT HELP
The number of tests Rick has taken are 7.
What is average?The average of given numbers is equal to the sum of all the values divided by the total number of values. It generally refers to a measure of central tendency or the typical value within a set of data points.
Define mean?The mean, or arithmetic mean, is the most commonly used type of average. It is calculated by adding up all the values in a data set and dividing by the total number of data points. Mathematically, the mean is represented as:
Mean = (Sum of all values) / (Total number of data points)
Based on the given conditions, formulate:
581/83 =7
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Write the equation of the line that passes through the points (−9,1) and (−6,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Maureen Webster, who is running for mayor in a city, claims that she is favored by 53% of all eligible voters of that city. Assume that this claim is true. What is the probability that in a random sample of 400 registered voters taken from this city, less than 49% will favor Maureen Webster?
The probability that a random sample of 400 registered voters from this town will have a Maureen Webster under the age of 49 is about 0.0951, or about 9.51%.
What does probability mean?Probability is simply how likely something is to happen. When we are uncertain about the outcome of an event, we can talk about the probability of certain outcomes—how likely they are.
We can use the binomial normal approximation to solve this problem because we have a large sample (400) and the probability (p) of preferring Maureen Webster is not too close to 0 or 1. First, we need to find the mean and standard deviation of the sample proportion, which is given by:
mean = p = 0.53
standard deviation = square (p*(1-p)/n) = square (0.53*0.47/400) = 0.0305
Next, we need to find the z-score corresponding to the sample proportion of 0.49 (which is the "less than 49 percent" threshold). It is given by:
z = (x - mean) / standard deviation = (0.49 - 0.53) / 0.0305 = -1.31
We can now use a standard normal distribution table or calculator to determine the probability that the standard normal variable is less than -1.31. This probability is approximately 0.0951.
Therefore, we can use the binomial normal approximation to solve this problem because we have a large sample (400) and the probability (p) of preferring Maureen Webster is not too close to 0 or 1.
First, we need to find the mean and standard deviation of the sample proportion, which is given by:
mean = p = 0.53
standard deviation = square (p*(1-p)/n) = square (0.53*0.47/400) = 0.0305
Next, we need to find the z-score corresponding to the sample proportion of 0.49 (which is the "less than 49 percent" threshold). It is given by:
z = (x - mean) / standard deviation = (0.49 - 0.53) / 0.0305 = -1.31
We can now use a standard normal distribution table or calculator to determine the probability that the standard normal variable is less than -1.31. This probability is approximately 0.0951.
Therefore, the probability that a random sample of 400 registered voters from this town is under the age of 49 Maureen Webster is about 0.0951, or about 9.51%.
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simplify into one fraction
Answer:
Step-by-step explanation:
The answer is not all true. Thank you for the help!
Answer:
false ,true ,true
Step-by-step explanation:
Assume a corporation has earnings before depreciation and taxes of $110,000, deprecation of $48,000, and that is has a 30 percent tax bracket.
A. Compute it's cash flow using the following format.
Earnings before depreciation and taxes?
Depreciation?
Earnings before taxes?
Taxes?
Earnings after taxes?
Depreciation?
Cash flow?
B. How much would cash flow be if there were only $16,000 in depreciation? All other factors are the same.
Cash flow?
C. How much cash flow is lost due to the reduced depreciation from $48,000 to $16,000?
Cash flow lost?
A. The cash flow would be $91,400 if the depreciation were $48,000.
B. The cash flow would be $81,800 if the depreciation were $16,000.
C. The lost cash flow due to the reduced depreciation from $48,000 to $16,000 is $9,600.
How cash flow interacts with depreciation:A) Depreciation of $48,000:Earnings before depreciation and taxes = $110,000
Depreciation = $48,000
Earnings before taxes = $62,000 ($110,000 - $48,000)
Taxes (30%) = $18,600 ($62,000 x 30%)
Earnings after taxes = $43,400 ($62,000 - $18,600)
Depreciation $48,000
Cash flow = $91,400 ($43,400 + $48,000)
B) Depreciation of $16,000:Earnings before depreciation and taxes = $110,000
Depreciation = $16,000
Earnings before taxes = $94,000 ($110,000 - $16,000)
Taxes (30%) = $28,200 ($94,000 x 30%)
Earnings after taxes = $65,800 ($94,000 - $28,200)
Depreciation $16,000
Cash flow = $81,800 ($65,800 + $16,000)
C) Lost Cash Flow:Cash flow at $48,000 depreciation = $91,400
Cash flow at $16,000 depreciation = $81,800
Lost cash flow = $9,600 ($91,400 - $81,800)
Thus, we can learn that reduced depreciation increases the tax liability, thereby reducing the cash flow.
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A. The cash flow would be $91,400 if the depreciation were $48,000.
B. The cash flow would be $81,800 if the depreciation were $16,000.
C. The lost cash flow due to the reduced depreciation from $48,000 to $16,000 is $9,600.
How cash flow interacts with depreciation:A) Depreciation of $48,000:Earnings before depreciation and taxes = $110,000
Depreciation = $48,000
Earnings before taxes = $62,000 ($110,000 - $48,000)
Taxes (30%) = $18,600 ($62,000 x 30%)
Earnings after taxes = $43,400 ($62,000 - $18,600)
Depreciation $48,000
Cash flow = $91,400 ($43,400 + $48,000)
B) Depreciation of $16,000:Earnings before depreciation and taxes = $110,000
Depreciation = $16,000
Earnings before taxes = $94,000 ($110,000 - $16,000)
Taxes (30%) = $28,200 ($94,000 x 30%)
Earnings after taxes = $65,800 ($94,000 - $28,200)
Depreciation $16,000
Cash flow = $81,800 ($65,800 + $16,000)
C) Lost Cash Flow:Cash flow at $48,000 depreciation = $91,400
Cash flow at $16,000 depreciation = $81,800
Lost cash flow = $9,600 ($91,400 - $81,800)
Thus, we can learn that reduced depreciation increases the tax liability, thereby reducing the cash flow.
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75 minutes after 8:15
A printer prints 17 prints per minute. How many minutes will it take to print 200 pages? Express your answer to the nearest whole number.
Answer:
12 minutes
Step-by-step explanation:
200/17
= 11.7
round up
12 minutes
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
People who made more money generally completed more years of college than those who made less money . So correct option is D.
Describe Graph?A graph is a visual representation of data or information that uses a set of points or nodes, connected by lines or curves, to convey relationships or patterns. Graphs can be used to illustrate data in a way that is easy to understand and analyze.
There are several types of graphs, each with its own strengths and weaknesses depending on the type of data being presented. Some common types of graphs include:
Line graph: A line graph displays data as a series of points connected by a line, and is commonly used to show trends or changes over time.
Bar graph: A bar graph displays data using rectangular bars, with the length or height of each bar representing the quantity of data being measured. Bar graphs are useful for comparing different values or categories.
Pie chart: A pie chart shows data as a circular graph, with each slice representing a portion of the whole. Pie charts are commonly used to show proportions or percentages.
Scatter plot: A scatter plot displays data as a set of points on a two-dimensional plane, with each point representing the values of two variables. Scatter plots are useful for identifying patterns or trends in the relationship between two variables.
Histogram: A histogram displays data as a set of bars, with the height of each bar representing the frequency or number of occurrences of data within a certain range or interval.
Graphs can be an effective way to communicate complex information in a simple and easy-to-understand way. They are commonly used in fields such as science, economics, and social sciences, as well as in everyday life to display data and make comparisons.
People who made more money generally completed more years of college than those who made less money .
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-12x to the power of 3 y to the power of 8
The mathematical expression is -12x³[tex]y^8[/tex].
We have,
-12x to the power of 3 y to the power of 8
Now, writing the mathematical expression
-12x to the power of 3 = -12x³
and, y to the power of 8 = [tex]y^8[/tex]
So, the expression can be written as
= -12x³[tex]y^8[/tex]
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What are all of the solutions to the trigonometric equation 2 cos²0-2sin²0= √3?
The solutions to the trigonometric equation 2 cos²0-2sin²0= √3 is option C.
What is a trigonometric equation?It should be noted that a trigonometric equation is one that contains a trigonometric function with a variable. For example, sin x + 2 = 1 is an example of a trigonometric equation.
The equations can be something as simple as this or more complex like sin2 x – 2 cos x – 2 = 0.
In this case, solutions to the trigonometric equation 2 cos²0-2sin²0= √3 is π/12 + πn and 11x/12 + πn
The correct option is C.
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A right rectangular prism has a length of 15 cm width of 10 cm and a height of 5 cm savanna claims that doubling the length width and height of the prism will double its surface area is Savannah, correct?
No, Savannah is incorrect. Doubling the length, width, and height of a right rectangular prism will not double its surface area.
What is surface area?Surface area is the total area of an object's exposed faces, including any external surface area. It is a measure of the size of a surface and is usually expressed in square units such as square meters or square centimeters. Surface area is a two-dimensional measurement, since it only takes into account the area of a surface, and not its thickness or volume.
The surface area of a right rectangular prism is calculated by multiplying the length by the width and then multiplying that number by two and adding the two products together.
For example, the surface area of a right rectangular prism with a length of 15 cm, a width of 10 cm, and a height of 5 cm is calculated as follows:
Surface area = (15 cm * 10 cm) + (15 cm * 5 cm) = 150 cm2 + 75 cm2 = 225 cm2
Doubling the length, width, and height of this right rectangular prism would give us a prism with a length of 30 cm, a width of 20 cm, and a height of 10 cm. The surface area of this new prism would be calculated as follows:
Surface area = (30 cm * 20 cm) + (30 cm * 10 cm) = 600 cm2 + 300 cm2 = 900 cm2
As you can see, doubling the length, width, and height of the right rectangular prism does not double its surface area - the surface area has increased by four times (900 cm2/225 cm2 = 4).
In conclusion, doubling the length, width, and height of a right rectangular prism does not double its surface area; rather, it increases the surface area by a factor of four.
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No, Savannah is incorrect. Doubling the length, width, and height of a right rectangular prism will not double its surface area.
What is surface area?Surface area is the total area of an object's exposed faces, including any external surface area. It is a measure of the size of a surface and is usually expressed in square units such as square meters or square centimeters. Surface area is a two-dimensional measurement, since it only takes into account the area of a surface, and not its thickness or volume.
The surface area of a right rectangular prism is calculated by multiplying the length by the width and then multiplying that number by two and adding the two products together.
For example, the surface area of a right rectangular prism with a length of 15 cm, a width of 10 cm, and a height of 5 cm is calculated as follows:
Surface area = (15 cm * 10 cm) + (15 cm * 5 cm) = 150 cm2 + 75 cm2 = 225 cm2
Doubling the length, width, and height of this right rectangular prism would give us a prism with a length of 30 cm, a width of 20 cm, and a height of 10 cm. The surface area of this new prism would be calculated as follows:
Surface area = (30 cm * 20 cm) + (30 cm * 10 cm) = 600 cm2 + 300 cm2 = 900 cm2
As you can see, doubling the length, width, and height of the right rectangular prism does not double its surface area - the surface area has increased by four times (900 cm2/225 cm2 = 4).
In conclusion, doubling the length, width, and height of a right rectangular prism does not double its surface area; rather, it increases the surface area by a factor of four.
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collect data on the OBSERVATION table in ANNEXURE A to record 30 days of the minimum and maximum temperature in your community
The observation table in Annexure A records the minimum and maximum temperature in a community for 30 days.
To collect data on the observation table in Annexure A for 30 days of minimum and maximum temperature in your community, follow these steps:
Obtain a reliable source for temperature data: You can use local weather stations, online weather platforms, or mobile apps that provide accurate and up-to-date temperature information for your community.
Prepare the observation table:
Create a table in Annexure A with columns for Date, Minimum Temperature, and Maximum Temperature.
Make sure there are 30 rows for each day of observation.
Record daily temperatures:
For each day, note down the date and the minimum and maximum temperatures in their respective columns.
Be consistent with the time of day you record these temperatures, ideally early morning for the minimum and late afternoon for the maximum.
Repeat the process:
Continue recording daily temperatures for a total of 30 days.
Review and analyze the data:
Once the 30-day period is complete, you can analyze the data to observe trends or patterns in temperature variation.
Remember to be consistent in your data collection to ensure accurate and reliable results.
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All four of these inequalities are true. Use them to find the single whole-number value of g. Use that whole number to unlock the door. Your answer g>0 g≤100 4 5.5 is greater than g?
if the distance between the line x+y-5 and 3x+3y-k=0 is √18, find the value of k.
Therefore, the value of k could be either 6 or 24 if the distance between the line x+y-5 and 3x+3y-k=0 is √18.
What is equation?An equation is a statement that two mathematical expressions are equal. It contains an equal sign and can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to solve problems, find unknown values, and model real-world situations.
Here,
To find the distance between the line x+y-5 and 3x+3y-k=0, we need to find the perpendicular distance between them.
The line x+y-5 can be written in slope-intercept form as y = -x + 5, and its slope is -1.
The line 3x+3y-k=0 can be rewritten as y = -x + k/3, and its slope is also -1.
Since the slopes of the two lines are the same, they are parallel. Therefore, the perpendicular distance between them is the distance between any point on one line and the other line.
Let's choose a point on the line x+y-5. We can choose (1,4) since it lies on the line. The distance between this point and the line 3x+3y-k=0 is:
|3(1) + 3(4) - k|/√(3²+3²)
Simplifying this, we get:
|15 - k|/3√2 = √18
Multiplying both sides by 3√2, we get:
|15 - k| = 3√2 * √18
= 9
This gives us two possible values for k:
15 - k = 9, which gives k = 6
or
k - 15 = 9, which gives k = 24
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