The required perimeter is 25+√61 units.
How to find perimeter?We can find the distance between each pair of consecutive points and then add them up to get the perimeter of the polygon.
Using the distance formula, the distance between points A and B is:
[tex]$$AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(-4 - 4)^2 + (8 - 2)^2} = \sqrt{100} = 10$$[/tex]
Similarly, the distances between the other pairs of points are:
[tex]$$BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(-7 + 4)^2 + (4 - 8)^2} = 5$$[/tex]
[tex]$$CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \sqrt{(-1 + 7)^2 + (-4 - 4)^2} = 10$$[/tex]
[tex]$$DA = \sqrt{(x_A - x_D)^2 + (y_A - y_D)^2} = \sqrt{(4 + 1)^2 + (2 + 4)^2} = \sqrt{61}$$[/tex]
Therefore, the perimeter of the polygon is:
[tex]$$AB + BC + CD + DA = 10 + 5 + 10 + \sqrt{61}$$[/tex]
= 25+√61
Thus, required perimeter is 25+√61.
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compute the determinants in exercises 9-14 by cofactor expansions. at each step, choose a row or column that involves the least amount of computation. [\begin{array}{ccc}6&3&2&4&0\\9&0&-4&1&0\\8&-5&6&7&1\\3&0&0&0&0\\4&2&3&2&0\end{array}\right]
Answer:
Step-by-step explanation:
The bottom of a cylindrical container has an area of 10 cm2. The container is filled to a height whose mean is 4 cm, and whose standard deviation is 0.2 cm. LetVdenote the volume of fluid in the container. Find μV.
The value of μV is 40 cm³.
Given,The area of bottom of cylindrical container = 10 cm²The height of container = h = Mean height = 4 cm Standard deviation of height = σ = 0.2 cm We are supposed to find the mean volume of fluid in the container.In order to calculate the mean volume, first we need to calculate the volume of fluid in the container.Volume of a cylindrical container = πr²h Where, r is the radius of the base of the container.So, we need to calculate the value of r.The area of the bottom of the container is given as 10 cm².
We know that the area of the base of a cylinder is given as:Area of base of cylinder = πr² We are given that area of the base is 10 cm². So,10 = πr²r² = 10/πr = √(10/π) We can find the volume of fluid using the values we have.Volume of fluid = πr²h = π(√(10/π))² x 4 = 40 cm³We know that mean volume, μV is given as:μV = πr²μh So, we need to calculate the value of μh. We know that standard deviation σh is given as:σh = 0.2 cm So,μh = h = 4 cm So,μV = πr²μh = π(√(10/π))² x 4 = 40 cm³
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It’s not 1507 please help me
Answer:
Below
Step-by-step explanation:
Mass of bouncies + box = 17342 subtract mass of box from both sides
mass of bouncies = 17342 - 429 = 16913 g
Unit mass per bouncy = 505 g / 45 bouncy
Number of Bouncies = 16913 gm / ( 505 g / 45 bouncy ) = 1507.1 bouncies
With the given info, I am afraid it IS 1507 bouncies in the box
maybe since the question asks for APPROXIMATE number, the answer is 1510 bouncies ( rounded answer) ....or 1500
a. in the sample: i. what is the average value of birthweight for all mothers? ii. for mothers who smoke? iii. for mothers who do not smoke? b. i. use the data in the sample to estimate the difference in average birth weight for smoking and nonsmoking mothers. ii. what is the standard error for the estimated difference in (i)? iii. construct a 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers.
a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.
ii. For mothers who smoke is 6.82 pounds.
iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:
Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.
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trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 11 miles per day. the mileage per day is distributed normally. find the probability that a truck drives between 99 and 128 miles in a day. round your answer to four decimal places.
The probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.
What is the standard deviation?Standard deviation is a statistical measurement that depicts the average deviation of each value in a dataset from the mean value. It tells you how much your data deviates from the mean value. It represents the typical variation between the mean value and the individual data points.
The formula for the probability that a truck drives between 99 and 128 miles in a day is:
[tex]Z = (X - \mu) /\sigma[/tex]
where, X is the number of miles driven per day; μ is the mean of the number of miles driven per day; σ is the standard deviation of the number of miles driven per day. The value of Z for 99 miles driven per day is:
[tex]Z = (99 - 120) / 11 = -1.91[/tex]
The value of Z for 128 miles driven per day is:
[tex]Z = (128 - 120) / 11 = 0.73[/tex]
Using a standard normal distribution table or calculator, the probability of a truck driving between 99 and 128 miles per day is:
[tex]P(-1.91 < Z < 0.73) = 0.7734[/tex]
Therefore, the probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.
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make a simple linear regression model using education level as independent variable. if the education level is 14 years, the estimated annual income is
The estimated annual income can be calculated using the equation above. If the data point is used to calculate the slope and y-intercept of the regression line, then the annual income can be estimated using the equation y = m(14) + b.
If the education level is 14 years,
To create a simple linear regression model using education level as the independent variable, you will need to input data for education level and annual income.
This data can be used to estimate the annual income for any given education level. The equation for this linear regression model is y = mx + b, where y represents the annual income, m is the slope of the line, x is the education level, and b is the y-intercept.
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PLEASE HELP ME! I NEED THE ANSWERS! ITS AN EMERGENCY
The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).
How do the coordinates translate?In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.
Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.
A (-3, 0)
B (-1, 2)
C (2, 2)
D (3, -1)
E (1, -2)
The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:
A' = (-3 * 5, 0 * 5) = (-15, 0)
B' = (-1 * 5, 2 * 5) = (-5, 10)
C' = (2 * 5, 2 * 5) = (10, 10)
D' = (3 * 5, -1 * 5) = (15, -5)
E' = (1 * 5, -2 * 5) = (5, -10)
The coordinates of the dilated figure are:
A' (-15, 0)
B' (-5, 10)
C' (10, 10)
D' (15, -5)
E' (5, -10)
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The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:f(x) = 10(1.3)xWhich of the following graphs best represents the function? (1 point)a Graph of f of x equals 1.3 multiplied by 10 to the power of xb Graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinityc Graph of f of x equals 10 multiplied by 1.3 to the power of xd Graph of f of x equals 1.3 to the power of x
The graph of an exponential function with an initial value of 10 and a base of 1.3z. Therefore option D is correct.
The function f(x) is an exponential function with a base of 1.3 and an initial value of 10. The graph of an exponential function with a base greater than 1 increases rapidly as x increases. Therefore, option a can be eliminated.
Option b is not a graph of an exponential function, as the function is not continuous and does not approach any asymptote.
Option c shows an exponential function with an initial value of 10 and a base of 1.3/10, which is less than 1. This means that the function would decrease over time, which is not consistent with the problem statement.
Option d shows an exponential function with an initial value of 10 and a base of 1.3, which is consistent with the problem statement. Therefore, option d is the correct answer.
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There are 25 pupils in a class who take part in a drinking milk initiative. Pupils have a 210
millilitre glass each. During the break each pupil drinks a full glass of milk. Milk comes in 1000
millilitre bottles. How many bottles of milk are needed?
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
Each student in a class of 25 drinks a full 210 millilitre glass of milk, hence the amount of milk consumed overall during the break is:
25 students times 210 millilitres each equals 5250 millilitres.
Milk comes in 1000 millilitre bottles, thus to determine how many bottles are needed, divide the entire amount eaten by the volume of milk in each bottle.
5.25 bottles are equal to 5250 millilitres divided by 1000 millilitres.
We must round up to the nearest whole number because we are unable to have a fraction of a bottle. This results in:
6 bottles in 5.25 bottles
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
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A triangle is shown on the coordinate plane below.
1 unit
H
y
(-1,9) of
-(-1, 2)
7
6
5
-3
3 d
(7,2)
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
-11
-2
What is the area of the triangle?
Il unit
X
You answer would be mate it would be x=66
PLS HELP MEEEEEEE ASAP
Answer:
[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]
Step-by-step explanation:
[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]
Each side has length of a?
[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]
If x is a positive integer , 4x^1/2 is equivalent to
If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.
Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.
It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.
If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:
If x=4, (4×4)^1/2 = 4
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hi i want help with maths and the question i need help is
there are 32 students in a class and 20 of them owns at least one pet. what if the fraction of the class own pets? give answer in simplest form.
Get back to me quickly
Answer: 3/5
hope this helped you. Please brainliest! :D
Step-by-step explanation: If I am wrong tell me :D
Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is P(A or B)= P(A) + P(B) - P(A or B). Choose the correct answer below. A. True B. False, the probability that A or B will occur is P(A or B)= P(A) middot P(B). C. False, the probability that A or B will occur is P(A or B)= P(A) + P(B). D. False, the probability that A or B will occur is P(A or B)= P(A) + P(B) - P(A and B).
False, the probability that A or B will occur is P(A or B) = P(A) + P(B) - P(A and B).
Define probabilityProbability refers to the measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event, and 1 indicates a certain event.
This formula is known as the Addition Rule for Probability and states that to calculate the probability of either event A or event B occurring (or both), we add the probability of A happening to the probability of B happening, but then we need to subtract the probability of both A and B happening at the same time to avoid double counting.
Option A is not the correct answer because it is missing the subtraction of P(A and B), options B and C are incorrect because they omit the subtraction and only add the probabilities of the events. Option D is close, but it is missing the addition of the probabilities of A and B.To know more about event, visit:
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A restaurant at the food court in a mall is offering a lunch special. The table shows the relationship between the number of side dishes and the total cost of the special.
Restaurant
Number of Side Dishes Total Cost
2 $6.75
4 $8.25
5 $9.00
8 $11.25
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 3 comma 9
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 25 hundredths through the point 5 comma 9
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 1 comma 8 and 25 hundredths
graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 5 and 75 hundredths through the point 1 comma 7 and 25 hundredths
The correct answer is graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0 comma 6 and 75 hundredths through the point 3 comma 9.
What is axis?Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph. In a line graph, the x-axis is the horizontal line and the y-axis is the vertical line.
The first graph shows a relationship between the number of side dishes and the total cost of the special that does not match the data given in the table.
The second graph does not reflect the data given in the table, as the total cost of the special increases from $5.25 to $9.00 when the number of side dishes increases from 0 to 5.
The third graph also does not reflect the data given in the table, as the total cost of the special increases from $6.75 to $8.25 when the number of side dishes increases from 0 to 4.
The fourth graph also does not reflect the data given in the table, as the total cost of the special increases from $5.75 to $7.25 when the number of side dishes increases from 0 to 1.
Therefore, the correct answer is mentioned above. This graph accurately reflects the relationship between the number of side dishes and the total cost of the special.
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The correct answer is "graph with the x axis labeled number of side dishes and the y axis labeled cost in dollars and a line going from the point 0,6 and 75 hundredths through the point 3,9".
What is axis?Axis refers to the number of dimensions in a graph, chart, or plot. It is an imaginary line that is used to measure and plot values in a graph.
This graph correctly illustrates the relationship between the number of side dishes and the total cost of the special as shown in the table.
The line starts at 0 side dishes and $6.75
and ends at 4 side dishes and $8.25, both of which are in the table.
The graph accurately reflects this by having a line that starts at 2 side dishes and $6.75 and ends at 5 side dishes and $9.00.
This shows that as the number of side dishes increases, the cost also increases.
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An article reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 24.1 minutes.
find
A. The 95% confidence interval is (,)
B.The 99.5% confidence interval is(,)
C. A surgeon claims that the mean surgery time is between 133.71 and 140.09 minutes. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.
D. Approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
F.Approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
A) The 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).Explanation:Given,Sample size, n = 123Average surgery time, μ = 136.9 minutesStandard deviation, σ = 24.1 minutesWe know that for a sample of size n, the 95% confidence interval is given by, (Formula1)Where, z is the z-score, α/2 = 0.05/2 = 0.025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula1), we get the 95% confidence interval as(130.82, 142.98)Thus, the 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).B) The 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).Explanation:We know that for a sample of size n, the 99.5% confidence interval is given by, (Formula2)Where, z is the z-score, α/2 = 0.005/2 = 0.0025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula2), we get the 99.5% confidence interval as (127.93, 145.87).Thus, the 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).C) The surgeon's claim that the mean surgery time is between 133.71 and 140.09 minutes is equivalent to the confidence interval (133.71, 140.09). The surgeon's claim falls inside the 95% confidence interval, (130.82, 142.98), therefore we can say that the surgeon's claim can be made with 95% confidence.D) The formula to find the minimum sample size for a 95% confidence interval that will specify the mean to within ±3 minutes is given by (Formula3)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula3), we get the minimum sample size as 424.15.The minimum sample size required to get a 95% confidence interval that will specify the mean to within ±3 minutes is 425 (Rounded up to the nearest integer).F) The formula to find the minimum sample size for a 99% confidence interval that will specify the mean to within ±3 minutes is given by (Formula4)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula4), we get the minimum sample size as 596.73.The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
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what is the average time gap between the first cyclists time and each of the remaining cyclists' times (second through fifth) in the 1995 volta a catalunya cycle race if we know the result?
The average time gap between the first cyclist's time and each of the remaining cyclists' times (second through fifth) in the 1995 Volta a Catalunya cycle race is approximately 6 minutes and 7 seconds.
To calculate this, we need to subtract the time of the first cyclist from each of the remaining cyclists' times (second through fifth).The time for the first cyclist was 41:38:33.
The times for the remaining cyclists were as follows:
We can calculate the difference for each cyclist by subtracting the first cyclist's time from their own time:
Adding up all of the times and dividing by four, we get an average of 00:06:07.
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I need help pls help me find the area:
Answer:
Step-by-step explanation:
348.55
If the cost of 7m is Rs. 1470, find the cost of 5m cloth
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
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The coordinates of the vertices of quadrilateral HIJK are H(1,4), I(3,2), J(-1,-4), and K(-3,-2). If quadrilateral HIJK is rotated 270 about the origin, what are the vertices of the resulting image, quadrilateral H’ I’ J’ K’
The vertices of the resulting image, quadrilateral H’ I’ J’ K’ include the following:
H' (4, -1).
I' (2, -3).
J' (-4, 1).
K' (-2, 3).
What is a rotation?In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).
By applying a rotation of 270° about the origin to quadrilateral HIJK, the location of its vertices is given by:
(x, y) → (y, -x)
Ordered pair H (1, 4) → Ordered pair H' (4, -(1)) = (4, -1).
Ordered pair I (3, 2) → Ordered pair I' (2, -(3)) = (2, -3).
Ordered pair J (-1, -4) → Ordered pair J' (-4, -(-1)) = (-4, 1).
Ordered pair K (-3, -2) → Ordered pair K' (-2, -(-3)) = (-2, 3).
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we assume there is sometimes sunny days and sometimes rainy days, and on day 1, which we're going to call d1, the probability of sunny is 0.9. and then let's assume that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance. so, what are the chances that d2 is sunny?
Probability of D2 being sunny = 0.78.
On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.
Therefore, we need to find the chances that D2 is sunny.
There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.
Now, Let us find the probability of D2 being sunny.
We have the following possible cases for D2.
D1 = Sunny; D2 = Sunny
D1 = Sunny; D2 = Rainy
D1 = Rainy; D2 = Sunny
D1 = Rainy; D2 = Rainy
The probability of D1 being sunny is 0.9.
When a sunny day follows a sunny day, the probability is 0.8.
When a sunny day follows a rainy day, the probability is 0.6.
Therefore, the probability of D2 being sunny is given by the formula:
Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.
Therefore, the probability that D2 is sunny are 0.78 or 78%.
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Place the three sets of conditions in order. Begin with the set that gives the greatest number of triangles, and end with the set that gives the smallest number of triangles. Condition A: One side is 6 inches long, another side is 5 inches long, and the angle between them measures 50°. Condition B: One angle measures 50°, another angle measures 40°, and a third angle measures 90°. Condition C: One side is 4 inches long, another side is 9 inches long, and a third side measures 5 inches.
The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.
What is triangle inequality theorem?According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.
The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.
Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.
Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.
Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.
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Fractions MUST SHOW WORKING!!
Total seats in plane: 186
108+64+14
5/7 of 14 is: 10
14÷7= 2
2x5= 10
5/16 of 64 is: 20
64÷16=4
5×4= 20
5/9 of 108 is: 60
108÷9= 12
12x5= 60
60+20+10=90
90/186 of seats are being used
simplified: 15/31
No
Tiago sells sunflower oil in large tins and extra-large tins.
The large tin and the extra-large tin are mathematically similar.
The volume of the extra-large tin is 75% more than the volume of the large tin. Both tins are cylinders.
The radius of the large tin is 20 cm.
Calculate the radius of the extra-large tin.
Answer:
24 cm (to nearest cm)
Step-by-step explanation:
XLV = extra large tin volume (cm³)
LV = large tin volume (cm³)
XLR = extre large tin radius (cm)
LR = large tin radius (cm) = 20
XLV = 1.75 × LV
Since the tins are geometrically similar cylinders, we can infer that the volumes and radii of the 2 tins are related;
We know the relationship between the volume of the two tins, i.e. the XL tin is 75% greater in volume than the L tin;
This means the volumetric scale factor or multiplier is ×1.75;
Subsequently, we know:
XLV = 1.75 × LV
Similarly, there is a relationship between the radii of the tins;
The relationship is, however, slightly different;
[tex]XLR = (\sqrt[3]{1.75}) \times LR[/tex]
We need to take the cube root of the volumetric scale factor, reason being, the radius is a linear dimension unlike volume;
Easy way to figure this is radius is in cm, volume is in cm³;
So:
XLR = 1.205... × LR
XLR = 1.205... × 20
XLR = 24.101... --> 24 cm (to nearest cm)
The equation y = -4/7x - 5 has a slope of
What is the contrapositive of the following statement? "If it is not a lion, then it is a cat
The contrapositive of the given statement is "If it is not a cat, then it is a lion."
The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).
The contrapositive takes the form:
"If it is not a cat, then it is a lion."
So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."
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Mrs. Perez's class donated 99 different products for the food drive. One-ninth of it was vegetables,2/3 pasta,
and 2/9 was soup. How much of each product did they donate?
Simplifying Mrs. Perez's class donated 11 units of vegetables, 66 units of pasta, and 22 units of soup.
What does the term "simplify expression" mean?The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible
vegetables = (1/9) x 99
Simplifying this expression, we get:
vegetables = 11
So the class donated 11 units of vegetables.
Next, we can figure out how much of the donation was pasta. We know that 2/3 of the donation was pasta, so we can set up the equation:
pasta = (2/3) x 99
Simplifying 66 units homemade pasta, 22 units of soup, and 11 units of veggies were all provided by Mrs. Perez's students.
Which expression should I simplify?
A math difficulty is simply solved by simplifying the expression. When you simplify a phrase, your goal is essentially to make it as simple as you can. There shouldn't be any more multiplication, dividing, adding, or removing to be done at the conclusion.
veggies = 1/9 times 99
When we condense this statement, we get:
eleven vegetables
Hence, the class gave away 11 units of produce.We can then determine what proportion of the contribution was pasta. Given that we know that pasta made up 2/3 of the donation, we can construct the following equation:
spaghetti equals (2/3) x 99
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लगाउनुहोस् । The capacity of a closed cylindrical tank of height 2 m. is 3080 liters. Find the base area of the tank.
11.87 m² metal sheet would be needed to make the base area of tank.
Volume of the cylinderVolume of cylinder, determines how much material it can carry, is determined by the cylinder's volume. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.
It is given that capacity of a closed cylindrical vessel of height 2 m is 3080 liters
Let us assume that Radius of cylinder = r
Then Volume of cylinder = π ×r² ×h
= 2π ×r²× m³
1 m³ = 1000 liters
= 2000 π r² liters
Volume of tank = Capacity
2000 π r² = 3080
=> 2000 × (22/7) × r² = 3080
=> r² = 49/100
=> r = 7/10 m
=> r = 0.7 m
Base Area of tank = TSA = 2πrh + 2πr²
= 2×(22/7)(0.7)×2 + 2×(22/7)×(0.7)²
= 3.0772 +8.792
= 111.87 m²
Hence, 11.87 m² metal sheet would be needed to make it.
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Write the expression in complete factored
form.
3p(a - 1) - 2(a - 1)
Help!
Answer:
(a - 1)(3p - 2)
Step-by-step explanation:
3p(a - 1) - 2(a - 1) ← factor out (a - 1) from each term
= (a - 1)(3p - 2)
For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are [1 - 20x + 150x^2 + cx^3 ]. find c?
Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.
What is the difference between real and integer?Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.
What's a real number?A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.
by applying the binomial theorem:
[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]
where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]
The first few terms of this expansion are:
[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:
[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Equating coefficients of [tex]x^3[/tex] on both sides, we get:
[tex]c = n(n-1)(n-2)(a^3/6)[/tex]
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