The local time in Sydney when the plane arrives will be 18:58, or 6:58 PM on a 24-hour clock.
How to find arrival time for the plane?The time difference between Speed and Sydney is 2 hours, and the plane will take some time to fly from Singapore to Sydney at an Speed of 757.2 km/h over a distance of 6310 km.
The time it takes the plane to fly from Speed to Sydney can be calculated as:
time = distance / Speed= 6310 km / 757.2 km/h = 8.33Speed
So the plane will take 8.33 hours to fly from Singapore toSpeed
Now we need to add the 2-hour time difference between Singapore and Sydney to determine the local time in Sydney when the plane arrives.
07:45 (Singapore time) + 8.33 hours (flight time) + 2 hours (time difference) = 18:58
Therefore, the local time in Sydney when the plane arrives will be 18:58, or 6:58 PM on a 24-hour clock.
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Find the perimeter of the semicircular region. Round your answer to the nearest hundredth
9 m
The perimeter is about
meters
The perimeter of the semicircular region is about 28.27 meters.
We know that the semicircular region is half of a circle.
Let's assume that the radius of the circle is r meters. Then the circumference of the circle is 2πr meters, and the perimeter of the semicircular region is half of that, which is πr meters.
We are given that the radius of the circle is 9 meters, so we can plug that in to get:
The perimeter of the semicircular region = πr
= π(9)
≈ 28.27
Rounding to the nearest hundredth, the perimeter of the semicircular region is about 28.27 meters.
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Mario is buying a number of hamburgers from the local store that cost \$2. 90$2. 90 each. He is also buying one packet of hamburger rolls at a cost of \$4. 75$4. 75. He has \$39. 55$39. 55 to spend at the store. Write and solve an inequality that shows how many hamburgers, hh, Mario can afford to buy. Write the inequality
Mario can afford to buy a maximum of 12 hamburgers from the local store.
How to find the number of hamburgers Mario can afford to buy given certain prices and a budget?Let's assume Mario can buy "h" hamburgers.
The cost of each hamburger is $2.90, and Mario wants to buy "h" hamburgers, so the total cost of hamburgers would be 2.90h.
He is also buying one packet of hamburger rolls, which costs $4.75.
Therefore, the total amount he can spend at the store must be less than or equal to his budget of $39.55.
Putting it all together, the inequality representing this situation is:
2.90h + 4.75 ≤ 39.55
To find out how many hamburgers Mario can afford to buy, we need to solve the inequality:
2.90h + 4.75 ≤ 39.55
Subtracting 4.75 from both sides of the inequality:
2.90h ≤ 34.80
Next, divide both sides of the inequality by 2.90:
h ≤ [tex]\frac{34.80 }{ 2.90}[/tex]
Simplifying the right side:
h ≤ 12
Therefore, Mario can afford to buy a maximum of 12 hamburgers from the local store.
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Part of the shape is drawn.
The line of symmetry of the shape is the dotted line.
complete the drawing of the shape and then rotate it by 180° about the origin
The remaining part of the given shape was drawn about to its symmetry. The complete shape obtained is similar to the Hexagon shape.
Given half shape has the following points,
(-3,-1)(-4,-1)(-5,-3)(-4,-4)(-3,-4)The points which are missing to complete the other symmetry are:
(-3,-1)(-2,-1)(-1,-3)(-2,-4)(-3,-4)By joining the above missing points, we can obtain the full symmetry of the shape.
To rotate the obtained shape of the Hexagon to 180° about the origin, we have to inverse the above complete symmetry points. It simply means if the above points are having positive values, we can inverse it to negative and vice-versa.
By rotating the obtained shape to 180° about the origin, we can obtain the below following points,
(3,1)(4,1)(5,3)(4,4)(3,4)(2,1)(1,3)(2,4)The images are attached below for the complete symmetry shape.
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Given question is not having enough required information, so I am attaching the image of the shape which we have to work on,
An square aquarium which is 15cm long has 1250 millilitres of water how much more water needed to fill the aquarium completely
You need to add 2125 milliliters of water to fill the square aquarium completely.
We need to find the volume of the square aquarium and then determine the additional water needed to fill it completely. Here are the steps:
1. Convert the given length to meters: 15 cm = 0.15 m
2. Calculate the volume of the square aquarium: Volume = length × width × height. Since it's a square aquarium, all sides are equal, so Volume = 0.15 m × 0.15 m × 0.15 m = 0.003375 cubic meters.
3. Convert the volume to milliliters: 0.003375 cubic meters × 1,000,000 mL/cubic meter = 3375 mL.
4. Calculate the additional water needed: Total volume - Current volume = 3375 mL - 1250 mL = 2125 mL.
You need to add 2125 milliliters of water to fill the square aquarium completely.
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The terminal side of angle λ intersects the unit circle at point (-0. 358, 0. 934). Based on these coordinates, what is the approximate decimal value of cot(λ)
If the terminal side of angle λ intersects the unit circle at point (-0. 358, 0. 934), the approximate decimal value of cot(λ) is -0.383.
To find the approximate decimal value of cot(λ), we first need to determine the values of x and y on the unit circle. Since the given point (-0.358, 0.934) lies on the unit circle, we can use the Pythagorean theorem to find the missing side:
x² + y² = 1
(-0.358)² + (0.934)² = 1
0.128 + 0.872 = 1
1 = 1
Therefore, we have x = -0.358 and y = 0.934. Since cot(λ) = cos(λ)/sin(λ), we can use the values of x and y to calculate the cosine and sine of λ:
cos(λ) = x = -0.358
sin(λ) = y = 0.934
Substituting these values into the formula for cot(λ), we get:
cot(λ) = cos(λ)/sin(λ) = -0.358/0.934 ≈ -0.383
Therefore, the approximate decimal value of cot(λ) is -0.383.
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Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary
slightly from bag to bag and are Normally distributed with mean ï. A representative of a consumer
advocacy group wishes to see if there is any evidence that the true mean net weight is less than advertised and
so intends to test the hypotheses
H0 : μ = 14
Ha : μ < 14A
Type I error in this situation would mean
a. Concluding that the bags are being under filled when they actually arenât.
b. Concluding that the bags are being under filled when they actually are.
c. Concluding that the bags are not being under filled when they actually are.
d. Concluding that the bags are not being under filled when they actually arenât.
e. None of these
Type I error in this situation would mean option a. Concluding that the bags are being under filled when they actually aren't.
A Type I error occurs when the null hypothesis (in this case, that the true mean net weight is 14 ounces) is rejected when it is actually true. In other words, it is the error of concluding that there is evidence for the alternative hypothesis (that the true mean net weight is less than 14 ounces) when there is not.
In this situation, if a Type I error is made, it would mean that the bags are being under filled (i.e. the true mean net weight is less than 14 ounces) when in reality they are not. This would lead to incorrect conclusions and potentially negative consequences for the manufacturer.
It's important to note that the probability of making a Type I error can be controlled by choosing an appropriate level of significance (usually denoted by alpha) for the hypothesis test. For example, if alpha is set at 0.05, there is a 5% chance of making a Type I error.
In summary, a Type I error in this situation would mean incorrectly concluding that the bags are being under filled when they actually are not, and the probability of making such an error can be controlled by choosing an appropriate level of significance for the hypothesis test.
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how many paths are there from point (0,0) to (90,160) if every step increments one coordinate and leaves the other unchanged and you want the path to go through (80,70)?
There are 4.097 x [tex]10^43[/tex] paths from (0,0) to (90,160) that pass through (80,70).
To calculate the number of paths from (0,0) to (90,160) while passing through (80,70), we need to break down the problem into smaller steps.
First, we can calculate the number of paths from (0,0) to (80,70) and then
multiply that by the number of paths from (80,70) to (90,160).
To go from (0,0) to (80,70), we need to take 80 steps to the right and 70 steps up, which gives us a total of 150 steps. The order in which we take these steps doesn't matter, so we can think of it as choosing 70 steps out of 150 to be up. This can be calculated using the binomial coefficient, which gives us (150 choose 70) = 2.364 x [tex]10^43[/tex]
To go from (80,70) to (90,160), we need to take 10 steps to the right and 90 steps up, which gives us a total of 100 steps. Using the same method as above, the number of paths from (80,70) to (90,160) is (100 choose 10) = 17,310,309.
Multiplying these two values together, we get the total number of paths from (0,0) to (90,160) that pass through (80,70):
(2.364 x 10^34) x (17,310,309) = 4.097 x [tex]10^43[/tex]
Therefore, there are 4.097 x [tex]10^43[/tex] paths from (0,0) to (90,160) that pass through (80,70).
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What is the volume of a container of 4 moles of gas at 200k with a pressure of 3 atm
The volume of the container is 2216 liters
How to determine the valueUsing the general gas law, we have that;
PV = nRT
Such that the parameters are given as;
P is the pressure of the gas measured in atmV is the volume of gas measured in litersn is the number of molesR is the universal gas constantT is the temperature measured in KelvinFrom the information given, we have that;
Substitute the values
3V = 4 × 8.31 × 200
Multiply the values, we have;
3V = 6648
Divide both sides by the coefficient of V, we get;
V = 2216 liters
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A recent survey reveals that one of the collie owners interviewed, 54% of them regularly groom their dogs, If there are 50,000 registered poodle owners in the county, how many owners are expected to regular groom their dos
Answer:
54% × 50000= 27000, the answer is 27000
A charity donates 40% of its proceeds to a local food bank. If the charity raised £1000, how much money did the food bank receive?
Answer:
£400
Step-by-step explanation:
first find 40% of £1000
40\100*1000
=400
Therefore answer is £400
find the extremum of each function using the symmetry of its graph. Classify the etremum of the function as maximum or a minimum and state the of x at which it occurs k(x)(300+10x)(5-0.2x)
The extremum of the function is a minimum at x = -2.5
The given function is k(x)(300+10x)(5-0.2x).
To check for symmetry about the y-axis, we replace x with -x in the given function and simplify as follows:
k(-x)(300-10x)(5+0.2x)
To check for symmetry about the x-axis, we replace y with -y in the given function and simplify as follows:
k(x)(300+10x)(5-0.2x) = -k(x)(-300-10x)(5+0.2x)
To find these points, we set the function equal to zero and solve for x:
k(x)(300+10x)(5-0.2x) = 0
This equation has three solutions:
x = 0
x = -30
x = 25.
The midpoint of the line segment connecting these points is
(x1+x2) ÷ 2 = (-30+25) ÷ 2 = -2.5.
To determine the type of extremum at this point, we need to check the sign of the second derivative. The second derivative of the function is:
k(x)(-1200+x)(0.2x+15)
Since the function is symmetric about the x-axis, the second derivative will be negative at the extremum if it is maximum and positive if it is a minimum.
When x = -2.5, the second derivative is positive, which means that the function has a minimum at x = -2.5.
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In the driest part of an Outback ranch, each cow needs about 40 acres for grazing. Use an equation to find how many cows can graze on 720 acres of land.
The calculated value of the number of cows that can graze on 720 acres of land is 18
From the question, the statements that can be used in our computation are given as
The area of grazing needed by each cow is 40 acres
From the above statement, the equation to use is
Cows = Area of land/Unit rate of cows
By substituting the given values in the above equation, we have the following equation
Cows = 720/40
Evaluate
Cows = 18
Hence, the calculated number of cows is 18
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At a show 4 adult tickets and 1 child ticket cost £33 2 adult tickets and 7 child tickets cost £36 Work out the cost of 10 adult tickets and 20 child tickets.
Answer:
10 adult tickets cost £75 , 20 child tickets cost £60
Step-by-step explanation:
let a be the cost of an adult ticket and c the cost of a child ticket , then
4a + c = 33 → (1)
2a + 7c = 36 → (2)
multiplying (2) by - 2 and adding to (1) will eliminate a
- 4a - 14c = - 72 → (3)
add (1) and (3) term by term to eliminate a
0 - 13c = - 39
- 13c = - 39 ( divide both sides by - 13 )
c = 3
substitute c = 3 into either of the 2 equations and solve for a
substituting into (1)
4a + 3 = 33 ( subtract 3 from both sides )
4a = 30 ( divide both sides by 4 )
a = 7.5
the cost of an adult ticket is £7.50
then 10 adult tickets cost 10 × £7.50 = £75
the cost of a child ticket is £3
the cost of 20 child tickets is 20 × £3 = £60
Calculating the relative frequencies from the data given in the table. Choose all that correctly describe an association between favorite subject and grade
From the given data, the statement "A higher percentage of 8th graders than 7th graders prefer Math/Science" is correct. So, correct option is C.
To calculate the relative frequencies, we need to divide the frequency of each category by the total number of responses.
For 7th grade:
Relative frequency of English: 38/116 = 0.3276
Relative frequency of History: 36/116 = 0.3103
Relative frequency of Math/Science: 28/116 = 0.2414
Relative frequency of Other: 14/116 = 0.1207
For 8th grade:
Relative frequency of English: 47/182 = 0.2582
Relative frequency of History: 45/182 = 0.2473
Relative frequency of Math/Science: 72/182 = 0.3956
Relative frequency of Other: 18/182 = 0.0989
From the data, we can see that a higher percentage of 8th graders prefer Math/Science than 7th graders. Therefore, the statement "A higher percentage of 8th graders than 7th graders prefer Math/Science" correctly describes the association between favorite subject and grade.
The statements "A higher percentage of 8th graders than 7th graders prefer History" and "A higher percentage of 7th graders than 8th graders prefer English" are incorrect as the relative frequencies for these subjects are similar in both grades.
Overall, we can conclude that the choice of favorite subject is not strongly associated with the grade level of the students.
So, correct option is C.
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Complete question is:
Calculating the relative frequencies from the data given in the table. Choose all that correctly describe an association between favorite subject and grade.
A) A higher percentage of 8th graders than 7th graders prefer History.
B) A higher percentage of 7th graders than 8th graders prefer English.
C) A higher percentage of 8th graders than 7th graders prefer Math/Science.
2.1.2. What is the sum of handshakes that will be made by the first and second
67 is the sum of handshakes given by the first and second participants.
Let n be the total number of participants in the workshop venue.
i.e, here n= 35
For the first participant, the number of handshakes is = (n-1)
= (35-1)
= 34
The number of handshakes by the second participant is also same as that of the first participant = 34
The number of handshakes given by the first and second participants together = (first participant handshake + second participant handshake - 1)
= (34 + 34 -1)
= 68-1
= 67
Hence 67 is the sum of handshakes given by the first and second participants.
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The complete question is =
A workshop venue has 35 participants . Each participant shakes hands with each each and every other participant . How is the sum of. Handshakes that will bemade bythe first and second participant
Jacinta compares the volume of two boxes. Both boxes have a width of 2. 5 inches, and a height of 10 inches. The larger box has a length of 8 inches. The smaller box has a length that is 75 % of the length of the larger box.
Volume of large box =
Volume of small box =
What is the difference in the volumes of the two boxes?
Which units should be used for each of these answers?
The volume of the large box is 200 cubic inches. The volume of the small box is 150 cubic inches. The difference in the volumes of the two boxes is 50 cubic inches. The units that should be used for each of these answers is cubic inches.
To find the volume of each box, we'll use the formula for the volume of a rectangular prism: Volume = Length × Width × Height.
For the larger box, the dimensions are:
Length = 8 inches
Width = 2.5 inches
Height = 10 inches
Volume of large box = 8 × 2.5 × 10 = 200 cubic inches
For the smaller box, its length is 75% of the larger box's length:
Length = 0.75 × 8 = 6 inches
The width and height remain the same, so the dimensions are:
Length = 6 inches
Width = 2.5 inches
Height = 10 inches
Volume of small box = 6 × 2.5 × 10 = 150 cubic inches
The difference in the volumes of the two boxes is:
200 cubic inches - 150 cubic inches = 50 cubic inches
So, the difference in the volumes of the two boxes is 50 cubic inches. The units used for these answers are cubic inches.
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PLEASE HURRY DUE IN 2 HOURS
Explain how the shapes shown have been sorted.
Two groups of shapes. In group A, one shape has four equal side lengths of three, and no right angles. The opposite sides are parallel. Two shapes have two pairs of opposite equal side lengths. One shape has side lengths of four and eight. The other side lengths are three and two. Opposite sides are parallel, and there are no right angles. In group B there are three four sided shapes. One has opposite equal side lengths of seven and four and four right angles. One shape has four equal side lengths of three and four right angles. One shape has one set of opposite parallel sides and one right angle. None of the side lengths in the last shape are equal.
The image is below if you don't want to read all that, And PLEASE actually answer the question.
The figure with opposite sides are parallel and equal is parallelogram.
From the group A:
In first image opposite sides are parallel and equal.
One pair of parallel sides = 4 units and the another pair of parallel sides = 8 units
So, it is parallelogram.
In second image opposite sides are parallel and all the sides are equal.
So, it is rhombus.
In third image opposite sides are parallel and equal.
One pair of parallel sides = 3 units and the another pair of parallel sides = 2 units
So, it is parallelogram.
From the group B:
In first image opposite sides are parallel and equal.
One pair of parallel sides = 4 units and the another pair of parallel sides = 7 units and all angles measures equal to 90°.
So, it is rectangle.
In second image one pair of opposite sides are parallel.
So it is trapezium.
In third image opposite sides are parallel and all sides equal.
All angles measures equal to 90°.
So it is square.
Therefore, the figure with opposite sides are parallel and equal is parallelogram.
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Find the cosine of K.
24
Save answer
26
blo
J
10
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
cos (K) =
K
Skip to
Step-by-step explanation:
remember the original trigonometric triangle inside the norm circle (radius = 1).
sine is the up/down distance from the triangle baseline or corresponding circle diameter.
cosine is the left/right distance from the center of the circle (and the point of the angle).
for larger triangles and circles all these function results need to be multiplied by the actual radius (which we skipped for the norm circle, as a multiplication by 1 is not changing anything).
when you look at the triangle with K representing the angle, we have 10 a the cosine value, 24 as the sine value and 26 as the radius.
so,
10 = cos(K) × 26
cos(K) = 10/26 = 5/13
Patricia bought 4 apples and 9 bananas for $12. 70 Jose bought 8 apples and I bananas for $17. 70 at the same grocery store What is the cost of one apple?
The cost of one apple is $2.15.
To find the cost of one apple, we can set up a system of equations with the given information. Let's use A for the cost of one apple and B for the cost of one banana:
1) 4A + 9B = $12.70
2) 8A + B = $17.70
Now, we can solve this system of equations. We can multiply equation 1 by 2 to match the number of apples in equation 2:
1) 8A + 18B = $25.40
Now subtract equation 2 from the modified equation 1:
(8A + 18B) - (8A + B) = $25.40 - $17.70
17B = $7.70
Now, divide by 17 to find the cost of one banana:
B = $7.70 / 17 = $0.45
Now that we know the cost of one banana, we can substitute B in equation 2 to find the cost of one apple:
8A + ($0.45) = $17.70
8A = $17.25
A = $17.25 / 8 = $2.15
So, the cost of one apple is $2.15.
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This is what I need help withhh helppppppp
The missing measures are given as follows:
OM = 46.PN = 23.ON = 32.5.MN = 32.5.What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The diagonal length is given as follows:
LN = OM = 46.
Half the diagonal is of:
PN = 0.5 x 46
PN = 23.
The diagonal is the hypotenuse of a right triangle of sides ON = MN = x, hence:
x² + x² = 46²
x² = 1058
[tex]x = \sqrt{1058}[/tex]
x = 32.5.
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In △abc , m∠b=20° and m∠c=40°. the angle bisector at a intersects side bc at point d. find the difference between bc and ab if ad = 1
In the △ABC, the the difference between bc and ab if ad = 1 is found to be 0.709.
We can use the angle bisector theorem to solve this problem. Let's denote the length of segment BD as x and the length of segment CD as y. Then, we can write,
BD/DC = AB/AC
Using the angle bisector theorem, we know that AB/AC = BD/DC, so we can substitute to get,
x/y = AB/AC
We can solve for AB by multiplying both sides by AC,
AB = x/y * AC
Now, we can use the law of sines to find the length of AC. We have,
sin(20°)/AB = sin(140°)/AC
Solving for AC, we get,
AC = AB * sin(20°) / sin(140°)
Substituting the expression we found for AB, we get,
AC = x/yACsin(20°) / sin(140°)
Simplifying, we get,
y = xsin(140°) / (sin(20°) - sin(140°))
We know that AD = 1, so we can use the Pythagorean theorem to find BC:
BC² = BD² + CD²
Substituting the expressions we found for BD and CD, we get,
BC² = x² + y²
Substituting the expression we found for y, we get,
BC² = x² + (xsin(140°) / (sin(20°) - sin(140°)))²
Simplifying, we get,
BC² = x²(1+sin²(140°)/(sin²(20°)-2sin(20°)sin(140°)+sin²(140°)))
Using the identity sin(140°) = sin(180° - 40°) = sin(40°), we can simplify further.
Now, we can substitute x = AD = 1 and sing a calculator, we can evaluate this expression to get,
BC² ≈ 2.917
Taking the square root, we get,
BC ≈ 1.709
Therefore, the difference between BC and AB is 0.709.
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13. the area of a rhombus is 484 square millimeters. one diagonal is one-half as long
as the other diagonal. find the length of each diagonal.
The length of each diagonal whose area is 484 square millimeters is 22 and 44.
Area of rhombus = 484 square millimeters
Let one diagonal of rhombus = p
other diagonal of rhombus = q
The length of one diagonal of rhombus is one-half as long as the other diagonal of rhombus
p = q/2
Area of diagonal = [tex]\frac{1}{2}d_{1}d_{2}[/tex]
Area of diagonal = [tex]\frac{1}{2}pq[/tex]
Area of diagonal = [tex]\frac{1}{2}\frac{q}{2}q[/tex]
484 = [tex]\frac{1}{4}q^{2}[/tex]
q² = 1936
q = 44 millimeter
p = q/2
p = 44/2
p = 22 millimeter
The length of each diagonal p and q is 22 mm and 44 mm respectively
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The probability that sue will go to mexico in the winter and to france
in the summer is
0. 40
. the probability that she will go to mexico in
the winter is
0. 60
. find the probability that she will go to france this
summer, given that she just returned from her winter vacation in
mexico
The evaluated probability that Sue travel to France this summer is 0.67, under the condition that she just returned from her winter vacation in Mexico.
For the required problem we have to apply Bayes' theorem.
Let us consider that A is the event that Sue goes to France in the summer and B be the event that Sue goes to Mexico in the winter.
Now,
P(A and B) = P(B) × P(A|B)
= 0.40
P(B) = 0.60
Therefore now we have to find P(A|B), which means the probability that Sue traveled to France after coming from Mexico
Applying Bayes' theorem,
P(A|B) = P(B|A) × P(A) / P(B)
It is given that P(B|A) = P(A and B) / P(A), then
P(A|B) = (P(A and B) / P(A)) × P(A) / P(B)
P(A|B) = P(A and B) / P(B)
Staging the values
P(A|B) = 0.40 / 0.60
P(A|B) = 0.67
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The complete question is
The probability that Sue will go to Mexico in the winter and to France in the summer is 0. 40. the probability that she will go to mexico in the winter is 0. 60. find the probability that she will go to France this summer, given that she just returned from her winter vacation in Mexico.
The ratio of length to width of a computer monitor is 2:1. Assume that Avery has a monitor
that is 15 cm wide.
a) What are the dimensions of a monitor that has a scale factor of 3.
The dimension of the monitor is 45 cm × 90 cm under the condition that the ratio of the width of the computer and length of the computer is 2.1.
The given ratio of length to width of a computer monitor is 2:1. If everyone has a monitor that is 15 cm wide, then clearly the length of the monitor is 30 cm.
Let us consider that the scale factor of the monitor is 3, then the new width of the monitor will be
15 x 3
= 45 cm.
Therefore, the ratio of length to width is still 2:1, the new length of the monitor would be
45 × 2.1
≈ 90 cm
Hence, the dimensions of a monitor that has a scale factor of 3 are 45 cm x 90 cm.
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The sides of the base of a right square pyramid are 3 meters in length, and its slant height is 6 meters. if the lengths of the sides of the base and the slant height are each multiplied by 3, by what factor is the surface area multiplied?
a. 12
b. 3^3
c. 3^2
d. 3
If the base and slant height both are divided by a factor of 3, the surface area will get multiplied by factor, option b, 3².
Here we are given that the square pyramid has a base of 3m and a slant height of 6 m.
The surface area formula for a square pyramid with square edge a and slant height h is
a² + 2a√(a²/4 + h²)
Here, a = 3 and h = 6. Hence we get
3² + 2X3√(3²/4 + 6²)
= 46.108
Now the base and slant height are multiplied by 3. Hence we will get
9a² + 6a√(9a²/4 + 9h²)
414.972
Now, dividing both obtained we will get
414.972/46.108
= 9
= 3²
Hence, it should be multiplied by 3².
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The coach recorded the time it took 14 students to run a mile. The times are as follows: 9:23, 8:15, 9:23, 9:01, 6:55, 7:20, 9:14, 6:21, 7:12, 7:34, 6:10, 9:15, 9:18. Use the data set to complete the frequency table. Then use the table to make a histogram
The histogram for the frequency table is illustrated below.
To create the frequency table, we need to count how many times each time appears in the data set. The time 9:23 appears twice, so we would put a frequency of 2 in the row corresponding to 9:23. We do this for each time in the data set.
Here is the completed frequency table:
Time Frequency
6:10 1
6:21 1
6:55 1
7:12 1
7:20 1
7:34 1
8:15 1
9:01 1
9:14 1
9:15 1
9:18 1
9:23 2
As you can see, each time appears only once or twice in the data set. This tells us that there is no dominant time that most students ran the mile in.
To create the histogram, we'll draw a bar above each time on the x-axis with a height equal to the frequency of that time. For example, there are two times of 9:23, so we'll draw a bar above 9:23 with a height of 2.
As you can see, the histogram shows a relatively even distribution of times. The most common times are around 9 minutes, but there are also several times below 8 minutes and one time below 7 minutes.
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Simplify the expression. 3.7 – 1.8 – 3.67 + 4.4 – 1.34 –1.29 1.29 8.63 –7.51
Answer:
2.41
Step-by-step explanation:
postive = add negative = subtract
Verify that the sample standard deviations use of ANO\A allow the the means to compare the population means. What do the suggest about the effect of the subject’s gender and attractiveness of the confederate on the evaluation of the product?
On performing an ANOVA test the p-value obtained is less than the chosen significance level, hence it is verified that the sample standard deviations use of ANOVA allow the the means to compare the population means. Since ANOVA test shows significant difference therefore, it suggests that these factors play a role in influencing the evaluation of the product.
To verify that the sample standard deviations use of ANOVA allows means to compare the population means, discuss the terms ANOVA, sample standard deviation, population means.
1. ANOVA (Analysis of Variance): ANOVA is a statistical method used to compare the means of multiple groups to determine if there's a significant difference between them.
2. Sample Standard Deviation: Sample standard deviation is a measure of how spread out the values in a sample are. It helps estimate the population standard deviation, which is necessary for calculating the F statistic in ANOVA.
a. Calculate the sample means and standard deviations for each group.
b. Perform an ANOVA test using calculated means and standard deviations.
c. Interpret results: If p-value obtained from the ANOVA test is less than the chosen significance level (e.g., 0.05), it means there is a significant difference between population means.
Regarding the effect of the subject's gender and attractiveness of the confederate on the evaluation of the product, if the ANOVA test shows a significant difference, it suggests that these factors play a role in influencing the evaluation of product. You can further analyze the data by performing post-hoc tests to identify which specific groups differ significantly.
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Amita, Monica and Rita are three sisters.
Monica is x years old.
Amita is 3 years older than Monica.
Rita is twice the age of Amita.
If the mean age of the three sisters is 15, how old is Amita?
Answer:
So Monica is 9 years old.
To find Amita's age, we substitute x into the expression for Amita's age:
Amita's age = 9 + 3 = 12
Therefore, Amita is 12 years old.
In circle P with m \angle NPQ= 104m∠NPQ=104 and NP=9NP=9 units find area of sector NPQ. Round to the nearest hundredth
To find the area of the sector NPQ, we first need to find the measure of the central angle that intercepts the arc PQ. We know that the measure of angle NPQ is 104 degrees, and since it is an inscribed angle, its measure is half the measure of the central angle that intercepts the same arc. Therefore, the central angle measure is 208 degrees.
To find the area of the sector, we use the formula:
Area of sector = (central angle measure/360) x pi x radius^2
We know that the radius of circle P is NP = 9 units. Plugging in the values, we get:
Area of sector NPQ = (208/360) x pi x 9^2
= (0.5778) x 81pi
= 46.99 square units
Rounding to the nearest hundredth, the area of the sector NPQ is 47.00 square units.
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