Hans had a mean score of 67 after his 6 games. What was his total score?
Answer:
402
Step-by-step explanation:
Mean is an average of his scores
Total score = Mean score x number of games
67 x 6 = 402
Consider two players A and B, each randomly selecting in turn 2 cards from 2 decks of 52
playing cards. Assume that A selects first and this is repeated until either player A or player B reach
his/her objective. A's objective is to obtain a sum of 14, and B's is to obtain a sum of 20. Assume
that all cards with faces count 10 points. Find the expected number of times player A plays a turn.
The expected number of times player A plays a turn is approximately 1.5.
The expected number of times that player A plays a turn can be found using the concept of conditional probability.What is probability?Probability is a branch of mathematics that deals with the probability of an event occurring in a certain situation or under specific circumstances. The total probability of any occurrence is always between 0 and 1. It is denoted by the symbol P, and it is measured by dividing the number of ways an event can happen by the total number of possible outcomes. The expected value can be defined as the sum of the possible outcomes of a random variable multiplied by their respective probabilities. The formula is given as follows:Expected Value = (sum of possible outcomes × their respective probabilities)Given:There are 2 players, A and B, and each player selects two cards from two decks of 52 playing cards. A goes first, and the game continues until either A or B achieves their goal. A's objective is to achieve a sum of 14, while B's objective is to achieve a sum of 20. Assume that all face cards are worth 10 points.
Find the expected number of turns A will play.Solution:The probability of A drawing two cards from the deck to obtain a sum of 14 is given by:P(sum = 14) = P(2 face cards) = 12/52 * 11/51The probability of B drawing two cards from the deck to obtain a sum of 20 is given by:P(sum = 20) = P(2 face cards) = 12/50 * 11/49Let's now look at the probabilities of the game being played in the first turn itself.P(A wins in first turn) = P(2 cards sum = 14) = 12/52 * 11/51P(B wins in first turn) = P(2 cards sum = 20) = 12/50 * 11/49There are 48 cards left after the first turn (as each player selects two cards in turn), and the game continues until a player reaches their goal. Let's say the probability of A winning from this point is P(A wins in subsequent turns). Then we can write:P(A wins) = P(A wins in first turn) + P(A wins in subsequent turns)Similarly,P(B wins) = P(B wins in first turn) + P(B wins in subsequent turns)The expected number of turns A plays can be obtained using the concept of conditional probability as follows:Let P(A) = probability of A winning = P(A wins)Let P(B) = probability of B winning = P(B wins)Let P(D) = probability of a draw or the game continuing indefinitely = 1 - P(A) - P(B)
Then the expected number of times that player A plays a turn is given by:Expected value = (1 × P(D)) + (1 × P(A)) + (1 + Expected value) × P(B)Substituting the values, we get:Expected value = 1 + P(B) × Expected valueDividing by P(B), we get:Expected value / P(B) = 1 + Expected valueSolving for Expected value, we get:Expected value = P(B) / (1 - P(B))P(B) can be calculated as follows:P(B) = P(B wins in first turn) + P(B wins in subsequent turns) = 12/50 * 11/49 + P(A wins in subsequent turns)P(A wins in subsequent turns) can be found using the concept of recursion, which is as follows:P(A wins in subsequent turns) = P(A wins on A's first turn) + (1 - P(A wins on A's first turn)) × P(B wins)P(A wins on A's first turn) = P(2 cards sum = 14) = 12/52 * 11/51Hence,P(A wins in subsequent turns) = 12/52 * 11/51 + (1 - 12/52 * 11/51) × (12/50 * 11/49) = 0.0642Using the above values, we can find the value of P(B):P(B) = 12/50 * 11/49 + 0.0642 = 0.1313Therefore,Expected value = P(B) / (1 - P(B)) = 0.1313 / (1 - 0.1313) ≈ 0.152 ≈ 1.5Thus, the expected number of times player A plays a turn is approximately 1.5.
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On Wednesday evening Sonto sent 1/2hour doing housework 45 minutes doing housework 1 hour visiting friends 1 1/2hours watching television. Write this as a ratio
The time Sonto spent doing housework to the time she spent visiting friends to the time she spent watching television can be expressed as 2 : 3 : 4 : 6 .
This is because we can convert each time interval to a common unit, such as minutes, and then simplify the resulting fractions to a ratio of whole numbers. Specifically, Sonto spent 30 minutes doing housework (1/2 hour), 45 minutes doing housework, 60 minutes visiting friends (1 hour), and 90 minutes watching television (1 1/2 hours = 60 + 30 minutes).
Simplifying these fractions gives us the ratio
30 : 45 : 60 : 90
Dividing by GCF 15
2 : 3 : 4 : 6
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For seven weeks Amy has a chance to work some extra hours on the weekends she will work at six extra hours each week. How much more we should make each week? How much more will she make in seven weeks?
The extra work hours which she should make in each week is equals to 2/7 th fraction of her working hours in week days, 2x/7 or 6 hours. The extra work hours which she should make in seven weeks is equals to double to the her working hours in week days, 42 hours.
We have Amy has a chance to work some extra hours on the weekends.
Number of extra hours she will work at each week = 6 hours
number of weeks she have for doing extra hours work at weekends = 7 weeks
Let amy works 'x hours' in each week. So, her working rate is x/7 hours/day. As we know very well that weekend consists two days ( Saturday and Sunday). So, she will make extra work each week = extra work in weekend ( 2 days)
The extra work that she will do in weekend or each week= 2(x/7) = 2x/7 hours = 6 hours
Now, The extra work hours that she make in seven weeks = Multiplication of 7 by the extra work hours that she make in each week
= 7(6) hours = 42 hours
Hence, required value of hours is 42 ( that is double of her working hours in week days).
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What is the volume of the figure below, which is composed of two cubes with side lengths of 5 units?
a. 15 cubic units
B.30 cubic units
C.125 cubic units
D.250 cubic units
The volume of the figure is D. 250 cubic units.
What is meant by volume?
Volume is a measure of the space occupied by a three-dimensional object, such as a solid, liquid, or gas. It is usually expressed in cubic units such as cubic meters, cubic centimetres, or cubic feet.
What is meant by a unit?
A unit refers to a standard quantity or measure of something used for comparison, calculation, or reference. It can refer to several things, such as a unit of measurement, a unit of currency, or a unit of product.
According to the given information
The volume of each cube with a side length of 5 units is 5 x 5 x 5 = 125 cubic units.
The figure is composed of two such cubes, so the total volume is:
2 x 125 = 250 cubic units.
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Hi, can you please help me with math, I think the exercises solving is probably with x and y.
Thank u very much:) 1. Two identical jars of cottage cheese and 3 buns of the same type cost 10 euros. A jar of cottage cheese is 2 euros more expensive than a bun. How much is a jar of cottage cheese and how much is a bun?
2. The sum of two numbers is 56 and the difference is 14. Find those numbers.
Again, Thank u!
Answer:
Step-by-step explanation:
a= first form a equation
lets call the cheese c and the buns b
2c+3b=10
c=2+b
3c+4b=12
now its a simultaneous equation
2c+3b=10 x3
3c+4b=12 x2
6c+9b=30
6c+8b=24
1b=6
b=6
now substitute it in to 2c+3b=10
2c+18=10
2c+-8
so c=$4
b= 56 difference 14
56/2=28
28-7
21
28+7=35
so the 2 numbers are 21 and 35
A farmer is planting crops on two different plots of land. The first is a circular plot with a radius of 40 yards. The second is a rectangular
plot with the dimensions 35√5 yards by 50 yards. What is the approximate difference between the areas of the plots of land the farmer is
using?
O 935 square yards
O 1,095 square yards
O 1, 110 square yards
O 1,270 square yards
A particle is moving in the x-y plane (measured in metres) at a constant speed of 4 m/s. Its motion is along a path given by the equation
y=(x^2/9)+3
so that its motion is from right to left (x coordinate is always decreasing). Find its velocity vector v when it passes through the point (-3,4)
The velocity vector of the particle when it passes through the point (-3,4) is determined as (-4, 8/3) m/s.
What is the particle's position?To find the velocity vector, we need to find the derivative of the position vector with respect to time. Since the speed is constant, we know that the magnitude of the velocity vector is also constant at 4 m/s.
We can write the position vector r(t) as r(t) = <x(t), y(t)>, where x(t) and y(t) are the x and y components of the position vector.
Given the equation for the path of the particle, we have:
y(t) = (x(t)²/9) + 3
Taking the derivative of both sides with respect to time t gives:
dy/dt = (2/9)x·dx/dt
We can now solve for dx/dt:
dx/dt = (9/2)dy/dt · (1/x)
We know that the speed of the particle is 4 m/s, so the magnitude of the velocity vector is:
|v| = √((dx/dt)² + (dy/dt)²) = 4 m/s
Substituting the values we know:
4 = √((dx/dt)² + (dy/dt)²)
Squaring both sides:
16 = (dx/dt)² + (dy/dt)²
Since we want the velocity vector at the point (-3,4), we can substitute these values into our equations:
y = (x²/9) + 3
y = ((-3)²/9) + 3 = 4
So the particle passes through the point (-3,4). Substituting these values into our equations, we get:
dy/dt = (2/9)x·dx/dt
4 = √((dx/dt)² + (dy/dt)²)
16 = (dx/dt)² + (dy/dt)²
We can solve for dx/dt:
dx/dt = (9/2)dy/dt · (1/x)
Substituting the values we know:
4 = √((dx/dt)² + (dy/dt)²)
16 = (dx/dt)² + (dy/dt)²
dy/dt = (2/9)(-3)(-4) = 8/3 m/s
dx/dt = (9/2)(8/3)(-1/3) = -4 m/s
So the velocity vector at the point (-3,4) is:
v = (dx/dt, dy/dt) = (-4, 8/3 )m/s.
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Mrs Burn buys a washing machine that costs R3 999 at a discount of 6%. Calculate the discount on washing machine and the amount she has to pay.
Answer:
Discount Rs 239.94= 240
She has to pay 3659
Step-by-step explanation:
6 % of 3999=239.94 or 240
She will get the discount of 240 rupees.
She has to pay other amount beside the discount.
The price of machine is 3999.
The price she has to pay after discount= actual price- discount.
So discounted price is Rs3659
Answer: If the original price of the washing machine is R3 999 and it is discounted by 6%, then the discount amount can be calculated as follows:
Discount amount = 6% of R3 999
= 0.06 x R3 999
= R239.94
Therefore, Mrs Burn will receive a discount of R239.94 on the washing machine.
The amount she has to pay can be calculated as follows:
Amount to be paid = Original price - Discount amount
= R3 999 - R239.94
= R3 759.06
Therefore, Mrs Burn has to pay R3 759.06 for the washing machine after the 6% discount.
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The given story has a sampling type known as: voluntary response sampling.
What type of sampling was used?Voluntary response sampling: This is similar to a convenience sample but a voluntary response sample is mainly based on ease of access. Instead of the researcher choosing participants and directly contacting them, people volunteer themselves (e.g. by responding to a public online survey).
For example, a person being called in a radio show poll might have powerful opinions over a topic in any direction. In a voluntary random sample, chooses themselves by answering a common appeal. These samples are unreliable because they are bias, hence the result is usually biased.
In this question, Mrs. Finn is dissatisfied with the hotel and voluntarily gives a response based on her experience and as such it fits with the definition of voluntary response sampling.
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Systems of Ordinary Differential Equations Problem:
Verify (by substitution and performing a matrix
multiplication) that there is a time-independent particular
solution of θj = 1
3 (j −1)π for α = 0 (corresponding to the
atoms sitting evenly spaced at equilibrium).
Confirm (again by substitution) that A has the eigenvectors and find the corresponding eigenvalues, λ, in terms of ω = pk/m. Briefly interpret to what motions
of the atoms these eigensolutions correspond.
At what forcing frequencies does the benzene ring resonate under the photon irradience?
Using various matrices, but without performing any detailed algebra or computing any inverses, find
the general solution of the problem when resonance does not occur. Highlight the problem with this
formal solution when the forcing frequency is resonant
To begin with, let us define the system of ordinary differential equations for the benzene ring:
[tex]d^2θj/dt^2 + αdθj/dt + ω^2(θj−1−2θj+θj+1) = F cos(γt)[/tex]
Verification of time-independent particular solution:
When α = 0, the system becomes time-independent, and the equation reduces to:
[tex]θj'' + ω^2(θj−1−2θj+θj+1) = F cos(γt)[/tex]
We can assume a time-independent solution of the form θj = Aj, where A is a constant. Substituting this into the equation, we get:
[tex]Aω^2(j-1 + j + j+1) = F cos(γt)[/tex]
By simplifying
3Aω^2j = F cos(γt)
Therefore, the time-independent particular solution is θj = (F/3ω^2)cos(γt) + Aj, where A is a constant.
Eigenvectors and eigenvalues:
predicting the solution θj = Aj e^(iλt),we can integrate into an equation
[tex]−A(λ^2+αλ+ω^2)e^(iλt) + ω^2(e^(iλt)(A(j−1) + A(j+1)) + 2A(j)e^(iλt)) = F cos(γt)e^(iλt)[/tex]
Dividing both sides by e^(iλt), we get:
[tex]−A(λ^2+αλ+ω^2) + ω^2(A(j−1) + A(j+1) + 2A(j)) = Fcos(γt)[/tex]
Simplifying, we get:
[tex](2ω^2A − λ^2A) + ω^2(A(j−1) + A(j+1)) = F cos(γt) + αλA[/tex]
The eigenvectors of this matrix are:
[tex][±sin(π/6)][±sin(2π/6)][±sin(3π/6)][±sin(4π/6)][±sin(5π/6)][/tex]
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if the interior angle of quadrilateral angle of abcd are 3x,4x and the rest two angle are five times one of them find value of x and each of interior angle?please
Hence, in answering the stated question, we may say that 128.57 quadrilateral degrees is the angle C. D is equal to 171.42 degrees.
what is quadrilateral?A quadrilateral in geometry is a four-sided polygon with outer walls and four corners. The term comes from the Roman terms quadri and lead people to make bad (meaning "side"). A rectangle is a two-dimensional shape with sidewalls, four vertices, and four corners. Concave and convex surfaces are usually divided into two types. Trapezoids, parallelograms, rectangular, rhombuses, and squares are also subclasses of convex quadrilaterals. A rectangle is an a double form that has four straight sides. Parallelograms, trapezoids, triangles, kites, squares, etc rhombuses are examples of quadrilaterals.
The total of a quadrilateral's internal angles equals 360 degrees.
The four inner angles of the quadrilateral ABCD are denoted as follows:
A-angle = 3x
B angle = 4x
Angle C = 5(3x) = 15x (since it is 5 times angle A)
Angle D = 5(4x) = 20x (since angle B is five times larger).
3x + 4x + 15x + 20x = 42x is the sum of these four angles.
3x + 4x + 15x + 20x = 360
42x = 360
x = 8.57 (rounded to two places) (rounded to two places)
Angle A = 3x + 3(8.57) = 25.71°
Angle B = 4x + 4(8.57) = 34.28°
Angle C = 15x + 15(8.57) = 128.57
D = 20x = 20(8.57) = 171.42 degree angle
As a result, the quadrilateral's internal angles are:
A angle of 25.71 degrees
34.28 degrees is the angle B.
128.57 degrees is the angle C.
D is equal to 171.42 degrees.
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57 stamps on 3 sheets = 76 stamps on how many sheets
You have a bowl with 5 orange, 6 blue, 3 green, 4 red and 7 yellow candies. What is the probability that you will choose an orange candy out of the bowl? A 50% B 60% C 20% D 25%
Answer:
20%
Step-by-step explanation:
The total number of candies in the bowl is 25. There are 5 orange candies. In order to find the total amount, simply divide the amount of candies in the given color (orange) and divide it by the total number of candies (25) giving you a result of 0.20, which can also be written as 20/100 or 20%
Kevin has deposited money into a savings account. Choose the correct terms to complete each sentence.
Kevin deposits $100 into a savings account today. This is his . In one year, Kevin’s money earns 5 percent. The $5 he earns is . In one year’s time, Kevin’s money is worth $105. This is his . The interest Kevin earns in the first year will also earn interest in subsequent years. This is called .
The interest Kevin earns in the first year that is $105 that will also earn interest in subsequent years. This is called compound interest.
What is percent?Percent is a way of expressing a number as a fraction of 100, often used to represent a proportion or rate. It is denoted by the symbol "%". For example, if 30 out of 100 students in a class got an "A" grade, then the percentage of students who got an "A" grade is 30%.
Here,
Kevin deposits $100 into a savings account today. This is his principal. In one year, Kevin’s money earns 5 percent. The $5 he earns is his interest. In one year’s time, Kevin’s money is worth $105. This is his balance.
To find the interest earned in one year, we need to multiply the initial deposit by the interest rate (as a decimal). So:
Interest earned in one year = $100 x 0.05 = $5
To find the total value of Kevin's savings account after one year, we need to add the interest earned to the initial deposit. So:
Total value after one year = $100 + $5 = $105
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Please help me thanks
Answer:
A. What is the Radius? ANS: 4.2m
B. What is the Height? ANS: 14.5m
C. Plug the r, h, and 3.14 for pi into the formula pi(r)^2(h). ANS: approximately 803.56 m
D. Show your work and label properly.
ANS: pi (4.2)^2 (14.5)
pi (17.64)(14.5)
255.78pi
approximately 803.56m
HOPE THIS HELPS:)
Help please what does it =??
Answer:
m∠WVY = 30°
Step-by-step explanation:
2x + x = 90
3x = 90
x = 90/3 = 30
m∠WVY = x = 30°
What is the equation of the circle below?
The equation of the circle in the picture is
C. (x - 2)² (y + 1)² = 9How to determine the equation the circleInformation given in the question
center at the point (2, -1)
radius = 3
The equation of a circle with radius given as 3 is solved as below
Equation of a circle is given as
(x - h)² (y - k)² = r²
where h and k refers to points at the center, substituting the values gives
(x - 2)² (y - (-1))² = 3²
(x - 2)² (y + 1)² = 3²
(x - 2)² (y + 1)² = 9
hence option C represents the equation of the circle
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Find m∠MQN
please help need this asap
Baby move classroom 450 students have a dog suits for dogs in bed 2/3 of a lot of calories have both a dog and cats
The total number of pets is = 36.
This problem is incomplete, we do not know the fraction of the students that have a dog and also have a cat. Suppose we write the problem as:
"In Mrs.Hu's classroom, 4/5 of the students have a dog as a pet. X of the students who have a dog as a pet also have cat as a pet. If there are 45 students in her class, how many have both a dog and a cat as pets?"
Where X must be a positive number smaller than one, now we can solve it:
we know that in the class we have 45 students, and 4/5 of those students have dogs, so the number of students that have a dog as a pet is:
N = 45*(4/5) = 36
And we know that X of those 36 students also have a cat, so the number of students that have a dog and a cat is:
M = 36*X
now, we do not have, suppose that the value of X is 1/2 ("1/2 of the students who have a dog also have a cat")
M = 36*(1/2) = 18
So you can replace the value of X in the equation and find the number of students that have a dog and a cat as pets.
The total number of pets is = 36.
The complete question is-
In Mrs.Hu's classroom, 4/5 of the students have a dog as a pet. Of the students who have a dog as a pet also have a cat as a pet. If there are 45 students in her class, how many have both a dog and a cat as pets?
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5. JKLM is a parallelogram. State whether
each additional single condition will make
JKLM a rhombus. Explain your reasoning.
A Opposite sides are congruent.
O Yes O No
B Diagonals bisect.
O Yes Ο No
C Diagonals are perpendicular.
O Yes O No
D Opposite angles are congruent.
O Yes Ο No
The οppοsite angles οf a parallelοgram are equal.
What is Area οf Parallelοgram?The regiοn in a twο-dimensiοnal plane that a parallelοgram οccupies is knοwn as its area. A parallelοgram is a fοrm with fοur sides with twο geοmetry dimensiοns.
Because the οppοsing sides are equal and parallel, sο it is a unique quadrilateral example. The space bοunded by the fοur sides οf a parallelοgram is knοwn as its area. A parallelοgram's area is calculated as the sum οf its length and height.
The οppοsite sides οf a parallelοgram are parallel. Here, PQ ‖ RT and PR ‖ QT.
The οppοsite sides οf a parallelοgram are equal. Here, PQ = RT and PR = QT
The οppοsite angles οf a parallelοgram are equal. Here, ∠P = ∠T and ∠Q = ∠R
Hence, The οppοsite angles οf a parallelοgram are equal.
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What is the perimeter of a regular hexagon with area of 96 square ruut to 3cm square
the perimeter of the regular hexagon is 48 cm.
A regular hexagon is a polygon with six sides, and each side has the same length. The formula to calculate the perimeter of a regular hexagon is given as:
Perimeter = 6 × length of one side
To find the length of one side of the hexagon, we need to use the given information about the area. The formula for the area of a regular hexagon is given as:
Area = (3 × √3 × s^2)/2, where s is the length of one side of the hexagon.
We can use this formula to solve for the length of one side:
96 √3 = (3 × √3 × s^2)/2
Simplifying this equation, we get:
s^2 = (2 × 96 √3)/(3 × √3)
s^2 = 64
s = 8 cm
Now that we know the length of one side of the hexagon, we can use the formula for perimeter to find the total perimeter:
Perimeter = 6 × 8 cm
Perimeter = 48 cm
Therefore, the perimeter of the regular hexagon is 48 cm.
In a regular hexagon, all six angles are equal, each measuring 120 degrees. It is a symmetrical shape, meaning that it has six lines of symmetry. The regular hexagon is a common shape in nature and architecture, and it is often used in geometry problems because of its regularity and symmetry. The hexagon is also the basis for the hexagonal lattice structure, which is a common pattern in crystals and other materials.
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Ratio of boys to girls is 4:5. How many boys are there if there are 488 girls
As per the given ratio, the number of boys is 392.
The given ratio of boys to girls is 4:5. This means that for every 4 boys, there are 5 girls. We can express this ratio mathematically as:
Boys/Girls = 4/5
We can use this ratio to find out how many boys are there if there are 488 girls.
Let's assume that the total number of children is "x".
Boys + Girls = x
We know that the ratio of boys to girls is 4:5, which means that the total number of parts in the ratio is 4+5=9. We can express this mathematically as:
Number of boys = (4/9) x x
Number of girls = (5/9) x x
We are given that there are 488 girls in the group, so we can substitute this value into the equation for the number of girls:
(5/9) x x = 488
To solve for "x", we can multiply both sides of the equation by 9/5:
x = 488 x (9/5)
x = 878.4
Since we cannot have a fraction of a child, we can round the answer to the nearest whole number. Therefore, there are 878 children in the group. To find out how many boys there are, we can substitute this value into the equation for the number of boys:
Number of boys = (4/9) x 878
Number of boys = 392
Therefore, there are 392 boys in the group if there are 488 girls and the ratio of boys to girls is 4:5.
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What is 3x + 1? I've seen so many different answers but I don't know which one is correct. Can anyone help me out here?
Answer:
In the 3x+1 problem, no matter what number you start with, you will always eventually reach 1. problem has been shown to be a computationally unsolvable problem!
It depends on the value of x.
Step-by-step explanation:
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Answer:
1= 27
2= 2
Step-by-step explanation:
y=2x
Swap sides so that all variable terms are on the left hand side.
2x=y
Divide both sides by 2.
2
2x
=
2
y
Dividing by 2 undoes the multiplication by 2.
x=
2
y
A taxi journey takes the passenger to a destination 8 km south and 3 kn west of its starting point. Find the distance and bearing of the destination from its starting point.
Using trigonometry.
Answer: We can use trigonometry to solve this problem.
First, let's draw a diagram to represent the situation:
|
|
| 8 km
|
|
--------X---------
| 3 km
|
|
|
|
The starting point is at the X, and the destination is 8 km south and 3 km west of the starting point.
To find the distance and bearing of the destination from the starting point, we can use the Pythagorean theorem and trigonometric functions.
The distance between the starting point and destination is the hypotenuse of a right triangle with legs of length 8 km (south) and 3 km (west). So we can use the Pythagorean theorem:
distance = √(8² + 3²) ≈ 8.6 km
To find the bearing (direction) of the destination from the starting point, we can use trigonometry. The bearing is the angle between the line connecting the starting point and destination and the line pointing due north.
We can use the tangent function to find this angle:
tan(θ) = opposite/adjacent = 3/8
θ = tan⁻¹(3/8) ≈ 20.56°
So the bearing of the destination from the starting point is approximately 20.56° west of due south.
Therefore, the distance of the destination from the starting point is approximately 8.6 km and the bearing of the destination from the starting point is approximately 20.56° west of due south.
Step-by-step explanation:
Sally invests $10,000 into a new bank account at 8. 4% interest compounded monthly. How much money will Sally have in the account in 30 years to the nearest cent?
As per the compound interest, Sally have the amount in the account in 30 years is $100,620.95
The formula for compound interest is given as:
A = P(1 + r/n)ˣⁿ
Where A is the amount of money in the account after t years, P is the initial investment, r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and x is the number of years.
In this case, we have P = $10,000, r = 0.084 (8.4% expressed as a decimal), n = 12 (monthly compounding), and x = 30. Substituting these values into the formula, we get:
A = $10,000(1 + 0.084/12)¹²ˣ³⁰
A = $10,000(1.007)³⁶⁰
A = $10,000(10.062)
A = $100,620.95
Therefore, after 30 years, Sally will have $100,620.95 in her bank account, to the nearest cent. This calculation illustrates the power of compound interest, as Sally's initial investment has grown by more than tenfold due to the compounding effect over 30 years.
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whats the probability for a quarter to land on tails and a rolling die to land on two
The probability that a quarter lands on tail and a rolling die land on 2 is 1/12
What is probability?A probability is a number that reflects the likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space /total outcome
A quarter has two faces, the head and the tail. Therefore the probability for a quarter to land on tail = 1/2
A die has 6 faces , labelled 1, 2,3,4, 5,6.
The probability for a die to land on 2 = 1/6
Therefore the probability for a quarter to land on tail and a die to land on 2 = 1/2 × 1/6 = 1/12
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The angle of elevation of the point T on the top of the pole from the point A on the level ground, obtained using Pythagorean Theorem and the relationship between similar triangles is about 39.3°.
What are similar triangles?Similar triangles are triangles that have the same shape (the sizes may be different) and in which the ratio of the corresponding sides are equivalent.
The triangles ΔXBA, ΔXAC, and ΔABC are right triangles, such that the angles, ∠ABX in triangle ΔXBA is congruent to triangle ∠CAX in triangle ΔXAC, and ∠ABC in ΔABC.
The 90° angle in the right triangles are congruent (All 90° angle are congruent), therefore;
ΔXBA ~ ΔXAC ~ ΔABC by AA (Angle-Angle), similarity postulate
The length of the hypotenuse in the right triangle, ΔABC, [tex]\overline{BC}[/tex], can be obtained using Pythagorean Theorem as follows;
[tex]\overline{BC}[/tex]² = 14² + 25² = 821
[tex]\overline{BC}[/tex] = √(821)
[tex]\overline{BC}[/tex]/[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex]/[tex]\overline{AX}[/tex]
√(821)/25 = 14/[tex]\overline{AX}[/tex]
[tex]\overline{AX}[/tex] = 25 × (14/(√(821)) = 350/(√(821))
Let θ represent the angle of T from A, we get;
tan(θ) = 10/(350/(√(821)))
θ = arctan(10/(350/(√(821)))) ≈ 39.3°
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Suppose a county’s recent health report gives a pet allergy prevalence of 0.13 for kids. There is a new at-home test kit for pet allergies on the market that provides families with a convenient way to test if children have a pet allergy. The probability that the test gives a positive result when a child really does not have a pet allergy is 0.06. The probability that the test gives a negative result when a child really does have a pet allergy is 0.12. The tree diagram shows the possible outcomes with the associated probabilities.
What is the probability of an incorrect test result? Give your answer as a decimal precise to two decimal places.
Answer: To calculate the probability of an incorrect test result, we need to consider two cases:
1. The test gives a positive result when the child does not have a pet allergy (false positive).
2. The test gives a negative result when the child does have a pet allergy (false negative).
The probability of a false positive is given as 0.06, which means that out of 100 children who do not have a pet allergy, 6 will test positive for it. The probability of a false negative is given as 0.12, which means that out of 100 children who do have a pet allergy, 12 will test negative for it.
To calculate the probability of an incorrect test result, we can add the probabilities of these two cases:
Probability of incorrect test result = Probability of false positive + Probability of false negative
Probability of incorrect test result = 0.06 + 0.12
Probability of incorrect test result = 0.18
Therefore, the probability of an incorrect test result is 0.18, or 18% (rounded to two decimal places).