The lines L1 and L2 are not parallel and intersect at a single point. We have also found the point of intersection.
If the direction vectors are parallel, then the lines are parallel. If the direction vectors are not parallel but do not intersect, then the lines are skew. If the direction vectors are not parallel and do intersect, then the lines intersect at a single point.
To determine whether the given lines are parallel, skew, or intersecting, we need to compare their direction vectors. The direction vectors of the lines are the coefficients of the parameters t and s in the respective equations. Thus, the direction vector of L1 is <2,-1,3> and the direction vector of L2 is <4,-2,5>.
To check whether the direction vectors are parallel, we can compute their cross product. If the cross product is the zero vector, then the direction vectors are parallel.
<2,-1,3> × <4,-2,5> = (7,2,-10)
Since the cross product is not zero, the direction vectors are not parallel. Thus, the lines are either skew or intersecting.
To determine whether the lines are intersecting, we can set the parametric equations of the lines equal to each other and solve for t and s. This will give us the point of intersection.
3 + 2t = 1 + 4s
4 - t = 3 - 2s
1 + 3t = 4 + 5s
Rearranging the equations, we get:
2t - 4s = -2
t + 2s = 1
3t - 5s = 3
Using Gaussian elimination or other methods, we can solve for t and s:
t = 11/13
s = 2/13
Substituting these values back into either equation gives us the point of intersection:
x = 3 + 2(11/13) = 37/13
y = 4 - (11/13) = 41/13
z = 1 + 3(11/13) = 40/13
Thus, the lines intersect at the point (37/13, 41/13, 40/13).
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Complete Question:
Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.
L1: x = 3 + 2t, y = 4 – t, z = 1 + 3t
L2: x = 1 + 4s, y = 3 – 2s, z = 4 + 5s
for the phrase “x times the quantity 5 plus y,” what part goes in parentheses?
1. x(5)
2. y
3. x
4 5+y
5. 5
The part of the expression x(5 + y) that goes to the parentheses is 5 + y.
The correct option is 4.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
A phrase: “x times the quantity 5 plus y.”
5 plus y 5 + y
x times the quantity 5 plus y = x(5 + y)
The complete expression is,
x(5 + y).
Therefore, 5 + y is the required expression.
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The probability distribution for the number of students in statistics classes at IRSC is given, but one value is
missing. Fill in the missing value, then answer the questions that follow. Round solutions to three decimal
places, if necessary.
The missing value is given as follows:
P(X = 28) = 0.31.
The mean and the standard deviation are given as follows:
Mean [tex]\mu = 27.17[/tex]Standard deviation [tex]\sigma = 1.289[/tex]How to obtain the measures?The sum of the probabilities of all the outcomes is of one, hence the missing value is obtained as follows:
0.14 + 0.18 + 0.21 + P(X = 28) + 0.16 = 1
0.69 + P(X = 28) = 1
P(X = 28) = 0.31.
The mean is given by the sum of all outcomes multiplied by their respective probabilities, hence:
E(X) = 25 x 0.14 + 26 x 0.18 + 27 x 0.21 + 28 x 0.31 + 29 x 0.16
E(X) = 27.17.
The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, multiplied by their respective probabilities, hence:
S(X) = sqrt((25-27.17)² x 0.14 + (26-27.17)² x 0.18 + (27-27.17)² x 0.21 + (28-27.17)² x 0.31 + (29-27.17)² x 0.16)
S(X) = 1.289.
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What is the probability of getting 3 heads in 4 coin tosses, given you get at least 2 heads?
The probability of getting 3 heads in 4 coin tosses, given that we get at least 2 heads, is 4/11 or 0.364.
To solve this problem, we can use the conditional probability formula. Let A be the event of getting 3 heads in 4 coin tosses, and let B be the event of getting at least 2 heads in 4 coin tosses. Then we want to find P(A|B), the probability of getting 3 heads in 4 coin tosses given that we get at least 2 heads.
By the definition of conditional probability, we have:
P(A|B) = P(A and B) / P(B)
To find P(B), the probability of getting at least 2 heads in 4 coin tosses, we can use the complement rule and find the probability of getting 0 or 1 heads:
P(B) = 1 - P(0 heads) - P(1 head)
To find P(0 heads), the probability of getting 0 heads in 4 coin tosses, we use the binomial probability formula:
P(0 heads) = (4 choose 0) * (0.5)^0 * (1-0.5)^(4-0) = 1/16
Similarly, we can find P(1 head):
P(1 head) = (4 choose 1) * (0.5)^1 * (1-0.5)^(4-1) = 4/16
So,
P(B) = 1 - P(0 heads) - P(1 head) = 11/16
To find P(A and B), the probability of getting 3 heads in 4 coin tosses and getting at least 2 heads, we can use the binomial probability formula again:
P(A and B) = (4 choose 3) * (0.5)^3 * (1-0.5)^(4-3) = 4/16
Therefore,
P(A|B) = P(A and B) / P(B) = (4/16) / (11/16) = 4/11
So the probability of getting 3 heads in 4 coin tosses, given that we get at least 2 heads, is 4/11 or approximately 0.364.
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Circle the two sets of lengths that DO NOT form a triangle.
A. 3 m, 5m, 7.3m
B. 12 yd, 25 yd, 13 yd
C. 5 ft, 9 ft, 16 ft
The two sets of lengths that do not form a triangle are the options B and C.
Which sets of lengths do not form a triangle?For a triangle with side lengths x, y, and z we know the triangular inequality, it says that the sum of any two sides must be larger than the other side, so we can write 3 inequalites:
x + y > z
x + z > y
z + y > x
So if for one of the given sets, one of these inequalities is false, then the set does not form a triangle.
For the second set:
12 yd, 25 yd, 13 yd
The inequality:
12 yd + 13yd > 25yd
25 yd> 25 yd
is false, so that set does not form a triangle.
And the last set:
5 ft, 9 ft, 16 ft
The inequality:
5ft + 9ft > 16ft
14ft > 16 ft
Is also false,
So B and C are the correct options.
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The heights of men (in inches) in the United States follow approximately N(69, 2.25). The heights of women (in inches) in the United States follow approximately N(64,2). A female volleyball player at your college is 6 feet 2 inches tall, and a male college soccer player is also 6 feet 2 inches tall. Based on the distribution above, who is taller in relation to the distribution of heights based on gender?
According to the distribution shown above, the heights of female is taller according to the gender based distribution of heights.
What exactly is normal distribution?
The normal distribution, also called the Gaussian distribution, is a probability distribution that is symmetric about the mean, demonstrating that data close to the mean occur more frequently than data distant from the mean. The normal distribution looks like a "bell curve" when represented graphically.
Considering the information provided,
The United States' average male population is 69.
In the US, men's standard deviation is 2.25.
In the US, the average gender distribution is 64.
Women in the US experience a 2 standard deviation.
Now z-score for,
Female players = [tex]\frac{74-64}{2}[/tex] = 5
Playing men = [tex]\frac{74-69}{2.25}[/tex] = 2.22
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What number has 6 ten thousands, 2 fewer thousands than ten thousands, the same number of hundreds as ten thousands, 1 fewer ten than ten thousands and 5 more ones than thousands?
Therefore, the number that satisfies all the given conditions is 60,649.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equals sign ("="). The expressions on either side of the equals sign are called the left-hand side and the right-hand side of the equation, respectively. The purpose of an equation is to describe a relationship between two or more variables or quantities, such as x + 3 = 7 or y = 2x - 5. Equations can be used to solve problems and answer questions in various fields of study, such as algebra, geometry, physics, chemistry, and engineering. Solving an equation typically involves finding the value or values of the variable(s) that make the equation true. Some equations may have a unique solution, while others may have multiple solutions or no solutions at all. The study of equations and their properties is a fundamental topic in mathematics.
Here,
Let's break down the clues given in the problem and use them to find the unknown number:
6 ten thousands: The number must start with 6.
2 fewer thousands than ten thousands: The number of thousands is 2 less than the number of ten thousands. Since there are 6 ten thousands, there are 4 thousands.
Same number of hundreds as ten thousands: The number of hundreds is the same as the number of ten thousands, which is 6.
1 fewer ten than ten thousands: The number of tens is 1 less than the number of ten thousands, which is 6-1=5.
5 more ones than thousands: The number of ones is 5 more than the number of thousands, which is 4+5=9.
Putting all of these clues together, we get the number: 60,649
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 On Monday, Jack bought 2 burgers and 3 fries for $11.25. On Tuesday, he bought 7 burgers and 5 fries
for $32.50. Find the price of each item.
The burgers is sold each for 3.75 dollars , while the fries is solde for 1.25 dollars each
How to solve for the equationWe would have to solve for the price of each of the items using the simultaneous linear equation method
2 burgers and 3 fries for $11.25
we would have:
Use the elimination method to solve the system of equations:
2 x+ 3 y = 11.25
7 x + 5 y = 32.50
Step 1 - Multiply Equation 1 by 7:
7 * (2x+3y=11.25) --> 14x + 21y = 78.75
Step 2 - Multiply Equation 2 by 2:
2 * (7x+5y=32.50) --> 14x + 10y = 65
Step 3 - s
14x + 21y = 78.75
-(14x + 10y = 65)
------------------------------
21y - 10y = 78.75 - 65
Step 4 - simplify and solve for y:
11y = 13.75
y = 13.75 / 11
y = 1.25
Step 5 - now that we have solved for y, let's rearrange Equation 1 to solve for x:
2x = 11.25 - 3y
Divide each side by 2
2x / 2 = 11.25 - 3y / 2
x = 11.25 - 3y / 2
Step 6 - we determined y = 1.25. Plug it into our Rearranged equation 1:
x = 11.25 - 3(1.25) / 2
x = 11.25 - 3.75 / 2
x = 7.5 / 2
x = 3.75
Since x is the burgers which is 3.75 dollars while y is the fries which is 1.25 dollars
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-3(-3c+7)5(4+2c I need hekppppp
Answer:
90c^2 -30c - 420
Step-by-step explanation:
-3(-3c+7)5(4+2c)
(9c - 21) (20 + 10c)
180c + 90c^2 - 420 - 210c
90c^2 -30c - 420
The angle 60 is shown below in standard position, together with a unit circle.
A circle with a radius of 1 is shown with its center located at the origin on a coordinate grid. The radius forms a terminal side that makes a 60-degree-angle with the positive x-axis. The terminal side intersects the circle at (one half, the square root of 3 over 2).
Use the coordinates of the point of intersection of the terminal side and the circle to compute cot 60
Answer: 60 = 1/√3.
Step-by-step explanation:
The cotangent of 60 degrees is equal to the x-coordinate of the point of intersection divided by the y-coordinate of the point of intersection. In this case, the x-coordinate is 0.5 and the y-coordinate is √3/2. Therefore, cot 60 = 0.5 / √3/2 = 1/√3.
So, cot 60 = 1/√3.
The radius y (in millimeters) of a chemical spill after x days is represented by the equation y=6x+50 .
a. Graph the linear equation
This function y = 6x + 50 has a graph that is a straight line with a 50-point y-intercept.
What is the slope?The slope is the rate of change of the y-axis with respect to the x-axis.
The equation of a line in slope-intercept form is y = mx + b, where
slope = m and y-intercept = b.
We know the greater the absolute value of a slope is the more steeper is its graph or the rate of change is large.
Given, The radius y after x days is represented by the equation y = 6x + 50.
Here, The initial radius was 50 mm and it is growing at a rate of 6 mm per day.
The graph of this function will be a straight line having a y-intercept at 50.
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If a coin is flipped 35 times and lands on heads 14 times, what is the relative
frequency of landing on heads?
OA. 0.35
OB. 0.14
OC. 0.5
OD. 0.4
The relative frequency of landing on heads is 0.4, then the correct option is D.
What is the relative frequency of landing on heads?When we have an experiment with some outcomes, and we perform the experiment N times, and in K of these N times we get a particular outcome, then the relative frequency for that outcome is K/N
In this case the coin is flipped 35 times and it lands on heasd 14 times, then the relative frequency of landing on heads is:
R = 14/35 = 0.4
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Consider the following program statement consisting of a while loop
while ¬B do S
Assume that the Boolean expression B takes the value true with probability p and the value false with probability q. Assume that the successive test on B are independent.
1. Find the probability that the loop will be executed k times.
2. Find the expected number of times the loop will be executed.
3. Considering the same above assumptions, suppose the loop is now changed to "repeat S until B". What is the expected number of times that the repeat loop will be executed?
The probability is P(k) = (q^(k-1)) * p for k>=1, and P(0) = q. The expected number of times the loop will be executed is 1/p.The expected number of times that the repeat loop will be executed is 1/p.
To find the probability that the loop will be executed k times, we can consider the probability of the event that B is false k-1 times followed by B being true. This probability is q^(k-1) * p.
The event of the loop not being executed at all corresponds to B being true in the first trial, which has a probability of q. Therefore, the probability that the loop will be executed k times is P(k) = (q^(k-1)) * p for k>=1, and P(0) = q.
The expected number of times the loop will be executed is the sum of the probabilities of executing the loop k times, weighted by k, i.e., E = Sum(kP(k)) for k>=1, and E = 0 if P(0) = q.
By using the expression for P(k), we can simplify this to E = Sum(kq^(k-1)*p) for k>=1, and E = 0 if P(0) = q. By applying the formula for the sum of a geometric series, we get E = 1/p.
For the "repeat S until B" loop, the expected number of times that the loop will be executed is the expected number of trials in a Bernoulli process until the first success, where the success probability is p. By using the formula for the expected value of a geometric distribution, we get E = 1/p.
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Solve the formula for t V = 6pirt + 4pir2
Answer: Given the formula:
V = 6pirt + 4pir^2
To solve for t, we'll isolate t by rearranging the equation.
First, subtract 4pir^2 from both sides:
V - 4pir^2 = 6pirt
Next, divide both sides by 6pi:
(V - 4pir^2)/6pi = t
So, t = (V - 4pir^2)/6pi.
This gives us the value of t in terms of V and the radius of the cylinder, r.
Step-by-step explanation:
5) A medium radio wave band lies btw two wavelength 100 m and 1000m. Determine the corresponding frequency range (take the velocity of the wave to be 299.8X10^6m/s)
Answer: The frequency (f) of a wave is related to its wavelength (λ) and velocity (v) by the equation:
f = v/λ
Given the wavelength range of 100 m to 1000 m for the medium radio wave band, we can calculate the frequency range as follows:
For the lower wavelength of 100 m:
f = v/λ = 299.8 × 10^6 m/s / 100 m = 2.998 × 10^6 Hz
For the higher wavelength of 1000 m:
f = v/λ = 299.8 × 10^6 m/s / 1000 m = 299.8 × 10^3 Hz
Therefore, the frequency range for the medium radio wave band is approximately 2.998 × 10^6 Hz to 299.8 × 10^3 Hz.
Step-by-step explanation:
Suppose a certain baseball diamond is a square 80 feet on a side. The pitching Fubber is located 55.5 feet from home plate on a line joining home plate and second base. a) How far is it from the pitching rubber to first base? b) How far is it from the pitching rubber to second base? c) If a pitcher faces home plate, through what angle does he need to turn to face
The distance from the pitching rubber to first base is 98.7ft, B - the distance from the pitching rubber to first base is 96.6ft and C - A pitcher must pivot to face in a 45-degree angle if he is facing home plate.
(a) To find the distance from the pitching rubber to first base, we can use the Pythagorean theorem, since the distance forms the hypotenuse of a right triangle with legs of length 80ft (the length of a side of the square) and 55.5ft (the distance from the pitching rubber to home plate along a diagonal line). Thus, we have:
distance to first base = [tex]\sqrt{ 80^{2} + 55.5^{2}[/tex] = 98.7ft
(b) To find the distance from the pitching rubber to second base, we can use the fact that second base is located at a distance of 80ft from home plate along a line perpendicular to the line connecting the pitching rubber and home plate. Using the Pythagorean theorem, we have:
distance to second base = [tex]\sqrt{55.5^{2} + 80^{2} }[/tex] = 96.6ft
(c) If a pitcher faces home plate, he needs to turn through an angle of 45 degrees to face second base. This is because second base is located at one corner of the square, and the angle formed by the lines connecting the pitching rubber to home plate and second base is a right angle (since the sides of the square are perpendicular).
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Find the domain and the range of the following function.
f(x) =
x+3, for x≤-5
-1,
1
3x,
for -5
for x ≥ 6
The domain and the range for the function in this problem are given as follows:
Domain: All real values.Range: (∞, -2] U {-1} U [2, ∞).How to find the domain and the range of a function?The domain of a function is the set that contains all the values assumed by the values of x of the function.The range of a function is the set that contains all the values assumed by the values of y of the function.For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.
The range is obtained as follows:
Up to x = -5: values of x from negative infinity to -5 + 3 = -2.Between x = -5 and x = 6: constant value of 1.x = 6 and greater: Minimum value of 6/3 = 2.Hence the composition of these three intervals is given as follows:
(∞, -2] U {-1} U [2, ∞).
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Question
A tower made of wooden blocks measures114 feet high. Then a block is added that increases the height of the tower by 8 inches.
What is the final height of the block tower?
Answer:
The final height of the tower is 114 feet 8 inches.
To solve this problem, we need to convert the additional 8 inches into feet. 8 inches is equal to 0.67 feet, so the new height of the tower is equal to 114 feet + 0.67 feet which is equal to 114 feet 8 inches.
The speed of a molecule in a uniform gas at equilibrium is a random variable V whose pdf is given by f(v)={kv2e−bv2,v>00, else where,where k is an appropriate constant and b depends on the absolute temperature and mass of the molecule, m, but we will consider b to be known.(a) Calculate k so that f(v) forms a proper pdf.(b) Find the pdf of the kinetic energy of the molecule W, where W=mV2/2.
What is 2/18 in simplest form
Answer: 1/9
Step-by-step explanation:
2/2=1
18/2=9
Quadrilateral ABCD has vertices A(-3,4), B(2,5), C(3,3), and D(-1,0).
AD is _____ to BC, and AB is _____ to DC. so the quadrilateral ABCD ______ a trapezoid. trapezoid ABCD _____ isosceles because AB ____ congruent to DC
The trapezoid ABCD not isosceles because AB is not congruent to DC.
What is a trapezoid?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.
Quadrilateral ABCD has vertices A(-3,4), B(2,5), C(3,3), and D(-1,0).
The diagram is given below.
From the diagram, the line segment AD and BC are parallel to each other.
The length AB is given as,
AB² = (2 + 3)² + (4 - 5)²
AB = 5.1 units
The length CD is given as,
CD² = (3 + 1)² + (3 - 0)²
CD= 5 units
The trapezoid ABCD not isosceles because AB is not congruent to DC.
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and one 10p. How much more must he save? 10 A train journey from London to Leed takes 2h 35min. At what time do these trains arrive at Leeds if they leave London at a 11:25 b 18:45?
The system of equations are solved
a) The train will reach at 2:00 PM if it leaves at 11:25 AM
b) The train will reach at 21:20 PM if it leaves at 18:45 PM
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A train journey from London to Leed takes 2h 35min
So , the total journey time is 155 minutes
a)
The time when the train reaches Leeds when it leaves at 11:25 AM is given by the equation A = 11:25 AM + 155 minutes
On simplifying the equation , we get
The train will reach at 2:00 PM if it leaves at 11:25 AM
b)
The time when the train reaches Leeds when it leaves at 18:45 PM is given by the equation A = 18:45 PM + 155 minutes
On simplifying the equation , we get
The train will reach at 21:20 PM if it leaves at 18:45 PM
Hence , the equations are solved
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Calculate the Mean Absolute Deviation (MAD) for the months of January through April using the following data:Month Actual Sales Forecast JAN 1000 600 FEB 1600 2500 MAR 2000 1500 APR 1800 2000
The Mean Absolute Deviation (MAD) for actual sales is 300 and for forecast is 600.
Mean Absolute Deviation evaluates the absolute difference between each data point to its mean. Mean Absolute Deviation can be calculated using formula:
MAD = ∑|x - x bar|
n
where:
x = data point
x bar = data mean
n = number of data
Based on the given data, we know that:
Mean Actual sales = (1,000 + 1,600 + 2,000 + 1,800) / 4
Mean actual sales = 1,600
MAD = |1,000 - 1,600| + |1,600 - 1,600| + | 2,000 - 1,600| + |1,800 - 1,600|
4
MAD = (600 + 0 + 400 + 200) / 4
MAD = 300
Mean Forecast = (600 + 2,500 + 1,500 + 2,000) / 4
Mean forecast = 1,650
MAD Frc = |600 - 1,650| + |2,500 - 1,650| + |1,500 - 1,650| + |2,000 - 1,650|
4
MAD Forecast = (1,050 + 850 + 150 + 350) / 4
MAD Forecast = 600
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In computing the sum of an infinite series ∑ [infinity] , x = nn = 1suppose that the answer is desired with an absolute error less than e. Is it safe to stop the addition of terms when their magnitude falls below s? Illustrate with the series ∑[infinity] (0.99)^nn = 1
No, it is not safe to stop the addition of terms when their magnitude falls below s, even if the desired absolute error is less than e.
This is because the magnitude of the terms in the series may not decrease monotonically, and there may be large fluctuations in the magnitudes of the terms.
Therefore, it is necessary to use convergence tests, such as the ratio test or the root test, to determine if the series converges absolutely.
For the series ∑ (0.99)^n, we can use the ratio test to check for absolute convergence:
lim (n → ∞) |(0.99)^(n+1)/(0.99)^n| = 0.99 < 1
Since the limit is less than 1, the series converges absolutely. However, we cannot simply stop adding terms when their magnitude falls below a certain value s, as the magnitude of the terms in the series may not decrease monotonically.
Instead, we need to use the convergence test to determine the number of terms required to achieve the desired absolute error e.
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Dakota earned $14.00 in interest in Account A and $15.75 in interest in Account B after 21 months. If the simple interest rate is 4% for Account A and 3% for Account B, which account has the greater principal?
The account with the greater principle is Account B
How to find the account ?First, find the principle on Account A to be :
= Interest earned in 14 months / Interest rate for 21 months
= 14 / ( 4 % / 12 months x 21 months )
= 14 / 7 %
= $ 200
Then find the principle on Account B using the same method :
= Interest earned in 14 months / Interest rate for 21 months
= 15.75 / ( 3 % / 12 months x 21 months )
= 15. 75 / 5. 25 %
= $ 300
Account B has the greater principal.
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A ring shaped region inner diameter is 14 cm and its outer diameter is 22 find the area shaded region
The region of the concealed district will be 226.08 square centimeters.
What is the area of the circle?It is the nearby bend of an equidistant point drawn from the middle. The sweep of a circle is the distance between the middle and the boundary.
Let d be the diameter of the circle. Then the area of the circle will be written as,
A = (π/4)d² square units
A ring-formed district's internal measurement is 14 cm and its external breadth is 22 cm. Then the region of the concealed district is given as,
A = (π / 4) (22² - 14²)
A = (3.14 / 4) (484 - 196)
A = 0.785 x 288
A = 226.08 square cm
The region of the concealed district will be 226.08 square centimeters.
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Select the correct answer. Consider triangle EFG. a right triangle EFG with base EG of 10, opposite EF of 8, and hypotenuse FG of 12. What is the approximate measure of angle G? A. 41,4 degree
b. 55,8 degree
c. 82,8 degree
d. 94,8 degree
The approximate measure of angle G.The correct answer is a. 41.4 degrees.
The measure of angle G in triangle EFG can be calculated using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In right triangle EFG, the two legs are EF and EG and the hypotenuse is FG. This can be expressed mathematically as [tex]8^2 + 10^2 = 12^2.[/tex] Simplifying the expression, the equation becomes 64 + 100 = 144. Solving this equation yields 64 = 144, which is true. To calculate the measure of angle G, we will use the inverse tangent function, which is written as [tex]tan^-1[/tex]. In this function, the inverse tangent of the ratio of the opposite side to the adjacent side is equal to the angle. This can be expressed mathematically as [tex]tan^-1 (8/10)[/tex] = G. Using a calculator, the inverse tangent of 8/10 is approximately 41.4 degrees. Therefore, the correct answer is a. 41.4 degrees.
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let be the solution to satisfying . (a) use euler's method with time step to approximate . -3 5.03421 5.03942 5.04269 5.04269 0.2(8e^(-5.04269)) (b) use separation of variables to find exactly.
Answer:
Step-by-step explanation:
c
At a high school, the probability that a student is a senior is 0.25. The
probability that a student plays a sport is 0.20. The probability that a student
is a senior and plays a sport is 0.08.
What is the probability that a randomly selected student plays a sport, given
that the student is a senior?
O A. 0.32
• B. 0.08
O C. 0.17
O D. 0.25
The probability that a randomly selected student plays a sport, given
that the student is a senior is A. 0.32
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
This is a case of conditional probability and we know,
Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Given, At a high school, the probability that a student is a senior is 0.25
and the probability that a student is a senior and plays a sport is 0.08.
Therefore, The probability that a randomly selected student plays a sport, given that the student is a senior is,
= 0.08/0.25.
= 0.32
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Stephen has a rectangular rug with a perimeter of 16 feet the width of the rug is 5 feet what is the length of the rug
The length of Stephen's rug is 3 feet.
How can you use the perimeter and width of Stephen's rug to find the length?To find the length of Stephen's rug, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. In this case, we know that the perimeter of the rug is 16 feet and the width is 5 feet. So, we can plug in these values into the formula and solve for L:
Let's use the formula for the perimeter of a rectangle to solve the problem: Perimeter = 2 x (Length + Width)
We know that the perimeter of the rug is 16 feet and the width is 5 feet. Plugging those values into the formula, we get: 16 = 2 x (Length + 5)
Simplifying the equation, we can divide both sides by 2:
8 = Length + 5
16 = 2L + 2(5)
16 = 2L + 10
2L = 6
L = 3
Therefore, the length of Stephen's rug is 3 feet.
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 On Monday, Jack bought 2 burgers and 3 fries for $11.25. On Tuesday, he bought 7 burgers and 5 fries
for $32.50. Find the price of each item.
The price of burger is $3.75 and the fries cost $1.25
How to calculate the price of the burger and the fries?
On Monday, Jack bought 2 burgers and 3 fries for $11.25
On Tuesday he bought 7 burgers and 5 fries for $32.50
Let a represent the cost of the burger
Let b represent the cost of the fries
2a + 3b= 11.25..........equation 1
7a + 5b= 32.50..........equation 2
Solve by elimination method
Multiply equation 1 by 7 and multiply equation 2 by 2
14a + 21b= 78.75
14a + 10b= 65
11b= 13.75
b= 13.75/11
b = 1.25
Substitute 1.25 for b in equation 2
7a + 5(1.25)= 32.50
7a + 6.25= 32.50
7a= 32.50-6.25
7a= 26.25
a= 26.25/7
a= 3.75
Hence the price of burger is $3.75 and the price of fries is $1.25
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