Order of the side lengths EF, FG, and GE from least to greatest is EF < FG < GE.
Give a brief account on Law of Coslnes?When the lengths of two sides and the size of the included angle are known (SAS) or when the lengths of all three sides are known (SSS), the Law of Cosines can be used to determine the remaining components of an oblique (non-right) triangle. We are unable to establish a solvable percentage in either of these scenarios, making it impossible to apply the Law of Sines.
According to the Law of Cosines:
c² = a² + b² - 2ab * cos(C)
With the exception of the third component, which equals zero if C is a straight angle and the Pythagorean Theorem results, this is similar to the Pythagorean Theorem. As a result, the Law of Cosines is a specific case of the Pythagorean Theorem.
Using the Law of Cosines
In the given triangle, we are given the measure of angle G and the length of side FG, so we can use the Law of Cosines to find the lengths of the other sides. The Law of Cosines states that for a triangle with sides a, b, and c and angle C opposite side c, the relationship between the sides and the angle is:
c² = a² + b² - 2ab * cos(C)
Given: angle G = 72°, FG = 6
We can use the Law of Cosines to find the lengths of the other sides:
EF² = FG² + GE² - 2FG * GE * cos(G)
EF = √(6² + GE² - 2 * 6 * GE * cos(72))
FG² = EF² + GE² - 2EF * GE * cos(F)
FG = √(EF² + GE² - 2 * EF * GE * cos(66))
As we don't have any value for GE, we can't calculate the exact values, but as we know that the side opposite to the largest angle is the longest side of a triangle, so we can order the sides as follows:
EF < FG < GE
It means that side GE is the longest side of the triangle, followed by side FG, and side EF is the shortest side of the triangle.
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Line q passes through the point 4,6 and 0,6 what is the equation for the line which is perpendicular to q and passes through the point -2,3
A x= -2
B x= -3
C y= -3
D y= -2
The equation for line q is y = mx + b where m is the slope and b is the y-intercept. Since the line passes through the point (4,6) and (0,6), we can find the slope by using the formula m = (y2 - y1) / (x2 - x1) = (6 - 6) / (4 - 0) = 0.
Since the line is perpendicular to line q, the slope of the new line is the negative reciprocal of 0, which is undefined. Therefore, the new line is a vertical line, and the equation is in the form x = a constant. Since the line passes through the point (-2,3), the equation is x = -2. Therefore, the answer is A: x = -2.
Fluffy laundry detergent reduced its regular size from 4.2 kg to 3.6 kg. The retail price dropped from $10.29 to $9.18. What was the percent change in the unit price?
Original Unit Price:
$10.29 / 4.2 kg = $2.45/kg
New Unit Price:
$9.18 / 3.6 kg = $2.55/kg
The price went up by $0.10/kg. If we compare that (divide that) by the starting unit price of $2.45, we get:
$0.10 / $2.45 ≈ 0.040816326530612
≈ 4.0816326530612 %
(You can round as accurately as your teacher needs.)
Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle’s name blank and write CNBD for “Cannot be determined” in place of the rule. ∆RED = ∆___ By rule ________
ΔRED ≅ ΔBUL, by rule SSA criterion.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
We have the triangles,
ΔRED and ΔBUL.
And given:
RE ≅ BU
RD ≅ BL
And ∠RDE ≅ ∠BLU.
Hence,
ΔRED ≅ ΔBUL, by SSA criterion.
Therefore, ΔRED ≅ ΔBUL, by SSA criterion.
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A drone rises 18 m every three seconds. After five seconds, the drone is at a height of 40 m how many meters is a drone rise each second
The height rises by the drone each second is 6 meters.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a drone rises 18 m every three seconds. After five seconds, the drone is at a height of 40 m.
The height will be calculated as:-
3 sec = 18 meters
1 sec = 18 / 3 meters
1 sec = 6 meters
Hence, the height in 1 second will be 3 meters.
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Help pls
A consumer purchased a computer after a 12% price reduction. If x represents the computer's original price, the reduced price can be represented by
If x represents the computer's original price, the reduced price can be represented by
We want to reduce x by 12%. Thus, the reduced price is:
x - 0.12x = 0.88x
More informally, if you take away 12%, you're left with 88%.
Answer:
We want to reduce x by 29%. Thus, the reduced price is:
x - 0.29x = 0.71x
More informally, if you take away 29%, you're left with 71%.
The constellation whose stars are used as pointers to the north celestial pole in the northern hemisphere at this time in history is:
A) Ursa Minor, the Little Bear, containing the bright star Polaris.
B) Leo, the Lion, containing the bright star Regulus.
C) Boötes, the Herdsman, containing the bright star Arcturus.
D) Ursa Major, the Big Dipper.
The correct option is (A). The correct answer is Ursa Minor, the Little Bear, containing the bright star Polaris.
Whereas stars spin or revolve from the northern hemisphere is the center of the sky, also known as the North Celestial Pole. Additionally, it marks the precise location of the Polaris or Northern Star constellation in full view. In addition, this served as a point of reference for the construction of sundials in earlier times.
When people go outside, especially at night, and try to find the Polaris constellation, it is evident that the stars close to this star formation circle in an east-to-west direction, in contrast to the northern star, which makes no movement whatsoever as the evening wears on.
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Find the general solution, in implicit form, to the differential equation dy/dx = 9 + 5x ^1/2 / 8+ (13y)^1/2 x>0, y>0Then, rearrange the solution that you get into the form f (x,y) = C, for some constant C.
A general solution is one which involves the integer 'n' and gives all solutions of a trigonometric equation.
What is general and particular solution of differential equation?A specific differential equation solution is one with the formula y = f(x), which lacks any arbitrary constants. The arbitrary constants a and b are used in the differential equation's general solution, which has the form y = f(x) or y = axe + b.The differential equation's solution can be quickly and easily found by integrating each variable once it has been separated. The formulas are: f(x)dx+g(y)dy=0, where f(x) and g(y) are respectively constants or functions of x and y.Any equation involving the unknown function y=f(x) and one or more of its derivatives is known as a differential equation. A function y=f(x) that satisfies the differential equation when f and its derivatives are replaced into the equation is a solution to a differential equation.Given data :
dy / dx = 9 + [tex]\frac{9 + (5x)^{1/2} }{8 + (13y)^{1/2} }[/tex] ; x > 0
The general solution of a differential equation in implicit form is obtained as follows
dy / dx = h(x) / g(y)
g(y)dy = {8 + (13y)^{1/2}
h(x) dx = {9 + (5x)^{1/2}
F(x,y) = C
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The perimeters of a triangle is 19 feet. One side of the triangle is 3 times the second side. The third side is 4 feet longer than the second side. Find the kength of each side?
Answer:
9 ft, 3 ft 7, ft
Step-by-step explanation:
Perimeter = 19 ft
Let side 2 = x
Side 1 = 3x
Side 3 = x + 4
perimeter = 3x + x + x + 4 = 19
5x + 4 = 19
5x = 15
x = 3
Side 1: 3x = 3(9) = 9
Side 2: x = 3
Side 3: x + 4 = 3 + 4 = 7
Answer:
9 ft, 3 ft 7, ft
Question 3 (5 points)
(05.02)
Solve log x = 2.
O a
Ob
Oc
Od
2
20
100
1,000
For logx = 2, the value of x would be 100.
Option (C) is correct.
What is a logarithm?
A logarithm is a mathematical function that calculates the power to which a given number (called the base) must be raised to produce a given value. The most common base used in logarithms is base 10, but logarithms can be defined with any base. If the base of a logarithm is not specified, it is assumed to be base 10. The logarithm of a number is represented by the symbol log.
The value of x in the equation logx = 2 can be found by solving for x. The logarithm of a number is the exponent that the base must be raised to in order to produce that number. So, in the equation logx = 2, x is equal to the base raised to the power of 2.
So,
logx = 2
x = 10^2
x = 100
if the base of the logarithm is not specified it is assumed to be base 10.
So, logx = 2 means x = 10^2 = 100
Hence, for logx = 2, the value of x would be 100.
Option (C) is correct.
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2. In the third paragraph, line number 10, it says "since each location on Earth has a
different magnetic signature...." what does it mean that each location on Earth has
its own magnetic signature?
Iron, which is a magnetic substance, makes up most of the core of the Earth, where the magnetic field of the planet first appears. The fluid outer core's movement around the solid inner core causes electric currents, which in turn creates and maintains the Earth's magnetic field.
How do you calculate the Earth's magnetic field?V(r) = m • r / (4 r3) = m cos / (4 r2) = scalar magnetic potential of dipole field. A spherical harmonic field expansion is used. Dipole is the first phrase (above). An approximate range of 25,000 to 65,000 nT is the Earth's magnetic field intensity (. 25 - . 65 gauss). The distance between magnetic north and true north is known as magnetic declination.The geomagnetic field, also referred to as the earth's magnetic field, is the magnetic field that emanates from the interior of the Earth into space and collides with the solar wind, a stream of charged particles that is emitted from the Sun.Fluxgate magnetometers, which provide information about the field's vector components, or proton precession magnetometers, which measure scalar field intensity, are typically used to measure the earth's magnetic field.To learn more about Earth's magnetic, refer to:
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If You write all numbers from 30 to 65 including 30 and 65 how many times would you write the digit 7?
Answer:
3 times.
Step-by-step explanation:
30, 31, 32, 33, 34, 35, 36, 37, 38, 39,40,41,42,43,44,45,46,47,48,49,50,51,
52,53,54,55,56,57,58,59,60,61,62,63,64,65.
37,47,57.
3 times
Robert earns $512 less than noel, john earns times as much as robert. if their total salaries sum to 47,645.25, how much is roberts salary?
n + (n - 512) + 3(n - 512) = 47645.25
Answer:
Robert's salary = $ 9426.65
Step-by-step explanation:
First we need to solve for n ( noel's salary)
And from there we can just sub n value into Robert's salary equation which is (n - 512) [ he earns $512 less than noel]
I need help please asap, it's missing
Answer:
f(g(8)) = 26
Step-by-step explanation:
to calculate f(g(8)) , evaluate g(8) , then substitute the value obtained into f(x)
g(8) = 8 - 6 = 2 , then
f(2) = 3(2)² + 2 + 12 = 3(4) + 14 = 12 + 14 = 26
Determine which of the lines, if any, are parallel or perpendicular. Explain. Line a passes through (2, 10) and (4,13). Line b passes through (4,9) and (6, 12) Line c passes through (2, 10) and (4,9). are parallel. The slopes are perpendicular to The slopes are
Line A is parallel to line B
We know, the slope of the line joining two points [tex](x_{1} ,y_{1} )[/tex] , [tex](x_{2} ,y_{2} )[/tex] is:
[tex]m = \frac{y_{2} - y_{1} }{x_{2}- x_{1}}[/tex]
Line A is passing through (2, 10) and (4,13).
The slope of line A
[tex]m_{1} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{13 - 10}{4-2} =\frac{3}{2}[/tex]
Line B is passing through (4,9) and (6, 12)
The slope of line B
[tex]m_{2} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{12 - 9}{6-4} =\frac{3}{2}[/tex]
Line C is passing through (2, 10), and (4,9).
The slope of line C
[tex]m_{3} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{9- 10}{4-2} =\frac{-1}{2}[/tex]
We also know that if the slope of two lines is equal that is [tex]m_{1} = m_{2}[/tex] then the lines are parallel and
if the slope of the two lines has a relation [tex]m_{1} * m_{2} = -1[/tex] , the lines are perpendicular to each other.
Here, since the slope of lines A and lines B are equal.
Hence, line A is parallel to line B.
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What would be the difference in interest received from an investment of $750 from an account paying 4% simple interest per annum and an account paying 0.3% monthly compound interest, over a one-year period? and which account paid the most interest
Answer:
The difference in interest received from an investment of $750 from an account paying 4% simple interest per annum and an account paying 0.3% monthly compound interest, over a one-year period is $19.75. The account paying 0.3% monthly compound interest will pay the most interest, yielding $102.50 in total.
The gate code at your apartment complex is three numerical digits followed by the "#" sign. If each code
contains non-repeating digits, how many possible gate codes does your apartment complex have?
There are a total of 720 possible gate codes for your apartment complex.
What is gate code?Gate codes are security codes used to control access to a restricted area. Gate codes are used in both residential and commercial settings to ensure the safety of the occupants and to protect the property. Gate codes can be used to unlock and lock a gate, door, or other access point, and typically consist of a combination of letters, numbers, and/or symbols.
This is because each code consists of three non-repeating digits (0-9).
For the first digit, there are 10 possible choices (0-9).
For the second digit, there are 9 possible choices (excluding the number chosen for the first digit).
For the third digit, there are 8 possible choices (excluding the numbers chosen for the first and second digits).
This means that the total number of possible gate codes is 10 x 9 x 8 = 720.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
2 + x = 5, x + (negative 4) = 7, Negative 5 + x = negative 2 are equivalent equations.
In the first equation 2+ x = 5, x = 3
In the second equation x + (negative 4) = 7, x = 11
In the third equation Negative 5 + x = negative 2, x = negative 3
Write the equation for the trend line in y=mx+b form.
Answer:
y=3/2x+86
Step-by-step explanation:
y=Mx+b
M is the slope and b is the y intercept. The slope of a line is rise/run, in this case 3/2 and the y intercept is where the line goes through the y axis which for this problem, is 86. So y=3/2x+86
The baggage handling services of On-Time Airlines is interested in how many baggage handlers they need on duty at various time of the day to ensure that passengers do not wait an unreasonable amount of time for their baggage. An airport executive performed a study and found that there is a correlation between the number of passengers arriving at given times and the number of baggage handlers needed. She sampled various times during the day and different days of the week including weekend. She recorded the number of passengers arriving within any 1-hour time block. The computer output from the regression equation analysis is shown below
The baggage handling services of On-Time Airlines are conducting a study to determine the correlation between the number of passengers arriving at a given time and the number of baggage handlers needed.
The study is performed by an airport executive who samples different times during the day and different days of the week including weekends. The main objective is to ensure that passengers do not wait an unreasonable amount of time for their baggage.
The study records the number of passengers arriving within any 1-hour time block. The data collected is then analyzed using a statistical technique called regression equation analysis, which is a method to estimate the strength and direction of the relationship between two or more variables.
The outcome or the result of the analysis is not provided in the given information.
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9 less than 10 and 6 times the letter n
The statement '9 less than 10 and 6 times the letter n' in the mathematical form will be 9 < 10 + 6n.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.
The statement is '9 less than 10 and 6 times the letter n'.
Convert the statement into a mathematical form. Then we have
9 < 10 + 6n
Simplify the inequality, then we have
9 < 10 + 6n
6n > - 1
n > - 1/6
The statement '9 less than 10 and 6 times the letter n' in the mathematical form will be 9 < 10 + 6n.
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I need to understand quadratic graphs. eg. y=x^2 +2x -3
A quadratic graph is a type of parabolic graph that can be represented by the equation y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of this equation is a parabola that opens either up or down, depending on the value of a.
The equation y = x^2 + 2x - 3 is an example of a quadratic graph. It can be written in the standard form of a quadratic equation as y = x^2 + 2x - 3, where a = 1, b = 2 and c = -3.
The x^2 term in the equation is known as the quadratic term, and it is responsible for the parabolic shape of the graph. The x term and the constant term, 2x and -3, respectively, determine the location of the vertex and the direction of the parabola.
The vertex of the parabola is the point where the parabola changes direction. It can be found by using the formula x = -b/2a, which in this case is x = -2/2 = -1 and y = f(-1) = -1.
The graph of y = x^2 + 2x - 3 is a parabola that opens upwards and the vertex of the parabola is (-1,-1)
In summary, a quadratic graph is a parabolic graph represented by the equation y = ax^2 + bx + c, where a, b, and c are constants. The x^2 term gives the parabolic shape to the graph, the x term and the constant term determine the vertex and the direction of the parabola respectively.
find a time interval [a,9] so that the average velocity of the top of the ladder on this time interval is -20 ft/sec i
The average velocity of the top of the ladder on this time interval is 8.75.
What is an average velocity?
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
Here, we have
Given: time interval [a,9] so that the average velocity of the top of the ladder on this time interval is -20 ft/sec.
v = Δy/Δt = 20 = (0 - √625 - (7+2a)²)/(9-a)
-20 = (-√4(144 - 7a - a²)/(9-a)
10 = √(16 + a)(9 - a)/(9-a)
10 = √(16 + a)/(9 - a)
a = √884/101 = 8.75
Hence, the average velocity of the top of the ladder on this time interval is 8.75.
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Verify that every member of the family of functions y=(lnx+C)/x is a solution of the differential equation x2y' + xy = 1
a) Find a solution of the differential equation that satisfies the initial condition y(7)=6. y=
b) Find a solution of the differential equation that satisfies the initial condition y(6)=7. y=
The solutions are:
a) y = (lnx + 42 - ln7)/x
b) y = (lnx + 42 - ln6)/x
What are differential equations?
A differential equation is an equation that relates a function to its derivatives.
To verify that every member of the family of functions y=(lnx+C)/x is a solution of the differential equation x^2y' + xy = 1, we can substitute the function into the equation and see if it holds true for all values of x.
y=(lnx+C)/x
y'= (1/x - lnx - C)/x^2
x^2(1/x - lnx - C)/x^2 + x(lnx+C)/x = 1
(1 - xlnx - xC) + (lnx+C) = 1
lnx + C = 1/x
The equation holds true for all x, so it is a solution of the differential equation.
a) To find a solution of the differential equation that satisfies the initial condition y(7)=6, we can use the fact that y=(lnx+C)/x is a solution and plug in the initial condition.
y(7) = (ln7+C)/7 = 6
ln7 + C = 42
C = 42 - ln7
y = (lnx + 42 - ln7)/x
b) To find a solution of the differential equation that satisfies the initial condition y(6)=7, we can use the fact that y=(lnx+C)/x is a solution and plug in the initial condition.
y(6) = (ln6+C)/6 = 7
ln6 + C = 42
C = 42 - ln6
y = (lnx + 42 - ln6)/x
Hence, the solutions are:
a) y = (lnx + 42 - ln7)/x
b) y = (lnx + 42 - ln6)/x
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In an office7by 9 chairs have wheels what is the ratio between the number if chairs with wheels and those without wheels
The ratio for number of chairs with wheels and number of chairs without wheels is 7:2.
What is ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
The ratio value is given as 7/9.
There are 7/9 chairs that are with wheels.
This means that the total number of chairs is 9.
Out of the 9 chairs 7 chairs have wheels.
The number of chairs that have no wheels is -
Total number of chairs - Number of chairs with wheels
= 9 - 7
= 2
So, the number of chairs with no wheels is 2
The ratio for number of chairs with wheels to no wheels is -
7:2
Therefore, the ratio value is obtained as 7:2.
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In a circle with centre O, the chord BC is intersected by a radius OA. If arc AC = arc AB and BC is an angle bisector of angle ABO, prove that triangle ABO is an equilateral triangle.
When two lines are perpendicular to one another, they are said to intersect at a right angle or a 90-degree angle.
What is meant by angle bisector?An angle is split in half equally by an angle bisector. Thus, divide the angle's degree count by 2 to determine the location of the angle bisector. At 80 degrees of the angle, the angle bisector is located.
An equal split of a line is created by a bisector. As a result, when we refer to a line segment's perpendicular bisector as AB, we mean that it bisects or divides AB into two equal halves.
According to the angle bisector theorem, if a point is on an angle bisector, it is equidistant from the angles' sides. The opposite is also true; if a point is equally far from each of the triangle's sides, it is on the angle's bisector.
Two lines are said to intersect at a right angle or a 90-degree angle when they are perpendicular to one another. A bisector, on the other hand, is a line that splits a line into two equally sized half.
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Consumer Reports gave a report about the life (hours) of size AA batteries in toys. A total of 16 random toys were tested which gave a mean life of 3.58 hours with sample standard deviation of 1.85 hours. a. The packaging for the batteries claims that the AA batteries last around 5 hours in toys. Does the sample differ from the claim? a = .05 b. Would your answer change if a - .001? Explain.
a. To determine if the sample differs from the claim, we can use a hypothesis test. The null hypothesis is that the mean life of the AA batteries in toys is 5 hours, and the alternative hypothesis is that the mean life is different from 5 hours.
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Using a t-test with a significance level of 0.05, we can calculate the t-statistic and the p-value.
The t-statistic is calculated as (mean - hypothesized mean) / (standard deviation / sqrt(sample size))
t = (3.58 - 5) / (1.85 / sqrt(16)) = -2.06
The p-value is the probability of getting a t-statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true.
p-value = P(t < -2.06) = 0.048
Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that the sample mean of 3.58 hours differs significantly from the claim of 5 hours.
b. The p-value is the probability of getting a t-statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true. If we change the significance level to 0.001, the p-value would be less than 0.001, which would still be less than the new significance level. Therefore the conclusion would still be the same, the sample mean of 3.58 hours differs significantly from the claim of 5 hours.
However, it's worth mentioning that a lower significance level (0.001) would require a stronger evidence against the null hypothesis, therefore it would be more stringent in accepting the alternative hypothesis.
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Virus C has 4 strains (a, b, c, d). It is known that in a sample of 10 people, each of them was sick with the C virus exactly 1 time, and someone was sick with each of the strains. In how many ways can the statistics of the disease be arranged under these conditions (it is important who was ill with which strain).
The number of ways that the people can be arranged is given as follows:
120,960.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
To choose four people from a set of 10, as the order matters, the permutation formula is used, hence:
10!/6! = 5040.
Then we have to consider the four strains, which can be arranged in 4! = 24 ways, hence the number of ways for which the statistics can be arranged is of:
24 x 5040 = 120,960.
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i need the answer and explain how you got it
The amount of money that the worker will earn in a week if he works 4 hours overtime is; $3180
How to solve Algebra Word Problems?We are given;
Number of work hours per week = 40 hours
Regular rate of work = $15.90 per hour
Overtime rate of work = 1.5(15.90) per hour
Since the regular rate is $15.90 per hour, then for a week, the money earned is; (15.90 * 40)
Now, he also works 4 hours overtime in a week and as such amount earned for overtime in the week = 4 * 1.5(15.90)
Thus;
Total amount earned in the entire week = (15.90 * 40) + (4 * 1.5(15.90))
= $3180
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URGENT!!! PLS HELP....
Answer:
Ex1
[tex] ln( \frac{ {y}^{4} { {e}^{2} } }{ \sqrt[3]{ {x}^{2} } } ) \\ = ln( {y}^{4} {e}^{2} ) - ln( \sqrt[3]{ {x}^{2} } ) \: \: \: \: (by \: quotient \: rue) \\ = ln( {y}^{4} ) + ln( {e}^{2} ) - ln( \sqrt[3]{ {x}^{2} } ) (by \: product \: rule) \\ = 2 + ln( {y}^{4} ) - ln( \sqrt[3]{ {x}^{2} } ) \\ = 2 + 4 ln(y) - \frac{3}{2} ln(x) \: \: \: \: (power \: rule)[/tex]
Ex2
[tex] log_{4}(x + 2) + log_{4}(x - 1) = 1 \\ log_{4}((x + 2)(x - 1)) = 1 \: (by \: product \: rue) \\ log_{4}( {x}^{2} + x - 2 ) = 1 \\ {x}^{2} + x - 2 = {4}^{1} \\ {x }^{2} + x - 6 = 0 \\ x = 3 \: \: or \: x = - 2[/tex]
the following equation can be used to model the deflection of a sailboat mast subject to a wind force:
d^2y/dz^2 = f/2EI*(L-z)^2
where f = wind force, E = modulus of elasticity, L = mast length, and I = moment of inertia. Calculate the deflection if y = 0 and dy/dz = 0 at z = 0. Use parameter values of f = 60, L = 30. E = 1.25*10^8, and I = 0.05 for your computation.
Use mid-point method to find y, up to z = 30, with a step size of 2, Use excel for performing the calculations, and clearly mark the variables
The midpoint method is a numerical integration technique for solving ordinary differential equations. To use it to solve the given equation, we start by discretizing the interval [0, L] into smaller steps of size h = 2, and use the midpoint of each interval to estimate the deflection at that point. Here's the algorithm:
Initialize z = 0, y = 0, and dydz = 0
Repeat the following steps for z = z + h until z = 30:
a. Calculate f1 = dydz
b. Calculate ymid = y + h/2 * f1
c. Calculate f2 = d2y/dz2 = f/2EI * (L-z-h/2)^2
d. Update y = y + h * f2
e. Update dydz = dydz + h * f2
The final value of y is the estimated deflection at z = 30.
The midpoint method is a numerical integration technique for solving ordinary differential equations. To use it to solve the given equation, we start by discretizing the interval [0, L] into smaller steps of size h = 2, and use the midpoint of each interval to estimate the deflection at that point. Here's the algorithm:
Initialize z = 0, y = 0, and dydz = 0
Repeat the following steps for z = z + h until z = 30:
a. Calculate f1 = dydz
b. Calculate ymid = y + h/2 * f1
c. Calculate f2 = d2y/dz2 = f/2EI * (L-z-h/2)^2
d. Update y = y + h * f2
e. Update dydz = dydz + h * f2
The final value of y is the estimated deflection at z = 30.
Plugging in the given parameter values, we have:
f = 60, E = 1.25 * 10^8, I = 0.05, L = 30
h = 2
z = 0, y = 0, dydz = 0
while z < 30:
f1 = dydz
ymid = y + h/2 * f1
f2 = f/2EI * (L-z-h/2)^2
y = y + h * f2
dydz = dydz + h * f2
z = z + h
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