Answer:
Step-by-step explanation:
3.00
Solve the differential equation by variation of parameters.
y'' − y = cosh x
The general solution is [tex]$$y=c_3 e^x+c_4 e^{-x}+\frac{1}{2} x \sinh x \text {. }$$[/tex]
Consider the following differential equation: y'' − y = cosh x
The given differential equation in the operator form will be: (D^2-1)y=coshx
The auxiliary equation of the corresponding homogeneous equation will be:
m^2-1 = 0
=>m^2=1
=>m=+1,-1
So, the complementary function will be [tex]y_c=c_1 e^x+c_2 e^{-x}.\alpha[/tex]
Now, let [tex]y_1=e^x, y_2=e^{-x}.[/tex]
Compute the Wronskian determinant:
[tex]$$\begin{aligned}W\left(y_1, y_2\right) & =\left|\begin{array}{ll}y_1 & y_2 \\y_1^{\prime} & y_2^{\prime}\end{array}\right| \\& =\left|\begin{array}{ll}e^x & e^{-x} \\e^x & -e^{-x}\end{array}\right| \\& =-e^x e^{-x}-e^x e^{-x} \\& =-2\end{aligned}$$[/tex]
Since the given differential equation is already in the form [tex]$y^{\prime \prime}+P(x) y^{\prime}+Q(x) y=f(x)$[/tex] (that is, the coefficient of y'' is 1 ),
So identify:
f(x)=cosh x
Then, calculate the values of u_1' and u_2', using formulas as follows:
[tex]$$\begin{aligned}u_1^{\prime} & =-\frac{y_2 f(x)}{W} & u_2^{\prime} & =\frac{y_1 f(x)}{W} \\& =-\frac{e^{-x} \cdot \cosh x}{-2} & & =\frac{e^x \cdot \cosh x}{-2} \\& =\frac{e^{-x} \cdot\left(\frac{e^x+e^{-x}}{2}\right)}{2} & \text { and } & =-\frac{e^x \cdot\left(\frac{e^x+e^{-x}}{2}\right)}{2} \\& =\frac{1}{4}\left(1+e^{-2 x}\right) & & =-\frac{1}{4}\left(e^{2 x}+1\right)\end{aligned}$$[/tex]
Integrate on both sides of u_1' and u_2' with respect to ' x', to get:
[tex]$$u_1=\frac{x}{4}-\frac{e^{-2 x}}{8} \text { and } u_2=-\frac{x}{4}-\frac{e^{2 x}}{8} .$$[/tex]
So, the particular solution is,
[tex]$$\begin{aligned}y_p & =u_1 y_1+u_2 y_2 \\& =\left(\frac{x}{4}-\frac{e^{-2 x}}{8}\right) e^x+\left(-\frac{x}{4}-\frac{e^{2 x}}{8}\right) e^{-x} \\& =\frac{1}{4} x\left(e^x-e^{-x}\right)-\frac{1}{8}\left(e^{-x}+e^x\right) \\& =\frac{1}{2} x \sinh x-\frac{1}{8}\left(e^{-x}+e^x\right)\end{aligned}$$[/tex]
Thus, the general solution of the given differential equation is,
[tex]$$\begin{aligned}y & =y_c+y_p \\& =c_1 e^x+c_2 e^{-x}+\frac{1}{2} x \sinh x-\frac{1}{8} e^{-x}-\frac{1}{8} e^x \\& =\left(c_1-\frac{1}{8}\right) e^x+\left(c_2-\frac{1}{8}\right) e^{-x}+\frac{1}{2} x \sinh x \\& =c_3 e^x+c_4 e^{-x}+\frac{1}{2} x \sinh x\end{aligned}$$[/tex]
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dont mind that i clicked on one lol but SOMONE PLEASE HELP RAHHAHAHAH
Here are the expressions that are equivalent to - 15 + 6x
What is an equivalent expression?
Expressions that are the same even if they may appear slightly different are called equivalent expressions. When you simplify equivalent expressions, they will all return the same value if you plug in the same variable value.
3(5 - 2x)
6x + (- 15)
15 + (- 6x)
The first one, -3(5-2x), can be simplified as -35+32x = -15 + 6x
The second one 6x + (- 15) is already in the same form as - 15 + 6x
The third one 15 + (- 6x) is just - 15 + 6x when you change the sign of -6x
The other expressions are not equivalent as they are not equal to - 15 + 6x
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Marisol writes the equation 1. 6 : n=0. 16. Right your answer using an exponent. Explain how you know your answer is correct.
The equation 1.6: n = 0.16 can be written as: [tex]1.6 = 2.511^n[/tex]
And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.
What is an exponent?
An exponent is a mathematical operation that represents the number of times a value is multiplied by itself. It is usually written as a small number raised to the power of a larger number, such as 2^3, which means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.
To write the equation 1.6: n=0.16 using an exponent, we can divide both sides of the equation by 1.6 to get: n = 0.16/1.6 = 0.1
And then we can raise the base 10 to the power of n: [tex]10^n = 10^{0.1} = 2.511[/tex]
Hence, the equation 1.6: n = 0.16 can be written as: [tex]1.6 = 2.511^n[/tex]
And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.
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The equation 1.6: n = 0.16 can be written as: 1.6 = [tex]2.511^n[/tex]
And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.
What is an exponent?
An exponent is a mathematical operation that represents the number of times a value is multiplied by itself. It is usually written as a small number raised to the power of a larger number, such as 2^3, which means 2 multiplied by itself 3 times, or 2 * 2 * 2 = 8.
To write the equation 1.6: n=0.16 using an exponent, we can divide both sides of the equation by 1.6 to get: n = 0.16/1.6 = 0.1
And then we can raise the base 10 to the power of n: [tex]10^n=10^{0.1}=2.511[/tex]
Hence, the equation 1.6: n = 0.16 can be written as: 1.6 = [tex]2.511^n[/tex]
And we know that this is correct because we can check that it is the equivalent by multiplying [tex]2.511^n[/tex] by itself n times which results in 1.6.
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John has the option to take the bus or a taxi to work each
day.
.
The bus costs $3. 00 per mile.
The taxi has a flat rate of
$4. 00 plus $1. 00 per mile.
Complete the blanks:
At _____miles, both the bus and the taxi will cost _____ dollars.
At 2 miles, both the bus and the taxi will cost $6.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given that the fare on bus is $3 per mile.
The taxi fare of taxi is $4. 00 plus $1. 00 per mile.
Assume that at x miles both fare will be the same.
The fare for x miles in bus is $3x.
The fare for x miles in taxi is $4 + $x
Equate to the fares:
3x = 4 + x
Subtract x from both sides:
3x - x = 4
2x = 4
Divide both sides by 2:
x = 4/2
x = 2.
The fare for 2 miles in bus is $3×2 = $6.
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5. There are 42 teachers who work in a school. On Monday, 29 teachers were present. What percentage of the teachers showed up for work?
Answer:
69%
Step-by-step explanation:
There are 42 teachers who work in a school. On Monday, 29 teachers were present. The percentage of the teachers that showed up for work will be:
= 29 / 42 × 100
= 69%
Answer:
Step-by-step explanation:
In any case where you're asked, "what percentage of A is B?" you can simply divide the number B by the A. The decimal you get is the answer. for example, if you're being asked what percentage 12 is of 25, you just divide 12 by 25 to get 0.48, which translates to 48 percent. in your case, 29/42 is 0.69 (rounded down from 0.6904761905) which equals 69%.
In a case where B is larger than A, you still do the same, only with the addition of the whole number. Ex: what percentage of 25 is 86?
86/25 is 3.44, so your answer is 344%.
Hope this helped :)
How do you prove inverse?
To prove the inverse :
In the equation expressing the function, swap out f(x) for y.Swap out x and y. To put it another way, swap out every x for a y and vice versa.Solve for y.Change y to [tex]f^{-1}[/tex] (x).You assemble the functions (that is, insert x into one function, plug that function into the suggested inverse function, then simplify) and check that you end up with simply "x" to establish (or refute) that two functions are the inverses of one another. The functions are inverses if you get x; otherwise, they are not.
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Could someone pls help me solve this ive been struggling for the past hour.no calculator allowed but im allowed a trigonometric circle.thx
The numeric value for each trigonometric expression is given as follows:
3. [tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \frac{5}{4}[/tex]
4. [tex]\frac{\sin{\left(\frac{\pi}{4}\right)}}{\cos^2{\left(\frac{\pi}{3}\right)}} = 2\sqrt{2}[/tex]
How to obtain the numeric value for the trigonometric expressions?The first trigonometric expression for this problem is defined as follows:
[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)}[/tex]
The numeric value of each term of the expression is given as follows, using equivalent angles on the trigonometric circle:
[tex]\sin{\left(-\frac{5\pi}{6}\right)} = \sin{\left(2\pi - \frac{5\pi}{6}\right)} = \sin{\left(\frac{7\pi}{6}\right)} = -\sin{\left(\frac{\pi}{6}\right)} = -\frac{1}{2}[/tex] (negative to positive, then find equivalent of the third quadrant angle on the first).[tex]\cos{\left(\frac{2\pi}{3}\right)} = -\cos{\left(\pi - \frac{2\pi}{3}\right)} = -\cos{\left(\frac{\pi}{3}\right)} = -\frac{1}{2}[/tex] (cosine on the second quadrant is negative).[tex]\cos{(-\pi)} = \cos{(\pi)} = -1[/tex] (cosine is an even function).Hence:
[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \left(-\frac{1}{2}\right)^2 + 1 = \frac{1}[4} + 1 = \frac{5}{4}[/tex]
For item 4, the angles are on the first quadrant, hence:
[tex]\sin{\left(\frac{\pi}{4}\right)} = \frac{\sqrt{2}}{2}[/tex][tex]\cos{\left(\frac{\pi}{3}\right) = \frac{1}{2}[/tex]Hence the numeric value of the expression is given as follows:
[tex]\frac{\frac{\sqrt{2}}{2}}{\left(\frac{1}{2}\right)^2} = 4 \times \frac{\sqrt{2}}{2} = 2\sqrt{2}[/tex]
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The three steps which Patel could use to solve the quadratic equation include the following:
A. 8(x² + 2x + (2/2)²) = -3 + 8.
B. x = -1 ±√5/8
E. 8(x² + 2x) = -3.
How to solve the quadratic equation?In order to solve the given quadratic equation, we would use the completing the square method as follows;
Separating the variables in the quadratic equation from constant, we have the following;
8x² + 16x + 3 = 0
8x² + 16x = -3
By factorizing the common variables in the quadratic equation from constant, we have the following;
8(x² + 2x) = -3 (step 1).
By completing the squares in the brackets and then balancing the expression on the right-hand side, we have the following;
8(x² + 2x + (2/2)²) = -3 + 8 (step 2).
8(x² + 2x + 1) = -3 + 8
8(x + 1)² = 5
Dividing both sides of the quadratic equation by 8, we have the following;
(x + 1)² = 5
Taking the square root of both sides of the quadratic equation, we have the following;
(x + 1) = ±√5/8
x = -1 ±√5/8 (step 3).
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•35 POINTS• don’t explain.
SSS
SAS
ASA
SAA
HL
Reason:
The tickmarks tell us that the pair of hypotenuses are congruent.
The shared horizontal sides at the bottom are the pair of congruent legs of the right triangles. Therefore, we can use the hypotenuse leg (HL) theorem. This theorem only works for right triangles.
You decide to make 10 lb of a peanut-and-raisin mixture to sell at the class snack sale. You can buy peanuts for $2.50 per pound and raisins for $1.75 per pound. If you want to sell the mixture for $2 per pound, how many pounds of peanuts and how many pounds of raisins should you use
On solving the provided question, we can say that by linear equation 10/3 pounds of peanuts and how many pounds of raisins should you use.
What is a linear equation?A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
the linear equation that is formed is
10p +7 (10 - p) = 80
10p + 70 - 7p = 80
3p = 70
p = 10/3
10/3 pounds of peanuts and how many pounds of raisins should you use
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Find the value of xx in the equation below.
11=
11=
\,\,x -6
x−6
Answer:
Find the value of xx in the equation below.
11=
11=
\,\,x -6
x−6
Step-by-step explanation:
The length of ome material i 8. 3m correct to 1 decimal place. Write the error interval for the length ,x, of the material
The error interval for the length ,x, of the material is [8.25, 8.35)
We know that error interval is nothing but the limits of accuracy when a number has been rounded.
It is the range of possible values that a number could have been before a number was rounded.
Here, The length L of a some material is 8.3 meters.
The length of the material has been rounded to 8.3 to one decimal place.
The number below 8.3 is 8.2 and the number above is 8.4
Consider a half way between 8.2 and 8.3 for the lower bound and half way between 8.3 and 8.4 for the upper bound.
This means, the length of the material must have been between 8.25 meters and 8.35 meters to round to 8.3 meters to one decimal place.
Therefore, the required error interval would be 8.25 ≤ x < 8.35
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This home work is due tonight but I don’t understand anything? Pls help!
Total distance travelled by the family in the truck is 497.98 miles
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
The rental of the truck has a base cost of $49.95, and $1.19 per mile. The average gas mileage is 18 miles per gallon.
Let us assume the total distance travelled was x miles, hence:
Total gas consumed = x miles / 18 miles per gallon = x/18 gallons
The cost is $3.89 per gallon, hence:
Total cost of gas = $3.89 per gallon * x/18 gallons = 3.89x/18
Total cost of journey = 1.19x + 3.89x/18 + 49.95 = 2531x/1800 + 49.95
If $724.85 was charged, hence:
724.85 = 2531x/1800 + 49.95
x = 497.98
Total distance is 497.98 miles
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Given the following set of numbers, use the measures of central tendency to
identify the type of distribution. Defend your answer.
70 67 75 60 67 65
The measure of the central tendency is 67 as the data in the set are integers.
What is a central tendency?A single number that seeks to characterize a set of data by pinpointing the center position within that set of data is referred to as a measure of central tendency.
As a result, measures of central location are occasionally used to refer to measures of central tendency. They also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.
Given, A data set 70, 67, 75, 60, 67, 65.
Arranging the data set in ascending order,
60, 65, 67, 67, 70, 75.
Now, The mean of the set is (60 + 65 + 67 + 67 + 70 + 75)/6.
= 67.33.
Mode of the data set 67.
So, The central tendency of the data set is 67 as the data in the set are all integers.
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Captain Kevin has a ship, the H. M. S. Khan. The ship is two furlongs from the dread pirate Ben and his merciless band of thieves. The Captain has probability \dfrac{3}{5} 5 3 of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability \dfrac{1}{5} 5 1 . If both fire their cannons at the same time, what is the probability that the Captain hits the pirate ship, but the pirate misses?
Probability that the Captain does NOT hit the pirate's ship × Probability that the pirate hits the Captain's ship = (2/5) × (1/5) = (2/25) = 0.08
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true.
The probability that the pirate hits the Captain's ship, but the Captain misses
= 2/25) = 0.08
P(C) = (3/5) is the likelihood that the captain will strike the pirate ship.
P(C') = 1 - (3/5) = (2/5) is the probability that the captain will miss the pirate ship.
P(p) = (1/5) is the likelihood that the pirate will sink the captain's vessel.
P(p') = 1 - (1/5) = (4/5) is the probability that the pirate will miss the captain's ship.
The likelihood that the pirate will hit the captain's ship while the captain misses is increased if they both fire their cannons at the same moment.
P(C' n p) is he needed probability.
P(C' n p) = P(C') P since the two events are independent of one another (p) The likelihood that the pirate will sink the captain's vessel but that the capain will miss = (Chance that the Captain misses the pirate's ship) (Chance that the pirate hits the Captain's ship) = (2/5) × (1/5) = (2/25) = 0.08
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Can someone help me please?
Answer:
(-3, -2)
Step-by-step explanation:
Notice how the lines intersect? that exact point is the solution.
Find the value of each trigonometric ratio.
tan A
39
15
36
B
The value of each trigonometric ratio is given by :
sin A = 5/13 , cos A = 12/13, tan A = 5 / 12
cosec A = 13 /5 , sec A = 13/12 , cot A = 12 /5.
As given in the question,
Let us consider a triangle be ABC,
Figure is attached.
Side length is given by:
AC = 39
AB = 36
BC = 15
AC represents the longest side
( 36 )² + (15)² = (39)²
⇒AB² + BC² = AC²
By Pythagorean triplets ABC is right angled triangle.
All trigonometric ratio with respect to angle A is given by :
sin A = BC / AC
= 15/39
= 5/13
cos A = AB / AC
= 36 /39
= 12 /13
tan A = BC / AB
= 5 /12
cosec A = 1/ sin A
= 13 /5
sec A = 1/ cos A
= 13 /12
cot A = 1 / tan A
= 12 /5
Therefore , the value of all six trigonometric ratio is equal to
sin A = 5/13 , cos A = 12/13, tan A = 5 / 12
cosec A = 13 /5 , sec A = 13/12 , cot A = 12 /5.
The above question is incomplete , the complete question is :
Find the value of each trigonometric ratio tan A
Figure is attached.
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When filling your gas tank, if you pay c dollars for g gallons of gas, you have the following table.
g c
4 15.80
8 31.60
11 43.45
15 57.25Choose all of the following statements that are true.
Select one or more:
a.
The range is {15.80, 31.60, 43.45, 57.25} .
b.
The set of independent values is {15.80, 31.60, 43.45, 57.25}.
c.
The range is {4, 8, 11, 15}.
d.
none of these
e.
The set of independent values is {4, 8, 11, 15}.
The two statements that are true about the table are:
A) "The range is {15.80, 31.60, 43.45, 57.25} ."
B) "The set of independent values is {4, 8, 11, 15}."
Which statements are true?Here we have the table for number of gallons and the costs of these:
g c
4 15.80
8 31.60
11 43.45
15 57.25
The statements that are true about that table are:
"The range is {15.80, 31.60, 43.45, 57.25} ."
This is true, the cost is the output of the table, thus, the range is that.
"The set of independent values is {4, 8, 11, 15}."
This is also called the domain, which is the input, in this case, the number of gallons of gas.
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Range of 63, 42, 28, 45, 36, 48, 32, 40, 57, 49
a)
b)
2
Complete the prime factor trees for 24 and 84:
24
2
||||
6
2
84
7
2
3
What is the Lowest Common Multiple of 24 and 84?
4
6
The prime factor trees for 24 and 84 are attached in the image below. The Lowest Common Multiple of 24 and 84 is 168.
What are prime factors?A natural number other than 1 whose only factors are 1 and itself is said to be a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). A prime factor is a natural integer, other than 1, whose sole factors are itself and 1. Actually, 2, 3, 5, 7, 11, and so forth are the first few prime numbers. The term "Lowest Common Multiple" refers to the common multiple of two or more natural integers that is the lowest (LCM).
The prime factors of 24 are: 2,2,2 and 3.
The prime factors of 84 are: 2,2,3 and 7.
Now, The Lowest Common Multiple (LCM) of 24 and 84 is calculated using the prime factors of both the numbers.
LCM= 2*2*2*3*7= 168
Hence, The Lowest Common Multiple of 24 and 84 is 168.
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If 23 jugs of water fills 184 cups how many cups will fill one jug show your math
Answer:
To find out how many cups a single jug of water fills, you can divide the total number of cups filled by the number of jugs:
184 cups / 23 jugs = <<184/23=8>>8 cups/jug
This means that one jug of water fills 8 cups.
Step-by-step explanation:
Please help me! I don't understand
Answer: 12
Step-by-step explanation:
The smaller triangles on the right can be proven congruent, so the other side also equals 6. 6+6=12
Find the equation of a line in General form passes through the points (7,5) and (-9,5)
Answer:
Step-by-step explanation:
54×54
A dishwasher at a restaurant washes 9 forks. These forks represent 4% of the forks owned by the restaurant. How many forks does the restaurant own?
Answer:
The restaurant owns 225 forks
Step-by-step explanation:
We can get our answer by displaying as an equality
9 to 4/100
x to 100/100
You can multiply 4 by 25 to get 100 so to get the amount of forks, multiply 9 by 25
9 * 25 = 225
Answer:
225 forks
Step-by-step explanation:
9 to 4/100
x to 100/100
Multiply 4 by 25 to get 100 so to get the number of forks, multiply 9 by 25!
9 * 25 = 225
Hope this helps.
four-part spinner is spun once. spinner with four parts labeled Q, R, S, and T List the sample space for the experiment. S = {Q, R, R, T} S = {Q, R, S, T} S = {R, A, T} S = {S, Q, Q}
The list of the sample space is s = {Q, R, S, T}. Option B is the correct option.
What is the sample space?
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.
The random experiment's sample spaces are written in curly brackets, "{ } ".
Given that a spinner wheel has four parts. It is labeled with the names Q, R, S, and T.
The elements of sample space are Q, R, S, and T.
The sample space is a set, thus write the elements in curly brackets.
The sample space is s = {Q, R, S, T}.
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P=-3w+9 solve for w
Pls help
Isolating for a variable: rearranging an equation so that a variable is on its own. This is done by performing inverse operations until a variable is isolated.
[tex]P-9=-3w+9-9[/tex]
[tex]p-9=-3w[/tex]
[tex]\frac{p-9}{-3}=\frac{-3w}{-3}[/tex]
[tex]-\frac{P-9}{3} =w[/tex]
A four-part spinner is spun once.
List the sample space for the experiment.
S = {Q, R, R, T}
S = {Q, R, S, T}
S = {R, A, T}
S = {S, Q, Q}
The sample space for the experiment, S= {Q, R, S, T}.
What is Sample Space in an Experiment?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given:
From the Spinner we can see four portions as
Q(Orange)
R(Green)
S(Blue)
T(Purple)
So, if the spinner spined then it will point Q, R, S or T which is the Sample space for the Spinner.
Hence, the Sample space is {Q, R, S, T}.
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Answer: B: S = {Q, R, S, T}
Step-by-step explanation:
This is the only answer listed with the letters on the spinner.
What is a sine ratio of an acute angle?
The sine of an acute angle in a right triangle is the ratio of the angle of the triangle to the opposite side of the hypotenuse.
Trigonometric ratios:
Trigonometric ratios are the ratios of the lengths of the sides of a triangle. These ratios in trigonometry relate the aspect ratio of a right triangle to each angle. A basic trigonometric ratio is the ratio of sin, cos, and tan, or the ratio of sin, cos, and tangent. Other important trigonometric ratios cosec, sec, and cot can be derived from sin, cos, and tan, respectively.
Acute Sine Ratio:
The tangent function examines the ratio of his two legs of a right triangle. You can also use the ratio of leg length divided by hypotenuse length.
In a right triangle, each angle has an opposite side and an adjacent side. And there is always a hypotenuse. On the opposite side and the hypotenuse we are dealing with the sine ratio. The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse. In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.
Let's examine some properties of the sine ratio using the Pythagorean theorem. For a right triangle, let the lengths of the triangle be a, b, and c. where a is the length of the other side of A and b is the length of the other side of B.
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How do you decide which technique to use when solving an equation?
Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Here,
Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.
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is y = 1/3x + 4 proportional