The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.
We have:
cos²θ + sin²θ = 1
Since sine is negative and cosine is positive, we know that:
sinθ = -sqrt(1 - cos²θ)
Substituting cosθ = 3√(2)/2, we get:
sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2
Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.
Since cosine is positive in the fourth quadrant, we have:
cos⁻¹(3√(2)/2) = π/4
Substituting this value, we get:
sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4
Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
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What are the values of x and y?
X=
Y=
Answer:
X = 6
Y = 17
Step-by-step explanation:
The points GHIJ for a cyclic quadrilateral.
The sum of opposite angles of a cyclic quadrilateral is 180°
So
∠J + ∠H = 180°
⇒ 6y + 78° = 180°
⇒ 6y = 180° - 78°
⇒ 6y = 102°
⇒ y = 102°/6
⇒ y = 17°
Similarly for angle x
∠I + ∠G = 180°
⇒ 16x + 14x = 180°
⇒ 30x = 180°
⇒ x = 180°/30
⇒ x = 6°
Denise is designing the seating arrangement for a concert at an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Explain to Denise how to create an equation to predict the number of seats in any row. Then using your equation. show your work to determine the number of seats in row 18.
Answer:113
Step-by-step Explanation:
To create an equation to predict the number of seats in any row, we need to start by defining a few variables:
Let's call the number of seats in the first row "a".
Let's call the number of additional seats in each row after the first row "d".
Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:
d = 6
We also know that the first row has 11 seats, so we can set a equal to 11:
a = 11
To find the number of seats in any row, we can use the following formula:
number of seats in a given row = a + (n - 1) * d
Where "n" is the number of the row we are interested in.
Using this formula, we can find the number of seats in row 18:
number of seats in row 18 = 11 + (18 - 1) * 6
= 11 + 102
= 113
Therefore, there are 113 seats in row 18.
v=? image attached please help
Answer:
v=12
Step-by-step explanation:
9/v = 6/8
9 = 6v/8
72= 6v
v= 12
Answer:
v = 12
Step-by-step explanation:
Now we have to,
→ Find the required value of v.
Given proportion,
→ (9/v) = (6/8)
Then the value of v will be,
→ (9/v) = (6/8)
→ 9 × 8 = 6 × v
→ 72 = 6v
→ 6v = 72
→ v = 72/6
→ [ v = 12 ]
Hence, the value of v is 12.
−9⋅(5j+k)
Apply the distributive property to create an equivalent expression.
Answer:
-45j - 9k
Step-by-step explanation:
-9(5j + k)
-9(5j) + -9(k)
-45j - 9k
Helping in the name of Jesus.
A local maximum of the function f(x) occurs for which x-value? A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 16, negative 2, 0, 6, 0, negative 2. Group of answer choices –4 –3 –2 –1
There is a local maximum at the point (-1,6), therefore, for x = -1
option D is correct
What do we mean by local maximum point?A local maximum point on a function is described as a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
We see that the function adopts values smaller than 6 to the left of x = -1, and to the right of it:
(-3, -2), (-2, 0) to the left of x = -1 where the function's value is 6
and (0, 0), and (1, -2) to the right of x = -1
Therefore, we can say that the pints (-1, 6) is a maximum, that is for x = -1, where the function renders a value of 6.
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Describe two trends you can find in the graph below. Use calculations and numbers to support your thinking.
The two trends on the graph are:
Positive correlationNegative correlationDescribing the two trends on the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The two trends on the graph are:
Positive correlationNegative correlationFor the positive correlation, we have
Upward trend from January till August
This is because the function values increase approximately in this domain
For the negative correlation, we have
Upward trend from August till December
This is because the function values decrease approximately in this domain
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Find a pair of integers whose difference gives zero.
A)8 and 1
B)8 and 2
C)8 and 3
D)-8 and -8
Answer:
Answer is D.
Please mark my answer as Brainliest if you found this one helpful.
the diagram below shows all the possible totals from adding the results of rolling a two fair dice.
a) whats the probability of rolling a total of 5? give ur answer as a fraction in its simplest form.
b) if you rolled a pair of fair dice 180 times, how many times would you expect to roll a total of five?
Answer:
Expected number of times to roll a total of 5 = Probability of rolling a total of 5 x Total number of rolls
= (1/9) x 180
= 20
Step-by-step explanation:
The diagram is not visible in the question. However, I can provide a general method to solve the problem.
a) To find the probability of rolling a total of 5, we need to count the number of ways we can get a sum of 5 and divide it by the total number of possible outcomes. From the diagram, we can see that there are four ways to get a sum of 5: (1,4), (2,3), (3,2), and (4,1). Since each die has six equally likely outcomes, there are 6 x 6 = 36 possible outcomes in total. Therefore, the probability of rolling a total of 5 is:
Probability of rolling a total of 5 = Number of ways to get a total of 5 / Total number of possible outcomes
= 4/36
= 1/9 (in its simplest form)
b) If we rolled a pair of fair dice 180 times, the expected number of times we would roll a total of 5 can be calculated as follows:
Expected number of times to roll a total of 5 = Probability of rolling a total of 5 x Total number of rolls
= (1/9) x 180
= 20
If sun x= 4/5 what is the value of b? 22.5 3b
By following trigonometry identities we get b equals **7**
Define trigonometry identities?Trigonometric identities are equations involving trigonometric functions that hold for all possible values of the variables that occur and for which both sides of the equation are specified. These identities come in use if trigonometric function-based formulas need to be made simpler 1.
There are numerous distinctive trigonometric identities that involve a triangle's side length and angle 2. Only the right-angle triangle 2 is covered by the trigonometric identities. The three main trigonometric functions are sine, cosine, and tangent, while the other three are cotangent, secant, and cosecant.
Some of the most popular trigonometric identities are listed below:
sin²(x) + cos²(x) = 1
- tan(x) = sin(x)/cos(x)
- cot(x) = cos(x)/sin(x)
- sec(x) = 1/cos(x)
- csc(x) = 1/sin(x)
- sin(2x) = 2sin(x)cos(x)
- cos(2x) = cos²(x) - sin²(x)
- tan(2x) = (2tan(x))/(1 - tan²(x))
The use of these identities
.One angle in a right triangle is x°, where sin x°=4/5 . With this knowledge, we can use the inverse sine function (arcsin) to calculate the value of x, which gives us x = arcsin(4/5) = 0.9272952180016122 radians .
In addition, we are informed that NL = 22.5 and NM = 3b. We can get the value of LM, which is equal to√(NL2 + NM2), using the Pythagorean theorem. 2. When the given values are substituted, we obtain LM = √((22.5)2 + (3b)2) = sqrt(506.25 + 9b2).
LM is equivalent to b times cos(x°) since it is the polar opposite of the right angle. Consequently, we can write:
b cos(x°) = √(506.25 + 9b²)
Substituting x = arcsin(4/5), we get:
b cos(arcsin(4/5)) = √(506.25 + 9b²)
Simplifying this equation using trigonometric identities, we get:
b * (√1 - sin²(arcsin(4/5)) = sqrt(506.25 + 9b²)
b × (√(1 - (4/5)²)) = sqrt(506.25 + 9b²)
b× (√(1 - 16/25)) = sqrt(506.25 + 9b²)
b× (√(9/25)) = sqrt(506.25 + 9b²)
3b/5 = √(506.25 + 9b²)
Squaring both sides of the equation, we get:
9b²/25 = 506.25 + 9b²
Solving for b, we get:
b = 7
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Need the right answer for problem 12
The distance of the point from the line is d =
Given data ,
Let the point be P ( 1 , 1 )
Let the equation of line be represented as e
where A ( -5 , 0 ) and B ( 1 , -2 ) lies on the line
So , slope m = ( 0 + 2 ) / ( -5 - 1 )
m = 2/-6
m = -1/3
So , the equation of line is
y - 0 = ( -1/3 ) ( x + 5 )
y = ( -1/3 ) ( x + 5 )
( 1/3 )x + y + 5/3 = 0
Now , the Distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
On simplifying , we get
D = | ( 1/3 )( 1 ) + ( 1 ) ( 1 ) + ( 5/3 ) | / √[ ( 1/3 )² + ( 1 )² ]
D = | ( 6/3 ) + 1 | / √ [ ( 1/9 ) + 1 ]
D = 3 / ( 10 ) / 9
D = 27/10
D = 2.7 units
Hence , the distance is 2.7 units
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Select the correct answer from each drop-down menu.
Consider the expression below.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions. 2. If the expression is set equal to 10x + 7, there would be no solution. 3. One solution.
What is like term?In algebra, like terms are those in which the same variables are raised to the same powers. For instance, the fact that the variable x has been raised to the first power makes the expressions 3x, 2x, and -5x similar. Related expressions include 4y², -y², and 7y², all of which have the variable y increased to the second power. By maintaining the variable and its exponent the same, like terms can be joined by adding or removing the coefficients (the numbers placed in front of the variables).
The given expression is given as 12x - 6x + 4x + 5 = 10x + 5.
Simplifying the expression we het 10 x + 5.
1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions as it will always be true.
2. If the expression is set equal to 10x + 7, there would be no solution, as the variable is eliminated.
3. If the expression is set equal to -10x + 5, there would be only one solution.
10x + 5 = -10x + 5
20x = 0
x = 0
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The prism below is made of cubes which measure
1
4
of an inch on one side. What is the volume?
A 3D illustration view of a blank tabular with 5 rows and 2 columns.
Note: Figure is not drawn to scale.
A.
15
32
cubic in
B.
5
2
cubic in
C.
30
cubic in
D.
15
2
cubic in
The volume of the prism is B. 2.5 cubic inches.
How to calculate the volumeAccording to the question, the prism measures 1/4 of an inch on one side. Now we will assign values to the length, width, and height of this prism as follows:
Length = 2 × 1/4
Width = 5 × 1/4
Height = 3 × 1/4
= 2/4 + 5/4 + 3/4
= 2 2/4
= 2.5 cubic inches.
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A $162,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $14,650 annual income from the investments, how much should the bank invest in bonds? (It's okay to use your calculator to solve the system you set up on this problem.
The bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
How to solve for the amount(162,000 - 2x) is invested in mortgages.
The annual income earned from the bond investment is:
0.09x
The annual income earned from the CD investment is:
0.07x
The annual income earned from the mortgage investment is:
0.10(162,000 - 2x) = 16,200 - 0.20x
The total annual income earned from the investments is:
0.09x + 0.07x + 16,200 - 0.20x = 14,650
Simplifying and solving for x, we get:
-0.04x + 16,200 = 14,650
-0.04x = -1,550
x = 38,750
Therefore, the bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
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Study the system of equations below.
x + y =-4
x - y = 10 What is the solution to the system of
equations?
A (-4, 10)
B (10, 4)
C(3,-7)
D(7,-3)
Answer:
Option C
Step-by-step explanation:
To solve this system of equations, we can use the method of elimination. Adding the two equations together eliminates the y variable, and we get:
2x = 6
Simplifying, we get:
x = 3
Substituting x = 3 into either of the original equations, we get:
3 + y = -4
Solving for y, we get:
y = -7
Therefore, the solution to the system of equations is (3, -7), which is option C.
i need an answer for this with explanation
Answer: 76
Step-by-step explanation:
The surface area is all of the area faces added together
The blue is 5*4 but I have 2 of those faces so I multiply by 2
(5*4*2)=40
The red is 4*2 but I have 2 of those faces so I multiply by 2
(4*2*2)=16
The green is 5*2 but I have 2 of those faces so I multiply by 2
(5*2*2)=20
Add those together
A=40+16+20=76
Angles in parallelograms maze
The values of angles x in the parallelogram maze are calculated below
Calculating the angles x in the parallelogram mazeThe question is solved by taking the shapes from left to right on each row
So, we have
x + 65 = 180 --- adjacent angles
x = 115
x + 103 = 180 --- adjacent angles
x = 77
9x = 90 --- angles in a rectangle
x = 10
x + 85 = 180 --- adjacent angles
x = 95
x + 60 = 180 --- adjacent angles
x = 120
2x = 90 --- angles in a rectangle
x = 45
x = 98 -- opposite angles in a parallelogram
3x = 81 -- opposite angles in a parallelogram
x = 27
4x + 76 = 180 --- adjacent angles
x = 26
3x = 78 -- opposite angles in a parallelogram
x = 26
8x + 68 = 180 --- adjacent angles
x = 14
4x = 72 -- opposite angles in a parallelogram
x = 18
x + 126 = 180 --- adjacent angles
x = 54
x = 90 -- opposite angles in a parallelogram
6x = 90 -- opposite angles in a parallelogram
x = 15
2x + 62 = 180 --- adjacent angles
x = 59
6x = 106 --- opposite angles in a parallelogram
x = 17.6
5x = 90 --- angles in a rectangle
x = 18
5x + 80 = 180 --- adjacent angles
x = 20
10x = 90 --- angles in a rectangle
x = 9
2x = 100 --- opposite angles in a parallelogram
x = 50
6x = 96 --- opposite angles in a parallelogram
x = 16
x + 105 = 180 --- adjacent angles
x = 75
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The table describes the quadratic function p(x). x p(x) -4 24 -3 9 -20 -1 -3 0 2 0 What is the equation of p(x) in vertex form? Op(x) = 2(x - 1)² - 3 p(x) = 2(x + 1)² - 3 Op(x) = 3(x - 1)² – 3 p(x) = 3(x - 1)² – 3
The equation of p(x) in vertex form is p(x) = 3(x + 1)² - 3.
Option C is the correct answer.
Since, Polynomial is an equation written as the sum of terms of the form kxⁿ.
where k and n are positive integers.
We have,
From the table,
From p(x) = 24 to p(x) = -3 the value of p(x) is decreasing and from p(x) = -3 to p(x) = 24 it is increasing.
So,
The vertex is (- 1, -3).
The vertex form of p(x).
p(x) = a ( x - h)² + k
Where (h, k) is the vertex.
Now,
(-1, -3) = (h, k)
Make (- 2, 0) = (x, p(x))
0 = a (- 2 + 1)² + (-3)
0 = a x 1 - 3
a = 3
Thus, The vertex equation of p(x).
p(x) = 3(x + 1)² - 3
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Suppose a polynomial function of degree 4 with rational coefficients has the given numbers as zeros. Find the other zeros.
1+2i, 1+√5
The other zeros are
(Use a comma to separate answers.)
Answer:
The other zeros are:
1 - 2i, 1 - √5
I need help please
I need to answer the white box i don't know the answer
The expression of the matrix row operation is 1/4 Row 1 ⇒ Row 1
Determing the matrix row operation and expressionFrom the question, we have the following parameters that can be used in our computation:
[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]
From the above matrices, we understand that
Dividing the first row of the first matrix by 4 gives the first row of the second matrix Other corresponding row elements of the second and third rows remain unchangedThis means that
row 1 = 1/4(row 1)
This in other words means that
row 1 = (row 1)/4
When these values are evaluated, we have
[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]
This means that we replace -24, -24, 12, and 20 in row 1 with -6, -6, 3 and 5
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HELP ASAP WILL GIVE BRAINLIEST
Use the graph to answer the question.
2
O
21/1/201
O
D'
IN
A
2
Determine the scale factor used to create the image.
C'
2.5
B'
D
A
11
C
2
В
B
Answer:
1/4
Step-by-step explanation:
The scaled image is 1/4 of the size of the original, we can see this as one side of the original shape is 4 units, and the scaled side is 1 unit.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
9.6
Step-by-step explanation:
sin(angle)= opposite/hypotenuse
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
X=9.6
Answer:
Step-by-step explanation:
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
sin(42°)=6.4/X
X*SIN(42°)=6.4
X=6.4/SIN(42)
X=9.6
The following playing cards are used in a game. 1, 2, 3, 4, 5, 6, 7
Find the P (not prime)
When a number is selected at random, the probability that a number that is not a prime number would be selected would be = 3/7.
How to determine the probability of a non prime numbers?Prime numbers are defined as those numbers that are greater than one that cannot be divided by a whole number apart from themselves without a remainder.
To calculate the probability of non prime numbers from a game of cards the formula for probability should be used. That is;
Probability = possible outcome/sample space
The possible outcome = 1,4,6 = 3
The sample space = 7
Therefore probability = 3/7
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The whole page Tysm plsssssss step by step btw
The sum of all the pets in the list is 11.
The average number of pets that the students own is 1.375.
How to calculate the sumIt should be noted that to find the sum of all the pets in the list, we simply add up all the values:
0 + 1 + 2 + 3 + 1 + 2 + 0 + 2 = 11
Therefore, the sum of all the pets in the list is 11.
Since Cameron asked eight of his classmates, we divide the sum of pets by 8 to find the mean:
11 ÷ 8 = 1.375
Therefore, the average number of pets that the students own is 1.375.
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The measures of center can be used to summarize the number of pets that students own. Cueton asked eight of his classmates how many pets they own. The results are listed below.
0 1 2 3 1 2 0 2
What is The sum of all the pets in the list
What is the average number of pets that the students own
Can the following list represent a complete probability model? P(2)= 1/12 P(3) = 2/3 P(4) = 1/4
Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.
What exactly is probability?The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.
=> P(2) + P(3) + P(4)
=> 1/12 + 2/3 + 1/4
=> (1 + 8 + 3) / 12
=> 12 / 12 = 1
In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.
In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.
Therefore, a complete probability model cannot be represented by this list.
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Find the value of 11 3/8 -7/8
The value of 11 3/8 -7/8 is 10 1/2
What is subtraction?Subtraction is the operation or process of finding the difference between two numbers or quantities . For examples, if out 100 students In a school , 40 are boys , the number of girls in the school is calculated by subtracting the number of boys from the total number of students.i.e 100 - 40 = 60
Solving 11 3/8 -7/8
= 91/8 - 7/8
= (91-7)/8
= 84/8
= 21/2
= 10 1/2
Therefore the value of 11 3/8 -7/8 is 10 1/2
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The reciprocal of h.C.F and lcm of two number are 1/12 and 1/312 respectively. If one of the number is 24. Find the other number?
The other number is 156.
Let a and b be two numbers, with a = 24.
We know that the product of two numbers' HCF and LCM is equal to the product of the two numbers.
So, we have:
HCF × LCM = a × b
We are given that the reciprocal of HCF is 1/12.
So, HCF = 1 / (1/12) = 12.
We are also given that the reciprocal of LCM is 1/312.
So, LCM = 1 / (1/312) = 312.
12 × 312 = 24 × b
Simplifying, we get:
b = (12 × 312) / 24 = 156
Therefore, the other number is 156.
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please help, due in an hour !!
Answer:
Step-by-step explanation:
During a game, a spinner landed on several different colors. During a game, a spinner landed on several different colors.
Considering this data, how many of the next 13 spins should you expect to land on purple?
First, we need to find the experimental probability (probability using the provided data) of landing on purple.
Experimental probability of purple = # of purple / total #
Experimental probability of purple = 2 / 26 = 1 / 13 (simplified)
Next, we need to consider the probability in the context of 13 spins, as per the question. Our experimental probability tells us that 1 out of every 13 spins will be purple. Therefore, we can expect 1 of the next 13 spins to land on purple.
Answer: 1 spin
Hope this helps!
There are 16 green balls and 4 white balls in a bag. Four balls are drawn randomly from the bag. Let X be the number of white balls drawn.
(a) Find the expectation and variance of X.
Answer:
the variance of X is 0.126.
Step-by-step explanation:
The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:
P(X = k) = (nCk)(N-nCk) / (NCk)
where C denotes the combination function.
(a) Expectation of X:
E(X) = np = nK/N = (4/20) * 4 = 0.8
Therefore, the expected number of white balls drawn is 0.8.
(b) Variance of X:
Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126
Therefore, the variance of X is 0.126.
Answer:
The expected number of white balls drawn is 0.4 and the variance of X is 0.24.
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST
what will the coordinates be if Point A (-4,-5) of the trapezoid was reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction.
Answer:
If point A (-4,-5) of the trapezoid is reflected across the y-axis, the x-coordinate will change sign while the y-coordinate remains the same. This gives us the point A' (4, -5).
Next, if we shift the point A' by -6 units in the x-direction and 7 units in the y-direction, we get the new point A":
A" = (4 - 6, -5 + 7) = (-2, 2)
Therefore, the coordinates of point A after it is reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction are (-2, 2).
Step-by-step explanation:
Answer:
(-2, 2)
Step-by-step explanation:
I did the test
Hope this helps :)
