Question 7 Write the ratios for sin X and cos X. X 12 5 20 sin X- O sin X= √√119, cos X = 5 O sin X = √119 12 5 -, cos X= 12 √√119 sin X- B ,cos X= 5 119 2, cos X = 119 119 119, co
Answers
Ratios help to establish the relationship between them by a comparison of the size, quantity, or degree. In trigonometry, we use ratios to establish a relationship between different angles in a right-angled triangle.In this case, we are to write the ratios for sin X and cos X. We have;sin X- O
sin X= √√119,
cos X = 5O
sin X = √119 / 12 5 / - cos X
= 12 / √√119 119 / 2,
cos X = 119 / 119 119 / 119, co
To obtain the ratio of sin X, we divide the opposite side by the hypotenuse: sin X = opposite / hypotenuse
For X = 12, we have;
sin X- O
sin X= √√119 = opposite / hypotenuse;
Opposite side = √119,
hypotenuse = 12
sin X = √119 / 12
For X = 5,
we have;sin X= 5/ √√119
To obtain the ratio of cos X, we divide the adjacent side by the hypotenuse: cos X = adjacent / hypotenuse
For X = 12,
we have;cos X = 5 / 12
For X = 5,
we have;cos X= 12 / √√119
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Related Questions
¿3.r2y es un monomio?
Answers
Answer:
A
Step-by-step explanation:
EDGE
10) Write the explicit formula for the arithmetic sequence below and use it to find the 52nd term:
37,29,21,13
Answers
The sequence of arithmetic sequence be 37, 29, 21, 13 then the 52nd term exists 445.
What is meant by arithmetic sequence?The term "arithmetic sequence" refers to an ordered collection of numbers with a common difference between each succeeding word.
Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant.
An arithmetic sequence, also known as an arithmetic progression, is a set of numbers where each term differs from the one before it. The arithmetic sequence formula makes it simple to determine a term's value and the sequence's common difference.
The AP's first period is 37.
Common difference = 37 - 29 = 29 - 21 = 8.
Let the equation of arithmetic sequence be a + ( n - 1 )d, where d is the common difference and a is the first term.
To find the 52nd term, we get
substitute the values in the above equation, we get
⇒ 37 + ( 52 - 1 )8
simplifying the above equation, we get
⇒ 37 + ( 51 )8
⇒ 37 + 408
⇒ 445
Therefore, the 52nd term of the arithmetic sequence exists 445.
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in a bag, there are 4 red shapes, 5 blue shapes, and 3 yellow shapes. there is one triangle, one square, and one circle in each group. there is 1 red and blue rectangle, and 1 blue hexagon. what is the probability of selecting a shape that is blue or a triangle?
Answers
Explanation:
The general addition rule is as follows: P(a or b) = P(a) + P(b) - P(a and b). In the context of this problem, the probability that selecting a shape that is blue is 5/12. The probability of selecting a triangle is 3/12. The probability that the shape is blue and a triangle is 1/12. If we substitute these values into the equation, we get P(B or T) = 5/12 + 3/12 - 1/12 = 7/12. We subtract the probability of the shape being blue and a triangle because we do not want to count a shape twice.
(1 point) A coin, thrown upward at time t = 0 from an office in the Empire State Building, has height in feet above the ground t
seconds later given by
h(t) = -16t2 + 48t+448 = -16(t – 7)(t + 4).
(a) From what height is the coin thrown? Include units in your answer. 512 feet
help (units)
(b) At what time does the coin hit the ground? Include units in your answer.
help (units)
Answers
Answer:
The coin was thrown from 448 feet
Time to hit the ground is 7 seconds
Step-by-step explanation:
Given
\(h(t) = -16(t - 7)(t + 4)\)
Solving (a): Height when coin is thrown
At this point t = 0
So, we have:
\(h(0) = -16(0 - 7)(0 + 4)\)
Solve expressions in the brackets
\(h(0) = -16(-7)(4)\)
\(h(0) = 448\)
Hence, the coin was thrown from 448 feet
Solving (b): Time to hit the ground
At this point, h = 0.
So, we have:
\(0 = -16(t - 7)(t + 4)\)
Reorder
\(-16(t - 7)(t + 4) = 0\)
Divide both sides by -16
\((t - 7)(t + 4) = 0\)
This gives:
\(t - 7 = 0\) or \(t + 4 = 0\)
\(t = 7\) or \(t = -4\)
Since, time can't be negative;
\(Time = 7\ seconds\)
Consider the following data set
5
6
7
15
22
Be careful with this question tick every correct option note that the 50 th percentile would be the middle numbe a. the mean is 11.00 b. the mean is 14.70 c. The median (the 50 th percentile) is 7.00 d. The median (the 50th percentile) is 10.75
Answers
a. The mean is 11.00 (correct)
b. The mean is 14.70 (incorrect)
c. The median (the 50th percentile) is 7.00 (correct)
d. The median (the 50th percentile) is 10.75 (incorrect)
5, 6, 7, 15, 22
The mean is calculated by adding up all the numbers and dividing by the total count:
Mean = (5 + 6 + 7 + 15 + 22) / 5 = 11
So option a. The mean is 11.00 is correct.
The median (the 50th percentile) is the middle number when the dataset is arranged in ascending order. Since we have an odd number of values, the median is the middle value itself.
So option d. The median (the 50th percentile) is 10.75 is incorrect.
The median of the dataset is 7 since it is the middle number when the dataset is arranged in ascending order.
So option c. The median (the 50th percentile) is 7.00 is correct.
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When constructing a perpendicular bisector why must the compass opening be greater than 1/2.
Answers
It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.
What is perpendicular bisector?A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.
Now, consider an example;
When you wish to build a perpendicular line on a line segment, like line AB, you do the following;
Set the compass on a radius more than half the length of the line AB.Using A as your center, draw an arc above and below line AB.With the same radius and B as our center, draw additional arcs on top or below line AB to join a first arcs on the both side of the line.Join the two arc intersections to cut line AB at M.A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.
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Given that Z is a standard normal random variable, what is the probability P(Z > 1.96)?
a. 0.7745
b. 0.8413
c. 0.0919
d. 0.9332
Answers
A standard normal random variable probability is 0.0250.
The probability P(Z > 1.96) found by subtracting the cumulative probability from 1.
Using a standard normal distribution table or calculator, find the cumulative probability corresponding to 1.96, which is approximately 0.9750.
P(Z > 1.96) = 1 - P(Z ≤ 1.96) = 1 - 0.9750 = 0.0250.
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Which is a multiple of 10?
30 25 15 0
Answers
Answer:
30 is the multiple of 10.
Answer:
30
Step-by-step explanation:
Multiples of 10 would include:
10
20
30
40
50
and so on...
Ralph has a new rectangular back yard. The area of the back yard is 32 feet. The Length of the rectangle is 2 times the Width. Find the perimeter of the rectangular back yard.
Answers
Answer:
24 feet
Step-by-step explanation:
Let w represent the width of the rectangle. Then its length is 2w, and its area is ...
A = Lw
32 = (2w)(w) = 2w^2 . . . fill in the given values
16 = w^2 . . . . . . . . . . . . divide by 2
4 = w . . . . . . . . . . . . . . take the square root
8 = 2w = L . . . . . . . . . find the length
The dimensions of the yard are 8 feet long and 4 feet wide.
__
The perimeter is ...
P = 2(L +w) = 2(8 +4) = 2(12) = 24 . . . . feet
The perimeter of the rectangular back yard is 24 feet.
Question 2 of 6 View Policies Current Attempt in Progress Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____
Answers
Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.
Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____
Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.
Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)
Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14
Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.
Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w
Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w
Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.
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In the diagram, JL = 138. What is JK? (Round to two decimals if Needed)
Answers
Step by step
We can add both line segments JK and KL together to equal JL (138)
4x + 6 + 7x + 15 = 138
Combine like terms
11x + 21 = 138
Subtract 21 from both sides to isolate variables
11x + 21 - 21 = 138 - 21
11x = 117
Divide both sides by 11 to solve
X = 10.64
Now we are looking for JK which is stated to be 4x + 6
Substitute our x value in for x
4 (10.64) + 6
42.56 + 6
JK = 48.56
if a is a square matrix and a = kat where k 6= ±1, show that a = 0.
Answers
If a is a square matrix and \(a = ka^t\) where k is not equal to ±1 then a = 0.
What is the matrix?A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.
Let's assume that "a" is an n x n square matrix, where "k" is a scalar, and "a^t" is the transpose of "a".
If \(a = ka^t\), then we can multiply both sides by "\(a^t\)" to get:
\(a * a^t = k * a^t * a^t\)
Since "\(a^t\) * a" is a symmetric matrix, its transpose is equal to itself:
\(a^t * a = (a^t * a)^t\)
So, substituting this in the previous equation:
\(a * a^t = k * (a^t * a)^t\)
Since a^t * a is symmetric, its eigenvalues are real. Let λ1, λ2, ..., λn be the eigenvalues of a^t * a. Then, the eigenvalues of a * a^t are also λ1, λ2, ..., λn, so we have:
\(a * a^t = k * λ1 * I = k * λ2 * I = ... = k * λn * I\)
Where "I" is the identity matrix.
Since the eigenvalues of \(a * a^t\) are all equal, it follows that the matrix must be a scalar multiple of the identity matrix. But since k is not equal to ±1, we have:
\(a * a^t = 0 * I = 0\)
So,\(a * a^t = 0\), and since "\(a^t * a\)" is positive definite, it follows that "a = 0".
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can you explain how to solve using BAII financial calculator ? 19. Your grandmother has been putting $1000 into a savings account on every birthday since your first (that is,when you turned one.The account pays an interest rate of 3%.How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday?
Answers
The amount of money that will be in the account immediately after your grandmother makes the deposit on your 18th birthday is $29,960.28.
We need to find the amount of money that will be in the savings account after your grandmother makes the deposit on your 18th birthday.
We have the following data:
Present Value (PV) = $1000
Number of payments (N) = 18
Interest rate (I/Y) = 3% per annum.
Using the BAII financial calculator, we can find the future value of this savings account as follows:
1: Clear the calculator. Press the [2nd] [FV] key and then the [C] key.
2: Enter the present value of the savings account. Press the [1000] key and then the [+/-] key.Step 3: Enter the number of payments. Press the [18] key and then the [N] key.
4: Enter the interest rate per period. The interest rate is given in annual terms, so we need to divide it by the number of compounding periods per year. The account pays an interest rate of 3%, so we divide it by 1, since the interest is compounded annually.
Press the [3] key, then the [÷] key, then the [1] key, and finally the [%] key.
5: Calculate the future value. Press the [FV] key. The calculator should display $29,960.28 (rounded to the nearest cent).
Therefore, the amount of money that will be in the account immediately after your grandmother makes the deposit on your 18th birthday is $29,960.28.
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A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
nequals=7
pequals=0.65 xequals=6
(Do not round until the final answer. Then round to four decimal places as needed.)
Answers
The probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.
Using the binomial probability formula, the probability of x successes in n independent trials with a probability of success p can be calculated as:
P(x) = (n choose x) * p^x * (1-p)^(n-x)
where "n choose x" represents the number of ways to choose x items from a set of n items, and is calculated as:
(n choose x) = n! / (x! * (n-x)!)
So, for the given parameters nequals=7, pequals=0.65, xequals=6, we have:
P(6) = (7 choose 6) * 0.65^6 * (1-0.65)^(7-6)
= 7 * 0.65^6 * 0.35^1
= 0.3052
Therefore, the probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.
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at the mp donut hole factory, niraek, theo, and akshaj are coating spherical donut holes in powdered sugar. niraek's donut holes have radius $6$ mm, theo's donut holes have radius $8$ mm, and akshaj's donut holes have radius $10$ mm. all three workers coat the surface of the donut holes at the same rate and start at the same time. assuming that the powdered sugar coating has negligible thickness and is distributed equally on all donut holes, how many donut holes will niraek have covered by the first time all three workers finish their current donut hole at the same time?
Answers
Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.
The time it takes to coat a donut hole is directly proportional to the surface area of the donut hole.
The surface area of a sphere is given by the formula:
Surface Area = 4πr²
Here, r is the radius of the sphere.
Comparing the surface areas of the donut holes:
Niraek's donut hole: Surface Area = 4π(6²)
Theo's donut hole: Surface Area = 4π(8²)
Akshaj's donut hole: Surface Area = 4π(10²)
Now, let's find the LCM of the surface areas to determine the time it takes for all workers to finish:
LCM(144π, 256π, 400π) = 57600π mm²
This means that it will take the same amount of time for all three workers to finish their current donut holes when they have covered a total surface area of 57600π mm².
Number of donut holes = (Total surface area) / (Surface area of Niraek's donut hole)
= (57600π mm²) / (144π mm²)
= 57600 / 144
= 400
Therefore, Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.
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Amazon is offering a $1200 hiring bonus and they will pay $16 per hour for 25 hours per week. UPS is offering a $50 weekly bonus for working on Sunday and they will pay $18 per hour for 30 hours per week. Assuming you will earn the bonus from either place, how many weeks will you have to work to make the same total pay? Round your answer to the nearest whole number.
Answers
Using mathematical expressions equated to each other, it will take approximately 6 weeks to make the same total pay at Amazon and UPS.
What are mathematical expressions?Mathematically, an expression is a statement without an equation or inequality symbol.
Mathematical expressions are like phrases in the English language because they do not make complete sense.
Mathematical expressions combine variables, constants, arithmetic operators, and numbers to state values.
Amazon:Amazon's hiring bonus (fixed) = $1,200
Hourly pay = $16
The number of work hours per week = 25 hours
Amozon's total pay per week = $1,200 + $16(25)
= 1,200 + 400
UPS:UPS's weekly bonus for Sunday work = $50
Hourly pay = $18
The number of work hours per week = 30 hours
UPS's total pay per week = $50 + $18(30)
= 590
Let the number of weeks = x
Expressions:The total pay for x weeks at Amazon = 1,200 + 400x ... Expression 1
The total pay for x weeks at UPS = 590x ... Expression 2
For the total pay at both companies to be equal, Expression 1 will be equal to Expression 2:
1,200 + 400x = 590x
590x = 1,200 + 400x
190x = 1,200
x = 6 weeks
Thus, if you choose to work at either Amazon or UPS, you will need to work 6 weeks to make the same pay.
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The digit 6 in which number represents a value of 6 ones?
Answers
Answer:16.4
Step-by-step explanation:
For the diagram below, which equation is the correct use of the distance formula?
Help please guys....
Answers
The equation that portrays the correct use of the distance formula is 6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² )
Which equation is the correct use of the distance formula?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
From the diagram;
Point A (5,6)
x₁ = 5y₁ = 6Point B (11,y₂)
x₂ = 11y₂ = y₂Distance d = 6.71
Plug the given values into the distance formula.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² )
Therefore, the correct use of the formula is 6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² ).
Option D) 6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² ) is the correct answer.
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Quick math: What's 2+1-3?
Answers
Answer:
2+1=3, 3-3=0
Step-by-step explanation:
the base of a triangle is 2 feet greater in length than its height. If the area of the triangle is 40 square feet, find the length of the base and the height of the triangle.
Answers
write a recursive formula for the sequence 5, 18, 31, 44, 57 then find the next term
Answers
A recursive formula is an equation that is defined in terms of itself. The recursive formula is used to determine the next term in the sequence, as each term in the sequence is generated based on the preceding term's value.
The following is the recursive formula for the sequence 5, 18, 31, 44, 57:`a_n = a_{n-1} + 13` where `a_n` represents the nth term in the sequence. To find the next term, substitute n = 6 into the formula: `a_6 = a_{6-1} + 13 = a_5 + 13 = 57 + 13 = 70`Therefore, the next term in the sequence is 70.
The recursive formula can be used to find any term in the sequence by substituting the appropriate value of n. This is how you can write a recursive formula for the sequence 5, 18, 31, 44, 57 and find the next term.
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Is the number 1 a prime or composite number?
Explain your answer.
Answers
Answer:
prime because you can't multiply anything to get more than what you multiplied it by.
Step-by-step explanation:
Answer:
The number 1 is neither prime nor composite
Step-by-step explanation:
When the area of a rectangle is a prime number, there is only one set of possible dimensions for that rectangle. When the area of a rectangle is a composite number, there are two or more sets of possible dimensions for that rectangle.
Please help with this I nnneeeeeeeed help
Answers
The complete equation for each variable given above would be given as follows;
5.) 8²× 8⁹ = 8¹¹
6.) 5⁷×5^-⁴ = 5³
7.) X¹² × X⁰ = X¹²
How to determine the complete equation for the given variables?To determine the complete equation for the given question above, the following steps needs to be taken.
For question 5.)
8² * 8^x = 8¹¹
Here ; 2+X = 11
X = 11-2 = 9
For questions 6.)
5⁷×5^b = 5³
That is;
7+ b = 3
n = 3-7 = -4
For question 7.)
X¹² × X⁰ = X¹²
That is,
12+ n =12
n = 12-12 = 0
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Find a game on the coolmath.com (links to an external site.) site or another math game site and play it, preferably with a child, family member, or friend. give the name of the game and your experience playing it. was it fun? difficult?
Answers
To find a math game on coolmath.com or another math game site, you can simply go to the site and browse through the available games. Choose a game that seems interesting to you and fits your skill level. I can recommend a popular math game called "Number Munchers" available on coolmathgames.com.
Number Munchers is an educational game where you navigate a little green character around a grid filled with numbers. Your goal is to eat the correct numbers based on the given criteria, such as multiples of a specific number or prime numbers. The game helps improve math skills while being enjoyable.
The individual experiences with games may vary, as everyone has different preferences and levels of difficulty. I suggest trying it out with a child, family member, or friend and discussing your experiences afterward.
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True/False: When a form is created based on two or more tables, a relationship must be defined between queries.
Answers
True: When a form is created based on two or more tables, a relationship must be defined between queries.
True. When a form is created based on two or more tables, a relationship must be defined between queries in order to ensure that the form displays accurate data. Queries are used to pull data from multiple tables and present it in a single view, so it is important to define the relationships between these tables to avoid inconsistencies or errors in the displayed data. This ensures that the data from the related tables can be properly displayed and managed within the form.
When you drag and search a field from an "other" (unrelated) table, a new one-to-many relationship is created from the table in the list and the table from which you dragged the field. This relationship is established by Access, which does not enforce integrity by default.
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What is the slope of the line that passes through points A(-6, -2) and B(3, 5).
Answers
Answer:
7/9
Step-by-step explanation:
The slope of the line between two given points is found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (5 -(-2))/(3 -(-6)) = (5+2)/(3+6) = 7/9
The slope of the line is 7/9.
_____
Additional comment
The slope of a line is the same everywhere, so the slope of the segment from (x, y) to A is the same:
(y -(-2))/(x -(-6)) = 7/9 . . . . use the slope equation
9(y +2) = 7(x +6) . . . . . . . multiply by 9(x+6)
9y +18 = 7x +42 . . . . . . eliminate parentheses
7x -9y = -24 . . . . . . . subtract 9y+42
This is the standard form of the equation for the line through the two points. The slope-intercept form would be ...
y = 7/9x +8/3
How much money is pictured below?
Answers
The amount of money in the picture is $1.1.
What is money?Money simply means the medium of exchange and it's used for transactions purpose.
From the picture, there a 1dollar bill. Also, it can be seen in the picture that there are 10 1 cents.
Therefore the total amount will be the addition of the paper money and the coins. This will be:
= $1 + 10(1 cent)
= $1 + 10 cents
= $1 + $0.1
= $1.1
This is the value of the money.
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Determine the measure of each indicated angle. Show all necessary steps!
Answers
a)
We know that a 4-sided polygon's angles add up to 360 degrees
so to find x:
360-(69+118+84)=89 degrees
b)
For a 4-sided polygon we also know that the outside angles add up to 360 degree.
so to find p:
360-(100+62+106)=92 degrees
Hope it helps!
The sun is at a focus of Earth's elliptical orbit.
a. Find the distance from the sun to the other focus.
Answers
The distance from the sun to the other focus is 5.01 × 10⁹ m.
What is the distance from the sun?
(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;
2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.
(b) To express this in terms of solar radii, we set up a ratio;
(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2
Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.
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Complete question is;
The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.
Simply the expression below
(10-3i)(2-5i)
Answers
Answer:
7i and 3i
hope this helps <33
Answer:
Step-by-step explanation:
Use foil method
(10 - 3i) (2 -5i) = 10*2 + 10*(-5i) + (-3i)*2 + (-3i)*(-5i)
= 20 - 50i -6i + 15i²
= 20 - 50i - 6i + 15*(-1) {i² = -1}
= 20 - 50i - 6i - 15
= 20 - 15 - 50i - 6i
= 5 - 56i