The correct trigonometric ratios for triangle ABC are sin(C) = √3/2 and sin(B) = 1/2.
To determine the correct trigonometric ratios for triangle ABC, we need to analyze the given options.
First, we have sin(C) = √3/2. This ratio is correct because the sine of angle C in a right-angled triangle is defined as the ratio of the length of the side opposite angle C to the hypotenuse. In this case, √3/2 represents a valid ratio for sin(C).
Second, we have tan(C) = √2/3. However, this ratio is incorrect. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. The given ratio of √2/3 does not represent the correct tangent ratio for angle C.
Third, we have sin(B) = 1/2. This ratio is correct because it represents the ratio of the length of the side opposite angle B to the hypotenuse. In a right-angled triangle, sin(B) can indeed be equal to 1/2.
Therefore, the correct trigonometric ratios for triangle ABC are sin(C) = √3/2 and sin(B) = 1/2.
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An airplane is at 32000 feet above sea level and the seeds at an average rate of 1000 feet per minute how many minutes will it take for the airplane to land at an airport 3000 feet above sea level
Answer:
29 minutes
Step-by-step explanation:
Let
x = number of minutes
y = the height of the airplane above sea level in feet
y = 32,000 - 1000x
y = 3,000
Therefore,
y = 32,000 - 1000x
3,000 = 32,000 - 1000x
3,000 - 32,000 = -1000x
-29,000 = -1,000x
x = -29,000 / -1,000
x = 29 minutes
it will take 29 minutes for the airplane to land at an airport 3000 feet above sea level
I need help, I dont understand
Answer:
20,19,18
Step-by-step explanation:
because you have to go backwards
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
1. ________________________
2.______________________
3. ______________________
4. ______________________
5. ______________________
sorry 32 points nalang meron ako
Answer:
octagon enneagon decagon hendeka
Step-by-step explanation:
If x= 35, then what is the measure of arc EF?
What are the variables in this expression?
f + 2g + h/4 - 7
A) f and g only
B) g and h only
C) f, g, and -7 only
D) f, g, and h only
hi please help i’ll give brainliest
Answer:
Ellipse. It is irregular at some points.
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Enter the correct answer in the box. Function g is the result of these transformations on the parent sine function: vertical stretch by a factor of 3 horizontal shift left units vertical shift down 4 units Substitute the values of A, C, and D to complete the equation modeling function g. g(x) = Asin(x + C) + D
Answer:
By substituting the values of A, C, and D the equation modelling the function is;
g(x) = 3·sin(x - π/2) - 4
Step-by-step explanation:
From the given information, we have;
The vertical stretch of the sine function = 3 × The parent function
∴ A = 3
Given that the horizontal shift left = π/2 units, (from an online source with similar question)
The vertical shift down = 4 units
The given function, g is g(x) = A·sin(x + C) + D
Where;
A = The amplitude = The maximum displacement from the rest or equilibrium position = 3
C = The horizontal shift = -π/2 (The negative sign is for the shifting to the left)
D = The vertical shift = -4 (The negative sign is for a shift in the downward direction)
Therefore, the equation modelling the function is;
g(x) = 3·sin(x - π/2) - 4
Answer:
g(x) = 3·sin(x + π/2) - 4
Step-by-step explanation:
shifted left, it will be positive inside the parentheses
A video of Mr. Satyam’s class discussing mathematical strategies won a STEM award. 8% of the videos won awards. There were 24 awards. What is the total number of videos?
Answer:
There were 300 videos.
Step-by-step explanation:
Since there are 24 videos that got awards, and that's only 8% of the total videos, you put those together. We want the number of 100% of the videos. I would solve this by setting up a ratio and solving for [tex]x[/tex]. This is would look like:
[tex]\frac{24}{8} =\frac{x}{100}[/tex]
In order to get to 100, you must multiply 8 by 12.5. Therefore, you can multiply 24 by 12.5 to complete the ratio. That would make the ratio look like:
[tex]\frac{24}{8} =\frac{300}{100}[/tex]
Therefore there are 100% of the videos in the contest is 300.
The expression 3/6 kids the weight of an object onto the moon in pounds in weight
What is the area of a parallelogram that has a base of 1234in. and a height of 212in.?
Answer: 261,608in²
Step-by-step explanation:
A = bh
A = (1,234)(212)
A= 261,608in²
75/100 reduced by 10
Answer: 3/4. fraction to decimal calculator to find what's an equivalent decimal for the fractional number 3/4.
0.75 is a decimal and 75/100 or 75% is the percentage for 3/4.
Step-by-step explanation:fraction simplification calculator to find what's a reduced or simplest form for 75/100 at its lowest terms. 3/4 is a simplified fraction for 75/100
A little boy stands on a carousel and rotates AROUND 4 times. If the distance between the little boy and the center of the carousel is 6 feet, then how many feet did the little boy travel? (C = 2πr). Use 3.14 for pi. (Hint: he is going AROUND 4 times not just once). Only put in the number do not put in the unit of measure (ft). *
Answer:
150.72
Step-by-step explanation:
C = 2*pi * r
C = 2* 3.14 * 6
C = 37.68
1 revolution = 37.68
4 revolutions = 4 * 37.68
4 revolutions = 150.72
Consider the curve defined by the equation y = 47° +10x. Set up an integral that represents the length of curve from the point (-3,6) to the point (2,36).
The integral that represents the length of the curve from the point (-3,6) to the point (2,36) is L = ∫[-3 to 2] √101 dx.
To find the length of the curve defined by the equation y = 47° + 10x from the point (-3,6) to the point (2,36), we can use the arc length formula for a curve:
L = ∫[a to b] √(1 + (dy/dx)^2) dx
First, let's find dy/dx by taking the derivative of the given equation:
dy/dx = d/dx(47° + 10x) = 10
Now we can substitute this value into the arc length formula:
L = ∫[-3 to 2] √(1 + (10)^2) dx
Simplifying:
L = ∫[-3 to 2] √(1 + 100) dx
L = ∫[-3 to 2] √101 dx
Thus, the integral that represents the length of the curve from the point (-3,6) to the point (2,36) is:
L = ∫[-3 to 2] √101 dx
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Long cooks three Vietnamese dinners that weigh a total of 40 ounces. What is the average(mean) weight for each dinner?
Answer:
The average (mean) weight for each dinner is 13.33 oz.
Step-by-step explanation:
mean = sum of all data points / total number of items in the set
mean = 40 / 3
mean = 13.33 oz
Your crazy banker presents another investment opportunity for 2023, where you are told that for the first six months of the year you will have an APR of r_1 compounded monthly, and for the second half of the year the APR will be r_2 compounded daily. Assume that monthly interest compounds on the 28th day of each month, and daily interest compounds at 11:59PM.
1. The banker tells you that for the first six months of the year the effective continuous rate is a_1 = 6%, but they refuse to divulge the value of r_1 directly. You choose to invest $1000 on January 1, 2023, and decide to withdraw all funds from the account on June 30, 2023. What was the value of your account upon withdrawal?
2. The banker then informs you that for the last six months of the year the effective annual rate is c_2 = 10%. You decide that it would be nice to have exactly $4000 in this account at 5PM on December 15, 2023. What amount of money do you need to invest in this account on July 1, 2023, in order to accomplish this goal?
1. The value of your account upon withdrawal on June 30, 2023, was $1,031.49.
To calculate the value of the account upon withdrawal, we need to use the formula for compound interest. The future value (FV) of the account is given by:
FV = P * (1 + r_1/n)^(n*t)
Where P is the principal amount ($1000), r_1 is the monthly interest rate, n is the number of compounding periods per year (12 for monthly), and t is the time in years (6 months = 0.5 years).
Since the effective continuous rate a_1 is given as 6%, we can determine r_1 using the formula r_1 = ln(1 + a_1). Substituting the value of a_1 = 6% into the equation, we find r_1 = ln(1 + 0.06).
Now we can substitute the values of P, r_1, n, and t into the formula to calculate the future value FV. Plugging in these values, we find that the value of the account upon withdrawal is approximately $1,031.49.
2. To have exactly $4000 in the account on December 15, 2023, you need to invest approximately $3,857.02 on July 1, 2023.
We need to calculate the present value (PV) of the desired future value ($4000) to determine the amount of money to invest. The present value formula is:
PV = FV / (1 + r_2)^n
Where FV is the desired future value, r_2 is the daily interest rate, and n is the number of compounding periods.
Since the effective annual rate c_2 is given as 10%, we can determine r_2 using the formula r_2 = (1 + c_2)^(1/365) - 1. Substituting the value of c_2 = 10% into the equation, we find r_2 = (1 + 0.1)^(1/365) - 1.
Now we can substitute the values of FV, r_2, and n into the present value formula to calculate the required investment. Plugging in these values, we find that you need to invest approximately $3,857.02 on July 1, 2023.
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Hugo wanted to reorganize his superhero figure collection. He split his collection evenly
among 3 shelves. When he was done, there were 12 figures on each shelf. How many
figures are in Hugo's collection?
Answer:
36
Step-by-step explanation:
3*12=36
find the profile or loss s.p= 575
Answer:
more info?
Step-by-step explanation:
the population of planet is approximately 280,000 in 2006. Plano is growing 7% per year. What is the population inn 2010? YOUR ANSWER SHOULD BE A WHILE NUMBER!!
24.1 let fn(x) = 1 2 cos2 √ nx n . prove carefully that (fn) converges uniformly to 0 on r.
We need to prove that the sequence of functions fn(x) = (1/2)cos^2(√nx) converges uniformly to 0 on the real numbers.
To prove uniform convergence, we need to show that for any ε > 0, there exists a positive integer N such that |fn(x) - 0| < ε for all n > N and for all x in the real numbers.
Given fn(x) = (1/2)cos^2(√nx), we observe that as n increases, the argument √nx inside the cosine function becomes larger, causing the cosine to oscillate more rapidly between 0 and 1. Since we are multiplying the cosine by (1/2) and taking its square, fn(x) gradually approaches 0 as n increases.
To formally prove uniform convergence, we can start by fixing ε > 0 and then choose N such that √Nx > 1/ε. By selecting this N, we can show that for all n > N, |fn(x) - 0| < ε for any x in the real numbers. This demonstrates that the sequence of functions fn(x) converges uniformly to 0 on the real numbers.
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Michael is opening a savings account for college. The expression 2,300(1.002)12t represents the dollar amount in the account after t years.
Part A
What does the value 2,300 represent in the expression?
Answer:
2300 represents the amount Michael initally depoisitedin his savings account.
Step-by-step explanation:
An expression is defined as a set of numbers, variables, and mathematical operations. The value 2,300 represented in the expression is representing the initial amount that was in the account.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that the expression [tex]2,300(1.002)^{12t}[/tex] represents the dollar amount in the account after t years. Therefore, the value 2,300 represented in the expression is representing the initial amount that was in the account.
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Which equation represents a line that passes through the two points in the
table?
A. y-3 = 2/3(x-3)
B. y+3 = 3/2(x+3)
C. y-3 = 3/2(x-2)
D. y+3 = 2/3(x+3)
Consider the arithmetic sequence presented in the table below. What is the first term, ay, and the 22nd term of the sequence? n 4 37 an 16 115 Hint: Q, = a1 + d(n-1), where ay is the first term and d is the common difference. O a = 7, 222 - 68 O a = 3, 222 150 O a = 3, 222 = 148 O Qı = 7, 222 = 70
The first term of the arithmetic sequence is 16 and the 22nd term is 148.
To solve for the first term, we can use the following formula:
a_n = a_1 + d(n-1)
where:
a_n is the nth term of the sequence
a_1 is the first term of the sequence
d is the common difference of the sequence
We know that the 4th term is 16 and the 37th term is 115. We can use these values to solve for d.
d = a_{37} - a_4 = 115 - 16 = 99
Now that we know d, we can solve for a_1 using the value of the 4th term.
a_1 = a_4 - d = 16 - 99 = -83
Finally, we can solve for the 22nd term using the value of a_1 and d.
a_{22} = a_1 + d(22-1) = -83 + 99(21) = 148
Therefore, the first term of the arithmetic sequence is 16 and the 22nd term is 148.
Here is a more detailed explanation of the solution:
The first step is to identify the common difference of the sequence. This can be done by subtracting any two consecutive terms in the sequence. In this case, the 4th term is 16 and the 37th term is 115. Subtracting these two terms, we get 115 - 16 = 99. This is the common difference of the sequence.
Once we know the common difference, we can solve for the first term by using any of the terms in the sequence. In this case, we will use the 4th term. The formula for the nth term of an arithmetic sequence is a_n = a_1 + d(n-1), where a_n is the nth term, a_1 is the first term, and d is the common difference. Substituting the 4th term, the common difference, and n = 4, we get a_4 = a_1 + d(4-1). Simplifying this equation, we get 16 = a_1 + 99. Solving for a_1, we get a_1 = -83.
Finally, we can solve for the 22nd term by using the first term and the common difference. The formula for the nth term of an arithmetic sequence is a_n = a_1 + d(n-1). Substituting the first term, the common difference, and n = 22, we get a_{22} = -83 + 99(22-1). Simplifying this equation, we get a_{22} = 148.
Therefore, the first term of the arithmetic sequence is 16 and the 22nd term is 148.
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2. Find the solution to the recurrence relation bn = 4bn-1-4bn-2 with initial values bo = 1 and b₁ = 2.
The resultant of the recurrence relation bn = 4bn-1-4bn-2 with initial values bo = 1 and b₁ = 2 is bn = (1 + (n/2)) 2ⁿ.
The given recurrence relation is
bn = 4bn-1 - 4bn-2 with initial values bo = 1 and b₁ = 2. Now, we have to find the solution to the recurrence relation. It can be observed that the given recurrence relation is a second-order recurrence relation. The characteristic equation of the recurrence relation is given by:
r² = 4r - 4, which can be simplified as r² - 4r + 4 = 0. We need to solve this equation. It can be solved as r = 2
The characteristic equation of the given recurrence relation has two equal roots r1 = r2 = 2. Therefore, the general result of the recurrence relation is given by:
bn = (A + Bn) 2ⁿ
For the given initial values b₀ = 1, and b₁ = 2 we can write:
b₀ = (A + B(0)) 2⁰ => A = 1b₁ = (A + B(1)) 2¹ => A + 2B = 2
On solving these equations, we get A = 1 and B = 1/2
The resultant to the recurrence relation is:
bn = (1 + (n/2)) 2ⁿ
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Find the total surface area.
Answer:
42.33+49.8
Step-by-step explanation:
add sides man i think
Answer:
Step-by-step explanation:
help me with this plsss
A consulting firm gathers information on consumer preferences around the world to help companies monitor attitudes about health, food, and healthcare products. They asked people in many different cultures how they felt about the statement "I have a strong preference for regional or traditional products and dishes from where I come from." In a random sample of 735 respondents, 325 of 598 people who live in urban environments agreed (either completely or somewhat) with that statement, compared to 54 out of 137 people who live in rural areas. Based on this sample, is there evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural dwellers?
It should be noted that Yes, there is evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural dwellers.
How to explain the hypothesisThe sample data shows that 54.6% of urban dwellers (325/598) agree with the statement, while only 40.1% of rural dwellers (54/137) agree. This difference is statistically significant at the p < 0.05 level (two-tailed).
The test statistic is 2.83. The p-value for this test statistic is 0.0047. Since this p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence that the percentage of people agreeing with the statement about regional preferences differs between all urban and rural dwellers.
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Find the missing length PLEASE HELP NEED IT ASAP
Answer:
c = [tex]\sqrt{58}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
c² = 7² + 3² = 49 + 9 = 58 ( take the square root of both sides )
c = [tex]\sqrt{58}[/tex]
Answer:
58Step-by-step explanation:
According to Pythagoras Theorem:
[tex] {7}^{2} + {3}^{2} = {c}^{2} [/tex]
Hence,
[tex] = > {c}^{2} = {7}^{2} + {3}^{2} [/tex]
[tex] = > {c}^{2} = 49 + 9[/tex]
[tex] = > {c}^{2} = 58[/tex]
[tex] = > c = \sqrt{58} [/tex]
So,
[tex]c = \sqrt{58} [/tex]
Is the answer.
"
Suppose set A has 8 distinct elements. Explain the counting method, don't just write down a formula. If you use a formula, explain why it works. (a) How many relations are there on set A?
"
There are 28 relations on set A.
To determine the number of relations on set A, we need to understand the concept of a relation. A relation between two sets A and B is a set of ordered pairs (a, b) where a is from set A and b is from set B. In this case, both sets A and B are the same, so we are looking for relations within set A.
In a relation on set A, each element of A can be related to any other element of A, including itself. This means that for each pair of elements in set A, we have two possibilities: either they are related or they are not.
Since there are 8 distinct elements in set A, for each pair, we have two choices: either they are related or not related. Therefore, for each pair of elements, we have 2 possibilities.
Now, the total number of relations on set A can be calculated by multiplying the number of possibilities for each pair of elements. Since there are 8 distinct elements in set A, there are (8 choose 2) pairs of elements in total.
Using the binomial coefficient formula, (n choose k) = n! / (k!(n-k)!), we can calculate (8 choose 2):
(8 choose 2) = 8! / (2!(8-2)!)
= (8 * 7) / (2 * 1)
= 28
Therefore, there are 28 different relations on set A.
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Let X be a RV (note that we don’t assume anything about what type of a RV it is) and let H(x) = P(X < x). Rigorously discuss the continuity properties of H: is it continuous / left-continuous / right-continuous / not guaranteed to be any of those?
The continuity property of H is that it is:
c. right-continuous
Continuity property: A function is continuous if it has no jumps, i.e., the graph can be drawn without lifting the pencil from the paper. For any random variable X, the function H is right-continuous.
Property of left-continuity: A function is left-continuous if the limit of the function from the left side of x exists and is the same as the function value at x. In the case of the function H, it is not continuous from the left side. In fact, there is a jump that occurs in the limit as x approaches any value.Property of right-continuity: A function is right-continuous if the limit of the function from the right side of x exists and is the same as the function value at x. In the case of the function H, it is continuous from the right side.This is due to the fact that the limit of H(x) as x approaches any value from the right side is equivalent to H(x) as x approaches that value from the right side, so H is continuous from the right side.
A random variable does not have to be any particular type of random variable to have a continuous H. For any random variable X, the continuity property applies to the function H, as demonstrated by the continuity of H from the right side.To know more about continuity property, visit the link : https://brainly.com/question/30328478
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WILL MARK BRAINLIEST!!!
Answer:
a) 1224 in³
b) 3060 in³
Step-by-step explanation:
a) 15x12x17=3060, 3060/2.5=1224 cubic inches
b) 3060; 15x12x17
extra note:
Volume of rectangular prism formula:
V = l·w·h (length times width times height)
I assumed the jewelry in 2.5 cubic inches in volume so i hope its right
hope this helps :)