How many radians are contained in the angle AOT in the figure? Round your answer to three decimal places.
A. 0.459 radian
B. 2.178 radians
C. 1.047 radians
D. 0.955 radian
Answer:
Option C. 1.047 radians
Step-by-step explanation:
We have to find the measure of angle AOT in radians.
To convert measure of an angle from degree to radians we use the formula
[tex]\text{radians}=\frac{\pi(\text{degrees})}{180}[/tex]
= [tex]\frac{\pi(60)}{180}=\frac{\pi }{3}[/tex]
(Since measure of angle AOT is 60°)
= [tex]\frac{3.14}{3}[/tex] (since π = 3.14)
= 1.047 radians
Therefore, option C. 1.047 radians is the correct option.
Find the slopes of the asymptotes of the hyperbola with the following equation.
36 = 9x ^{2} - 4y^{2}
The given equation is a hyperbola, and by converting it to standard form we find a = 2 and b = 3. Therefore, the slopes of the asymptotes are ±3/2.
Explanation:The equation given is in the form of a hyperbola equation which could be written as [tex]x^2/a^2 - y^2/b^2 = 1.[/tex] This suggests that the transverse axis is horizontal meaning the hyperbola opens to the left and right. The slopes of the asymptotes for hyperbola is given by ±b/a.
First, we need to rewrite our equation in standard form. The equation given is [tex]36 = 9x^{2} - 4y^{2}.[/tex] To convert it into the standard form, we divide whole equation by 36 to isolate 1 on one side. This yields [tex](x^2/4) - (y^2/9) = 1.[/tex] Now, it is in the standard form of hyperbola.
By comparing it with the standard equation, we see that [tex]a^2 = 4 \ and\ b^2 = 9[/tex]which gives a = 2 and b = 3. Based on these, we can now find the slope of the asymptotes which is ±b/a = ±3/2.
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Jessica attains a height of 4.7 feet above the launch and landing ramps after 1 second. Her initial velocity is 25 feet per second. Find the angle of her launch. a. Which equation can you use with the given information to solve for ?
Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
What is the length of segment QM'?
Answer: 6 units
Step-by-step explanation:
Given: Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
Since in dilation , to calculate the distance of a point on image from center point we need to multiply scale factor to the distance of corresponding point on pre-image from center point .
Thus we have,
[tex]QM'=2\times QM\\\\\Rightarrow QM'=2\times3\\\\\Rightarrow QM'=6[/tex]
Hence, the length of segment QM' = 6 units.
Answer:
6 units
Step-by-step explanation:
Find the selling price of an item listed at $400 subject to a discounted series of $25%, 10%, and 5%
A. $256.50
B. $270.00
C. $225.00
D. $300.00
Answer:
Selling price of an item is $256.50 (A).
Step-by-step explanation:
Given : WE have given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .
To find : Find the selling price of an item.
Formula used : Selling price = marked price - discount.
Solution : We have an item listed at = $400.
Discount percentage = $25% , $10% , $5.
Discount 1 = $400 ×[tex]\frac{25}{100}[/tex] = $100.
Selling price = $400-100 = $300.
Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.
Selling price = $300-30 = $270.
Discount 3 = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.
Final selling price = $270-13.50 = $256.50.
Therefore, Selling price of an item is $256.50 (A).
Probability theory predicts that there is a 44% chance of a water polo team winning any particular match. If the water polo team playing 2 matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?
Find the slope in line perpendicular x-y=16
slope of -8 and Y intercept of (0, 12) in slope intercept form.
The three sides of a triangle are consecutive odd integers. If the perimeter of the triangle is 39 inches find the lengths of the sides of the triangle
To answer that question
Hey there! I would like some help please :) Thanks!
Determine the value of a so that the line whose equation is ax+y-4=0 is perpendicular to the line containing the points (2,-5) and (-3,2)
Kenji buys 3 yards of fabric for 7.47$. Then he realizes that he needs 2 more yards. How much will the extra fabric cost?
You are 9 miles away from home. You start biking home at a speed of 6 miles per hour.
a. write an equation. in standard form that represents your distance from home y after x hours.
b. find the y-intercept of the graph. what does this represent?
c. find the x-intercept of the graph. what does this represent?
The distance and speed are illustrations of linear equations
The standard form is [tex]\mathbf{6x + y = 9}[/tex]The y-intercept is 9The x-intercept is 1.5The given parameters are:
[tex]\mathbf{Rate = 6}[/tex]
[tex]\mathbf{Initial = 9}[/tex]
(a) The standard equation
Because the distance reduces with time, the equation is:
[tex]\mathbf{y = Initial-Rate \times x}[/tex]
This gives
[tex]\mathbf{y = 9 - 6\times x}[/tex]
[tex]\mathbf{y = 9 - 6x}[/tex]
Add 6x to both sides
[tex]\mathbf{6x + y = 9}[/tex]
(b) The y-intercept
This is the initial distance away from home.
So, the y-intercept is 9
(c) The x-intercept
Set y to 0, to calculate the x-intercept
[tex]\mathbf{6x + y = 9}[/tex]
[tex]\mathbf{6x + 0 = 9}[/tex]
[tex]\mathbf{6x = 9}[/tex]
Divide both sides by 6
[tex]\mathbf{x = 1.5}[/tex]
This is the initial time away from home.
So, the x-intercept is 1.5
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A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in.2 find the radius of the beach ball. use the formula , where a is the surface area and r is the radius of the sphere. 576 in. 48 in. 75 in. 24 in.
The given problem supplies as with the surface area of the beach ball and we are to look for the required radius. Assuming that the beach ball is perfectly shaped in the form of a sphere, then the formula for calculating the surface area of a sphere is given as:
SA = 4 π r^2
where r is the radius of the sphere and SA is the surface area which is given to be 7238 in^2
Rewriting the formula in terms of r:
r^2 = SA / 4 π
r = sqrt (SA / 4 π)
Solving for r:
r = sqrt (7238 in^2 / 4 π)
r = 24 in
Answer:
24 inches
Use the table to determine the appropriate model of the function, x 1 2 3 4 5 f(x) 15 12 9 6 3 linear quadratic cubic exponential
The appropriate model of the function is:
Linear model
Step-by-step explanation:We are given a table of values as:
x f(x)
1 15
2 12
3 9
4 6
5 3
Clearly we could observe that with each increasing value of x the value of function decreases by 3.
This means that the range of change is constant.
Hence, the relation is linear ( as the rate of change is constant )
Also, the equation that models this data set is given by:
[tex]y=f(x)=18-3x[/tex]
find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1
The point on the terminal side is (1,-1) and this can be determined by using the trigonometric functions.
Given :
The point on the terminal side of θ = negative three [tex]\pi[/tex] divided by four that has an x coordinate of negative 1.
The following steps can be used in order to determine the point on the terminal side:
Step 1 - Write the given expression.
[tex]\theta = -\dfrac{3\pi}{4}[/tex]
Step 2 - The value of the trigonometric function is given by:
[tex]\rm tan \dfrac{3\pi}{4} =-1[/tex]
Step 3 - The trigonometric function can also be written as:
[tex]\rm tan \theta=\dfrac{y}{x}=-1[/tex]
Step 4 - Substitute the value of 'x' in the above expression.
y = -1
So, the point on the terminal side is (1,-1).
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What is the value of X that makes the given equation true? 4x-16=6(3+x)
help me plox 20 points
if they were rounded to the tens place
18 would round to 20
16 would round to 20
17 would round to 20
14 would round to 10
so April would be different.
True or false an inscribed angle is formed by two radii that share an endpoint
True or false an inscribed angle is formed by two radii that share an endpoint
the correct answer is : FALSE
Answer:
The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
Step-by-step explanation:
Inscribed angle is a angle which is formed inside the circle by joining of two intersecting chords inside a circle.
The inscribed angle is explained with the help of a diagram below :
In the diagram attached below, ∠ABC is an inscribed angle with an intercepted minor arc from A to C.
Thus, the inscribed angle is not formed with the help of radii that share a common end point.
Hence, The given statement : an inscribed angle is formed by two radii that share an endpoint is an FALSE statement.
A rectangular picture frame measures 4.0 inches by 5.5 inches. To cover
the picture inside the frame with glass costs $0.99 per square inch.
What will be the cost of the glass to cover the picture?
area = 4 x 5.5 = 22 square inches
cost is 0.99 per sq. inch
22 * 0.99 = 21.78
cost is $21.98
To find the cost of the glass for a 4.0 inch by 5.5 inch picture frame, calculate the frame's area and multiply it by the cost per square inch. The glass would cost $21.78.
To calculate the cost of the glass needed to cover the picture, you first need to determine the area of the glass required. The frame measures 4.0 inches by 5.5 inches, so the area can be found using the formula for the area of a rectangle, which is length multiplied by width.
The area is therefore 4.0 inches × 5.5 inches = 22.0 square inches. With the cost of glass being $0.99 per square inch, the total cost can be calculated by multiplying the area of the glass by the cost per square inch:
Total cost = 22.0 square inches × $0.99/square inch = $21.78.
Therefore, the cost of the glass to cover the picture would be $21.78.
Find an exact value. sin(17pi/12)
a. √6 - √2 / 4
b. -√6 - √2 / 4
c. √6 + √2 / 4
d. √2 - √6 / 4
The required exact value of the given trigonometric function is sin(17π/12) = (√6 + √2)/4
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric function is given in the question, as follows:
sin(17π/12)
To find the value of sin(17π/12), we can use the following trigonometric identity:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
In this case, we can write:
sin(17π/12) = sin(π/3 + π/4)
We know that sin(π/3) = √3/2 and cos(π/3) = 1/2, and sin(π/4) = cos(π/4) = √2/2.
Therefore, we can use the above identity to get:
sin(17π/12) = sin(π/3)cos(π/4) + cos(π/3)sin(π/4)
= (√3/2)(√2/2) + (1/2)(√2/2)
= (√6/4) + (√2/4)
= (√6 + √2)/4
So the answer is option (c): √6 + √2 / 4.
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The figures in each pair are similar. Find the value of each variable. Show your work.
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 13 in. by 8 in.
9log9(4) =
A. 3
B. 4
C. 9
D. 81
Can someone simplify 2y-3x^2+6x^2-3y ?
Write a segment addition problem using three points that asks the student to solve for x but has a solution x = 20
The segment addition problem was given below which gives the value of x as 20.
Segment addition problem:
Consider three points on a line: A, B, and C. Point B is located between points A and C.
The lengths of the line segments are as follows:
Length of segment AB: 12
Length of segment BC: x
Length of segment AC: 32
Find the value of x.
We have the equation for segment addition: AB + BC = AC
Substitute the given values:
12 + x = 32
Now, solve for x:
x = 32 - 12
x = 20
Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.
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To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.
Explanation:To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:
AB + BC = AC
x + (20 - x) = 20
By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.
Here is the step-by-step problem phrased as a question:
Let points A, B, and C be collinear with B between A and C.If AB = x and BC = 20 - x, and AC = 20, find the value of x.please help me idk how to do this at all I've been stuck on it for awhile.
when numbers are in parenthesis the first number is x the second is y
(x,y)
sine they give you (2, blank)
2 = x so replace x in the equation with 2
so y=2x+5 becomes y=2(2)+5
so y = 2*2+5 = 9
y=9
so it should be (2,9)
Sixty-five percent of men consider themselves knowledgeable football fans. if 12 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.
Answer:
P(x)= 0.0198
Step-by-step explanation:
Given : 65% men are knowledgeable football fans, 12 are randomly selected ,
To find : Probability that exactly four of them will consider themselves knowledgeable fans.
Solution : Let P is the success rate = 65% = 0.65
Let Q is the failure rate = 100-65= 35%= 0.35
Let n be the total number of fans selected = 12
Let r be the probability of getting exactly four = 4
Formula used : The binomial probability
[tex]P(x)= \frac{n!}{(n-r)!r!}P^rQ^{n-r}[/tex]
putting values in the formula we get ,
[tex]P(x)= \frac{12!}{(12-4)!4!}(0.65)^4(0.35)^{12-4}[/tex]
[tex]P(x)= (495)(0.1785)(o.ooo22 )[/tex]
P(x)= 0.0198
The probability that exactly four out of the twelve randomly selected men will consider themselves knowledgeable football fans is approximately 0.236 or 23.6%.
Step 1: Model Selection (Binomial Distribution)
This scenario can be modeled using the binomial distribution if the following conditions are met:
Fixed number of trials (n): In this case, we have a fixed number of men being selected (n = 12).Binary outcome: Each man can be classified into two categories: either a "knowledgeable fan" (success) or a "not knowledgeable fan" (failure).Independent trials: The knowledge level of one man doesn't affect the selection of another.Constant probability (p): The probability (p) of a man being a knowledgeable fan remains constant throughout the random selection (given as 65%).Since these conditions seem reasonable, the binomial distribution is a suitable model for this scenario.
Step 2: Formula and Values
The probability (P(x)) of exactly x successes (knowledgeable fans) in n trials (men selected) with probability p of success (knowledgeable fan) can be calculated using the binomial probability formula:
P(x) = nCx * p^x * (1 - p)^(n-x)
where:
n = number of trials (12 men)x = number of successes (4 knowledgeable fans - what we're interested in)p = probability of success (knowledgeable fan - 65% converted to decimal: 0.65)(1 - p) = probability of failure (not knowledgeable fan)Step 3: Apply the Formula
We are interested in the probability of exactly 4 men being knowledgeable fans (x = 4). Substitute the known values into the formula:P(4) = 12C4 * 0.65 ^ 4 * (1 - 0.65) ^ (12 - 4)Step 4: Calculate Using Calculator or Software
While it's possible to calculate 12C4 (combinations of 12 choosing 4) by hand, using a calculator or statistical software is often easier.12C4 = 495 (combinations of 12 elements taken 4 at a time)Step 5: Complete the Calculation
Now you have all the values to complete the calculation:P(4) = 495 * 0.65 ^ 4 * (1 - 0.65) ^ 8Using a calculator or software, evaluate the expression. You'll get an answer around 0.236.Which graph represents the solution to the system of inequalities? x + y ≥ 4 2x + 3y < 12