In a circle with an 8-inch radius, a central angle has a measure of 60°. How long is the segment joining the endpoints of the arc cut off by the angle?
Answers
C = 2πr
C = 2(3.14159)(8 inches)
C = 50.265 inches
then 60/360 = 1/6 of the circle
50.265 inches / 6
= 8.378 inches (Round answer as needed)
Answer:
The length of segment joining the endpoints of the arc is [tex]8\ in[/tex]
Step-by-step explanation:
we know that
In the triangle ABC
see the attached figure to better understand the problem
[tex]AC=BC[/tex] -----> is the radius of the circle
[tex]m<CAB=m<CBA[/tex]
[tex]m<ACB=60\°[/tex] ----> given problem (central angle)
Initially the triangle ABC is an isosceles triangle
Remember that
the sum of the internal angles of triangle must be equal to [tex]180\°[/tex]
For this particular case, the isosceles triangle ABC becomes an equilateral triangle, as the three angles are equal to [tex]60\°[/tex]
The equilateral triangle has three equal sides and tree equal angles
so
[tex]AC=BC=AB[/tex]
Hence
The length of segment joining the endpoints of the arc is [tex]8\ in[/tex]
Related Questions
Determine the width of the garden. Nina must put 60 feet of fencing around her rectangular garden. The length of the garden is three feet longer than twice the width. What is the solution set for 2w + 2(2w + 3) = 60 given the replacement set {6, 7, 8, 9}?
Answers
2w+2(2w+3)=60
2w+4w+6=60
6w+6=60
6w=54
w=54/6 =9
the width is 9 feet
Answer:
9 is a solution.
Step-by-step explanation:
The replacement set is the set of values that can be substituted in the equation (for the variables).
Given a replacement set, we need to substitute every value of the set in our equation and see if the equation holds for that value. If it does, then the value is a solution of the equation.
In this problem we have the equation 2w + 2(2w + 3) = 60 and the replacement set is {6,7,8,9}
We are going to start replacing the different values of the set.
w = 6[tex]2w + 2(2w + 3) = 60\\2(6) + 2(2(6)+3) = 60\\12 + 2(12+3) = 60\\12 + 2(15) = 60\\12 + 30 \neq 60[/tex]
Thus, 6 is not a solution.
w = 7[tex]2w + 2(2w + 3) = 60\\2(7) + 2(2(7) +3) = 60\\14 + 2 (14+3) =60\\14 + 2(17)=60\\14+34=60\\48 \neq 60[/tex]
Thus, 7 is not a solution.
w = 8[tex]2w + 2(2w + 3) = 60\\2(8) + 2(2(8)+3) = 60\\16 + 2(16+3)=60\\16 +2 (19) =60\\16 + 38 \neq 54[/tex]
Thus, 8 is not solution.
w = 9[tex]2w + 2(2w + 3) = 60\\2(9) + 2(2(9) + 3) =60\\18 + 2 (18+3) =60\\18 +2(21)=60\\60=60[/tex]
Thus, 9 is a solution.
A six-sided die is rolled three times. what is the probability that all three rolls will be 6?
Answers
you have a 1/6 probability of rolling a 6
so for 3 6's it would be
1/6 x 1/6 x 1/6 = 1/216
A family has ninenine children. if this family has exactly threethree boysboysâ, how many different birth and gender orders areâ possible
Answers
You can calculate it as:
[tex]\binom{9}{3} = \frac{9!}{3! \cdot 6!} = \frac{362880}{6\cdot720} = 84[/tex]
Use the graph below to answer the question that follows:
What is the average rate of change between the interval of x = 0 and x = pi/2?
A) 2/pi
B) pi/2
C) pi/4
D) 4/pi
Answers
Answer:
the correct answer is option D.
Step-by-step explanation:
average rate of change in the graph in interval x = 0 and x = pi/2
when we look into the graph between interval x = 0 and x = pi/2
we can see that on y - axis
at x = 0 value of y = 3 and
at x = π/2 value of y = 5
rate of change = [tex]\frac{change\ in y-axis}{change\ in\ x-axis}[/tex]
= [tex]\dfrac{y_2-y_1}{x_2- x_1}[/tex]
=[tex]\dfrac{5-3}{\frac{\pi}{4} - 0}[/tex]
= 4/π
hence, the correct answer comes out to be 4/π
hence, the correct answer is option D.
The probability of a randomly selected car crashing during a year in a certain country is 0.04770.0477. if a family has threethree cars, find the probability that at least one of them has a car crash during a year. is there any reason why the probability might be wrong?
Answers
P(having NO crash) = 1- 0.0477 = 0.9523
ⁿCₓ(p)ˣ. (1-p)ⁿ⁻ˣ
n= number of cars
x = number of crashes
p = 0.0477 (1 crash)
1-p = 0.9523 (NO crash:
Probability of NO crashes at all:
³C₀(0.0477)⁰(0.9523)⁽³⁻⁰⁾
³C₀(1)(0.9523)³ = 0.9523³ = 0.8636 Then P(NO CRASH) = 0.8636
P(at LEAST one crash) = 1 - 0.8636
P(at LEAST one crash) = 0.136
So we are going to find P(none of the cars crashes), then we will subtract it from 1, since:
P(at least one car crashes)+P(no car crashes)=1, as they are 2 disjoint complement events, either one or the other will happen, so the probability that either one or the other happens is 1.
P(a car not crashing)=1-0.0477=0.9523
P(car 1 not crash, car 2 not crash, car 3 not crash)=[tex]0.9523^{3}= 0.864[/tex]
P(at least 1 of the cars crashes)=1-P(none of the 3 cars crash)=[tex]1-0.9523^{3}=1-0.864=0.136[/tex]
Simplify the following expression: (Multiple Choice)
a + 2c − 5b − c + a − b
1. 2a − 6b + 2c
2. 2a − 6b + c
3. a − 6b + c
4. a − 5b + 2c
Answers
Answer:
a + a - 5b - b + 2c - c
2a - 6b + c
the answer is 2
GRADE 12 DATA MANAGEMENT!!! HELP PLEASE
The Leafs’ coach stated that “the likelihood of us winning the next game are 2/9, the likelihood of tying the next game are 1/2, and likelihood of us loosing the next game are 2/5”. Can the coach’s predictions be entirely correct? Justify your response
Answers
2/5+1/2+2/9
(36+45+20)/90
101/90
So he obviously has serious issues with mathematics :P
By these numbers there is about 112% chance that they will either win, lose, or tie. However there can be at most a 100% chance of anything :)
The coach's predictions cannot be entirely correct because the sum of the probabilities given by the coach does not equal 1. Therefore, the coach's predictions are not consistent with the rules of probability.
Explanation:The coach's predictions cannot be entirely correct because the sum of the probabilities of all possible outcomes must equal 1. In this case, the sum of the probabilities given by the coach is 2/9 + 1/2 + 2/5 = 49/90, which is not equal to 1. Therefore, the coach's predictions are not consistent with the rules of probability.
To justify this, we can add up the probabilities of winning, tying, and losing the next game. The correct probabilities should add up to 1 since these are the only possible outcomes.
If we add these probabilities together: 2/9 + 1/2 + 2/5 = 49/90, which is not equal to 1. Therefore, the coach's predictions cannot be entirely correct.
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In the formula that gives the circumference of a circle, which quantity is multiplied by 2 ?
Answers
Answer (APEX):
- Radius
Name three common measurements that are expressed as a ratio of two units.
Answers
Density , Speed and Mileage(Fuel Economy) are the three common measurements which can be expressed as a ratio of two units.
What are Fundamental Units?
A fundamental unit is a tool for measuring a base quantity. Any physical quantity that cannot be expressed in terms of another physical quantity is referred to as a basic quantity. They are
Length - meter (m)Time - second (s)Amount of substance - mole (mole)Electric current - ampere (A)Temperature - kelvin (K)Luminous intensity - candela (cd)Mass - kilogram (kg)Three Common Measurements be Density , Speed and Mileage where
Density = [tex]\frac{kg}{m^{3} }[/tex]
Speed = [tex]\frac{m}{s}[/tex]
Mileage = [tex]\frac{km}{L}[/tex]
Hence , the three common measurements which can be expressed as a ratio of two units are Density , Speed and Mileage
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Need help. First to answer correctly gets brainliest
Answers
(a^2-b^2) which always factors to (a-b)(a+b)
In this case the square root of 4b^2=2b and the square root of 16=4 so its factors are:
(2b+4)(2b-4) now we can factor out 2 from both terms...
2(b+2)2(b-2) to get
4(b+2)(b-2) (answer B.)
The length of a rectangle is three inches more than the width. the area of the rectangle is 460 inches. if the width is x, what is the length in terms of x?
Answers
l=3+x if x is the width
The length and width of the given rectangle are 23 and 20 inches respectively.
Suppose the width of the given rectangle=x inch
So, the length of the given rectangle = x+3 inch
What is the area of a rectangle?The area of a rectangle with length l and width b is lb.
So, the area of the given rectangle = x(x+3)
Given that area of the rectangle = 460 squared inches
So, x(x+3)=460
[tex]x^{2} +3x=460[/tex]
[tex]x^{2} +x-460=0[/tex]
[tex]x^{2} +23x-20x-460=0[/tex]
[tex]x(x+23)-20(x+23) =0[/tex]
[tex](x+23) (x-20)=0[/tex]
[tex]x=-23[/tex]...Not possible
[tex]x=20[/tex]
The width of the rectangle =20 inches
So, the length of the rectangle =20+3 = 23 inches
Therefore, the length and width of the given rectangle are 23 and 20 inches respectively.
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Find the perimeter and area of a square with side lengths of 16
Answers
perimeter = 4S = 16*4 = 64 units
area = S^2 = 16^2 = 256 square units
Answer:
The perimeter of a square with side lengths of 16 units is 64 units.
The area of a square with side lengths of 16 units is [tex]256 unit^2[/tex].
Step-by-step explanation:
Length of the square = a = 16 units
Perimeter of the square = P = [tex\]4\times a[/tex]
[tex]P=4\times 16 units = 64 units[/tex]
Area of the square = A = [tex]a^2[/tex]
[tex]A=a^2=(16 unit)^2=256 unit^2[/tex]
The perimeter of a square with side lengths of 16 units is 64 units.
The area of a square with side lengths of 16 units is [tex]256 unit^2[/tex].
PLEASE HELP!!!! IMAGE ATTACHED find the value of x
Answers
If the triangles are congruent then x = 7.
Billy Goats invested some money in stocks and bonds. The total amount he invested was $\$165,\!000$. If he invested 4.5 times as much in stocks as he did in bonds, what was his total investment in stocks?
Answers
s + b = 165,000
s = 4.5b
4.5b + b = 165,000
5.5b = 165,000
b = 165,000/5.5
b = 30,000...his investment in bonds
s + b = 165,000
s + 30,000 = 165,000
s = 165,000 - 30,000
s = 135,000 <=== his investment in stocks
An equation is formed when two equal expressions. The total investment that Billy made in stocks is $135,000.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount that is invested in stocks be represented by x, while the amount that is been invested in bonds is represented by y.
Given that Bily invested 4.5 times as much in stocks as he did in bonds. Therefore, the equation to represent the given situation can be written as,
x = 4.5y
Also, given that the total amount that Billy invested is $165,000. Therefore, the total invested amount can be written as,
$165,000 = x + y
Substitute the value of x in the equation,
$165,000 = 4.5y + y
$165,000 = 5.5y
y = $165,000 / 5.5
y = $30,000
Now substitute the value of y in the first equation to know Billy's investment in stocks.
x = 4.5y
x = 4.5($30,000)
x = $135,000
Hence, the total investment that Billy made in stocks is $135,000.
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think of a number. add two. multiply by three. add your original number. multiply by 2. add 2. subtract your original number. divide by 7. add three. subtract your original number. add five. Why is the answer always ten?
Answers
adding 2 we get x+2
multiply by 3 we get 3x+6
add original number we get 4x+6
multiply by 2 we get 8x+12
add 2 we get 8x+14
minus original number we get 7x+14
divide by 7 we get x+2
add 3 we get x+5
minus original number we get 5
add 5 we get 10
because the numer you pick cancels out in the end
we can write it out fully into one big equation
if x is the number
then the resulting expression is looking like this
[tex]\frac{2(3(x+2)+x)+2-x}{7}+3-x+5[/tex]
A fire hydrant that is 1.5 feet high casts a shadow that is 2.5 feet long. At the same time of day, a lamppost casts a shadow 15 feet long. What is the height of the lamppost?
Answers
Answer:
9 feet
Step-by-step explanation:
A triangle has squares on its three sides as shown below. What is the value of x? Three squares having side lengths 6 cm, x cm, and 8 cm joining to form right triangle at the centre 2 centimeters 6 centimeters 8 centimeters 10 centimeters
Answers
The third side of the triangle is AC = 10 centimeters
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measures of the sides of the triangle are
The measure of side AB = 6 cm
The measure of side BC = 8 cm
Now , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
On simplifying , we get
The measure of side AC = √ ( AB )² + ( BC )²
The measure of side AC = √ ( 6 )² + ( 8 )²
The measure of side AC = √ ( 36 + 64 )
The measure of side AC = √ ( 100 )
The measure of side AC = 10 cm
Therefore , the value of AC is 10 cm
Hence , the right triangle is solved and the side AC = 10 cm
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can someone explain how to do this plzz
Answers
1 of the shapes will be a small square. The dimensions for it would be 4 by 3 (12)
The second shape, the bigger rectangle has the dimensions, 12 by 6 (72)
Now add these two values 12+72 and you get, 84
you answer is A 84 square inches
Solve (2/3)-(1/x)=5/6
Answers
[tex]2 - \frac{1(3)}{x} = \frac{5(3)}{6} [/tex] Simplify the numerators
[tex]2 - \frac{3}{x} = \frac{15}{6} [/tex] Multiply both sides by 6
[tex]12 - \frac{3(6)}{x} = 15[/tex] Simplify the numerator
[tex]12 - \frac{18}{x} = 15[/tex] Multiply both sides by x
12x - 18 = 15x Subtract 12x from both sides
-18 = 3x Divide both sides by 3
-6 = x Switch the sides to make it easier to read
x = -6
Check your answer by plugging -6 in for the x in the original problem:
[tex] \frac{2}{3} - \frac{1}{x} = \frac{5}{6} [/tex] Plug in -6 for x
[tex] \frac{2}{3} - \frac{1}{-6} = \frac{5}{6} [/tex] Change [tex] \frac{2}{3} [/tex] to [tex] \frac{4}{6} [/tex] so all denominators are the same
[tex] \frac{4}{6} - \frac{1}{-6} = \frac{5}{6} [/tex] Change [tex] \frac{1}{-6} [/tex] to [tex] \frac{-1}{6} [/tex] for easier work
[tex] \frac{4}{6} - \frac{-1}{6} = \frac{5}{6} [/tex] Subtract the numerators (4 - (-1) )
[tex] \frac{5}{6} [/tex] = [tex] \frac{5}{6} [/tex]
So, x = -6 .
If a convex polyhedron has 18 edges and 12 vertices, then how many faces does it have?
Answers
V + F - E = 2
12 + F - 18 = 2
F - 6 = 2
add 6 to both sides
F = 8
CHECK:12 + 8 - 18 ??=?? 2
20 - 18 = 2 checks
Find the area of the shaded region.
Round to the nearest hundredth.
Answers
First find the area of the square.
To do this, find the length of one of the sides.
4 + 4 = 8
Since it's a square, all of the sides are 8.
8 x 8 = 64
Now find the area of the circle. (r² · π)
4² · π = 50.27
64 - 50.27 = 13.73
The answer is 13.73
Hope this helps! :)
Choose the equation that represents the line passing through the point (-2,-3) with a slope of -6
Awnsers are
A) y=-6x-15
B) y=-6x-20
C) y=-6x+15
D) y=-6x+20
Answers
The slope : m = - 6
The line passes through the point ( x, y ) = ( - 2, - 3 )
- 3 = ( - 6 ) * (- 2 ) + b
- 3 = 12 + b
b = - 3 - 12
b = - 15
Answer:
A ) y = - 6 x - 15
Answer:A
Step-by-step explanation:
Point m is the midpoint of ab¯¯¯¯¯ . am=3x+3, and ab=8x−6. what is the length of am¯¯¯¯¯¯ ?
Answers
So we can write
[tex]am = \frac{ab}{2} [/tex]
As given am = 3x+3 , ab = 8x - 6.
So [tex]3x+3 = \frac{8x - 6}{2} [/tex]
[tex]3x+3 = \frac{2(4x - 3)}{2} [/tex]
[tex]3x+3 = 4x - 3[/tex]
[tex]3+3 = 4x - 3x [/tex]
[tex]6 = x[/tex]
So x = 6.
So length of am = 3x+3 = 3*6 + 3 = 21
When a positive integer k is divided by 6, the remainder is 1. what is the remainder when 5k is divided by 3?
Answers
Final answer:
The remainder when 5k is divided by 3 is 2. This is because k can be represented as 6n + 1 where n is the quotient, and when 5 is multiplied by k and then divided by 3, after simplifying, only the term +5 contributes to the remainder.
Explanation:
When a positive integer k is divided by 6, the remainder is 1. Thus, we can write k as 6n + 1 where n is a quotient. To find the remainder when 5k is divided by 3, we must first multiply k by 5, resulting in 5(6n + 1) = 30n + 5.
Breaking down 30n + 5, we see that 30n is divisible by 3 since 30 is a multiple of 3. Hence, it will not contribute to the remainder when divided by 3. All that is left to consider is the +5 part. The closest multiple of 3 to 5 is 3 itself, meaning 5 divided by 3 will leave a remainder of 2. Therefore, the remainder when 5k is divided by 3 is 2.
*PLEASE HELP!!* The minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let v
represent the wind speed.
Answers
Answer:
Using [tex]|X-a|=b[/tex]
where a is the center or average and b is the distance from the center or the range
Here, v represents the wind speed.
As per the statement:
Minimum sustained wind speed(A)= 74 miles per hour.
Maximum sustained wind speed(B) = 95 miles per hour.
Use the center and distance to write an absolute value equation:
[tex]\text{Center} = \frac{\text{A+B}}{2}[/tex]
then;
[tex]\text{Center (a)} = \frac{74+95}{2}=\frac{169}{2}=84.5[/tex]
Distance from the center(b)= 95-84.5 = 10.5
then;
[tex]|v-84.5| =10.5[/tex]
Therefore, an absolute value equation that represents the minimum and maximum speeds is, [tex]|v-84.5| =10.5[/tex]
A construction worker needs to put a rectangular window in the side of a building. He knows from measuring that the top and bottom of the window have a width of 9 feet and the sides have a length of 12 feet. He also measured one diagonal to be 15 feet. What is the length of the other diagonal?
Answers
Answer: 15 feet
Step-by-step explanation:
The length of other diagonal is 15 feet.
What are properties of diagonal of rectangle?Both diagonals bisect opposite angles of the quadrilateral. Both diagonals form symmetry lines for the quadrilateral. The diagonals divide the quadrilateral into four congruent right triangles. The intersection point of the diagonals is the incenter of the quadrilateral
Given:
width= 9 feet
length= 12 feet
Diagonal length = 15 feet
We know the diagonals of a rectangle are equal and bisect each other.
So,
The length of other diagonal is 15 feet.
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what is the 8th term of this geometric sequence? 5,-10,20,-40
Answers
term 1: 5
term 2: -10
terms 3: 20
term 4: -40
term 5: 80
term 6: -160
term 7: 320
term 8: -640
So, the 8th term is -640. Hope this helps, please mark brainliest and have an amazing day!
The 8th term of this geometric sequence 5,-10,20,-40 = -640.
What is a geometric sequence?A geometric sequence is one in which every number is the product of its previous number and a constant ratio.
The first term is taken as a, the constant ratio is taken as r. The n-th term of such a series is given as aₙ = a.rⁿ⁻¹.
How to solve the given question?In the question, we are asked to find the 8th term of the geometric sequence 5, -10, 20, -40.
The first term (a) = 5.
The constant ratio (r) = -10/5 = -2.
We will find the 8th term using the formula of the n-th term aₙ = a.rⁿ⁻¹.
Therefore, 8th term = 5(-2)⁸⁻¹ = 5 * (-2)⁷ = 5 * (-128) = -640.
The 8th term of this geometric sequence 5,-10,20,-40 = -640.
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The mean diastolic blood pressure for a random sample of 70 people was 94 millimeters of mercury. if the standard deviation of individual blood pressure readings is known to be 12 millimeters of mercury, find a 90% confidence interval for the true mean diastolic blood pressure of all people.
Answers
To solve this problem, we make use of the formula for Confidence Interval:
Confidence Interval = X ± z * σ / sqrt (n)
where X is the mean value, z is the z score which is taken from the standard tables, σ is the standard deviation, and n is the number of samples
z = 1.645 (at 90% Confidence Level)
Substituting the values into the equation:
Confidence Interval = 94 ± 1.645 * 12 / sqrt (70)
Confidence Interval = 94 ± 2.36
Confidence Interval = 91.64, 96.36
Therefore at 90% confidence level, the blood pressure reading ranges from 91.64 mmHg to 96.36 mmHg.
Negative numbers are less than positive numbers. Does this mean that the absolute value of a negative number must be less than the absolute value of a positive number? Explain.
Answers
Example: |-6| > |4|
A runner sprints around a circular track of radius 110 m at a constant speed of 7 m/s. the runner's friend is standing at a distance 220 m from the center of the track. how fast is the distance between the friends changing when the distance between them is 220 m? (round your answer to two decimal places.)m/s
Answers
The distance between the friends changing with the rate of 7√15/4 meter per sec.
Let B represents the position of runner, A represents the position of the friend and C represents the position of centre of the circular track. ( shown below ),
We need to find: dc/dt
By the cosine law,
[tex]c^2 =a^2+b^2+2abcosC[/tex]
Differentiating with respect to t ( time ),
[tex]2c \frac{dc}{dt}=2absinC \frac{dc}{dt}[/tex]
[tex]\frac{dc}{dt}=\frac{2absinC\frac{dc}{dt}}{2c}[/tex]..(1)
Now, by arc length formula,
Radius( say r ) × angle = arc length ( say l )
r × ∠C= l
Differentiating w. r. t. t,
[tex]r \times \frac{dC}{dt} + \angle C \times \frac{dr}{dt} = \frac{dl}{dt}[/tex]
Here dl/dt=7 m per sec
dr/dt=0
r=110
dC/dt=7/110
Now again , [tex]C^2= a^2+b^2-2abcosC[/tex]
[tex]220^2 = 110^2 + 220^2 -2(110)(220)cosC[/tex]
[tex]48400=12100+48400-48400cosC[/tex]
[tex]-12100=-48400cosC[/tex]
[tex]1/4=cosC[/tex]..(2)
[tex]sinC=\frac{\sqrt{15}}{4}[/tex] ...(3)
From equation (1), (2) and (3),
[tex]dC/dt = \frac{(110)(220)\sqrt{15}/4. 7/110}{220}[/tex]
=7√15/4 meter per second.
Hence, the distance between the friends changing with the rate of 7√15/4 meter per sec.
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When the runner's distance from his friend is same as the distance from the friend to center of the track, the runner is moving in a way that the distance between him and his friend isn't changing. Hence, at those specific moments, their relative speed is zero m/s.
Explanation:This problem involves the concept of relative velocities in a plane. Since the runner is moving along a circular path with a constant speed of 7 m/s, the runner's speed towards or away from his friend depends on the runner's location on the track. However, when the runner is at a distance of 220 m from his friend (which is also the distance from the friend to the center of the track), the runner is moving perpendicular to the line joining the runner and his friend. This is because, in this particular case, the runner is moving along a tangent to the circle that intersects the friend's location. Therefore, the distance between the friends isn't changing at all during those moments - their relative speed is zero m/s.
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