Answers
Answer:
a) 52.0 cm
b) 62.8 cm
c) 114.8 cm
Conversion:
120° = 2π/3 radians
(a) Find Length of chord PR;
⇒ 2(radius)sin(θ/2)
⇒ 2(30)sin((2π/3)/2)
⇒ 2(30)sin((2(3.142)/3)/2)
⇒ 30√3
⇒ 52.0 cm
(b) Find Length of arc PQR;
⇒ radius(θ)
⇒ 30(2π/3)
⇒ 30(2(3.142)/3)
⇒ 62.8 cm
(c) The perimeter of shaded region;
⇒ Length of chord + Length of arc
⇒ 62.84 + 51.965
⇒ 114.8 cm
Answer:
(a) 52.0 cm
(b) 62.8 cm
(c) 115 cm
Step-by-step explanation:
Part (a)
[tex]\textsf{Chord length}=2r \sin \left(\dfrac{\theta}{2}\right)[/tex]
where:
r = radius[tex]\theta[/tex] = central angle (measured in degrees)Given:
r = 30 cm[tex]\theta[/tex] = 120°chord = PRSubstitute the given values into the formula:
[tex]\begin{aligned}\implies PR & =2(30)\sin \left(\dfrac{120^{\circ}}{2}\right)\\\\& = 30\sqrt{3}\\\\ & = 52.0\:\sf cm\:(3\:sf)\end{aligned}[/tex]
Part (b)
[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad[/tex]
where:
r = radius[tex]\theta[/tex] = central angle (measured in degrees)Given:
r = 30 cm[tex]\theta[/tex] = 120°arc = PQR[tex]\pi[/tex] = 3.142Substitute the given values into the formula:
[tex]\begin{aligned}\implies PQR & =2 (3.142)(30)\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \quad\\\\ & = \dfrac{1571}{25}\\\\ & = 62.8 \sf \:\:cm \:(3 \:sf)\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}\textsf{Perimeter of shaded portion} & = \textsf{chord length} + \textsf{arc length}\\\\ & = 30\sqrt{3}+\dfrac{1571}{25}\\\\ & = 114.80152...\\\\ & = 115\:\: \sf cm\:(3\:sf)\end{aligned}[/tex]
Related Questions
Genevieve is in charge of creating a five-digit code to lock and unlock a secure cabinet. she can use any code from 0 through 9 and she could use each digit as many times as she wants she knows wants to start the code with a prime number. how many possible codes that start with the prime number could Genvieve create?
A.40,000
B.50,000
C.400,000
D.500,000
Answers
Answer:
40,000
Step-by-step explanation:
I took the test
There are 40,000 possible codes that start with the prime number could Genvieve create.
For the first digit, Genevieve wants to start with a prime number.
The prime numbers between 0 and 9 are 2, 3, 5, and 7.
So, there are 4 choices for the first digit.
For the remaining four digits, she can choose any number from 0 through 9, including the prime numbers.
Since there are 10 choices for each of the four remaining digits, the total number of possible codes for those digits is 10⁴.
To calculate the total number of possible codes that start with a prime number, we multiply the number of choices for the first digit (4) by the number of choices for the remaining four digits (10⁴):
4 × 10⁴ = 40,000
Therefore, the correct answer is A) 40,000.
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If x > 3, Which of these numbers could be a possible number for x?
A. 3
B. -22
C. 0
D. 4
(will mark brainliest)
Answers
Answer:
D. 4
Step-by-step explanation:
x is greater than 3, which means x has to be a higher number. the only option here that is higher than 3 is 4.
Answer:
D
Step-by-step explanation:
the Awnser is D because x is greater than three and 4 is the only number listed that is larger than 3
Function g can be thought of as a scaled version of f ( x ) = ∣ x ∣
Answers
Using translation concepts, it is found that the equation for function g(x) is given by:
[tex]y = -\frac{2}{3}|x|[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
f(x) = |x|.
Researching the problem on the internet, function g(x) was reflected over the x-axis, and compressed by a factor of 2/3, hence it is multiplied by -2/3(negative due to the reflection), and the equation for function g(x) is given by:
[tex]y = -\frac{2}{3}|x|[/tex]
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slove this math problem
Answers
Answer:
That's all
Step-by-step explanation:
1-We find 5% of 200
2-Cross multiply
3-add 5% of 200 to the original price
-11 2/3 x (-4 1/5) help I need it
Answers
Answer:
Step-by-step explanation:
[tex]-11 \frac{2}{3} x -4\frac{1}{5} =[/tex]
First we change the mix number fractions into a improper fraction
[tex]\frac{-11*3+2 }{3} x- \frac{4*5+1}{5} =[/tex]
[tex]\frac{-33+2}{3} x- \frac{20+1}{5} =[/tex]
[tex]\frac{-31}{3}x - \frac{21}{5} =[/tex]
Give both fractions the common denominator 15 and subtract the fractions
[tex]\frac{-31x*5}{15} - \frac{21*3}{15}=[/tex]
[tex]\frac{-155x -63}{15}[/tex]
Mr. Graham invested some of his $18,000 in bonds that made a 5% profit and the rest in bonds that made a 12% profit. If the profit on the 12% bonds was $885 more than the profit on the 5% bonds, how much did Mr. Graham
invest in the 5% bonds?
Answers
Answer:
$7500
Step-by-step explanation:
Let investment in 5% bond be x
(18000 - x) * 12% - x * 5% = 885
18000*12 - 12x - 5x = 88500
216000 - 88500 = 17x
x = 7500
1. New school desks were made for your school for the upcoming school year. The total
cost of making these desks is related to the amount that are made. This is shownin the
table below:
pls help its 100 points
Answers
Take 2 points
(21,1517)(47,2609)#a
Find slope
m=2609-1517/47-21m=1092/26m=$42#b
Find equation y inetercept is our answer
y-1517=42(x-21)y-1517=42x-882y=42x+635b=635
#c
Put x=250So
y=42(250)+635y=$11135Please help will mark brainliest 5 points
Answers
Answer:
D. Graph D
Step-by-step explanation:
First, off me know that that equation is in slope-intercept form.
Therefore, your y-intercept is (0,1)
Then you need to find the slope by using two points on a graph and using the y2-y1/x2-x1 equation.
Now you need to pay attention to the sigh. It's [tex]\leq[/tex].
That means it is greater than or equal to ur y-intercept, it must be shaded do the side of numbers greater to 1 (ur y-intercept.)
Giving you D.
The line is solid and on the right side
pls help w b. also not sure if what ive written down is right
Answers
Answer:
See below
Step-by-step explanation:
b) 200 ft = -16 (t-2)^2 + 400
200 / 16 = (t-2)^2
sqrt (12.5 ) = t-2
2 + sqrt (12.5) = t
13. Solve the system of equation using substitution.
5x – 2y = 33
y = 7x – 39
Answers
Answer:
The correct answer is x=5
While walking to school you pass a barn with a silo. Looking up to the top of the silo you estimate the angle of
elevation to the top of the silo to be about 14°. You continue walking and find that you were around 40 m from
the silo. What is the height of the silo?
Answers
Answer:
9.97 meters
Step-by-step explanation:
The silo is one leg of a right triangle the other leg is the distance from the silo
for a right triangle tan = opposite side / adjacent side
tan(14) = height/40
40 tan 14 = height = 9.97 m
Find the indicated missing angle measure. Solve for the value of 0. Round to the nearest whole degree.
Answers
Answer:
67 degrees
Step-by-step explanation:
Calculator!
The sides lengths 4, 6, 9 can be used to form the sides of a triangle.
Answers
Step-by-Step Explanation:
We can simply use the Triangle Inequality Theorem which states that the sum of 2 sides of a triangle is greater than the third side.
Therefore,
=> 4 + 6 = 10 (Greater than 9)
=> 6 + 9 = 15 (Greater than 4)
=> 4 + 9 = 13 (Greater than 6)
Hence the side lengths 4, 6, 9 can be used to form the sides of a triangle.
how many times larger than 3*10^2 is 12*10^4
Answers
Hey there!
3 * 10^2
= 3 * 10 * 10
= 3 * 100
= 300
AND
12 * 10^4
= 12 * 10 * 10 * 10 * 10
= 12 * 100 * 100
= 12 * 10,000
= 120,000
SIMPLIFYING the ANSWER
120,000 - 300
= 119,700
≈ 100,000
Therefore, your answer should be:
100,000
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which equation can be used to find the surface area of the cylinder? a cylinder with a radius of 4 inches and height of 16 inches. s = 2 pi (4) squared 2 pi (4) (16) s = 2 pi (8) squared 2 pi (8) (16) s = 2 pi (16) squared 2 pi (16) (4) s = 2 (4) squared 2 (4) (16)
Answers
The equation we can use to find the surface area of the cylinder is: 2π(4)(16 + 4).
What is the Surface Area of a Cylinder?Surface area of a cylinder = 2πr(h + r), where h is the height and r is the radius of the cylinder.
Given the following:
Radius = 4 in.Height = 16 in.Equation to find the surface area of the cylinder = 2π(4)(16 + 4)
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Help me with theses problems
Answers
Answer:
1: 22cm 2: 30m 3: 78.54
Step-by-step explanation:
1: (6x2)+(5x2)
12+10
22
2: 11+4=15
15x2
30
3: 25/2=12.5
3.14x2=6.28
12.5x6.28=78.54
Decide if the situation involves permutations, combinations, or neither. explain your reasoning.
the number of ways you can choose 5 beach towels from a selection of 8 to bring on vacation
Answers
The number of ways you can choose 5 beach towels from a selection of 8 to bring on vacation is a combination problem
Permutation and combinationPermutation has to do with arrangement while combination has to do with selection.
When choosing an object from other pool of object, we will have what is called combination.
From the given question, we are told that the number of ways you can choose 5 beach towels from a selection of 8 to bring on vacation, since they are selecting, hence the situation involves combination.
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A company that manufactures playing cards ensures the cards can be stacked in a deck and
placed in a box to be sold. Which units are most appropriate for measuring the thickness of a
playing card?
Answers
Work out the length of x
(The diagram is not drawn accurately)
Answers
Answer:
x = 7
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 24² = 25²
x² + 576 = 625 ( subtract 576 from both sides )
x² = 49 ( take square root of both sides )
x = [tex]\sqrt{49}[/tex] = 7
Hey ! there
Answer:
Length of x is 7 cmStep-by-step explanation:
In this question we are provided with a right angle triangle having hypotenuse 25 cm , base 24 cm and perpendicular x . And we are asked to find the length of x .
For finding the length of x we'll use Pythagorean Theorem . Pythagorean Theorem states that sum of square of perpendicular and base is equal to the square of hypotenuse in right angle triangle that is ,
[tex] \: \qquad \: \qquad \: \underline{\boxed{ \frak{H {}^{2} = P {}^{2} + B {}^{2} }}}[/tex]
Where ,
H refers to HypotenuseP refers to PerpendicularB refers to BaseSOLUTION : -
Here in the triangle ,
Hypotenuse is 25 cmBase is 24 cmPerpendicular is xApplying Pythagorean Theorem :
[tex] \quad \longmapsto \qquad \: (25) {}^{2} = (x ){}^{2} + (24) {}^{2} [/tex]
On squaring 24 and 24 we get ,
[tex] \quad \longmapsto \qquad \:625 = (x) {}^{2} + 476[/tex]
Subtracting 576 on both sides :
[tex] \quad \longmapsto \qquad \:625 - 576 = (x) {}^{2} + \cancel{ 576} - \cancel{576}[/tex]
We get ,
[tex] \quad \longmapsto \qquad \:49 = (x) {}^{2} [/tex]
Applying square root on both sides :
[tex] \quad \longmapsto \qquad \: \sqrt{49} = \sqrt{(x) {}^{2} } [/tex]
We get ,
[tex] \quad \longmapsto \qquad \: \blue{ \underline{\boxed{\frak{7 \: cm = x}}}} \quad \bigstar[/tex]
Henceforth , length of x is ❝ 7 cm ❞ .Verifying : -
We are verifying our answer by substituting all the values of hypotenuse , perpendicular and base in Pythagorean Theorem . So ,
( 25 )² = ( 7 )² + ( 24 )²625 = 49 + 576625 = 625L.H.S = R.H.SHence , Verified .Therefore, our answer is correct .
#Keep LearningI need help with this question !!
Answers
Answer:
K^1= (-8,10)
L^1 = (-4,10)
m^1 =(-5,10)
Step-by-step explanation:
all you have to do is move the points 90 degrees counterclockwise, which then you would get the points above.
please help me solve this
Answers
Answer:
1364.26 mm^2
Step-by-step explanation:
If this is correct: side length a =
30
side length b =
10
side length c =
24
prism height h =
18
then the answer would be 1364.26 mm^2
Which expressions are equivalent to 25x4 −64? select three options. 25x4 40x − 40x − 64 25x4 13x − 13x − 64 (5x2 8)(5x2 − 8) (x2 13)(x2 – 13) (5x2 – 8)2
Answers
The three expressions that the given expression is equivalent to are, (5x^2-8)(5x^2+8), [tex]25x^4 + 40x - 40x - 64[/tex] and [tex]25x^4 + 13x - 13x - 64[/tex]
Difference of two squareThe standard expression for difference of two square is given as:
a^2- b^2 = (a-b)(a+b)
Given the equation
[tex]25x^4 -64[/tex]
This can also be expressed as:
[tex](5x^2)^2-8^2\\(5x^2-8)(5x^2+8)[/tex]
This expression is also equivalent to [tex]25x^4 + 40x - 40x - 64[/tex] and [tex]25x^4 + 13x - 13x - 64[/tex]
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(a) state the value of cos(30°)
(b) state the value of sin(30°)
Answers
1/2
Find the Lowest Common Multiple of a and b.
Answers
Answer:
181104
Step-by-step explanation:
2 x 2 x 2 x 2 x 3 x 7 x 7 x 7 x 11 = 181104
Answer:
181104
Step-by-step explanation:
2 x 2 x 2 x 2 x 3 x 7 x 7 x 7 x 11 = 181104
Light bulbs manufactured at a certain factory have a 3% probability of being defective. what is the probability that 5 out of a shipment of 30 will be defective? a. 0.25 b. 0.0016 c. 0.0035 d. 0.167
Answers
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that 5 out of a shipment of 30 will be defective is 0.001617.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
The probability of the bulb being defective is 3%(0.03) and the probability of the bulb not being defective is 97%(0.97).
Now, it is needed to be found that the probability that 5 out of a shipment of 30 will be defective can be written as,
P(x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾
P(x=5) = ³⁰C₅ (0.03)⁵ (0.97)²⁵
P(x=5) = 0.001617
Hence, the probability that 5 out of a shipment of 30 will be defective is 0.001617.
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solve for x !
[tex]\longrightarrow\bold{4x {}^{2} + 10x + 4 = 0}[/tex]
ty! ~
Answers
Step-by-step explanation:
We could easily solve this by factoring.
Given eqn:
[tex]\rm{4x ^{2} + 10x + 4 = 0}[/tex]
Solution:
Factor left side:
[tex] = > 2(2x + 1)(x + 2) = 0[/tex]
Write the factors to 0 to get our solution:
[tex] = > 2x + 1 = 0[/tex]
[tex] = > \boxed{ x = - \cfrac{1}{2} }[/tex]
or else,
[tex] = > x + 2 = 0[/tex]
[tex] = > \boxed{ x = - 2}[/tex]
[tex] \rule{225pt}{2pt}[/tex]
ANSWER ASAP!!! 25 POINTS!!!
In this unit, you’re working with a variety of methods for solving quadratic equations. Which method do you prefer over the others? Describe the method in your own words, and give an example of a quadratic equation that could be solved with this method. Show and explain the steps for solving the equation.
Please follow these guidelines for your discussion posts:
Write at least 150–300 words.
Make sure your posts are grammatically and mechanically correct.
Address all parts of the prompt.
Provide at least one example to support your response. (Example choices include an anecdote, statistic, and/or textual evidence.)
Answers
Quadratic formula – is the method that is used most often for solving a quadratic equation. If you are using factoring or the quadratic formula, make sure that the equation is in standard form.
There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.
1 is greater than w, and -5 is less than w.
Use w only once in your inequality.
Answers
Answer: As an inequality —> -5 < w < 1
A survey asked a sample of vacationers how far they drove to get to their destination. What is the margin of
error if the interval estimate is (200 miles, 250 miles)?
What is the length of the interval?
Answers
The margin of error for the interval (200 miles, 250 miles) is 25 miles.
What is an equation?An equation is an expression that shows the relationship between two or more variables and number.
The confidence interval = mean (m) ± margin of error (e) = m ± e
Hence:
m + e = 250 (1)
m - e = 200 (2)
From the both equations:
m = 225, e = 25
The margin of error for the interval (200 miles, 250 miles) is 25 miles.
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What is the sum of the first 45 terms of the sequence?
-282,-266,-250,-234,...
S45 =
Answers
Use the attachment (It has a full explanation and answer).