Help me , it is 50 point
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]
There are 15 boys in school base ball team , they represent 5% of grace Christian school , In all how many are there in school
Answer:
300
Step-by-step explanation:
[tex]5\% \: of \: x = 15 \\ x = 1500 \div 5 = 300[/tex]
A rectangular courtyard has a length of 16 m and a width of 10 m. Find the perimeter of the rectangle defined by this courtyard. In other words, what is the length of the fence required to encompass the courtyard?
Answer:
26^2 meters
Step-by-step explanation:
l + b
16 + 10
= 26m×2
what’s the area and perimeter for this problem?
Answer:
area: 1.9×0.75÷2
0.7125
perimeter: 2+0.75+2.25
5
Can someone please answer this by today
In the last 10 presidential elections, the democratic candidate has won six times in Michigan and four times in Ohio. What is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election?
0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
In the last 10 presidential elections, the democratic candidate has won six times in Michigan and four times in Ohio
We need to find the probability of that the democratic candidate wins both Michigan and Ohio in the next presidential election
As 6 wons from Michigan out of 10, so it 6/10
4 wons from Ohio out of 10, so it 4/10
The probability is 6/10/×4/10
24/100=0.24
In the next year also democratic candidate wons then the probabiltiy will be same 0.24
Hence 0.24 is the probability that the democratic candidate wins both Michigan and Ohio in the next presidential election
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PLEASE HELP!!
Identify an obtuse angle and give its measure.
Answer:
Angle HEF
105*
Step-by-step explanation:
Suppose that you have 8 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards without replacement.
Your question is Incomplete. Please read below for the missing content.
Total cards = 8 + 5 = 13
The selections are being made with replacement. Hence,
a) P(G1 and G2) = P(G1)*P(G2) = (8/13)*(8/13) = 0.3787
b) P(Atleast 1 green) = 1 - P(No green) = 1 - (5/13)*(5/13) = 0.8521
c) P(G2 | G1) = P(G2) = 8/13 = 0.6154
What is the probability of replacement?
Probability with replacement is used for questions where the outcomes are back again to the sample space again. which means that when the object is selected, then its miles changed and returned to the sample space, so the range of elements of the sample space remains unchanged.
Conclusion: The chance of two consecutive attracts without a replacement from a deck of playing cards is calculated because the range of viable successes over the variety of viable results, is expanded together for each case. accordingly, for the primary ace, there may be a 4/52 possibility and for the second there is a 3/51 probability.
Suppose that you have 8 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacements. Round your answers to four decimal places.
G1 = the first card drawn is green
G2 = the second card drawn is green
a. P(G1 and G2) =
b. P(At least 1 green) =
c. P(G2|G1) =
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Kelly used the vertical line test to determine whether or not the curve that she
had been given is a function. After conducting the vertical line test, Kelly
determined that the curve is a function. Which of the following choices
represents the result of Kelly's vertical line test?
A. All vertical lines intersected the curve at exactly 2 points.
B. One vertical line intersected the curve at exactly 2 points.
C. One vertical line intersected the curve at exactly 1 point, while
another vertical line intersected the curve at exactly 2 points.
OD. All vertical lines intersected the curve at exactly 1 point.
All vertical lines intersected the curve at exactly 1 point.
===========================================================
Explanation:
If there is a case when a single vertical line crosses 2 or more points on the curve, then it will not be a function. In this situation, it is said that the curve fails the vertical line test.
Passing the vertical line test means that every vertical line passes through exactly one point on the curve. Each x input leads to exactly one output. If such a situation happens, then we have a function.
Since Kelly concluded that the curve is a function, this means the curve passed the vertical line test, and it points us to choice D as the answer.
The art club raised \$248$248dollar sign, 248 through fundraisers. Then they spent \$206$206dollar sign, 206 to set up an art show. They raised another \$316$316dollar sign, 316 at the art show. How much money did the art club have after the show
Considering the amount they raised and the amount they spent, it is found that the art club had $358 after the show.
How to find the net amount of the art club?The net amount is found by the subtraction of the amount raised by the amount spent.
In this problem:
The amount raised, in dollars, is of 248 + 316 = 564.The amount spent is of $206.Then:
A = 564 - 206 = $358.
The art club had $358 after the show.
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AYO HELP ME OUT ASAP :(
Answer:
122.7 cm³
Step-by-step explanation:
Volume of composite figure:Square pyramid:
a = 4 cm ; h = 4 cm
[tex]\boxed{\text{Volume of square pyramid = $\dfrac{1}{3}$*base area * height}}[/tex]
[tex]\sf = \dfrac{1}{3}*a^{2}*h\\\\ =\dfrac{1}{3}*4*4*4\\\\ = 21.3 \ cm^3[/tex]
Rectangular prism:
l = 6 cm ; w = 6 cm ; h = 4 cm
[tex]\boxed{\text{Volume of rectangular prism = l*w*h}}[/tex]
= 6 * 6 * 4
= 144 cm³
Volume of composite figure = volume of rectangular prism - volume of pyramid= 144 - 21.3
= 122.7 cm³
Which translations of the pentagon below will result in a diagram of the pentagon and its image with line symmetry?
i) L6
ii) D5
iii) R2
iv) U3
Answer:
iii) R2
Step-by-step explanation:
log^2 8 = 3 in exponent form
Answer:
2³ = 8
Step-by-step explanation:
㏒ₐ ᵇ = ⁿ ⇔ aⁿ = b
I need the formula for this graph
Answer:
y=[tex]\frac{1}{12} x+\frac{1}{4}[/tex]
Step-by-step explanation:
Volume of cylinder Radius 3.5 Height 3.5
Answer:
I think the volume is 538.51 in^3.
Step-by-step explanation:
I have tried my hardest sorry if i am wrong
Evaluate the function 2/3t , when t = 30.
Question 2 options:
10
15
20
25
Answer:
20
Step-by-step explanation:
2/3(30)
=20
Find all sets of four consecutive even integers whose sum is between 155 and 165
Answer:
36 38 40 42
and
38 40 42 44.
Step-by-step explanation:
160 / 4 = 40 so the numbers are close to 40.
38 + 40 + 42 + 44 = 164
36 + 38 + 40 + 42 = 156.
Susie is thinking about changing her auto insurance policy at fret-no-more auto insurance. her current policy includes the following options: $50/100,000 limit for bodily injury, $25,000 limit for property damage, $250 deductible for collision, and $50 deductible for comprehensive. which of the following changes would increase susie’s limits the most without increasing her monthly premium by more than $5.00? fret-no-more auto insurance type of insurance coverage coverage limits annual premiums bodily injury $25/50,000 $21.35 $50/100,000 $32.78 $100/300,000 $42.10 property damage $25,000 $115.50 $50,000 $142.44 $100,000 $193.78 collision $100 deductible $490.25 $250 deductible $343.33 $500 deductible $248.08 comprehensive $50 deductible $105.79 $100 deductible $88.23 a. increase coverage on bodily injury to $100/300,000. b. increase coverage on property damage to $50,000. c. increase coverage on bodily injury to $100/300,000 and on property damage to $50,000. d. increase coverage on bodily injury to $100/300,000 and on property damage to $100,000.
The change that would increase Susie’s limits is C. increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.
What is an insurance?It should be noted that an insurance simply means a form of risk reduction that is taken regarding an asset.
In this case, the change that would increase Susie’s limits is to increase coverage on bodily injury to $100/300,000 and on property damage to $50,000.
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When developing functions a, b, and c, the studio restricted the domain of each function to the interval [0, 10). What are
some possible reasons for restricting the domain in this way?
Answer: The domain wouldn’t include negative because it’s not possible to backward in time. The studio might limit the domain to numbers less than or equal to 10 because for x > 10 the number of views is unrealistically big. Also, viral marking slow after a while so the functions may not fit the data as well after 10 days.
Answer:
The answer above is the exact same as on edmentum that the teacher put, just so you know.
Hey guys! Sorry to bother but I need help with these. 5th grade math, will give brainliest! (If you see multiple questions by me that look the same, they are all different.)
Answer:
Question seven is 14, Question 8 is 16
Step-by-step explanation:
hoped this helped
What is the solution to the following equation?
-3+x=-8
A. X-11
OB. x=-11
OC. x=5
D. x=-5
Answer:
x = -5
Step-by-step explanation:
-3+x = -8
Add 3 to each side to isolate x
-3+x+3 = -8+3
x = -5
Rick went on a hike with his family in Big Bend National Park. During the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes.
Rick has a pet snake, so he was most excited to see the snakes. What percent of the animals were snakes?
10 per cent of the animals were snakes in the given question.
What is the percentage?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
During the hike, he saw 6 lizards, 1 scorpion, 2 foxes, 3 jackrabbits, 6 deer, and 2 snakes.What per cent of the animals were snakes.The percentage will be calculated as:=
Snake percentage = ( 2 / 20 ) x 100 = 0.1 x 100 = 10 %
Therefore, 10 per cent of the animals were snakes in the given question.
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I need help ASAP with this pyramid scale factor question!
Answer:
C
Step-by-step explanation:
because 14 is 7 x 2 the scale factor from the small pyramid to the big pyramid would be 1/2
Answer:
(b) 1/8
Step-by-step explanation:
You want the ratio of the volume of the small pyramid to that of the larger one, given their base lengths are 7 and 14 units.
Scale factorThe pyramids are presumed to be similar, so the ratio of the sides given is also the ratio of the unmarked sides and the heights. The volume ratio is the cube of this ratio of side lengths:
smaller/larger sides = 7/14 = 1/2
smaller/larger volumes = (1/2)³ = 1/8
The ratio of the volume of the small pyramid to the larger is 1/8.
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Which of the following is the shape of a cross-section of the figure shown
below?
A. Rectangle
B. Square
C. Prism
D. Pentagon
Answer:rectangle
Step-by-step explanation:
I will gove you 100 points
To find side given angle and two sides:
a² = b² + c² − 2bc cos(A)
Here given:
a = AC cmb = 10 cmc = 7 cmangle A = 120°Solve for AC (a):
a² = (10)² + (7)² − 2(10)(7) cos(120)a² = 219a = √219a = 14.7986 cma = 14.8 cmAnswer:
AC = 14.8 cm (1 dp)
Step-by-step explanation:
Cosine rule
[tex]\sf b^2=a^2+c^2-2ac \cos B[/tex]
(where a, b and c are the sides, and B is the angle opposite side b)
Given:
a = 10 cmc = 7 cmB = 120°b = ACSubstituting the given values into the formula and solving for b:
[tex]\implies \sf AC^2=10^2+7^2-2(10)(7) \cos 120^{\circ}[/tex]
[tex]\implies \sf AC^2=100+49+70[/tex]
[tex]\implies \sf AC^2=219[/tex]
[tex]\implies \sf AC=\pm\sqrt{219}[/tex]
As length is positive,
[tex]\implies \sf AC=\sqrt{219}\:cm[/tex]
[tex]\implies \sf AC=14.8\:cm\:(1\:dp)[/tex]
Pls help!
Simplify sin θ/√1-sin^2 θ
A) tan Θ
B) tan^2 Θ
C) 1
D) -1
Answer:
hope this will help you ( ◜‿◝ )♡
Step-by-step explanation:
[tex] \frac{ \sin(theta) }{ \sqrt{1 - \sin {}^{2} ( theta) } } \\ \frac{ \sin(theta) }{ \cos(theta) } \\ \tan(theta) [/tex]
The volume of a cone is 108 pi cubic inches. Its height is 4 inches. What is the radius of the cone? Round the answer to the nearest tenth if necessary. 5. 2 in. 9 in. 34. 7 in. 81 in.
Answer:
im gonna say it would be around 9 inches, because the actual answer, a decimal, isnt an option so the closest would be around 9 in.
PLS HElp answer is below give me a answer for each one and a complete sentence pls il give brainiest and 5 stars
Answer:
1. She should use Length x Width x Height.
2. The unit of the answer is 30.
3. The volume of the box is 30 units.
( multiplying matrixes please help) Find the product of the following two
matrices.
[tex]\left[\begin{array}{cc}1&3\\0&-2& \end{array}\right] \begin{bmatrix} 3& 1&-1& 0 \\ -1& 0&3&-1\end{bmatrix}\\\\\\=\begin{bmatrix} 3-3& 1+0&-1+9&0-3\\ 0+2&0-0&0-6&0+2\end{bmatrix}\\\\\\=\begin{bmatrix} 0&1&8&-3\\2&0&-6&2\end{bmatrix}[/tex]
John was visiting four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 2),
C(1, -4) and D(-3, -2). What is the area of the space that cities enclose? Round your
answer to the nearest whole number. Do not include units in your answer.
Answer:
30
Step-by-step explanation:
