Answers
Answer:
a) 23.56 ft (2 dp)
b) 58.90 ft² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=r \theta[/tex]
[tex]\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}[/tex]
Calculation
Given:
[tex]\theta=\dfrac{3 \pi}{2}[/tex] r = 5 ft[tex]\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 5\left(\dfrac{3 \pi}{2}\right)\\& = \dfrac{15}{2} \pi \\& = 23.56\: \sf ft\:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(5^2) \left(\dfrac{3 \pi}{2}\right)\\\\& = \dfrac{25}{2}\left(\dfrac{3 \pi}{2}\right)\\\\ & = \dfrac{75}{4} \pi \\\\& = 58.90 \: \sf ft^2\:(2\:dp)\end{aligned}[/tex]
Related Questions
I need help! Asap please.
Answers
The area of the given triangle will be [tex]\dfrac{5\sqrt{2}}{2}[/tex]
What is the triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
Given points of the triangle are:-
( -6,5 ) (-5,3 ) and (-8, 2)
Now we will apply the area formula for the triangle:-
[tex]A = \dfrac{1}{2} \times B\times H[/tex]
The base will be = [tex]\sqrt{(-5++8)^2+(3-2)^2)}=\sqrt{9+1}=\sqrt{10}}[/tex]
The Height will be = [tex]\sqrt{(-5+6)^2+(5-3)^2}=\sqrt5[/tex]
The area will be calculated as:-
[tex]A =\dfrac{1}{2}\times \sqrt{10}\times \sqrt{5}=\dfrac{5\sqrt{2}}{2}}[/tex]
Therefore the area of the given triangle will be [tex]\dfrac{5\sqrt{2}}{2}[/tex]
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Which quadratic model best represents the data? f(x) = –16x2 99x 6 f(x) = –36x2 37x 5 f(x) = 36x2 37x 5 f(x) = 16x2 99x 6
Answers
The quadratic model that represents the data will be A. -16x² - 99x + 6.
What is a quadratic model?It should be noted that a quadratic model simply means a model that is represented by a quadratic equation in the form of y = ax² + bx + c.
From the complete question, the quadratic model that represents the data will be -16x² - 99x + 6.
In conclusion, the correct option is A.
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Answer:
Step-by-step explanation:
HELP ASAP PLSS
A local water park has two types of season passes. Plan A costs a one-time fee of $143 for admission plus $8 for parking every trip. Plan B costs a one-time fee of $52 for parking plus $21 for admission every trip. How many visits must a person make for plan A and plan B to be equal in value?
Answers
kyle is pulled back on a swing so that the rope forms an angle of 30 degress with the vertical the distance from the top of the swing set directly to the ground is 12 feet find kyles height off the ground
Answers
Answer:
12 ft - 2 ft = 10 ft
The rope is 10 feet long.
10 · cos 30° = 10 · √3 / 2 = 8.66 ft
x = 12 - 8.66 = 3.34 ft
Answer:
A ) 3.34 feet
jeff can solve 16 math problems in 25 minutes. How many problems can he solve in 42 minutes?
Answers
Answer:
27
step by step explanationfrom the explanation,
let the number of maths that can be solved in 42 minutes = X
16 maths--------------25minutes
x maths --------------42 minutes
cross multiplying
X×25= 16×42
dividing bothsides by 25
25X/25 = 16×42/25
X = 672/25
X = 26.88 = 27 (approximately)
therefore 27 problems can be solved in 42 minutes
The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. the linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. according to the model, for what price is each comb being sold? startlayout enlarged left-brace 1st row y = startfraction x over 2 endfraction 2nd row y = negative 0.03 (x minus 95) squared 550 $0.03 $0.50 $0.95 $2.00
Answers
The price of each comb is $0.5, and the total income from selling x plastic combs is y = x/2
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The linear equation y = x/2 models the income, in dollars, from selling x plastic combs. Hence:
Price of each comb = (x/2) / x = 0.5
The price of each comb is $0.5, and the total income from selling x plastic combs is y = x/2
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Answer: B. $0.50
Step-by-step explanation:
Took the Test/Exam
What is the product? 2/3×1/5
Answers
Answer:
0.13
Step-by-step explanation:
2/3×1/5 = 0.13
PLEASE HELP WILL MARK BRAINLIEST
8-10
Answers
Answer:
[8] Area is = to 1017.36 Circumference is = to 113.04
[9] Area is = 490.625 Circumference is = 78.5
[10] D = 16 R = 8
Step-by-step explanation:
[8]
Area is = to 1017.36
Circumference is = to 113.04
Formula:
Area = πr²
Circumference = 2πr
Solve:
A = πr²
A = 3.14(18) ²
A = 3.14(324)
A = 1017.36
C= 2πr
C = 2(3.14)(18)
C = 113.04
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Area = 490.625
Circumference is = 78.5
Formula:
Area = πr²
Circumference = 2πr
Solve:
Area = πr²
A = 3.14(12.5)²
A = 3.14(156.25)
A = 490.625
Circumference = 2πr
C = 2(3.14)(12.5)
C = 78.5
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
[10]
Circle area = π * r² = π * 64 [cm²] ≈ 201.06 [cm²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 8 [cm] * 2 = 16 [cm]
Hence,
D = 16
R = 8
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Kavinsky
Greenwood Middle School is having a math competition. Four students are called to the stand to answer a question. The question is:
51.32 – 11.98
Answers
Answer: 39.34
Step-by-step explanation:
I need help please !!!!!!!
Answers
Answer:
4 and 3/4 is the 5th shortest piece
a third of 4 and 3/4 is 1 and 7/12
the answer is: 1 7/12 in.
Step-by-step explanation:
4 and 3/4 is 19/4
19/4 divided 3 is 19/4 *1/3 = 19/12 = 1 7/12
An apple orchard's workers pick 12,500 apples in the month of October. A sample of 500 of these apples shows that 30 of them are damaged. what is the best estimate of the percentage of apples picked at the orchard in October that are damaged?
Answers
The best estimate of the percentage of apples picked at the orchard in October that is damaged will be 6%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.
An apple orchard's workers pick 12,500 apples in the month of October.
A sample of 500 of these apples shows that 30 of them are damaged.
Then the best estimate of the percentage of apples picked at the orchard in October that is damaged will be
P = 30/500 x 100
P = 6%
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A lightbulb manufacturer must test a sample of lightbulbs to ensure that quality and safety standards are being met. Which of these methods will produce the most representative sample of the population of lightbulbs made by this company? OA. The manufacturer tests every lightbulb made on Monday. B. The manufacturer tests the last 100 lightbulbs produced each month. OC. The manufacturer tests the first lightbulb off the production line each day OD. The manufacturer tests every 1000th lightbulb off the production
Answers
Answer:
D
Step-by-step explanation:
It makes the most sense
When graphing an inequality, what is drawn to show that the number named
in the inequality is included in the solution?
Answers
Answer:
The line would be a solid line.
Step-by-step explanation:
To draw inequality graphs, solid lines represent [tex]\geq or \leq[/tex] and dotted lines show > or <. Hope this helps.
Lukas is researching animals for a project. He has already researched 8 animals in school and continues to research 2 new animals each week from home. Choose the equation where w represents the number of weeks since Lukas started his research at home and n represents the number of animals Lukas has researched.
PLEASE ANSWER
Answers
Answer:
8+2w=y
Step-by-step explanation:
please help! 7th grade math
Answers
Answer:
q 3 = 3/12.2/9 q4 = 15/40.14/39
Najib cuts out a rectangle that has a perimeter of 50 inches and a length of 17 inches.He cuts out another rectangle that is the same length and twice as wide. What is the perimeter of the new rectangle.
Answers
Answer:
66 inches
Step-by-step explanation:
perimeter = 2(l+b)
here, perimeter is 50 and length is 17
let the width be x,
=> 50 = 2(17+x)
=> 50 = (2*17)+(2*x)
=> 50 = 34 + 2x
=> 50 - 34 = 2x [transposing method]
=> 16 = 2x
=> 16/2 = x
=> 8 = x
8 inches = width of the first triangle
we know, the other rectangle's length is 17
and it is said that the width is twice the width of the first triangle
so the length = 17, width = 2*8 = 16
for the perimeter
p = 2(l+b),
=> p = 2(17+16)
=> p = (2*17)+(2*16)
=> p = 34+32
=> p = 66
so the perimeter of the other rectangle is 66
Answer:
66
Step-by-step explanation:
that answer was incorrect. change your answer and try again!
Given that XY is a line segment with the angle a = 46 degrees, work out the value of the angle marked b.
B = ?
Answers
Answer:
The answers should be b=44°
Step-by-step explanation:
b=180°–90°–a
b=180°–90°–46°
b=44°
rose is making trail mix bags for her hiking club. she will use 20 ounces of walnuts, 11.1 ounces of almonds, and 15.4 ounces of cashews. this amount makes 25 bags of trail mix. how many ounces are in each bag? (please have explanation and answer)
Answers
Answer: 1.86 oz. per bag
Step-by-step explanation: First we add the amount of ounces from each ingredient. 20+11.1+15.4 = 46.5
Then we divide by 25 to find out how many ounces per bag. 46.5/25=1.86
Answer:
2.15 ounces
Step-by-step explanation:
The total ounces of nuts in the bag is calculated as:
20 ounces of walnuts + 11.1 ounces of almonds + 24.8 ounces of cashews = 55.9 ounces.
From the question we are told that these amounts make 26 bags.
The number of ounces that are in each bag is calculated as:
26 bags = 55.9 ounces
1 bag = x ounces
Cross Multiply
26 bags × x ounces = 1 bag × 55.9 ounces
x ounces = 1 bag × 55.9 ounces/26 bags
x ounces = 2.15 ounces
Therefore, there are 1.94 ounces in each bag
△ABC ≅ △DEF.
Find the measures of the given angles or the lengths of the given angles.
1). m∠B=3y, m∠E=6y-12
2). AC=7a+5, DF=5a+9
Answers
The measures for the given angles B and E are 12° .
Similarity TriangleTriangles are similar when the correspondent angles and the ratio of correspondent sides are equal. Also, it must present the same shape, but it is not mandatory the same dimension.
Like the triangles are similar, ∠B=∠E. Then,
∠B=∠E
3y=6y-12
3y-6y=-12
-3y=-12
y=4
You can write too:
AC=DF
7a+5=5a+9
7a-5a=9-5
2a=4
a=2
Therefore,
∠B=3y= 3* 4 =12
m∠E=6y-12=6*4-12=21-12=12
AC=7a+5= 7*2+5=14+5=19
DF=5a+9=5*2+9=10+9=19
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Simplify $\frac{4}{\sqrt{3}}$
Answers
Decimal form is 2.3094
Find the area of a trapezoid with bases of 10 inches and a height of 5 inches?
Answers
Answer:
50in^2
Step-by-step explanation:
[tex]A=\frac{a+b}{2}(h)\\ \frac{10+10}{2}(5)[/tex]
Use f(x)=x^2+4x-12 Does the graph of a function open upward or downward?
Answers
Answer:
Upward
Step-by-step explanation:
Because of the positive leading coefficient, the graph of the function will open upwards, being a parabola.
open upwards and being a parabpla
PLEASE HELP ME ON THIS ONE
Answers
Answer:
8m
Step-by-step explanation:
Find the volume of the sphere first :
V sphere = [tex]\frac{4}{3}[/tex] π 6^3 = 902.51
Then use the volume of the sphere to find the height :
Formula = V/π[tex]r^{2}[/tex]
902.51/π(6)^2 = 8.004 (rounded is 8)
hope this helped :)
Answer:
8 m
Step-by-step explanation:
Given,
Volume of sphere = Volume of cylinder
Radius ( r ) = 6 m
Formula : -
Volume of sphere = 4/3 πr³
Note : -
The value of π is 3.14
Volume of sphere
= 4/3 x 3.14 x 6³
= 4/3 x 3.14 x 6 x 6 x 6
= 904.32 m³
Hence,
The volume of sphere is 904.32 m³.
Since,
Volume of sphere = Volume of cylinder
So,
Volume of cylinder = 904.32 m³
Formula : -
Volume of cylinder = πr²h
πr²h = 904.32
3.14 x 6 x 6 x h = 904.32
113.04 x h = 904.32
Divide 113.04 on both sides,
h = 904.32 / 113.04
h = 8 m
Which statements are true? check all that apply. the total possible outcomes can be found using 52c5. the total possible outcomes can be found using 52p5. the probability of choosing two diamonds and three hearts is 0.089. the probability of choosing five spades is roughly 0.05 the probability of choosing five clubs is roughly 0.0005.
Answers
A deck of playing cards has four suits, with thirteen cards in each suit consisting of the numbers 2 through 10, a jack, a queen, a king, and an ace. The true statements about the cards are
The total possible outcomes can be found using 52C5. The probability of choosing five clubs is roughly 0.0005. What is Probability?Generally, Probability is simply defined as the position or attribute of being likely.
In conclusion, The accurate assertions are: The total number of potential outcomes may be calculated using 52C5, and the chance of selecting five clubs is around 0.0005.
CQ
A deck of playing cards has four suits, with thirteen cards in each suit consisting of the numbers 2 through 10, a jack, a queen, a king, and an ace. The four suits are hearts, diamonds, spades, and clubs. A hand of five cards will be chosen at random. Which statements are true? Check all that apply. The total possible outcomes can be found using 52C5. The total possible outcomes can be found using 52P5. The probability of choosing two diamonds and three hearts is 0.089. The probability of choosing five spades is roughly 0.05 The probability of choosing five clubs is roughly 0.0005.
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Answer:
A & D
Step-by-step explanation:
E2020 Geometry B!! :33
In a board game, there is a 29 chance of drawing a card that gives a player a double turn. The remaining cards are single-turn cards. A player wants to run a simulation to estimate the probability of drawing two double-turn cards in a row, assuming the first card is replaced, and the deck is shuffled afterward.
Answers
Probability helps us to know the chances of an event occurring. The probability of getting a double card in a row is 0.311.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The probability of drawing a single double turn card for the first time, therefore,
Probability = 29/52
Further, given the card is replaced and reshuffled, therefore, the probability of getting a double card again will be,
Probability = 29/52
Thus, the probability of getting a double card in a row can be written as,
Probability = (29/52)×(29/52) = 0.311
Hence, the probability of getting a double card in a row is 0.311.
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Factor 6x^2+14x.
Please, help
Answers
Factor 2x from 6x².
2x (3x)+14x
Factor 2x from 14x.
2x (3x) + 2x (7)
Factor 2x from 2x (3x) + 2x (7).
2x(3x+7) ====> Answers
Answer:
(2x)(3x + 7)
Step-by-step explanation:
Hello!
We can factor this expression by taking out the GCF of both the terms.
The GCF is 2x, because it is the largest factor that is in common between 6x² and 14x
Factor6x² + 14x2x(3x) + 2x(7)(2x)(3x + 7)The factored expression is (2x)(3x + 7)
Select the correct answer from each drop-down menu. a container holds 50 electronic components, of which 10 are defective. if 6 components are drawn at random from the container, the probability that at least 4 are not defective is . if 8 components are drawn at random from the container, the probability that exactly 3 of them are defective is .
Answers
The probability of exactly 3 of the containers being defective is given as 0.1468
How to solve for the probabilityWe have to set p as the probability of container being non- defective
We have p as the probability of container being defective 50 - 10 = 40
p = 40/50
= 0.8
q = 10/50
= 0.2
P(3) = 8c3 * 0.2² * 0.8⁵
= 0.1468
Hence the probability that the container has exactly 3 defective containers is 0.1468
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Find the unit rate.
392 orders in 4 days =
orders per day
Answers
---Divide the numerator and denominator by 4. We do this because we want to know how many orders are in 1 day and 4 / 4 = 1.
392 orders / 4 days
98 orders / 1 day
Hope this helps!
The ordered pairs in this table lie in the graph of a linear function. Which equation represents the same linear function?
X Y
4 11
0 -1
-2 -7
-5 -16
A. y = x + 2
B. y = 3x – 1
C. y = 3x
D. y = x – 3
Answers
The linear equation that represent the pair of points (0, -1) and (4, 11) is y = 3x - 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the table, using the point (0, -1) and (4, 11), hence:
y - (-1) = [(11 - (-1))/(4 - 0)](x - 0)
y = 3x - 1
The linear equation that represent the pair of points (0, -1) and (4, 11) is y = 3x - 1
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Answer: B
Step-by-step explanation:
If a circular playground has an area of 144 m2. What is the diameter of the playground?
Answers
Answer:
The diameter is about 13.55m
Step-by-step explanation:
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