Given:
Area of a sector = 64 m²
The central angle is [tex]\theta=\dfrac{\pi}{6}[/tex].
To find:
The radius or the value of r.
Solution:
Area of a sector is:
[tex]A=\dfrac{1}{2}r^2\theta[/tex]
Where, r is the radius of the circle and [tex]\theta [/tex] is the central angle of the sector in radian.
Putting [tex]A=64,\theta=\dfrac{\pi}{6}[/tex], we get
[tex]64=\dfrac{1}{2}r^2\times \dfrac{\pi}{6}[/tex]
[tex]64=\dfrac{\pi}{12}r^2[/tex]
[tex]64\times \dfrac{12}{\pi}=r^2[/tex]
[tex]\dfrac{768}{\pi}=r^2[/tex]
Taking square root on both sides, we get
[tex]\sqrt{\dfrac{768}{\pi}}=r[/tex]
[tex]16\sqrt{\dfrac{3}{\pi}}=r[/tex]
Therefore, the value of r is [tex]16\sqrt{\dfrac{3}{\pi}}[/tex] m.
tell which property the statement illustrates. please help with this question i will mark u brainliest !
Answer:
associative property of multiplication
Step-by-step explanation:
Solve the 5 questions!!!
Answer:
What is the answer you're looking for?
Step-by-step explanation:
What is the length of HG?
Answer:
HG = 3
Step-by-step explanation:
HF = HG + GF
11 = HG + 8
11 - 8 = HG
3 = HG
Answer:
HG = 3
Step-by-step explanation:
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Solve the following equations for x,
if 0 ≤ x ≤ 2π.
i. 3csc² x – 4 = 0
ii. 4cos² x + 2cos x – 2 = 0
help me solve pls
(i) 3 csc²(x) - 4 = 0
3 csc²(x) = 4
csc²(x) = 4/3
sin²(x) = 3/4
sin(x) = ± √3/2
x = arcsin(√3/2) + 2nπ or x = arcsin(-√3/2) + 2nπ
x = π/3 + 2nπ or x = -π/3 + 2nπ
where n is any integer. The general result follows from the fact that sin(x) is 2π-periodic.
In the interval 0 ≤ x ≤ 2π, the first family of solutions gives x = π/3 and x = 4π/3 for n = 0 and n = 1, respectively; the second family gives x = 2π/3 and x = 5π/3 for n = 1 and n = 2.
(ii) 4 cos²(x) + 2 cos(x) - 2 = 0
2 cos²(x) + cos(x) - 1 = 0
(2 cos(x) - 1) (cos(x) + 1) = 0
2 cos(x) - 1 = 0 or cos(x) + 1 = 0
2 cos(x) = 1 or cos(x) = -1
cos(x) = 1/2 or cos(x) = -1
[x = arccos(1/2) + 2nπ or x = 2π - arccos(1/2) + 2nπ] or x = arccos(-1) + 2nπ
[x = π/3 + 2nπ or x = 5π/3 + 2nπ] or x = π + 2nπ
For 0 ≤ x ≤ 2π, the solutions are x = π/3, x = 5π/3, and x = π.
3X TO THE POWER 6 * 2Y TO THE POWER 12 =??
9514 1404 393
Answer:
6·x^6·y^12
Step-by-step explanation:
(3x^6)(2y^12) = (3)(2)x^6·y^12 = 6·x^6·y^12
Answer:
6 x ⁶ y ¹²
Step-by-step explanation:
= ( 3 x ⁶ ) ( 2 y¹² )
= ( 3 ×2 ) x ⁶ y ¹²
= 6 x⁶ y ¹²
A box has a height of 6 inches.
6 in.
Base
The area of the base is 40 squbere inches.
What is the volume of the box?
Pleaseee
Answer:
the awnser is 216
Step-by-step explanation:
i need help on #10. very confused
Step-by-step explanation:
[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{f(x + h) - f(x)}{h}[/tex]
[tex]\:\:\:\:\:\displaystyle = \lim_{h \to 0} \dfrac{(x+h)^2 -7 -(x^2 - 7)}{h}[/tex]
[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} \dfrac{(x^2 +2hx + h^2 -7) - (x^2 -7)}{h}[/tex]
[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} \dfrac{2hx + h^2}{h}[/tex]
[tex]\:\:\:\:\: \displaystyle= \lim_{h \to 0} (2x +h)[/tex]
[tex]\:\:\:\:\: \displaystyle= 2x[/tex]
4x - 9 + 23x in the simplest form
Answer:
Step-by-step explanation:
4x - 9 + 23x
Combine like terms
4x+23x -9
27x -9
Simplest form is combining all the like terms.
4x + 23x = 27x
Then you have -9
Simplest form = 27x -9
I
69. A car is driving at a speed of 55 mi/h. What is the speed of the car in feet per minute
Answer: [tex]4840\ ft/min[/tex]
Step-by-step explanation:
Given
Speed is [tex]v=55\ mi/h[/tex]
Also, 1 mile is equal to 5280 ft
1 hour is equal to 60 min
Substitutes this values
[tex]\Rightarrow 55\times \dfrac{5280}{60}\\\\\Rightarrow 55\times 88\\\Rightarrow 4840\ ft/min[/tex]
Which equation graphs as the parabola?
A) Ax) = x² + 4
B) f(x) = x2 + 2x + 4
C) Ax) = x² + 5x- 4
OD) Ax) = x² + 3x-4
In which quadrant does θ lie given that sinθ<0 and cosθ<0?
The third quadrant.⠀⠀⠀⠀⠀⠀⠀⠀
Answer:
θ would lie in Quadrant III
Step-by-step explanation:
Review the attached file
NO LINKS OR ELSE YOU'LL BE REPORTED!Only answer if you're very good at Math.No guessing please.
Angelo's Pizza is having a ticket raffle to raise money for new soccer uniforms.A $1 ticket gives an even chance to win one $25 gift certificate,one $15 gift certificate,or three $5 gift certificates.What is the expected profit or loss for purchasing 1 ticket if 100 total tickets are sold?
A: a gain of $0.45
B: a gain of $0.55
C: a loss of $0.55
D: a loss of $0.45
===============================================
Explanation:
Let x be the net winnings the customer gets
Saying something like x = 24 means you've walked away with $24. This occurs when you pay $1, and get $25 back in prizes, so 25-1 = 24 dollars overall.
The probability of this event occurring is 1/100 since there's only one ticket with the $25 prize
Make a table as shown below. It represents all the possible x values which are all the possible net winnings. Note how 1/100 = 0.01, 3/100 = 0.03 and 95/100 = 0.95
The third column is x*p(x) which is the product of the first two columns. Adding everything in the third column (that isn't highlighted in yellow) gets us the value -0.45 which is the expected value for the customer.
This represents a loss of $0.45, aka a loss of 45 cents. This is from the perspective of the customer.
Flipping things around, the pizza company will see this is as a gain of $0.45 or a gain of 45 cents.
----------------
Here's another way to see why this works:
The pizza company earns $100 in revenue since 100 tickets are sold for a dollar each. The company pays out 25+15+3*5 = 55 dollars in prizes overall. That means the company will make a profit of 100-55 = 45 dollars. So the average profit per ticket is 45/100 = $0.45 aka 45 cents and this is from the viewpoint of the pizza company (not the customer). The positive average profit represents a gain.
approximate 12256 to 3 significant figures
Answer:
123 is the answer
hope that helps bby<3
please help me find the area
Area: 126ft
Hope it helps...
Please HELP❗️40 points
Answer:
Q1This is acute angle since 75° < 90°Q2This is an isosceles triangleQ3Exterior angle is the sum of non-adjacent interior angles:
4x + 7 + 6x - 9 = 11810x - 2 = 11810x = 120x = 12m∠L = 4*12 + 7 = 48 + 7 = 55°
Q4The triangles are congruent and corresponding sides are equal:
3x - 5 = 2x + 13x - 2x = 1 + 5x = 6Side lengths are:
3*6 - 5 = 13HELP ME ASAPPPP PLZZZ
Answer:
[tex]x \leqslant \frac{18}{5} [/tex]
Step-by-step explanation:
1: Solve the inequality:
[tex] - 5x + 3 \geqslant - 15 \\ rearrange \: unknown \: terms \: to \: the \: left \: side \: of \: the \: equation \\ - 5x \geqslant - 15 - 3 \\ reduce \: the \: greatest \: common \: factor \: for \: both \: sides \: of \: the \: inequality \\ 5x \leqslant 15 + 3 \\ calculate \: the \: sum \: or \: differences \\ 5x \leqslant 18 \\ divide \: both \: side \: of \: the \: inequality \: by \: the \: coefficient \: of \: variable \\ x \leqslant 18 \div 5 \\ rewrite \: as \: a \: fraction \\ x \leqslant \frac{18}{5} [/tex]
2: Plot:
[tex]x \leqslant \frac{18}{5} \\ graph \: on \: number \: line: [/tex]
Hajar makes 1 can of purple paint by mixing 2 red paint with 3 blue paint. She makes 8 purple cans in total. How many red and blue paint did she use each?
Answer:
16 red and 24 blue
Step-by-step explanation:
2 red×8=16
3 blue×8=24
sorry if it's not true
How many plants are shorter than 27 inches?
How many different ID cards can be made if there are 8 digits on a card if digits can be repeated?
Answer:
10*9*8*7*6*5*4*3 = 10!/2 = 1814400 Cheers
Step-by-step explanation:
hope it works.
If 8 x - 4 = 6 - 3 x then x =
Answer:
4th option is correct
Step-by-step explanation:
[tex]8 x - 4 = 6 - 3 x[/tex]
[tex]8x−4+3x=6[/tex]
[tex]11x−4=6[/tex]
[tex]11x=6+4[/tex]
[tex]11x=10[/tex]
[tex]x = \frac{10}{11} [/tex]Hope it is helpful...Answer:
option 4 ,
x=10/11
is the answer of your question
explanation is attached below .
hope it is helpful to you
I need some help on this math question. Please explain how you found the answer too!
Answer:
A
Step-by-step explanation:
The table represents a proportional function which has a rate of proportionality equal to 5
In fact
5:1 = 5
15 : 3 = 5
25 : 5 = 5
35 : 7 = 5
If we make 90 : 18, the result is 5, so this dates can be part of the table
The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 20 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.The probability that the combined sample will test positive is
Answer:
0.0954 = 9.54% probability that the combined sample tests positive for the virus. This probability is higher than 5%, and thus, it is not unlikely for such a combined sample to test positive.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they test positive, or they do not. The probability of a person testing positive is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability of a randomly selected adult in one country being infected with a certain virus is 0.005.
This means that [tex]p = 0.005[/tex]
Samples from 20 people
This means that [tex]n = 20[/tex]
What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive?
Probability of at least one positive test, which is:
[tex]P(X geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.005)^{0}.(0.995)^{20} = 0.9046[/tex]
Then
[tex]P(X geq 1) = 1 - P(X = 0) = 1 - 0.9046 = 0.0954[/tex]
0.0954 = 9.54% probability that the combined sample tests positive for the virus. This probability is higher than 5%, and thus, it is not unlikely for such a combined sample to test positive.
Perform the operation and, if possible, simplify
21/20 - 4/15
Answer:
47/60
Step-by-step explanation:
Find the LCM and multiply to get there.
LCM is 60
63/60-16/60
47/60
EASY QUESTION!!!!!!!!!! PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!
What is one benefit of displaying data from multiple samples in a graph or table?
It can save time from doing number crunching and analysis because it's an easy to see visual.
What is the area of the parallelogram below?
7 in2
14 in2
18 in2
28 in2
Answer:
14 (B)
Step-by-step explanation:
Area = L * h
L = 7 in^2
h = 2
Area = 7 * 2
Area = 14 in^2
Answer:
14
Step-by-step explanation:
Did lesson
- b/0.1 +2.9= -35.1 no links or anything just the answer
Answer:
b = 3.8
Step-by-step explanation:
- b/0.1 +2.9= -35.1
Subtract 2.9 from each side
- b/0.1 +2.9-2.9= -35.1-2.9
-b/.1 = -38
Multiply each side by -.1
-b/.1 * (-.1) = -38 *(-.1)
b = 3.8
help pls? asap. pls and ty :)
Answer:
a
Step-by-step explanation:
1/2x-30aaaaaaaaaaaaaaaa
is 2(9x) and 18x
Equivalent?
Explain why
PLEASE HELP ME
Solve:
24t = 72
OA) t= 3
OB) t= 4
OC) t=- 2/1
OD) t= 1/3
Answer:
t =3
Step-by-step explanation:
24t = 72
Divide each side by 24
24t/24 = 72/24
t=3
Answer:
A
Step-by-step explanation:
24 t = 72
divide both sides by 24
Thus, t = 72/24
t = 3
Bye ! :-)
why do we need imaginary numbers?explain how can we expand (a+ib)^5. finally provide the expanded solution of (a+ib)^5.(write a 100 words paragraph and show the working to expand (a+ib)^5.
Answer:
a. We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution.
b. (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵
Step-by-step explanation:
a. Why do we need imaginary numbers?
We need imaginary numbers to be able to solve equations which have the square-root of a negative number as part of the solution. For example, the equation of the form x² + 2x + 1 = 0 has the solution (x - 1)(x + 1) = 0 , x = 1 twice. The equation x² + 1 = 0 has the solution x² = -1 ⇒ x = √-1. Since we cannot find the square-root of a negative number, the identity i = √-1 was developed to be the solution to the problem of solving quadratic equations which have the square-root of a negative number.
b. Expand (a + ib)⁵
(a + ib)⁵ = (a + ib)(a + ib)⁴ = (a + ib)(a + ib)²(a + ib)²
(a + ib)² = (a + ib)(a + ib) = a² + 2iab + (ib)² = a² + 2iab - b²
(a + ib)²(a + ib)² = (a² + 2iab - b²)(a² + 2iab - b²)
= a⁴ + 2ia³b - a²b² + 2ia³b + (2iab)² - 2iab³ - a²b² - 2iab³ + b⁴
= a⁴ + 2ia³b - a²b² + 2ia³b - 4a²b² - 2iab³ - a²b² - 2iab³ + b⁴
collecting like terms, we have
= a⁴ + 2ia³b + 2ia³b - a²b² - 4a²b² - a²b² - 2iab³ - 2iab³ + b⁴
= a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴
(a + ib)(a + ib)⁴ = (a + ib)(a⁴ + 4ia³b - 6a²b² - 4iab³ + b⁴)
= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b + 4i²a³b² - 6ia²b³ - 4i²ab⁴ + ib⁵
= a⁵ + 4ia⁴b - 6a³b² - 4ia²b³ + ab⁴ + ia⁴b - 4a³b² - 6ia²b³ + 4ab⁴ + ib⁵
collecting like terms, we have
= a⁵ + 4ia⁴b + ia⁴b - 6a³b² - 4a³b² - 4ia²b³ - 6ia²b³ + ab⁴ + 4ab⁴ + ib⁵
= a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵
So, (a + ib)⁵ = a⁵ + 5ia⁴b - 10a³b² - 10ia²b³ + 5ab⁴ + ib⁵
