[tex] \boxed{\Large {\mathcal {{{\color{orange}{Area \: of \: circle \: = \: πr²}}}}}}[/tex]
r = 7.15m[tex]\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large πr²\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:{7.15}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:51.1225 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{ \cancel7} \: \times\: \cancel{51.1225} \: \: ^{ \red{7.303} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \:Area \: of \: circle }\:\large\blue\implies \tt \large {22} \: \times\:7.303 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \: 160.666 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Hence , the area of circle is 160.66 m²
Given :-
Radius of circle = 7.15mTo Find :-
Area of circleSolution :-
Area of Circle = πr²
putting the value of π and rArea = 3.14×(7.15)² m²
= 160.52465 , which rounded off to 2DP would be 160.52 m²
Can I add [tex]2\sqrt{3} + 5\sqrt{3}[/tex] further?
Yes, they can be added and simplified further. 2√3 + 5√3 = 7√3 .
Take √3 as common factor:
2√3 + 5√3
(2 + 5)√3
7√3
The two irrational numbers sums to form another irrational number 7√3 . In decimals that is 12.12435...
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Yes, The terms assigned above are alike so they can be added easily by simple algebric method where root number can be treated as a variable.
[tex]\qquad \sf \dashrightarrow \: 2 \sqrt{3} + 5 \sqrt{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: (2 + 5) \sqrt{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 7 \sqrt{3} [/tex]
Work out the bearing of Y from W.
(Not drawn accurately)
Answer:
206°
Step-by-step explanation:
The bearing of y from w is the angle y makes with w moving from the north pole in clockwise direction.
So from the north pole, move in clockwise direction and stop at the line joining w and y
the angles there are 90+116= 206°
Therefore the bearing of Y from W is 206°
Using the relationships between
perpendicular lines and their slopes, explain
why horizontal and vertical lines will always
be perpendicular.
Be sure to include the slopes of horizontal
and vertical lines as part of your answer
Answer:
They will always intersect at one point
Step-by-step explanation:
^^
a) Write 2 expressions for the area of the shaded region.
b) Find the length of the shaded region if the perimeter is 48cm.
c) Find the area of the shaded region if perimeter is 48cm.
Answer:
(a)9×3=37' 97 and 8 are factors of 37
In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s?
Circle O is shown. Line segments A O and B O are radii with length r. Angle A O B has a measure of theta. Arc A B has a measure of s.
s = Θ · r
r = Θ · s
s = Θ + r
r = Θ + s
The equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r
How to determine the arc length?The attached image completes the question
The given parameters are:
Angle = ΘRadius = rSince, the angle is in radians.
The arc length is calculated as:
Arc length = Angle * Radius
So, we have:
s = Θ * r
Hence, the equation that represents the relationship between the radius, r, and arc length, s is s = Θ * r
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A camper ties a rope from a tree to the ground to help build a shelter. The rope is 8 feet long, and it is tied 6 feet up the tree. How far from the tree is the rope anchored to the ground? Use the Pythagorean theorem to find the answer.
Answer:
≈5.3 feet,63.6 inches
Step-by-step explanation:
36+b²=64
-36 -36
b²=28
if we square root both sides we can get the radical/exact answer or the rounded one
radical: 4√7
rounded to the nearest tenth: 5.3 feet
Please help fast, thank you! I only have 20 minutes! I always appreciate your help!
Answer:
ur missing the question
Step-by-step explanation:
tGive the values of a, b, and c from the standard form of the equation (2x + 1)(x - 2) = 0.
Answer:
a = 2
b = -3
c = -2
Step-by-step explanation:
The standard form of a quadratic equation:
ax² + bx + c = 0
…………………………
in order to determine the equation
in standard form ,we have to expand the given expression :
(2x + 1)(x - 2) = 2x² - 4x + x - 2
= 2x² - (4x - x) - 2
= 2x² - 3x - 2
Then the standard form is :
2x² - 3x - 2
The following data table represents the total cost of a monthly cell phone bill as a function of the number of minutes that the phone is used each month. Minutes 500 750 1,000 1,250 1,500 Total Monthly Cost (in dollars) $62 $77 $92 $107 $122Choose the correct linear model that represents the total monthly cost as a function of time. A y = 0.06 x + 500, B y = 16 x + 32,C y = 62 x + 16, D y = 0.06 x + 32 .
Answer:
ytyt
Step-by-step explanation:
tyt5667
Write the algebraic expression for the following statement.
A number decreased by 7 is 5.
Answer:
the algebraic expression is ; x-7=5
What is (-2)-(-2 1/6) and how do i get that answer?
Answer:
1/6
Step-by-step explanation:
-2 - (-2 1/6)
multiply the number in the parentheses by -1
-2 + 2 1/6
-2 + 2 cancels out
Leaving 1/6 as your answer.
please help me find the HCF of this
Answer: a
Step-by-step explanation:
[tex]a^{2}=a \cdot a\\a^{2}+ab=a(a+b)[/tex]
Therefore, the HCF is a.
Answer:
a
Step-by-step explanation:
Factorizing both terms :
a² = a × aa² + ab = a × (a + b)The HCF of the terms is a.
Select all that apply. Which of the following corresponds to absolute zero?
In thermodynamic system, Absolute Zero is that temperature implies Lowest energy level i.e. option a) 0 K or -273° C.
What is Absolute Zero?
Absolute Zero can describe as, in a thermodynamic system, there are certain energy levels depending upon the potentials of temperature. At Absolute zero the potentials of temperature are 0 K in Kelvin scale and -273° C in Celsius scale.
The question seem's to be incomplete. The option could be.
a) 0 K and -273° C
b) 273 K and 0° C
c) -273 K and 0° C
d) 0 K and 273° C
Hence, As per theory Value of The absolute zero is 0 K and -273° C
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Which ordered pair is not a solution of the linear equation shown?
1
y=-x
2
OA) (2, 1)
B) (1.-—-)
1,
2
OC) (4,8)
OD) (-2,-1)
Answer:
C : (4,8)
Step-by-step explanation:
The equation y = (1/2) x
Or, 2y = x ==> x = 2y
means that, for any value of x, the y value must be one-half that value or, in other words, for any value of y, x must be twice the value of y
A, B and D will satisfy the above equation if you plug in values of x and y given
In C we have x = 4 and y =8 so x = y/2 NOT 2y
The summer solstice can occur on any day of the week, with each day being
equally likely. What is the probability the summer solstice will occur on a
weekday?
О А.
O B.
7
115
517
O C.
O D. 1/1/20
The probability that the summer solstice will occur on a weekday is equal to 5/7.
How to calculate the probability?Generally, there are seven days in a week and two among these days are weekends while five are weekdays. Thus, this can be represented as follows:
Total number of days = 7.Number of weekends = 2.Number of weekdays = 5.Therefore, the probability that the summer solstice will occur on a weekday is given by:
P = 5/7.
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PLEASE HELP ME WITH THIS MATH PROBLEM!!
Step-by-step explanation:
in general we would need a probabilty table or a probability calculator service on the internet.
but in this case we know.
the man value is 64. and the standard deviation is 6.
so, one standard deviation +/- interval from the mean value is 70 and 58.
and the interval of 2 standard deviations from the mean value is 76 and 52.
and 64 and 76 are exactly the limits we are asked for.
so, remember the normal distribution rule :
68% are within 1 standard deviation.
95% are within 2 standard deviations.
99.7% are within 3 standard deviations.
and 50% are below (and also above) the mean value.
so, we know, 50% of the 350 (= 175) students scored below 64.
95% of the students scored between 76 and 52. as there are 5% left, half of these 5% (= 2.5%) scored even below 52).
so, 95% + 2.5% = 97.5% of the 350 (= 341.25) students scored below 76.
therefore, the number of students that scored between 64 and 76 is
341.25 - 175 = 166.25 ≈ 166
Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.
1. At what time will Lindsey be 30 feet in the air?
2. How high is the diving board? Explain your thinking.
Answer:
1. [tex]x = 2.45s[/tex]
2. The diving board is 45 ft high.
Step-by-step explanation:
• When Lindsey is 30 feet in the air, y = 30.
[tex]30 = -16x^2 + 33x +45\\\\-16x^2 + 33x +15 = 0\\\\16x^2 - 33x -15 = 0\\[/tex]
Using quadratic formula, solve for x:
[tex]x = \frac{33 + \sqrt[]{(-33)^2 - 4(16)(-15)} }{2(16)}[/tex]
[tex]x = 2.45s[/tex]
• If we calculate the height of Lindsey in the air when she is standing on the diving board, we can find the height of the diving board above the ground.
When she is standing on the board, x = 0 as no time has passed after jumping.
[tex]y = -16(0)^2 + 33(0) +45\\\\y = 45 ft[/tex]
(c) Given that the average speed for the entire journey was 80 km/h, form an equation in x and solve the equation.
Answer:
80x = y
Step-by-step explanation:
Which numbers are the extremes of the proportion shown below?
3-604
=
8
A. 3 and 8
B. 3 and 6
C. 4 and 6
D. 4 and 8
Answer:
A 3 and 8
Step-by-step explanation:
if a/b=c/d, the extremes are "a" and "d". The means would then be "b" and "c"
The extremes of the proportion are 3 and 8.
To find the extremes of a proportion, we need to identify the numbers that are positioned at the far ends of the proportion. In the given proportion:
3/4 = 6/8
The numerator of the first fraction, 3, and the denominator of the second fraction, 8, are the extremes. These numbers form the far ends of the proportion.
Therefore, the extremes of the proportion are 3 and 8.
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How is the graph of the parent function y = x squared transformed to produce the graph of y = 3 (x + 1) squared?
It is translated 1 unit right and compressed vertically by a factor of 3.
It is translated 1 unit left and compressed vertically by a factor of 3.
It is translated 1 unit right and stretched vertically by a factor of 3.
It is translated 1 unit left and stretched vertically by a factor of 3.
Answer:
D.
Step-by-step explanation:
Round 508.0219 to the nearest hundredth
Answer:
508.02
HOPE THIS HELPS
Todo <3
Step-by-step explanation:
Given lJK , which is an isosceles right triangle, IJ=4 and m
As IJK is isosceles
IJ=JKHypotenuse must not counted counted among equal sides so
IK²=2(LJ)²Apply roots
IK=LJ√2Option C
Use the FOIL method to evaluate the expression:
Answer:
[tex]\sf b.) \ 1 +2\sqrt{7}[/tex]
Explanation:
Foil method: (a + b)(c + d) = ac + ad + bc + bd
Solving steps:
[tex](4 - \sqrt{7} )(2 + \sqrt{7} )[/tex]
[tex](4)(2) + 4(\sqrt{7} ) + (-\sqrt{7} )(2) + (-\sqrt{7} )(\sqrt{7} )[/tex]
[tex]8 + 4\sqrt{7} - 2\sqrt{7} - 7[/tex]
[tex]8 -7 + 4\sqrt{7} - 2\sqrt{7}[/tex]
[tex]1 +2\sqrt{7}[/tex]
option b) 1 + 2√7
Step-by-step explanation:Foil property method :-
[tex] \red{ \boxed{ \orange{ \rm (a + b)(c + d) = ac + ad + bc + bd}}}[/tex]
then, on substituting the values,
[tex]\sf⇒ \: \: 8 + 4 \sqrt{7} - 2 \sqrt{7} - 7[/tex]
[tex]\sf⇒ \: \: \green{ \underline{\bold{ \red{1 + 2 \sqrt{7} }}}}[/tex]
32 divided by 4x [16x1/2]-2
find the pattern of 1,2,6,18 and state if its arithmetic or geometric
Answer:
its a geometric sequence where each term is 3 times the previous term.
Step-by-step explanation:
{2,6,18,54,162,486,1458...}
The probability of a drawing a blue marble from a box of 18 marbles is 2/3. How many green marbles should be added to the box in order to reduce the probability to 1/2?
Answer:
6 green marbles should be added.
Step-by-step explanation:
If the probability of drawing a blue marble from 18 marbles is 2/3 then there are 12 blue marbles because 18 times 2/3 is 12. This means that to reduce this probability to 1/2 you need to add 6 more marbles to the total amount to get it to 24. Now the probability of getting a blue marble is 12/24 which is 1/2.
A school is watching students as they enter the football game for students who are dressed
inappropriately. they estimate that 7% of all students are dressed inappropriately. out of a group
of 40 students, what is the probability that exactly 2 are dressed inappropriately? round to 3 decimal places.
Using the binomial distribution, it is found that there is a 0.242 = 24.2% probability that exactly 2 are dressed inappropriately.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 40, p = 0.07.
The probability that exactly 2 are dressed inappropriately is given by P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{40,2}.(0.07)^{2}.(0.93)^{38} = 0.242[/tex]
0.242 = 24.2% probability that exactly 2 are dressed inappropriately.
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Progress
Solve for x. Round to the nearest tenth, if necessary
Answer:
x ≈ 1.1
Step-by-step explanation:
using the cosine ratio in the right triangle
cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{0.8}{x}[/tex] ( multiply both sides by x )
x × cos41° = 0.8 ( divide both sides by cos41° )
x = [tex]\frac{0.8}{cos41}[/tex] ≈ 1.1 ( to the nearest tenth )
Question 3(Multiple Choice Worth 5 points)
(06.03 LC)
Determine the equation of the graph, and select the correct answer below.
(-1, 3)
albert worked for 8 hours and earned $24. how much does albert earn for 24 hours
Answer:
$72
Step-by-step explanation:
