The required probability that there are at least 1 blue candy and 1 green candy left in the jar when you have taken out all the red candies is 7/12 .
Probability is defined as the ratio of total numbers of outcomes of an event to the favouable outcomes of an event.
We have , Red candies in the jar = 10
green canides in the jar = 30
blue candies in the jar = 20
total number of candies in jar = 60 i.e total number of outcomes = 60
The Probability that the last of sixty candies drawn is one of thirty green candies = 30/60 = 1/2
Ignoring green canides, probability that the last of the thirty other candies drawn is one of twenty blue = 20/30 = 2/3
The Probability that the last of sixty candies drawn is one of twenty blue candies = 20/60 = 1/3
The Probability that the last of sixty candies drawn is not one of twenty blue candies = 1 - 1/3
= 2/3
Probability that last draw would be blue and the last not blue would be green = 20/60 × 30/40
= 1/4 ----(1)
Probability that last draw would be green and the last not green would be blue = 30/60× 20/30
= 1/3 ------(2)
Now , Required probability that last draw would be either blue or green canidy = sum of above probabilty from equation (1)and (2)
= 1/4 + 1/3 = 7/12
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Determine whether each of these functions from {a,b,c,d} to itself is bijection if it is than find f -¹.
f(a)=b, f(b)=a, f(c)=d, f(d)=c
f(a)=a, f(b)=b, f(c)=c, f(d)=d
Only function (a) is one-to-one.
What is a one-one function?A mathematical function with individuality known as an injective function, injective, or one-one function never translates discrete components of its domain to equivalent elements of its codomain. We can say that each element of the codomain is only a representation of a single element in the domain.acc to our question-
If every element of the range of the function corresponds to exactly one element of the domain, then the function is called one-to-one.
The elements of a function are
A = {a,b,c,d}
Therefore, this function is one-to-one.
(b).f (a) = b, f (b) = b, f (c) = d, f (d) = c.
Here, the value of function is b for x=a and x=b. For two domains the functions has same range.
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answer the question please i would appreciate it man
The scientific notation representation is 2.6 x [tex]10^{-2}[/tex].
What is scientific Notation?Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
Given:
(0. 00032) (5.2 x [tex]10^6[/tex])/ 6.4 x [tex]10^5[/tex]
Now, solving the above expression
= 0.001664 x 10² / 6.4
= 0.00026 x 10²
= 2.6 x [tex]10^{-2}[/tex]
Hence, the scientific notation representation is 2.6 x [tex]10^{-2}[/tex].
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Hong made $153 for 9 hours of work.
At the same rate, how many hours would he have to work to make $187?
hours
X
Answer:
11 hours
Step-by-step explanation:
153 divided by 9 (which is 17) 17$ per hour so add 17 and 17 together which would be 34 and add it to 153 which would be 187$ he worked 2 more hours so in total he worked 11 hours.
and i know that was a bad explanation but its whatever hope this helped.
the hypotenuse of a triangle is 4x one of the legs . the other leg in 3(sqrt 5 units. find the length of the hypotenus?
The length of the hypotenuse is 4√3 units.
Given that hypotenuse is 4 times the length of one leg of a triangle. So here we can assume that length to be x. Hence the hypotenuse length is 4x. To calculate hypotenuse we have the formula a²=b² + c², where b and c are two sides of the triangle and a is the hypotenuse. If we put these values in the formula we get,
16x² = x² + (3√5)²
15x² = 45
x² = 3
x = ±√3
Since length cannot be negative, the final value of x = √3, and since the length of the hypotenuse was 4x, the final value of the hypotenuse is 4√3.
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The Venn diagam represents the
information from the following sets.
= {Prime numbers less than 38}
R = {2, 3, 5, 17, 19, 37}
S = {3, 5, 7, 11, 13, 37}
R
17 5
2
19 37
3/13
S
11
231 23
Find P(RUS)
P(RUS) =
=======================================================
Explanation:
The U refers to set union. We combine the elements of set R and set S together in one big set. Toss out any duplicates. Sorting the items is optional, but I recommend it.
R U S = {2, 3, 5, 17, 19, 37} U {3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 17, 19, 37, 3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 7, 11, 13, 17, 19, 37}
This list of values consist of items in set R, set S, or both.
There are 9 items in set R U S.
This is out of 12 items total in the universal set rectangle.
The probability of randomly selecting something from set R U S is 9/12 = 3/4
write equations for each line given the following points. Remember you must first find the slope and then determine the Y intercept, then write out the equation in slope intercept form. Remember if the Y intercept b is zero, then, there is no need to put it there, and if the slope is one, then you only need to write x, not 1 X
(-3,2) and (5,7)
The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is: [tex]y = \frac{5}{8} x + \frac{1}{8}[/tex]
What is the slope-intercept form?One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,Slope-intercept formPoint slope formTwo-point formIntercept formCalculation
from ( - 3, 2) and (5, 7)
slope(m) = [tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]
[tex]=\frac{7 - 2}{5 - (-3)}[/tex]
[tex]= \frac{5}{8}[/tex]
from slope-intercept equation
⇒y = mx+ c
⇒( - 3, 2) , [tex]2 = \frac{5}{8} * (-3) + b[/tex]
⇒[tex]2 = \frac{15}{8} + b[/tex]
⇒[tex]2 - \frac{15}{8} = b[/tex]
⇒[tex]\frac{16+15}{8} = b[/tex]
⇒[tex]\frac{31}{8} = b[/tex]
Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :
⇒[tex]y = \frac{5}{8} x +\frac{31}{8}[/tex]
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The slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is:
What is the slope-intercept form?One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line.
When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
The equation of a line is the equation that each point on the line fulfills. There are several ways to solve the straight line equation given as,
Slope-intercept form
Point slope form
Two-point form
Intercept form
from ( - 3, 2) and (5, 7)
slope(m) = y²-[tex]y^{1}[/tex]/x²-[tex]x^{1}[/tex]
=7-(-2)/5-(-3)
=5/8
from slope-intercept equation
⇒y = mx+ c
⇒( - 3, 2) , 2=5/8*(-3)+b
⇒2=15/8+b
⇒2-15/8=b
⇒16+15/8
31/8=b
Therefore, the slope-intercept form of the equation of the line that passes through (-3, 2) and (5, 7) is :
⇒y=5/8x +31/8
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help meeeeeeeeeeeeeee pleaseee
The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2
The curve opens downward.
from, the graph, the roots of the equation are -4 and 0
so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.
The equation of the curve is the product of the factors of the curve which is y = x(x + 4)
y = [tex]x^{2}[/tex] + 4x
the x coordinate of the vertex = -b/2a = axis of symmetry
where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x
so a = 1, b = 4
x coordinate of vertex = -4/2 = -2
substitute x = -2 into y = [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex
y = [tex](-2)^{2}[/tex] + 4(-2)
y = 4 -8
y = -4
vertex is (-2, -4)
The axis of symmetry is -b/2a which is -2
The curve opens downward as the vertex is at -4
In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward
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on the grid,draw the graph of y=2x-3 for values of x from -3 to 5
The graph of the equation y = 2x - 3 at the interval of -3 to 5 is attached below.
Graph:
Graph means the diagram that shows the variation of a variable in comparison with that of one or more other variables.
Given,
Here we have the equation y = 2x - 3
Now, we need to plot the graph of the given equation at the interval of -3 to 5..
To plot the graph for the given function,
The given interval is taken as the value of x and we have to calculate the value of y from it,
Now, we have to take the given interval -3, -2, -1, 0, 1, 2, 3, 4, 5 are the samples value for x.
So, we have to apply the values on the equation,
Then we get the value of the function as,
x = -3 => y = 2(-3) - 3 = -6 - 3 = 9
x = -2 => y = 2(-2) - 3 = -4 - 3 = -7
x = -1 => y = 2(-1) - 3 = -2 - 3 = -5
x = 0 => y = 2(0) - 3 = 0 - 3 = -3
x = 1 => y = 2(1) - 3 = 2 - 3 = -1
x = 2 => y = 2(2) - 3 = 4 - 3 = 1
x = 3 => y = 2(3) - 3 = 6 - 3 = 3
x = 4 => y = 2(4) - 3 = 8 - 3 = 5
x = 5 => y = 2(5) - 3 = 10 - 3 = 7
The completed table is attached below.
Now, we have to plot the graph through the derived table, then we get the graph like the following.
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engineers must consider the diameters of heads when designing helmets. the company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4-in and a standard deviation of 0.9-in. due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 1.4% or largest 1.4%. what is the minimum head diameter that will fit the clientele? min
The largest head diameter that can accommodate the clientele is 8.5743
Mean, u = 6.4
Standard deviation = 0.9
We must utilize the inverse of the common normal table to obtain our values.
the smallest head width possible.
P(Z < z) = 1.4%
P(Z < z) = 0.014
P(Z < -2.0749) = 0.014
z = -2.0749
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
We already have:
z = -2.0749
u = 6.5
s.d = 1
Replacing numbers,
x = (-2.0749 × 1) + 6.5
x = 4.4251
The clientele requires a minimum head breadth of 4.4251.
The largest head width that can be accommodated.
P(Z > z) = 1.4%
1 - P(Z < z) = 0.014
P(Z < z) = 1 - 0.014 = 0.981
P(Z < 2.0749) = 0.981
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
z = 2.0749
u = 6.5
s.d = 1
Substituting figures,
x = (2.0749 × 1) + 6.5
x = 4.4251
x = 8.5743
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a supermarket employee wants to construct an open-top box from a 14 by 30 in piece of cardboard. to do this, the employee plans to cut out squares of equal size from the four corners so the four sides can be bent upwards. what size should the squares be in order to create a box with the largest possible volume?
The size of the squares should be 3 inches in order to create a box with the largest possible volume.
If squares of equal sizes are to be cut out from the four corners so the four sides can be bent upwards, then the length of these squares will be the height of the box. Also twice of this length subtracted from the initial length and width of the material will be the new length and width of the box, respectively.
let x = length of square to be cut = height of the box
length of the box = 30 - 2x
width of the box = 14 - 2x
The volume of the box, which is a rectangular prism, is the product of the length, height and width.
V = l x w x h
V = (30 - 2x)(14 - 2x)(x)
V = 420x - 88x² + 4x³
To obtain the largest volume possible, the first derivative of the volume should be equal to zero.
V'(x) = 0
V = 420x - 88x² + 4x³
420 - 176x + 12x² = 0
Simplify and solve for the value of x.
12x² - 176x + 420 = 0
3x² - 44x + 105 = 0
(3x - 35)(x - 3) = 0
x = 35/3 ; x = 3
Check each value.
When x = 35/3 = h
l = 30 - 2x = 20/3
w = 14 - 2x = -28/3 ( length should be positive)
When x = 3 = h
l = 30 - 2x = 24
w = 14 - 2x = 8
Hence, the length of square to be cut is 3 in.
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Convert 17 weeks into days
Answer:
119days
Step-by-step explanation:
1 week= 7 days
take week as w
so 1w=7 or w=7
now 17 weeks=??
17w=??
w=7 so input in above statement:
17(7)=119days
Answer: 119 days
Step-by-step explanation:
We can set up a dimensional analysis problem to solve.
[tex]\displaystyle 17 \;\text{weeks}\;(\frac{7\;\text{days}}{1\;\text{week}} )[/tex]
The units of [tex]\frac{weeks}{weeks}[/tex] cancel out, leaving us with days. Since we are being asked to find days, this will leave us at the right point.
[tex]\displaystyle \frac{17*7}{1} =119\;\text{days}[/tex]
annual revenue for corning supplies grew by 5.5% in 2007; 1.1% in 2008; -3.5% in 2009; -1.1% in 2010; and 1.8% in 2011. what is the mean growth annual rate over this period? round your answer to four decimal places. do not round intermediate calculations.
The mean yearly growth rate for this period is 0.0036.
Define annual growth rate.The average annualized return of a portfolio, asset, or cash flow over time is known as the average annual growth rate, or AAGR. The basic arithmetic mean of a set of returns is used to calculate AAGR.
The change in a measurement's value over a year is known as the annual growth rate (AGR).
The sum of the growth rates for each year divided by the total number of years yields the mean growth annual rate.
Where the annual growth rate is calculated as follows: 5.5 + 1.1 - 3.5 - 1.1 + 1.8 = 3.8%
And the total number of years is 5.
Then ,
The average annual growth rate for this time period is = 3.8/5
Over this time span, the average yearly growth rate was 0.76%.
Make a decimal conversion
= 0.76% = 0.0076
Therefore, the mean yearly growth rate for this period is 0.0036.
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What is cos 60°?
A.1
B. √3/2
C. √3
D.1/2
E.1/√2
F.1/√3
Answer:
The trigonometric functions, sin, cos and tan for an angle are the primary functions. The value for cos 60 degrees and other trigonometry ratios for all the degrees 0°, 30°, 45°, 90°, 180° are generally used in trigonometry equations. These trigonometric values are easy to memorize with the help trigonometry table.
Cos 60 Degree Value
In a right-angled triangle, the cosine of ∠α is a ratio of the length of the adjacent side (base) to the ∠α and its hypotenuse, where ∠α is the angle formed between the adjacent side and the hypotenuse.
Cos 60 Degree value
Cosine α = Adjacent Side / Hypotenuse
Cos α = AC / AB
Cos α = b / h
Now, to find the value of cos 60 degrees, let us consider, an equilateral triangle ABC as given below:
Cos 60 Degree
Here, AB = BC = AC and AD is perpendicular bisecting BC into two equal parts.
As we know, cos B = BD/AB
Let us consider the length of each side as 2 units, such as AB = BC = AC = 2 units and BD = CD = 1 unit.
Therefore, the value of cos 60° = BD/AB = ½
In the same way, we can write the value of sin 60° and tan 60° by evaluating the required sides.
In right triangle ABD, by Pythagoras theorem:
AB2 = AD2+ BD2
22 = AD2 + 12
AD2 = 22 -12
AD2 = 4 – 1
AD2 = 3
AD = √3
Now, we have got all the sides of triangle ABD.
Sin 60° = AD/AB = √3/2
Tan 60° = AD/BD = √3 / 1 = √3
We can also write the value of cos 60 degrees in decimal form as:
cos 60° = 1/2 = 0.5
Also, we can write the values of sine, cosine and tangent with respect to all the degrees in a table.
Let us draw a table with respect to degrees and radians for sine, cosine and tangent functions.
Angle in Degrees 0 30 45 60 90 180 270 360
Angle in Radians 0 π/6 π/4 π/3 π/2 π 3π/2 2π
Sin 0 1/2 1/√2 √3/2 1 0 -1 0
Cos 1 √3/2 1/√2 1/2 0 -1 0 1
Tan 0 1/√3 1 √3 ∞ 0 ∞ 0
Unit Circle in Trigonometry
It is possible to give the values of trigonometric ratios with respect to radians equivalent to degrees, in case of a unit circle, whose radius is equal to one. The radian for a unit circle is denoted by π. In the below figure, the angle values are represented in degrees instead of radians.
Cos 60 Degree graph
You have learned about cos 60 degrees value along with other degree’s values here now. Also, the derived values for sin and tan with respect to degrees and radians. In the same way, we can find the values for other trigonometric ratios like secant, cosecant and cotangent.
Let us see some example where we can use the value of cos 60 degrees.
Example 1: Find the value of cos 60° + sin 30°.
Solution:
cos 60° + sin 30°
= cos 60° + sin (90° – 60°)
= cos 60° + cos 60°
= (1/2) + (1/2)
= (1 + 1)/2
= 2/2
= 1
Alternatively, cos 60° + sin 30° = (1/2) + (1/2) = (1 + 1)/2 = 2/2 = 1
Example 2: Calculate: 2 sin 60° – 4 cos 60°
Solution:
We know that, sin 60° = √3/2 and cos 60° = 1/2
Thus, 2 sin 60° – 4 cos 60° = 2(√3/2) – 4(1/2)
= √3 – 2
therefore it 3/2
Step-by-step explanation: Peace Out.... Have a good day
PLEASE GIVE MARK BRAINIEST I WORK SO HARD IT TOOK ALL DAY!!!
Which number is greatest?
57
10
O 5. 84
51
√33, 5. 84,
0 5. 7
OV33
51
9
The greatest number among the given numbers is= 57
What are greatest numbers?largest and smallest number formation We are aware of how to list the numbers in both ascending and descending order. The highest number is created by placing the specified digits in ascending order, and the lowest number is created by placing them in descending order, as we have already learned.. A number has more places when the digit at the very left is in that position. Therefore, to increase the value of the number, the largest digit should be positioned at the very left of the number.The digit 0 is never written at the very leftmost position when one of the given digits is 0, but rather in the second place from the left to obtain the smallest number.learn more about greatest numbers click here:
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can you give me an answer i don't know how to do this
Answer:
It should be ≈ 6,6
calculated the angle <CAB and both are 90°. But that would mean BC is wrong
What is the additive in verse of 16 5/7?
Answer:
the additive inverse of 16 5/7 IS 26/7
Write this ratio another way.
120/150
The ratio 120/150 represented in the simplest form is 4 : 5 .
The given ratio is 120 /150 .
Now if we write the expression in the form of the simplest ratio we have to divide the ratio by the highest common factor.
The HCF of the number is 30. Hence the ratio in simplest form will be
120÷30 : 150÷30 = 4 : 5 .
By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.
Ratio can be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value that this fraction represents.
Ratios of counts are rational numbers that can also be rational numbers and are occasionally expressed by (non-zero) natural numbers.
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please give me the right answer on this so I can turn it in to my math teacher
Answer: 16/18 and 10/16
Step-by-step explanation: The least common denominator would be 18 and 16 because you would multiply by 2.
Hoped This Helped!
You have 84,000 grams of a radioactive kind of tellurium. How much will be left after 75
minutes if its half-life is 25 minutes?
grams
Answer:
10,500 g
Step-by-step explanation:
Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 25 minutes. After 75 minutes, then, the amount of radioactive atoms is halved three times. Therefore:
1st half-life: [tex]84000\text{ g}\div{2}=42000\text{ g}[/tex]
2nd half-life: [tex]42000\text{ g}\div{2}=21000\text{ g}[/tex]
3rd half-life: [tex]21000\text{ g}\div{2}=10500\text{ g}[/tex]
Which of the coordinate pairs below are separated by a vertical
distance of greater than 6 units? Select all that apply.
A) (5.1, -3.3) and (5.1, 3.4)
B) (-1, 2.6) and (-1, -4.2)
C) (3.7, 2.2) and (3.7, -3.4)
D) (6, 1.5) and (6, -2)
Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.
Given that,
The coordinate pairs separated by a vertical distance of greater than 6 units is to be determined.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
here,
(A)
Since the x coordinate is the same in all the pairs, distance on the y axis can only be calculated.
(5.1, -3.3) and (5.1, 3.4)
y = 3.4 - (-3.3)
y = 6.7
Similarly distance,
(B) y = 6.8
(C) y = 5.6
(D) y = 3.5
Thus, Pairs (-1, 2.6) and (-1, -4.2), and (5.1, -3.3) and (5.1, 3.4) has distance greater than 6 unit. Options A and B are correct.
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The range of f(x) = |x| is y ≥ 0. If a < 0 and b ≠ 0 for g(x) = a|x| + b, what is the range of function g?
The range of the function g, given the premises for f(x) = |x| and a < 0 while b ≠ 0 is; the set of all real numbers.
Range of a functionIt follows from the task content that the range of the function g(x) = a|x| + b is to be determined given the parameters as in the task content.
Since the function f(x) = |x| has a range of y ≥ 0, and a is a negative number ( < 0), it therefore means that the a|x| is always a number less than 0 (<0).
However, the possible values of constant, b include all real numbers except 0.
On this note, the function g(x) = a|x| + b has a range which is the set of all real numbers. This is so because, g(x) > 0 when a|x| < b and g(x) < 0 when a|x| > b.
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I NEED HELP PLEASEEEEE ASAPPPPPPP
Answer:
7x+40=180
Step-by-step explanation:
(5x+40)+(2x)=180
7x+40=180
if you were to solve
subtract 40 from each side
7x=140
divide both sides by 7
x=20
check your answer
5(20)+40+2(20)=180
100+40+40=180
this is correct
hope this helps..and with future questions if you need to solve it
To find BCD
we know that C is 40 degrees and we know that triangle is also 180
we can also see that B is a right triangle or 90 degree
so 90+40+A=180
130+A=180
subtract 130 from 180
A=50
Kenneth has c toy cars. Jennifer has 3 times as many toy cars as Kenneth. Write an expression that shows how many toy cars Jennifer has.
Answer:
3c
3c mean 3xc
but just write 3c
Referring to the figure, find the perimeter of the regular polygon
shown. [Note: do not approximate the value of any radicals; thus, if you
obtain, for example, 45 times the square root of 3, simply type 45SQR(3)
as your final answer.]
Referring to the Fig. in Question #1, find the area of the regular polygon
shown. [Note: do not approximate the value of any radicals; thus, if you
obtain, for example, 45 times the square root of 3, simply type 45SQR(3)
as your final answer.]
Answer:
Perimeter = 18√3 = 18SQR(3)
Area = 27√3 = 27SQR(3)
Step-by-step explanation:
The sides of a regular polygon are congruent.
Therefore, as the triangle is a regular polygon, it is an equilateral triangle since its sides (and interior angles) are congruent.
The interior angles of a triangle sum to 180°. Therefore, each interior angle of the equilateral triangle is 60°.
Therefore, the right triangle formed inside the equilateral triangle by the perpendicular bisectors is a 30-60-90 triangle with hypotenuse of 6 units.
The ratio of the side lengths of a 30-60-90 triangle is b : b√3 : 2b, where:
b = shortest side opposite the 30° angle.b√3 = side opposite the 60° angle.2b = longest side (hypotenuse) is opposite the right angle.As the hypotenuse of the 30-60-90 right triangle is 6 units:
[tex]2b = 6 \implies b=3[/tex]
Therefore, the length of the longest leg of the right triangle is 3√3.
As this is half the length of one side of the equilateral triangle:
[tex]\implies \sf Perimeter = 6 \times 3 \sqrt{3}=18\sqrt{3}\; units[/tex]
Heron's Formula allows us to find the area of a triangle in terms of its side lengths.
Heron's Formula
[tex]\sf Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
where:
a, b and c are the side lengths of the triangle.s is half the perimeter.Given:
Each side length = 6√3 unitsHalf perimeter = 9√3 unitsSubstitute these values into the Heron's formula to calculate the area of the equilateral triangle:
[tex]\begin{aligned}\implies \sf Area &= \sf \sqrt{9\sqrt{3}(9\sqrt{3}-6\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(3\sqrt{3})^3}\\ &= \sf \sqrt{9\sqrt{3}(81\sqrt{3})}\\&=\sf \sqrt{2187}\\&=\sf \sqrt{729 \cdot 3}\\&=\sf \sqrt{729}\sqrt{3}\\&=\sf 27\sqrt{3} \;\;units^2\end{aligned}[/tex]
cosec 2A + cosec 4A = cot A - cot 4A
The given expression is proved by the necessary changes.
cosec 2A + cosec 4A = cot A - cot 4A
Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A
Taking LHS :
⇒Cosec 2 A + Cot 4 A
⇒Cosec 2 A + ( Cot 2 A )2
⇒Cosec 2 A + ( Cosec 2 A - 1 )2 ( we know:1+ Cot 2 θ = Cosec 2 θ )
⇒Cosec 2 A + Cosec 4 A + 1 - 2 Cosec 2 A
⇒ Cosec 4 A + 1 - Cosec 2 A
⇒ Cosec 4 A + 1 - ( 1 + Cot 2 A)
⇒ Cosec 4 A + 1 - 1 - Cot 2 A
⇒ Cosec 4 A - Cot 2 A
or cosec2A+cosec4A=cotA-cot4A
Hence Proved.
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The bottom of a 5.5-meter ladder is 3.3 meters from the base of a wall, and it just reaches the bottom of a window in the wall. If the window is 1 meter high, what is the distance from the top of the window to the base of the wall?
The distance from the top of the window to the base of the wall is 5.4 m.
According to the question,
We have the following information:
The bottom of a 5.5-meter ladder is 3.3 meters from the base of a wall, and it just reaches the bottom of a window in the wall. And the window is 1 meter high.
Now, we know that the ladder, wall and base will make a right-angled triangle. We can use Pythagoras theorem to find height of the wall.
(Pythagoras theorem: square of hypotenuse = sum of squares of base and height)
Let's take height of the wall to be h meters.
[tex]h^{2}[/tex] = [tex](5.5)^{2} -(3.3)^{2}[/tex]
[tex]h^{2}[/tex] = 30.25-10.89
19.36
h = √19.36
h = 4.4 m
Now, the distance from the top of the wall window to the base of the wall is:
4.4 + height of the window
4.4+1
5.4 m
Hence, the distance from the top of the window to the base of the wall is 5.4 m.
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0.000007328 rounded to the nearest millioneth,the numbers is about
When the numerical data (number) 0.000007328 is rounded to the nearest millionth, the number is about 0.000007.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsTen thousandthsHundred thousandthsMillionths.UnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.Based on the numerical data (number) provided above, the place value of seven (7) is millionth and it would be rounded up as seven (7) because the next number on its right (3) is less than five (5) and as such, it can seven (7) rounded up to eight (8).
In this context, we can reasonably infer and logically deduce that 0.000007 is a numerical data (number) that represents millionth based on the place value of seven (7).
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Please Help!
Solve the inequality and graph it’s solution.
Answer:
Step-by-step explanation:
You have to multiply both sides by 3 so its -9>-5+n. Then add each side by 5. The answer is n<-4 (D)
Answer:
D) n<-4
Step-by-step explanation:
let x represent one number and let Y represent another number.
The sum of two numbers is -7.
If one number is subtracted from the other, their difference is 11.
Use the given conditions to write a system of equations.
Solve the system and find the numbers
Answer:
c I got you ok answer c
Step-by-step explanation:
bc I got this correct
Answer:
Its D, x+y=-7;x-y=11. Also Part 2 is 2,-9
Step-by-step explanation:
Just did it Pearson 2022
Multiply 2.9x and 5x.
(Multiplying Linear Expressions LC)
14.5x2
7.9x2
14.5x
7.9x
Multiplication of 2.9x and 5x gives 14.5x²
How to multiply algebraic expressions?The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants
Given: 2.9x and 5x
To multiply 2.9x and 5x, multiply the numbers and multiply the letters:
2.9x × 5x = 2.9 × 5 × x × x = 14.5x²
Therefore, 2.9x multiplied by 5x is 14.5x²
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