The result essentially follows directly from the triple-angle identities,
sin(3A) = 3 sin(A) cos²(A) - sin³(A)
cos(3A) = cos³(A) - 3 sin²(A) cos(A)
Then
sin(3A)/sin(A) = 3 cos²(A) - sin²(A)
cos(3A)/cos(A) = cos²(A) - 3 sin²(A)
and
sin(3A)/sin(A) - cos(3A)/cos(A)
= 3(cos²(A) + sin²(A)) - (sin²(A) + cos²(A))
= 3 - 1
= 2
Below are the ratings for a sample of 12 hotels in small Ontario towns:
1.1 4.7 4.8 4.8 5.3 6.5 6.7 7.1 7.1 7.3 8.1 9.2
The critical values of this data set are given:
Q1=4.8 Q2=6.6 Q3=7.2
a) Determine the following and show all work: [3 marks]
i) interquartile range (IQR)
ii) upper boundary and lower boundary
iii) any outlier(s)
b) Create a modified box plot for the data, showing any outlier(s). [1 mark]
c) In order for a hotel to be recommended by travel blog TravelWell, its score must be the 80th percentile or higher. What is the minimum rating a hotel can achieve in order to be recommended by TravelWell based on this sample? [2 marks]
Answer:
a)
i) Interquartile range is 2.4
ii) Upper boundary is 10.8
The Lower boundary is 1.2
iii) Outliers are points above the upper boundary or below the lower boundary
There is one outlier: 1.1
b) The modified boxplot with one outlier is given in the diagram.
c) The 80th percentile is
The minimum rating the hotel can get is 7.3
Step-by-step explanation:
a)
i) Interquartile range is
IQR = Q3-Q1 = 7.2-4.8 = 2.4
ii) Upper boundary = Q3+ 1.5 *IQR = 7.2+1.5*2.4 = 10.8
Lower boundary = Q1 - 1.5*IQR = 4.8- 1.5*2.4 = 1.2
iii) Outliers are points above the upper boundary or below the lower boundary
There is one outlier: 1.1
c) The 80th percentile is given by
n= 12
k = 0.80
Index is given by k*n =0.80*12 = 9.6
Round to nearest whole number, that is 10th
80th percentile is the 10th number (arranged in ascending order)
80th percentile = 7.3
The minimum rating the hotel can get is 7.3.
b) The modified boxplot with one outlier is given as follows,
find the median and mean of the data set below :
Answer:
Median = 15
Mean = 22
Step-by-step explanation:
Median = first lets arrange the data type from smallest to biggest and select the middle number as it will be our median
1, 11, 14, 15, 31, 35, 47
the middle number is 15
so 15 will be our median
Mean = [tex]\frac{sum of all numbers }{total numbers\\}[/tex] sum of all numbers divided by the number of values in the set
[tex]\frac{1 + 11 + 14 + 15 + 31 + 35 + 47}{7}[/tex]
= [tex]\frac{154}{7}[/tex]
= 22
so our mean will be 22
If a fourth plant produces 150 widgets in 60 days, which statement is true?
A. It makes more than Plant A.
B. It makes less than Plant B.
C. It makes less than Plant A.
====================================================
Explanation:
At the 60 day mark, the following number of widgets are produced
Plant A = 300 widgetsPlant B = 100 widgetsPlant C = 200 widgetsThe fourth plant makes 150 widgets, which is between B and C
We see that the fourth plant does not make more than Plant A, so we can rule out choice A.
The fourth plant does not make less than Plant B, which allows us to rule out choice B.
The only thing left is choice C. Sure enough, this statement is true since 150 widgets made at the fourth plant is less than 300 made in Plant A. This is why choice C is the answer.
Use
inductive reasoning
to
describe the pattern. Then find the next two numbers in the pattern.
-3, 9, -27, 81, ...
Answer:
I don't know what inductive reasoning is but, the next two numbers in the pattern are -243 and +729
Step-by-step explanation:
each number is being multiplied by a factor of (-3).
Which sequence is arithmetic? Check all that apply.
•0, 8, 16, 24
•7, 12, 17, 22
•6, 12, 24, 48
•8, 14, 20, 26
•11, 18, 23, 30
•12, 17, 22, 29
•15, 30, 60, 120
Answer:
Sequences 1,2, and 4 are arithmetic.
Step-by-step explanation:
Each term in sequence 1 gets added by 8.
Each term in sequence 2 gets added by 5.
Each term in sequence 4 gets added by 6.
The interquartile range is determined by the formula _________.
A. Third quartile - First quartile
B. Third quartile + first quartile
C. First quartile - third quartile
D. Maximum - minimum
Answer:
A)
Step-by-step explanation:
The inter quartile range is determined by the formula Third quartile - first quartile.
In a set, an inter quartile range is a measure of where the bulk of the data's lie
the ratio of 62 miles to 100 kilometers
9514 1404 393
Answer:
0.99779328
Step-by-step explanation:
The exact conversion factor is ...
1 mi = 1.609344
Then 62 miles is 62×1.609344 km = 99.779328 km.
The ratio of this to 100 km is ...
99.779328/100 = 0.99779328 . . . . ratio of 62 miles to 100 km
find f(x)•g(x)
f(x) = 3x - 1
g(x) = x^2 + 4
1. the question is asking you to multiply the two function expressions together
2. so all we do is (3x - 1)(x² + 4) which gives you 3x³ + 12x - x² - 4
Analyze the diagram below and complete the instructions that follow.
10
6
B.
'C С
8
Find sin ZA
A 3
5
B. 4
C 1
Answer:4
Step-by-step explanation:just had this
Which of the following are irrational numbers?
5
8.555...
N
1
Submit
Work it out
Not feeling ready yet? This can help:
Answer:
8.555.... is a irrationtional number .
find the length of one side of a regular hexagon if its perimeter is 24 x+48
A. 3x+3
B. 6x+12
C. 4x+8
D. 8x+16
Answer:
C ) 4 x + 8
Step-by-step explanation:
( 24 x + 48 ) / 6
4 x + 48
The length of a regular hexagon is:
4x ₊ 8
How many sides do a hexagon have? How do we calculate the length and parameter of it?
A regular hexagon have six sides.
The area of a regular hexagon can be calculated using the formula (33 s2)/2, where s is the side length. The lengths of all six sides of a hexagon can be added to determine its perimeter. Perimeter = 6 s, where s is the length of one side, is the formula used to determine the size of a regular hexagon.
Solution:
Given,
parameter of a hexagon = 24x ₊ 48
length of one side of a hexagon s = p ÷ 6
s = 24x ₊ 48 ÷6
s = 4x ₊ 8
Hence we get the length of one side as 4x ₊ 8
Learn more about "shapes" here-
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please answer this question!
Answer:
<A = 51
Step-by-step explanation:
Since AB = AC ( shown by the lines on the sides) we know that this is an isosceles triangle
Since the sides are the same, the base angles are the same
<A = <C
<C = 51 so <A = 51
12^-2 in the simplest form
Because there's a negative sign, it suggests that you should inverse the expression. After inverting it, the power will be positive, and you can square like normal.
Algebra 1 need help fast
Answer:
1st option
Step-by-step explanation:
at the 3rd hour, the money was $100
At 7th hour, the money increased to $160
Now, the rate is,
(160-100)/(7-3)
= 60/4
= 15
so, $15 per hour
What is the average rate of change for the function f(x) = –4x2 + 1 over the interval –3/2 ≤ x ≤ 0?
Answer:
6
Step-by-step explanation:
To find the average rate of change, we must calculate the slope over the interval -3/2 to 0. We can use the formula below.
f(b) - f(a) / b - a
f(0) - f(-3/2) / 0 - -3/2
1 - -8 / 3/2
9 / 3/2
18/3
6
Brainliest, please!
Given m LM=130, find m KLM
Answer:
65 degrees because tangent chord angles are half the size of the arc
Help me please, IXL keeps messing me up
I need help ASAP!!Please help me
Answer:
Below
Step-by-step explanation:
To find the volume of a rectangular prism find the area of a face and multiply it by the height
V = lwh
= (12)(5)(12)
= 720 km^3
Hope this helps!
HELP PLS
18-8×2+10= ?
f(x) = -4(x+3)+6(x+4)
Answer:
zero of the function occurs at x = -6
Step-by-step explanation:
Given f(x) = -4(x+3)+6(x+4)
Since the question is incomplete, we can as well find the zero of the given function. The zero exists when f(x) = 0
Hence;
-4(x+3)+6(x+4) = 0
Expand
-4x - 12 + 6x + 24 = 0
Collect the like terms
-4x + 6x - 12 +24 = 0
2x + 12 = 0
2x = -12
x = -12/2
x = -6
Hence the zero of the function occurs at x = -6
the sum of two numbers is 20,one number is 4 less than the other.find the number
*PLEASE* PLEASE PLEASE HELP ME SOMEBODY !3RD! TIME POSTING THIS AND I REALLY BADLY NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Are the two triangles similar? If so, state the reason and the similarity statement. Question options: A) Impossible to determine. B) Yes; SAS; ΔVWX ∼ ΔYZX C) Yes; SSS; ΔVWX ∼ ΔYZX D) The triangles are not similar.
Answer:I think its not similar
Step-by-step explanation:
they dnot look the same
what is soil erosion
Answer:
Soil erosion is the natural process in which the topsoil of a field is carried away by physical sources such as wind and water. In this process, the soil particles are loosened or washed away in the valleys, oceans, rivers, streams or far away lands.
It occurs when the impact of water or wind separates and removes soil particles, causing the soil to deteriorate. Soil deterioration and low water quality due to erosion and surface runoff have become severe problems worldwide.
Evaluate the expression 34 ÷ (14 − 5) × 2.
I'm pretty confused can someone explain it to me? I will give branliest
Answer:
[tex]7\frac{5}{9}[/tex]
Step-by-step explanation:
Hi there!
We are given this expression:
34÷(14-5)×2
And we want to evaluate it
We'll be using the order of operations
Depending on the country you're in, the acronym can be different, but in the US, the typical acronym used for the order of operations is PEMDAS, or Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
The order of operations states that we should start with any expressions in parentheses
In this case, it's (14-5), which is equal to 9
The expression now becomes
34÷9×2
There are no exponents, so let's skip that
Now this is where it gets tricky:
Based on the acronym alone, we should be doing 9*2 next, however, we should always work left to right, even if in a case like this, we'll be doing division instead of multiplication
Divide 34 by 9
[tex]\frac{34}{9}[/tex]×2
Now multiply [tex]\frac{34}{9}[/tex] by 2
[tex]\frac{68}{9}[/tex]
(as a mixed fraction, it's 7[tex]\frac{5}{9}[/tex])
Hope this helps!
Z varies directly as x/y² and y varies inversely as x,if z=⅓ when x =2 and y=¼. Express (a). Y interms of x and (b). Z interms of x
Answer:
Baba
Step-by-step explanation:
Booey
Is a – b a positive number or a negative number? How do you know?
b b
a
1
Please help I will give you Brainlyest
Answer:
A positive number.
Any negative subtracted from a positive will always be positive.
Answer:
a-b will be and will always be a POSITIVE number.
This is because a is positive, and b is negative.
However, when you subtract a negative number, you are actually just adding it.
So, a - (-b) = a+b.
This is why, it will always be positive.
Let me know if this helps!
Question 5 of 41
Which of the following best describes the volume of a solid?
A. It is the sum of the base area plus the lateral area of the solid.
B. It is the amount of three-dimensional space inside the solid.
C. It is the distance around the base of the figure.
D. It is the total area of the exterior surface of the solid.
SUBMIT
B. It is the amount of three-dimensional space inside the solid.
What is volume?Volume, measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m³), a derived unit, is the SI unit of volume. Volume is another word for capacity.
The volume of a solid is the measure of the amount of three-dimensional space that is occupied by the solid.
It is a measure of the physical space that the solid occupies in three-dimensional space. It is different from the surface area or perimeter of a solid which measure the amount of space that is taken up by the solid in two dimensions.
In summary, the volume of a solid refers to the amount of three-dimensional space that is enclosed by the solid, and it is an important measurement in many fields including engineering, architecture, and physics.
Learn more about Volume here:
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A Boy obtained 80 percent marks.If the full marks is 800,how much did he get?
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Answer:
640 marks
Step-by-step explanation:
80% of 800 is ...
0.80 × 800 = 640
He got 640 marks.
michelle is 3 times as old as her sister tina. Tina is 4 years younger than michelle. How old is tina now?
Answer:
Tina's age = 2 years
Step-by-step explanation:
Tina's age = x
Michelle's age = 3 * x = 3x
Tina is 4 years younger than Michelle.
x = 3x - 4
Add 4 to both side
x +4 = 3x
Subtract x from both sides
4 = 3x - x
4 = 2x
Divide both sides by 2
4/2 = x
2 = x
Tina's age = 2 years
What is a 14 of the sequence 2, 11, 20, ...?
A. 140
B. 128
C. 119
D. 137
Answer:
The answer is 119
Step-by-step explanation:
Just count, but I did it a different way but multiplying then subtracting.
