The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Ranks in a dancing competition: This is an illustration of ordinal measurement since the values can be ranked or ordered, but the differences between the values are meaningless.
Basketball player heights: Although there isn't a genuine zero point, the values have significant variances between them, making this an example of an interval measurement.
Monthly electric bills are an example of a ratio measurement because there are real zero points and significant variances between the values.
Calendar day count: Because the values are categorical and cannot be ranked or sorted, this is an example of a nominal measurement.
Score on an aptitude test: This is an instance of an interval measurement because there are actual disparities between the results, but no actual zero point.
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For questions 16 - 19, write each expression in the standard form for the complex number a + bi. 1/2(cos(72)+isin(72))^5
Given:
The expression is:
[tex]\dfrac{1}{2}(\cos (72)+i\sin (72))^5[/tex]
To find:
The [tex]a+bi[/tex] form for the given expression.
Solution:
According to De Moivre's theorem,
[tex](\cos \theta+i\sin \theta)^n=\cos (n\theta )+i\sin (n\theta )[/tex]
We have,
[tex]\dfrac{1}{2}(\cos (72)+i\sin (72))^5[/tex]
Using De Moivre's theorem, we get
[tex]=\dfrac{1}{2}(\cos (72\times 5)+i\sin (72\times 5))[/tex]
[tex]=\dfrac{1}{2}(\cos (360)+i\sin (360))[/tex]
[tex]=\dfrac{1}{2}(1+i(0))[/tex]
[tex]=\dfrac{1}{2}+0i[/tex]
It is the [tex]a+bi[/tex] form of the given expression. Here, [tex]a=\dfrac{1}{2},\ b=0[/tex].
Therefore, the required expression is [tex]\dfrac{1}{2}+0i[/tex].
A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table below shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function which best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)
Help! Write a recursive for formula
Answer:
cc
Step-by-step explanation:
I don’t get it. Can someone explain this to me?
Answer:
18.285 in.²
Step-by-step explanation:
3 in. × 4 in. = 12 in.²
A = πr²
A = 12.57 in.²
12.57 in.² ÷ 2 = 6.285 in.²
6.285 in.² + 12 in.²
18.285 in.²
plz solve it CORRECTLY step by step
Answer:
[tex]\dfrac{6}{10}ab[/tex]
Step-by-step explanation:
Given that,
The first number is [tex]\dfrac{-3a}{7}[/tex]
The second number is [tex]\dfrac{-21b}{15}[/tex]
We need to find the product of the first number and second number. Product means we need to multiply i.e.
[tex]\dfrac{-3a}{7}\times \dfrac{-21b}{15}=0.6ab\\\\=\dfrac{6}{10}ab[/tex]
Hence, the product of the given numbers is equal to [tex]\dfrac{6}{10}ab[/tex].
A small cake is cut into 4 equal pieces. What fraction represents the entire cake? Explain.
Answer:
4/4 ?
Step-by-step explanation:
Answer:
4/4
Step-by-step explanation:
Since there are four pieces and none of them is eaten or taken we just do the number of total of pieces as the denominator and the number of pieces taken away on the numerator, since there wasn't any taken away we put it as 4 because there are 4 pieces still there of cake.
i will give Brainiest if you are right
Answer:
The answer is $22.75! (A)
Step-by-step explanation:
All you have to do is subtract $36.50 by $13.75 and get the amount of the 2nd piggy bank.
22.75 + 13.75 = 36.50
Solve the inequality. graph the solution given below
2 < -y/5
Answer: Inequality Form: y<-10 or Interval Notation: (-∞,-10)
Answer:
y<-10
Step-by-step explanation:
to remove the fraction then set to 0 and solve
A triangle has these coordinates:
Point A: (-8,-3)
Point B: (8,7)
Point C: (8,-3)
What is the length of side AC?
Answer:
16
Step-by-step explanation:
From Point A use -8 subtracted by Point C 8 and get
16. It is positive because the length of side can't be negative.
what is 9-3 3/7? answer pls
Answer:
6.5
Step-by-step explanation:
6.5
Answer:
5 4/7
Step-by-step explanation:
if i read your question right that is the answer
what is the are of of the triangle which has 17in Hight and 26in long
Answer:
base times height divide by two
26 times 17=442/2=221
the answer is 221
Step-by-step explanation:
The force F (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length L (in inches) of the handle. A force of 30 pounds is needed when the handle is 4 inches long. If a person needs 25 pounds of force to loosen the bolt, estimate the length of the wrench handle. Round answer to two decimal places if necessary.
____ inches
Step-by-step explanation:
See the photo for the method
Given OG = 16 and PE =9, what is the length of GE?
Answer:
Option (2)
Step-by-step explanation:
From the picture attached,
Length of OG = 16
Length of PE = 9
Let us draw a perpendicular AE to OG which intersects at A.
Length of AG = OG - PE
= 16 - 9
= 7
Length of AE = OP
= OT + TP
= OG + PE [Since, OT = OG and TP = PE, radii of the circles]
= 16 + 9
= 25
By applying Pythagoras theorem in ΔGAE,
GE² = AG² + AE²
GE² = 7² + 25²
GE = √674
GE = 25.96
≈ 26
Option (2) will be the correct option.
Solve for x.
23
13
[21
Answer:
x = 24
Step-by-step explanation:
The angles are supplementary therefor
(5x + 13) + (x + 23) = 180
Combine like terms
6x + 36 = 180
Subtract 36 from both sides
6x = 144
Divde both sides by 6
x = 24
Answer:
5x+13+x+23=180°[exterior corresponding angle is supplementary.
6x=180-36
x=144/6
x=24
The perimeters of two squares are in the ratio 2 : 4. The perimeter of
the larger square is 16 centimeters.
What is the perimeter of the smaller square?
Answer:
8
Step-by-step explanation:
2 : 4
8 : 16
Jonah has a 3-pound bag of soil todistribute equally between 6 flower pots.How much soil will be in each pot?
3 Divided 6 = 3 or 6 Divided 3 = 2?????????
-
6
Step-by-step explanation:
3 -> 6
? -> 1
? x 6 = 3 x 1
? = 3 / 6 = 1/2 pound bag of soil
1/2 pound soil will be in each bag
There _____________ with angle measures of 30°, 70°, and 80°
.A.is no triangle
B.is exactly 1 triangle
C.are exactly 2 triangles
D.are more than 2 triangles
need correct answer and no link then i will give you brainiest and b is wrong just saying..
Answer:
more than 2 triangles
Step-by-step explanation:
well, all triangles have angles add up to 180 degrees, so it is an infinite amount
HELP ME PLEASEEEEEEEEEEEE
Answer:
it needs me to type more but answer is
-5,-4
Answer:
S will be at (-5,-4)
Step-by-step explanation:
T is located at (0,-4)
To move to the left, the x coordinate moves.
(0-5, -4)
S will be at (-5,-4)
Find f(3) for f(x)=1/2(4)^x.
O A. 32
O B. 64
O c. 6
6
O D. 8
Answer:
A) 32
Step-by-step explanation:
f(3)=1/2(4)^(3)
Question #6
Show steps
Correct answer is A
We'll first need to determine what the composite function f(g(x)) is equal to.
Start with the outer function f(x). Then replace every copy of x with g(x). Afterward, plug in g(x) = 3x-2
So we get the following:
[tex]f(x) = \sqrt{x^2-4}\\\\f(g(x)) = \sqrt{(g(x))^2-4}\\\\f(g(x)) = \sqrt{(3x-2)^2-4}\\\\f(g(x)) = \sqrt{9x^2-12x+4-4}\\\\f(g(x)) = \sqrt{9x^2-12x}\\\\[/tex]
Next, we apply the derivative
[tex]f(g(x)) = \sqrt{9x^2-12x}\\\\f(g(x)) = (9x^2-12x)^{1/2}\\\\f'(g(x)) = \frac{1}{2}(9x^2-12x)^{-1/2}*\frac{d}{dx}(9x^2-12x)\\\\f'(g(x)) = \frac{1}{2}(9x^2-12x)^{-1/2}*(18x-12)\\\\f'(g(x)) = \frac{9x-6}{\sqrt{9x^2-12x}}\\\\[/tex]
Don't forget about the chain rule. The chain rule is applied in step 3 of that block of steps shown above.
The last thing we do is plug in x = 3 and simplify.
[tex]f'(g(x)) = \frac{9x-6}{\sqrt{9x^2-12x}}\\\\f'(g(3)) = \frac{9*3-6}{\sqrt{9*3^2-12*3}}\\\\f'(g(3)) = \frac{21}{\sqrt{45}}\\\\f'(g(3)) = \frac{21}{\sqrt{9*5}}\\\\f'(g(3)) = \frac{21}{\sqrt{9}*\sqrt{5}}\\\\f'(g(3)) = \frac{21}{3*\sqrt{5}}\\\\f'(g(3)) = \frac{7}{\sqrt{5}}\\\\[/tex]
Side note: if you choose to rationalize the denominator, then you'll multiply both top and bottom by sqrt(5) to end up with [tex]f'(g(3)) = \frac{7\sqrt{5}}{5}\\\\[/tex]; however, your teacher has chosen not to rationalize the denominator.
What is the value of b on the number line below?
The graph of -4x +3y-5= 0 passes through two points, A(2a, -1) and B(4,b). What is the value of a-b?
Answer:
-8
Step-by-step explanation:
The steps are in the photo I attatched
Compute the permutation.
5 P 4
5
20
120
Answer:
Step-by-step explanation:
5P4=5×4×3×2=120
11 There are 20 marbles in a bag. 0/1 . 4 marbles are green. • 7 marbles are red. 5 marbles are white. • 4 marbles are purple. Based on this information, what is the probability a marble choosen will be green or purple? Show Your Work y Green y Purple u 8 8 20 5 4 니 + 20 marbles You have responded to 11 of 11 questions 1 response does not have any content.
Answer:
1 There are 20 marbles in a bag. 0/1 . 4 marbles are green. • 7 marbles are red. 5 marbles are white. • 4 marbles are purple. Based on this information, what is the probability a marble choosen will be green or purple? Show Your Work y Green y Purple u 8 8 20 5 4 니 + 20 marbles You have responded to 11 of 11 questions 1 response does not have any content.
Step-by-step explanation:
What is (+12) – (-8)?
Answer:
+12+8＝+20
Step-by-step explanation:
Hope it helps you!
Answer:
[tex]{\huge\red{\fbox{{࿐αɴѕωєя࿐}}}}[/tex]
[tex]( + 12) - ( - 8) \\ = 12 + 8 \\ = + 20[/tex]
[tex]{\boxed{\boxed{\tt { Note :-}}}} \ [/tex]
[tex] - + - = + [/tex]
One urn contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn contains two red balls (R4 and R5) and two blue balls (B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. a. Construct the possibility tree showing all possible outcomes of this experiment. b. What is the total number of outcomes of this experiment
Answer:
(a) See attachment for tree diagram
(b) 24 possible outcomes
Step-by-step explanation:
Given
[tex]Urn\ 1 = \{B_1, R_1, R_2, R_3\}[/tex]
[tex]Urn\ 2 = \{R_4, R_5, B_2, B_3\}[/tex]
Solving (a): A possibility tree
If urn 1 is selected, the following selection exists:
[tex]B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2][/tex]
If urn 2 is selected, the following selection exists:
[tex]B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4][/tex]
See attachment for possibility tree
Solving (b): The total number of outcome
For urn 1
There are 4 balls in urn 1
[tex]n = \{B_1,R_1,R_2,R_3\}[/tex]
Each of the balls has 3 subsets. i.e.
[tex]B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2][/tex]
So, the selection is:
[tex]Urn\ 1 = 4 * 3[/tex]
[tex]Urn\ 1 = 12[/tex]
For urn 2
There are 4 balls in urn 2
[tex]n = \{B_2,B_3,R_4,R_5\}[/tex]
Each of the balls has 3 subsets. i.e.
[tex]B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4][/tex]
So, the selection is:
[tex]Urn\ 2 = 4 * 3[/tex]
[tex]Urn\ 2 = 12[/tex]
Total number of outcomes is:
[tex]Total = Urn\ 1 + Urn\ 2[/tex]
[tex]Total = 12 + 12[/tex]
[tex]Total = 24[/tex]
Question 6
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>
Find the equation of the line through the points (-4,6) and (1,-9). Write your answer in the form
y = mx + b.
Answer:
m=Y2–Y1/X2–X1
[tex]m = \frac{ - 9 - (6)}{1 - ( - 4)} \\ m = \frac{ - 15}{5} = - 3 \\ y = mx + b \\ y = - 3x + b[/tex]
Answer: y = -5x - 14
Step-by-step explanation:
first find the difference between the x variables x1 = 1 and x2=-4 to find the slope(m)
-4 - 1 = -5
next find the difference between the y variables to find b
-9 - 6 = -14
first to reply i will give brainliest btw there is no qusetion
Answer: Hii!
Step-by-step explanation:
if a number is added to it's square, the result is six. Find the number
Answer:
is the number 2?
Step-by-step explanation:
Answer:
The number could be
1 1/2 or -2
explanation:
From the data, taking the number to be x, we write:
2x^2 + x =6
Subtract 6 from both sides.
2x^2 + x - 6 = 0
Factorise.
2x^2 + 4x - 3x - 6 = 0
2x(x + 2) - 3(x + 2) = 0
(2x - 3)(x + 2) = 0
2x - 3 = 0 or x +2 = -2
x = 3/2 = 1 1/2 or x = -2
Find the radius of a circle, when the diameter is 29 cm
Answer:
14.5cm
Step-by-step explanation:
radius is half of diameter
29 / 2 = 14.5