Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \: \sin {}^{4} ( \alpha) + 2 \sin {}^{2} ( \alpha) \cos {}^{2} ( \alpha) + { \cos {}^{4} ( \alpha) }^{} [/tex]
[tex] \qquad❖ \: \sf \:( \sin {}^{2} ( \alpha) ) {}^{2} + 2( \sin {}^{2} ( \alpha))( \cos {}^{2} ( \alpha)) + {( \cos {}^{2} ( \alpha)) }^{} [/tex]
( use identity a² + 2ab + b² = (a + b)² )
[tex] \qquad❖ \: \sf \:( {\sin {}^{2}( { \alpha}) + \cos {}^{2} ( \alpha)) }^{2} [/tex]
( sin² x + cos ² x = 1 )
[tex] \qquad❖ \: \sf \: {1}^{2} [/tex]
[tex] \qquad❖ \: \sf \: {1}^{} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Value of that expression is 1
Related Questions
what is the definition of prime and composite numbers??please answer fast
Answers
Answer:
'A prime number is a number which has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer.'
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the definition of prime & composite numbers?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
A prime number can be evenly divided by 1 and itself. These are its only two factors.
A composite number can be evenly divided by 1, itself, and something else. In other words, composite numbers have more than 2 factors.
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{\begin{cases}\bf{Primes\;have\;only\;2\;factors} \\ \bf{Composites\;have\;3\;or\;more\;factors} \end{cases}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic\not1\theta l}}[/tex]
Easy 40 ptS!!!!!! Functions transformations
Answers
Answer:
Step-by-step explanation:
the total drive is 450 miles, mila drives x mph for the first 200 miles, for the remaining distance she drives x + 30 mph
Answers
Time taken= 200/x
Second part of the trip:
Time taken= 250/(×+30)
Average:
Time taken= 450/30
Time taken= 15 hours
200/x + 250/(×+3) = 15
-15x^2+405x+600=0
x=28.40805152
I need help ?
A model car is to be an exact replica of the original, but at the size. If
the actual car is 240 cm long, how many centimeters long should the
12
model be?
Answers
Answer:
20cm
Step-by-step explanation:
You divide by 12
AC=
Help me please!! Thanks so much
Answers
Answer:
AC = 6√3 in
Step-by-step explanation:
Finding the length of the chord:Join OC. Now ΔAOC is an isosceles triangle as OA = OC =radius.
∠A = ∠C = 30.
∠A + ∠C + ∠AOC = 180 {angle sum property of traingle}
30 + 30 + ∠AOC = 180°
∠AOC = 180 -60
∠AOC = Ф = 120°
Find the length of radius using the bellow formula.
[tex]\sf \boxed{\bf Arc \ length = \dfrac{\theta}{180}\pi r}[/tex]
Ф = 120°
Arc length = 4π
[tex]\sf 4\pi =\dfrac{120}{180}*\pi *r\\\\ r =\dfrac{4\pi * 180}{120*\pi }\\\\ r = 6 \ in[/tex]
[tex]\sf \boxed{\bf chord \ length = 2rSin \ \dfrac{\theta}{2}}[/tex]
[tex]\sf b = 2*6*Sin \ \dfrac{120}{2}\\\\ b = 2 *6 * Sin \ 60^\circ\\\\ b = 2 * 6 * \dfrac{\sqrt{3}}{2}\\\\ \b = 6\sqrt{3}[/tex]
[tex]\sf \boxed{\bf AC = 6\sqrt{3} \ in}[/tex]
Paco pago $105.0 por 10 tacos cual es el precio de cada taco si todos tienen el mismo precio
Answers
The price of each taco is $10.5
What is unitary method?
We can solve this question by unitary method.
The unitary method is a method of finding the value of one unit and then finding the value of the required number of units. While solving a problem it is important to recognize the units and values.
In this question, 10 tacos cost $105.
Let's represent the cost of 1 taco as [tex]x[/tex]
10 tacos =$ 105
1 taco = [tex]x[/tex]
10[tex]x[/tex] = 105
[tex]x[/tex] = [tex]\frac{105}{10}[/tex]
[tex]x[/tex] = 10.5
Each taco cost $10,5
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Joaquin deposits $1,000 into an account that accrues 4% annual interest continuously compounded. What is the value of his investment after 3 years to the nearest cent?
Answers
Deposit: $1,000
Annual interest: 4% = 0.04
Years: 3
For this type of question, when the question asks you to "continuously compound", you use this formula: [tex]Pe^{rt}[/tex]
Solving:
[tex]1000e^{(0.04)(3)} \\1000e^{0.12} \\=1127.50[/tex]
The value of Joaquin's investment after 3 years = 1,127.50$
Math again yay!...Ew math
Answers
Answer:
The graph of g(x) is wider.
Step-by-step explanation:
Parent function:
[tex]f(x)=x^2[/tex]
New function:
[tex]g(x)=\left(\dfrac{1}{2}x\right)^2=\dfrac{1}{4}x^2[/tex]
Transformations:
For a > 0
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}[/tex]
[tex]\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}[/tex]
If the parent function is shifted ¹/₄ unit up:
[tex]\implies g(x)=x^2+\dfrac{1}{4}[/tex]
If the parent function is shifted ¹/₄ unit down:
[tex]\implies g(x)=x^2-\dfrac{1}{4}[/tex]
If the parent function is compressed vertically by a factor of ¹/₄:
[tex]\implies g(x)=\dfrac{1}{4}x^2[/tex]
If the parent function is stretched horizontally by a factor of ¹/₂:
[tex]\implies g(x)=\left(\dfrac{1}{2}x\right)^2[/tex]
Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.
The population of a small industrial town was 12 910 in 2000. Each year, the population
decreases by an average of 5%. Estimate the population in the year 2020. Round to the nearestwhole number.
Answers
The population in the year 2020 is 4628
How to determine the population?The given parameters are:
Initial, a = 12910
Rate, r = 5%
Since the population decreases, then we make use of an exponential decay function.
This is represented as:
f(n) = a * (1 - r)^n
So, we have:
f(n) = 12910 * (1 - 5%)^n
Evaluate the difference
f(n) = 12910 * 0.95^n
2020 is 20 years from 2000.
So, we have:
f(20) = 12910 * 0.95^20
Evaluate
f(20) = 4628
Hence, the population in the year 2020 is 4628
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The equation of a circuits in the form: (in the picture)
If the circle is centered in Quadrant I, what must be true of h and k?
(Answer choices in the picture as well)
Answers
Answer: h>0 and k>0
Step-by-step explanation:
If the circle is centered in Quadrant I, then both the x and y coordinates of the center are positive.
This means that h>0 and k>0.
The graph shows the height of an elevator over a period of time.
On which intervals could the elevator be traveling from a higher floor to a lower floor?
A. Between A and B and between C and D
B. Between B and C and between D and E
C. Between E and F and between G and H
D. Between F and G
Answers
C. Between E and F and between G and H the elevator could be travelling from a higher floor to a lower floor.
We have to justify all the options with respect to the graph :-
Option A : Between A and B, the elevator would be travelling from a lower floor to a higher floor. Also between C and D, the elevator would be travelling from a lower floor to a slightly higher floor.
So, this option is not correct.
Option B : Between B and C, the elevator wouldn't go higher. And also the same would happen in between D and E.
So, this option is not correct.
Option C : Between E and F, the elevator would be travelling from higher floor to lower and also between G and H.
So, this option is correct.
Option 4 : Between F and G, there would not have much changes. So it will be omitted.
So, this option is not correct.
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3 quick algebra 1 questions for 50 points!
Only answer if you know the answer, tysm for the help!
Answers
Step-by-step explanation for each question:
For Question 6, the range of a function is all the possible outputs of the function. Since the function can only take the inputs 0, 4, and 7, we can just plug in each into the formula and find their corresponding outputs.
g(0) = 0² - 9 = 0 - 9 = -9
g(4) = 4² - 9 = 16 - 9 = 7
g(7) = 7² - 9 = 49 - 9 = 40
Therefore the only possible outputs of function g, or the range, is {-9, 7, 40}.
For question 4, the input t is a given time, and h(t) is the height of the football at that time.
Hence, h(2.5) is the height of the football (in feet) at 2.5 seconds. The value 2.5 can be plugged into the function [tex]-16t^2+58t+2[/tex] to get the height. This gives us
[tex]-16(2.5)^2 + 58(2.5) + 2[/tex]
[tex]-16(6.25) + 58(2.5) + 2[/tex] [Squaring 2.5]
[tex]-100 + 145 + 2[/tex] [Multiplying]
[tex]47[/tex] [Combining all terms]
We find that the height of the football at 2.5 seconds is 47 feet.
For Question 5, the table of values show all the possible values x can be (or the domain), and what the output of the function f(x) would give for each.
A) f(-3) = 5, as the row with -3 for x has -5 for y.
B) f(0) = 0, as the row with 0 for x has 0 for y.
C) f(1) = -3, as the row with 1 for x has -3 for y.
The range of the function will be -9,7 and 40.
What is the difference between domain and range?The domain denotes all potential x values, while the range denotes all possible y values.
Given equation;
g(x) = x²-9
The range of the given domain is found by putting the values one by one in the above equation as;
g(x) = x²-9
a)For x = 0
g(x) = 0²-9
g(x) =-9
b)For x =4
g(x) = 4²-9
g(x) =16-9
g(x) = 7
c)For x =7
g(x) = 7²-9
g(x) =49-9
g(x) = 40
Hence, the range of the function will be -9,7 and 40.
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For which value of b can the expression x2 + bx + 18 be factored?
Answers
Answers:
b = -19b = -11b = -9b = 19b = 11b = 9====================================================
Explanation:
Here are all the ways to multiply to 18 when using integers only:
-1*(-18) = 18-2*(-9) = 18-3*(-6) = 181*18 = 182*9 = 183*6 = 18Sum each pair of factors to find out a possible value of b.
-1 + (-18) = -19-2 + (-9) = -11-3 + (-6) = -91 + 18 = 192 + 9 = 113 + 6 = 9Therefore, the possible values of b are
b = -19b = -11b = -9b = 19b = 11b = 9which are the final answers.
----------------------
An example:
Let's say b = 11. This would mean [tex]x^2+bx+18[/tex] becomes [tex]x^2+11x+18[/tex]
It would factor to [tex](x+2)(x+9)[/tex] since it was stated earlier that:
2+9 = 11
2 * 9 = 18
You can use the FOIL rule, distributive property, or the box method to confirm that [tex]x^2+11x+18 = (x+2)(x+9)[/tex] is a true equation for all real numbers x.
This same idea applies for the other values of b.
----------------------
If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)
Use the FOIL rule to get [tex](x+p)(x+q) = x^2+qx+px+pq = x^2+(p+q)x + pq[/tex]
The middle term [tex](p+q)x[/tex] has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).
what does y =4 in coordinates look like
Answers
Puja limbu did 8 out of 10 math problems and raju lama did 11 out of 15 similar maths problems.express the number of problems solved by each of them in fractions and identify who did better performance.
Answers
Puja Limbu had the better performance than Raju Limbu.
Such question are generally solved using percentages.
In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.
Percentage of Raju limba = [tex]\frac{11}{15}[/tex] X 100 = 73.3%
Percentage of Puja Limba = [tex]\frac{8}{10}[/tex] x 100 = 80%
As percentage of Puja Limba is greater than that of Raju Limba .
Hence performance of Puja Limba is better
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prove the equation (2x+5)2 = 4x (x + 5) +25
Answers
Answer: x = -5/2 and x = -3/2
Step-by-step explanation:
(2x + 5)2 = 4x (x + 5) +25
4x + 10 = 4x² + 20x + 25
[minus 4x on both sides.]
10 = 4x² + 16x + 25
[minus 10 on both sides.]
0 = 4x² + 16x + 15
ac = 4(15) = 60,then find the factors that add up to 16, which is 6 and 10.
0 = 4x² + 6x + 10x + 15
0 = 2x(2x + 3) + 5(2x + 3)
0 = (2x + 5)(2x + 3)
2x + 5 = 0 2x + 3 = 0
2x = -5 2x = -3
x = -5/2 x = -3/2
[tex]\huge\text{Hey there!}[/tex]
[tex]\textbf{Assuming you meant: }\mathsf{(2x + 5)^2 = 4x(x + 5) + 25}[/tex]
[tex]\textbf{If so, simplify both sides of your equation you're working with}[/tex]
[tex]\mathsf{ 4x^2 + 20x + 25 = 4x^2 + 20x + 25}[/tex]
[tex]\textbf{SUBTRACT }\rm{\bf 4x^2}\text{ \bf to BOTH of the SIDES}[/tex]
[tex]\mathsf{4x^2 + 20x + 25 - 4x^2 = 4x^2 + 20x + 25 - 4x^2}[/tex]
[tex]\textbf{Simplify it!}[/tex]
[tex]\mathsf{20x + 25 = 20x + 25}[/tex]
[tex]\textbf{SUBTRACT 20x to BOTH of the SIDES}[/tex]
[tex]\mathsf{20x + 25 - 20x = 20x + 25 - 20x}[/tex]
[tex]\large\textbf{SIMPLIFY IT! (as well)}[/tex]
[tex]\mathsf{25 = 25}[/tex]
[tex]\textbf{SUBTRACT 25 to BOTH of the SIDES}[/tex]
[tex]\mathsf{25 - 25 = 25 - 25}[/tex]
[tex]\textbf{Lastly, SIMPLIFY THAT!}[/tex]
[tex]\textbf{We get: }\mathsf{0 = 0}[/tex]
[tex]\large\textsf{This means that your \boxed{\textsf{solutions}} are \bf REAL NUMBERS.}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: }\\\boxed{\mathsf{All\ \underline{\underline{REAL\ NUMBERS}}\ are\ solutions.}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Two hikers are wandering through heavy woods with walkie talkies. The walkie talkies have a range of 100 yards. From their starting point, they head off at an angle of 109°10' of each other. Hiker 1 walks 0.24 miles per hour, hiker 2 walks 0.17 miles per hour. If each continues to go straight, how long will it be before they can no longer communicate?
Answers
Answer: after t hours, the distance d between the hikers is
d^2 = (.24t)^2 + (.17t)^2 - 2(.24t)(.17t)cos109.167°
so, find t when d = 0.0568182
10 minutesStep-by-step explanation:
An equation is shown. the
Which describes n?
n = 1 ÷17
Answers
-
17
decimal form 0.05882352
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
An equation is shown. What is the value of n? [tex]\bf{n=1:17}[/tex] is shown
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\bf{n=1:17}[/tex] | divide
[tex]\bf{n=\dfrac{1}{17}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=n=\dfrac{1}{17}}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
Which of the following sets represents the range of the diagram below? 2 3. 00 4 4 5 5 f(x) O A. {2, 4, 5) OB. (1, 3, 4, 5} OC. (2, 3, 4, 5, 6, 7} D. {1, 2, 3, 4, 5)
Answers
Answer:
D
Step-by-step explanation:
the answer is D because the range is the lowest possible value up to the highest possible value and when listed it doesn't repeat
(-6) x 8
What is this ?????
Answers
Answer:
-(6) x 8
ans: - 48
I believe that is the ans:
Answer:
-48
Step-by-step explanation:
Integer multiplication:When we multiply a negative integer by a positive integer , we will get a negative integer.
(-6) * 8 = (-48)
negative integer * negative integer = positive integer
(-2) * (-3) = 6
negative integer * positive integer = negative integer
(-2) * 3 = (-6)
Positive integer *negative integer = negative integer
2 * (-3) = (-6)
The students in Ms. Yuri's class reported the number of hours they watched television last week.
Which is the interquartile range of the number of hours last week that the students watched television?
Answers
The interquartile range is 12.
What is the interquartile range?The interquartile range is the difference between the third quartile and the first quartile. The first quartile is the first line on the box while the third quartile is the third line on the box.
First quartile = 11
Third quartile = 23
Interquartile range = 23 - 11 = 12
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pls help lol !!! i am unsure about this
Answers
The component form of the vectors shown is (-6, -5)
Difference of vectorsIn order to determine the component of the vectors shown, we will subtract the coordinate points from both each other.
Given the vector coordinates on the line. as (-5, -3) and (1, 2). Take the difference;
Difference = [(-5-1), (-3-2])
Difference = (-6, -5)
Hence the component form of the vectors shown is (-6, -5)
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4. Try It #4 Write the point-slope form of an equation of a line that passes through the points (-1,3) and (0,0). Then rewrite it in the slope-intercept form.
Answers
Answer:
Point-slope form of equation of a line that passes from (-1,3) and (0,0) is given as y-3=-3(x+1).
Slope-intercept form of equation is given as y=-3x.
Step-by-step explanation:
In the question, it is given that the line passes from (-1,3) and (0,0).
It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.
Step 1 of 2
Passing point of line is (-1,3).
Hence, [tex]$x_{1}=-1$[/tex] and
[tex]$$y_{1}=3 \text {. }$$[/tex]
Also, Passing point of line is (0,0).
Hence, [tex]$x_{2}=0$[/tex] and
[tex]$$y_{2}=0 \text {. }$$[/tex]
Substitute the above values to find the slope of line which is given by [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{0-3}{0-(-1)} \\m &=\frac{-3}{1} \\m &=-3\end{aligned}$$[/tex]
Hence, slope of the line is -3
Step 2 of 3
It is obtained that m=-3
[tex]$y_{1}=3$[/tex]
and [tex]$x_{1}=-1$[/tex]
Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$y-y_{1}=m\left(x-x_{1}\right)$\\ $y-3=-3(x-(-1)$\\ $y-3=-3(x+1)$[/tex]
Hence, point-slope form of equation given as y-3=-3(x+1).
Step 3 of 3
Solve y-3=-3(x+1) to write it as slope-intercept form given by y=mx+c
[tex]$y-3=-3(x+1)$\\ $y-3=-3 x-3$\\ $y=-3 x-3+3$\\ $y=-3 x$[/tex]
Hence, slope-intercept form of equation is given as y=-3x.
factor this polynomial expression. x2 – 16
Answers
Answer:
(×-4) (x + 4)
Step-by-step explanation:
first of all, recognize that the polynomial expression is a difference of two squares.
thus
X^2-16
(x -4)(x+4)
⊱________________________________________________________⊰
[tex]\\[/tex][tex]\\[/tex]
Answer:
(x+4)(x-4), by using the difference of squares ruleStep-by-step explanation:
[tex]\large\begin{gathered} \sf{To \ factor \ this \ polynomial, \ we \ must \ first \ recognise \ it. \ Isn't \ it \ the \ difference} \\ \sf{of \ two \ squares?} \\ \rm{It \ is! } \\ \sf{Polynomials \ like \ (a^2-b^2) are \ factored \ like \ this\!\!:} \\ \sf{(a+b)(a-b).} \\ \sf{Similarly, \ (x^2-16) \ is \ factored \ as \ (x+4)(x-4). \end{gathered}[/tex]
Done!!
⊰_____________________________________________________⊱
[tex]\\[/tex][tex]\\[/tex]
[tex]\boldsymbol{\rm{\triangleright\overbrace{C}\triangleleft\underbrace{A}\triangleright\overbrace{L}\triangleleft\underbrace{L}}\triangleright\overbrace{\stackrel\bigstar{I}}\triangleleft\underbrace{G}\triangleright\overbrace{R}\triangleleft\underbrace{A}\triangleright\overbrace{P}\triangleleft\underbrace{H}\triangleright{Y}}}[/tex]
Your friend writes an equation of the line shown. Is your friend correct?
Student work is shown. A line is graphed on a coordinate plane. The line passes through the points at ordered pair (0,-2) and ordered pair (4,0). Your friend writes an equation of the line shown. Is your friend correct? Their equation was y = 1/2x + 4.
Answers
Answer:
No. The correct equation is
y= 1/2 x - 2
Step-by-step explanation:
See picture
Identify a horizontal or vertical stretch or compression of the function f(x)=\sqrt(x) by observing the equation of the function g(x)=\sqrt((3)/(2)x)
kind of urgent lol
Answers
By applying the concept of transformation, the transformed function g(x) = √[(3/2) · x] is the consequence of applying a stretch factor of 3/2 on the parent function f(x) = √x.
How to compare two functions by concepts of transformationIn this question we have a parent function g(x) = √[(3/2) · x] and a transformed function f(x) = √x. Transformations are operations in which parent functions are modified in their relationships between inputs and outputs.
In this case, the difference between f(x) and g(x) occurred because of the application of a operation known as vertical stretch, defined below:
f(x) = g(k · x), k > 0 (1)
Where k is the stretch factor. There is a compression for 0 ≤ k < 1.
By applying the concept of transformation, the transformed function g(x) = √[(3/2) · x] is the consequence of applying a stretch factor of 2/3 on the parent function f(x) = √x. (Right choice: C)
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alyssa has 144 coins. of the coins 3/12 are nickels, 8/12 are dimes, and the rest are quarters what is the ratio of Alyssa’s nickels to dimes to quarters?
Answers
3:8:1
step-by-step explanation:3/12 x 144= 36
8/12 x 144= 96
96+36= 132
144-132= 12
12/12=1
Therefore, the ratio of Alyssa's nickels to dimes to quarters is 3:8:1
To estimate the percentage of a state's voters who support the current
governor for reelection, three newspapers each survey a simple random
sample of voters. Each paper calculates the percentage of voters in its
sample who support the governor and uses that as an estimate for the
population parameter. Here are the results:
• The Tribune.n=700 voters sampled; sample estimate = 68%
• The Herald. n = 500 voters sampled; sample estimate = 64%
• The Times. n = 300 voters sampled; sample estimate = 78%
All else being equal, which newspaper's estimate is likely to be closest to the
actual percentage of voters who support the governor for reelection?
OA. The Tribune, at 68%
B. The Herald, at 64%
C. The Times, at 78%
Answers
Using the Central Limit Theorem, the percentage that is expected to be the closest to the actual percentage is:
A. The Tribune, at 68%.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard error [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
From this, a larger sample size leads to a smaller error estimate. Since the Tribune had the largest sample size, option A is correct.
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can you teach me this
Answers
The percentiles are: P40 = 33, P70 = 45, and P89 = 54.1, while the quartiles are Q1 = 28.5 and Q3 = 47.5
How to determine the percentiles?The sorted dataset is:
22, 22, 24, 25, 26, 27, 27, 30, 30, 32,
33, 33, 35, 37, 38, 38, 40, 42, 44, 44,
45, 47, 48, 48, 49, 52, 55, 58, 62, 68
The number of data elements is:
N = 30
The 40th percentile (P40)
This is calculated using:
Element = (40% * N)th
So, we have:
Element = (40% * 30)th
Evaluate
Element = 12th
The 12th element is 33
Hence, the value of P40 is 33
The 70th percentile (P70)
This is calculated using:
Element = (70% * N)th
So, we have:
Element = (70% * 30)th
Evaluate
Element = 21st
The 21st element is 45
Hence, the value of P70 is 45
The 89th percentile (P89)
This is calculated using:
Element = (89% * N)th
So, we have:
Element = (89% * 30)th
Evaluate
Element = 26.7th
The element is calculated as:
Element = 26th + 0.7 * (27th - 26th)
So, we have:
Element = 52 + 0.7 * (55 - 52)
Element = 54.1
Hence, the value of P89 is 54.1
How to determine the quartiles?The 1st quartile (Q1)
This is calculated using:
Element = (1/4 * N)th
So, we have:
Element = (1/4 * 30)th
Evaluate
Element = 7.5th
The element is calculated as:
Element = 7th + 0.5 * (8th - 7th)
So, we have:
Element = 27 + 0.5 * (30- 27)
Element = 28.5
Hence, the value of Q1 is 28.5
The 3rd quartile (Q3)
This is calculated using:
Element = (3/4 * N)th
So, we have:
Element = (3/4 * 30)th
Evaluate
Element = 22.5th
The element is calculated as:
Element = 22nd + 0.5 * (23rd - 22nd)
So, we have:
Element = 47 + 0.5 * (48- 47)
Element = 47.5
Hence, the value of Q3 is 47.5
The 5th quartile (Q5)
There is no such thing as Q5 i.e. the 5th quartile
Read more about quartiles and percentiles at:
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While the goal of hypothesis testing is to test a claim, the goal of estimation is to estimate a
Answers
The estimation goal is to estimate a population parameter. The estimation process uses sample statistics.
What is the goal of hypothesis testing?The goal of hypothesis testing is testing to claim whether it is right or wrong.
The hypothesis testing also uses statistics to determine whether or not a treatment has an effect.
What is the goal of estimation?The estimation goal is to estimate a population parameter. The estimation is used to determine how much effect a treatment has.
To estimate a parameter, a sample statistics of the parameter is used.
Thus, the estimation is to estimate a population parameter.
Learn more about estimation and hypothesis testing here:
https://brainly.com/question/20367153
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