What are the coordinates of the terminal point for 8 = 330°?
1
A.
-
I
22
1
V3
O B.
2
V3
1
O c.
2
D.
1 3
2 2
Answers
Answer:
Step-by-step explanation:
If you plot this angle in the coordinate plane, you will find yourself in the fourth quadrant with a referencew angle of 30. Constructing the triangle from that reference angle and using the Pythagorean triple for a 30-60-90 triangle, you get that the side adjacent to the reference angle is √3, the side opposite the reference angle is a -1, and the hypotenuse (which is NEVER negative!) is 2. The x and y coordinates of the terminal point result from the cos (related to the x coordinate) and the sin (related to the y coordinate). The cos of 30:
[tex]cos(30)=\frac{\sqrt{3} }{2}[/tex] and the sin of 30:
[tex]sin(30)=-\frac{1}{2}[/tex] so the coordinates of the terminal point on that angle are
[tex](\frac{\sqrt{3} }{2},-\frac{1}{2})[/tex]
You could also just go to your unit circle, find the angle 330 and look at the coordiantes they give you there for (cos, sin). But I'm a high school math teacher so I wanted you to know how to find this outside of the unti circle. Cuz what if you lost it!?
Related Questions
Find m angle TUV if m angle TUN=1+38 pi m angle NUV=66^ m angle TUV=105x
Answers
Answer:
m∠TUV = 105
Step-by-step explanation:
From the question given above, the following data were obtained:
m∠TUN = 1 + 38x
m∠NUV = 66°
m∠TUV = 105x
m∠TUV =?
Next, we shall determine the value of x. This can be obtained as illustrated below:
m∠TUV = m∠TUN + m∠NUV
105x = (1 + 38x) + 66
105x = 1 + 38x + 66
Collect like terms
105x – 38x = 1 + 66
67x = 67
Divide both side by 67
x = 67 / 67
x = 1
Finally, we shall determine the value of m∠TUV. This can be obtained as shown below:
m∠TUV = 105x
x = 1
m∠TUV = 105(1)
m∠TUV = 105
PLEASE HELP ME BE CORRECT PLEASE
TELL ME WHERE to PUT EACH POINT
Answers
Answer:
Point A:
(3, -5)
Point B:
(6, -2)
Point C:
(5, -7)
Step-by-step explanation:
Background:
Moving to the right means adding to the x.
Moving to the left means subtracting from the x.
Moving up means adding to the y.
Moving down means subtracting from the y.
So take each point and add 3 to the x, and subtract 4 from they y.
Point B:
(3, 2) → (6, -2)
Point A:
(0, -1) → (3, -5)
Point C:
(2, -3) → (5, -7)
Question 5
Points 1
duction
st
Which of the following is a polynomial of degree 5?
est
7x+ 5x2-3
0 2x7-5
O x1/7 + 1
0 12x4 - 5x3 + 6x - 4
Answers
Answer:
You can go ahead with this!
Step-by-step explanation:
Option A
Is the write answer
\int (x+1)\sqrt(2x-1)dx
Answers
Answer:
[tex]\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C[/tex]
Step-by-step explanation:
[tex]\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}[/tex]
[tex]\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du[/tex]
[tex]= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ][/tex]
[tex]= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\[/tex]
21. The mean salary of twelve men is $58,000, and the
mean salary of eight women is $42,000. Find the
mean salary of all twenty people.
Answers
(58000 + 42000)/2 = 50000
Write the range of the function using interval notation.
Answers
Given:
The graph of a function.
To find:
The range of the given function using interval notation.
Solution:
Range: The set of y-values or output values are known as range.
From the given graph, it is clear that the function is defined for [tex]0<x<4[/tex] and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.
Range [tex]=\{y|-2<y\leq 2\}[/tex]
The interval notation is:
Range [tex]=(-2,2][/tex]
Therefore, the range of the given function is (-2,2].
The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft. A rock formation rises to a peak 171 ft above the ocean floor. How many feet below the top of the rock formation is the diver?
Answers
Answer:
The ocean surface is at 0 ft elevation. A diver is underwater at a depth of 138 ft. In this area, the ocean floor has a depth of 247 ft.
Step-by-step explanation:
When 50% of a number is added to the number, the results is 165
Answers
Answer:
this would look like
0.5x+x=165
1.5x=165
x=110
Hope This Helps!!!
About 6% of the population has a particular genetic mutation. 100 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 100.
Answers
Answer:
The standard deviation for the number of people with the genetic mutation in such groups of 100=[tex]2.375[/tex]
Step-by-step explanation:-
We are given that
Total number of selected people, n=100
p=6%=0.06
We have to find the standard deviation for the number of people with the genetic mutation in such groups of 100.
Let X denote the number of people with the genetic mutation in such groups of 100.
[tex]\implies X\sim Bin(n=100,p=0.06)[/tex]
We know that
Standard deviation
=[tex]\sqrt{np(1-p)}[/tex]
Using the formula
Standard deviation
=[tex]\sqrt{100\times 0.06(1-0.06)}[/tex]
=[tex]\sqrt{6(0.94)}[/tex]
=[tex]2.375[/tex]
Hence, the standard deviation for the number of people with the genetic mutation in such groups of 100=[tex]2.375[/tex]
What is 75% as a fraction
Answers
Answer:
[tex]\frac{75}{100}[/tex]
Step-by-step explanation:
75 percent is 3/4 of 100 percent.
If p = 7, q = 2, r = 4; find the value of q (5p - r).
Answers
Answer: 62
Step-by-step explanation:
Given
p = 7, q = 2, r = 4
Solve
q ( 5p - r )
Substitute
(2) (5(7) - (4))
Simplify
(2) (35 - 4)
(2) (31)
62
Hope this helps!! :)
Please let me know if you have any questions
the volume of a rectangular pyramid with a length of 7 feet, a width of 6 feet, and a height of 4.5 feet.
Answers
Answer:
Volume = 63 feet
Step-by-step explanation:
To find the volume of a cube or a rectangular prism, the formula is
(L x W x H)/3. In other words, it is the length of the prism, times the width of the prism, times the height of the prism, whole divided by three, since it has a "triangular shape."
Let's substitute in values for these letters, L, W, and H. You said the length was 7, the width was 6, and the height was 4.5. Therefore, it will result in
(7 x 6 x 4.5)/3. That results in 189/3, which is 63.
Hope this helped!!!
g In the year 2005, the age-adjusted death rate per 100,000 Americans for heart disease was 222.3. In the year 2009, the age-adjusted death rate per 100,000 Americans for heart disease had changed to 213.4. a) Find an exponential model for this data, where t
Answers
This question is incomplete, the complete question is;
In the year 2005, the age-adjusted death rate per 100,000 Americans for heart disease was 222.3. In the year 2009, the age-adjusted death rate per 100,000 Americans for heart disease had changed to 213.4.
a) Find an exponential model for this data, where t = 0 corresponds to 1999
Answer:
the exponential model for this data will be; y = 222.3( 0.9898 )^t
Step-by-step explanation:
Given the data in the question;
{ 2005 }, at t = 0, death rate was 222.3
In 2009, { 2009 - 2005 = 4 }, at t = 4 death rate was 213.4
Now, let the exponential equation be;
y = ab^(t)
so at t = 0
222.3 = a × b^(0)
222.3 = a × 1
a = 222.3
at t = 4
213.4 = a × b^(4)
213.4 = 222.3 × b^(4)
b⁴ = 213.4 / 222.3
b = ( 213.4 / 222.3 )^(1/4)
b = 0.9898
y = ab^(t)
Hence, the exponential model for this data will be; y = 222.3( 0.9898 )^t
Christian and Tanae both leave Disneyland at the same time. Christian travels north at 65 mph. Tanae travels south at 55 mph. How long will it take them to be 540 miles apart? Which of the following equations would you use to solve this word problem?
65t + 55(t − 1) = 540.
65t + 55t = 540.
65t + 55(t + 1) = 540.
None of these choices are correct.
Answers
Answer:
Step-by-step explanation:
B looks like it would work.
You add speeds * time when you are travelling in opposite directions.
I don't know why you would add or subtract 1 as in A and C
120 * t = 540
t = 540/120
t = 4.5 hours.
So after 4.5 hours they are 540 miles apart.
Answer:
b
Step-by-step explanation:
Select all of the following statments that are true
Answers
Answer:
A. -¾ + 0 = -¾
B. -¾ - ¾ = -(¾ + ¾)
C. ¾ - ¾ = ¾ + (-¾)
E. -¾ + ¾ = ¾ + (-¾)
F. -¾ + ¾ = 0
Step-by-step explanation:
Let's check each equation to determine whether they are true or false.
If what we have in the both sides are equal, then the equation is true, if they're not, them it is false.
✔️-¾ + 0 = -¾
Add everything on your left together
-¾ = -¾ (TRUE)
✔️-¾ - ¾ = -(¾ + ¾)
Add everything on both sides together respectively
(-3 - 3)/4 = -(3 + 3)/4
-6/4 = -6/4 (TRUE)
✔️¾ - ¾ = ¾ + (-¾)
0 = ¾ - ¾ (+ × - = -)
0 = 0 (TRUE)
✔️-¾ + ¾ = ¾ - (-¾)
0 = ¾ + ¾ (- × - = +)
0 = 6/4 (FALSE)
✔️-¾ + ¾ = ¾ + (-¾)
0 = ¾ - ¾ (+ × - = -)
0 = 0 (TRUE)
✔️-¾ + ¾ = 0
0 = 0 (TRUE)
6. Convert 3−i into polar form and hence evaluate
[tex] {(3 - i)}^{7} [/tex]
Answers
9514 1404 393
Answer:
≈ 1000√10∠-129.04464° = -1992 -2456i
Step-by-step explanation:
3 -i = √(3³+(-1)²)∠arctan(-1/3) ≈ √10∠-18.4349°
Then (3-i)^7 = 10^(7/2)∠(7×-18.4349°) = 1000√10∠-129.04464°
= 1000√10(cos(-129.04464°) +i·sin(-129.04464°))
= -1992 -2456i
William invested $12,000 in a bank account that pays 9 percent simple interest. His friend invested the same amount at another bank that pays 8 percent interest compounded quarterly. These two functions, where t is time in years, represent the value of the investments: f(t) = 12(1.02)4t g(t) = 12(1.09)t The functions are graphed, and the point of intersection lies between 0.5 and 1.2. Based on the table, approximately how long will it be until both investments have the same value? Value of t f(t) = 12(1.02)4t g(t) = 12(1.09)t 0.5 12.48 6.54 0.6 12.58 7.84 0.7 12.68 9.16 0.8 12.79 10.46 0.9 12.89 11.87 1.0 12.99 13.08 1.1 13.09 14.39 1.2 13.20 15.70 A. 0.9 year B. 1.0 year C. 1.1 years D. 1.2 years
Answers
===========================================================
Explanation:
We have these two functions
f(t) = 12(1.02)^(4t)g(t) = 12(1.09)twhich represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.
The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1
The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.
I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0
So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0
It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.
It takes about a year for the two accounts to have the same approximate amount of money.
Answer:
B
Step-by-step explanation:
use the discriminant to determine the number of solutions to the quadratic equation −6z2−10z−3=0. What are the real solutions and complex solutions?
Answers
Answer:
Step-by-step explanation:
-6z²-10z-3=0
multiply by -1
6z²+10z+3=0
disc .=b²-4ac=10²-4×6×3=100-72=28≥0
also it is not a perfect square.
so roots are real,irrational and different.
[tex]z=\frac{-6 \pm\sqrt{28} }{2 \times 6} \\=\frac{-6 \pm 2 \sqrt{7}}{12} \\=\frac{-3 \pm\sqrt{7} }{6}[/tex]
Match the pairs of equivalent exMatch the pairs of equivalent expressions.
pressions.
Answers
Answer:
Give us the picture or numbers please.
Step-by-step explanation:
Answer: add pic pls
Step-by-step explanation:
How can one estimate a car annual fuel expense
Answers
Answer:
determine the number of miles the car drives in a year.
divide that number by the cars average MPG (miles per gallon) then multiply that number by the average cost of a gallon of gas in your area.
Step-by-step explanation:
I need help nowww!! 16 points
Answers
Answer:
A: x = 0
B: x = All real numbers
Step-by-step explanation:
A.
Any number to the power of (0) equals one. This applies true for the given situation; one is given an expression which is as follows;
[tex](6^2)^x=1[/tex]
Simplifying that will result in;
[tex]36^x=1[/tex]
As stated above, any number to the power of (0) equals (1), thus (x) must equal (0) for this equation to hold true.
[tex]36^0=1\\x=0[/tex]
B.
As stated in part (A), any number to the power (0) equals (1). Therefore, when given the following expression;
[tex](6^0)^x=1[/tex]
One can simplify that;
[tex]1^x=1[/tex]
However, (1) to any degree still equals (1). Thus, (x) can be any value, and the equation will still hold true.
[tex]x=All\ real \ numbers[/tex]
I need help with question 9
Answers
9514 1404 393
Answer:
a) yes
b) see attached
c) see discussion
d) neither
e) increasing (2,5); decreasing (-2, 2)
Step-by-step explanation:
a) The graph passes the vertical line test, so is the graph of a function.
__
b) A table of values is attached
__
c) Generally, this sort of function would be defined piecewise:
[tex]\displaystyle f(x)=\begin{cases}-\dfrac{1}{2}x+1&\text{for }-2\le x<2\\2x-4&\text{for }2\le x \le5\end{cases}[/tex]
In the attachment, we have shown the use of the "maximum" function to define it. The effect is the same.
__
d) The function has no symmetry about the origin or the y-axis, so is neither odd nor even.
__
e) The function is increasing where the line has positive slope, on the interval (2, 5). The function is decreasing where the line has negative slope, on the interval (-2, 2).
Ralph bought a computer monitor with an area of 384 square inches. The length of the monitor is six times the quantity of five less than half its width.
Answers
Answer:
eh width = 103.5 inches
Step-by-step explanation:
x = width
Length = (x/2 - 5 )*6
so 384=x+3x-30
414=4x
x=414/4=103.5 inches
which equation has the steepest graph ?
Answers
Answer:
Step-by-step explanation:
A.
[tex] \green{\huge{\red{\boxed{\green{\mathfrak{QUESTION}}}}}} [/tex]
which equation has the steepest graph ?
[tex] \red{ \bold{ \textit{STANDARD \: EQUATION}}}[/tex]
[tex]y = mx + c[/tex]
[tex]WHERE \\ m = SLOPE \\ c = Y - INTERCEPT[/tex]
[tex] \huge\green{\boxed{\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}}}[/tex]
[tex] \blue{A.T.Q}[/tex]
PART A:-
[tex]y = mx + c \sim y= -14x+1 [/tex]
[tex] \orange{SO}[/tex]
m= (-14)
which is equal to the slope of the equation .
PART B:-
[tex]y = mx + c \sim y= ¾x-9 [/tex]
[tex] \orange{SO}[/tex]
m= (¾)
PART C:-
[tex]y = mx + c \sim y= 10x-5[/tex]
[tex] \orange{SO}[/tex]
m= (10)
PART D:-
[tex]y = mx + c \sim y= 2x+8[/tex]
[tex] \orange{SO}[/tex]
m= (2)
SO MAXIMUM SLOPE IS :-( -14 )Negative shows Slope is in negative direction.
[tex] \red \star{Thanks \: And \: Brainlist} \blue\star \\ \green\star If \: U \: Liked \: My \: Answer \purple \star[/tex]
What is the value of q?
2/5
2/14
Answers
Answer:
2√14 prob I'm not 100% sure
A regression was run to determine whether there is a relationship between hours of tv watched per day(x) and number of sit-ups a person can do (y). The results of the regression are given below. Use this to predict the number of sit-ups a person who watches 11 hours of tv can do
Y=ax+b
A=-1.341
B=32.234
R=-0.896
Answers
Answer:
17
Step-by-step explanation:
Given the regression model :
Y=ax+b
x = Hours of TV watched per day
y= number of sit-ups a person can do
A=-1.341
B=32.234
Y = - 1.341x + 32.234
Predict Y, when x = 11
Y = - 1.341(11) + 32.234
Y = −14.751 + 32.234
Y = 17.483
Hence, the person Cann do approximately 17 sit-ups
The Cougar Swim Club acquired some Speedo Fastskin bodysuits and decided to test them out. A number of the club's fastest swimmers performed a 50m freestyle swim in a regular spandex bodysuit and in a Speedo Fastskin suit. The table below summarizes their times in seconds.Swimmer Spandex Speedo Fastskin1 31.1 29.12 28.9 30.43 31.4 32.04 34.9 31.75 27.7 28.26 36.7 32.97 33.3 28.68 30.8 26.2Perform a t-test for dependent means to determine if there is a difference between the regular spandex suit and the Fastskin bodysuit in terms of performance.t = _____df = _____Critical value of t = _____ (use alpha = 0.05)Would you reject the null hypothesis?
Answers
Answer:
T = 2.215
df = 7
Critical value = 2.364
Fail to reject the null
Step-by-step explanation:
Swimmer __Spandex __Speedo Fastskin__ d
1 __________31.1 _______29.1 __ 2
2_________ 28.9 ______30.4 __ -1.5
3_________ 31.4 ______ 32.0 __ - 0.6
4_________ 34.9 ______31.7 __ 3.2
5 _________27.7 ______28.2 __ - 0.5
6_________ 36.7 _____ 32.9 ___ 3.8
7 _________ 33.3 _____28.6 ___ 4.7
8_________ 30.8 _____26.2 ___ 4.6
The mean difference = Σd / n
2, - 1.5, - 0.6, 3.2, - 0.5, 3.8, 4.7, 4.6
μd = Σd / n = 15.7 / 8 = 1.9625
Sd = standard deviation of difference = 2.5065 (using calculator)
H0 : μd = 0
H1 : μd ≠ 0
The test statistic:
T = μd / (Sd/√n)
T = 1.9625 / (2.5065/√8)
T = 2.2145574
The degree of freedom, df = n - 1 = 8 - 1 = 7
Using a Pvalue calculator :
α = 0.05
Critical value, Tcritical = 2.364 (T distribution table)
Since Test statistic < Critical value
we fail to reject H0 ;
In this triangle, D is the midpoint of AB and E is the midpoint of BCIf AC = 36 what is the length of DE?
Answers
Answer:
A. 18
Step-by-step explanation:
Recall: the Mid-segment Theorem states that the length of the mid-segment theorem of a triangle is half the length of its third side.
DE = ½(AC) (Triangle Mid-segment Theorem)
AC = 36 (given)
Plug in the value
DE = ½(36)
DE = 18
A statistician calculates that 8% of Americans own a Rolls Royce. If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
Answers
Answer:
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A statistician calculates that 8% of Americans own a Rolls Royce.
This means that [tex]p = 0.08[/tex]
Sample of 595:
This means that [tex]n = 595[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.08[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.08*0.92}{595}} = 0.0111[/tex]
What is the probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%?
Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Since the normal distribution is symmetric, these probabilities are equal, and so we find one of them and multiply by 2.
Probability the proportion is less than 5%:
P-value of Z when X = 0.05. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.05 - 0.08}{0.0111}[/tex]
[tex]Z = -2.7[/tex]
[tex]Z = -2.7[/tex] has a p-value of 0.0035
2*0.0035 = 0.0070
0.007 = 0.7% probability that the proportion of Rolls Royce owners in a sample of 595 Americans would differ from the population proportion by more than 3%
A study of the pay of corporate chief executive officers (CEOs) examined the increase in cash compensation of the CEOs of 104 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x¯=6.9%, and the standard deviation of the increases was s=55%. Is this good evidence that the mean real compensation μ of all CEOs increased that year? The hypotheses are
Answers
Answer:
The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.
Step-by-step explanation:
At the null hypothesis, we test if there was no increase, that is, the mean is 0, so:
[tex]H_0: \mu = 0[/tex]
At the alternative hypothesis, we test if there was an increase, that is, the mean is greater than 0, so:
[tex]H_1: \mu > 0[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
104 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x¯=6.9%, and the standard deviation of the increases was s=55%.
This means that [tex]n = 104, X = 6.9, s = 55[/tex]
Value of the test-statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{6.9 - 0}{\frac{55}{\sqrt{104}}}[/tex]
[tex]t = 1.28[/tex]
P-value of the test:
The p-value of the test is a right-tailed test(test if the mean is greater than a value), with 104 - 1 = 103 df and t = 1.28.
Using a t-distribution calculator, this p-value is of 0.1017.
The p-value of the test is 0.1017, which is greater than the standard significance level of 0.05, which means that this is not good evidence that the mean real compensation μ of all CEOs increased that year.
