Option A
[tex]\cos 3 x=\cos x-4 \cos x \sin ^{2} x[/tex]
Solution:
Given that we have to rewrite with only sin x and cos x
Given is cos 3x
[tex]cos 3x = cos(x + 2x)[/tex]
We know that,
[tex]\cos (a+b)=\cos a \cos b-\sin a \sin b[/tex]
Therefore,
[tex]\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x[/tex] ---- eqn 1
We know that,
[tex]\sin 2 x=2 \sin x \cos x[/tex]
[tex]\cos 2 x=\cos ^{2} x-\sin ^{2} x[/tex]
Substituting these values in eqn 1
[tex]\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)[/tex] -------- eqn 2
We know that,
[tex]\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x[/tex]
Applying this in above eqn 2, we get
[tex]\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)[/tex]
[tex]\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}[/tex]
[tex]\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x[/tex]
Therefore,
[tex]\cos 3 x=\cos x-4 \cos x \sin ^{2} x[/tex]
Option A is correct
Which correlation coefficient best represents a moderate relationship showing fewer anxiety symptoms in people who report higher life satisfaction? –0.5 +0.7 –0.2 +0.4
Answer:
-0.5
Step-by-step explanation:
The correlation coefficient represents the relationship between two variables and here two variables are anxiety symptoms and life satisfaction. As it is mentioned in the statement that less anxiety symptoms are present in the individuals who have higher life satisfaction, so there is negative/ inverse relationship between anxiety symptoms and life satisfaction. Just to be clear the inverse relationship means that increase in one variable lead to decrease in second variable and vice versa. Also according to rule of thumb 0.5 represents the moderation correlation because correlation coefficient ranges from -1 to +1 and 0.5 is a middle value. So the correlation coefficient in the given scenario is -0.5.
Linear function f(x) = x is graphed on a coordinate plane. The graph of a new line is formed by changing the slope of the original line to 2/3 and the y-intercept to 4. Which statement about the relationship between these two graphs is true?a. The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated down.b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up.c. The graph of the new line is steeper than the graph of the original line, and the y-intercept has been translated up.d. The graph of the new line is less steep than the graph of the original line, and they-intercept has been translated down.
Answer:
b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up
Option b is right.
Step-by-step explanation:
Given that linear function f(x)=x is graphed on a coordinate plane.
The graph of a new line is formed by changing the slope of the original line to 2/3 and the y-intercept to 4.
The original slope was 1. Now changed to 2/3 i.e. slope is reduced. Hence the new line will be less steeper.
Also original line y =x has y intercept at the origin.
By changing y intercept to 4, we changed y intercept to upwards by 4 units.
Thus there is a vertical shift of 4 units.
b. The graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up
Option b is right.
A linear function is represented by a straight line.
The true statement is: (b) the graph of the new line is less steep than the graph of the original line, and the y-intercept has been translated up.
The function f(x) is given as:
[tex]\mathbf{f(x) = x}[/tex]
The attributes of the new function are:
Slope = 2/3y-intercept = 4So, the new function is:
[tex]\mathbf{f'(x) = \frac23x + 4}[/tex]
The slope of [tex]\mathbf{f(x) = x}[/tex] is 1.
2/3 is less than 1.
So, the new line is less steep
The y-intercept (4) means that:
The new line is shifted up by 4 units
Hence, the correct statement is: (b)
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The telephone pole is _____ feet tall. (Round to the nearest whole number)
14 ft
42 ft
33 ft
85 ft
Answer:
33 ft
Step-by-step explanation:
sin( angle ) = opposite / hypotenuse
A certain club has 20 members. What is the ratio of the number of 5-member committees that can be formed from the members of the club to the number of 4-member committees that can be formed from the members of the club?
A. 16 to 1
B. 15 to 1
C. 16 to 5
D. 15 to 6
E. 5 to 4
Answer:
C
Step-by-step explanation:
This is a combination question.
In the first instance, we select 5 from 20 and in the second case , we select 4 from 20.
The total number of ways to solve the first instance is 20C5 = 15504 ways
The total number of ways to solve the second instance is 20C4 = 4,845
The ratio of the first to the second scenario is 15,504/4,845 = 3.2 = 16 to 5
Can someone help me
Answer:
6 < x < 23.206
Step-by-step explanation:
To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.
The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...
(2x -12)/2 = arcsin(16/22×sin(24°))
x ≈ 23.206°
Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...
2x -12 = 0
x -6 = 0 . . . . . divide by 2
x = 6 . . . . . . . add 6
Then the range of values of x will be ...
6 < x < 23.206
_____
* One way to do this is to make use of the law of cosines:
22² = AB² + AC² -2·AB·AC·cos(48°)
16² = AD² + AC² -2·AD·AC·cos(2x-12)
The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...
22² = 2·AB²·(1-cos(48°))
16² = 2·AB²·(1 -cos(2x-12))
The value of AB drops out of the ratio of these equations, and the result for x is as above.
Answer 6<x<30:
Step-by-step explanation:
Write the equation of the line that passes through the point (–6, 2) and is parallel to the line whose equation is x = –10, then write the equation of the line that passes through the point (–6, 2) and is perpendicular to the line whose equation is x = –10.
a. x=-6, y=-6
b. x=-6, y=2
c. x=2, y=2
d. x=10, y=2
Answer:
B. x=-6, y=2
Step-by-step explanation:
IM BEGGING YOU, IF YOU SEE THIS PLEASE TRY AND ANSWER IT!!! BRAINLIEST WOULD BE ALL YOURS!
Max is stacking logs at his campground for firewood. After his first load of logs, he has 8 logs on the stack. After the seventh load, he has 62 logs on the stack. Use sequence notation to represent the arithmetic function.
A] an = 8 + 6(n - 1)
B] an = 62 + 6(n - 1)
C] an = 8 + 9(n - 1)
D] an = 62 + 9(n - 1)
Answer:
[tex]\displaystyle a_n=8+9(n-1)[/tex]
Correct option: C]
Step-by-step explanation:
Arithmetic Sequences
Each term in an arithmetic sequence is obtained as the previous term plus a constant number called the common difference. The general term is
[tex]\displaystyle a_n=a_1+(n-1).r[/tex]
We are given this information
[tex]\displaystyle a_1=8\ ,\ a_7=62[/tex]
Replacing those values in the formula
[tex]\displaystyle 62=8+(7-1).r[/tex]
Solving for r
[tex]\displaystyle r=\frac{62-8}{6}=\frac{54}{6}=9[/tex]
[tex]\displaystyle r=9[/tex]
The general term is, then
[tex]\displaystyle a_n=8+(n-1)9[/tex]
Or equivalently
[tex]\displaystyle a_n=8+9(n-1)[/tex]
Correct option: C]
Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0 bullet p(-1) = 8 determine the value of p(0).
Answer:
p(0) = 35
Step-by-step explanation:
-3, √7 and 1-√6 are all roots, hence, we can factorize (x-(-3)) = (x+3), (x-√7) and (x- (1-√6)) = (x-1+√6) from p. Since p has rational coefficients, then we need to cancel out both √7 and √6. To do so we should multiply by the rational conjugate, of the expressions (x-1+√6) and (x-√7), that means, where a square root of a non square positive number appears, place the opposing sign there.
The rational conjugate of (x-√7) is (x+√7), and
(x-√7)*(x+√7) = x²-7
On the other hand, the rational conjugate of (x-1+√6) is (x-1-√6), and
(x-1+√6) * (x-1-√6) = ( (x-1) + √6) * ((x-1) -√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5.
Thus, both x²-7 and x²-2x-5 are factors of p. The polynomial has the form
[tex]P(x) = c(x+3)(x^2-7)(x^2-2x-5)[/tex]
Where c is a constant. To determine c, we need to use the other piece of information given: p(-1) = 8
When we evaluate in -1, we get
[tex]p(-1) = c*(-1+3)((-1)^2-7)((-1)^2-2(-1)-5) = c* 2*(-6)*(-2) = c*24 = 8[/tex]
Thus, c = 8/24 = 1/3.
Therefore,
[tex]p(0) = \frac{1}{3} * (0+3)(0^2-7)(0^2-2*0-5) = \frac{1}{3}*3*(-7)*(-5) = 35[/tex]
I hope that works for you!
AM i correct?
rational expression question
Answer:
[tex] \frac{16}{7(x + 4)} + \frac{5}{7(x - 3)} [/tex]
your answer is not correct.
I NEED THE ANSWER FOR THIS TOO PLEASE
Answer:
Translated in numerical form: x - 2 ≤ 33.
The solution graph on a numbered line is shown in figure a.
The solution in a set notation: {x|x ≤ 35}
The solution in interval notation: (-∞, 35]
Step-by-step explanation:
"two less than a number is less than or equal to thirty three".
let's say the number is x.
Translated in numerical form: x - 2 ≤ 33.
Lets solve it:
x - 2 ≤ 33
x ≤ 33 + 2
x ≤ 35
The solution graph on a numbered line is shown in figure a.
The solution in a set notation: {x|x ≤ 35}
The solution in interval notation: (-∞, 35]
Keywords: inequality, graph
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Matthew has 63 pages to read in 2-5 days. He wants to read the same whole number of pages each day and the greatest number of pages in the fewest days possible. What is the best number of days for Matthew's reading plan?
Answer:
3
Step-by-step explanation:
63 can be factored as ...
61 = 1×63 = 3×21 = 7×9
The only plan that meets Matthew's requirement for number of days is to read 21 pages on each of 3 days.
Can someone please help me?? Im not quite sure how to get this answer.
What is the area of the shaded region in the figure below? Leave answer in terms of pi and in simplest radical form.
Answer:
C. 54π + 20.25√3 cm²
Step-by-step explanation:
The shaded area can be split into two areas: a sector and an isosceles triangle.
Area of a sector is:
A = (θ/360°) πr²
where θ is the central angle and r is the radius.
Area of an isosceles triangle can be found with SAS formula:
A = ½ ab sin θ
where a and b are two sides of a triangle and θ is the angle between them.
In this case, r = a = b = 9 cm. The central angle of the sector is 240°, and the vertex angle of the triangle is 120°. Therefore, the total area is:
A = (240°/360°) π (9 cm)² + ½ (9 cm) (9 cm) sin 120°
A = 54π + 20.25√3 cm²
On a certain hot summer's day, 539539 people used the public swimming pool. The daily prices are $ 1.25$1.25 for children and $ 2.50$2.50 for adults. The receipts for admission totaled $ 1023.75 .$1023.75. How many children and how many adults swam at the public pool that day?
Answer:the number of children that swam at the public pool is 259
the number of adult that swam at the public pool is 280
Step-by-step explanation:
Let x represent the number of children that swam at the public pool that day.
Let y represent the number of adult that swam at the public pool that day.
On a certain hot summer's day,539 people used the public swimming pool. This means that
x+ y = 539
The daily prices are $ 1.25 for children and $ 2.50 for adults. The receipts for admission totaled $ 1023.75. This means that
1.25x + 2.5y = 1023.75 - - - - - - - - - -1
Substituting x = 539 - y into equation 1, it becomes
1.25(539 - y) + 2.5y = 1023.75
683.75 - 1.25y + 2.5y = 1023.75
- 1.25y + 2.5y = 1023.75 - 683.75
1.25y = 350
y = 350/1.25 = 280
Substituting y = 280 into x = 539 - y , it becomes
x = 539 - 280 = 259
One interior angle of a convex polygon is 160 degrees. The rest of the interior angles of the polygon are each 112 degrees. How many sides does the polygon have?
Answer:
Step-by-step explanation:
160+112n=180k
112n=180k-160
for k=1
180-160=20(not divisible by 112)
k=2
180*2-160=360-160=200(not divisible by 112)
k=3
180*3-160=540-160=380(not divisible by 112)
180*4-160=720-160=560(divisible by 112)
so number of sides=560/112 +1=5+1=6
or (n-2)180=720
n-2=720/180=4
n=4+2=6
Answer:
6
Step-by-step explanation:
The sum of interior angle of a polygon is (n - 2)180.
But in the convex polygon given in the question, we know that the sum of the interior angles is as follows: : 160 + 112(n - 1)
Equating both will yield the following:
180n -360 = 112n - 112 + 160
180n - 360 = 112n + 48
180n - 112n = 360 + 48
68n = 408
n = 408/68 = 6
Hence , the convex polygon has 6 sides
An architecture firm creates blueprints for office buildings. Last week, they produced four rectangular blueprints for four different projects. Project A: A 20-inch by 15-inch blueprint with a scale of 1 inch to 4 feet and a projected cost of $22,000. Project B: A 10-inch by 8-inch blueprint with a scale of 1 inch to 8 feet and a projected cost of $25,000. Project C: A 15-inch by 12-inch blueprint with a scale of 1 inch to 6 feet and a projected cost of $27,000. Project D: An 8-inch by 6-inch blueprint with a scale of 1 inch to 12 feet and a projected cost of $30,000. Order the projects from greatest to least projected cost per square foot of the actual offices. Project C Project B Project D Project A
Answer:
Cost in decreasing order: Project B>Project A>Project D>Project C
Step-by-step explanation:
Project A
Area: [tex]A=20 in*15 in= 300 in^2[/tex]
Scale: [tex]S=\frac{4 ft *4ft}{1 in*1in}=16 \frac{ft^2}{in^2}[/tex]
Cost:
[tex]C=\frac{22000}{300 in^2*16 \frac{ft^2}{in^2}}[/tex]
[tex]C=\frac{4.58}{ft^2}[/tex]
Project B
Area: [tex]A=10 in*8 in= 80 in^2[/tex]
Scale: [tex]S=\frac{8 ft *8ft}{1 in*1in}=64 \frac{ft^2}{in^2}[/tex]
Cost:
[tex]C=\frac{25000}{80 in^2*64 \frac{ft^2}{in^2}}[/tex]
[tex]C=\frac{4.88}{ft^2}[/tex]
Project C
Area: [tex]A=15 in*12 in= 180 in^2[/tex]
Scale: [tex]S=\frac{6 ft *6ft}{1 in*1in}=36 \frac{ft^2}{in^2}[/tex]
Cost:
[tex]C=\frac{27000}{180 in^2*36 \frac{ft^2}{in^2}}[/tex]
[tex]C=\frac{4.16}{ft^2}[/tex]
Project D
Area: [tex]A=8 in*6 in=48 in^2[/tex]
Scale: [tex]S=\frac{12 ft *12ft}{1 in*1in}=144 \frac{ft^2}{in^2}[/tex]
Cost:
[tex]C=\frac{30000}{48 in^2*144 \frac{ft^2}{in^2}}[/tex]
[tex]C=\frac{4.34}{ft^2}[/tex]
Which statement best describes a solution to the system of equations 3x+Y=17 X+2y=49 A. It has no solution B. It has infinite solutions C. It has a single solution x=15 y=17 D. It has a single solution x=-3 y=26
Answer:
It has a single solution x=-3 y=26
Step-by-step explanation:
The ratios of coefficients of x and y are different, so the pair of equations has one solution. It is easy to tell the first offered solution (15, 17) does not satisfy the first equation, so that choice is eliminated.
Fortunately, the second offered solution, (x, y) = (-3, 26), satisfies both equations.
The equations have a single solution: (x, y) = (-3, 26).
Answer: The equation has a single solution x = -3 , y = 26.
( -3, 26 )
Step-by-step explanation:
3x + y =17 ---------------------(1)
x + 2y = 49 -------------------(2)
Using substitution approach
From (2)
x = 49 - 2y --------------------(3)
Now put (3) in equation (1) and solve.
3(49 - 2y) + y = 17
Open the bracket and solve
3 x 48 - 3 x 2y + y = 17
147 - 6y + y = 17
Gather like terms
-5y = 17 - 147
-5y = -130
Multiple through by (-1)
5y = 130
Divide by 5
y = 130/5
y = 26.
Substitute for y now in equation (3) to get the value of x
3x + y = 17
3x + 26 = 17
3x = 17 - 26
3x = -9
Now , divide by 3
x = -3
The equation had a single solution of x = -3 , y = 26
Chech.
3 x -3 + 26
-9 + 26
= 17
If the null hypothesis of an experiment is "The true mean weight of the piglets is at least 39lbs" what is the alternate hypothesis?
if its correct will give brainliest
Answer:
Alternate Hypothesis: The true weight of the piglets is greater than or equal to 39 lbs.
Step-by-step explanation:
Hypothesis testing is more like a binary process in which only one (Either Null or Alternate Hypothesis can be true) and we have to infer that whether our Null hypothesis is true or false.
The hypothesis testing involves following 4 general steps:
State the 2 hypothesis by making sure that they don't overlap with each otherDevelop the analysis plan or any statistical method to know whether the Null hypothesis should be accepted or rejectedExecute the developed plan and analyze the dataIn the end, after analyzing the data accept or reject the null hypothesisAs in the given question, if a number (X) is less than another number (Y) then it can't be less, equal or greater simultaneously.
A wheel of 0.5 m radius rolls without slipping on a horizontal surface. The axle of the wheel advances at constant velocity, moving a distance of 20 m in 5 s. The angular speed of the wheel about its point of contact on the surface is:
The angular speed of the wheel at its point of contact on the surface is 8 radians per second.
Given that:
A wheel is rolling on a horizontal surface.
The radius of the wheel, r = 0.5 m
The velocity of the axle of the wheel is constant.
Here, the linear velocity can be found by taking the ratio of the distance to the time taken to cover that distance.
So, the linear speed is:
[tex]\text{v}=\frac{20}{5}[/tex]
[tex]=4 \text{ m/s}[/tex]
Now, the relationship between the angular speed and the linear speed is:
[tex]\omega=\frac{v}{r}[/tex]
[tex]=\frac{4}{0.5}[/tex]
[tex]=8[/tex] rad/s
Hence, the angular speed is 8 radians per second.
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The angular speed of the wheel about its point of contact on the surface is 8 rad/s.
To find the angular speed of the wheel about its point of contact on the surface, we can use the relationship between linear and angular velocity.
The linear velocity of a point on the wheel is given by:
v = ω * r
Where:
v is the linear velocity
ω is the angular velocity (angular speed)
r is the radius of the wheel
In this case, we know that the wheel rolls without slipping, which means the linear velocity of the point of contact with the surface is equal to the velocity of the axle. Since the axle moves a distance of 20 m in 5 s, the linear velocity can be calculated as:
v = 20 m / 5 s = 4 m/s
Given that the radius of the wheel is 0.5 m, we can rearrange the equation to solve for ω:
ω = v / r
ω = 4 m/s / 0.5 m
ω = 8 rad/s
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A woman went shopping. First she spent 4/5 of all the money she had in her purse and then she lost 2/3 of what was remaining. Now she has $10 left. How much money did she spend?
Answer:
$120
Step-by-step explanation:
Suppose the woman had x dollars in her purse at the beginning of the shopping.
First, she spent 4/5 of all the money she had, therefore she had 1-4/5=1/5 left
1/5 of x = (1/5)x or 0.2x
Then she lost 2/3 of what was remaining, which is 2/3 * (1/5)x= (2/15)x
What will be left will be (1-2/3) or 1/3 of that 1/5x left after shopping.
This will be 1/3*(1/5)x=(1/15)x
It is given from the problem statement that this is $10 left.
Therefore, (1/15)x= 10
Multiplying through by 15 and simplifying,
x= $150.
Now she spent 4/5 of this $150, which is
(4/5)*150=$120
To find out how much money the woman spent, we need to determine the amount she had in her purse and then calculate the difference after spending and losing some. We can solve this using a step-by-step approach.
Explanation:To calculate how much money the woman spent, we need to follow these steps:
First, she spent 4/5 of all the money she had in her purse. Let's call this amount X.After spending 4/5 of X, she lost 2/3 of what was remaining. This means she has 1/3 of what was remaining left. Let's call this amount Y.We know that Y is equal to $10. So, we can set up the equation Y = $10 and solve for X.Once we find X, we can calculate how much money the woman spent by subtracting X from the original amount she had in her purse.Let's solve this step-by-step:
Step 1: X = Amount she had in her purse
Step 2: Y = (4/5) * X * (1/3)
Step 3: Y = $10
Step 4: Calculate X - Y to find how much money she spent.
In the figure below, what is the length of line BC? Photo provided
I can't see the photo ....
Victor read a total of 12 books over 4 months. After belonging to the book club for 5 months ,how many books will Victor have read in all? Solve using unit rates.
Answer:
15 books
Step-by-step explanation:
Given that Victor read a total of 12 books over 4 months which means for 1 month he reads 12/4 = 3 books
Also given that he belongs to the book club for 5 months
We know that he reads 3 books in 1 month
So in 5 months he reads [tex]5\times3=15books[/tex]
Cindy's puppy, Zoey, has a basket of toys. There are 3 balls in the basket. There are 2 times as many stuffed animals as balls in the basket. There is 1 fewer bone than stuffed animals. How many toys are in Zoey's basket?
There are 14 toys in Zoey's basket.
Step-by-step explanation:
Given,
Balls in basket = 3
Stuffed animals = 2 times as balls in basket
Stuffed animals = 2*3 = 6
Bones = 1 fewer than stuffed animals.
Fewer means subtraction
Bones = 6-1 = 5
Total toys = Balls + stuffed animals + bones
Total toys= 3+6+5 = 14
There are 14 toys in Zoey's basket.
Keywords: addition, multiplication
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Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15.If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00?
a. 0.91
b. 0.09
c. 0.14
d. 0.86
To find the approximate probability that the total amount paid for the second movies will exceed $15.00 is (a) 0.91, we need to use the expected value and standard deviation to calculate a z-score and then find the corresponding probability.
Explanation:To find the approximate probability that the total amount paid for the second movies will exceed $15.00, we need to use the expected value and standard deviation to calculate a z-score and then find the corresponding probability. First, we calculate the standard deviation using the formula: standard deviation = 0.15 * sqrt(30) = 0.2598.
Then, we calculate the z-score using the formula: z = (15 - 0.47) / 0.2598 = 57.05. Using a standard normal distribution table or a calculator, we find that the probability of getting a z-score greater than 57.05 is extremely close to 1.
Therefore, the approximate probability that the total amount paid for these second movies will exceed $15.00 is 0.91, option (a).
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Two random samples are taken, with each group asked if they support a particular candidate. A summary of the sample sizes and proportions of each group answering ``yes'' are given below: Pop1: n1=92 p1=0.768 Pop2: n2=95 p2=0.646 Suppose that the data yields (-0.0313, 0.2753) for a confidence interval for the difference p1-p2 of the population proportions. What is the confidence level? (Give your answer in terms of percentages.)
Answer:
And we got [tex]\alpha/2 =0.01[/tex] so then the value for [tex]\alpha=0.02[/tex] and then the confidence level is given by: [tex]Conf=1-0.02=0.98[/tex[ or 98%
Step-by-step explanation:
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]p_1[/tex] represent the real population proportion for 1
[tex]\hat p_1 =0.768[/tex] represent the estimated proportion for 1
[tex]n_1=92[/tex] is the sample size required for 1
[tex]p_2[/tex] represent the real population proportion for 2
[tex]\hat p_2 =0.646[/tex] represent the estimated proportion for 2
[tex]n_2=95[/tex] is the sample size required for 2
[tex]z[/tex] represent the critical value for the margin of error
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
For this case we have the confidence interval given by: (-0.0313,0.2753). From this we can find the margin of erro on this way:
[tex]ME= \frac{0.2753-(-0.0313)}{2}=0.1533[/tex]
And we know that the margin of erro is given by:
[tex]ME=z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
We have all the values except the value for [tex]z_{\alpha/2}[/tex]
So we can find it like this:
[tex]0.1533=z_{\alpha/2} \sqrt{\frac{0.768(1-0.768)}{92} +\frac{0.646 (1-0.646)}{95}}[/tex]
And solving for [tex]z_{\alpha/2}[/tex] we got:
[tex]z_{\alpha/2}=2.326[/tex]
And we can find the value for [tex]\alpha/2[/tex] with the following excel code:
"=1-NORM.DIST(2.326,0,1,TRUE)"
And we got [tex]\alpha/2 =0.01[/tex] so then the value for [tex]\alpha=0.02[/tex] and then the confidence level is given by: [tex]Conf=1-0.02=0.98[/tex] or 98%
The confidence level is 95%. This conclusion is reached by converting the upper bound of the confidence interval into a standard z-score and comparing it to the z-scores for common confidence levels.
Explanation:To determine the confidence level of interval, we need to look at the proportion of the total area under the standard normal curve that falls within the interval when converted into a standard z-score. For instance, a 90% confidence interval corresponds to an area of 0.90 under the curve, with 0.05 in each tail, and a Z score of ±1.645. A 95% confidence interval corresponds to an area of 0.95 under the curve, with 0.025 in each tail, and a Z score of ±1.96. A 99% confidence level corresponds to an area 0.99 under the curve, with 0.005 in each tail, and a Z score of ±2.575.
In this case, with a confidence interval of (-0.0313, 0.2753) and the estimated proportions of p1=0.768 and p2=0.646, we find the estimated difference is 0.122 and its standard deviation is 0.0782.
Converting the upper bound of the confidence interval into a standard z-score: (0.2753 - 0.122) / 0.0782 = 1.959, which corresponds to a 95% confidence level. Thus, the inference can be that if we were to sample from these populations many times, in 95% of the cases, the true difference between p1 and p2 would lie within the interval (-0.0313, 0.2753).
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Kira goes running Monday, Wednesday, and Friday of each week. Each Monday she runs 2.5 miles, each Wednesday she runs 5.75 miles, and each Friday she runs 7.75 miles. How many total miles does she run in 9 weeks
Kira runs 144 miles in 9 weeks.
Step-by-step explanation:
Given,
Distance ran on Monday = 2.5 miles
Distance ran on Wednesday = 5.75 miles
Distance ran on Friday = 7.75 miles
Distance ran in one week = 2.5+5.75+7.75 = 16 miles
Distance ran in 9 weeks = Number of weeks * Distance ran in one week
Distance ran in 9 weeks = 16*9 = 144 miles
Kira runs 144 miles in 9 weeks.
Keywords: multiplication, addition
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Which of the following approaches is most suitable for auditing the finance and investment cycle?
Answer:
I would approach it with a graph or chart because that is the best way to go about a problem like this. don't quote me on this though because im only a freshmen in highschool. I hope this helps>
Step-by-step explanation:
Answer:
The question is not complete; the options are not given.
This is the complete question
Which of the following approaches is most suitable for auditing the finance and investment cycle?
a) perform extensive tests of controls and limit substantive procedures to analytical procedures
b) Ignore internal controls and perform extensive substantive procedures
c) Gain an understanding of internal controls and perform extensive substantive procedures
d) Ignore internal controls and limit substantive procedures to analytical procedures
Step-by-step explanation:
The right option is option c)
Gain an understanding of internal controls and perform extensive substantive procedures.
The approaches which is most suitable for auditing the finance and investment cycle is gaining an understanding of internal controls and perform extensive substantive procedures. Which makes option c the right option.
Given the following triangle, solve for angle X
A. 41.77
B. 40.46
C. 40.15
D. 39.69
Cos(Angle) = Adjacent leg / Hypotenuse
Cos(X) = 3.5/4.6
X = arccos(3.5/4.6)
X = 40.46 degrees.
HELP HELP HELP 100PTS
sin(x)= - 0.8. If x and y are complementary, what is cos(y)
Answer:
Step-by-step explanation:
[tex]sin (x)=-0.8\\x+y=90\\x=90-y\\sin(90-y)=-0.8\\cos (y)=-0.8\\sin (90-\alpha )=cos\alpha[/tex]
Answer:
cos x
Step-by-step explanation:
Captain salamander is collecting Christmas trees to sell to the market. He collects 31 trees. He sells all his trees to 3 of his friends. Frazer has 3 more trees than Sally. Sally has 7 fewer trees than Flame. How many trees do each of his friends each get
Answer:
Flame has 14 trees, Sally has 7 trees and Frazer has 10 trees.
Step-by-step explanation:
Given;
Total Trees = 31
Let the number of trees Flame has be 'x'.
Now given:
Sally has 7 fewer trees than Flame.
framing in equation form we get;
Number of trees Sally has = [tex]x-7[/tex]
Also Given:
Frazer has 3 more trees than Sally.
framing on equation form we get;
Number of trees Frazer has = [tex]x-7+3 = x-4[/tex]
Now We know that Captain salamander total trees in 3 friends.
Hence we can say that;
Total Number of trees is equal to sum of number of trees Flame has and Number of trees Sally has and Number of trees Frazer has.
framing in equation form we get;
[tex]x+(x-7)+(x-4)=31\\\\x+x-7+x-4=31\\\\3x-11=31\\\\3x=31+11\\\\3x = 42\\\\x = \frac{42}{3} = 14[/tex]
Hence Number of trees Flame has = 14 trees
Number of trees Sally has = [tex]x-7 = 14-7 =7 \ trees[/tex]
Number of trees Frazer has = [tex]x-4 = 14-4 = 10 \ trees[/tex]
Hence Flame has 14 trees, Sally has 7 trees and Frazer has 10 trees.
A local pizza shop has a membership program for frequent buyers. The membership costs $5 per month and members get a discounted price of $1.50 per slice of pizza. Evan purchased a membership to this pizza shop. How much would Evan have to pay the pizza shop if he bought 7 slices of pizza this month? What would be the monthly cost for x x slices of pizza? Monthly cost for 7 slices: Monthly cost for x x slices:
Evan would have to pay $10.50 to the pizza shop if he bought 7 slices of pizza. The monthly cost for x slices of pizza would be $1.50x.
Explanation:Evan purchased a membership to a pizza shop that has a membership program for frequent buyers. The membership costs $5 per month and members get a discounted price of $1.50 per slice of pizza. If Evan bought 7 slices of pizza this month, he would have to pay $1.50 per slice, since he is a member. Therefore, Evan would have to pay 7 x $1.50 = $10.50 to the pizza shop.
The monthly cost for x slices of pizza can be calculated by multiplying the cost per slice ($1.50) by the number of slices (x). So, the monthly cost for x slices would be x x $1.50 = $1.50x.
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