In this circumstance, the sample consists of 1,200 inhabitants living within a ten-mile radius of the movie theater that were selected for random deliberation by the overseer.
What is a sample?Samples are frequently utilized to gain information concerning a larger population through the study of a single set of individuals or objects. The aim of selecting a sample is to inspect the populace by delving into a representative, relatively small group.
Surveys, polls, and experiments often utilize samples to make evidence-based inferences regarding the target population. For exact and dependable results, an instance should be randomly chosen, accurately mirroring those present in the whole population so as to reduce prejudice and fully optimize the evaluation.
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In 2011 Staci invested $14,500 in a savings account for her newborn son. The account pays 3.5% interest each year. Determine the accrued value of the account in the year 2029, when her son will go to college. Round your answer the nearest cent.
The accrued value of Staci's investment in the account in the year 2029 is $26933.59
Calculating the accrued value of the accountThe statements in the question can be sumarrized as
Invested amount = $14,500Rate of interest = 3.5% compounded annually.The formula to calculate amount on investment is
Amount = P * (1 + r)ⁿ
Where
P = Principal = 14,500r = Rate = 3.5%n = time = 2029 - 2011 = 18When the values are substituted in the amount equation, we have
Amount = 14500 * (1 + 3.5%)¹⁸
Evaluate
Amount = 26933.59
Hence, the amount after the investment is $26933.59
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Jackson's Ice Cream Shop must have a mean of 110 visitors per day in order to make a profit. The table below shows the number of visitors during 1 week.
Day of the week | No of Visitors
Sunday.................... 63
Monday.................. 77
Tuesday.................. 121
Wednesday............... 96
Thursday .......................137
Friday................................ 154
Based on the table, how many visitors will need to go to Jackson's Ice Cream shop on Saturday in order for the company to make a profit for the week?
A-108
B-110
C-122
D-222
Please add work/ explain!!
To find out how many visitors Jackson's Ice Cream Shop needs on Saturday to make a profit for the week, we need to first calculate the total number of visitors for the six days already given in the table. Then we can find out the number of visitors needed on Saturday to reach the required mean of 110 visitors per day for the week.
Total number of visitors for the six days = 63 + 77 + 121 + 96 + 137 + 154 = 648
To make a profit for the week, the total number of visitors for the entire week needs to be:
110 visitors/day × 7 days/week = 770 visitors/week
We already have 648 visitors for the six days, so the number of visitors needed on Saturday to make a profit can be found by subtracting the total number of visitors already counted from the total number of visitors needed for the week:
770 - 648 = 122
Therefore, the answer is (C) 122 visitors on Saturday are needed to make a profit for the week.
Asynchronous activity
In the triangles given the analysis for same is given below
What is the analysis of the two triangles given above?1) the corresponding vertices are
R ~ C and
E ~ 0
2) The corresponding angle are
∠E ~∠O and
∠ R ~ ∠C
3)
The corresponding sides are;
ER ~ CO;
MO ~ EM
CM ~ RM
4) the congruent angles are:
∠REM ≅ ∠MOC
∠ERM ≅ ∠MCO
∠CMO ≅ EMR
5) the congruent sides are:
ER ≅ CO;
MO ≅ EM
CM ≅ RM
6) the congruent triangles are;
ΔMER ≅ ΔMOC
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1. A rectangular block of wood has dimensions 24 cm by 9 cm by 7 cm. It is cut up into children's bricks. Each brick is a cube of side 3 cm.
(a) Find the largest number of bricks that can be cut from the block.
(b) Find the volume of wood that is left.
The dimensions of the rectangular block indicates;
(a) The largest number of bricks that can be cut from the block is 48 bricks
(b) The volume of the wood left is 216 cm³
What is the volume of a rectangular block?The volume of the rectangular block is the product of the length, L, width, W, and height, H.
1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³
The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;
Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48
48 cube bricks can be cut from the block(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216
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Please solve this for me!
Answer: 1; 520/9 number 2: 9/2 number 3: d number 4:d number 5: 151.7
Step-by-step explanation:
please answer the question in pic
Note that given the factors above, Orr should replace the above plant. This has to do with depreciation and book value.
Why is this so ?We need to first compute the current total cost of keeping the old plant.
Book value = $4,500,000 - $1,000,000/year x 4 years
= $500,000
Thi smean that the current total cost of keeping the old plan tfor the reamining 10 year is
Total cost of keeping old plant = $1,000,000/year x 10 years - $500,000 + $150,000
= $9 650 000
Now lets calculate the total cost of purchasing the new plant for 10 years.
$600,000 - $150,000
= $450,000 per year.
The salvage value after 10 years is $0.
Total cost of new plant = $3,500,000 + $450,000/year x 10 years = $8,000,000
Since the cost of keeping is higher than the new one, then Orr should get a new plant.
$9 650 000 > $8,000,000
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A political pollster wants to know what proportion of voters are planning to
vote for the incumbent candidate in an upcoming election. A poll of 150
randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent
candidate.
Based on this sample, which of the following is a 90% confidence interval
for the proportion of all voters who plan to vote for the incumbent
candidate?
Choose 1 answer:
780.067
78±0.080
0.520.067
The confidence interval is 0.52±0.067.(option c)
What is confidence interval?
In statistics, confidence interval means that the probability in which a population parameter will fall between a set of values for a certain proportion of times.
A political pollster wants to know what proportion of voters are planning to
vote for the incumbent candidate in an upcoming election. A poll of 150
randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent
candidate.
The formula for confidence interval(CI) is given by:
CI= p ± z √{p(1-p)/n} ----------------(1)
Here from the given data p= 78/150= 0.52
n= 150
For 90% confidence interval the value of z= 1.645.
Putting all the values in equation (1) we get,
CI= 0.52± 1.645√{(0.52×0.48)/150}
= 0.52±1.645×0.04
= 0.52±0.067
Hence, the confidence interval is 0.52±0.067.
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The administrator of a county's museum is considering increasing the price of an annual pass by 1% from $25 to $25.25. At the current price, the museum sells 2500 annual passes and the point of elasticity is 0.73. What effect would the increase in price have on the museum's annual pass revenue?
Answer: the increase in price from $25 to $25.25 would result in a small increase in annual pass revenue of $178.50 or about 0.3%.
Step-by-step explanation: we can calculate the modern yearly pass income by increasing the modern amount requested by the unused cost of $25.25:
Unused yearly pass income = Modern cost x Modern amount requested
Unused yearly pass income = $25.25 x 2482 = $62,678.50
We as of now know that the ancient yearly pass income is $62,500 (since 2500 passes were sold at $25 each), so ready to calculate the alter in yearly pass income:
Alter in yearly pass income = Unused yearly pass income - Ancient yearly pass income
Alter in yearly pass income = $62,678.50 - $62,500 = $178.50
Write an equation that represents the line.
Answer:
y = (3/4)x + 2
Step-by-step explanation:
A line (or linear function) can be represented by the equation y = mx + b where "m" is the slope and "b" is the y-intercept.
The y-intercept is when x = 0 or when the line crosses the y-axis. In the graph, notice that the line crosses at (0, 2). Thus, the y-intercept is at y = 2 and "b" must be "2".
Next, we have to find the slope, "m". The slope is defined as a change in "y" divided by a change in "x". Lets use the two points which are marked on the graph already, (4, 5) and (0, 2). We first subtract the y-values, and then divide that by the difference between corresponding x-values:
(5 - 2)/(4 - 0) = 3/4 The slope is 3/4, so m = 3/4
Now, plug "m" and "b" into the equation:
y = (3/4)x + 2
Answer:
y=(3/4)x+2
Step-by-step explanation:
So first you need to find the slope (3/4). To find that you can use the rise over run method. In this case they have already chosen two points on the line, but you could use any exact points. Count how many up from 2 to 5 (in green), which is 3 then how many across (in red) which is 4. Then put the rise (3) over the run (4) so 3/4.
Then b (2) is equal to y in the y intercept which is (0,2)
Which of the following numbers is shown plotted on the number line?
0
0 2.75 0 2 0-3 0-2 0-15
Answer:
-3 3/8
Step-by-step explanation:
The only number we're given on the number line is 0, but we can assume that each tick on the number line represents 1 units. We see that between the ticks that are 4 and 3 spaces away from 0.Since the point is to the left of 0, we know the number must be negative.The only answer that would make sense is -3 3/8, since the tick 4 places away from 0 is -4 and the tick 3 units away from 0 is -3 and -3 3/8 lies between -3 and -4When a retired police officer passes away, he leaves $300,000 to be divided among his three children and six grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?
Answer:
so first off if its six grandchildren and 3 children then that means 9 people but if the children get double the amount distributed then lets treat it like 12 people so 25,000 each meaning each child of the police officer gets 50 thousand and each grandchild gets 25 thousand
Step-by-step explanation:
hope this helps !
If it takes 15 minutes for water in a pot to boil, the expression 20x+ 15 can be used to find the total time needed to cook x batches of boiled cornbread. Which expression can also be used to determine the total time needed to cook x batches of boiled cornbread? PLS ANSWER ASAPP I REALLY NEED TO ANSWER THIS QUESTION
A 18x + 4x + 6 + 7
B 10x + 10x + 20 - 5
C 6(5x + 5) - 10x + 15
D 3(x + x + x + 3)+ 2x + 15
the correct expression which can also be used to determine the total time needed to cook x batches of boiled cornbread is,
B) 10x + 10x + 20 - 5.
Given that;
The expression 20x + 15 represents the total time needed to cook x batches of boiled cornbread.
We can simplify this expression by factoring out the common factor of 5: = 20x + 15
= 5(4x + 3)
Therefore, the expression that can also be used to determine the total time needed to cook x batches of boiled cornbread must have a factor of 5 in it.
Option A:
18x + 4x + 6 + 7 does not have a factor of 5,
so it cannot be the correct answer.
Option B:
10x + 10x + 20 - 5
= 20x + 15,
which is the same as the original expression.
Therefore, Option B is equivalent to the original expression and can also be used to determine the total time needed to cook x batches of boiled cornbread.
Option C:
6(5x + 5) - 10x + 15 = 30x + 15 - 10x + 15 = 20x + 30,
which does not have a factor of 5.
Therefore, Option C is not correct.
Option D:
3(x + x + x + 3) + 2x + 15 = 9x + 6 + 2x + 15 = 11x + 21,
which does not have a factor of 5.
Therefore, Option D is not correct.
Therefore, the correct answer is,
B) 10x + 10x + 20 - 5.
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100 POINTS
Question:
read the paragraph and then you’d have all the information that you need
Answer:
First braclets coast 3$ and necklaces coast 6$ so now in the box you can put 3in the first one then 6 in the next and keep going its like multiples of 3 and 6 :) Hope this helps.
Step-by-step explanation:
A study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23. A random sample of
100 consultants in the industry has a mean hourly fee of $113. Find a 99% confidence interval for the true mean hourly fee of all consultants in the industry.
Then give its lower limit and upper limit.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
5
If a study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23. the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).
How to find the confidence interval?The formula for a confidence interval for the population mean is:
CI = X- bar ± z* (σ/√n)
where:
X- bar = sample mean
z* = z-score for the desired level of confidence (99% in this case)
σ = population standard deviation
n = sample size
Substituting the given values, we get:
CI = 113 ± 2.576 * (23/√100)
Calculating the standard error:
SE = σ/√n = 23/√100 = 2.3
Now we can substitute this value into the formula:
CI = 113 ± 2.576 * 2.3
CI = 113 ± 5.92
So,
Lower limit: 107.1
Upper limit: 118.9
Therefore, the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).
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The amount of money in a savings account increases by 0.2% every month.
Part A
Write a function for the amount of money in the account, B, after t months with an initial deposit of $100.
B(t) =
(
)t
Part B
By what factor does the amount in the account increase every month? Every year? Every 5 years? Round answers to the nearest thousandth.
each month:
each year:
every five years:
a) A function for the amount of money in the account, B, after t months with an initial deposit of $100 isB(t) = [tex]100(1 + 0.002)^t[/tex]
b) The amount in the account increases by a factor of approximately 1.002 every month, approximately 1.025 every year and approximately 1.099 every five years.
a) The function for the amount of money in the account after t months with an initial deposit of $100 and an increase of 0.2% per month can be written as:
B(t) = [tex]100(1 + 0.002)^t[/tex]
where t is the number of months.
b) To determine the factor by which the amount in the account increases every month, year, and five years, we can calculate the value of the function for t = 1, t = 12, and t = 60, respectively, and then divide each value by the previous one.
For each month:
B(1) = 100(1 + 0.002) = $100.20
B(2) = 100(1 + 0.002)² = $100.40
B(2)/B(1) = $100.40/$100.20 = 1.001993
The amount in the account increases by a factor of approximately 1.002 every month.
For each year:
B(12) = 100(1 + 0.002)¹² = $102.44
B(24) = 100(1 + 0.002)²⁴ = $105.01
B(24)/B(12) = $105.01/$102.44 = 1.0249
The amount in the account increases by a factor of approximately 1.025 every year.
For every five years:
B(60) = 100(1 + 0.002)⁶⁰ = $110.41
B(120) = 100(1 + 0.002)¹²⁰ = $121.20
B(120)/B(60) = $121.20/$110.41 = 1.0991
The amount in the account increases by a factor of approximately 1.099 every five years. Therefore, the amount in the account increases by a small factor every month, a moderate factor every year, and a larger factor every five years.
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express 7 min 30 sec. as a percentage of 1 hour
Answer:
12.5 is the answer
Step-by-step explanation:
7 × 60 ( 7 being the minutes, 60 being the hour )
= 420
+ 30
= 450
450 ÷ 3600 × 100
45000 ÷ 3600
450 ÷ 30
= 12.5
12.5 being the answer
How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%? a previous study indicates that the proportion is 21%
Using the data given such as the margin of error, sample size and z-score, the maximum sample size required is 499
How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%?To solve this problem, we need to know the minimum sample size required. The formula for this is given as;
n = (z² * p(1 - p))/ E²
n = sample sizeE = Maximum margin of errorp = estimated proportion from the given previous studyz = z-scoreSubstituting the values into the formula;
n = (1.645² * 0.21(1 - 0.21))/ 0.03²
n = 498.8
The sample size should be at least approximately 499
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If the number 48700 is written in scientific notation, it will be in the form 4.87×10n. What is the value of n?
If the number 48700 is written in scientific notation, it will be in form 4.87×10ⁿ, and the value of n is 4.
What is scientific notation?Scientific notation describes the shorthand way of writing very large or very small numbers in standard forms.
Writing in scientific notation, a number between 1 and 10 is multiplied by a power of 10.
48700 = 4.87×10ⁿ = 4.87×10⁴
Thus, the n represents the exponent of power 10 to which the number is reduced.
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
The sum of both sides is 2x² + 4. The length of the third side is 5x³ - 4x² + 3x - 12
What is a triangle?A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, right angled, scalene, equilateral.
Given that the perimeter of the triangle is 5x³ - 2x² + 3x - 8. The length of side one is 3x² - 4x - 1 and that of side two is -x² + 4x + 5
The sum of side one and side two is:
Sum = side 1 + side 2 = (3x² - 4x - 1) + (-x² + 4x + 5) = 2x² + 4
The sum of both sides is 2x² + 4
The third side is:
Third side = Perimeter - Sum of two sides = (5x³ - 2x² + 3x - 8) - (2x² + 4) = 5x³ - 4x² + 3x - 12
The length of the third side is 5x³ - 4x² + 3x - 12
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What did Maleuvre write about Gauguin's views on Polynesian women?
Answer:
Step-by-step explanation:
Observation of the real life and way of life of the peoples of Oceania are intertwined in them with local myths.
The Morning Gazette offers employees 1.65% of the average of their last 3 years of annual compensation for each year of service. Rita began working for the Morning Gazette in 1994. She retired in 2016. In 2014, she made $76,000 per year. Thereafter, she received a 3% salary increase each year until she retired.
a) How much did she earn for each year from 2014 through 2016?
b) What is the average of her last five years of working?
c) How much was his annual retirement benefit?
She earn fοr each year frοm 2014 thrοugh 2016 is 80628.40. The average οf her last five years οf wοrking $78,302.80. His annual retirement benefit was $28,423.92.
a) Salary οf 2014 : $76000
Salary in 2014 is the salary in 2015 increased by 3% οf the salary
= $76,000+3%
Salary οf 2015 = $78,280
Salary in 2015 is the salary in 2016 increased by 3% οf the salary
=$78,280+3%
Salary οf 2016 = $80,628.40
Hence, she earn fοr each year frοm 2014 thrοugh 2016 is 80628.40
b) The average οf the last three years is the sum οf the salaries divided by the number οf salaries.
= $76,000+$78,280+$80,628.40 / 3
= $78,302.80
Hence, the average οf her last five years οf wοrking $78,302.80
c ) The annual retirement benefit is the prοduct οf the rate and the average and the number οf years οf service.
= 1.65%×$78,302.80×22
=$28,423.92
Hence, his annual retirement benefit was $28,423.92.
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 Cooper can purchase a item for $45.00, Which store has the best buy?
A. Store 1: 25% off coupon
B. Store 2: $15 dollars off
C. Store 3: 10% off
I’ll give brainly please help me
3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
(2x^2 + 23x) - (3x - 18)
Answer:
2 (x + 1)(x + 9)
Step-by-step explanation:
The given expression is
[tex]\left(2x^2\:+\:23x\right)\:-\:\left(3x\:-\:18\right)[/tex]
and we are asked to factor it
Step 1
Remove parentheses
[tex]\left(2x^2\:+\:23x\right) = 2x^2 + 23x\\\\-\:\left(3x\:-\:18\right) = - (3x) - (-18) = -3x + 18\\\\[/tex]
Step 2
Add the individual terms to correspond to the original expression:
[tex]\left(2x^2\:+\:23x\right)\:-\:\left(3x\:-\:18\right) \\\\= 2x^2 + 23x -3x + 18\\\\= 2x^2 + 20x + 18[/tex]
Step 3
Factor out common term 2
[tex]2x^2+20x+18 \\\\= 2\left(x^2+10x+9\right)[/tex]
Step 4
Factor [tex]x^2+10x+9[/tex]
To do this find two numbers such that their sum = 10 and product = 9
We can easily see that these two numbers are 1 and 9 because 1 + 9 = 10 and 1 x 9 = 9
Therefore, splitting the expression into groups we get
[tex]x^2 + 10x + 9 = x^2 + 1x + 9x + 9\\\\[/tex]
Step 5
Factor:
[tex]x^2 + 1x = x(x+ 1)\\9x + 9 = 9(x + 1)\\\\[/tex]
Therefore
[tex]x^2 + 1x + 9x + 9 = x(x + 1) + 9(x + 1)\\\\[/tex]
Step 6
Factor common term (x + 1) from the expression
[tex]x(x + 1) + 9(x + 1) = (x + 1)(x + 9)[/tex]
Step 7
Putting it all together
Remember we factored out the 2 in step 3 so we got to put it back into the factored expression giving the final factored expression as
[tex]2 (x + 1)(x + 9)[/tex]
How much money should Be deposited today in an account that earns 10.5 percent compounded monthly so that it will accumulate to $22,000 in four years
Answer:
$12,276.24
Step-by-step explanation:
22000 / (1 + 0.105/12)^4*12
12276.24
The function h(t) = 4 + 64t – 16t2 models the height h, in feet, of a ball thrown in the air, after t seconds.
Part A
What is the vertex of the graph of the function, (t, h(t))?
(
,
)
Part B
What does the t-coordinate of the vertex represent?
A. the ball's maximum height
B. the time it takes for the ball to reach its maximum height
C. the time it takes for the ball to hit the ground
D. the height the ball was thrown from
Part C
What does the h(t)-coordinate of the vertex represent?
A. the ball's maximum height
B. the time it takes for the ball to reach its maximum height
C. the time it takes for the ball to hit the ground
D. the height the ball was thrown from
Part A) The vertex of the graph of the function, (t, h(t)) is (2, 68).
Part B) The t-coordinate of the vertex represent is the time it takes for the ball to reach its maximum height (option b)
Part C) The h(t)-coordinate of the vertex represent is the ball's maximum height (option a).
Part A asks for the vertex of the graph of the function, which is the point where the function reaches its maximum or minimum value. To find the vertex of a quadratic function like
=> h(t) = 4 + 64t – 16t²,
we can use the formula
=> t = -b/2a,
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c and t is the input variable (in this case, the time).
The t-coordinate of the vertex is simply the value we get when we plug this formula into our equation.
So, for
=> h(t) = 4 + 64t – 16t²,
we have a = -16, b = 64, and c = 4.
Plugging these values into the formula
=> t = -b/2a,
we get
=> t = -64/(2*(-16)) = 2.
The t-coordinate of the vertex is therefore 2.
To find the h(t)-coordinate of the vertex, we can simply plug t = 2 into the function h(t) = 4 + 64t – 16t² and evaluate it.
This gives us
=> h(2) = 4 + 64(2) – 16(2²) = 68.
Therefore, the vertex of the graph of h(t) is (2, 68).
Part B asks what the t-coordinate of the vertex represents. We know that the t-coordinate is the time at which the ball reaches its maximum height.
Therefore, the correct answer is B: the time it takes for the ball to reach its maximum height.
Part C asks what the h(t)-coordinate of the vertex represents. We just found that the h(t)-coordinate of the vertex is the maximum height of the ball.
Therefore, the correct answer is A: the ball's maximum height.
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The value of x in the following equation 4x-5=7 is .........
Answer:
Step-by-step explanation:
4x - 5 = 7
4x = 7 + 5
4x = 12
x = 12/4
x = 3
At which values in the interval [0, 2π) will the functions f (x) = cos 2x + 1 and g(x) = sin x + 2 intersect?
x equals 0 comma pi over 6 comma 5 times pi over 6 comma pi
x equals 0 comma pi comma 7 times pi over 6 comma 11 times pi over 6
x equals pi over 2 comma 7 times pi over 6 comma 3 times pi over 2 comma 11 times pi over 6
x equals pi over 6 comma pi over 2 comma 5 times pi over 6 comma 3 times pi over 2
The functions f(x) = cos 2x + 1 and g(x) = sin x + 2 intersect at x = pi/6, pi/2, 5pi/6, and 3pi/2 in the interval [0, 2π).
To find the intersection points, we set f(x) equal to g(x) and solve for x.
cos 2x + 1 = sin x + 2
Rearranging, we get:
cos 2x = sin x + 1
Using the identity cos 2x = 1 - 2sin²x, we can rewrite this as:
1 - 2sin²x = sin x + 1
Simplifying and factoring, we get:
2sin²x + sin x = 0
sin x(2sin x + 1) = 0
Therefore, sin x = 0 or sin x = -1/2. Solving for x in the interval [0, 2π), we get x = pi/6, pi/2, 5pi/6, and 3pi/2. These are the values at which f(x) and g(x) intersect.
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please help with this question!
Answer:
The true statements:
6 is an element of D
12 is an element of D
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course:
−5,19,4,0,1
Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal.
Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
The critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).
What is the statistics?Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.
To find the critical value for an 80% confidence interval, we need to determine the z-score corresponding to the level of confidence. We can use a standard normal distribution table or a calculator to find this value.
Using a standard normal distribution table, we can find the z-score that corresponds to an 80% confidence level by finding the area between the mean and the upper tail of 10%, which is (100% - 80%)/2 = 10%.
The area between the mean and 10% is 0.5 - 0.10 = 0.40. Using the standard normal distribution table, the z-score that corresponds to an area of 0.40 is approximately 1.28.
Hence, the critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).
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Given the two concentric circles with center X below, find the area of the shaded region. Round your answer to the nearest tenth if necessary.
The area of the shaded region is given as follows:
298.3 units².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The larger circle has a radius of 7 + 5 = 12 units, hence it's area is given as follows:
A = 3.14 x 12²
A = 452.16 units².
The smaller circle has a radius of 7 units, hence it's area is given as follows:
A = 3.14 x 7²
A = 153.86 units².
Hence the area of the shaded region is given as follows:
452.16 - 153.86 = 298.3 units².
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