[9] X is a Gaussian random variable with variance 0.25. The mean of X is estimated by taking the sample mean of independent samples of X. If the mean needs to be estimated within 0.01 from the actual mean with a confidence coefficient of 0.99, find the minimum number of samples needed in the estimation.
Answer:
The minimum number of samples required is [tex]n = 16641 [/tex]
Step-by-step explanation:
From the question we are told that
The variance is [tex]\sigma^2 = 0.25[/tex]
The margin of error is [tex]E = 0.01[/tex]
From the question we are told the confidence coefficient is 0.99 , hence the level of significance is
[tex]\alpha = (1 - 0.99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the standard deviation is
[tex]\sigma =\sqrt{\sigma^2}[/tex]
=> [tex]\sigma =\sqrt{0.25}[/tex]
=> [tex]\sigma =0.5[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
=> [tex]n = [\frac{2.58 } * 0.5 }{0.01 } ] ^2[/tex]
=> [tex]n = 16641 [/tex]
How many laps would be 50 miles on a 2 1/2 mile track?
Answer:
20 laps
Step-by-step explanation:
50/2.5=20
Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.
Help quick.
Answer: y=8 and x=8 radical 3
pls can probability be expressed as percentage
Did ancient mathematicians use a ruler to determine the values of sine and cosine in a circle?
No answer needed! Just take points.
Answer and Explanation:
No, they did not use a ruler to compute the values of trig functions. They used geometry to prove theorems about trigonometry, then used those results and ordinary computations involving addition, subtraction, multiplication, division, and square roots to determine the entries in trigonometric tables.
Claudius Ptolemy (85 C.E.–165) created the first trig tables that we know of, and he included proofs of the theorems he used. One of the main theorems he used is what is now called Ptolemy’s theorem.
In order to prove his sum and difference forumlas, Ptolemy first proved what we now call Ptolemy’s theorem.
Ptolemy’s theorem. The product of the diagonals of a cyclic quadrilateral is equal to the sum of the products of the opposite sides.
A cyclic quadrilateral is a quadrilateral inscribed in a circle as ABCD. Ptolemy’s theorem says:
AC ⋅ BD = AB ⋅ CD + AD ⋅ BC
When one of the diagonals (like ) is a diameter of the circle, that gives you a way to determine the trig functions for sum and differences of angles.
Sometimes, the sum and difference formulas for sine and cosine are still called Ptolemy’s formulas.
sin(α + β) = sin α cos β + cos α sin β
cos(α + β) = cos α cos β − sin α sin β
sin(α − β) = sin α cos β − cos α sin β
cos(α − β) = cos α cos β + sin α sin β
Ptolemy started with angles he knew the trig functions for. These included angles in various isosceles triangles: 45°-45°-90°, 60°-60°-60°, and 36°-72°-72°, the last one described by Euclid in Proposition IV.10. That gave him the trig functions for 36°, 60°, and 90°. Using half-angle formulas (mentioned by Hipparchus (190–120 B.C.E.), he could compute trig functions for half of those angles and a quarter of those angles. Then using the sum and difference formulas he computed the rest of the numbers in his trig table.
Hope this helps! :)
i need help ASAP please and thanks
The acceleration of gravity on Mars is about 3.7 meters per second squared. Suppose a rock falls from a tall cliff on Mars. Which of the following equations indicates how fast the rock will be falling after 8 seconds?
An equation that indicates how fast (velocity) the rock will be falling after 8 seconds is V = (3.7 × 8) m/s.
Given the following data:
Time, t = 8 seconds.Acceleration of gravity on Mars, a = 3.7 meters per second squared (m/s²).How to determine the velocity of this rock?In order to determine the velocity at which this rock would fall after 8 seconds, we would apply the first equation of motion.
Mathematically, the first equation of motion is given by this formula:
V = u + at
Where:
V represents the final velocity.u represents the initial velocity.a represents the acceleration.t represents the time.Substituting the given parameters into the formula, we have;
V = 0 + 3.7 × 8
V = (3.7 × 8) m/s.
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Complete Question:
The acceleration of gravity on Mars is about 3.7 meters per second squared. Suppose a rock falls from a tall cliff on Mars. Write the equation that indicates how fast the rock will be falling after 8 seconds.
PLS HELP Solve 4 • (−6). (20 points)
a
−42
b
−24
c
10
d
24
Suppose you and 10 friends are taking a road trip for Spring Break. You plan on visiting multiple museums, national parks, and shopping locales along this trip. Your
road trip will a total of 10 days. You drive a total distance of 5000 miles. Some of the drive your average speed was 45 mph. While the rest of the trip was 70 mph.
1. How many hours were you driving each speed? Round 3 decimals
2. What distance did you drive for each speed? Round 3 decimals
Using the relation between velocity, distance and time, and supposing the group travels for 8 hours a day, it is found that:
1. You were driving 24 hours at 45 mph and 56 hours at 70 mph.
2. You drove 1080 miles at 45 mph and 3920 miles at 70 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For the first part, we have that:
The velocity is of 45 mph.The distance is of d.The time is of t.Hence:
v = d/t
45 = d/t
d = 45t.
For the second part, we have that:
The velocity is of 70 mph.The distance is of 5000 - d.The time is of 80 - t. (10 days of 8 hours driving = 80 hours).Hence:
70 = (5000 - d)/(80 - t).
d = 45t, hence:
70 = (5000 - 45t)/(240 - t).
5000 - 45t = 5600 - 70t
25t = 600.
t = 600/25
t = 24. -> (80 - 24) = 56.
d = 45t = 45 x 24 = 1080 -> (5000 - 1080) = 3920.
Hence:
1. You were driving 24 hours at 45 mph and 56 hours at 70 mph.
2. You drove 1080 miles at 45 mph and 3920 miles at 70 mph.
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Find the midpoint of GH
Answer:
2.3 is the mid point of gh
No I need 54 inches of wood to build a picture frame. if the wood cost $2.50 a foot, how much will be pay?
Answer:
135
Step-by-step explanation:
2 x 54 = 108 and .50 x 54 = 27 so 108 + 27 = 135
The cost function for a certain company is
C = 70x + 200
and the revenue is given by
R = 100x − 0.5x2.
Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $200.
Hence , the value of x (production level) that will create a profit of $200 are 40 and 20.
We have given cost function C = 70x + 200 and revenue function R = 100x − 0.5x² .
It is given that profit is revenue minus cost.
P = R -C
P = 100x − 0.5x² - 70x - 200
P = 30x − 0.5x² -200 ........(1)
It is also given that it will create a profit of $200 .
Putting P = 200 in equation (1) , we get
200 = 30x − 0.5x² -200
0.5x² - 30x + 400 = 0
Multiplying by 10 we get
5x² - 300x + 4000 = 0
Taking 5 common , we get
x² - 60x + 800 = 0
By splitting in the middle term this equation can be represented by
x² -(40+20)x +800 = 0
(x² - 40x ) - (20x-800) = 0
x(x-40) - 20( x - 40) = 0
(x - 40) (x- 20) = 0
On comparing , we get
x - 40 = 0
x = 40
and x - 20 = 0
x = 20
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1/sin10°-√3/cos10°=4
Answer:
[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=4[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{1}{\sin \left(10^{\circ \:}\right)}-\frac{\sqrt{3}}{\cos \left(10^{\circ \:}\right)}=4[/tex]
Taking the left-hand side and solving it
[tex]\frac{1}{\sin \left(10^{\circ \:}\right)}-\frac{\sqrt{3}}{\cos \left(10^{\circ \:}\right)}[/tex]
as
[tex]\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=5.76[/tex]
and
[tex]\frac{\sqrt{3}}{\cos \left(10^{\circ \:\:}\right)}=1.76[/tex]
so the expression becomes
[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=5.76-1.76[/tex]
[tex]=4[/tex]
Thus, we conclude that
[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=4[/tex]
PLEASE HELP!!! ALGEBRA 2A
Absolute value of 13+14
Answer:
27
Step-by-step explanation:
13 + 14 = 27
Answer: -13+-14
Step-by-step explanation: the Absolute value is the opposite value of something like 24-57 the absolute value of that would be -24-(-57)
The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced to a
mass of 5 mg.
What was the initial mass (in mg) of the sample?
What is the mass (in mg) 4 weeks after the start?
You may enter the exact value or round to 4 decimal places
Answer:
A = (Ao)(0.5^(t/t1.2))
1 = (Ao)(0.5^(20/4)) = Ao(0.03125)
Ao = 1/0.03125 = 32mg
5 weeks = 5(7) = 35 days
A = 32(0.5^(35/4)) = 32(0.0232) = 0.074mg
Step-by-step explanation:
find the domain of the graphed function
Answer:
Domain= [0, 13]
Step-by-step explanation:
Domain refers to the possible input values on the x-axis.
Bentley wants to ride his bicycle 39.6 miles this week. He has already ridden 8 miles.
If he rides for 4 more days, write and solve an equation which can be used to
determine x, the average number of miles he would have to ride each day to meet his
goal.
Answer:
Step-by-step explanation:
Using a linear function, it is found that he would have to ride his bicycle 7.9 miles a day to meet his goal.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The 8 miles he has already ridden is the intercept.The daily average he needs is the slope.When x = 4, y = 39.6, hence:
39.6 = 4m + 8
4m = 31.6
m = 31.6/4
m = 7.9.
He would have to ride his bicycle 7.9 miles a day to meet his goal.
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Find the equation of the line that contains a slope of 3/4 and a 'y'-intercept of (0,3). Write the answer in slope-intercept form.
Answer:
Step-by-step explanation:
y=-3/4 x-3
while in Manchester, england, chelsea bought a sweater for bitirsh pound 28 . when she returned, she saw the same sweater for C$38. which sweater cost more by how much in canadian dollar show your work pls
The sweater that cost more is the sweater bought in Manchester. It is more expensive by C$7.40.
Which sweater is more expensive?The exchange rate is the price at which one currency is exchanged for another currency. For example, if the exchange rate of the pound and Canadian dollars is 1.60. It means that 1 unit of the pound would buy 1.60 of the Canadian dollars.
The first step is to convert the cost of the sweater that is priced in the British pound to Canadian dollars.
The exchange rate : 1 British pound = 1.6215 CAD
28 X 1.6215 = 45.402
Difference in price = 45.402 - 38 = C$7.402
Based on the above calculation, the sweater when converted from the British pound to the Canadian dollars, it is more expensive to buy the sweater in Manchester than it is to buy it in Canada.
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Jocelyn has read 160 pages in a book. This is of the entire book. How many pages
does the book have?
you need more information to finish this question. You can't get an answer for a math question like this one with that little information.
Answer:
Step-by-step explanation:
lol it means 4/5,
your in rsm i aleready know
Omar’s watch shows that he takes 642 steps to walk a lap around his school’s track. If he takes a total of 12,198 steps while walking the track, how many laps does Omar walk? It is one of these.
a)18
b)19
c)20
d)21
Answer:
B. 19
12,198÷642 so the final answer will be 19.
ASAP PLEASE
what is 5/7 x 7/12 simplyfed
Answer:
I got 5/12 as my answer.
Given m| n, find the value of x.
Answer:
45°
Step-by-step explanation:
x° = (180 - 135)°
= 45°
Hope this helps
With interior alternate angles and adjacent angles concept, the value of x from the given parallel lines is 45°.
Given that, straight line m parallel to straight line n and t is the transversal.
When a transversal connects two coplanar lines, alternate interior angles are created. They are located on the transverse sides of the parallel lines, but on the inner side of the parallel lines. At two different locations, the transversal passes through the two lines that are coplanar.
Here, y=135° (Interior alternate angles are equal)
Now, y°+x°=180° (Adjacent angles on straight line)
135°+x°=180°
x°=45°
Therefore, the value of x from the given parallel lines is 45°.
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Evaluate the expression. Name the property used in each step.
3 (22-3-7)
= 3 (22-21)
=3 (1)
= 3
The value of the resulting expression is 3
Solving expressionsGiven the following expression as shown below;
3 (22-3-7)
According to the pemdas rule, the multiplication will come first inside the parenthesis
3 (22-3-7) = 3(22 - (21))
3 (22-3-7) = 3(22- 21)
Take the difference of the expression in parenthesis
3 (22-3-7) = 3(1)
Take the product of the result
3 (22-3-7) = 3
Hence the value of the resulting expression is 3
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300 feet above sea level??
Answer:
300
Step-by-step explanation:
if it is 300 feet ABOVE sea level, then it is a positive answer.
you would want to look for the words 'above' or 'below' if it is talking about sea level.
Jack wants to model a situation where the perimeter of the rectangle to the right is 6 feet plus or minus 1.5 feet. Because he is modeling a length "plus or minus" another length, he decides to use an absolute value equation for his model. Do you agree with his decision? Explain your reasoning.
The absolute value of the equation will not work because the value of x would have to be negative for the perimeter to be 6 ft plus or minus 1.5 ft.
What is the perimeter of the rectangle?The perimeter of the rectangle is given as:
Perimeter = 2(Length + Breadth)
The perimeter of a rectangle is 6 feet plus or minus 1.5 feet.
So, we have:
Perimeter = 2(Length + Breadth) = 6 feet ± 1.5 feet.
Then Substitute values for length and width
2(Length + Breadth) = 6 feet ± 1.5 feet.
2(4 + x) = 6 feet ± 1.5 feet.
Now,
2(4 + x) = 6 feet + 1.5 feet.
8 + 2x = 6.5 ft
2x = 6.5 - 8
x = -0.25 ft
2(4 + x) = 6 feet - 1.5 feet.
8 + 2x = 4.5 ft
2x = 4.5 - 8
x = -1.75ft
Here Both values of x are negative.
This means that the absolute value model can't work, because a rectangle cannot have a negative dimension.
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PLEASE HELPPPP IM ALMOST DONE IM REALLY SLEEPY AND I HAVE TO DO THIS TEST BEFORE I GO TO BED
Answer:
the tens place
Step-by-step explanation:
just need to know long division
Answer:
In the tens place :)
Step-by-step explanation:
Hope it helps. I am also doing a semester exam and would greatly appreciate if someone would help me with this:
Challenge A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the
coins, 12% are pennies and 40% are dimes. There are 5 more nickels than pennies. How much
money does the bag contain?
The bag contains $
Answer:
$5.86
Step-by-step explanation:
12% of 50=6 pennies
40% of 50= 20 dimes
6+5= 11 nickels
11+20+6= 37 coins
50 total coins-37= 13 quarters
13 quarters = $3.25
20 dimes = $2.00
11 nickels = $0.55
6 pennies = $0.06
$3.25+$2.00+$0.55+$0.06=$5.86
Answer:
$5.86
Step-by-step explanation:
Allen went out to dinner and hls total bill
came to $22.14. The tax on his meal was
8%, or $1.64. What was the subtotal of
his dinner?