Answer: Since cos(theta) = 2/3 and theta is in quadrant IV, we know that sin(theta) is negative. We can use the Pythagorean identity to find the value of sin(theta):
sin^2(theta) + cos^2(theta) = 1
Substituting cos(theta) = 2/3, we get:
sin^2(theta) + (2/3)^2 = 1
Simplifying, we get:
sin^2(theta) = 1 - (2/3)^2 = 1 - 4/9 = 5/9
Since sin(theta) is negative in quadrant IV, we have:
sin(theta) = -sqrt(5/9) = -sqrt(5)/3
Therefore, sin(theta) = -sqrt(5)/3.
Step-by-step explanation:
A utility company in a western city of the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population. If consumption does increase at this rate, find the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade.
The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.
Exponential growth:The problem involves the use of the exponential growth formula in mathematics, where we are given the current consumption of electricity in a city and we are asked to find the expected consumption of electricity after a certain period of time, assuming a fixed annual growth rate.
We can use the formula:
C = C₀ × (1 + r)ⁿHere we have
A utility company in a western city in the United States expects the consumption of electricity to increase by 11%/year during the next decade, due mainly to the expected increase in population.
Let C₀ be the current consumption of electricity in the western city of the United States, and let C₁₀ be the expected consumption of electricity at the end of the decade.
We can use the following formula to calculate C₁₀:
C₁₀ = C₀ × (1 + r)ⁿ
Where r is the annual growth rate, n is the number of years
The amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is given by the difference between C₁₀ and C₀
That is:
Amount of increase = C₁₀ - C₀
Substituting the values given in the problem, we get:
C₁₀ = C₀ (1 + 0.11)¹⁰
C₁₀/C₀ = (1.11)¹⁰
C₁₀/C₀ = (1.11)¹⁰
C₁₀ = C₀ × 2.84
Therefore, the amount by which the utility company will have to increase its generating capacity in order to meet the needs of the area at the end of the decade is:
Amount of increase =C₁₀ - C₀ = 2.853 × C₀ - C₀ = 1.853 × C₀
Therefore,
The utility company will have to increase its generating capacity by approximately 185.3% to meet the expected increase in electricity consumption over the next decade.
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Ten cards numbered 1 thru 10 are placed in a box. If a card is de random from the box, what is the probability of drawing a prime a 10% b 25% c 40% d 50%
The probability of drawing a prime is 40%.
Calculating probability:To calculate the probability of drawing a prime number, use the formula
P(E) = Number of favorable outcomes / Total number of outcomes
Where P(E) is the probability of event E, and we determine the number of favorable outcomes and total possible outcomes based on the given conditions.
Here we have
Ten cards numbered 1 to 10 are placed in a box.
The total number of outcomes will get in a random experiment = 10
Here set of prime numbers from 1 to 10 = {2, 3, 5, 7}
Number of favorable outcomes that are getting prime number = 4
Hence, the probability of getting a prime number
= 4/10 = 2/5 = 0.4 = 40% [ Multiplied by 100 ]
Therefore,
The probability of drawing a prime is 40%.
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(x²-8)
meters
Square
x meters
V...
What expression represents the total area of the
shaded figure. Simplify your expression.
The shaded figure consists of a square with side length x and four identical quarter circles with radius x/2.
The area of the square is given by (side length)^2, so the area of the square is x^2.
The area of one quarter circle is given by (1/4)π(radius)^2, so the area of all four quarter circles is π(x/2)^2 = (1/4)πx^2.
Therefore, the total area of the shaded figure is the area of the square plus the area of the quarter circles, which is:
x^2 + (1/4)πx^2 = (4/4)x^2 + (1/4)πx^2 = (4+π)/4 x^2
So, the expression that represents the total area of the shaded figure is ((4+π)/4)x^2, where x is measured in meters and the area is measured in square meters.
find exact value in radians
arccos(- square root 3/2)
Which represents the solution(s) of the system of equations, y + 4 = x² and y - x = 2?
graphing.
O (-2, 0)
O (-2, 0) and (2, 0)
O (-2, 0) and (3, 5)
Ono solutions
Answer(-2,0) and (3,5)
Step-by-step explanation:
trust me bro
The number of students who ride the school bus is 110%of the number of students who walk.How many students ride the school bus
If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:
1.10x
This is because 110% can be written as 1.10 (since 110% means 110 out of 100).
So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.
However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.
Answer:If the number of students who walk is represented by x, then the number of students who ride the school bus is 110% of x, which can be written as:
1.10x
This is because 110% can be written as 1.10 (since 110% means 110 out of 100).
So, if we know the value of x, we can multiply it by 1.10 to find the number of students who ride the school bus.
However, we don't know the value of x in this problem. Therefore, we cannot find the exact number of students who ride the school bus.
Step-by-step explanation:
A small cube's edges are 2.5 inches long. A large cube's edges are 5 inches long. How many small cubes would it take to fill the large cube?
It would take 64 small cubes to fill the large cube. This is because the volume of a cube is equal to the length of its edges.
What is volume?The amount of space occupied by an object or the amount of space an object can fill. It is usually expressed in cubic units, such as cubic centimeters or cubic meters.
This is because the volume of a cube is equal to the length of its edges cubed, or V = s³, where s is the length of the edge.
We can calculate the volume of the large cube by replacing the length of its edges with 5 inches, or V = 53 = 125 in³.
To find the number of small cubes, we must first figure out the volume of a single small cube.
We can do this by replacing the length of the small cube's edges with 2.5 inches, or V = 2.53 = 15.625 in³
We can then divide the volume of the large cube (125 in³) by the volume of the small cube (15.625 in³) to get the number of small cubes needed to fill the large cube, which is equal to
125 / 15.625 = 8 * 8 = 64.
Therefore, it would take 64 small cubes to fill the large cube.
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What is the value of
3
0 1000
27
0 1000
9
10
27
0 10
3
10
?
Answer:
27/1000 is your answer
Step-by-step explanation:
Question 2: Mention 5 countries that follow command economic system in and out of
Africa
Question 2: Mention 5 countries that follow mixed economic system in and out of Africa
Answer: command economic systems:
China: China's economy has been under the control of the Communist Party since 1949. Although the country has gradually introduced market-oriented reforms in recent decades, the government still exercises significant control over the economy.
Cuba: Since the Cuban Revolution in 1959, Cuba has been a one-party socialist state with a command economy. The government controls almost all economic activity, including the allocation of resources and setting of prices.
North Korea: North Korea is a communist state with a command economy. The government controls all economic activity and owns all major industries, including agriculture, manufacturing, and transportation.
Vietnam: Vietnam is a one-party socialist state with a command economy. The government controls the allocation of resources, sets prices, and owns much of the economy's key industries.
Venezuela: Venezuela is a socialist state with a command economy that has been in crisis in recent years. The government controls much of the economy, including the country's vast oil reserves, but the country has been plagued by hyperinflation and shortages of basic goods.
5 countries that follow mixed economic system in and out of Africa:
United States: The United States has a mixed economy, which means that it has both private and public ownership of the means of production. The government regulates some industries and provides social services, while others are left to the free market.
United Kingdom: The United Kingdom is another example of a mixed economy. It has a strong tradition of free-market capitalism, but the government also provides social services and regulates some industries.
South Africa: South Africa is a country in Africa that has a mixed economy. It has a well-developed private sector, but the government also provides social services and regulates certain industries.
Brazil: Brazil is a country in South America that has a mixed economy. It has a large and growing private sector, but the government also plays a significant role in the economy, particularly in areas such as energy, telecommunications, and transportation.
India: India is a country in South Asia that has a mixed economy. It has a large and diverse private sector, but the government also plays an active role in the economy through regulation, public ownership of some industries, and social services.
Find an angle in each quadrant with a common reference angle with 319°, from 0°≤θ<360°
The angles with a common reference angle of 319° in each quadrant are:
First quadrant: 319°, Second quadrant: -139°, Third quadrant: 139°, Fourth quadrant: 41°.
To find an angle in each quadrant with a common reference angle of 319°, we can start by subtracting 360° from 319° repeatedly until we get a result between 0° and 360°. This is because angles that differ by a multiple of 360° are coterminal, which means they have the same reference angle.
319° - 360° = -41° (not in the range 0° to 360°)
319° - 2(360°) = -401° (not in the range 0° to 360°)
319° - 3(360°) = -721° (not in the range 0° to 360°)
319° - 4(360°) = -1041° (not in the range 0° to 360°)
319° - 5(360°) = -1361° (not in the range 0° to 360°)
319° - 6(360°) = -1681° (not in the range 0° to 360°)
319° - 7(360°) = -2001° (not in the range 0° to 360°)
Since none of these results are in the range of 0° to 360°, we need to add multiples of 360° instead.
319° - 1(360°) = -41° (not in the range 0° to 360°)
319° - 0(360°) = 319°
319° + 1(360°) = 679° (not in the range 0° to 360°)
319° + 2(360°) = 1039° (not in the range 0° to 360°)
319° + 3(360°) = 1399° (not in the range 0° to 360°)
So, the angle with a common reference angle of 319° in the first quadrant (0° to 90°) is:
θ = 319° - 1(360°) = -41° + 360° = 319°
The angle with a common reference angle of 319° in the second quadrant (90° to 180°) is:
θ = 180° - 319° = -139°
The angle with a common reference angle of 319° in the third quadrant (180° to 270°) is:
θ = 319° - 180° = 139°
The angle with a common reference angle of 319° in the fourth quadrant (270° to 360°) is:
θ = 360° - 319° = 41°
Therefore, the angles with a common reference angle of 319° in each quadrant are:
First quadrant: 319°
Second quadrant: -139°
Third quadrant: 139°
Fourth quadrant: 41°
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Samantha invests $18,000 into an account at a yearly interest rate of 0.45% simple interest for 24 months. Calculate the interest earned on this account using the simple interest formula I = P R T
Using simple interest, we can find the value of interest here to be $162 per month.
What is simple interest?Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. The principal amount in the case of simple interest does not change, in contrast to compound-interest, where the interest is added to the principal to calculate the principal for the new principal for the following year.
Given in the question,
Principle, P = $18000
Rate of interest, R = 0.45%
= 0.45/100
Time in years, T = 24 months
= 2 years.
I = P R T
= 18000 × 0.45/100 × 2
= $162
Therefore, interest here is $162 per month.
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PART A: A can of cat food measures 1" tall and a diameter of 3.5". What is the volume of cat food in the can? To solve Give your answer in cubic inches. Round to the nearest hundredth.
PART B: Cat food is sold by ounces (weight).
If the can holds 5.8 ounces, write a ratio to show cubic inches (your answer from slide 3) to ounces.
A)The volume of cat food in the can is 9.62 cubic inches .
B) A ratio to show cubic inches to ounces is 4.83.
What is a cylinder?
A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.
The volume of a cylinder can be calculated using the formula
=> [tex]V = \pi r^2h,[/tex]
where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14).
To find the volume of the cat food in the can, we need to use the formula for the volume of a cylinder,
Since the diameter is 3.5 inches, the radius is half of that, which is 1.75 inches. The height is 1 inch.
So,[tex]V=3.14\times(1.75)^2\times1[/tex] = 9.62 cubic inches (rounded to the nearest hundredth).
Therefore, the volume of cat food in the can is approximately 9.62 cubic inches.
Now ,To find the ratio of cubic inches to ounces,
Since the can holds 5.8 ounces of cat food, we can find the volume of cat food in cubic inches by dividing the weight by the density:
=> 5.8 ounces / 1.2 ounces per cubic inch
= 4.83 cubic inches (rounded to the nearest hundredth).
Therefore, a ratio to show cubic inches to ounces is 4.83.
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HELP ASP 20 POINTS PLSp
Answer:
Step-by-step explanation:
$499.99 - 15% will give your answers
Answer:
424.99
Step-by-step explanation:
Graph the equation in
Desmos: -2x² + 8x + 10
List the key features: x-
intercepts, y-intercept, and
vertex.
Answer:
[tex] - 2(x - 5)(x + 1)[/tex]
Step-by-step explanation:
[tex]1. \: - 2(x {}^{2} - 4x - 5) \\ 2. \: - 2(x - 5)(x + 1)[/tex]
Let f(x)x and g(x). Perform the function operation and then find the domain.
g(x)f(x)
Part 1
g(x)f(x)
enter your response here (Simplify your answer.)
Answer:
[tex]x ^{2} - 4x + 1[/tex]
Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. Jeremy's drone is closer to him than to Leslie, and Leslie's drone is closer to her than to Jeremy. Jeremy's drone is 30 meters above the ground, and he is located 50 meters to
the left from the point directly below the drone. The angle of elevation from Leslie's location on the ground to her dronp is 55°, and the distance between her location on the ground and her drone is 70 meters.
1. Calculate whose drone is higher. Show all work.
2. The angle elevation from the lower drone to the higher drone is 25 degrees. Use this information to calculate the distance between Jeremy and Leslie. Show all work.
3. Jeremy now flies his drone vertically so that it is the same height as Leslie’s drone. Draw a new diagram that includes Jeremy, Leslie, and the drones after Jeremy flies his drone to the same height as Leslie’s.
4. Explain why the angle of elevation from Jeremy’s location on the ground to his drone is different from the angle of elevation between Leslie’s location on the ground and her drone, given that both drones are at the same elevation above the ground.
5. Calculate the angle of elevation from Jeremy’s location on the ground to his drone to validate your reasoning. Show all work.
The solutions are explained below.
Given that, Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them. The figure is attached.
Height of Jeremy's drone = 30 m
Height of Leslie's drone = x m
h / 70 = sin 53°
h = 70 × sin 53°
h = 57.34
Therefore, Leslie's drone is higher than Jeremy's drone.
Difference of height = 57.34 - 30 = 27.34 m
27.34 / x = tan25°
x = 58.63 m
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The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.74
5.74
millimeters and a standard deviation of 0.07
0.07
millimeters. Find the two diameters that separate the top 5%
5
%
and the bottom 5%
5
%
.
The diameter that separates the bottom 5% of bolt diameters produced in the machine shop is approximately 5.62985 millimeters.
We can use the Z-score formula to find the diameters that separate the top 5% and bottom 5% of the bolt diameters produced in the machine shop.
For the top 5%, we want to find the diameter such that 5% of the bolts have a larger diameter. Using a standard normal distribution table or calculator, we find that the Z-score corresponding to the top 5% is 1.645.
So, the Z-score formula gives us:
1.645 = (x - 5.74) / 0.07
Solving for x, we get:
x = 5.74 + 1.645 * 0.07
x = 5.85015
Therefore, the diameter that separates the top 5% of bolt diameters produced in the machine shop is approximately 5.85015 millimeters.
For the bottom 5%, we want to find the diameter such that 5% of the bolts have a smaller diameter. Using the same Z-score of 1.645, but with a negative sign, we get:
-1.645 = (x - 5.74) / 0.07
Solving for x, we get:
x = 5.74 - 1.645 * 0.07
x = 5.62985
Therefore, the diameter that separates the bottom 5% of bolt diameters produced in the machine shop is approximately 5.62985 millimeters.
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sophomores have 26% please help me with math!
Answer: 234 are sophomores
Step-by-step explanation:
You would take 26% of 900 to get 234
It's simple, don't overthink it :)
Have a nice day.
Step-by-step explanation:
Sophomores are 26 % of 900 students
26 % * 900 = the number of sophomores
26% * 900 = .26 * 900 = 234 sophomores
At one college, GPAs are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Find the 70th percentile.
The GPA corresponding to the 70th percentile at the college is approximately 3.246 based on standard deviation.
We can use the conventional normal distribution table or a calculator with a normal distribution function to determine the 70th percentile of GPAs at a college, which are normally distributed with a mean of 2.9 and a standard deviation of 0.6.
The inverse normal distribution function with a mean of 2.9, a standard deviation of 0.6, and a percentile of 70 can be used on a calculator. This results in:
[tex]3.246 for invNorm(0.7, 2.9, 0.6).[/tex]
As a result, the GPA that represents the 70th percentile is roughly 3.246.
We can determine the z-score corresponding to the 70th percentile, which is 0.5244, by using a common normal distribution table. Thus, we may apply the equation z = (x - ) /, where x is the GPA that corresponds to the 70%ile, is the mean, and is the standard deviation, and all three variables have values of 2.9. After finding x, we obtain:
0.5244 = (x - 2.9) / 0.6
x = 3.246
Once more, doing so yields the same outcome as using a calculator.
In conclusion, the GPA at the college that represents the 70th percentile is roughly 3.246.
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evaluate 1/6r+11/24 when r =1/4
Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $135 of the population mean, and the population standard deviation is known to be $538.
54
62
43
86
Answer:
the correct answer is option B.
Step-by-step explanation:
We can use the formula for the margin of error for a confidence interval for a population mean with a known population standard deviation:
Margin of error = z*σ/√n
where z is the critical value from the standard normal distribution for the desired confidence level (95% in this case), σ is the population standard deviation, and n is the sample size.
We are given that the margin of error is $135 and σ is $538. We need to find the sample size, n. To do this, we first need to find the appropriate value of z for a 95% confidence level. Using a standard normal distribution table or calculator, we can find that z = 1.96.
Substituting the values into the margin of error formula and solving for n, we have:
$135 = 1.96*($538)/√n
Squaring both sides and solving for n, we get:
n = [1.96*($538)/$135]^2 ≈ 62
Therefore, a sample size of 62 business students must be randomly selected to estimate the mean monthly earnings of business students at one college with 95% confidence that the sample mean is within $135 of the population mean, assuming the population standard deviation is known to be $538.
So the correct answer is option B.
There are 12 finalist in a singing competition. The top singers recieve prizes. how many singers finish first through sixth
There are 44,352 possible ways to select the top six finalists, and thus six singers finish first through sixth.
What is permutation and combination?There are two methods for counting the number of potential outcomes in a situation: permutations and combinations. Nevertheless, they differ in how they take into account the sequence in which the items were selected.
On the other hand, a combination is a collection of items chosen randomly. The number of possibilities of the three letters A, B, and C taken two at a time would be AB, AC, and BC using the same example.
The total number of singes are 12.
Using the multiplication rule we have:
12 x 11 x 10 x 9 x 8 x 7 = 44,352
Hence, there are 44,352 possible ways to select the top six finalists, and thus six singers finish first through sixth.
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Identify the vertex of the parabola. (EASY! 10 Points)
Answer:
B
Step-by-step explanation:
given a parabola in standard form
f(x) = ax² + bx + c (a ≠ 0 ) , then
the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = - 4x² - 16x - 13 ← is in standard form
with a = - 4 , b = - 16 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{-16}{2(-4)}[/tex] = - [tex]\frac{-16}{-8}[/tex] = - 2
substitute x = - 2 into f(x) for corresponding y- coordinate
f(- 2) = - 4(- 2)² - 16(- 2) - 13
= - 4(4) + 32 - 13
= - 16 + 19
= 3
vertex = (- 2, 3 )
please help me solve this
Step-by-step explanation:
what "normal" trigonometric function did this remind us of ?
it starts at "high" for x = 0.
"high" signs mean "1" for the standard functions.
the trigonometric function that starts with 1 at x = 0 is cosine.
so, this is a cosine function that we need to scale properly.
original value : 1
graph : 15
original value : -1
graph : 12
original value : 0
graph : (15+12)/2 = 27/2 = 13.5
so, we need to add this to the cosine function result.
the distance from the 0 level (13.5) to high or low is 1.5 (instead of originally 1).
Du, we need to stretch the cosine function result to go from -1.5 to +1.5 (12 to 15).
and for the x-axis :
12 hours = 180° or pi (the interval for cosine to go from +1 to -1).
1 hour = 180/12 = 15° or pi/12.
so, for cosine to react to the hour value as for the curdling degrees we need to multiply x by 180/12 or by pi/12.
so, our temperature function temp(x) is then
temp(x) = 1.5×cos(x×180/12) + 13.5
or
temp(x) = 1.5×cos(x×pi/12) + 13.5
each question answered correctly is worth 2 points. The first paper scored 30 points and the second scored 5o points. How many questions did the students answere correctly altogether?
The students answered 150 questions correctly in total based on proportions concept if points are given.
If the first paper scored 30 points and the second scored 50 points, then the total score is 30 + 50 = 80 points. Since each question answered correctly is worth 2 points, we can divide the total score by 2 to find the number of questions answered correctly altogether.
80 / 2 = 40
Therefore, the students answered 40 questions correctly in total.
Another way to approach this problem is to use proportions. Let's say that the number of questions answered correctly on the first paper is x, and the number of questions answered correctly on the second paper is y. Then we can set up a proportion:
x/15 + y/25 = 1
where 15 and 25 are the total number of questions on each paper, and 1 represents the total proportion of questions answered correctly.
Multiplying LHS and RHS by least common multiple of 15 and 25, which is 75:
5x + 3y = 75
If we know that x = 30 and y = 50, we substitute these values into equation and check that if its true:
5(30) + 3(50) = 150 + 150 = 300
Dividing sides by 2 to get:
300 / 2 = 150
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Let f(x)=2x-1, h(x) = -x-5.
Find (f o h)(-3).
(foh)(-3)=
So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3))
What is function?An input and an output are connected by a function. It functions similarly to a machine with an input and an output. Additionally, the input and output are somehow connected. The traditional format for writing a function is f(x) "f(x) =... "
To find (f o h)(-3), we need to first evaluate h(-3), and then plug that result into the function f(x).
Given:
f(x) = -2x - 1
h(x) = -x - 5
First, we evaluate h(-3):
h(-3) = -(-3) - 5
h(-3) = 3 - 5
h(-3) = -2
Now, we plug the result of h(-3) into the function f(x):
f(h(-3)) = f(-2)
f(h(-3)) = -2(-2) - 1
f(h(-3)) = 4 - 1
f(h(-3)) = 3
So, (f o h)(-3) = 3. This is the value of the composite function (f o h) at -3. Please note that (f o h)(-3) is equivalent to f(h(-3)), which means we first evaluate h(-3) and then plug that result into f(x). I hope this helps! Let me know if you have any further questions. :)
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1. Explain why rolling a die until a 3 shows can be modelled by a geometric distribution.
1/6 probability.
EX] = 3/6
2. In a hockey shoot out competition, a player scores on 80% of his shots.
a) What is the probability that the player will not miss the goal until his tenth try?
b) What is the expected number of shots before he misses?
3. A factory producing electric motors has a 0.2% defective rate. A quality control
inspector tests randomly selected motors from this production line.
a) What is the probability that the first defective motor will be the sixth one tested?
b) What is the probability that the first defective motor will be among the first six tes
c) What is the expected waiting time before the first defective motor is tested?
4. A computer has been programmed to generate a list of random numbers between
50.
"Rolling a die until a 3 shows" can be modeled by a geometric distribution due to independent trials with a constant probability of success, with an expected value of 6 rolls.
What is the geometric distribution and how does it model the rolling of a die until a 3 shows?
Rolling a die until a 3 shows can be modeled by a geometric distribution because:
It involves a sequence of independent trials, where each trial has only two possible outcomes: success (rolling a 3) or failure (rolling any other number).The probability of success is constant and equal to 1/6 for each trial.The experiment continues until the first success occurs, i.e., until a 3 is rolled for the first time.The geometric distribution models the number of trials needed to achieve the first success in a sequence of independent trials with a constant probability of success. In this case, the number of trials needed to roll a 3 for the first time can be modeled by a geometric distribution with a probability of success of 1/6.
The expected value of the geometric distribution is calculated as 1/p, where p is the probability of success. Therefore, the expected number of rolls needed to roll a 3 for the first time is 1/(1/6) = 6.
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Let f(x, y) = x² + xy + y². What is the direction of minimum rate of change at point (5,2)? (Enter a vector, using [,] brackets, such that the first coordinate (x-coordinate) is 1, 0, or -1.) Components of vector of minimum change direction are
Answer:
Step-by-step explanation:
To find the direction of minimum rate of change for the function f(x, y) = x² + xy + y² at the point (5, 2), we need to find the gradient vector (also known as the gradient or the vector of partial derivatives) and then find the direction orthogonal to the gradient vector, as this direction will have the minimum rate of change.
First, let's find the gradient vector by computing the partial derivatives of f(x, y) with respect to x and y:
∂f/∂x = 2x + y
∂f/∂y = x + 2y
Now, evaluate the gradient vector at the point (5, 2):
∇f(5, 2) = (2(5) + 2, 5 + 2(2)) = (12, 9)
The gradient vector is (12, 9). To find the direction orthogonal to the gradient vector, we can swap the x and y components and negate one of them. Since the question asks for a vector with an x-component of 1, 0, or -1, we'll negate the x-component:
Orthogonal vector = (-1, 12)
So, the direction of minimum rate of change at point (5, 2) is given by the vector [-1, 12].
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1 1/9 x 2 2/5 as a mixed number in simplest form
Answer:
2 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
1 1/9 x 2 2/5 = ?
1 1/9 = 10/9
2 2/5 = 12/5
[tex]\frac{10}{9}[/tex] x [tex]\frac{12}{5}[/tex] = [tex]\frac{120}{45}[/tex] = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex]
So, the answer is 2 [tex]\frac{2}{3}[/tex]