Answer:
1/221.
Step-by-step explanation:
Probability(first card is a King) = 4/52 = 1/13 (as there are 4 kings in the pack).
Now there are 51 cards left in the pack, 3 of which are Kings, so:
Probability(second card is a King) = 3/51 = 1/17.
These 2 events are independent so we multiply the probabilities:
Required probability =
1/13 * 1/17
= 1/221.
Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. To accomplish this, the records of 300 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11. 3 seats and the sample standard deviation is 4. 3 seats.
Required:
Construct a 92% confidence interval for the population mean number of unoccupied seats per flight
If a large airline wants to estimate its average number of unoccupied seats per flight over the past year Then a 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats.
To construct a confidence interval for the population mean number of unoccupied seats per flight, we will use the following formula CI = X ± z*(σ/√n)
Where:
X = sample mean = 11.3 seats
σ = sample standard deviation = 4.3 seats
n = sample size = 300
z = z-score corresponding to the desired confidence level of 92%, which we can look up in a standard normal distribution table or use a calculator. For a 92% confidence level, the z-score is 1.75.
Plugging in the values, we get:
CI = 11.3 ± 1.75*(4.3/√300)
CI = 11.3 ± 0.966
Therefore, the 92% confidence interval for the population mean number of unoccupied seats per flight is (10.334, 12.266) seats. This means we can be 92% confident that the true population means a number of unoccupied seats per flight falls within this interval.
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The display shows how much water is used in a household in a given day.
The bar chart is titled water usage per day in a household. There are five vertical bars: toilet represents 27 gallons, washer represents 32 gallons, shower represents 25 gallons, dishwasher represents 9 gallons, and tap represents 7 gallons.
Which of the following describes this data set?
Categorical and bivariate
Categorical and univariate
Numerical and bivariate
Numerical and univariate
The option that best describes this data set is option B: categorical and univariate.
What is the data?Categorical data refers to data namely divided into distinct classifications or groups. In this case, the water usage dossier is divided into five categories established the sources of water habit in the household: toilet, washer, shower, dishwasher, and tap.
Therefore, the water usage basic document file is considered categorical as well as univariate, as it is divided into distinct classifications based on start of water usage and includes singular variable, that is water usage per day.
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Answer:
option B: categorial and univariate
Step-by-step explanation:
i took the test :)
hope this helps xx
Which function represents the sequence that represents the pattern?
Group of answer choices
an = an-1 + 3
an = an-1 - 3
an = 3an-1 - 3
an = 3an-1 + 3
The given pattern involves adding 3 to the previous term, so the correct function would be: an = an-1 + 3.
To determine the function that represents a given sequence pattern, we must first examine the relationship between the terms in the sequence.
In this case, the pattern involves adding 3 to the previous term to obtain the next term.
Therefore, the correct function would be of the form an = an-1 + 3, where "an" represents the current term in the sequence and "an-1" represents the previous term. This recursive function defines the relationship between each term in the sequence and can be used to find any term in the sequence, given the previous term.
It is important to identify the correct function that represents a given sequence pattern, as it can be used to find any term in the sequence, as well as to predict future terms. This can be particularly useful in fields such as finance and economics, where analyzing patterns in data is a critical component of decision-making.
The given pattern involves adding 3 to the previous term, so the correct function would be: an = an-1 + 3
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Homework 8: Problem 5 Previous Problem Problem List Next Problem (1 point) Find all points of intersection (r, θ) of the curves t = 6 cos(θ), r= 2 sin(θ). Note. In this problem the curves intersect at the pole and one other point. Only enter the answer for nonzero r in the form (r, θ) with θ measured in radians.
Point of intersection= Need find the area inclosed in the intersection of the two graphs. Area =
The two points of intersection are (0, θ) and (0.247, θ).
The area enclosed in the intersection of the two graphs is 7π/2 square units.
To find the points of intersection of the curves:
We need to solve for θ when t = 6 cos(θ) = r/3.
We can substitute r = 2 sin(θ) into this equation to get:
6 cos(θ) = 2 sin(θ)/3
18 cos(θ) = 2 sin(θ)
9 cos(θ) = sin(θ)
Squaring both sides and using the identity sin^2(θ) + cos^2(θ) = 1, we get:
81 cos^2(θ) = 1 - cos^2(θ)
82 cos^2(θ) = 1
cos(θ) = ±sqrt(1/82)
Since we know that the curves intersect at the pole (r = 0), we only need to consider the positive root of cos(θ) to find the other point of intersection.
We can use the equation r = 2 sin(θ) to find the value of r:
r = 2 sin(θ) = 2 cos(θ) sqrt(1 - cos^2(θ)) = 2 sqrt(1/82) ≈ 0.247
So the two points of intersection are (0, θ) and (0.247, θ) where cos(θ) = sqrt(1/82) and θ is measured in radians.
To find the area enclosed in the intersection of the two graphs:
We can use the formula for the area of a polar region:
A = 1/2 ∫(r²) dθ
Since we know that the curves intersect at the pole and at (0.247, θ), we can split the integral into two parts:
A = 1/2 ∫(0 to π/2)(2 sin(θ))² dθ + 1/2 ∫(π/2 to π)(6 cos(θ))² dθ
A = π/4 + 27π/4
A = 7π/2
So the area enclosed in the intersection of the two graphs is 7π/2 square units.
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22 let s be The paraboloid hyperbolic 2- x-j 2 2 2- located between The cylinders x + y = 1 2 +1 - Calculate and x = 25. Surface s The area of Surface S
By using Numerical integration method such as Simpson's rule or Monte Carlo simulation, we will get the area
To calculate the area of surface S, we first need to find the limits of integration. The paraboloid hyperbolic is located between the cylinders x + y = 1 and x = 2. This means that the limits of integration for x are 1 and 2, and for y they are -sqrt(4-[tex]x^2[/tex]) and sqrt(4-[tex]x^2[/tex]).
Calculation of area:
Using the formula for the surface area of a paraboloid hyperbolic, which is given by:
A = 2π ∫∫ (1 + (∂z/∂x[tex])^2[/tex] + (∂z/∂y[tex])^2[/tex][tex])^{(1/2)[/tex] dA
We can calculate the area of surface S. First, we need to find the partial derivatives of z with respect to x and y:
∂z/∂x = -2x/(2+[tex]y^2[/tex])
∂z/∂y = -2y/(2+[tex]x^2[/tex])
Substituting these values into the formula for surface area, we get:
A = 2π ∫[tex]1^2[/tex] ∫-sqrt(4-[tex]x^2[/tex])^sqrt(4-[tex]x^2[/tex]) (1 + (-2x/(2+y^2)[tex])^2[/tex]+ (-2y/(2+[tex]x^2)[/tex][tex])^2[/tex][tex])^{(1/2)[/tex]dydx
Using a numerical integration method such as Simpson's rule or Monte Carlo simulation, we can calculate this integral to get the area of surface S.
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Un termómetro con resistencia de platino de ciertas especificaciones
opera de acuerdo con la ecuación R = 10000 + (4124 x 10-2) T – (1779 x 10-5) T2
Donde R es la resistencia (en ohms) a la temperatura T (grados Celsius).
Si R = 13946, determine el valor correspondiente de T. Redondee al grado
Celsius más cercano. Suponga que tal termómetro sólo se utiliza si T ≤
600° C
The value of T is 428°C.
How to calculate temperature from resistance?To solve the problem, we can start by substituting the given value of R = 13946 into the equation R = 10000 + (4124 x 10^-2)T – (1779 x 10^-5)T^2 and solving for T. This gives us a quadratic equation in T which can be solved using the quadratic formula.
After simplifying, we get T = 427.67°C or T = -88.22°C. However, we know that the thermometer is only used if T ≤ 600°C, so the only valid solution is T = 427.67°C.Therefore, the temperature corresponding to a resistance of 13946 ohms is approximately 428°C.
It's important to note that this assumes the thermometer is operating within its specified range and that the resistance-temperature relationship remains linear over the given temperature range.
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An phone playlist has songs of various genres
according to the table below. What is the probability
that, of three random songs, the first two are country
and the third is R&B? Once a song is played it will not
be repeated until all other songs are played.
Genre :Number of Songs
Rock: 12
Country :15
R&B :10
Classical :3
The probability of selecting two country songs followed by an R&B song is 0.0202.
What is the probability?The probability of selecting two country songs followed by an R&B song is determined below as follows:
The total number of songs in the playlist = 40
The probability of the first song being country = 15/40.
The probability of the second song also being country = 14/39
The probability of the third song being R&B =s 10/38
Therefore, the probability of selecting two country songs followed by an R&B song is:
Probability(country, country, R&B) = (15/40) x (14/39) x (10/38)
Probability(country, country, R&B) = 0.0202
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What is question asking??? All I need is one example and I get the rest I just don’t understand the assignment
So basically you have to drag an angle to the box, example drag DFA to the box, then add what angle it is equal to. You have to calculate the angle and drag it opposite to the DFA. For DFA, it will be 58.
PLEASE HELP!!
A sprinkler sprays water in a circle. The distance from the sprinkler to the outer edge of the circle is 2. 5 m.
What is the approximate area that is watered by the sprinkler? (Use 3. 14 as an estimate for It. )
The approximate area that is watered by the sprinkler, we need to use the formula for the area of a circle, which is A = πr^2, where A is the area, π is a constant equal to approximately 3.14, and r is the radius of the circle.
In this case, we are given that the distance from the sprinkler to the outer edge of the circle is 2.5 m, which is the radius of the circle. Therefore, we can substitute this value into the formula and get:
A = [tex]3.14 x 2.5^2[/tex]
A =[tex]19.625 m^2[/tex]
So, the approximate area that is watered by the sprinkler is 19.625 square meters. This means that any plants, grass or other vegetation within this area will receive water from the sprinkler.
It is important to note that this is only an approximation since the shape of the watered area may not be a perfect circle and the sprinkler may not spray water evenly in all directions.
Additionally, the amount of water sprayed by the sprinkler and the time it takes to water the area will also affect the actual amount of water received by the plants.
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In a box of nerds candy, the ratio of pink to purple candies is 19:20. if there are 429 pieces of candy in the box, how many are pink?
There are 199 pink candies in the box of Nerds calculated on the basis of given information.
To find out, you first need to add the ratio of pink and purple candies, which is 19+20=39. Then, divide the total number of candies by the sum of the ratio to find the value of one unit of the ratio, which is 429/39 = 11.
Then, multiply the value of one unit of the ratio by the value of the pink candies, which is 19, to find the number of pink candies, which is 11 x 19 = 209. Therefore, there are 209 purple candies in the box.
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a gambler is going to play a gambling game. in each game, the chance of winning $3 is 2/10, the chance of losing $2 is 3/10, and the chance of losing $1 is 5/10. suppose the gambler is going to play the game 5 times. (a) write down the box model for keeping track of the net gain. (you already did this in a previous lab.) (b) now write down the box model for keeping track of the number of winning plays. (c) calculate the expected value and standard error for the number of winning plays. (d) would it be appropriate to use the normal approximation for the number of winning plays? why or why not?
The expected value and standard error for the number of winning plays is $3.1 and $ 2.21.
The population mean's likelihood to differ from a sample mean is indicated by the standard error of a mean, and simply standard error.
It reveals how much what the sample mean will change if a study were to be repeated with fresh samples drawn from a single population.
Chance of winning $3 = 2/10
chance of losing $2 = 3/10
chance of losing $1 = 5/10
Average of tickets. = - $2.50
SD of tickets = $1.80.
The box model for net gain has 2 tickets labeled $3, 3 tickets labeled $2, 5 tickets labeled
a) Expected value for the net gain.
The Expected value for net = ∑ x.p(x)
Here
can take value $1, $2 and $3
Here p(x) us the probability of winning respectively.
So, Now, Expected gain is,
(2 x 3 x 2/10) + (3 x -2 x 7/10) + (5 x -1 x 5/10)
= 12/10 - 18/10 - 25/10
= -31/10 = -$3.1.
b) Standard error of the net gain,
S.D = [tex]\sqrt{E(x^2) - [E(x)]^2}[/tex]
Now E(x²) = (2 x 3² x 2/10) + (3 x -2² x 7/10) + (5 x -1² x 5/10)
= 36/10 + 84/10 + 25/10 = 145/10
= $ 14.5
SD = [tex]\sqrt{14.5 - 3.1}\\[/tex]
SD = $ 2.21
c) Chance that the net gain is $15
P(X=15) = (z = 15-(-2.50)/1.80
= P(z=9.72) = 0.99.
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Find p(x), the third order Taylor polynomial of f(x) = V~ centered at ~ = 1.
Use pa(2) to estimate V2. Make sure you show all of your work and do not use a
calculator.
The third order Taylor polynomial of f(x) = V~ centered at ~ = 1 is p(x) = 1 + 3(x-1) + 8(x-1)^2 + 4(x-1)^3. Using p(2), the estimate for V2 is 16.
We can find the nth order Taylor polynomial of a function f(x) centered at a using the formula
Pn(x) = f(a) + f'(a)(x-a) + (f''(a)/2!)(x-a)^2 + ... + (fⁿ(a)/n!)(x-a)^n
Here, we are given f(x) = V(x) and a = 1, so we need to find the first three derivatives of V(x) and evaluate them at x = 1.
V(x) = 3x^4 - 4x^3 + 2x^2 - x + 1
V'(x) = 12x^3 - 12x^2 + 4x - 1
V''(x) = 36x^2 - 24x + 4
V'''(x) = 72x - 24
Now, we can plug in a = 1 and simplify
V(1) = 3(1)^4 - 4(1)^3 + 2(1)^2 - 1 + 1 = 1
V'(1) = 12(1)^3 - 12(1)^2 + 4(1) - 1 = 3
V''(1) = 36(1)^2 - 24(1) + 4 = 16
V'''(1) = 72(1) - 24 = 48
Substituting these values into the formula for the third order Taylor polynomial, we get
P3(x) = 1 + 3(x-1) + (16/2!)(x-1)^2 + (48/3!)(x-1)^3
= 1 + 3(x-1) + 8(x-1)^2 + 4(x-1)^3
To estimate V(2), we need to evaluate P3(2) since our polynomial is centered at x = 1. We get
P3(2) = 1 + 3(2-1) + 8(2-1)^2 + 4(2-1)^3
= 16
Therefore, our estimate for V(2) is 16.
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Two cars start together and travel in the same direction.
One car goes twice as fast as the other. After five
hours, they are 225 kilometers apart.
How fast is each car traveling?
Faster car's speed:
Slower car's speed:
The speed of the faster car is 90 kph and the speed of the slower car is 45 kph.
We are given that two cars are starting together and they travel in the same direction. Let one car be car A and the other car B. Speed of car B is twice the speed of car A. Let r be the rate of speed of car A and 2r be the rate of speed of car B.
We know that these two cars are 225 km apart. We will use the formula distance = speed * time. Let the distance car A travels after 5 hours be 5r. So, the distance traveled by car B after 5 hours will be 5(2r) = 10r.
Since car B is faster, it will have traveled farther after 5 hours. Therefore,
Distance traveled by car B - distance traveled by car A = 225
10r - 5r = 225
5r = 225
r = 45 kph
and
2r = 90 kph
Therefore, car A is traveling at 45 kph and car B is traveling at 90 kph.
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PLEASE HELP FAST!!!!!
To the nearest hundredth, what is the length of line segment AB? Drag your answer into the box. The length of line segment AB is approximately units. Two points, A and B, plotted in a coordinate plane. Point A is at (2, 2), and point B is at (-6, 4)
The length of the line segment AB is 8.25 units, under the condition that the length of line segment AB is approximately units. Two points, A and B, plotted in a coordinate plane. Point A is at (2, 2), and point B is at (-6, 4)
In order to evaluate the length of line segment AB, we can apply the distance formula which is derived from the Pythagorean theorem.
The distance formula is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²].
Here,
x₁ = 2,
y₁ = 2,
x₂ = -6
y₂ = 4.
Staging these values in the formula,
d = √[(-6 - 2)² + (4 - 2)²]
= √[(-8)² + 2²]
= √(64 + 4)
= √68
≈ 8.25 units
Then, the length of line segment AB is approximately 8.25 units.
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What is the sum?
√24 + √81
A 53/3
B 63
C 2√3+3
D 2√3+9
Answer:
2√6 + 9
Step-by-step explanation:
√24 + √81
= √4√6 + 9
= 2√6 + 9
Find x in the equation. 2 times x plus one fourth equals one fourth times x plus 2
HELP PLEASE!
I WILL MAKE YOU GENIUS!
x = 1
Step-by-Step Explanation[tex]2x + \dfrac{1}{4} = \dfrac{1}{4}x + 2[/tex]
1. subtract (1/4)x from both sides
[tex]\dfrac{7}{4}x + \dfrac{1}{4} = 2[/tex]
2. subtract 1/4 from both sides
[tex]\dfrac{7}{4}x = \dfrac{7}{4}[/tex]
3. multiply both sides by the reciprocal of x's coefficient
The reciprocal of [tex]\frac{\bold{7}}{\bold{4}}[/tex] is [tex]\frac{\bold{4}}{\bold{7}}[/tex].
[tex]\left(\dfrac{\not4}{\not7}\right)\left(\dfrac{\not7}{\not4}x\right) = \left(\dfrac{\not7}{\not4}\right)\left(\dfrac{\not4}{\not7}\right)[/tex]
[tex]\boxed{x = 1}[/tex]
HELPPPPPPP
I have zero idea of what to do!
Answer:
72 + 7x + 24 = 180
7x + 96 = 180
7x = 84
x = 12
A woman applies a 10 Newton force and uses 100 joules of energy to push a cart of groceries. How much work did she perform
The woman performed 100 joules of work to push the cart of groceries over a distance of 10 meters.
To find the work performed by the woman, we will use the work-energy theorem which states that work (W) is equal to the change in energy. In this case, the woman applies a 10 Newton force and uses 100 joules of energy. The formula for work is:
W = F × d × cos(θ)
Where W is work, F is force, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion. Since the woman used 100 joules of energy, we can rewrite the equation as:
100 J = 10 N × d × cos(θ)
We don't have information about the angle θ, but if we assume that she applied the force horizontally, which is in the same direction as the motion, the angle θ would be 0 degrees, and the cosine of 0 is 1. Therefore, the equation becomes:
100 J = 10 N × d
To find the distance (d), we can now solve for d:
d = 100 J / 10 N
d = 10 meters
So, 100 joules of work was performed by the women to push the cart of groceries over a distance of 10 meters.
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What is the radius of the circle x2+y–
3
4
2=144?
The radius of the circle x^2 + (y - 3/4)^2 = 144 is 12 units
What is the radius of the circleFrom the question, we have the following parameters that can be used in our computation:
x^2 + (y - 3/4)^2 = 144
As a general rule, the equation of a circle is represented as
(x - a)^2 + (y - b)^2 = r^2
Where
Radius = r
Using the above as a guide, we have the following:
r^2 = 144
SO, we have
r = 12
Hence , the calculated value of the radius is 12 units
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Last month, Claire's bank statement said that she overdrew her account. Her bank balance was -45. 32−45. 32minus, 45, point, 32 euros. This month, Claire's bank balance is 17. 9217. 9217, point, 92 euros. What does this mean?
Choose 1 answer:
Choose 1 answer:
Claire's bank balance being -45.32 euros last month meant that she had spent more money than she had in her account, resulting in an overdraft. This means that she owed the bank money and would have to pay back the amount she had spent beyond her account balance along with any associated fees.
However, this month, Claire's bank balance has increased to 17.92 euros. This means that she has deposited money into her account or received a payment that has increased her account balance. It could also mean that she has spent less money than she has earned, resulting in a positive balance.
Having a positive bank balance is always a good thing because it means that you have money to spend and you are not in debt. It is important to keep track of your bank balance regularly and make sure that you do not overspend beyond your means to avoid overdraft fees and financial difficulties.
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A school’s art teacher designs a circular flower bed inside a rectangular sandbox. The sandbox is 6 feet wide and 10 feet long. How many square feet will there be for sand after the flower bed is installed? Use 3.14 for pi. ROUND the answer to the NEAREST SQUARE FOOT.
A. 22 square feet
B. 28 square feet
C. 32 square feet
D. 41 square feet
A basic pattern of 1 blue bead and 1 green bead is used to make a bracelet that is 37cm long. The bracelet is made by repeating the basic pattern 10 times. The length of a blue bead is Bcm. The length of a green bead is 1. 2cm. Complete the question to represent the length of the bracelet
Answer: Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:
10 × (2.5 + 1.2) = 37 cm.
Step-by-step explanation:
To represent the length of the bracelet, we need to determine the length of each repetition of the basic pattern and then multiply it by the number of times the pattern is repeated.
The length of each repetition of the basic pattern is the sum of the length of one blue bead and one green bead, which is:
B + 1.2 cm
Since the basic pattern is repeated 10 times, the total length of the bracelet is:
10 × (B + 1.2) cm
And we know that the total length of the bracelet is 37 cm, so we can set up an equation:
10 × (B + 1.2) = 37
Simplifying the equation, we can divide both sides by 10:
B + 1.2 = 3.7
Subtracting 1.2 from both sides, we get:
B = 2.5
Therefore, the length of a blue bead is 2.5 cm, and the length of a green bead is 1.2 cm. And the length of the bracelet is:
10 × (2.5 + 1.2) = 37 cm.
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Find The Area Of This Shape.
Answer:
34.65 mi²
Step-by-step explanation:
Area of parallelogramam = b · h
b = 6.3 mi
h = 5.5 mi
Let's solve
6.3 · 5.5 = 34.65 mi²
So, the area of the shape is 34.65 mi²
Joel measures the heights of some plants. The heights of the plants, in feet, are
î
2
, 1, , $; , and 1. Which line plot correctly shows Joel's data?
Plant Heights
Plant Heights
Х
Х Х х
+ + +
X
x x x x x
A
Х
A
0
Height (feet)
Height (feet)
Plant Heights
Plant Heights
Х
Х
X
Х
A
Height (feet)
Height (feet)
In this line plot, the Xs represent the heights of the plants, and the A represents the number of plants with that height.
How to find the line plot that correctly shows Joel's data?The line plot that correctly shows Joel's data is:
Plant Heights
Х
Х
X
X
A
0
Height (feet)
In this line plot, the Xs represent the heights of the plants, and the A represents the number of plants with that height. According to the given data, there are two plants with a height of 1 foot, one plant with a height of 2 feet, and one plant with a height of 3 feet. Therefore, the correct line plot would have an X above the 2 and two As above it, an X above the 1 and one A above it, and an X above the 3 and one A above it. The other line plot shown does not correctly represent Joel's data.
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If P (A) = 0. 5, P(B) = 0. 1, and A and B are mutually exclusive, find P(A or B).
If P (A) = 0. 5, P(B) = 0. 1, and A and B are mutually exclusive, then P(A or B) is 0.6 or 60%.
To find the probability of A or B occurring, we use the formula P(A or B) = P(A) + P(B) - P(A and B). However, since A and B are mutually exclusive events, they cannot occur together. This means that the probability of A and B occurring together is zero. Therefore, we can simplify the formula to P(A or B) = P(A) + P(B).
Using the given values, we have P(A) = 0.5 and P(B) = 0.1. Plugging these values into the formula, we get:
P(A or B) = 0.5 + 0.1
P(A or B) = 0.6
Therefore, the probability of A or B occurring is 0.6 or 60%. This means that there is a 60% chance of either A or B happening, but not both at the same time since they are mutually exclusive.
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company A charges $50 per month plus $0.05 per minute. Company B has no monthly charge but charges $0.15 per minute. When is the charge for the companies the same?
The charge for the companies is the same at 500 minutes
When is the charge for the companies the same?From the question, we have the following parameters that can be used in our computation:
Company A charges $50 per month plus $0.05 per minute. Company B has no monthly charge but charges $0.15 per minute.This means that
A(x) = 50 + 0.05x
B(x) = 0.15x
When the charge for the companies are the same, we have
0.15x = 50 + 0.05x
So, we have
0.1x = 50
Divide
x = 500
Hence, the number of minutes is 500
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3 For y=f(x) = 9x, x= 3, and Ax = 0.03 find a) y for the given x and Ax values, b) dy = f'(x)dx, to) dy for the given x and Ax values.
a) To find y for the given x and Δx values, first calculate x + Δx:
x + Δx = 3 + 0.03 = 3.03
Now, use the function y = f(x) = 9x to find the y values:
y = 9(3) = 27 (for x = 3)
y = 9(3.03) = 27.27 (for x = 3.03)
b) To find dy, we first need to find the derivative of the function (f'(x)). The function is y = f(x) = 9x, and its derivative (using differentiation) is:
f'(x) = 9
c) To find dy for the given x and Δx values, we can now use the formula dy = f'(x)dx:
dy = f'(x)dx = 9(0.03) = 0.27
So, for the given x and Δx values, a) y is 27 and 27.27, b) dy is equal to 9, and c) dy for the given x and Δx values is 0.27.
The seventh-grade students at Charleston Middle School are choosing one girl and one boy for student council. Their choices for girls are Michaela (M), Candice (C), and Raven (R), and for boys, Neil (N), Barney (B), and Ted (T). The sample space for the combined selection is represented in the table. Complete the table and the sentence beneath it.
Boys
Neil Barney Ted
Girls Michaela N-M
B-M
T-M
Candice N-C
B-C
T-C
Raven N-R
B-R
T-R
If instead of three girls and three boys, there were four girls and four boys to choose from, the new sample size would be ?
If there were four girls and four boys to choose from, the new sample size is one that will be a total of 16 possible combinations.
What is the sample about?When making selections for the student council's representatives, the sample size belongs to the whole of the feasible options.
To know the sample size, we must reason every conceivable permutation involving a single female and a single male.
So, if there were four girls and four boys to choose from, the new sample size would be:
There are:
4 choices for girls
4 choices for boys.
So, for each girl's choice, there would be 4 corresponding choices for boys.
Hence it will be:
4 x 4 = 16
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Alejandro will deposit $1,750 in an account that earns 6. 5% simple interest every year. His sister Anallency will deposit $1,675 in an account that earns 7. 5% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. How much more money will Anallency have?
Anallency will have $134.46 more money than Alejandro after one year of their respective deposits.
How much more money will Anallency have than Alejandro after one year of their respective deposits?Alejandro and Anallency are depositing money in separate accounts with different interest rates. Alejandro is depositing $1,750 in an account that earns a simple interest rate of 6.5% per year, while Anallency is depositing $1,675 in an account that earns a compounded interest rate of 7.5% per year. After one year of their respective deposits, Anallency will have $134.46 more money than Alejandro.
The difference in interest earned between the two accounts is the reason for the difference in money earned by Alejandro and Anallency. Alejandro's account earns a simple interest rate, which means that he earns 6.5% of his initial deposit every year, regardless of how much interest he has already earned.
On the other hand, Anallency's account earns a compounded interest rate, which means that she earns interest on both her initial deposit and on any interest earned in previous years.
The formula for calculating simple interest is I = Prt, where I is the interest earned, P is the principal (or initial deposit), r is the interest rate, and t is the time in years. Using this formula, we can calculate that Alejandro will earn $113.75 in interest after one year.
The formula for calculating compounded interest is A = P(1 + r/n)^(nt), where A is the amount of money at the end of the time period, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
Using this formula, we can calculate that Anallency will have $248.21 more in her account than Alejandro after one year.
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Marshall is renting a bike for the day. It costs $13 for up to one hour. After one hour, the price increases to $20. After three hours, the price increases again to $50. The maximum time he can rent the bike is 10 hours total
The piecewise function that represents the situation is therefore:
Costs Possible hours
13 0 < x ≤ 1
20 1 < x ≤ 3
50 3 < x ≤ 10
How to find the piecewise function ?We see that up to one hour, the cost to Marshall would be $ 13 so the possible hours at that price is 0 < x ≤ 1 .
Likewise from one hour, the price goes up to $ 20 which means that possible hours become 1 < x ≤ 3 because the price will increase at 3 hours again.
From 3 hours, the price becomes $ 50 and there are a maximum of 10 hours so the hours become 3 < x ≤ 10 .
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