Answer: Cost = $70 + ($13)(n)
Step-by-step explanation: As we can see that the cost of the banquet is 70$ and for each person attending there will be a 13$ extra so as to model this problem, let's from an expression. The expression that models the problem can be written as -
Cost = $70 + ($13)(n)
In this expression 'n' will be the number of people attending the banquet at that time.
In this expression the 'x' will be the number of people attending the banquet. 'y' will be the cost of the banquet. y-intercept will be 70$, which is actually the cost of the banquet and the slope will be 13$ which is the cost for each person that will be attending.
If a dozen eggs (12 eggs) are worth 3 cowry shells, how much would 6 dozen eggs be worth?
A.
36 cowry shells
B.
9 cowry shells
C.
18 cowry shells
D.
15 cowry shells
Answer:
18 cowry shells
Step-by-step explanation:
1 dozen which is 1(12) eggs = 3 shells
6 dozens will be 6(12) eggs = ?
Cross Multiply
(72 eggs × 3 shells) ÷ 12
= 216 ÷ 12
= 18
The point (0, 0) is a solution to which of these inequalities?
In order to set premiums at profitable levels, insurance companies must estimate how much they will have to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of a randomly selected car of one model to the insurance company. The probability distribution of C is given below. C $0 $1500 $5000 $15000 PC 0.60 0.05 0.13 0.22 The expected value for the above distribution is $4025. Which of the following is the best interpretation of expected value? (In the choices below. "Exp(C)" represents the expected value).
O If the company insures a large number of these cars, they can expect the variability in cost per car to average approximately Exp(C). O If the company Insures a large number of these cars, they can expect the cost per car to average approximately Exp(C). O The maximum cost to the company for insuring this car model is Exp(C) per car. O If the company insures 10 cars of this model, they know they will incur 10xExp(C) in costs. O The company must insure at least Exp(C) of these cars to make a profit
The expected value for a random variable is defined as the sum of the product of the values and probabilities of the variable.
In this case, the expected value for C is calculated by multiplying each possible value by its probability and adding the products. This is represented mathematically as:
Exp(C) = 0 x 0.60 + 1500 x 0.05 + 5000 x 0.13 + 15000 x 0.22 = 4025
The expected value of C can be interpreted as the average cost that the insurance company can expect to pay out for a randomly selected car of this model. This means that if the company insures a large number of these cars, they can expect the cost per car to average approximately $4025. The expected value does not represent the maximum cost for insuring this car model, or the cost for insuring a set number of cars. Instead, it provides an estimate of what the average cost per car will be.
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Let R be the region bounded by the graph of y = e^(2x-x^2) and the horizontal line y = 2, and let S be the region bounded by the graph of y = e^(2x-x^2) and the horizontal lines y = 1 and y = 2, as shown above.
(a) Find the area of R.
(b) Find the area of S.
(c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y = 1.
The area of R can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1.
The integral expression is ∫e^(2x-x^2)dx = ∫e^u du = e^u + C = e^(2x-x^2) + C. Evaluating the integral between x = 0 and x = 1 gives the area of R as e^2 - 1.
(b) The area of S can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1, minus the integral of the function y = 1 between x = 0 and x = 1. The integral expression for S is ∫e^(2x-x^2)dx - ∫1dx = ∫e^u du - x = e^u + C - x = e^(2x-x^2) + C - x. Evaluating the integral between x = 0 and x = 1 gives the area of S as e^2 - 1 - 1.
(c) The volume of the solid generated when R is rotated about the horizontal line y = 1 can be found using the integral expression ∫2πx(e^(2x-x^2) - 1)dx. This expression represents the area of the circular cross-sections of the solid multiplied by 2πx, which is the circumference of the circle. When evaluated between x = 0 and x = 1, this integral gives the volume of the solid generated when R is rotated about the horizontal line y = 1.
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perpendicular to line y=1/2x-8 passes through (7,-6) point slope form
An equation that is perpendicular to line y = 1/2x - 8 and passes through (7, -6) in point-slope form is y + 6 = -2(x - 7).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the information provided, an equation of the first line is given by;
y = 1/2x - 8
Therefore, slope (m) = 1/2
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
1/2 × m₂ = -1
m₂ = -2
Note: m represents the slope.
At point (7, -6), an equation of the line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-6) = -2(x - 7)
y + 6 = -2(x - 7)
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Complete Question:
Write an equation perpendicular to line y = 1/2x - 8 and passes through (7, -6) in point-slope form.
of the 80 seniors at central high 32 are enrolled in at least one ap class and 35 are in a club 18 not enralled random
Of the 18 number of seniors not enrolled in an AP class or a club, 8 are enrolled in an AP class but not a club, and 10 are not enrolled in an AP class or a club.
First, we need to calculate the total number of seniors enrolled in AP classes and clubs. We know that 32 number of seniors are enrolled in at least one AP class and 35 are in a club. That means that there are 67 seniors total enrolled in either an AP class or a club.
Next, we need to determine the number of seniors enrolled in both an AP class and a club. We can subtract the total number of seniors enrolled in either an AP class or a club from the total number of seniors at the school (80). This will give us the number of seniors not enrolled in either an AP class or a club, which is 18.
Finally, we can calculate the number of seniors enrolled in an AP class but not a club, and the number of seniors not enrolled in an AP class or a club. We know that there are 18 seniors not enrolled in either an AP class or a club, so we can subtract the number of seniors enrolled in an AP class (32) from 18 to get the number of seniors enrolled in an AP class but not a club, which is 8. We can also subtract the number of seniors enrolled in both an AP class and a club (67) from 18 to get the number of seniors not enrolled
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How do you find the area of the shaded region? Many geometry students struggle to solve shaded areas. The best way to find a shaded region's area is to familiarize yourself with the area decomposition method. The area decomposition method separates the basic shapes found in a given complex figure for fast and organized analysis. Two cases are present in obtaining the areas of the shaded regions – figures with holes and composite figures.
The area of the shaded region can be found by Area Decomposition Method.
Outer Area Minus Inner Area: Area of the shaded region = Area of the outer shape - Area of the unshaded inner shape
Area of Composite Figures: Area of the shaded region = Area of Region 1 + Area of Region 2 + ...... + Area of nth Region
The Area Decomposition Method:
Understanding the area decomposition method is the key to determining the area of a darkened zone.
For quick and efficient analysis, the area decomposition approach divides the fundamental forms present in a given complex figure.
To obtain the areas of the shaded zones, there are two scenarios.
They are of:
(1) Figures with holes and
(2) Composite figures.
Outer Area Minus Inner Area:
In figures with holes, take into account the area of the figure as a whole without the hole or hollow. By deducting the punch hole area from the whole figure, the remaining area can be found.
The area of the shaded region is equal to the Area of the outer shape minus the Area of the unshaded inner shape
Area of Composite Figures:
A composite plane figure's overall area is the same as the sum of its component areas.
The area of the shaded region is equal to the sum of the Area of Region 1, Area of Region 2, ......, Area of nth Region.
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Write an expression for the sequence of operations described below. raise 10 to the 5th power, then add the result to 7 Do not simplify any part of the expression.
The expression which represents the given word phrase as required to be written is; 10⁵ + 7.
Which expression represents the mathematical representation of the word phrase?It follows from the task content that the expression which represents the sequence of operations described be written.
First, the word phrase says; raise 10 to the 5th power, therefore, we have;
10⁵
Finally, the word phrase says to add the result to 7; Hence, the final expression is; 10⁵ + 7.
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Error Analysis Holly was asked to estimate the solution of the system of equations.
She incorrectly said the solution is (-1, -0.5). Estimate the solution of the system by
graphing the equations. What mistake might Holly have made?
y-2x=0
y=8x+3
The solution is (-0.5, -1). The graph of the system of linear equations is attached below.
What is a linear equation?
A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.
We are given two equations:
y-2x=0
⇒ y=2x
and y=8x+3
So,
⇒2x = 8x+3
⇒-6x = 3
⇒x = -0.5
Putting this value in y=2x, we get
y= -1
Thus, the solution is (-0.5, -1).
The graph of the system of linear equations is attached below wherein the blue line represents y-2x=0 and green line represents y=8x+3.
Holly must have got confused in the x-coordinates and the y- coordinates while writing the ordered pair.
Hence, the solution is (-0.5, -1).
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A rodent species has a population of 25,000 and is decreasing in size at a factor of per year
due to the increase in snake population.
a. Write an exponential model that will estimate the rodent's population.
b. Describe the meaning of "a" and "b" in the context.
c. Copy the table and complete.
X Y
0
1
2
3
4
5
bookmarks
d. Using the model in part A, how many estimated population after 10 years. Write your
answer in whole number.
The exponential model for the rodent's population is 25,000[tex](0.08)^{x}[/tex], where x is the number of years and 0.8 is the rate of decrease in population size per year.
What is an exponent?An exponent is a mathematical notation that indicates how many times a number has been multiplied by itself. It is commonly shown as a superscript next to the basic number, such as [tex]4^{2}[/tex], which equals 4 x 4 = 16.
a. The exponential model for the rodent's population is Y = 25,000[tex](0.08)^{x}[/tex], where x is the number of years.
b. The "a" in the exponential model is 25,000, which is the starting population of the rodent species. The "b" is 0.8, which is the rate of decrease in population size per year.
c.
X Y
0 25000
1 20000
2 16000
3 12800
4 10240
5 8192
d. After 10 years, the estimated population of the rodents is 2048. This is because the population decreases by a factor of 0.8 each year, so the population after 10 years is 25000[tex](0.8)^{10}[/tex] = 2048.
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Mai is playing a game of chance in which she rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random.
This game is this: Mai rolls the number cube once. She wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and $4 if a 4 is rolled. She loses $6.50 if a 5 or 6 is rolled.
(A) She gains __ per roll
(B) She loose __ per roll
(C) She neither gains or looses
The correct option regarding the expected value of her game is given as follows:
B. She looses $0.5 per roll.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
As each outcome is equally as likely, the distribution of earnings for her game is given as follows:
E(X = 1) = 1/6.E(X = 2) = 1/6.E(X = 3) = 1/6.E(X = 4) = 1/6.E(X = -6.5) = 2/6.Hence the expected value for the game is of:
E(X) = (1 + 2 + 3 + 4) x 1/6 - 6.5 x 2/6
E(X) = -$0.5.
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The area of one of the bases of the figure shown above is about 6.9 cm^2. What is the surface area?
Answer:
Step-by-step explanation:
adadadadadadadadadadadada
Let X be a binomial random variable with n=75 and p=0.6.
a) What is ?
b) What is ?
c) What is the probability of (≥) , solve this part Without continuity correction and with continuity correction.
The mean is 45 and the variance is 18
The probability values are 0.951 and 0.937
a) What is μ?From the question, we have the following parameters that can be used in our computation:
n = 75
p = 0.6
The notation μ is the mean and it is calculated as
μ = n*p
So, we have
= 0.6*0.75
Evaluate
= 45.
b) What is σ²?The notation σ² is the variance and it is calculated as
σ² = n*p*(1-p)
So, we have
= 75*0.6*(1-0.6)
Evaluate
= 18.
c) What is the probability of P(x≥52)Without continuity correction
The probability P(x>=52) without continuity correction is represented as
normalcdf(52, μ, σ)
So, we have
normalcdf(52, 45, √18)
Using a calculator, we get:
P(x>=52) = 0.951
With continuity correction.
The probability P(x>=52) with continuity correction is represented as
normalcdf(51.5, μ, σ)
So, we have
normalcdf(51.5, 45, √18)
Using a calculator, we get:
P(x>=52) = 0.937
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Complete question
Let X be a binomial random variable with n = 75 and p = 0.6
a) What is μ?
b) What is σ2?
c) What is the probability of P(x≥52), without continuity correction and with continuity correction.
Andrew is creating a rectangular dog run in his back yard. The length of the dog run is 22 feet. The perimeter of the dog run must be at least 52 feet and no more than 88 feet. Use a compound inequality to find the range of values for the width of the dog run. Use
x
when writing your inequality.
A compound inequality to find the range of values for the width include the following:
x ≥ 8.
x ≤ 44.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this equation;
P = 2(L + x)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.x represents the width of a rectangle.Note: The length of the dog run is 22 feet.
Since the perimeter of the dog run must be at least 52 feet, an inequality that models the situation is given by:
2(22) + x ≥ 52.
44 + x ≥ 52.
x ≥ 52 - 44
x ≥ 8.
Since the perimeter of the dog run must be no more than 88 feet, an inequality that models the situation is given by:
2(22) + x ≤ 88.
44 + x ≤ 88
x ≤ 88 - 44
x ≤ 44.
Therefore, a compound inequality to find the range of values for the width is 8 ≤ x ≤ 44.
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Find the equation of the plane containing all the points equidistant from the points (3,-7,c) and (1,-3,0). Assume that c is a constant.
The equation of the plane is 2(x-2) + 4(y+5) - c(z-c/2) = 0
How to determine the equation of the planeFrom the question, we have the following parameters that can be used in our computation:
points (3,-7,c) and (1,-3,0)
The equation is then calculated as follows:
Start by calculating the midpoint M
M = ( (3+1)/2 , (-7-3)/2 , (c+0)/2 ) = (2,-5,c/2)
Then we need to find the vector parallel to the line, which is given by
v = (1-3, -3-(-7), 0-c) = (-2,4,-c)
Substitute the coordinates of the midpoint and the normal vector into the equation of a plane "ax + by + cz = d"
Where (a,b,c) is the normal vector and d is a constant.
-2(x-2) + 4(y+5) - c(z-c/2) = 0
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what is the answer to this please
Answer:
the rise would be 4 and the run would be -8.
Step-by-step explanation:
So, we would write it in a y=mx+b formula. It would be y=4x-8.
Answer:
complicated
Step-by-step explanation:
so your screen quality is os$ so ill just tell you what to do.
first look at to points on the graph the meet on the line
second, find how much the rise is (it will be a negative number.)
third, find the run (how far the x moves)
put rise over run and theres your answer
suppose a certain home improvement outlet knows that the monthly demand for framing studs is 2,500 when the price is $3.25 each but that the demand is 3,900 when the price is $2.83 each. assuming that the demand function is linear, write its equation. use p for price (in dollars) and q for quantity.
The demand function is linear, so we can write it in the form of:
q = a - bp
Where a and b are constants and q is the quantity demanded and p is the price. We have two points, one at a price of $3.25 with a quantity of 2,500, and another at a price of $2.83 with a quantity of 3,900.
We can use these two points to solve for the values of a and b in the equation.
Plugging in the first point:
2500 = a - (3.25)b
Plugging in the second point:
3900 = a - (2.83)b
We can then solve this system of equation by substituting the first equation with the second one
3900 = a - (2.83)b
=2500 + 1400 = a - (3.25)b + (2.83)b
=a - (0.42)b
So the equation is:
q = 3900 - 0.42p
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Erica wants to buy new headphones for sixth graders. She can buy 4 headphones for $48. She needs to buy 25 headphones. How much will that cost?
Help me pls
Answer:
$300
Step-by-step explanation:
We know
4 headphones = $48
1 headphones = $12
25 headphones = $12 x 25 = $300
Jenny is making jewelry for an arts and crafts show. She Would like to make at least $100 in sales. She estimates that she will sell at most 50 pieces of jewelry. The bracelets that she is selling cost $2 and the necklaces cost $3
The Inequalities that represent the above situation are => x + y ≤ 50 and 2x + 3y ≥ 100 and the possible combinations are (20, 30) and (30, 20).
[ Graphs are given below ].
To form the required inequalities, represent the unknown quantities with variables like x, y,..etc.
In the given problem, we don't know the number of items that Jenny will sell so here we represent them with variables 'x' and 'y'.
And obtain expression according to the condition of the given problem. Since we need to represent them in inequalities use signs like less than, greater than, etc.
Here we have
Jenny would like to make at least $100 in sales.
She estimates that she will sell at most 50 pieces of jewelry.
The bracelets that she is selling cost $2 and the necklaces cost $3
Let Jenny sold 'x' bracelets and 'y' necklaces
Number of pieces that Jenny estimated = 50
=> x + y ≤ 50 ----- (1)
Jenny would like to make at least $100 in sales.
=> 2x + 3y ≥ 100 ---- (2)
Let Jenny sell 20 bracelets and 30 necklaces
=> 2(20) + 3(30) ≥ 100
=> 40 + 90 ≥ 100
=> 130 ≥ 100 [ which is true ]
Let Jenny sell 30 bracelets and 20 necklace
=> 2(30) + 3(20) ≥ 100
=> 60 + 60 ≥ 100
=> 120 ≥ 100
∴ The possible combinations are (20, 30) and (30, 20)
Therefore,
The Inequalities that represent the above situation are => x + y ≤ 50 and 2x + 3y ≥ 100 and the possible combinations are (20, 30) and (30, 20).
[ Graphs are given below ].
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HELP ME OUT PLEASE!!!!!!!
What is the domain of the function shown in the graph below?
Answer:
X ≥ -4
Step-by-step explanation:
Remember domain only focuses on the X values, so we can immediately rule out the answers containing Y. We can observe that the graph has a closed circle over x=-4. This tells us it will be included and so we must have "≥" in the answer choice. By simple process of elimination A, the first answer choice is the correct answer.
Also note that it would be read as "X is greater than or equal to negative 4," which is exactly what our graph depicts. The second choice, which looks like it could be correct at first would be read as "X is greater than negative 4," which excludes negative 4 in the answer. We need that negative 4 for it to be correct.
D. Apply Your Knowledge (See Ex 5) 10. Suppose a football is kicked from the ground and its height, h, in feet above the ground is given by h = -3.9t² + 15.6t. The time, t, represents the number of seconds after the ball is kicke At what time does the football hit the ground? SHOW YOUR WORK and include units of measurement.
Answer:
To solve for the time when the football hits the ground, we need to set h = 0 and solve for t. We can do this using the quadratic equation: 0 = -3.9t² + 15.6t. Solving for t results in t = 0 or t = 4. Therefore, the football hits the ground at t = 0 seconds or 4 seconds after it is kicked. The units of measurement for time are seconds.
Last year, Ivanna opened an investment account with $5500. At the end of the year, the amount in the account had decreased by 28.8%. How much is this decrease in dollars? How much money was in her account at the end of last year?
Answer:
$ 3916
Step-by-step explanation:
Amount= $5500
%decrease= 28.8% or .288
Amount decreased= 5500 x .288; $1584.
End of last year= 5500 - 1584; 3916
f(x) is a direct variation function
f(3)= 12
f(x)= ?
f(2)= ?
The function f(x) will be : f(x) = 4x and f(2) = 8.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine the order of operations and other aspects of logical syntax.
Given that f(x) is a direct variation function.
Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically -
{K} = y/x = constant
Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.
It is given that -
f(3) = 12
We can write the slope of f(x) as -
m = (12 - 0)/(3 - 0)
m = 12/3
m = 4
So, f(x) will be -
f(x) = 4x
f(2) will be -
f(2) = 8
Therefore, the function f(x) will be : f(x) = 4x and f(2) = 8.
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my grade depends on this, help, ive been stuck on it since im not the brightest
The domain and the range of the relation shown to the right are given as follows:
Domain: x >= -3.Range: All real values.The relation is not a function, as there are inputs that are mapped to multiple outputs.
How to obtain the domain and the range of the relation?The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, thus the domain is of:
x >= -5.
The range of a function is the set that contains all the output values of the function, hence on the graph it is the values of y, thus the domain is of:
All real values.
Tracing a vertical line through the graph of the function, there are values of x for which the graph would be crossed two times, meaning that the relation is not a function.
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Choose the term that describes the slope of the line of a graph representing the data in the table.
The slope of a line graphed to represent the volume of water in a pool over time would be described as
Answer:
Answer is Negative
Step-by-step explanation:
picture at the bottom provides proof.
Crickets chirp to attract other crickets. The temperatures and rates of their chirping are graphed above. Which statement below is most likely true for the data represented in the graph?
answer choices
A. The cooler the temperature, the louder the crickets chirp.
B. The crickets cannot chirp at temperatures lower than 10 degrees Celcius
C. The warmer the temperature, the more often crickets chirp.
D. The temperature and the chirping of crickets are not related.
C. The warmer the temperature, the more often crickets chirp.
The graph shows a direct correlation between temperature and the rate of chirping. As the temperature increases, the rate of chirping increases as well. Using the formula y=mx+b, where m is the slope of the line and b is the y-intercept, the slope of the line in the graph is approximately 0.5, which means that for every 1 degree Celcius increase in temperature, the rate of chirping increases by 0.5 chirps per second. This proves that the warmer the temperature, the more often the crickets chirp.
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In a presentation about voter turnout, you are illustrating various data with charts. Which type of information would you present in a pie chart?
A. the decline of voter turnout by county
B. trends in voter turnout over the part 10 years
C. what percentage of the whole population voted
D. how many people voted in various geographic regions on a map
The percentage of the whole population voted. A pie chart is best used to show the percentage of the whole that different categories represent, in this case the percentage of the whole population that voted.
A pie chart is one of the most commonly used types of data visualization because it provides an easy way to understand the proportional distribution of the data that is being presented. In a presentation about voter turnout, a pie chart would be an excellent way to illustrate what percentage of the whole population voted. Pie charts can be used to show how a whole is divided into different categories, and how much of the whole each category represents. This type of chart is especially useful for presenting data in a visually appealing way and for making comparisons between different categories. In the case of voter turnout, a pie chart would be ideal for showing the percentage of the population that voted, and for comparing the proportions of those who did and did not vote.
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In each part, assume the random variable X has a binomial distribution with the given parameters. Compute the probability of the event.
(a) n=3,p=0.7
Pr(X=0)=
(b) n=5,p=0.4
Pr(X=5)=
(c) n=4,p=0.6
Pr(X=1)=
(d) n=5,p=0.4
Pr(X=2)=
the probabilities are p(0)=0.027 p(5)=0.4 p(1)= 0.243 and p(2)= 0.9
and P(x) = nCx p^x (1 - p)^(n - x) = n! / (x!(n - x)!) * p^x * q^(n - x)
For n = 5, x = 1, p = 0.2:
P(1) = 5! / (1! (5 - 1)!) * 0.2^1 * (1 - 0.2)^(5 - 1) = 5 * 0.2 * 0.4096 = 0.4096
For n = 4, x = 2, q = 0.4:
P(2) = 4! / (2! (4 - 2)!) * (1 - 0.4)^2 * 0.4^(4 - 2) = 6 * 0.36 * 0.16 = 0.3456
For n = 3, x = 0, p = 0.7:
P(0) = 3! / (0! (3 - 0)!) * 0.7^0 * (1 - 0.7)^(3 - 0) = 1 * 1 * 0.027 = 0.027
For n = 5, x = 3, p = 0.1
P(3) = 5! / (3! (5 - 3)!) * 0.1^3 * (1 - 0.1)^(5 - 3) = 10 * 0.001 * 0.81 = 0.0081
For n = 4, x = 2, q = 0.6
P(2) = 4! / (2! (4 - 2)!) * (1 - 0.6)^2 * 0.6^(4 - 2) = 6 * 0.16 * 0.36 = 0.3456
For n = 3, x = 1, q = 0.9
P(1) = 3! / (1! (3 - 1)!) * (1 - 0.9)^1 * 0.9^(3 - 1) = 3 * 0.1 * 0.81 = 0.243
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The probability of an event in a binomial distribution is calculated using the formula Pr(X=x)=C(n,x)p^x(1-p)^(n-x)
(a) Pr(X=0)=C(3,0)p^0(1-p)^3=C(3,0)(0.7)^0(0.3)^3=0.027
(b) Pr(X=5)=C(5,5)p^5(1-p)^0=C(5,5)(0.4)^5(0.6)^0=0.01024
(c) Pr(X=1)=C(4,1)p^1(1-p)^3=C(4,1)(0.6)^1(0.4)^3=0.2304
(d) Pr(X=2)=C(5,2)p^2(1-p)^3=C(5,2)(0.4)^2(0.6)^3=0.3456
The probability of an event in a binomial distribution is calculated using the formula Pr(X=x)=C(n,x)p^x(1-p)^(n-x), where n is the number of trials, p is the probability of success, x is the number of successes, and C(n,x) is the number of combinations of n things taken x at a time. To calculate each of the probabilities given above, we first calculate the combinations C(n,x), followed by the probabilities for success and failure, and then multiply these values together to get the probability of the event. For example, in part (a), we calculate C(3,0)=1, p^0=1, and (1-p)^3=0.027, and the probability of the event Pr(X=0)=1*1*0.027=0.027.
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Shorts that regurlarly sell at 175 are sold for 131.25 determine the discoun and rate of discount
Answer:
25%
Step-by-step explanation:
Discount is 175 - 131.25 = 43.75
Rate of discount = 43.75/175 x 100 = 25%
a clerk is wrapping two cube-shaped packages and wants to know the smallest amount of wrapping paper that can wrap each package. the edge length of the larger package is 3in. the greater than the length of the smaller package. the surface area of the larger package is 384 in^2. what is the surface area of the smaller package?
The surface area of the smaller cubical package is given S = 150 inches²
What is the surface area of cube?The formula for surface area of a cube is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube.It is basically the total surface area.
Surface area S = 6a² ,
where a is the side of the cube
Given data ,
Let the surface area of the smaller cube be represented as S
Now , the surface area of the larger cube L = 384 inches²
And , side length of smaller cube = side length of larger cube - 3
Now , the equation will be
Surface area of the larger cube L = 6 ( A )² ,
where A is the side length of the larger cube
So , substituting the values in the equation , we get
6 ( A )² = 384
Divide by 6 on both sides of the equation , we get
A² = 64
Taking square roots on both sides of the equation , we get
A = 8 inches
Now , side length of smaller cube a = 8 - 3 = 5 inches
So , surface area of the smaller cube S = 6 ( a )²
Substituting the values in the equation , we get
Surface area of the smaller cube S = 6 ( 5 )²
Surface area of the smaller cube S = 6 x 25
Surface area of the smaller cube S = 150 inches²
Hence , the surface area is 150 inches²
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