The expected number of schools that will be attended by at least one top applicant is [tex]( M \cdot \left( 1 - \left( \frac{M-1}{M} \right)^N \right))[/tex].
If there are N top applicants and M schools to choose from, then the expected number of schools that will be attended by at least one top applicant is [tex]\frac{M \choose N}{M^N}[/tex]. This is because each of the N top applicants can choose any of the M schools independently, and the probability of any one top applicant attending any given school is[tex](\frac{1}{M})[/tex]. Thus, the probability of at least one top applicant attending any given school is[tex](1 - \left( \frac{M-1}{M} \right)^N)[/tex]. Therefore, the expected number of schools that will be attended by at least one top applicant is [tex]( M \cdot \left( 1 - \left( \frac{M-1}{M} \right)^N \right)).[/tex]
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5. An article priced at £15 in London cost R183 in 2012. How much would it have costed in rand to buy an item that was priced at £37, using the same exchange rate?
It would cost R451.4 to buy an item that was priced at £37
How to calculate the amount it will cost to buy the item at £37?
During 2012, the article was priced at £15 to R183
Therefore the cost of the item in rand when the article is priced at £37 can be calculated as follows
£15= R183
£1= x
cross multiply both sides
15x= 183
x= 183/15
x= 12.2
£1= R12.2
£37= Y
Cross multiply both sides
y= 12.2 ×37
= 451.4
Hence the price of the item when it was priced at £37 is $451.4
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5.3x10^6 x 1.1x10^7 combined
Answer:
5.83 x 10^13.
Step-by-step explanation:
5.3x10^6 x 1.1x10^7
= 5.3 x 1.1 x 10^(6+7)
= 5.83 x 10^13.
a new dog park is being designed by a city planner. the park is enclosed by a fence and shaped like a parallelogram. what is the area and perimeter of the dog park? round your answers to the nearest hundredth, if necessary.
A new dog park is enclosed by a fence and shaped like a parallelogram. So, the area and perimeter of the dog park is 2125 m² and 202.5 m.
Pictures can be seen in the attachment.
Determine the area and perimeter of the dog parkThese are the specified parameters:
Coordinate points in the image = (-8, 0), (5, 5), (9, 0), and (-4, -5).
1 unit = 5 m
The area of the parallelogram of the dog park
Triangular base (b) = (9 - (-8)) × 5 m = 85 m
Triangle height (h) = (0 + 5) × 5 = 25 m
A = 2 × 1/2 × b × h
= 2 × 1/2 × 85 m × 25 m
= 2125 m²
Perimeter of the dog park
The line a goes through the point (-8, 0) and (5, 5)
a² = (5 - (-8))² + (5 - 0)²
= 13² + 5²
= 169 + 25
= 194
a = √192
a = 13.85
Length a = 13.85 × 5 m = 69.25 m
The line b goes through the point (5, 5) and (9, 0).
b² = (9 - 5)² + (0 - 5²
= 4² + (-5)²
= 16 + 25
= 41
b = √41
b = 6.4
Length b = 6.4 × 5 m = 32 m
Perimeter = 2 × (a + b)
= 2 × (69.25 m + 32 m)
= 2 × 101.25 m
= 202.5 m
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When you left the next morning you needed to fill the car up. 50l of diesel from Sasol costs R799,59 and 40l of diesel from Shell costs R619,60. Which quantity of diesel works out the cheapest per litre?
The rate of diesel in the second case is less. Then the Shell cost is the cheapest per liter.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
50L of diesel from Sasol costs R 799.59. Then the rate is given as,
⇒ 799.59 / 50
⇒ R 15.9918 per liter
40L of diesel from Shell costs R 619.60. Then the rate is given as,
⇒ 619.60 / 40
⇒ R 15.49 per liter
The rate of diesel in the second case is less. Then the Shell cost is the cheapest per liter.
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Help! Look in the image below 15 points
Answer:
1/2 base * height = 16 in^2
1/2 * 8 in * H = 16 in^2
H = 32 in^2 / 8 in = 4 in Equation # 4
Which are always attributes of both rectangles and squares?
Answer:right angles, two sets of parallel sides, and opposite sides equal.
Step-by-step explanation:
the manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of his car and its make (foreign or domestic). a car was randomly selected from the lot. given that the car selected was a domestic car, what is the probability that it was older than 2 years?
The probability that the car selected was a domestic car and older than 2 years is 0.63 or 63%.
Probability is a mathematical concept that quantifies the likelihood or chance of an event occurring. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between, probabilities reflect the degree of certainty that an event will occur, with values closer to 1 indicating a higher likelihood of occurrence and values closer to 0 indicating a lower likelihood.
The probability of an event is calculated by taking the ratio of the number of favorable outcomes to the total number of possible outcomes.
domestic car older than 2 years/total domestic cars = (28 + 12 + 23)/100 = 63/100 = 0.63 = 63%
Therefore, the probability of selecting a car that is less than 2 year given that it is a domestic car is 0.63 or 63%.
*The problem seems incomplete, attached might be the complete version of it.
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vsuppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after 7 hours of burning, a candle has a height of 23.3 centimeters. after 23 hours of burning, its height is 21.7 centimeters. what is the height of the candle after 17 hours?n
Using the linear relationship the height of the candle after 17 hours is 22.3 cm.
As it is given that the height of the candle is linear to the amount of time. The linear relationship is the relationship between two variables such that it follows a straight line.
Now, let the time be on the x-axis and the y-axis is the height of the candle. therefore, the slope of the linear relationship can be represented as,
(x₁, y₁) = (7, 23.3)
(x₂, y₂) = (23, 21.7)
Since we know the two points of the linear relationship, therefore, the slope can be written as,
m = (y₂ - y₁)/(x₂ - x₁)
m = (21.7 - 23.3)/(23 - 7)
m = -1.6/16
m = -1/10
Now, the equation of the linear relationship can be written as,
y - y₁ = m( x - x₁)
y - 23.3 = (-1/10)(x - 7)
10y - 233 = -x + 7
x + 10 y = 240 --(1)
We are asked to determine the height of the candle after 17 hours. So, put x = 17 and find y
17 + 10y = 240
10y = 223
y = 22.3
Hence, the height of the candle after 17 hours is 22.3cm.
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Sales : 1,253.70 commision : 18.6%
The commission earned on the sale of $1253.70 is $233.20
What is commission?A fee paid to an agent or employee for transacting a piece of business or performing a service is called commission.
Given that, there is a commission of 18.6% on the sale of $1253.70
Therefore,
The commission earned = 1253.70 × 18.6%
= 1253.70 × 18.6 / 100
= 233.20
Hence, the commission earned on the sale of $1253.70 is $233.20
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when there are an even number of observations, and the observations are in order from smallest to largest, the median is... multiple choice question. the last observation the average of the two middle observations the first observation the middle observation average of the first and last observation.
When there are an even number of observations, and the observations are in order from smallest to largest, the median is:The average of the two middle observations.
The median is a measure of central tendency that is commonly used for data sets with an odd number of observations. When there are an even number of observations, the median is defined as the average of the two middle observations. This provides a representative value that splits the data set in half, with half of the observations having values lower than the median, and half having values higher.
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The cost of breakfast cereal is R36 for 1kg. Calculate how much 5kg of breakfast cereal will cost.
Step 1: To calculate the cost of 5kg of breakfast cereal, we need to multiply the cost of 1kg by 5.
Step 2: R36 x 5 = R180
Step 3: Therefore, 5kg of breakfast cereal will cost R180.
HELP ASAP
The graph of y = g(x) is shown here. Choose the description that matches how the graph y = g(x+4) shifts relative to y = g(x)
Options
a. left 4
b. right 4
c. down 4
d. up 4
The curve will get shifted left side by four units. Then the correct option is A.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
y = g(x)
If the g(x) is replaced with g(x + 4). Then the curve will get shifted left side by four units.
Thus, the correct option is A.
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What is the slope of the line that contains the points (7, -1) and (6, - 4)?
Answer:
-1/-3 s the slope
Step-by-step explanation:
(7,-1) and (6,-4)
-4-(-1)=-3
6-7=-1
so -1/-3 is the slope
What is the slope of the graphed line?
O
I
5/2
O
O
5/2
O
7/2
10
9
8
7
6
5
4
31
21
1
1 2 3
4
5
6
7
8
9 10
Answer:
Step-by-step explanation:
OK YOU ARE GOOD OH AND IT
5/8
write an exponential expression for the value of each investment. do not evaluate
can someone please help me on number 27 i kind of understand it but i don’t really understand where you have to do the fraction part :)
The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
y = a (1 ± r)ˣ
The rate is 6% for 20 years semiannually. Then the rate is given as,
r = 0.06 / 2
r = 0.03
Then the time is given as,
x = 20 (2)
x = 40
Then the exponential function is given as,
A = $2000 × (1 + 0.03)⁴⁰
A = $2000 × (1.03)⁴⁰
A = $2000 × 3.262
A = $6524.1
The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.
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Please help asap!! Try ur best <3 • will give u brainliest
The solution of the system of equation is , x= -4 & y= -8.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
from the given graph we get,
one line is passing through the points (0,10) , ( 4,28)
so, the equation of the line can be,
4y= 18x + 40
and, second line is passing through the points (0,8) , (1,12)
so, the equation of the line can be,
y= 4x+8
solving the equations we get,
x= -4
y= -8
Hence, The solution of the system of equation is , x= -4 & y= -8.
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PLEASE HELP ! HURRY !! NWEA TEST
Part A- what is the OUTPUT when the INPUT is 2.
Part B- what is the INPUT when the OUTPUT is -1
The ouput at x = 2 is 3 and the input at y = -1 is 0
Part A- what is the OUTPUT when the INPUT is 2.From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
f(2) = 3
This means that the output is 3
Part B- what is the INPUT when the OUTPUT is -1From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
f(0) = -1
This means that the input is 0
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What if John found a coupon online for $4 off the original cost of the trip and Andy found a different coupon for 10% off. Who would have saved more and how do you know?
Answer:
There is no given price so lets say I need something that is 85$ and I have a 10% off coupon well I will be saving 8.50$ and only needing to pay 76.50.
4$ would not take that much off only would be paying 81$
Step-by-step explanation:
85 divided by 100 x10 = 8.50
85$-4=81
Calculate the sum of the partial sequence.
[tex]\sum_{n=1}^{75} (12n-9)[/tex]
The required sum of the given partial sequence is 33525.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The sum of the partial sequence.
[tex]= \sum_{n=1}^{75}12n - 9[/tex]
[tex]= \sum_{n=1}^{75}12n - \sum_{n=1}^{75} 9\\= 34200-675\\=33525[/tex]
Thus, The required sum of the given partial sequence is 33525.
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given a two-dimensional pore geometry of packed squares as below, plot the porosity as a function of the averaging length scale. the black grains are separated by a distance equal to the grain size in the x and y directions. use a square as the averaging volume and the edge of the square as the averaging length scale. what is the representative elemental volume?
Porosity calculated as ratio of pore to total vol. Plot of porosity vs averaging length scale (edge of square used for averaging). Rep. elemental vol = vol of square used for averaging.
The porosity as a function of the averaging length scale can be calculated as follows:
Define the pore geometry: A two-dimensional pore geometry of packed squares is given, with black grains separated by a distance equal to the grain size in the x and y directions.Select the averaging volume: The averaging volume is defined as a square.Determine the porosity: The porosity is calculated as the ratio of the pore volume to the total volume of the material. In this case, the pore volume is the volume between the black grains and the total volume is the volume of the material.Plot the porosity as a function of the averaging length scale: The averaging length scale is defined as the edge of the square used for averaging. The porosity can be calculated for various values of the averaging length scale and plotted as a function of the averaging length scale.Representative elemental volume: The representative elemental volume is the volume of a single element (e.g. a square in this case) used in the averaging calculation. In this case, the representative elemental volume is equal to the volume of the square used for averaging.Learn more about geometry :
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Please help me with this
The value of the variable, x is 45 degrees
How to determine the valueWe have that the polygon is one with eight sides, that is, it is a regular octagon.
To determine the interior angle, we have
(n - 2) 180
n is the number of sides
(8-2)180
1080 degrees
Now, divide it by the number of sides
1080/8 = 135 degrees
Note that angles on a straight line is equal to 180
Then,
x + 135 = 180
Collect like terms
x = 180 -135
subtract the values
x = 45 degrees
Hence, the value is 45 degrees
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using diagonals from a common vertex, how many triangles could be formed from the polygon pictured below tiiip
5 triangles could be formed from the polygon pictured.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The given figure is an irregular heptagon (7 unequal sides).
Now,
Taking a common vertex A we can draw the triangles as given below.
We see that,
There are 5 triangles that can be drawn.
Thus,
5 triangles can be formed.
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explain why you would expect most overdetermined linear systems to be inconsistent. can an overdetermined linear system have one solution or infinitely many solutions? give examples.
As per the linear equation the system has one solution, which is x = 1 and y = 1.
A linear equation is a mathematical expression that represents a straight line. A linear equation has a set of variables, and the coefficients (numbers in front of the variables) are constant.
The reason why most overdetermined linear systems are inconsistent is that there are more restrictions placed on the variables than what is required to find a solution.
It is possible for an overdetermined linear system to have one solution, but this is a rare occurrence.
When an overdetermined system has infinitely many solutions, this means that there are an infinite number of combinations of values that satisfy all of the equations simultaneously.
For example, consider the following system of linear equations:
2x + 3y = 6
4x + 6y = 12
This system is overdetermined because there are two equations and only one variable (x and y). In this case, the system has one solution, which is x = 1 and y = 1.
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The line representing the equation part of the constraint 7x1 + 4x2 28 goes through the following two points a. (4,0) and (7,0)b. (0,4) and (7,0) c. (4,0) and (0,7) d. (0,4) and (0,7) e. none of the above
The line representing the equation part of the constraint 7x1 + 4x2 28 goes through the following two points e. none of the above.
The equation of a line can be represented as y = mx + b, where m is the slope of the line and b is the y-intercept. The line representing the equation of a constraint, such as 7x1 + 4x2 = 28, would be a straight line in a two-dimensional graph.
The points given in the options a, b, c, and d are pairs of x and y coordinates. To determine if any of these points lie on the line representing the constraint equation, we would need to substitute the x and y values into the equation and see if the equality holds.
For example, for option a, if we substitute x = 4 and y = 0 into the equation, we get 7 * 4 + 4 * 0 = 28, which is not true. Hence, none of the given points in the options lie on the line representing the constraint equation.
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There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
Several trials are performed with the results shown in the table. What is the experimental probability of randomly drawing a green marble?
Red Blue Green
10 12 28
What is the experimental probability of randomly drawing a green marble?
What is the theoretical probability of randomly drawing a green marble?
What would you expect to happen if more trials of the experiment are performed? Explain your reasoning using complete sentences.
The probability of randomly drawing a green marble form the bag would be = 12/25
What is probability?Probability is defined as the expression that show the possible outcome of an event.
The number of red marbles = 5
The number of blue marbles = 8
The number of green marbles = 12
The total number of marbles = 5+12+8 = 25
Therefore the probability of randomly drawing a green marble = 12/25
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Help me on this please I need it this Maths homework is to hard for my brain
Answer:
15√2
Step-by-step explanation:
3[tex]\sqrt{50}[/tex] = 3√25·2 = 3·5√2 = 15√2
susan can pick 4 lbs of coffee beans in an hour or gather 2 lbs of nuts. tom can pick 2 lbs of coffee beans in an hour or gather 4 lbs of nuts. each works 6 hrs per day. if they only pick coffee, what is the maximum amount of coffee the two can gather in a day? if they only pick nuts, what is the maximum amount of nuts the two can gather in a day? write the answer as x lbs, y lbs.
Answer:
see below
Step-by-step explanation:
Susan
4lbs of coffee
2lbs of nuts
Tom
2lbs of coffee
4lbs of nuts
6 hrs per day.
if only coffee x = (4+2)*6=36lbs
if only nuts y = (4+2)*6=36lbs
The figure is made up of a semicircle and a triangle.
Find the area of the figure.
Use
�
=
3.14
π=3.14
The area of the figure made up of a semicircle and a triangle is 63.25 ft²
How to solve an equation?An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.
The figure is made up of a semicircle and a triangle.
The semicircle has a diameter of 10 feet. Hence:
Area of semicircle = (1/2) * π * diameter²/4
Substituting:
Area of semicircle = (1/2) * π * 10²/4 = 39.25 ft²
The triangle has a base of 8 ft and height of 6 ft. hence:
Area of triangle = (1/2) * base * height
Substituting:
Area of triangle = (1/2) * 8 ft * 6 ft = 24 ft²
The area of the figure = Area of triangle + Area of semicircle
Area of figure = 24 ft² + 39.25 ft² = 63.25 ft²
The area of the figure is 63.25 ft²
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Directions: Based on the information given in the following problem, compute the gross pay.
Annual pay: $14,900. Calculate monthly pay.
Round your answers to two decimal places.
gross pay: $
per month
The gross monthly pay for the given service is $1241.67
What is monthly pay?Monthly pay means the wages paid by an employer to an employee for the whole or part of the month during which the employee is employed by the employer.
Given that, the annual pay of some service is $14900, we need to calculate the monthly pay of same,
Therefore,
To find, monthly pay, we will divide annual pay by 12, because there are 12 months in a year,
Monthly pay = annual pay / 12
= 14900 / 12
= 1241.67
Hence, the gross monthly pay is $1241.67.
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Choose two equations that make up the system represented by the graph.
The equations which are represents in the graph are y = 0.86x & y = -2.4x + 6
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The two points form of equation of a straight line is y-y₁ = y₂-y₁/x₂-x₁(x-x₁),
Given that,
A graph, In which two lines are given,
Line 1 is passing through following points,
(0, 0) and (1.75, 1.5)
Line 2 is passing through following points,
(2.5, 0) and (0, 6)
Equation of line 1
y - 0 = (1.5-0)/(1.75-0) (x - 0),
y = 0.86(x - 0),
y = 0.86x,
Equation of line 2,
y - 6 = (0 - 6)/(2.5 - 0)(x - 0),
y - 6 = -2.4 (x - 0),
y - 6 = -2.4x
y = -2.4x + 6
Hence, the equations are y = 0.86x & y = -2.4x + 6
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