Answers
Answer:
38.part A) 3p = 25.47
partB) $8.49
Step-by-step explanation:
38) to get the price of a game ,$25.47 will be divided by
25.47÷3=$8.49
the price of 1 game =&8.49
to get the price of 1 game , the equation will be
3p=25.47
p=25.47÷3
p=$8.49
Related Questions
based on the value of r^2, which modeling equation is best fit for the data set? a. y=16.5839•1.0185^x
b. y=0.985515x-2.81333
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
d. y=0.00182197x^2+0.785098x+1.195
Answers
Okay, let's analyze the r^2 values for the 4 options:
a. y=16.5839•1.0185^x
r^2 is undefined, as this is an exponential model. We cannot determine how well it fits the data based only on r^2.
b. y=0.985515x-2.81333
This is a linear model, so r^2 would be between 0 and 1. Without knowing the actual r^2 value, we cannot determine how good the fit is.
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
This is a 3rd order polynomial model. Again, without the r^2 value, we cannot determine the quality of fit. It could be a good or poor fit.
d. y=0.00182197x^2+0.785098x+1.195
If this model has the highest r^2 value (closest to 1), it would indicate the best fit to the data of the options.
In summary, without seeing the actual r^2 values calculated from the data for each model, we cannot definitively say which option is the "best fit". The model with the r^2 closest to 1 would likely be the best, but r^2 only tells part of the story. Other factors like complexity, interpretability, and residual analysis also matter. But based solely on r^2, the quadratic model d seems the most likely to be the best fit, as long as its r^2 value is high.
Does this help explain the approach? Let me know if you have any other questions!
Football is 360ft.long 160ft.wide use 8lb. Fertilizer per 1000sqft it come in 50lb bag. How many bags will I need
Answers
We number of bags is 10 bags of fertilizer to complete the job.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of mathematical symbols and their manipulation. It involves the use of letters, symbols, and equations to represent and solve mathematical problems.
In algebra, we use letters and symbols to represent unknown quantities and then use mathematical operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate those quantities and solve equations. We can use algebra to model and solve real-world problems in various fields such as science, engineering, economics, and finance.
The total area of the football field is:
360 feet × 160 feet = 57,600 square feet
To find out how many bags of fertilizer are needed, we need to calculate how many 1000-square-foot areas there are on the field:
57,600 square feet ÷ 1000 square feet/area = 57.6 areas
So there are 57.6 areas on the football field.
We need 8 pounds of fertilizer per 1000 square feet, so to find out how many pounds we need for the whole field, we can multiply by the number of areas:
8 pounds/1000 square feet × 57.6 areas = 460.8 pounds
Therefore, we need 460.8 pounds of fertilizer to cover the football field.
Since the fertilizer comes in 50-pound bags, we can divide the total amount of fertilizer needed by 50 to find out how many bags we need:
460.8 pounds ÷ 50 pounds/bag ≈ 9.22 bags
We can't buy a fraction of a bag, so we need to round up to the nearest whole bag. Therefore, we need 10 bags of fertilizer to complete the job.
To know more about area visit:
https://brainly.com/question/16121667
#SPJ9
The complete question is:
You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1000 square feet. The fertilizer comes in 50- pound bags. How many bags of fertilizer will you need to complete this job?
When the student gets home, she gives 1/2 of her remaining fudge to her sister.
How many ounces of fudge does she give her sister?
Answers
The amount of fudge the student gives to her sister, which is (1/2) of her remaining fudge, calculated using fractions is 16 ounces
What is a fraction?A fraction is a representation of a part of a whole, by setting the quantity representing the part as the numerator and the quantity representing the whole as the denominator with both quantities separated by the fraction bar.
Part of the question obtained from a similar question posted online can be presented as follows;
The amount of fudge the student has = 3 pounds
The amount of fudge the student eats = 1 pound of the fudge
Required; The amount of fudge the student has left
The amount of fudge the student has left = 3 - 1 = 2 pounds
The fraction of the remaining fudge the student gives to her sister = (1/2)
Therefore;
The amount of fudge the student gives her sister = (1/2) × 2 pounds = 1 pound
1 pound = 16 ounces
The amount of fudge she gives her sister in ounces = 16 ouncesLearn more on fractions here: https://brainly.com/question/11249421
#SPJ1
Answer the question below
Answers
Answer:
B represents a function.
Solve the system of equations.
y = 2 - 6x
1/2y - x = 1
Question 4 options:
(0,-2)
(2,0)
(-2,0)
(0,0)
(1,-4)
Answers
Answer:
a
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=2 and x=0 making it (0,2)
Draw fraction strips to show the following fractions: 4/6,1/6, and 5/6. Then write the three fractions in order from least to greatest.
Answers
```
4/6: | | | | / / /
1/6: | / / / / / /
5/6: | | | | | / /
```
Writing the fractions in order from least to greatest:
1/6, 4/6, 5/6.
y = |x - 5| + |x + 5| if -5 < x < 5
Answers
Step-by-step explanation:
This function has two pieces, each of which is the absolute value of a linear expression. We need to consider the function separately for different ranges of x.
When -5 < x < 0, then x + 5 is negative and x - 5 is also negative. Therefore, we have:
y = -(x - 5) - (x + 5) = -2x
When 0 ≤ x < 5, then x + 5 is positive and x - 5 is negative. Therefore, we have:
y = (x - 5) + (x + 5) = 2x
So the function y = |x - 5| + |x + 5| can be written as:
y =
-2x if -5 < x < 0
2x if 0 ≤ x < 5
Notice that the function is not defined for x ≤ -5 or x ≥ 5.
19 center: (8, 2), point on circle: (14, -1)
Answers
The radius of this circle with center (8, 2) is equal to 6.71 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given points into the distance formula, the radius of this circle can be calculated as follows;
Distance = √[(14 - 8)² + (-1 - 2)²]
Distance = √[(6)² + (-3)²]
Distance = √[36 + 9]
Distance = √45
Distance = 6.71 units.
Read more on distance here: brainly.com/question/12470464
#SPJ1
Complete Question:
What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places
How does this work lol?
Answers
Answer:
this is the Pythagorean theorem this is the formula a^2 + b^2 = c^2
Step-by-step explanation:
please mark as brainliest have a great day :D
Which equation models the relationship between c cups of flour and m muffins baked?
Answers
Answer:
constant of proportionality: A 4equation: D m = 4cStep-by-step explanation:
Given a graph of muffins versus cups of flour, you want to know the constant of proportionality and the equation relating muffins (m) and cups (c).
SlopeThe slope of the line on the graph is easily found by looking at the "muffins" (y) value for "cups" (x) equal to 1. That point is (c, m) = (1, 4).
The line goes through the origin (0, 0), so the slope is the ratio of y to x.
m = y/x = 4/1 = 4
This is the constant of proportionality.
The constant of proportionality is 4, choice A.
EquationThe equation of a proportional relationship is ...
y = kx . . . . . . where k is the constant of proportionality
Here, the independent variable (horizontal axis) is "cups", represented by 'c'. The dependent variable is "muffins", represented by 'm'. Using the above constant of proportionality, the equation is ...
m = 4c . . . . . choice D
<95141404393>
During halftime of a basketball game, a sling shot launches T-shirts at the crowd. A T-shirt is launched with an initial upward velocity of 78 feet per second. The hight of the t-shirt (h) in feet after t seconds is given by the function h=-16t^2+78t+5. How long will it take the T-shirt to reach its maximum height? What is its maximum height?
Answers
A T-shirt is launched with an initial upward velocity of 78 feet per second, the T-shirt will reach its maximum height in approximately 2.44 seconds.
The height of the T-shirt is given by the function h(t) = -16t^2 + 78t + 5, where h is the height in feet and t is the time in seconds.
To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function.
The vertex occurs at the time t = -b/2a, where a = -16 and b = 78 are the coefficients of the quadratic function.
t = -b/2a = -78/(2*(-16)) = 2.4375
Therefore, the T-shirt will reach its maximum height in approximately 2.44 seconds.
To find the maximum height, we substitute this value of t into the equation for h:
h(2.4375) = -16(2.4375)^2 + 78(2.4375) + 5 ≈ 97.19 feet
Therefore, the maximum height of the T-shirt is approximately 97.19 feet.
For more details regarding velocity, visit:
https://brainly.com/question/17127206
#SPJ1
question in screenshot
Answers
Answer:
hope this might help you!!
1.- If f(x)= x^8, then f'(x) =
2.- If g(x)= -4x^4 then g'(x) =
3.- If h(x)= 1/x^5 then h'(x) =
Answers
1.
f'(x) = 8 · x^(8-1) = 8·x^7
2.
g'(x) = -4· 4·x^(4-1) = -16·x^3
3.
h(x) = 1/x^5 = x^(-5), so
h'(x) = -5·x^(-5-1) = -5·x^(-6) or -5 / x^6
Experiment 4: You have a bag of 15 scrabble tiles. 3 of the
tiles are the letter O. And the other 2 tiles are the letter U.
a. What is the probability of getting an O on the first draw?
b. What is the probability of getting a U if you didn't replace the O?
What is the probability of getting O and then U if you don't
replace the O?
c.
Answers
Answer:
a. The probability of getting an O on the first draw can be calculated by dividing the number of O tiles by the total number of tiles in the bag:
```
P(O on first draw) = 3/15 = 0.2
```
Therefore, the probability of getting an O on the first draw is 0.2 or 20%.
b. After removing one O tile, there are 14 tiles left in the bag, of which 2 are U tiles. Therefore, the probability of getting a U if you didn't replace the O is:
```
P(U without replacing O) = 2/14 = 1/7 ≈ 0.143
```
Therefore, the probability of getting a U if you didn't replace the O is approximately 0.143 or 14.3%.
c. The probability of getting O and then U if you don't replace the O can be calculated as follows:
```
P(O and then U) = P(O on first draw) * P(U without replacing O)
= 3/15 * 2/14
= 1/35
≈ 0.029
```
Therefore, the probability of getting O and then U if you don't replace the O is approximately 0.029 or 2.9%.
Step-by-step explanation:
Running for public office is not a decision to be taken lightly, and requires considerable investments of both time and money. A local businesswoman is considering running for mayor, but will only do so if she has the support of more than 60% of voters in the city. She commissions a polling company, who take a random sample of eligible voters and find 64% would support this businesswoman.
(a) Which hypotheses should the businesswoman test, to determine if she has sufficient community support?
H0:
Ha:
(b) The polling company finds the p-value = 0.076. For = 0.05, what does this suggest the businesswoman should do?
____ for office. There is ___ evidence she ____ enough supporters.
Answers
The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6, and the proportion of eligible voters who would support the businesswoman is greater than 0.6.
What is a hypothesis?In statistics, a hypothesis is a statement or assumption about a population parameter that is being tested for its truthfulness based on sample data. It is a tentative explanation for an observation or phenomenon and is used to make predictions about the outcome of an experiment or study. Hypotheses can be either null hypotheses, which state that there is no significant difference or relationship between variables, or alternative hypotheses, which propose that there is a significant difference or relationship.
(a) The hypotheses that the businesswoman should test are:
H0: The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6.
Ha: The proportion of eligible voters who would support the businesswoman is greater than 0.6.
(b) The p-value is greater than the significance level of 0.05, which suggests that the results are not statistically significant. Therefore, the businesswoman should not run for office. There is not enough evidence she has enough supporters.
To know more about hypothesis visit:
brainly.com/question/29519577
#SPJ1
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range.
y = negative 0.5 x squared + 0.7 x minus 5.1
a.
D: all real numbers
R: (y less-than-or-equal-to negative 5.1)
c.
D: all real numbers
R: (y less-than-or-equal-to negative 4.855)
b.
D: all real numbers
R: (y greater-than-or-equal-to 4.855)
d.
D: all real numbers
R: (y less-than-or-equal-to negative 5.345)
Please select the best answer from the choices provided
A
B
C
D
Answers
The domain is all real numbers, and the range is (y ≤ -4.855). (option b)
To sketch the graph of a quadratic equation, you can use a graphing calculator, which is a handy tool that can produce a visual representation of the equation. For instance, let's take the quadratic equation y = -0.5x² + 0.7x - 5.1 and sketch its graph using a graphing calculator.
When we enter this equation into the graphing calculator, we can see a U-shaped curve that is symmetric about the vertical line passing through the vertex. The vertex is the point where the parabola changes direction and is given by the formula x = -b/2a, y = f(x), where f(x) is the value of y at the vertex.
Now let's examine the given options and determine their domain and range based on the graph of the quadratic equation.
all real numbers, R: (y ≤ -4.855)
For this option, we can observe that the parabola opens upward, and the vertex is at (0.7, -5.35).
To know more about quadratic equation here
https://brainly.com/question/30098550
#SPJ1
Based on the graph below, what will be the coordinates of the point that represents the number of snowballs needed to make 2 snowmen?
Answers
the coordinates of the point that represents the number of snowballs needed to make 2 snowmen should be option C. which is (2,6)
2(x-1)+3(x+1)=4(x+4)
Answers
1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.
That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.
1. Distribute. Everything. 2x - 2 + 3x + 3 = 4x + 16.
2. Add your like terms. (must be on the same side) 5x + 1 = 4x + 16
3. Single out x by subtracting 1. 5x = 4x + 16 - 1.
4. Simplify. 5x = 4x + 15
5. Subtract 4x from both sides to combine like terms. 5x - 4x = 15.
6. Simplify. 1x = 15.
That means your final answer would be x = 15. If you were to input 15 into every x, it would simplify to 76 = 76, which means x is definitely 15.
Answer:
x = 15
Step-by-step explanation:
Simplifying the expression:
2(x - 1) + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4x + 16Add the numbers:
2x - 2 + 3x + 3 = 4x + 162x + 3x - 2 + 3 = 4x + 162x + 3x + 1 = 4x + 16Combine like terms:
2x + 3x + 1 = 4x + 165x + 1 = 4x + 16Subtract 1 from both sides:
5x + 1 - 1 = 4x + 16 - 15x = 4x + 15Subtract 4x from both sides:
5x - 4x = 4x - 4x + 15x = 15Answer:
x = 15
Step-by-step explanation:
Simplifying the expression:
2(x - 1) + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3(x + 1) = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4(x + 4)2x - 2 + 3x + 3 = 4x + 16Add the numbers:
2x - 2 + 3x + 3 = 4x + 162x + 3x - 2 + 3 = 4x + 162x + 3x + 1 = 4x + 16Combine like terms:
2x + 3x + 1 = 4x + 165x + 1 = 4x + 16Subtract 1 from both sides:
5x + 1 - 1 = 4x + 16 - 15x = 4x + 15Subtract 4x from both sides:
5x - 4x = 4x - 4x + 15x = 15traveled 1/5 miles in 3/2 hour. how many in 1 hour. show model fraction representation
Answers
a)Traveled 0.3 miles in 1 hour.
b) The fraction representation is 3/10 miles per hour.
a) To find out how many miles the person traveled in 1 hour, we need to divide the distance traveled by the time taken.
Distance traveled = 1/5 miles
Time taken = 3/2 hours
To make it easier to divide, we can convert the time taken to a fraction with a common denominator of 10:
3/2 = 15/10
Now we can divide the distance by the time:
1/5 ÷ 15/10 = 1/5 x 10/15 = 2/15
This tells us that the person traveled 2/15 miles in one-tenth of an hour (i.e., 6 minutes).
To find out how many miles per hour they traveled, we can convert the fraction to a rate by multiplying it by the reciprocal of the time fraction (i.e., 10/3):
2/15 x 10/3 = 2/9
Therefore, the person traveled 2/9 miles per hour.
b) To write this as a model fraction representation, we can express it as a single fraction:
2/9 = 3/10 (rounded to the nearest tenth)
So the person traveled at a rate of 3/10 miles per hour.
Lo learn more about fraction here
https://brainly.com/question/10354322
#SPJ1
If you drive from Dublin to Galway at a constant speed of 70 miles per hour, but pause
for 30 minutes for lunch, how long is your trip in total? Round your final answer to the
nearest tenth of an hour
Answers
If you drive at a constant speed of 70 miles per hour, it will take you 125 / 70 = 1.79 hours to get to Galway.
Pausing for 30 minutes for lunch means you will add 0.5 hours to your trip.
So, your trip in total will be 1.79 + 0.5 = 2.29 hours.
Rounding to the nearest tenth of an hour, your trip will take 2.3 hours in total.
Find a polynomial with integer coefficients that satisfies the following conditions :
Degree of polynomial : 3
Zeros : 2, 4
-intercept : −96
Answers
Convert the rectangular coordinates to polar coordinates with
r > 0 and 0 ≤ < 2.
(1, −2)
Help I'm stuck with this one :(
Answers
If you want to transform rectangular coordinates (x, y) into its polar counterpart (r, θ), do the following:
The StepsFirstly, obtain r by computing the distance from the origin to point (x,y), making use of the Pythagorean theorem or simply put, by evaluating r = sqrt(x^2 + y^2).
Secondly, acquire θ which denotes the angle formed between the positive x-axis and a line correlating the origin and the coordinate (x,y). Calculate this via inverse tangent function: θ = atan2(y, x).
Thirdly, in case the measurement for θ is indicated in radians while you require degrees instead, multiply by 180/π to convert it.
Usually expressed as (r, θ), where r indicates proximity disentangled between the origin and the point (x,y), whilst θ identifies the aforementioned angle.
Read more about polar coordinates here:
https://brainly.com/question/4522672
#SPJ1
Evaluate each expression (a) log7 1/7 =
(b) log 3 27 = 9
Answers
(b) log3 27 = 3
Explanation:
(a) The logarithm of 1/7 to the base 7 is -1. This is because 7 raised to the power of -1 equals 1/7. Therefore, log7 1/7 = -1.
(b) The logarithm of 27 to the base 3 is 3. This is because 3 raised to the power of 3 equals 27. Therefore, log3 27 = 3.
Two forces of 637 newtons and 238 newtons act a point.The resultant force is 714 newtons. find the angle between the forces
Answers
714^2 = 637^2 + 238^2 - 2 * 637 * 238 * cos(θ)
Rearranging and solving for cos(θ), we get:
cos(θ) = (637^2 + 238^2 - 714^2) / (2 * 637 * 238)
cos(θ) = -0.0130
Taking the inverse cosine, we get:
θ = 180° - acos(-0.0130)
θ = 175.8° (rounded to one decimal place)
Therefore, the angle between the two forces is approximately 175.8 degrees.
4. Gabriel wants to learn how to play darts, so
he researches the costs of different dartboards
at stores in his area. What would be the most
appropriate way for him to display his data?
Answer will be marked!!
Answers
Answer:
a line graph
Step-by-step explanation:
based on the value of r^2, which modeling equation is best fit for the data set? a. y=16.5839•1.0185^x
b. y=0.985515x-2.81333
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
d. y=0.00182197x^2+0.785098x+1.195
Answers
Okay, let's evaluate each modeling equation candidate based on the r^2 value:
a. y=16.5839•1.0185^x
No r^2 value given, so cannot determine if this is the best fit.
b. y=0.985515x-2.81333
No r^2 value given for this linear model, so cannot determine if it is the best fit.
c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667
This is a 3rd order polynomial model, but no r^2 is given, so cannot determine if it is the best fit.
d. y=0.00182197x^2+0.785098x+1.195
If this model has the highest r^2 value, it would be the best fit.
Based on the information provided, the only option that could potentially be the best fit is choice d, the quadratic model y=0.00182197x^2+0.785098x+1.195, if it has the highest r^2 value. But without the actual r^2 values for each model, a definitive determination cannot be made.
Does this help explain the approach? Let me know if you have any other questions!
Plot - 1 1/4 and 5/2 on the number line below.
Answers
The number line where we plotted 1 1/4 and 5/2 is added as an attachment
Plotting -1 1/4 and 5/2 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-1 1/4 and 5/2
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-5/4 and 5/2
Rewrite the denominators of the fractions
So, we have
-5/4 and 10/4
This means that we can plot -5/4 at -5 and 10/4 at point 10 where the difference in each interval is 1/4
Using the above as a guide, we have the following:
The number line is attached
Read more about number line at
brainly.com/question/24644930
#SPJ1
Jan has set the sales target for 35,000 ice cream makers, which she thinks she can achieve by an additional fixed selling expense of $200,000 for advertising. All other costs remain as per the data in the above table. What will be the operating profit if the additional $200,000 is spent on advertising and sales rise to 35,000 units?
Answers
The company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.
What do sales mean?Sales generally refer to the total amount of goods or services that a business sells during a given period of time, typically measured in monetary terms. Sales can also refer to the process of selling products or services, including activities such as prospecting, lead generation, sales presentations, and closing deals.
According to the given informationTo calculate the operating profit with sales of 35,000 units and an additional selling expense of $200,000, we need to first calculate the total revenue and the total cost, and then subtract the total cost from the total revenue.
From the table provided, we can see that the selling price per unit is $900 and the variable cost per unit is $600. Therefore, the contribution margin per unit is:
Contribution margin per unit = Selling price per unit - Variable cost per unit
= $900 - $600
= $300
Since the sales target is 35,000 units, the total contribution margin is:
Total contribution margin = Contribution margin per unit x Number of units sold
= $300 x 35,000
= $10,500,000
The total cost can be calculated as follows:
Total cost = Fixed cost + Variable cost
= $3,500,000 + ($600 x 35,000)
= $25,100,000
Adding the additional selling expense of $200,000, the new total cost becomes:
New total cost = $25,100,000 + $200,000
= $25,300,000
Therefore, the operating profit with sales of 35,000 units and an additional selling expense of $200,000 is:
Operating profit = Total revenue - Total cost
= ($900 x 35,000) - $25,300,000
= $10,500,000 - $25,300,000
= -$14,800,000
This indicates that the company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.
To know more about the loss and profit visit:
brainly.com/question/12634106
#SPJ1
Five friends-Allison, Beth, Carol, Diane, and Evelyn- have identical calculators and are studying for a statistics exam. They set their calculators down in a pile before taking a study break and then pick them up in random order when they return from the break. What is the probability that at least one of the five gets her own calculator? [Hint: Let A be the event that Alice gets her own calculator, and define events B, C, D, and E analogously for the other four stu- dents.] How can the event (at least one gets her own calcu- lator} be expressed in terms of the five events A, B, C, D, and E? Now use a general law of probability. [Note: This is called the matching problem. Its solution is easily extended to individuals. Can you recognize the result when n is large (the approximation to the resulting series)?]
Answers
P(at least one gets her own calculator) = 1 - P(none of them get their own calculator)
To calculate P(none of them get their own calculator), we can use the principle of inclusion-exclusion:
P(none of them get their own calculator) = 5!/(5-5)!*(0!)- 4!/(5-4)!*(1!)+ 3!/(5-3)!*(2!)- 2!/(5-2)!*(3!)+ 1!/(5-1)!*(4!)
= 1 - 1 + 10/120 - 15/120 + 24/120
= 8/15
Therefore, the probability that at least one of the five friends gets her own calculator is:
P(at least one gets her own calculator) = 1 - P(none of them get their own calculator)
= 1 - 8/15
= 7/15
A recipe uses teaspoon of cinnamon for every 4 cups of granola mix.
How many teaspoons are needed for 12 cups of granola mix?
Answers
Okay, here are the steps to solve this:
* The recipe calls for 1 teaspoon of cinnamon for every 4 cups of granola mix.
* We are making 12 cups of granola.
* So to make 12 cups, we need 12 / 4 = 3 times as much cinnamon.
* Since each 4 cups uses 1 teaspoon, 12 cups will need 3 teaspoons.
Therefore, for 12 cups of granola mix, the recipe will call for 3 teaspoons of cinnamon.