PLEASE HELP
Draw the graph of the equation x+5y=6
The graph of the function x + 5y = 6 is added as an attachment
How to determine the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
x+5y=6
Express the equation properly
So, we have
x + 5y = 6
The above expression is a an equation of a linear function
Make y the subject
So, we have
y = -x/5 + 6/5
So, we have
slope = -1/5y-intercept = 6/5Next, we plot the graph using a graphing tool
To plot the graph, we enter the equation in a graphing tool and attach the display
See attachment for the graph of the function
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Please help!!!
What is the answer to 27+18+13+11?
Answer:
69
Step-by-step explanation:
27 + 18 + 13 + 11 = 69
Therefore, the sum of 27, 18, 13, and 11 is 69
Your welcome
Answer:
The answer to your problem is, 69
Step-by-step explanation:
First lets split the problem into the following:
27 + 18 13 + 11
First we are going to do, 27 + 18
27 + 18 = 45. Done
Next we are going to do, 13 + 11
13 + 11 = 24. Done
Add them, 24 + 45
24 + 45 = 69
Thus the answer to your problem is, 69
Decide if the triangle is a right triangle. Use pencil and paper. How can you use your results to decide if a triangle with side lengths 3, 4, and 5 is a right triangle? The figure is not drawn to scale.
1.5
2
2.5
Answer:
Yes, the 3-4-5 triangle and the 1.5, 2, 2.5 triangles are both working right triangles.
Step-by-step explanation:
I am assuming that the triangle we are given below is 1.5, 2, 2.5, and not necessarily a Pythagorean triple (we are asked to check if it is). We can check if this triangle meets the Pythagorean Theorem, which states that:
a^2+b^2=c^2
Where a and b are both the legs of the triangle and c is the hypotenuse (longest side). Now we can simply plug in 1.5, 2, and 2.5 and see if we get a working Pythagorean triple (if so, then the equation will be true).
(1.5)^2+2^2= 2.25 + 4= 6.25
and
(2.5)^2=6.25
This works! Giving that:
(1.5)^2+2^2=(2.5)^2 in the form of: a^2 + b^2=c^2
Now for the second part of the problem, how can we figure out if a 3,4, and 5 triangle is also a working Pythagorean triple by using our existing knowledge about the 1.5, 2, 2.5? Well, the 3, 4, and 5 triangle is also the right triangle! This is because every number in the set "1.5, 2, 2.5" is simply multiplied by 2, which is alike to scaled triangles. We can see so like this:
1.5*2=3
2*2=4
2.5*2=5
It is scaled up from the 1.5, 2, and 2.5 triangles! Now lets double check our work and see if we are correct.
3^2+4^2=9+16=25
5^2=25
Thus,
(3)^2+(4)^2=(5)^2
So, yes, the 3, 4, and 5, triangles and the 1.5, 2, 2.5, triangles are both working Pythagorean triples, we were able to prove this by scaling up and existing triple to find new ones. Have a great day!
Destiny invest $4000 in an account that earns 3.5% interest per years compound annually. The amount of money in her account after x years can be modeled by g(x)=4000(1.035)^x. Describe the dilation in g(x) as it relates to the parent function f(x)=1.035^x.
Answer:
Step-by-step explanation:
The function g(x) is a dilation of the parent function f(x) = 1.035^x.
Specifically, g(x) = 4000(1.035)^x is a vertical dilation of f(x) = 1.035^x by a factor of 4000.
This means that the graph of g(x) is the same shape as the graph of f(x), but it is vertically stretched by a factor of 4000.
In other words, the values of g(x) are 4000 times greater than the values of f(x) for any given value of x.
For example, when x = 1, f(1) = 1.035 and g(1) = 4000(1.035) = 4140. This means that the amount of money in Destiny's account after one year is 4000 times greater than the initial amount she invested.
Overall, the dilation in g(x) as it relates to the parent function f(x) is a vertical dilation by a factor of 4000.
Review the graph of function g(x). On a coordinate plane, y = g (x) has a straight line connecting point (negative 5, 4) and (negative 2, 1), a curved line connected (negative 2, 1) and (0, negative 1), and a straight line connecting (0, negative 1) and (4, negative 2). Determine the value of g–1(4). –5 Negative one-half 2 3
The value of the inverse function at x = 4 is:
[tex]y = g^-^1^(^4^) =-5[/tex]
From the attachment of graph :
Points available on the graph 'g' are (-5, 4), (-2, 1), (0, -1), (4, -2).
Since, rule to get the points lying on the graph of the inverse of the given function is,
(x, y) → (y, x)
And, (x, y) is the function of g and (y , x) is the inverse function of the g.
By the given rule, points on [tex]g^-^1^(^x^)[/tex] will be,
(4, -5), (1, -2), (-1, 0), (-2, 4)
Therefore, value of the inverse function at x = 4 will be:
[tex]y = g^-^1^(^4^) =-5[/tex]
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what is the measure of angle r
The value of angle R is 28.03( nearest hundredth)
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
The two legs of the right angled triangle are opposite sides and adjascent while he third side is hypotenuse.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Here, using angle R, opp = 8cm , adj = 15cm and hyp = 17cm
Therefore sin(R) = 8/17
sin(R) = 0.47
R = sin^-1( 0.47)
R = 28.03( nearest hundredth)
therefore the value of angle R is 28.03°
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someon help me i need to tern this in today pls help
The statements regarding the triangles can be completed with the following:
c must equal u.the triangles are congruent.right anglecongruent.right trianglePythagoras' theoremWhat is the converse Pythagoras theorem?The converse Pythagoras theorem states that a triangle is a right triangle if the square of its longest side equals the sum of its squares on the other two sides.
The converse Pythagoras theorem can be used to determine whether a triangle is acute, right, or obtuse by comparing the sum of its two sides to the square of its third side.
Proof: If the square of the longest side in a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right-angled traingle.
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What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
-6 -4 2
O X-2
x-1
OX+2
Ox+3
S
-
19
8
X
K
A factor of the polynomial graphed is
O X + 2How to determine the factor of the polynomialThe zeros, which is the solution of the graph is used find the factor of the polynomial on the graph.
The graph shows that zeros includes
x = -2, x = 0 and x = 3
x = -2 is same as x + 2 = 0 hence this is a factor as in the third option.
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SOMEONE HELP ME ON MY MATH HOMEWORK ON PERSONAL BUDGETS! The table says rent for $800 food for $450 utilities for $125 car payment for $325, and gas for $125 I need to know what the percentages are for all of them! PLEASE HELP!!
a study was conducted on students from a particular high school over the last 8 years. the following information was found regarding standardized tests used for college admitance. scores on the sat test are normally distributed with a mean of 1019 and a standard deviation of 201. scores on the act test are normally distributed with a mean of 20 and a standard deviation of 5.1. it is assumed that the two tests measure the same aptitude, but use different scales. if a student gets an sat score that is the 27-percentile, find the actual sat score. sat score
For a normal distribution of SAT, scores of students particular high school over the last 8 years. The actual SAT score is equals the 224.213.
A normalized value called z-score can be associated to every data, (x) which is normally distributed. The z-score formula is an extremely used way of comparing data sets which are normally distributed. We have a study of students which is conducted from a particular high school over the last 8 yrs. In case of SAT scores
Mean of score, μ = 1019
Standard deviations of score, σ = 201
The scores on sat test are normally distributed. In case of ACT score, Mean of score = 20
Standard deviations of score = 5.1
Now, if a student got sat score that is the 27-percentile. We have to determine actual sat score. Probability value for varible, p value = 0.27
So, using normal distribution table or P value to Z-score calculator value of 27th percentile corresponds to a z-score of 0.613. Using Z-score formula,
[tex]z = \frac{ X - \mu}{ \sigma}[/tex]
so, [tex] 0.613= \frac{ X - 1019}{ 201}[/tex]
Solve the expression,
=> 201 × 0.613 = X - 101
=> X= 101 + 123.213
=> X = 224.213
Therefore, a score of 224.213 corresponds to the 27th percentile .
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data visualization is important because: group of answer choices people can synthesize data better than visual representation none of these are correct everybody likes charts and graphs 90% of the information transmitted to the brain is visual
Data visualization is important because option (a) 90% of the information transmitted to the brain is visual.
Data visualization is important because the human brain is wired to process visual information more efficiently than text or numbers. Research shows that about 90% of the information transmitted to the brain is visual, and we can process visual information much faster than text.
Therefore, data visualization is an effective way to represent complex data in a way that is easy to understand and analyze. It allows us to identify patterns, trends, and outliers that might be difficult to detect in raw data.
Therefore, the correct option is (a) 90% of the information transmitted to the brain is visual.
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The given question is incomplete, the complete question is:
Data visualization is important because: a) 90% of the information transmitted to the brain is visual b) None of these are correct c) People can synthesize data better than visual representation d) Everybody likes chart and graphs
A rectangular container 8 cm long and 9cm wide was filled with water to a depth of 6cm. When 12 marbles of equal size were added to the container, the depth of the water became 7. 5 cm. Find the volume of one marble
The volume of one marble is 27 cubic centimeters.
First, let's calculate the initial volume of water in the container. We know that the container is 8 cm long, 9 cm wide, and filled with water to a depth of 6 cm. Therefore, the initial volume of water in the container can be calculated as follows:
Volume of water = length x width x height
= 8 cm x 9 cm x 6 cm
= 432 cm³
Next, we need to find the final volume of water in the container after the 12 marbles were added. We are given that the depth of the water increased from 6 cm to 7.5 cm. Therefore, the final height of the water can be calculated as follows:
Final height of water = 7.5 cm - 6 cm
= 1.5 cm
Now, we can find the final volume of water in the container as follows:
Volume of water = length x width x height
= 8 cm x 9 cm x 1.5 cm
= 108 cm³
The difference between the initial volume of water and the final volume of water is equal to the volume of 12 marbles that were added to the container. Therefore, we can calculate the volume of one marble as follows:
Volume of one marble = (Final volume of water - Initial volume of water) / Number of marbles
= (108 cm³ - 432 cm³) / 12
= 324 cm³ / 12
= 27 cm³
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Rayn's backyard deck cost $87. 85 per square to build. The deck is 8 yards wide and 12 yards long. How much did it cost to build the deck?
Answer:
$8421.60
Step-by-step explanation:
First, we need to convert the dimensions of the deck from yards to square yards, since the cost is given per square yard.
The area of the deck is the product of its length and width:
8 yards * 12 yards = 96 square yards
So, the cost to build the deck is:
$87.85/square yard * 96 square yards = $8421.60
Therefore, it cost $8421.60 to build the deck.
Can someone help me with this.
The slope of the linear equation:
y = -4x + 2/5
is -4.
How to identify the slope of the linear equation?A general linear equation is written as:
y = ax + b
Where a (the coefficient that multiplies the variable) is called the slope, and b is the y-intercept.
Here the linear equation is:
y = -4x + 2/5
We can see that the coefficient that multiplies the variable is -4, so that is the slope of the line.
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Reflect the triangle in the mirror line
I’m so stuck
If all the gold that has been produced in
the last 500 years could be melted to
form a single cube, each side would
measure about 16 m. How many cubic
meters of gold is this?
Step-by-step explanation:
just find the cubic of 16
[tex] {16}^{3} = {2}^{12} = 4096[/tex]
Here r two right angle triangles.............. :)
The value of x for the right triangles is derived to be x = 1 or x = -2/3 using the trigonometric ratio of tangent for the angles a and b
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
tan a = (x + 2)/x and tan b = 4/(3x - 1) {opposite/adjacent}
(x + 2)/x = 4/(3x - 1)
(3x - 1)(x + 2) = 4x {cross multiplication}
by expansion we have a quadratic equation;
3x² - x - 2 = 0
we can rewrite the equation and factorise as follows;
3x² + 2x - 3x - 2 =0
x(3x + 2) - 1(3x + 2) = 0
(x - 1)(3x + 2) = 0
x = 1 or x = -2/3
Therefore, the value of x for the right triangles is derived to be x = 1 or x = -2/3 using the trigonometric ratio of tangent for the angles a and b.
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please help due today, i need solution too pls
The value of the variable x are;
31. x = 1
32. x = 2
33. x = -3
34. x = 5
35. x= 17
How to determine the valuesFrom the information given, we have to know that;
corresponding angles are equalalternating angles are equalAngles on a straight line is 180 degreesWe then have;
m<2 and m< 7 are corresponding angles
Then,
2x = 8x - 6
collect the like terms
x = 1
m<1 = m< 8; corresponding angles
3x - 2 = 5x - 4
collect the like terms
x = 1
m<2 = m<5
6x + 4 = 8x + 10
collect the like terms
x = -3
m<1 = m< 6
2x - 5 = x
collect the like terms
x = 5
m<3 + m< 4 = 180
3x + 6 + 7x + 4 = 180
collect the terms
10x = 170
x = 17
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Please answer ASAP thank youuu!
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{10400}\qquad \leftarrow 6400+4000\\ a=\stackrel{adjacent}{4000}\\ o=\stackrel{opposite}{SP} \end{cases} \\\\\\ SP=\sqrt{ 10400^2 - 4000^2}\implies SP=\sqrt{ 108160000 - 16000000 } \\\\\\ SP=\sqrt{ 92160000 }\implies SP=9600~mi[/tex]
the standard error of estimate can be used for constructing a(n) __________ interval about a value.
The standard error of estimate can be used for constructing a confidence interval about a value.
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. inside a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.
The size of a 90% confidence interval for a given estimate is one method to gauge how "good" it is; the greater the range, the more care must be used when utilizing the estimate. A crucial reminder of the limits of the estimations is provided by confidence intervals.
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Which box-and-whisker plot matches the data?
The box and whisker plot that matches the data-set is given as follows:
Second plot.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.The ordered data-set for this problem is given as follows:
13, 18, 18, 20, 27, 27, 27, 31, 31, 33, 37, 37
Hence the halves are given as follows:
First half of 13, 18, 18, 20, 27 with minimum value of 13 and median = first quartile of 18.Second half of 31, 31, 33, 37, 37, with maximum value of 37 and median = third quartile of 33.The median of the data-set is given as follows:
(27 + 27)/2 = 27.
Hence the second plot is the correct plot.
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How to solve question 3 helpppppp
Answer:
3) Plot the points on the graphing calculator. Then generate a linear regression function. That function is:
y = -.112x + 23.448
4) (2) is correct.
when representing a frequency distribution with a bar graph which bars will be the tallest? A) a bar representing a frequency of 15 B) a bar representing a frequency of 5 C) a bar representing a frequency of 20 D) a bar representing a frequency of 10
The bar graph representing a frequency of 20 will be the tallest
Given data ,
The tallest bar in a bar graph will represent the highest frequency. So, in the given options:
A) a bar representing a frequency of 15
B) a bar representing a frequency of 5
C) a bar representing a frequency of 20
D) a bar representing a frequency of 10
The tallest bar will be C) a bar representing a frequency of 20, as it has the highest frequency among the options given.
In a bar graph, the frequency or count of a certain category or data point is represented by the height of the bars, with larger bars denoting greater frequencies or counts.
Hence , the bar graph is solved
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(Circle Graphs MC)
A group of 450 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports, documentaries 24 percent, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Sports television genre?
99
79
78
22
Answer:
99
Step-by-step explanation:
The circle graph shows that the "Sports" section represents 24% of the total. To find out how many students that corresponds to, we can calculate 24% of the total number of students:
24% of 450 = 0.24 × 450 = 108
Therefore, there are 108 students who prefer the Sports television genre. However, none of the answer choices match this result exactly. The closest option is 99, which is approximately 91.7% of 108. If we round 91.7% up to the nearest whole number, we get 92, which is closer to 99 than any of the other answer choices. So we can conclude that the answer is:
99 (approximately)
Answer:
(a) 99
Step-by-step explanation:
You want to know the number of middle school students who prefer the Sports television genre, given 14, 24, 20, and 20 percent of 450 students prefer drama, documentaries, reality, and sci-fi, respectively.
PercentThe percentage of students who prefer Sports is the difference between 100% and the sum of the other percentages:
sports = 100% -(14 +24 +20 +20)% = 22%
This fraction of the 450 students is ...
0.22 × 450 = 99
99 middle school student prefer the Sports genre, choice A.
<95141404393>
Your answer should be in the form p(x) + k/x-1 where P is a polynomial and k is an integer
x^2+2/x-1=
The answer in the form of polynomial is:
x² + 2/(x-1) = x + 3 + 1/(x-1)
What is polynomial?An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial.
To write x² + 2/(x-1) in the form of p(x) + k/(x-1), we need to perform partial fraction decomposition:
x² + 2/(x-1) = (Ax + B)/(x-1) + Cx + D
Multiplying both sides by (x-1), we get:
x² + 2 = (Ax + B) + (Cx + D)(x-1)
Expanding the right-hand side, we get:
x² + 2 = Ax + B + Cx² - Cx + Dx - D
Matching coefficients on both sides, we get the following system of equations:
C = 1
D - B = 2
A - C = 0
-B + D = 0
Solving for A, B, C, and D, we get:
A = 1
B = -1
C = 1
D = 1
Therefore, we have:
x² + 2/(x-1) = (x-1)/x-1 + x + 1
= x + 2 + 1/(x-1)
Hence, the answer is:
x² + 2/(x-1) = x + 3 + 1/(x-1)
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Nadire determines that there are no fractions equivalent to 2/10 with a denominator greater than 10 but less than 20 they have in whole number numerator and denominator is Nadia correct
Find the domain and range of the relation. Then determine whether the relation is a function
{(4, -7), (3,-7), (2,0), (4,0)}
Answer:
Domain: {4, 3, 2}
Range: {-7,0}
This IS NOT a function
Step-by-step explanation:
Since x=4 produces y=−7 and y=0, the relation (4,−7),(3,−7), (2,0),(4,0) is not a function.
have a good day :)
A bag contains 6 marbles. There are 2 red marbles, 2 green marbles, and 2 yellow marbles. A marble is randomly selected from the bag and then set aside. A second marble is then selected from the bag. What is the probability that both marbles are red?
The probability that both marbles are red is 0.33
Probability :The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes.
P(A) = Number of favorable outcomes/ total no. of possible outcomes
We have the information from the question:
Total marbles are there in bag is = 6
Red Marbles = 2
Green Marbles = 2
Yellow Marbles = 2
To find the probability that both marbles are red.
Now, According to the question:
The probabilities that are desirable for our cases are:
P(RR) = 2/6 = 1/3 = 0.33
Hence, The probability that both marbles are red is 0.33
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A group of 70 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73. The group of 70 students in the study reported an average of 4.45 drinks per with a standard deviation of 3.92 drinks.
Find the p-value for the hypothesis test.
The p-value for the hypothesis test is approximately 0.65.
To find the p-value for the hypothesis test, we need to determine the test statistic and the corresponding probability.
First, we need to state the null and alternative hypotheses:
Null Hypothesis: The mean number of alcoholic drinks for college students at the liberal arts college is equal to the mean number of alcoholic drinks for U.S. college students in general, which is 4.73.
Alternative Hypothesis: The mean number of alcoholic drinks for college students at the liberal arts college is not equal to the mean number of alcoholic drinks for U.S. college students in general.
Next, we need to determine the test statistic, which is calculated as follows:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
t = (4.45 - 4.73) / (3.92 / sqrt(70))
t = -0.28 / 0.47
t = -0.596
Using a t-distribution table with 69 degrees of freedom (70 - 1), we find the corresponding two-tailed probability to be 0.553.
Therefore, the p-value for the hypothesis test is 0.553. This means that if we assume the null hypothesis is true, there is a 55.3% chance of observing a sample mean of 4.45 drinks per week or more extreme. Since this p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean number of alcoholic drinks for college students at the liberal arts college differs from the mean number of alcoholic drinks for U.S. college students in general.
To find the p-value for the hypothesis test, we first need to set up the null and alternative hypotheses:
Null hypothesis (H₀): The mean number of alcoholic drinks for college students at this liberal arts college is equal to the national mean (µ = 4.73).
Alternative hypothesis (H₁): The mean number of alcoholic drinks for college students at this liberal arts college is different from the national mean (µ ≠ 4.73).
Next, we'll perform a t-test, since we have a sample mean, standard deviation, and sample size, but not the population standard deviation.
First, calculate the t-statistic:
t = (sample mean - population mean) / (sample standard deviation / √sample size)
t = (4.45 - 4.73) / (3.92 / √70)
t ≈ -0.46
Now, we need to find the degrees of freedom (df) for the t-distribution:
df = sample size - 1
df = 70 - 1 = 69
Using a t-table or t-distribution calculator, we can find the p-value for a two-tailed test (since we're testing for a difference, not specifically greater or lesser) with t ≈ -0.46 and df = 69. The p-value is approximately 0.65.
Your answer: The p-value for the hypothesis test is approximately 0.65.
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ten different people walk into a delicatessen to buy a sandwich. four always order tuna fish, two always order chicken, two always order roast beef, and two order any of the three types of sandwich. (a) (5 points) how many different sequences of sandwiches are possible? (b) (5 points) how many different (unordered) collections of sandwiches are possible?
(a) There are 81 different sequences of sandwiches are possible
(b) The total number of different (unordered) collections of sandwiches is 3.
First, we need to determine the number of ways the four tuna fish sandwiches can be ordered. Since all four sandwiches are the same, there is only one way to order them. Similarly, there is only one way to order the two chicken sandwiches and the two roast beef sandwiches. For the two people who can choose any sandwich, there are three options for each person, giving a total of 3 x 3 = 9 possible sandwich combinations.
Therefore, the total number of different sequences of sandwiches is:
1 (tuna fish) x 1 (chicken) x 1 (roast beef) x 9 (any sandwich) x 9 (any sandwich) = 81
For part (b), we need to determine the number of different (unordered) collections of sandwiches. We can use combinations to solve this problem. We need to select 10 sandwiches from the total of 10 sandwiches available. Since there are four tuna fish sandwiches, we need to select four of them.
Similarly, we need to select two chicken sandwiches and two roast beef sandwiches. Finally, we need to select two more sandwiches from the remaining three (since two people can choose any sandwich). The number of ways to select these sandwiches is:
combination(4,4) x combination(2,2) x combination(2,2) x combination(3,2) = 3
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