Jane can select 80 different types of dinner consisting of 3 different items from 5 different vegetarian items and 4 different meat items available.
For finding the various combination of dinners available which has atleast one vegetarian item we will apply combination formula with the given data i.e., [tex]^{n} C_{r} = \frac{n!}{(n-r)!.r!}[/tex]
A combination is a way of selecting items from a collection where the order of selection does not matter.
We will have to apply the formula separately for vegetarian and meat items.
Combinations available
A. 1 vegetarian item and 2 meat items
[tex]^{5} C_{1} and ^{4} C_{2}[/tex] (In combination "and" means to multiply)
= [tex]\frac{5!}{(5-1)!.1!} . \frac{4!}{(4-2)!.2!}[/tex]
= [tex]\frac{5!}{(4)!.1!} . \frac{4!}{(2)!.2!}[/tex]
= [tex]\frac{5.4.3.2.1}{(4.3.2.1).(1)}. \frac{4.3.2.1}{(2.1).(2.1)}[/tex]
= 5.3.2
= 5.6
= 30
B. 2 vegetarian items and 1 meat item
[tex]^{5} C_{2} and ^{4} C_{1}[/tex]
= [tex]\frac{5!}{(5-2)!.2!} . \frac{4!}{(4-1)!.1!}[/tex]
= [tex]\frac{5!}{(3)!.2!} . \frac{4!}{(3)!.1!}[/tex]
= [tex]\frac{5.4.3.2.1}{(3.2.1).(2.1)}. \frac{4.3.2.1}{(3.2.1).(1)}[/tex]
= 5.2.4
= 10.4
= 40
C. 3 vegetarian items and no meat item
= [tex]^{5} C_{3} and ^{4} C_{0}[/tex]
= [tex]\frac{5!}{(5-3)!.3!} . \frac{4!}{(4-0)!.0!}[/tex]
= [tex]\frac{5.4.3.2.1}{(2.1).(3.2.1)}. 1[/tex]
= 5.2
= 10
Now, we will add all the different combination
Total combinations = 30+40+10
= 80 different type of dinners
To know more about combination
https://brainly.com/question/13387529
#SPJ4
the value of a building is $180,000. the value is expected to increase by 3.5% each year. write a function that represents the value y (in dollars) of the building after x years. the predict the value after 10 years
If you drove at 50 mph in 5 hours, how far will you have traveled? NEED ASAP
a. 200 miles
b. 10 miles
c. 250 miles
d. 300 miles
Answer:
c
Step-by-step explanation:
in a class of 26 students,15 of them like maths,13 of them like english and 9 doesnt like eitherwhats the probability that a student choosen at random likes english but not maths
The probability that a student choosen at random likes english but not maths is 299/676.
Let A be the event that a student likes math, and B be the event that a student likes English.
From the given information, we know that:
P(A) = 15/26
P(B) = 13/26
P(neither A nor B) = 9/26
To find the probability that a student chosen at random likes English but not math, we can use the formula:
P(B and not A) = P(B) - P(A and B)
The probability of A and B can be found by multiplying the probabilities of A and B together, since they are not independent:
P(A and B) = P(A) × P(B) = (15/26) × (13/26) = 195/676
Substituting the given probabilities into the formula, we get:
P(B and not A) = (13/26) - (195/676)
Simplifying, we get:
P(B and not A) = 299/676
Therefore, the probability that a student chosen at random likes English but not math is 299/676.
To know more about probability:
https://brainly.com/question/23704607
#SPJ4
Please Answer ASAP!
Please Give A Clear Answer Too!!
Answer:
x + y = -9
Step-by-step explanation:
let x = -8, y = -1
the equation that passes through the point (-8,-1) is x + y = -9
2. In rectangle HOME, HM and OE are diagonals that intersect at P.
Write at least 6 unique statements about HOME and justify your statements with definitions, postulates or theorems
1. It should be noted that HD = EM and HE = OM. In this case, the opposite sides are equal in the rectangle.
2. It should be noted that EHO = HOM = OME = MEH = 90°. In this case, all angles are equal to 90°.
What are postulate?Postulates are assertions that, in the absence of evidence, are taken to be true. Postulates have two functions: they define undefined terms and act as a foundation for the proof of subsequent propositions.
A line segment is determined by two points. A line segment may be extended along a line indefinitely. The other information is attached.
Learn more about postulate on:
https://brainly.com/question/25292087
#SPJ1
What is the answer to question 5
Anwer: EG=EF+EG => 6x+12+48=144
6x=144-12-48
6x=84
x=14
d)x=14
Helppppppppppp meeeeee guyssssssss
Answer:
2. $9.99
3. 45 tickets for $27
4. 20 cents
Step-by-step explanation:
2. 79.92/8 = 9.99
3. 27/45 0.6 and 15/20 = 0.75 and 60 cents is less than 75 cents
4. 6/30 = 20
Answer:
Step-by-step explanation:
79.92/8= 9.12 per cd
15/20= .75
27/45=.6 better deal because it is .60 cents per ticket
6/30= .20 per can
hey can someone help me
the following dot plot summarizes the distance roger ran in each of his tennis matches last month. each dot represents one game. based on this data, what is a reasonable estimate of the probability that roger runs less than 5 55 km kmstart text, k, m, end text in his next tennis match? choose the best answer. choose 1 answer: choose 1 answer:
The estimated probability that Roger runs less than 5 km in his next tennis match is 33%.
The dot plot summarizes the distance Roger ran in his recent tennis matches. To estimate the probability that he will run less than 5 km in the next match, we can use the data from the dot plot.
So according to question, there are kilometres as :
3 km, 4 km, 5 km, 6 km, and 7 km.
Total matches he played
for 3 km- 1 match , for 4 km- 2 matches , for 5 km- 4 matches, for 6 km- 0 matches, and for 7 km- 2 matches.
Out of 9 matches, he ran less than 5 km in 3 matches.
So the probability that Roger runs less than 5 km in his next tennis match is: 3/9 = 1/3
So the percentage will be : 33.33% ≈ 33%
Therefore, the estimated probabilityrobability that Roger runs less than 5 km in his next tennis match is 1/3 or about 33%.
Learn more about probability here brainly.com/question/30034780
#SPJ4
Answer: 33%
Step-by-step explanation:
1. Find the geometric mean of the
two numbers.
4 and 42.25
Answer:
13
Step-by-step explanation:
Question 7(Multiple Choice Worth 2 points) (09.06 LC) How many hectometers are in 580 millimeters? O 0.0058 hectometers O0.058 hectometers O58,000 hectometers O 580,000 hectometers
Answer: B. 0.058 hectometers
Step-by-step explanation: To convert millimeters to hectometers, you need to divide the number of millimeters by 10,000.
Given that there are 580 millimeters, the conversion to hectometers can be calculated as follows:
580 millimeters ÷ 10,000 = 0.058 hectometers
Which of the following is equivalent to the fraction above?
OA. 13
-7
OB. 7
13
OC. -13
-7
OD. 3
-13
-(13)
The Equivalent Fraction of -117 / 63 is -13/7.
What is Equivalent Fraction?The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½.
A rule that says the outcome of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.
Given:
We have the Fraction -117 / 63
As, Equivalent fraction can have different numerators but the denominators should be necessarily same.
Now, simplifying the fraction
= -117/ 63
= - (13 x 9) / (7 x 9)
= -13 / 7
Learn more about equivalent Fraction here:
https://brainly.com/question/25813932
#SPJ9
pls help me i dont understand
Answer:
y+3=-3/4(x+4)
Step-by-step explanation:
the formula is
y-y1=m(x-x1)
y1 is -4 and x1 is -3 and m is slope
when the x or y is a negitive it then is added
There is a total of
wholes in 72
.
The remaining fractional part is .
2
The whole number whose sum is 72 cannot be in the ratio C. 3/4.
How to explain the ratioRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them
The whole number must be divided by sum of two ratio particularly
A.5 + 7=12
72 can be divided by 12
B.3+5=8
72 can be divided by 8
C.4+3=7
72 can not be divided by 7
D.4+5=9
72 can be divided by 9
Learn more about ratio on:
https://brainly.com/question/2328454
#SPJ1
The whole number whose sum is 72 cannot be in the ratio
A. 5/7
B. 3/5
C. 3/4
D. 4/5
what is the probability that the sample mean annual insurance cost is greater than $620? show your work.
The probability of the sample mean annual insurance cost being greater than $620 is very low, that is 0.00317% which indicating that it is unlikely to happen by chance.
Probability is a branch of mathematics that deals with the likelihood of an event happening. It is used in various fields, such as insurance, finance, and science.
To calculate the probability, we need to use the central limit theorem, which states that the distribution of sample means of a population approaches a normal distribution as the sample size increases. We also need to know the mean and standard deviation of the population.
Assuming that the population is normally distributed, we can use the following formula to calculate the probability:
z = (x - μ) / (σ / √(n))
where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we don't know the population mean and standard deviation, but we can use the sample mean and standard deviation as estimates. Let's say we have a sample of 100 insurance costs with a mean of $600 and a standard deviation of $50.
Now, we can calculate the z-score:
z = (620 - 600) / (50 / √(100)) = 4
The z-score of 4 indicates that the sample mean of $620 is 4 standard deviations away from the mean of $600. We can use a standard normal distribution table or a calculator to find the probability of getting a z-score of 4 or higher. The probability is very small, approximately 0.0000317 or 0.00317%.
To know more about probability here.
https://brainly.com/question/11234923
#SPJ4
On a certain hot summer's day, 455 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $952.25. How many
children and how many adults swam at the public pool that day?
The number of children and adults that swam at the public pool are 247 and 208 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
Represent the number of children by x and the number of adult by y
this means;
x+y = 455 equation 1
1.75x + 2.5y = 952.25 equation 2
using substitution method,
x = 455-y
substitute 455-y for x in equation 2
1.75(455-y) + 2.5y = 952.25
796.25-1.75y+2.5y = 952.25
0.75y = 952.25-796.25
0.75y = 156
divide both sides by 0.75
y = 156/0.75
y = 208
substitute 208 for y in equation 1
x = 455-208
x = 247
therefore the number of children and adults in the pool are 247 and 208 respectively.
learn more about Simultaneous equation from
https://brainly.com/question/16863577
#SPJ1
State the maximum and minimum values if they exist.
The maximum and minimum values are 34.5 and 2
How to determine the maximum and minimum valuesfrom the question, we have the following parameters that can be used in our computation:
P = 2x + 7y
Subject to:
4x - 2y <= 5
x >= 1
0 <= y <= 4
Next, we plot the constraints on a graph
From the graph, we have the following vertices
(1, 0), (4, 0) and (3.25, 4)
This gives
P = 2(1) + 7(0) = 2
P = 2(4) + 7(0) = 8
P = 2(3.25) + 7(4) = 34.5
Hence, the minimum is 2 and the maximum is 34.5
Read more about objective function at
https://brainly.com/question/14309521
#SPJ1
Which equations are correct? select each correct answer. 8x3(3x2)=24x6 4x3(6x2)=24x6 6b3(−2b3)=−12b6 3a3(−3a4)=−9a7?
The correct equations are:8x^3 * (3x^2) = 24x^5, 6b^3 * (-2b^3) = -12b^6, 3a^3 * (-3a^4) = -9a^7. The equations are correct because they follow the rules of algebra. The equation 4x^3 * (6x^2) = 24x^5 is not correct.
The distributive property of multiplication over addition allows us to multiply a factor by each term inside a set of parentheses. In the equation 8x^3 * (3x^2), we can use the distributive property to multiply 8x^3 by each term inside the parentheses, giving us 24x^5.
Similarly, the product of two negative numbers is positive, which explains why the equation 6b^3 * (-2b^3) equals -12b^6.
Finally, multiplying two terms with the same base means we add the exponents, so in the equation 3a^3 * (-3a^4), we get -9a^7.
Therefore, these equations are correct and follow the rules of algebra.
To learn more about distributive property Click here:
brainly.com/question/5637942
#SPJ4
community college faculty is negotiating a new contract with the school board. The distribution of faculty salaries is skewed right by several faculty members who make over $100,000 per year. If the faculty impression that they deserve higher sales should they a r e the meanor median of their current salaries? A. The faculty should use the mean to make their argument. The mean will be higher than the median since the mean is influenced by the few extremely high res.B. The faculty should use the mean to make o rgument. The man will be lower than the median since it will be henced by the few high salariesC. The faculty should use the median to make their argument. The median will be higher than the mean since the media is unced by the high e s D. The faculty should use the median to make their argument. The median will be lower than me since the means i nced by the extremely histories
Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.
Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.
So for example, if the salaries of any 5 faculty members are as follows:
$10,000 , $50,000 , $80,000 , $150,000 , $160,000
Mean= (10,000+50,000+80,000+150,000+160,000) / 5
Mean= $90,000
Median= (5+1) / 2
Median= 6/2
Median= 3rd value
As the data is already arranged in ascending order, Median is $80,000
Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.
To know more about Median
https://brainly.com/question/13168193
#SPJ4
a bakery sells blueberry muffins for 2.50 each. it costs c dollars to make each muttij the profit for selling m muffins is described by the expression below in the expression what is the meaning of (2.5-c)
Answer:
7.8
Step-by-step explanation:
In this regular hexagon, all of the exterior
angles marked r are the same size.
Find the value of r.
Give your answer in degrees (°).
Answer:
60 degrees
Step-by-step explanation:
Simplify quantity 4 x squared plus 12 x minus 16 all over quantity 2x plus 10 over quantity 6 x plus 24 over quantity x squared plus 9x plus 20 . (2 points)
Answer:
So the simplified expression is:
2x - 4 / (x^2 + 9x + 20)
Step-by-step explanation:
To simplify the expression, we need to simplify the numerator and denominator separately, and then simplify the entire expression.
Starting with the numerator:
4x^2 + 12x - 16
For the denominator:
The first fraction: 2x + 10 can be simplified as follows: 2x + 10 = (2)(x) + (2)(5) = 2x + 10
The second fraction: 6x + 24 over x^2 + 9x + 20
We can simplify the denominator by using partial fraction decomposition. To do that, we need to write the denominator as a sum of simpler fractions, each with a numerator that is a constant. In other words, we write:
6x + 24 / (x^2 + 9x + 20) = (A x + B) / (x^2 + 9x + 20) + (C x + D) / (x^2 + 9x + 20)
Multiplying both sides by the denominator, we get:
6x + 24 = (A x + B)(x^2 + 9x + 20) + (C x + D)(x^2 + 9x + 20)
Expanding the right-hand side, we obtain:
6x + 24 = Ax^3 + (A 9 + B) x^2 + (A 20 + B 9 + C) x + (B 20 + D)
Comparing the coefficients of the polynomials on both sides, we get the following system of linear equations:
A = 0
B = 6
C = 0
D = -24
Therefore, the partial fraction decomposition of the denominator is:
6x + 24 / (x^2 + 9x + 20) = (6x + 24) / (x^2 + 9x + 20)
Putting it all together, we have:
4x^2 + 12x - 16 / (2x + 10) / (6x + 24) / (x^2 + 9x + 20) = (4x^2 + 12x - 16) / (2x)(6x + 24) / (x^2 + 9x + 20) = 2x - 4 / (x^2 + 9x + 20)
So the simplified expression is:
2x - 4 / (x^2 + 9x + 20)
A study shows that at the end of a school day teenagers typically have 40% of their cell phone battery left when plugged in phone charge at a rate of 3% per minute when using the newest fast charger.
a: write an inequality to represent how many more minutes are needed to reach at least 80% battery life.
b. use the inequality to determine the how many more minutes it will take to have at least 80% battery life
The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the number of minutes and 'y' be the total battery percentage. Then the equation is given as,
y = 3x + 40
The inequality that represents the more minutes are needed to reach 80 of battery is given as,
3x + 40 ≤ 80
Simplify the inequality, then we have
3x + 40 ≤ 80
3x ≤ 40
x ≤ 13.33 minutes
The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ1
a certain shop repairs both audio and video components. let a denote the event that the next component brought in for repair is an audio component, and let b be the event that the next component is a compact disc player (so the event b is contained in a). suppose that p(a) 5 .6 and p(b) 5 .05. what is p(bua)?
The probability that the next component brought in for repair is a compact disc player given that it is already known to be an audio component is 0.83 or 83%.
Probability is a fundamental concept in mathematics, statistics, and various fields of science. It is used to measure the likelihood of an event occurring
In the given scenario, we are told that a certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player. We are also given that P(A) = 0.6 and P(B) = 0.5.
The probability of B given A, denoted by P(B|A), represents the probability that event B will occur given that event A has already occurred. In other words, it tells us how likely it is that the next component brought in for repair is a compact disc player given that it is already known to be an audio component.
To calculate P(B|A), we use the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
Here, P(A and B) denotes the probability that both events A and B occur. We know that event B is contained in event A, so it follows that P(A and B) = P(B). Therefore:
P(B|A) = P(B) / P(A)
Substituting the given values, we have:
P(B|A) = 0.5 / 0.6
P(B|A) = 5/6 or 0.83 (rounded to two decimal places)
To know more about probability here.
https://brainly.com/question/11234923
#SPJ4
Complete Question:
A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A) = .6and P(B) = .5. What is P(B|A) ?
Question: Use the partial products 3,840 and 640 to find the product 128 x 35. How many pens arr in 35 full boxes?
Answer:
hope this helps
Step-by-step explanation:
nine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. let the probability that each delegate sits next to at least one delegate from another country be $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
The ones we don't want are those. We only want 410 of the 560 total, thus the cost is $097.
Contact nations A, B, and C. At the northernmost position for configurations, someone from A is seated. Since the only thing the problem mentions about how delegates can differ is by their country, I decided to represent people in my solution by their respective nations. Now, we can see that there are nCr(8, 2) * nCr(6, 3) = 560 possible arrangements (8 seats choose 2 for the rest of the A country, 6 seats choose 3 for B). It is clear that configurations with three delegates in a row are the ones we don't want. Take note that scenarios for A, B, and C to be together are still valid despite my placing of A at the start.We now apply the inclusion-exclusion principle. Two cases for an A three in a row. First. A, Master A, A: $20 for B seats at nCr(6, 3). Additionally, there is $20 for each "slant" A set. =$60. *3=180. A and B both: Two cases once more! We identify four ways for B to get three in a row: A, Master A, A, and A. $12 is the same for slant. *3 = $36 (AB, BC, or CA). For all three: This time, we have two of the three aforementioned A circumstances, for a total of six. 180-36+6 Equals 150 in the end. The ones we don't want are those. We only want 410 of the 560 total, thus the cost is $097.
Learn more about cost from
brainly.com/question/481029
#SPJ4
Question 5
BLUEPRINTS Ezra is redrawing the blueprint shown of a stage he is planning to build for his band. By what percentage should he multiply the
dimensions of the stage so that the dimensions of the image are the size of the original blueprint? What will be the perimeter of the updated
blueprint?
10 units
LF
4 units
8 units
%; The perimeter of the updated blueprint will be
10 units
2 units
units.
The perimeter of the updated blueprint would be = 62units.
How to calculate the perimeter of the blueprint?The percentage that she can use to multiply the dimensions of the stage so that the dimensions of the image is half the size of the original blueprint would be = 50%.
To calculate the perimeter of the blueprint is to add the sides of the whole blue print that was given. That is;
= 10+4+2+4+2+4+10+2+2+8+2+2
= 62 units.
Learn more about perimeter here:
https://brainly.com/question/24571594
#SPJ1
Help meee
Which one is it?
Answer:
the number of shirts sold
Step-by-step explanation:
that's what the question is asking
What is the minimum value for the function shown in the graph?
Enter your answer in the box.
Answer:
The minimum value is 2.5.
Step-by-step explanation:
This is a sine wave that is parallel to the x axis. It will never go below 2.5, as shown on the graph.
SOMEBODY PLEASE LOOK AT THE PICTURE AND HELP MEEEE
The equation that represent the graph is C = 1.5m + 200.
How to represent linear equation?A moving company charges a one time fee and cost per miles of it service. Therefore, the relationship is between the total cost and the number of miles.
Therefore, let's use equation to represent the relationship between the total cost C and number of miles travelled, m.
Hence, using slope intercept form
y = mx + b
where
m = slopeb = y-interceptHence,
using (0, 200) (200, 500)
m = 500 - 200 / 200 - 0
m = 300 / 200
m = 1.5
Hence,
y-intercept = 200
Therefore, the equation is C = 1.5m + 200
learn more on equation here: https://brainly.com/question/29739212
#SPJ1
