Answers
Answer:
Semi circle:39.26990817
Trapezoid:27
Triangle:15
Figure:81.26990817
I personally think this is F,unless I did it wrong,was I supposed to multiply the shapes together or add the areas of the shapes together? Even if I multiplied, it would still not be listed....
Step-by-step explanation:
Answer:
F) not listed
Step-by-step explanation:
We can break this down into 3 separate shapes
top = semi-circle
middle = trapezoid
bottom = triangle
the area formulas for each are as follows
semi-circle = (1/2)pi r^2 : r = radius
trapezoid = (1/2)h(a+b) : h = height a = top base b = bottom base
triangle = (1/2)bh : b = base h =height
top calculation:
(1/2)pi(5)^2 = (1/2)pi(25) = 39.23
middle calculation:
(1/2)(3)(10+8) = 27
bottom calculation:
1/2(8-1.5-1.5)(6) = 15
39+27+15 = 81 in^2
Related Questions
a simple random sample of 100 8th graders at a large suburban middle school indicated that 86% of them are involved with some type of after school activity. find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. a) (0.699, 0.941) b) (0.829, 0.834) c) (0.779, 0.941) d) (0.679, 0.891) e) (0.779, 0.741) f) none of the above
Answers
For a random sample of 100 students related to aftee school activity. The 98% confidence interval that estimates the proportion of students who are involved in an after school activity is equals to (0.779, 0.941). So, option (c) is right one.
Confidence intervals represents the variation around a statistical estimate. A confidence interval is a range of interval of estimates for an unknown parameter.
[tex]CI = \hat p ± z_ \frac{ \alpha}{2}\sqrt{\frac{ ( 1 - \hat p)\hat p}{n}}[/tex]
where [tex]\hat p[/tex]-->sample proportion
n --> sample size
We have a simple random sample of 8ᵗʰ graders at a large suburban middle school. Sample size, n = 100
Sample proportion for students who involved with some type of school activity, [tex]\hat p[/tex] = 86% = 0.86
We have to calculate the 98% confidence interval that estimates the proportion of students sample.
Level of significance, α = 98%
= 0.98
Using the normal distribution table, value of z-score for 98% of confidence interval is 2.326 . Now, plug all known values in following confidence interval formula,
[tex]CI = \hat p ± z_ \frac{ \alpha}{2}\sqrt{\frac{ ( 1 - \hat p)\hat p}{n}}[/tex]
[tex]= 0.86 ± (2.326) \sqrt{\frac{ ( 1 - 0.86)0.86}{100}}[/tex]
[tex]= 0.86 ± (2.326) \sqrt{\frac{ ( 0.14)0.86}{100}}[/tex]
[tex]= 0.86 ± 0.081 [/tex]
[tex]= (0.86 - 0.081 , 0.86 + 0.081) [/tex]
= (0.779, 0.941)
Hence, required value is (0.779, 0.941).
For more information about confidence interval, visit:
https://brainly.com/question/15712887
#SPJ4
Any help? Please. Whoever answer it first gets brainliest!
Answers
Answer:
[tex]c + 15 > 24[/tex]
[tex]c > 9[/tex]
The additional amount will be more than $9.
does the calculated percent fat from the experimental data in question 2 agree with the percent fat calculated from the label in question 3? why or why not? group of answer choices yes, they are the same. the two values differ by less than 1%. no, they are different. the two values differ by more than 1%.
Answers
If the experimental value is 10.1% and the label value is 10%, then the relative difference is 1%, which is equal to 1%. Therefore, you can say that they agree.
To determine if the calculated per cent fat from the experimental data in question 2 agrees with the per cent fat calculated from the label in question 3, follow these steps:
1. Calculate the per cent fat from the experimental data in question 2.
2. Calculate the per cent fat from the label in question 3.
3. Compare the two values.
If the two values are the same or differ by less than 1%, then the answer is yes, they agree. If the two values differ by more than 1%, then the answer is no, they do not agree.
Without the specific data from questions 2 and 3, I cannot provide a definite answer. However, you can use the steps provided above to determine if the calculated per cent fat from the experimental data agrees with the per cent fat calculated from the label.
Learn more about Experimental Data here: brainly.com/question/30777101
#SPJ11
what are the first four terms if a1=2 and an= an-1 +3?
Answers
The first four terms of the sequence are a₁ = 2, a₂ = 5, a₃ = 8, a₄ = 11.
What is arithmetic progression?The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP). A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by adding 4 to the previous term.
The given sequence is defined as a₁=2 and aₙ= aₙ₋₁ + 3 for n > 1.
To find the first four terms of the sequence, we can use the recursive formula repeatedly:
a₁ = 2 (given)
a₂ = a₁ + 3 = 2 + 3 = 5
a₃ = a₂ + 3 = 5 + 3 = 8
a₄ = a₃ + 3 = 8 + 3 = 11
Therefore, the first four terms of the sequence are a₁ = 2, a₂ = 5, a₃ = 8, a₄ = 11.
Learn more about arithmetic progression on:
https://brainly.com/question/16947807
#SPJ1
suppose that 30% of new yorkers own a dog, 25% of new yorkers own a cat and 15% of new yorkers own a cat given they own a dog. a new yorker is chosen at random and reported to own a cat. what is the probability they also own a dog?
Answers
The probability that a New Yorker who possesses a cat also owns a dog is 0.103. if a new yorker is chosen at random.
New Yorkers own a dog (D) = 30%
New Yorkers own a cat (C) = 25%
New Yorkers own a cat and dog = 15%
This problem can be calculated using Bayes' theorem, which notes that the possibility of an event A given event B is equal to the possibility of event B given A times the probability of A, divided by the probability of event B.
P(D) = 0.30
P(C) = 0.25
P(C|D) = 0.15
Using Bayes' theorem:
P(D|C) = P(C|D) * P(D) / P(C)
P(C) = [tex]P(C|D) * P(D) + P(C|not D) * P(not D)[/tex]
P(C) = [tex]P(C|D) * P(D) + P(C) * P(not D)[/tex]
P(C) =[tex]P(C|D) * P(D) / (1 - P(D) * P(C|not D))[/tex]
Now we can substitute these values into the Bayes' theorem formula:
P(D|C) = P(C|D) * P(D) / P(C)
P(D|C) = [tex]0.15 * 0.3 / (P(C|D) * P(D) + P(C) * P(not D))[/tex]
P(D|C) = [tex]0.15 * 0.3 / (0.15 * 0.3 + P(C) * 0.7)[/tex]
P(C) = [tex]0.15 * 0.3 / (1 - 0.3 * 0.25)[/tex]
P(C) = 0.16
P(D|C) = [tex]0.15 * 0.3 / (0.15 * 0.3 + 0.16 * 0.7)[/tex]
P(D|C) = 0.103
Therefore, we can conclude that the probability that a New Yorker who owns a cat also owns a dog is 0.103.
To learn more about Probability
https://brainly.com/question/30034780
#SPJ4
Chelsea is buying mini candy bars for her classmates. She has four different options for buying the candy bars. The list below gives different options for quantity and price.
If Chelsea wants to spend the lowest amount per mini candy bar, then which option should she buy?
Answers
Answer:
small
Step-by-step explanation:
You can divide the number of mini candy bars over the price, and the lowest would be the smallest one, with 8.33.
Find the measure of Angle A and round the answer to the nearest tenth.
(Show work if you can, thank you).
Answers
68.5 is the measure of Angle A and round the answer to the nearest tenth.
What is Trigonometry?Trigonometry is the area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangential (tan), cotangent (cot), secant (sec), & cosecant (csc) are their names, respectively.
Here we have to use the tan ratio to find the answer.
tanθ = base/perpendicular
Given: perpendicular = 19, base = 22
tan θ = 19/22
θ = tan^-1 (19/22)
tan θ = 1.2
so the angle θ is
68.5 degree
Answer: B) 68.5 degrees
To know more about Angle, visit:
https://brainly.com/question/1309590
#SPJ1
Answer:
The measure of angle A is 40.8° to the nearest tenth.
Step-by-step explanation:
The given triangle ABC is a right triangle.
We want to find the measure of angle A, and have been given the length of the sides opposite and adjacent to angle A.
The tangent ratio of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side of that angle.
Therefore, we can use the tangent trigonometric ratio to find the measure of angle A.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
Given values:
θ = angle A = xO = side BC = 19A = side AC = 22Substitute the given values into the ratio and solve for x:
[tex]\implies \tan(x)=\dfrac{19}{22}[/tex]
[tex]\implies x=\tan^{-1}\left(\dfrac{19}{22}\right)[/tex]
[tex]\implies x=40.8150838...^{\circ}[/tex]
[tex]\implies x=40.8^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the measure of angle A is 40.8° to the nearest tenth.
Your classmates Sarah, Gene and Paul are proposing plans for a class fundraiser. Each presents his or her proposal for the amount of money raised, y, for x number of hours worked, in different ways. Part A: Are each of the proposals represented by linear functions? Explain. Refer to lesson 7. 4 Comparing Linear and Non-Linear Functions. Part B: Does the class have any money in the account now? How can you tell? Calculate the y-intercept in order to find your answer. Part C: Which fundraising proposal raises money at the fastest rate? Explain. Refer to lesson 7. 2 Representations of Functions Part D: If Sarah and her classmates are hoping to raise $200, which proposal do you recommend that Sarah and her classmates choose? Analyze your answers to explain why you recommend that proposal. Note that there are different ways to analyze and display your thinking
Answers
All the plans proposed by classmates Sarah, Gene and Paul represents linear function.
Total money in the account at (0 ,0 ) is $24.
Fundraising proposal showing fastest rate is of Sarah proposal plan.
To raise $200 recommended plan is of Sarah.
Standard linear function is y = mx + c
'm' is the slope and 'c' is the y-intercept.
For attached question
Let y represents the amount of money
And x represents the number of hours worked.
Proposing plan of Sarah represents the straight line
From graph consider two points
( x₁ , y₁ ) = ( 1, 20 )
(x₂ , y₂ ) = ( 2 , 30 )
Slope 'm' = ( y₂ - y₁ ) / ( x₂ - x₁ )
= (30 -20 ) / ( 2 - 1 )
= 10 /1
y = mx + c
⇒ 20 = 10(1) + c
⇒ c = 10
Linear function for Sarah is y = 10x + 10
Gene proposal ,
( x₁ , y₁ ) = ( 5, 42 )
(x₂ , y₂ ) = ( 10 , 77 )
Slope 'm' = ( y₂ - y₁ ) / ( x₂ - x₁ )
= (77 -42 ) / ( 10 - 5 )
= 35 /5
= 7
y = mx + c
⇒ 112 = 7(15) + c
⇒ c = 7
Linear equation for Sarah is y = 7x + 7
Paul proposal is,
y = 10x + 7
Linear function.
This implies all proposal plans represents linear function .
As they are in form y = mx + c.
Yes class has money in the account.
Sarah has 10 , Gene has 7 and Paul has 7 in his account.
Total money in account = 24
If we put x = 5 in all the plans
Sarah raised
y = 10(5) + 10
= 60
Gene raised
y = 7x + 7
= 7(5) + 7
= 42
Paul raised
y = 10x + 7
= 10(5) + 7
= 57
This implies Sarah plan raised the money at fastest rate.
Sarah and her classmates are hoping to raise $200
Sarah plan,
200 = 10x + 10
⇒ x = 19 hours
Gene plan
200 = 7x + 7
⇒ x = 27.6 hours
Paul plan
y = 10x + 7
⇒ 200 = 10x + 7
⇒x = 19.3hours
Recommended plan is of Sarah.
Therefore, all the proposal plans represents linear function.
Class has $24 in the account.
Sarah plan raises at the fastest rate.
Recommended plan is Sarah proposal plan.
learn more about linear function here
brainly.com/question/25293058
#SPJ4
The above question is incomplete, the complete question is:
Attached question.
Can someone help me asap? It’s due tomorrow.
Answers
The sampling method used by the principal is Stratified sampling.
What is Stratified sampling?
Stratified sampling is a sampling method where the population is divided into non-overlapping subgroups, called strata, based on certain characteristics or attributes, and then a random sample is drawn from each stratum.
In this case, the principal organized the school's population by grade level, which created four strata: freshman, sophomore, junior, and senior classes. The principal then randomly sampled fifty students from each of these four strata to collect data on their preferred elective course. This approach ensures that each grade level is represented in the sample, which can provide a more accurate and representative picture of the preferences of students in each grade level, compared to other sampling methods.
Learn more about Stratified sampling here: https://brainly.com/question/20544692
#SPJ1
Use the image to answer the question. A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3.
Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4. Find the solution to both equations.(1 point)
The intersection point is ()
Answers
The equations given are x - 5y = 3 and 3x - 2y = -4. To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
Find the solution to both equations?One way to solve this system of equations is by substitution. We can solve one equation for x or y, and then substitute that expression into the other equation to eliminate one variable. Let's solve the first equation for x:
x - 5y = 3
x = 5y + 3
Now we can substitute this expression for x into the second equation:
3x - 2y = -4
3(5y + 3) - 2y = -4
15y + 9 - 2y = -4
13y = -13
y = -1
We can now substitute this value for y back into either equation to find the value of x:
x - 5y = 3
x - 5(-1) = 3
x + 5 = 3
x = -2
Therefore, the solution to the system of equations x - 5y = 3 and 3x - 2y = -4 is (-2, -1). This is the point where the solid line and dotted line intersect, as shown in the image.
to know more about equations
brainly.com/question/29657983
#SPJ1
Raphael wants to create a histogram to display the results of a survey in which his coworkers were asked how many hours they spend on the Internet each week. The results of the survey are shown below.
{14, 22, 10, 6, 9, 3, 13, 7, 12, 2, 26, 11, 13, 25}
Match each interval with its corresponding frequency.
Answers
To create a histogram, we need to divide the range of the data into a set of intervals or "bins" and count the number of data points that fall in each bin. We can then represent this information using a bar chart, where the height of each bar corresponds to the frequency (i.e., number of data points) in that bin.
To determine appropriate bin intervals, we can use the range of the data and the number of bins to create equal-width intervals. For example, we could create 5 bins of width 5:
Bin 1: 2 - 6 Bin 2: 7 - 11 Bin 3: 12 - 16 Bin 4: 17 - 21 Bin 5: 22 - 26
We can then count the number of data points that fall in each bin:
Bin 1: 2 Bin 2: 4 Bin 3: 3 Bin 4: 0 Bin 5: 3
Therefore, the intervals and their corresponding frequencies are:
Interval: 2 - 6 Frequency: 2
Interval: 7 - 11 Frequency: 4
Interval: 12 - 16 Frequency: 3
Interval: 17 - 21 Frequency: 0
Interval: 22 - 26 Frequency: 3
We can then use this information to create a histogram, where the x-axis represents the intervals and the y-axis represents the frequencies, with each bar corresponding to an interval and having a height equal to the frequency in that interval.
Identify the type of sampling used. A travel industry researcher interviews all of the passengers on five randomly selected cruises. What sanging ladriganism O A. simple random OB. convenience O C. systematic OD. cluster O E. stratified
Answers
The type of sampling used in this scenario is cluster sampling. This is because the researcher selects five specific cruises to survey, rather than randomly selecting individual passengers from all cruises. The passengers on each of the selected cruises represent a cluster, and the researcher surveys all of them.
Cluster sampling is often used when it is not feasible to sample every individual in a population, but it is possible to identify and sample specific groups or clusters within the population.
Here's a step-by-step explanation:
1. The travel industry researcher selects five cruises randomly. This random selection is the first stage of cluster sampling.
2. The researcher interviews all passengers on these selected cruises, which forms the clusters (groups) in this sampling method.
3. By interviewing every passenger within the chosen clusters, the researcher gathers data for the study.
Cluster sampling is chosen when it's more practical and cost-effective to study specific groups within a population, rather than trying to reach every individual using simple random, convenience, systematic, or stratified sampling. In this case, the clusters are the cruises, and all passengers within those cruises are interviewed.
To learn more about sampling : brainly.com/question/11045407
#SPJ11
EMERGENCY I NEED HELP
Answers
Answer: x = 112
Step-by-step explanation:
a pair of angles which are on the same side but one is interior other exterior.
so the 2 angles are equal
A rock of radioactive material has 500 atoms in it. The number of atoms decreases at a rate of 11% a day. Write an exponential function that models this situation. f(x) type your answer... (1 choose your answer... choose your answer... ✓)^x
Answers
Answer:
[tex]f(x) = 500( {.89}^{x} )[/tex]
Susan's cell phone plan includes unlimited texting. The amount she pays for texting each
month can be described by the function y = 20, where y is the number of dollars spent on
texting as a function of x, the number of texts.
What is true about the function?
It is linear because the rate of change is zero.
It is linear because the rate of change is increasing.
It is nonlinear because the rate of change is zero.
It is nonlinear because the rate of change is
increasing.
Answers
The scale factor of the larger of two similar triangular prisms is 6. The surface area of the smaller prism is 36 ft2. Identify the surface area, rounded to the nearest tenth, of the larger prism
Answers
The surface area, rounded to the nearest tenth, of the larger prism is 1296 square feet.
If the scale factor of the larger prism to the smaller prism is 6, then the corresponding ratio of their surface areas is 6² or 36:1.
Scale factor is the ratio of the lengths of corresponding sides of two similar figures. It is used to determine how much larger or smaller one figure is compared to another, and it is often expressed as a fraction or a decimal.
We know that the surface area of the smaller prism is 36 ft², so we can set up the equation
x = 36 × 36
where x is the surface area of the larger prism.
Simplifying the equation
x = 1296 square feet
Learn more about surface area here
brainly.com/question/28016184
#SPJ4
If anyone is reading this, rn i would be so flipping happy if u got this for me ive been waiting for so long and got nothing please answer correctly please
Answers
Answer: The answer is A.
Step-by-step explanation: Because I am smart don't underestimate me.
Answer:
C
Step-by-step explanation: (look at attachment)
3x + 4 = -2x -2
By looking at the y-intercepts, you automatically know the answer is C.
The y-intercept of the pink line is 4 because of 3x + 4.
The y-intercept of the blue line is -2, because of -2x - 2.
Which equation represents the inverse function m(p),which uses problem we did as the input, and gives minutes worked as the output?
Answers
Answer: Without knowing the specific problem you are referring to, it is impossible to determine the equation for the inverse function m(p).
However, in general, to find the inverse function of a given function f(x), we can follow these steps:
Replace f(x) with y: y = f(x)
Swap x and y: x = f(y)
Solve for y: y = f^-1(x)
The resulting equation y = f^-1(x) represents the inverse function of f(x).
For example, if the function f(x) = 2x + 5, the inverse function can be found as follows:
Replace f(x) with y: y = 2x + 5
Swap x and y: x = 2y + 5
Solve for y: y = (x - 5) / 2
Therefore, the inverse function of f(x) = 2x + 5 is f^-1(x) = (x - 5) / 2.
If you provide more information about the specific problem you are referring to, I can help you find the inverse function.
Step-by-step explanation:
why is it more common to report the standard deviation for grouped data rather than variance for grouped data?
Answers
It is more common to report the standard deviation for grouped data rather than variance for grouped data because the standard deviation is easier to interpret and compare between different groups.
The variance is a measure of the spread of the data, but it is not in the same unit as the original data, making it difficult to interpret. The standard deviation, on the other hand, is in the same unit as the original data, and it provides a more intuitive measure of the spread of the data.
Additionally, the standard deviation can be used to calculate confidence intervals and perform hypothesis tests, which are important statistical tools for analyzing grouped data. Overall, the standard deviation is a more useful and informative measure of variability for grouped data than the variance.
Learn more about deviation:
https://brainly.com/question/475676
#SPJ11
At a grocery store a four pack of yogurt cost $3.95 how much does each container of yogurt cost explain?
Answers
Answer: ~$0.99 (0.9875)
Just divide 3.95 by 4
given: weight a: 140 pounds at 17 inches aft of datum weight b: 120 pounds at 110 inches aft of datum weight c: 85 pounds at 210 inches aft of datum based on this information, the cg would be located how far aft of datum?
Answers
The center of gravity is located 96.7 inches aft of the datum.
To determine the location of the center of gravity (CG) of the system, we need to calculate the moment of each weight about the datum, and then divide the sum of the moments by the total weight of the system.
The moment of each weight is equal to its weight multiplied by its distance from the datum. In this case:
Moment of weight a = 140 pounds x 17 inches = 2,380 inch-pounds
Moment of weight b = 120 pounds x 110 inches = 13,200 inch-pounds
Moment of weight c = 85 pounds x 210 inches = 17,850 inch-pounds
The total weight of the system is:
Total weight = weight a + weight b + weight c = 140 + 120 + 85 = 345 pounds
Therefore, the location of the CG can be calculated as follows:
CG location = (Moment of weight a + Moment of weight b + Moment of weight c) / Total weight
CG location = (2,380 + 13,200 + 17,850) / 345
CG location = 33,430 / 345
CG location = 96.7 inches aft of datum
As a result, the center of gravity is 96.7 inches aft of the datum.
To know more about the Datum, here
https://brainly.com/question/15138411
#SPJ4
ou wish to buy 10 pieces of fruit. there are (indistinguishable) bananas, apples, pears, and strawberries. how many ways are there to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores
Answers
There are 3,256 ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores, assuming that only apples have inedible cores.
To solve this problem, we need to first identify which fruits have inedible cores. We know that apples have cores, but we don't know about the other fruits. Let's assume that only apples have inedible cores for the purposes of this problem.
We want to buy 10 pieces of fruit, but we can only buy at most 2 pieces with inedible cores. This means that we can buy either 0, 1, or 2 apples.
Case 1: 0 apples with inedible cores
If we buy 0 apples with inedible cores, then we can buy any combination of bananas, pears, and strawberries. This is a classic stars and bars problem, and the solution is (10 + 3 - 1) choose (3 - 1) = 66.
Case 2: 1 apple with inedible core
If we buy 1 apple with inedible core, then we need to choose one of the 10 pieces of fruit to be an apple with inedible core. We can then buy any combination of the remaining 9 fruits, which is again a stars and bars problem. The solution is 10 * (9 + 2 - 1) choose (2 - 1) = 220.
Case 3: 2 apples with inedible cores
If we buy 2 apples with inedible cores, then we need to choose two of the 10 pieces of fruit to be apples with inedible cores. We can then buy any combination of the remaining 8 fruits, which is once again a stars and bars problem. The solution is (10 choose 2) * (8 + 3 - 1) choose (3 - 1) = 2,970.
Finally, we add up the number of ways to buy 10 pieces of fruit with at most 2 pieces with inedible cores: 66 + 220 + 2,970 = 3,256.
Therefore, there are 3,256 ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores, assuming that only apples have inedible cores.
Learn more about pieces here:
https://brainly.com/question/31520171
#SPJ11
The coefficient of [tex]x^{10}[/tex] in the expanded polynomial, which represents the total number of ways to buy 10 pieces of fruit with at most 2 inedible cores.
The number of each type of fruit as a polynomial.
Let B(x), A(x), P(x), and S(x) be the generating functions for bananas, apples, pears, and strawberries, respectively.
We can write:
[tex]B(x) = 1 + x + x^2 + x^3 + ...[/tex]
[tex]A(x) = 1 + x + x^2 + x^3 + ...[/tex]
[tex]P(x) = 1 + x + x^2 + x^3 + ...[/tex]
[tex]S(x) = 1 + x + x^2 + x^3 + ...[/tex]
The coefficient of [tex]x^n[/tex]in each polynomial represents the number of fruits of that type you can buy with n selections.
The 1 term in each polynomial represents the possibility of buying 0 fruits of that type.
To count the number of ways to buy 10 pieces of fruit with at most 2 inedible cores, we need to find the coefficient of[tex]x^{10}[/tex] in the polynomial:
[tex](B(x) + A(x) + P(x) + S(x))^{10}[/tex]
Combination of 10 fruits from the total pool of bananas, apples, pears, and strawberries, subject to the constraint that we can only choose up to 2 fruits with inedible cores.
Polynomial using the binomial theorem:
the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
According to the theorem, it is possible to expand the polynomial. [tex](x + y)^n[/tex]into a sum involving terms of the form. [tex]ax^by^c,[/tex] where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b.
For example, for n = 4,
[tex]{\displaystyle (x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}.}[/tex]
The coefficient a in the term of[tex]ax^by^c[/tex] is known as the binomial coefficient. [tex](^n_b)[/tex] or [tex](^n_c)[/tex] (the two have the same value).
These coefficients for varying n and b can be arranged to form Pascal's triangle.
These numbers also occur in combinatorics, where.
[tex](^n_b)[/tex] gives the number of different combinations of b elements that can be chosen from an n-element set.
Therefore
[tex](^n_b)[/tex] is often pronounced as "n choose b".
[tex](B(x) + A(x) + P(x) + S(x))^{10} = (B(x) + A(x) + P(x) + S(x))^8(B(x) + A(x) + P(x) + S(x))^2[/tex]
The right-hand side has the coefficient of [tex]x^8[/tex] in each term as the number of ways to choose 8 fruits from the total pool with at most 2 inedible cores.
The second factor has the coefficient of [tex]x^2[/tex]in each term as the number of ways to choose 2 fruits from the total pool with at most 2 inedible cores. We can expand each of these factors using the binomial theorem, then multiply the resulting polynomials together and find the coefficient of [tex]x^{10}[/tex].
Cumbersome calculation, but it can be simplified by using some algebraic manipulations to group like terms and reduce the number of calculations needed.
For similar questions on Inedible cores
https://brainly.com/question/1529121
#SPJ11
the town council wants to estimate the proportion of all adults in their medium-sized town who favor a tax increase to support the local school system. which of the following sampling plans is most appropriate for estimating this proportion? a random sample of 250 names from the local phone book a random sample of 200 parents whose children attend one of the local schools a sample consisting of 500 people from the city who take an online survey about the issue a random sample of 300 homeowners in the town a random sample of 100 people from an alphabetical list of all adults who live in the town
Answers
The most appropriate sampling plan for estimating the proportion of all adults in the medium-sized town who favor a tax increase to support the local school system is D) a random sample of 100 people from an alphabetical list of all adults who live in the town.
A random sample is needed to ensure that each member of the population has an equal chance of being included in the sample. Among the given options, a random sample of 100 people from an alphabetical list of all adults who live in the town is the most appropriate because it is a representative sample of the entire population of adults in the town.
The other options have potential sources of bias, as follows:
A random sample of 250 names from the local phone book may exclude people who do not have a phone or whose numbers are unlisted.
A random sample of 200 parents whose children attend one of the local schools may be biased towards those who have children in the school system, which may not accurately represent the views of all adults in the town.
A sample consisting of 500 people from the city who take an online survey about the issue may only capture the opinions of those who have access to the internet and are willing to participate in the survey, which may not represent the views of all adults in the town.
A random sample of 300 homeowners in the town may be biased towards those who own homes, which may not represent the views of all adults in the town.
Therefore, a random sample of 100 people from an alphabetical list of all adults who live in the town is the most appropriate sampling plan for estimating the proportion of all adults in the medium-sized town who favor a tax increase to support the local school system. So d is correct option.
For more questions like Sample click the link below:
https://brainly.com/question/31101410
#SPJ11
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches. Which lengths, in inches, could be the length of the third side?
Answers
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
Triangle Inequality Theorem:In a triangle, the length of any side must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides.
We can apply this rule to find the possible lengths of the third side of the triangle, given that the lengths of the two sides are 5.2 inches and 3.1 inches.
Here we have
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches
Let's denote the length of the third side as x. Then, we have:
3.1 + 5.2 > x > 5.2 - 3.1
8.3 > x > 2.1
Therefore, the length of the third side x must be greater than 2.1 inches and less than 8.3 inches.
We can write this as an inequality:
2.1 < x < 8.3
Therefore,
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
Learn more about Triangles at
https://brainly.com/question/12943336
#SPJ1
2. Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his school, 1 mile from his house. The function d gives the distance d(t), in miles, of Tyler from his house t minutes after 7:00 a.m. a. Explain what d(5) = 0.25 means in this context. b. On snowy days, Tyler's school has a 2 hour delayed start time (120 minutes). The function is gives Tyler's distance s(t), in miles, from home t minutes after 7:00 a.m. with a 120 minute delayed start time. If d(5) = 0.25, then what is the corresponding point on the function s? c. Write an expression for s in terms of d. A new function, n, is defined as n(t) = d(t +60) explain what this means in terms of Tyler's distance from school.
Answers
Answer: a. In this context, d(5) = 0.25 means that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. This is because the function d(t) gives the distance of Tyler from his house t minutes after 7:00 a.m.
b. If d(5) = 0.25, then we know that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. If there is a 120-minute delayed start time, then Tyler will walk for 20 + 120 = 140 minutes to reach his school. We want to find the corresponding point on the function s, which gives Tyler's distance from home t minutes after 7:00 a.m. with a 120-minute delayed start time. Since Tyler walks the same distance regardless of the delayed start time, we can use the same function for s as we did for d. Therefore, s(145) = 1.25, since Tyler is 1 mile away from his house after walking for 140 minutes and then an additional 5 minutes to account for the delayed start time.
c. Since Tyler walks the same distance regardless of the delayed start time, we can express s(t) in terms of d(t) by adding 120 minutes to the time t. Therefore, s(t) = d(t + 120).
d. The function n(t) = d(t + 60) gives Tyler's distance from his house t minutes after 8:00 a.m. This is because adding 60 minutes to t corresponds to adding one hour to the time, which means that Tyler leaves his house at 8:00 a.m. instead of 7:00 a.m. Therefore, n(t) gives Tyler's distance from school one hour after he leaves his house.
Step-by-step explanation:
Find the distance, d, of AB.
Answers
The distance between A and B is approximately 8.06 units.
In order to find the distance, d, of AB, we need to use the distance formula. The distance formula gives us the distance between two points in a coordinate plane. It is given as:$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where (x1, y1) and (x2, y2) are the coordinates of the two points in question.
In this case, A and B are the two points for which we need to find the distance. Let's assume that the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2).
Then the distance formula becomes:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
$$d = \sqrt{((8 + 4) - 2)^2 + ((5 - 1) - 3)^2}$$
$$d = \sqrt{(10 - 2)^2 + (4 - 3)^2}$$
$$d = \sqrt{(8)^2 + (1)^2}$$
$$d = \sqrt{64 + 1}$$
$$d \approx \sqrt{65}$$
$$d \approx 8.06$$
Therefore, the distance between A and B is approximately 8.06 units.
For more such questions on distance, click on:
https://brainly.com/question/26550516
#SPJ8
Three machines are used to produce nails. The table displays the total number of nails produced by the 3 machines
over different lengths of time.
Nail Production with 3 Machines
Time (minutes)
Number of Nails
(thousands)
15
16
45
48
55
593
ON
If each machine produces nails at the same rate, how many nails can 1 machine produce in 1 hour?
nails
Answers
One machine can produce 600,000 nails in one hour.
Finding the total number of nails produced by the three machines in a minute and dividing that number by three to obtain the number of nails produced by a single machine in a minute are the first two steps in the solution to this problem.
The number of nails produced by a single machine in an hour can then be calculated by multiplying that number by 60.
Now, we add up the total number of nails produced during :
(15 + 16 + 45 + 48 + 55 + 59 + 3) / 7 = 30
To find the number of nails produced by one machine in one hour, we multiply by 60: 10,000 x 60 = 600,000
To know more about multiplying, here
brainly.com/question/30875464
#SPJ4
justin developed the below hypothesis. h1: younger adults (18-28 years old) spend more time on social media than the middle-aged (29-65 years old) group and older adults (older than 65 years old). what statistical test should he use to test his hypothesis?
Answers
To verify if older adults and middles ages people spend less time on social media, Justin can use the Analysis of variance (ANOVA) test.
ANOVA is used to compare means across two or more groups. Justin can use this test on the different category of younger adults, middle-aged and older adult. This test is done when there is statistically significant difference between the group of samples.
Justin can utilize post-hoc tests (such as Tukey's HSD and Bonferroni) to identify whether particular groups are statistically different from one another if an ANOVA shows a significant difference.
To know more about ANOVA test, visit,
https://brainly.com/question/30127764
#SPJ4
21st term: 3,8,13,18 What is the indicated term
Answers
The 21st term of the sequence 3, 8, 13, 18, .. is 103
To find the indicated term in the sequence, we first need to identify the pattern followed by the sequence. It appears that each term is obtained by adding 5 to the previous term. So, we can write the general formula for the nth term of the arithmetic sequence as
a(n) = a(1) + (n-1)d
where a(1) is the first term of the sequence, d is the common difference, and n is the term number.
In this case, we have:
a(1) = 3 (the first term)
d = 5 (the common difference)
To find the 21st term, we substitute n = 21 in the formula:
a(21) = a(1) + (21-1)d
a(21) = 3 + 20(5)
a(21) = 103
Learn more about arithmetic sequence here
brainly.com/question/16671654
#SPJ4
it is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. an experienced travel agent believes this is wrong. of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. we want to test the travel agent's theory with a hypothesis test. if you used a significance level of 0.05, what is your decision?
Answers
Based on the given information, we can set up the following hypotheses for the hypothesis test:
Null Hypothesis (H0): The actual proportion of people taking the cruise within 1 year is equal to the believed proportion of 5%.
Alternative Hypothesis (H1): The actual proportion of people taking the cruise within 1 year is not equal to the believed proportion of 5%.
Let p be the proportion of people taking the cruise within 1 year. We can use the sample proportion, denoted as p-hat, which is calculated as the ratio of the number of people who took the cruise within 1 year (3 in this case) to the total number of people who requested the brochures (100 in this case).
Given that the significance level is 0.05, we can use a z-test to compare the sample proportion with the believed proportion of 5%. The z-test statistic is calculated as:
z = (p-hat - p) / sqrt(p * (1 - p) / n)
where n is the sample size, which is 100 in this case.
Now we can calculate the z-test statistic and compare it with the critical value for a two-tailed test at a significance level of 0.05. If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis; otherwise, we would fail to reject the null hypothesis.
Since the sample proportion p-hat is 3/100 = 0.03, and the believed proportion p is 0.05, we can substitute these values into the z-test formula:
z = (0.03 - 0.05) / sqrt(0.05 * (1 - 0.05) / 100)
Calculating the above expression, we get the value of z. We can then compare this value with the critical value for a two-tailed test at a significance level of 0.05 from a standard normal distribution table or using a statistical calculator.
If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis and conclude that the actual proportion of people taking the cruise within 1 year is different from the believed proportion of 5%. If the calculated z-test statistic falls within the critical value, we would fail to reject the null hypothesis and not conclude that the actual proportion is different from the believed proportion.
Without the actual values of the calculated z-test statistic and the critical value, we cannot provide a specific decision for this hypothesis test. Please note that hypothesis testing requires careful consideration of the sample size, significance level, and other relevant factors, and should be conducted with caution and in consultation with a qualified statistician or expert in statistical analysis.