The equation of the circle on the y-axis is x² +(y-3)² = 36.
Here we have to find the equation of the circle
Data provided:
diameter(d) = 12 units
so radius(r) = 6 units
The center lies on the y-axis
The general equation of the circle:
(x-x1)² + (y - y1)² = r²
where (x1, y1) is the point on the circle.
So by putting x1 = 0 and y1 = 3 and r = 6 as the center lies of y-axis
x² + ( y - 3)² = 6²
x² + (y-3)² = 36
Therefore we get the equation as x² + (y-3)² = 36
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a college prep school advertises that their students are more prepared to succeed in college than other schools. to verify this, they categorize gpa's into 4 groups and look up the proportion of students at a state college in each category. they find that 7% have a 0-0.99, 21% have a 1-1.99, 37% have a 2-2.99, and 35% have a 3-4.00 in gpa. they then take a random sample of 200 of their graduates at the state college and find that 19 has a 0-0.99, 28 have a 1-1.99, 82 have a 2-2.99, and 71 have a 3-4.00. can they conclude that the grades of their graduates are distributed differently than the general population at the school? test at the 0.05 level of significance.
Answer:
Yes, they can conclude that the grades of their graduates are distributed differently than the general population at the school. This is because the test statistic, chi-squared, is greater than the critical value, which is 7.81. This means that the difference between the observed and expected frequencies is statistically significant.
Step-by-step explanation:
There is a difference between the general population and college prep students in GPA.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
Numbers Observed Proportion Expected (O - E) (O - E)² (O - E)²/E
0 - 0.99 19 0.07 14 5 25 1.79
1 - 1.99 28 0.21 42 -14 196 4.67
2 - 2.99 82 0.37 74 8 64 0.865
3 - 3.99 71 0.35 70 1 1 0.0142
Now, X² = the sum of (O - E)²/E
= 8.33
The P-Value is .039662. The result is significant at p < .05.
Hence,
H₀: There is no difference between the general population and the college prep students in GPA.
H1: There is a difference between the general population and the college prep students in GPA.
Test statistic = 8.33
p - Value = 0.039662
Therefore, the alternate hypothesis is true.
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Complete the equation so that it has infinitely many solutions.
Enter the correct answer in the box in the equation.
Answer:
(2x-286)
Step-by-step explanation:
Answer:
(2x-286
Step-by-step explanation:
step by step
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an eyewitness to a crime said that the license plate of the getaway car began with the letters y and v, but he could not remember the order. the rest of the plate had the numbers 4, 1, 6, 0, and 3, but again he did not recall the order. how many license plates must the police investigate to find the car?
Police must investigate 50 cars to find the car.
What is permutation and combination?
A combination could be a choice of things from a collection that has distinct members, such the order of choice doesn't matter.
Main body:
there are 2 possible position for the first letter.
there is 1 possible position for the second letter.
there are 5 possible position for the first number.
there are 4 possible position for the second number.
there is 3 possible position for the third number.
there are 2 possible position for the second number.
there is 1 possible position for the third number.
the total possibilities are 2 * 1 * 5 * 4* 3 * 2 * 1 = 50
Or we can solve by saying:
There are 2 letters T and V that can be in the first two positions in any order that is 2!, and there are 5 numbers (1,4 , 6 , 0 and 3) that can be in the last 5 positions in any order that is 5!.
Therefore possible arrangement
2! * 5! = 2 * 1 * 5 * 4 * 3 * 2 * 1 = 50
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according to the book of odds, the probability that a randomly selected u.s. adult usually eats breakfast is 0.61.1a) explain what probability 0.61 means in this setting.
The probability of finding such people will get closer to 0.61 as the sample gets bigger.
a) This means that if you were to take a large sample of US adults and inquire them about having breakfast, about 61%(i.e. 0.61) will say that they usually have breakfast.
b) It is, for sure, expected that if we take a sample of 100, around 61% of these americans will say that they usually eat breakfast. But if the number will be 61 exactly is not a certainty and it will vary from sample to sample.
The probability of finding such people will get closer to 0.61 as the sample gets bigger.
Explanation has been provided in the answers above due to their descriptive nature.
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Find the difference between 54 and 9. Is the
answer even or odd?
Answer:
45, odd
Step-by-step explanation:
54-9=45
why in models such as logistic regression we need to estimate the marginal effects of each independent variable in order to understand how a change in one independent variable affects our dependent variable.
Marginal effects can be used to express how the predicted probability of a binary outcome changes with a change in a risk factor. For example, how does 1-year mortality risk change with a 1-year increase in age or for a patient with diabetes compared with a patient without diabetes
Logistic regression, also known as logit regression, logit model, or just logit, is one of the most regression analyses taught at universities and used in data analysis. It is a non-linear model which predicts the outcome of a categorical dependent variable with respect to a vector of independent variables. When performing a logit regression with a statistical package, such as Stata, R or Python, the coefficients are usually provided by log-odds scale. In short, this means that point estimates are complicated to interpret, however the sign and the confidence interval of estimates can be interpreted. For that reason, it is interesting to interpret the logit model in the probability scale, i.e. as probabilities.
Marginal effect:Marginal effects measure the impact that an instantaneous change in one variable has on the outcome variable while all other variables are held constant. In the simple OLS model with linear effects, estimated coefficients are always equal to marginal effects.
Independent Variable:An Independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable. Other factors (such as what they eat, how much they go to school, how much television they watch) aren't going to change a person's age. In fact, when you are looking for some kind of relationship between variables you are trying to see if the independent variable causes some kind of change in the other variables, or dependent variables.
Dependent Variable:Just like an independent variable, a dependent variable is exactly what it sounds like. It is something that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it. Usually when you are looking for a relationship between two things you are trying to find out what makes the dependent variable change the way it does.
Many people have trouble remembering which is the independent variable and which is the dependent variable. An easy way to remember is to insert the names of the two variables you are using in this sentence in they way that makes the most sense. Then you can figure out which is the independent variable and which is the dependent variable:
(Independent variable) causes a change in (Dependent Variable) and it isn't possible that (Dependent Variable) could cause a change in (Independent Variable).
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The image below is my question
The value of the side c which is the hypotenuse of the given right angle triangle using Pythagoras theorem is; c = √148
How to use Pythagoras Theorem?
Pythagoras Theorem is simply the way that we can find the missing length of a right angled triangle. The right angle triangle has three sides, namely the hypotenuse (which is the longest side), Opposite (which does not touch the hypotenuse) and then the adjacent side (which is between the opposite side and the hypotenuse).
The formula is literally;
c² = a² + b²
where;
c is hypotenuse and a and b are opposite and adjacent sides. Thus;
c² = 2² + 12²
c² = 4 + 144
c² = 148
c = √148
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what is the answer i need answers now
Answer:
The answer is third one, 6 and 7/20.
Step-by-step explanation:
First, rewrite the decimal number as a fraction with 1 as the denominator.
[tex]\frac{6.35}{1}[/tex]
Then, multiply to remove 2 decimal places.
[tex]\frac{6.35}{1} *\frac{100}{100} = \frac{635}{100}[/tex]
Next, find the GCF(Greatest common factor) of 635 and 100, which is 5.
Divide both the numerator (top) and denominator (bottom) by the GCF (5)
Simply the improper fraction.
There you go!
a person stands on a scale in an elevator. as the elevator starts, the scale has a constant reading of 590 n. as the elevator later stops, the scale reading is 386 n. assume the magnitude of the acceleration is the same during starting and stopping.
Assuming the person's weight and magnitude, we can estimate their weight to be 491N.
What do we mean by magnitude?A mathematical object's magnitude or size defines whether it is greater or smaller than other items of its kind.
In formal terms, an object's size can be thought of as the outward manifestation of an ordering—of the class of objects to which it belongs.
So, the person's weight will be:
The scale calculates the floor's usual upward force on the passenger.
The most force is produced when going up (when starting an upward trip or ending a downward trip).
The normal force is lowest when there is a downward acceleration.
Regarding any such situation
∑F y =ma y changes to +391Nmg = ma for halting and +591Nmg=+ma for starting. (Where a represents the size of the acceleration.)
Add these two simultaneous equations to eliminate a and determine mg:
+591N−mg+391N−mg=0
OR
982N–2mg=0
Fg = mg = 982N/2 = 491N
Therefore, assuming the person's weight and magnitude, we can estimate their weight to be 491N.
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Complete question:
A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591N. As the elevator later stops, the scale reading is 391N. Assuming the magnitude of the acceleration is the same during starting and stopping, determine the weight of the person.
Consider n circles in a plane. Into how many regions will they divide the plane?
Suppose that n circles divide the plane into rn regions. Now you add another circle, C, that non-trivially intersects each of the first n circles. Start at any point on C and travel around C; you will cross one of the other n circles 2n times.
If p0 and p1 are two consecutive crossings, the arc of C from p0 to p1 divides one of the original rnregions into two smaller regions. You do this 2n times,that gives you a recurrence,
rn+1=rn+some simple function of n,
and you can fairly easily turn it into an expression for rn that is just a summation. If you do it right, it’s a summation that you can evaluate pretty easily in closed form to get a formula for rn.
The plane divide the circle into rn regions.
What is circle?
A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.
Main body:
Suppose that n circles divide the plane into rn regions. Now you add another circle, C, that non-trivially intersects each of the first n circles. Start at any point on C and travel around C; you will cross one of the other n circles 2n times.
If p0 and p1 are two consecutive crossings, the arc of C from p0 to p1 divides one of the original rn regions into two smaller regions. You do this 2n times,that gives you a recurrence,
rn+1=rn+some simple function of n,
and you can fairly easily turn it into an expression for rn that is just a summation. If you do it right, it’s a summation that you can evaluate pretty easily in closed form to get a formula for rn.
Hence , the plane divide the region into rn regions.
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research question: is the average number of people who visit the er every day increasing? it is known the average number of people who visit the er is 145. a sample is collected of 20 hospitals. the average number of people who came to the ers per day was 162, with a sample standard deviation of 45. conduct a hypothesis test based on the research question presented. using an alpha of .05
The result of hypothesis test on the given data null hypothesis is accepted and alternate hypothesis is rejected.
What is hypothesis test?Hypothesis testing is a type of measurable deduction that utilizes information from an example to make determinations about a populace boundary or a populace probability distribution. Initial, a conditional supposition that is made about the boundary or dispersion. This supposition that is known as the invalid speculation and is meant by H0.
According to question:We have,
mean(X) = 162, n = 20 , standard deviation(σ) = 45,
Let us consider Null hypothesis H₀: μ=145
And alternate hypothesis Hₐ : μ[tex]\neq[/tex] 145
So, Z = X - μ/σ/√n
Z = 162 - 145/45/√20 = 1.68
Now Level of significance(α)= 0.05
From the Z table,
Z = 1.96
So, 1.68 < 1.96
Thus, Null hypothesis is accepted and alternate hypothesis is rejected.
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Which equation has the solution x = 5? Select each correct answer. Responses 32−4x=12 32 minus 4 x equals 12 25x+4=9 25 over x end fraction plus 4 equals 9 x5+5=6 x over 5 end fraction plus 5 equals 6 18−2x=9 18 minus 2 x equals 9 11 + 6x = 22
Answer:
32−4x=12,
25 over x end fraction plus 4 equals 9 ((25)/(x)+ 4 equals 9), and
x over 5 end fraction plus 5 equals 6 ((x)/(5) plus 5 equals 6)
Step-by-step explanation:
hope this help
Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number
The lateral surface area is 667.92 m² and surface area is 1081.92 m².
What is lateral surface area?The lateral surface area of a three-dimensional object is the surface area of the object minus the area of its bases.
Given is a triangular prism,
Lateral surface area = (side1 + side2 + side3)xh = (8+9+12.04)x23 = 667.92 m²
Surface area = (side1 + side2 + side3)xh + 2base area = 667.92 + 9x23x2 = 1081.92 m².
Hence, The lateral surface area is 667.92 m² and surface area is 1081.92 m².
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20 students selected macaroni and cheese and 16 students chose the cajun potato barrels. each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). which of the following prevents this study from being a well-designed experiment?
The students weren't assigned the treatments (new menu item) at random.
In an experiment, randomization refers to assigning volunteers randomly to the treatment. For example, we may define randomization as setting people to therapy at random.
The results are fair because randomization eliminates bias. To make the results of the experiment precise, it ensures that the groups created for experimenting are as similar to one another as possible.
In the given example, the menu items are not randomly assigned. Because the students were given a choice to choose a menu item instead of selecting the new menu item randomly. If randomly assigned all the new menu items will have an equal probability of being chosen.
Therefore, option b is the correct option.
The complete question is -
Thirty-six students at a local middle school were randomly selected to participate in a taste test to select a new menu item for a cafeteria. Each student was given a choice between the macaroni and cheese and the Cajun potato barrels. From the sample, 20 students selected macaroni and cheese and 16 students chose the Cajun potato barrels. Each student was asked to rate the item they chose on a scale from 1 (extremely dislike) to 9 (extremely like). Which of the following prevents this study from being a well-designed experiment?
a) There was no replication because students did not eat both menu items.
b) The treatments (new menu item) were not randomly assigned to the students.
c) An item that is currently on the menu should have been used as a control.
d) Students should not have been randomly selected.
e) There were no problems, and the study was a well-designed experiment.
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Kai is using 16-inch square tiles to tile a square area that is 9 feet long on each side. What is the least number of tiles he can use for the square area?
Answer:
144 if u multiply u will get ur answer because it is asking for the least number if 144 is to high that its got to be 1 which it can't that's if u divide it answer - 144
If staff salaries were $44,000/month last year and $53,000/month this year, what is the approximate labor cost increase in percentage?.
Given that the pay was $44,000 last year and $53,000 this year, the compensation will have increased by 20.45%.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal parts are considered to make up the whole.
Here,
Salary of staff last year=$44,000
Salary of staff this year=$53,000
The percent increase,
=(53000-44000)/44000*100
=20.45%
The percent increase in the salary will be 20.45% as the salary last year was $44,000 and the salary this year is $53,000.
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(-7, 8) and (-7, 5)
Find the slope
Answer:
Slope is undefined
Step-by-step explanation:
slope = [tex]\frac{\Delta y}{\Delta x}[/tex]
[tex]\frac{5-8}{-7-(-7)}=\frac{-3}{0}[/tex]
Anything divided by zero is undefined
This should make sense visually as the points describe a vertical line at [tex]x=-7[/tex]
which equation represents a proportional relationship A. y=4x B. 5x+2 C. y= 7 D. y= 3x²
Answer:
The answer is A) [tex]y=4x[/tex]
Step-by-step explanation:
This is because y directly corresponds to x, if x is 1, then y = 4, if x is 2, then y = 8 and so on.
a test of which hypothesis is most important when deciding whether to use a simple linear regression model to predict y from x?
The most important measure used in regression diagnostics is the simple residual.
What is linear rigression?
In statistics, a scalar response and one or more explanatory factors are modeled using a linear approach called linear regression. Simple linear regression is used when there is only one explanatory variable; multiple linear regression is used when there are numerous explanatory variables.
Hypothesis testing is used to confirm if our beta coefficients are significant in a linear regression model. Every time we run the linear regression model, we test if the line is significant or not by checking if the coefficient is significant.
If there is a significant linear relationship between the independent variable X and the dependent variable Y, the slope will not equal zero.
The null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.
The most important measure used in regression diagnostics is the simple residual (e). This is the difference between each observed and predicted value of Y.
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x+y=8 now let x=0 what is y
Answer: Y = 8
Step-by-step explanation: If x = to 0 then 0+y=8 therefore y=8
Hope this helps
Answer:
y = 8
Step-by-step explanation:
Given information,
→ x + y = 8
→ x = 0
Now the value of y will be,
→ x + y = 8
→ 0 + y = 8
→ y = 8 - 0
→ [ y = 8 ]
Hence, the value of y is 8.
if the mean result from the four tests is compared to the criterion 140 mg/dl, what is the probability that shelia is diagnosed as having gestational diabetes?
The probability that Shelia is diagnosed as having gestational diabetes is 0.003.
In the given question,
A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested.
Mean 129 mg/dl and standard deviation 9 mg/dl.
I have to find the probability that Shelia is diagnosed as having gestational diabetes
Z value corresponding to the mean result of 140 mg/dl is
(140-129)/4 = 2.75
Thus, the probability that Shelia is diagnosed as having gestational diabetes = P(Z > 2.75) = 0.003
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The right question is:
Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with mean 129 mg/dl and standard deviation 9 mg/dl. Let LL denote a patient's glucose level.
If the mean result from the four tests is compared to the criterion 140 mg/dl, what is the probability that Shelia is diagnosed as having gestational diabetes?
If units of a certain commodity are produced, then the marginal cost is dc/da = 9x^2+4x+15x ^1/4 + 10. Suppose the total cost of producing the 1st unit is 100. Calculate the total cost of producing the first 16 units. (calculus 1)
If a certain unit of a commodity is produced with a marginal cost of [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex], the cost of producing the first 126 units is 289.4
How to differentiate a function?
Differentiation is a way of showing rate of change of a function at a given time.
The given function [tex]\frac{dc}{da} =9x^{2}+4x+15x^{1/4} +10[/tex],
Differentiate with respect to x
[tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]
input the value 100 for the value of x,
This implies that [tex]\frac{dc}{da} =18x+4+\frac{15}{4} x-^{3/4}[/tex]
[tex]\frac{dc}{da}[/tex]=1800+4+[tex]\frac{15}{4}[/tex] x[tex]\frac{1}{\sqrt[4]{100^{3} } }[/tex]
[tex]\frac{dc}{da}=1800+4+\frac{15}{4}x\frac{1}{3.16}[/tex]
Simplifying further
[tex]\frac{da}{da} =1804+4.75[/tex]
[tex]\frac{dc}{da} =1808.75\\[/tex]
To produce the first 16 units,
[tex]\frac{1808.75}{100} }[/tex] x [tex]\frac{16}{1}[/tex]
The cost of producing the first 16 units is 289.4
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mary spent a total of $322.58 for a party. she spent $200.14 on food, plus an additional $30.61 for each hour of the party. how long was the party?
Answer: 4 hours
Step-by-step explanation:
322.58 - 200.14 = 122.44
122.44 divided by 30.61 = 4
1
5
Lian's dog eats of a bag of dog food each week. Lian currently has of a bag
20
8
remaining.
How many weeks will it take Lian's dog to finish this remaining food? .
weeks
It will take Lian's dog 12.5 weeks to finish the remaining food
How to determine how many weeks will it take Lian's dog to finish the remaining food?Fractions are numbers written as a quotient, in which a numerator is divided by a denominator
Given that:
Lian's dog eats 1/20 of a bag of dog food each week
Lian currently has of a bag 5/8 remaining
Since Lian's dog eats 1/20 in one week and 5/8 is remaining.
In order to find the number of weeks it will take the dog to finish the remaining food. We can say:
Number of weeks = remaining food / food for one week
Number of weeks = (5/8) / (1/20) = 12.5 weeks
Therefore, it will take Lian's dog 12.5 weeks to finish the remaining food
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Complete Question
Lian's dog eats 1/20 of a bag of dog food each week. Lian currently has 5/8 of a bag remaining.
How many weeks will it take Lian's dog to finish this remaining food?
a 26 year old policyholder with a car worth $20,000 is predicted to make 28 claims. b) holding x2 constant, a one year increase in x1 will result in a decrease of 0.5 in the predicted value of y. c) holding x1 constant, a one thousand dollar increase in x2 will result in an increase of 0.1 in the predicted value of y.
The answer statements,
a) True
b) False
c) True
IHI Insurance in the given question is implemented using the linear regression analysis because it is used in the question to calculate the value of the number of yearly claims led by policyholders for motor insurance (y) (x2).
As per the question, at random 500 policyholders were selected.
The range of ages of people are between 16 to 70 years
The price range for the cars is between $1100 to $52000
According to the linear regression equation given in the question,
⇒ I = 13 + (-0.5)x1i + (0.1)x2i
a) [tex]y^{i}[/tex] = 13 + (0.5)x1i + (0.1)x2i
Given, x1i = 26, x2i = 20
⇒ [tex]y^{i}[/tex] = 13 + (-0.5)(26) + (0.1)(20)
⇒ [tex]y^{i}[/tex] = 2
Thus, it is not equal to the claim i.e. 28, so option b is false
According to the answer derived in option b,
We can see that the coefficient of x 1i is negative and such that it will be decreased by 0.5
Thus, option a is true
Now as the coefficient of x 2i is positive it will increase by 0.1
Thus, option c is true
Therefore, option a) is true, option b) is false and option c) is true.
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IHI Insurance has conducted a multiple linear regression analysis to predict the value of the number of annual claims incurred by a motor insurance policyholder (y)based on the age of the policyholder in years (x1) and the value of the car insured in thousands of dollars (x2). The analysis was based on a random sample of 500 policyholders. The ages in the sample ranged from 16 to 70 and the values of the cars in the sample ranged from $1,100 to $52,000. The multiple linear regression equation corresponding to IHI's analysis is y^i = 13 + (-0.5)x1i + (0.1)x2i.
Select whether the following statements regarding the multiple linear regression equation are true or false:
a 26-year-old policyholder with a car worth $20,000 is predicted to make 28 claims.
b) holding x2 constant, a one-year increase in x1 will result in a decrease of 0.5 in the predicted value of y.
c) holding x1 constant, a one thousand dollar increase in x2 will result in an increase of 0.1 in the predicted value of y.
Which of the following expressions is equivalent to (y − 3)4?
A) y4 − 12y3 + 54y2 − 108y + 81
B) y4 + 12y3 + 54y2 + 108y + 81
C) y4 − 27y3 + 9y2 − 3
D) y3 − 9y2 + 27y − 27
The binomial expansion of (y - 3)⁴ is B) y⁴ - 12y³ + 54y² - 108y + 81.
What is the binomial theorem?The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.
An expression of two terms having a degree n can be represented as,
(a - b)ⁿ = [tex]^nC_na^n - ^nC_{n-1}a^{n-1}b+^{n}C_{n-2}a^{n-2}b^2+...(-1)^n\times^nC_0a^0b^n[/tex].
Given, (y - 3)⁴ = [tex]^4C_4y^4.3^0 - ^4C_3y^3.3 + ^4C_2y^23^2-^4C_1y.3^3+^4C_0y^03^4[/tex].
(y - 3)⁴ = y⁴ - 12y³ + 54y² - 108y + 81.
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suppose we play a game where we roll a six sided dice. if a 4,5 or 6 is rolled, i get 1 point if a 1,2,3 is rolled,you get 1 point. we play first to 5 but the winner must also win by 2. if we are tied at 5, what's the probability that you win the game?
The probability that you win the game is 50%.
The game is symmetrical for you and your opponent. Thus, your probability of winning is as good as your opponent's, so, you have a 50% of winning.
What does symmetric mean in probability?Symmetry goes into play in probability theory in this way: if different outcomes are equivalent, they would have the same probability.
A symmetrical distribution happens when the values of variables come at regular frequencies and usually the mean, median, and mode all happen at the same point.
In general, if there are N symmetrical outcomes, the probability of any given one of them happening is taken to be 1/N.
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three couples have reserved seats in a row for a concert. in how many different ways can they be seated when
a) If there are no seating restrictions, there are 720 different ways that three couples can be seated.
b) If each couple sits together, there are 48 different arrangements for three couples to be seated.
What is Fundamental counting principle?
If an event can happen in m different ways and another event can happen in n different ways, then the sum of the occurrences of the two events is m x n.
Given:
Three couples have reserved seats in a row for a concert.
(a) There are 3 couples, so 6 people must be seated in seats in row.
It is permutation of 6 elements, therefore, there are
6!=720 ways three couples can be seated when there is no seating restriction.
(b) We want that each couple sits together.
First we will find the number of permutations of 3 couples:
There are 3!=6 permutations of couple. (they can be ordered in 6 different ways).
Now we will find the number of permutations of each couple:
There are 2!=2 permutations of 2 people that makes a couple.
Therefore, by Fundamental Counting Principle, there are
3! ⋅ 2! ⋅ 2! ⋅ 2! = 6 ⋅ 2 ⋅ 2 ⋅ 2 = 48
ways three couples can be seated when each couple sits together.
Hence,
a) If there are no seating restrictions, there are 720 different ways that three couples can be seated.
b) If each couple sits together, there are 48 different arrangements for three couples to be seated.
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Complete question:
Three couples have reserved seats in a row for a concert. In how many different ways can they be seated when (a) there are no seating restrictions? (b) each couple sits together?
3. The function h(x) is a transformed function of f(x) = |x|. The transformation is as follows: 3 units vertical shift down, 2 units horizontal shift right.
a. Write the transformed equation, h(x).
b. Graph f(x) and h(x) on the same coordinate plane. Be sure to label the functions f(x) and h(x). This must be graphed by hand or by using the tools in Word. You may not use a web-based graphing program.
a. The transformed equation is given as follows: h(x) = |x - 2| - 3.
b. The graph of the two functions is shown by the image presented at the end of the answer.
What are translations?The translations are movements to the triangle in each of these directions:
Up.Down.Left.Right.The parent function in this problem is given as follows:
f(x) = |x|.
The first translation was a vertical translation three units down, hence we have that:
g(x) = f(x) - 3 = |x| - 3.
The second translation was a horizontal translation two units right, hence the have that the definition of the transformed equation h(x) is given as follows:
h(x) = g(x - 2) = |x - 2| - 3.
The graph of the functions is given by the image shown at the end of the answer, and the translations are verified on every point of the function, but especially the vertices.
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Trapezoid abcd has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1). Is this trapezoid an isosceles trapezoid? select from the drop-down menu to correctly complete the statement. Trapezoid abcd choose. An isosceles trapezoid.
The given trapezoid ABCD is an isosceles trapezoid and has vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1).
What is trapezoid?Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides. This article provides formulas for the area of the trapezium as well as its types, properties, and other trapezoids.
Here,
Segments AB and CD are parallel and 3 units apart.
Point D is 2 units left of point A, and point C is 2 units right of point B. The trapezoid is symmetrical about the line x = 3.5, so is isosceles.
The given Trapezoid ABCD that has given vertices a(2, 4), b(5, 4), c(7, 1), and d(0, 1) is a isosceles trapezoid.
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