Answer:
16
Step-by-step explanation:
When we divide the entire equation by 1/-2 to get rid of the coefficient of n we get n = 16.
In terms of the water lily population change, the value 3.915 represents: the value 1.106 represents:
The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x.
In the given regression equation y = 3.915(1.106)x:
The value 3.915 represents the y-intercept or the predicted value of y when x=0. In the context of the water lily population change, this value could represent the initial population of water lilies or the minimum population that can sustain in the given environment.The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x. In the context of the water lily population change, this value could represent the rate at which the water lily population increases or decreases with respect to some independent variable x, such as time or environmental factors.Learn more about slope here https://brainly.com/question/19131126
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You want to cover a circular window with tinted paper. The window has a radius of 6 inches. How many square inches of tinted paper will you need to use to cover the window
Answer:113.04 in squared
Step-by-step explanation: a=3.14Rsquared
A=3.14 x 6squared 6 x 6=36
A=3.14 x 36
3.14 x 36 = 113.04 inches squared or 113 inches squared
To cover the circular window, you will require a piece of tinted paper measuring approximately 113 in²
The area of the circular window can be found using the formula for the area of a circle:
A = πr²
where A is the area of the circle, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.
In this case, the radius is given as 6 inches, so we can substitute that value into the formula:
A = π (6 inches)²
A = π (36 square inches)
A ≈ 113.04 square inches
Rounding to the nearest tenth gives:
A ≈ 113 square inches
Therefore, you will need approximately 113 square inches of tinted paper to cover the circular window.
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a 3 didget whole number thats divisBle by 6,9,4
gtrgrghtrhthjAnswer:
Step-by-step explanation:
g
Answer:
36
Step-by-step explanation:
4*9=36
9*4=36
6*5=36
what is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?
The probability of having exactly 10 pedestrians crossing from left to right during a 2-minute period is extremely low, at approximately 0.00118%.
We can approach this problem by using the Poisson distribution, which describes the probability of a certain number of events occurring within a given time period, given a known rate of occurrence.
Let X be the number of pedestrians crossing from left to right during a 2-minute period. Since the arrival processes from the left and right sides are independent Poisson processes with rates λL and λR, respectively, we can model X as a Poisson random variable with rate λ = λL + λR = 6.
Therefore, the probability of having exactly k pedestrians crossing from left to right during a 2-minute period is given by the Poisson distribution:
P(X = k) = (e^(-λ) * λ^k) / k!
Now we want to find the probability that in a particular crossing, there are a total of 10 pedestrians crossing from left to right. Let Y be the total number of pedestrians crossing in both directions during a 2-minute period.
Since the arrival processes from the left and right sides are independent, we can model Y as a Poisson random variable with rate 2λ = 12.
Since we know that there are 10 pedestrians crossing from left to right, there must be a total of 10 pedestrians crossing in both directions. Therefore, we want to find the probability that out of the 10 pedestrians, exactly 10 of them are crossing from left to right.
We can use the binomial distribution to calculate this probability. Let Z be the number of pedestrians crossing from left to right out of the 10 pedestrians. Since each pedestrian has an independent probability of crossing from left to right of 1/2, we have:
P(Z = 10) = (10 choose 10) * (1/2)^10
= 1/1024
Therefore, the probability that in a particular crossing, there are a total of 10 pedestrians and they are all crossing from left to right is:
P(X = 10, Y = 10) = P(X = 10) * P(Z = 10)
= (e^(-6) * 6^10 / 10!) * (1/1024)
≈ 0.0000118
Writing this probability in percentage gives = 0.0000118 x 100% = 0.00118%
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Complete question is:
Pedestrians approach a crossing from the left and right sides following independent Poisson processes with average arrival rates of λL = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a light is flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right or from right to left). Assume that the left and right arrival processes are independent, that the light flashes every T = 2 minutes, and that crossing takes zero time – it is instantaneous.
1. What is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?
Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails. To the nearest percent, what is the experimental probability of Project A?
Answer:
Step-by-step explanation:
Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails.
To the nearest percent, what is the experimental probability of Project B?
The experimental probability of Project A is 0.53.
What is Probability?A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
As per the given data:
We are given that there are two projects, Project A and Project B.
A student has to choose one out of the two projects and, the student's choice is represented by the flip of a coin where heads representing Project A and tails representing Project B.
Head's = Project A
Tail's = Project B
Total number of trials = 110
Number of heads in the trials = 58 heads
Number of tails in the trials = 52 tails
For finding out the experimental probability of Project A:
= Number of favorable outcomes / Total number of trials
Number of favorable outcomes = Number of heads
= Number of heads / Total number of trials
= 58 / 110
= 0.53 (approx)
The experimental probability of Project A is 0.53.
Hence, The experimental probability of Project A is 0.53.
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A set of blocks contains blocks of heights 1, 2, and 4 centimeters. Imagine constructing towers by piling blocks of different heights directly on top of one another. (A tower of height 6 cm could be obtained using six 1 cm blocks, three 2 cm blocks, one 2 cm block with one 4 cm block on top, one 4 cm block with one 2 cm block on top, and so forth.) Lett, be the number of ways to construct a tower of height n cm using blocks from the set. (Assume an unlimited supply of blocks of each size.) Use recursive thinking to obtain a recurrence relation for ty, ty, tzo Imagine a tower of height k cm. Either the bottom block has height 1 cm or it has height 2 cm or it has height cm. If the bottom block has height 1 cm, then the remaining blocks make up a tower of height x cm. By definition of t, there are tk-1 such towers. If the bottom block has height 2 cm, then the remaining blocks make up a tower of height x cm. By definition of there are x cm, then the remaining blocks make tx-2 such towers. If the bottom block has height such towers up a tower of height x cm. By definition of there are 1 Select X Therefore, for each integer, n 25,
Answer: Based on the problem statement, we can define a recurrence relation as follows:
t(n) = t(n-1) + t(n-2) + t(n-4)
This means that the number of ways to construct a tower of height n cm can be obtained by considering the possible heights of the bottom block in the tower. If the bottom block has height 1 cm, then the remaining blocks make up a tower of height (n-1) cm, for which there are t(n-1) ways to construct it. If the bottom block has height 2 cm, then the remaining blocks make up a tower of height (n-2) cm, for which there are t(n-2) ways to construct it. If the bottom block has height 4 cm, then the remaining blocks make up a tower of height (n-4) cm, for which there are t(n-4) ways to construct it.
Since we are assuming an unlimited supply of blocks of each size, we can use these blocks repeatedly to construct towers of different heights. Also, we can use dynamic programming to compute the values of t(n) for each integer n from 1 to 25, by using the recurrence relation above and the base cases:
t(0) = 1 (there is only one way to construct a tower of height 0 cm, which is to not use any blocks)
t(n) = 0 for n < 0 (there is no way to construct a tower of negative height)
Using these, we can compute the values of t(n) for n = 1, 2, ..., 25, as follows:
t(0) = 1
t(1) = t(0) = 1
t(2) = t(1) + t(0) = 2
t(3) = t(2) + t(1) = 3
t(4) = t(3) + t(2) + t(0) = 6
t(5) = t(4) + t(3) + t(1) = 10
t(6) = t(5) + t(4) + t(2) = 19
t(7) = t(6) + t(5) + t(3) = 32
t(8) = t(7) + t(6) + t(4) = 61
t(9) = t(8) + t(7) + t(5) = 104
t(10) = t(9) + t(8) + t(6) = 195
t(11) = t(10) + t(9) + t(7) = 332
t(12) = t(11) + t(10) + t(8) = 626
t(13) = t(12) + t(11) + t(9) = 1065
t(14) = t(13) + t(12) + t(10) = 2002
t(15) = t(14) + t(13) + t(11) = 3405
t(16) = t(15) + t(14) + t(12) = 6403
t(17) = t(16) + t(15) + t(13) = 10946
t(18) = t(17) + t(16) + t(14) = 20618
t(19) = t(18) + t(17) + t(15) = 350
Step-by-step explanation:
X^4-3x^2+9x name the polynomial
Answer:
biquadratic polynomial
Step-by-step explanation:
it has degree 4
begging for help lol pleaseee
Step-by-step explanation:
Find the area of the yellow circle using pie times radius squared. Then find the area of the entire circle using the same formula then take the answer for the area of the entire circle - area of the yellow circle
A triangle with side lengths 7, 6, 4 is
Acute
Right
Obtuse
Right
so 7 is the hypotenuse because it is the biggest. so you have to use 6 and 4 in the formula to see if they equal 7.
(a)²+(b)²=c²
(6)²+(4)²=c²
36+16=c²
(square root) 52=c²
the square root of 52 is 7
so therefore it is a right triangle.
Water tank A has 220 gallons of water and is being drained at a constant rate of 5 gallons per minute.
• Water tank B has 180 gallons of water and is being drained at a constant rate of 3 gallons per minute.
Part A
How much time, in minutes, do water tank A and water tank B have to be drained in order for them to have the same amount of water?
PART B
Which water tank, A or B, will be completely drained first?
How much less time, in minutes, will it take this water tank to completely drain than the other water tank?
By answering the presented question, we may conclude that
a) both tanks will have the same amount of water after 20 minutes.
b) difference in time required to thoroughly drain them is: 60 - 44 = 16 minutes.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Part A:
Let's assume that after t minutes, the amount of water remaining in tank A is x gallons, and the amount of water remaining in tank B is also x gallons. We can write equations based on the given information:
Tank A: x = 220 - 5t
Tank B: x = 180 - 3t
To find the time when both tanks have the same amount of water, we can set these two equations equal to each other and solve for t:
220 - 5t = 180 - 3t
40 = 2t
t = 20
Therefore, both tanks will have the same amount of water after 20 minutes.
Part B:
To determine which tank will be completely drained first, we need to find the time it takes for each tank to be completely drained. For tank A, we can set x = 0 in the equation we found in part A:
0 = 220 - 5t
t = 44
So it will take 44 minutes for tank A to be completely drained.
For tank B, we can set x = 0 in the equation given in the problem:
0 = 180 - 3t
t = 60
So it will take 60 minutes for tank B to be completely drained.
Therefore, tank A will be completely drained first. The amount of time it takes for tank A to be completely drained is 44 minutes, and the amount of time it takes for tank B to be completely drained is 60 minutes. The difference in time is:
60 - 44 = 16 minutes.
The difference in time required to thoroughly drain them is: 60 - 44 = 16 minutes.
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the nonparametric tests discussed in your book (wilcoxon rank sum test, sign test, wilcoxon signed rank sum test, kruskal-wallis test, and friedman test) all require that the probability distributions be:
Nonparametric tests can be useful in situations where the data may not follow a specific distribution or where the assumptions of a parametric test are not met.
The nonparametric tests mentioned in your question do not assume any specific probability distribution for the data. Hence, they are called nonparametric tests. These tests are used when the assumptions required for parametric tests (e.g., normality) are not met, or when the data is measured on ordinal or nominal scales rather than continuous ones.
The Wilcoxon rank-sum test, sign test, and Wilcoxon signed-rank test are used to compare two independent or dependent samples. The Kruskal-Wallis test and Friedman test are used to compare three or more independent or dependent samples.
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A figure displays two complementary nonadjacent angles. If one angle measure is 79", what is the other angle measure?
(1 point)
O 21"
O 121°
O 101'
O 11"
ANSWER-
Let the nonadhacent anglesof complementary angle be x and y where, x=79 and y =?
WE KNOW,
x+y=90
or,79+y=90
or, y=90-79
:. y=11,,
calculate the width of an 80% ci for the mean of a normal distribution with unknown variance, sample mean 9, sample variance 6 and sample size 15. use two decimal places.
With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.
The following formula can be used to determine the width of an 80% confidence interval (CI) for the mean of a normal distribution with unknown variance, the sample mean 9, sample variance 6, and sample size 15:
width = t * (s / √(n))
where s is the sample standard deviation (the square root of the sample variance), n is the sample size, and t is the value from the t-distribution with n-1 degrees of freedom for an 80% CI (from a t-table or calculator).
We must first determine the sample standard deviation:
s = √(6) ≈ 2.45
Then, we can find the worth of t from a t-table or mini-computer for a 80% CI with 14 levels of opportunity (15-1):
t = 1.339Lastly, these numbers can be used to calculate the 80% CI width:
width = 1.339 * (2.45 / √(15)) = 1.5With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.
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Given f(x)=5x+7 and g(x)=2x+2, find g(g(1-3w))
Enter as the final value or expression without parentheses
As a result, the final number or expression is g(g(1-3w)) ≈ -12w + 10 (without parenthesis).
Which of these are they known as?When adding extraneous information or perhaps an afterthought to a sentence, parentheses, a pair or punctuation marks, are most frequently utilized. Two curving vertical lines can be seen in parentheses: ( ).
We must first evaluate g(1-3w) and then re-insert that result into g(x) in order to determine g(g(1-3w)).
We must first determine g(1-3w):
Substitute x with 1-3w to get g(x) ≈ 2x + 2 and g(1-3w) ≈ 2(1-3w) + 2.
g(1-3w) ≈ 2 - 6w + 2 (distribute the 2)
g(1-3w) ≈ -6w + 4 (combine similar terms) (combine like terms)
We can again again enter the result of g(1-3w) into g(x):
If you substitute g(1-3w) for x, then g(x) ≈ 2x + 2 g(g(1-3w)) ≈ 2(-6w Plus 4) + 2
g(g(1-3w)) ≈ -12w + 8 + 2 (allocate the 2) (distribute the 2)
g(g(1-3w)) ≈ -12w + 10 (combine comparable terms) (combine like terms)
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Which function results after applying the sequence of transformations to
f(x) = x5?
• stretch vertically by 3
• translate up 1 unit
• translate left 2 units
Answer:
[tex]3(x + 2)^5 + 1[/tex]
Step-by-step explanation:
we have,
[tex]y = x^5[/tex]
1. stretch vertically up by 3
[tex]y = 3x^5[/tex]
2. translate up 1 unit (Y = y + 1)
[tex]y = 3x^5 + 1[/tex]
3. translate left 2 units (X = x + 2)
[tex]y = 3(x + 2)^5 + 1[/tex]
Hopefully this answer helped you!!!
ASAP
Ω = {whole numbers from 2 to 9} A = {even numbers} B = {prime numbers} List the elements in:
a. A’
b. A∩B
c. A∪B
Answer:
a. A' = {3, 5, 7, 9} (complement of A)
b. A∩B = {2} (intersection of A and B, which contains only the even prime number 2)
c. A∪B = {2, 4, 6, 8, 3, 5, 7} (union of A and B, which contains all even numbers and all prime numbers between 2 and 9)
Arrange jn order smallest to largest. 11%, 0. 2, 13%, 3/20, 1/8
Arranged from smallest to largest, the given values are 0.2, 3/20, 1/8, 11%, and 13%.
To compare these values, we need to convert the percentages to decimals. We can do this by dividing them by 100. So, 11% becomes 0.11 and 13% becomes 0.13.
Next, we can convert 3/20 and 1/8 to decimals by dividing them using a calculator. We get:
3/20 = 0.15
1/8 = 0.125
Now, we can arrange these values in ascending order:
0.2 < 0.125 < 0.15 < 0.11 < 0.13
Therefore, the values arranged in order from smallest to largest are 0.2, 3/20, 1/8, 11%, and 13%.
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HELP ME PLEASE ILL GIVE YOU STARS
Answer:
multiply BD and AC and you got it
Step-by-step explanation:
if yuo put ABD triangle over CEB you got a sqare, if you do it again you got a aqare 20x10
Rita started the day with R apps. then she deleted 5 apps and still had twice the amount of Cora (36). write an equation that represents the number of apps both girls have
Answer:
Step-by-step explanation:lllllLet's start by using "R" to represent the number of apps that Rita started with, and "C" to represent the number of apps that Cora started with.
We know that Rita deleted 5 apps, so she would have (R-5) apps remaining. And we know that she still had twice the amount of Cora, which is 36.
So we can write the equation:
R-5 = 2C
And we also know that Cora had 36 apps, so we can substitute that value in for C:
R-5 = 2(36)
Simplifying the right side:
R-5 = 72
Finally, we can solve for R by adding 5 to both sides:
R = 77
So Rita started with 77 apps, and Cora started with 36 apps. We can check that Rita deleted 5 and had twice as many as Cora by plugging our values into the original equation:
77 - 5 = 72
2(36) = 72
Both sides are equal, so our solution is correct.
9 km
7 km
3 km
3 km
3 km
2 km
8 km
9 km
3 km
7 km
Answer: what do you mean? I need more info-
Step-by-step explanation:
I can answer it with more info :)
suppose the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. based on this information, what interval of prices would we expect at least 95% of new car prices to fall within?
New car prices to fall within is $18,300 - $41,900
Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.
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A gamer is observing her score, y, as she plays a video game. She currently has 3,200 points and is gaining 200 points for every minute, x, she plays.
Which of the following equations can be used to describe this linear relationship?
A. y = 3,200x − 200
B.y = 3,200x + 200
C. y = 200x − 3,200
D. y = 200x + 3,200
Answer: d
Step-by-step explanation:
the slope is positive 200 because she is gaining 200 points for every minute which is x. 200x or 200 multiplied by x is her slope and her y intercept is 3200
I will give brainliest to whoever gets it right first along with 20 points. ONLY ANSWER IF YOU KNOW IT!!!!
Ms. Leon will have a total of $840 in her savings account by the end of 4 years.
To calculate the total amount that Ms. Leon will have in her account at the end of 4 years with simple interest, we can use the following formula:
A = P(1 + rt)
where:
A = the total amount in the account at the end of the time period
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
t = the time period (in years)
Putting in the given values, we get:
A = 750(1 + 0.03 × 4)
A = 750(1.12)
A = $840
Therefore, at the end of 4 years, Ms. Leon will have a total of $840 in her savings account.
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Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. ( − 3 , − 4 ) and ( − 5 , − 6 ) (−3,−4) and (−5,−6)
The length of the hypotenuse is 2 times the square root of 5. The Pythagorean theorem can be used to determine the length of the hypotenuse.
How to find distance between two points ?To graph the right triangle with the given points as the hypotenuse, we first plot the points on a coordinate plane . The two points form the endpoints of the hypotenuse, which is the line segment connecting them. We can find the length of this line segment using the distance formula:
distance = [[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2]}[/tex]
In this case, we have:
distance = [[tex]\sqrt{(-5 - (-3))^2 + (-6 - (-4))^2}[/tex]]
distance = [tex]\sqrt{(-5 - (-3))^2 + (-6 - (-4))^2}[/tex]]
distance = [[tex]\sqrt{4 + 4}[/tex]]
distance = [[tex]\sqrt{8}[/tex]]
We can simplify [tex]\sqrt{8}[/tex] by factoring out the perfect square factor of 4:
distance = [[tex]\sqrt{4 * 2}[/tex]]
distance = [tex]\sqrt{4} *\sqrt{2}[/tex]
distance = 2 * [tex]\sqrt{2}[/tex]
Thus, the distance between the two points is 2 * [tex]\sqrt{2}[/tex] ] units.
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130.25.122.63mario's pizzeria bakes olive pieces in the outer crust of its 20-inch (diameter) pizza. there is at least one olive piece per inch of crust. how many olive pieces will you get in one slice of pizza? assume the pizza is cut into eight slices.
By using circumference of circle, we find that In one slice of pizza you will get about 8 olive pieces from Mario's Pizzeria.
The circumference of circle of a 20-inch diameter pizza can be calculated as follows:
Circumference = π × diameter
Circumference = 3.14 × 20
Circumference = 62.8 inches
If there is at least one olive piece per inch of crust, then there will be 62.8 olive pieces on the outer crust of the entire pizza.
If the pizza is cut into eight slices, each slice will have 1/8th of the total circumference of the pizza. Therefore, each slice will have:
62.8 inches ÷ 8 slices = 7.85 inches of outer crust
Since there is at least one olive piece per inch of crust, each slice will have approximately 8 olive pieces on the outer crust.
Therefore, you can expect to get about 8 olive pieces in one slice of pizza from Mario's Pizzeria.
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
40 min 25 min
Answer:
Part A is 8/13 of the whole
Part B is 5/13 of the whole
Step-by-step explanation:
Assuming there are no other parts,
the Whole = A + B is the denominator:
Whole = 40 + 25 = 65
Part A = 40 and Part B = 25 are numerators for each fraction.
The fractions are then:
40/65 and 25/65
Meaning:
Part A is 40/65 of the whole
Part B is 25/65 of the whole
Reducing the fractions, it is also true that:
Part A = 8/13 of the whole
Part B = 5/13 of the whole
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Answer:
(a) No, because for each input there is not exactly one output.
Step-by-step explanation:
You want to know if the relation shown in the graph is a function.
FunctionA relation is a function if its graph passes the vertical line test. That is, a vertical line cannot intercept the graph of the relation at more than one point.
The points (-1, -2) and (-1, 3) will both be intercepted by the vertical line x = -1. This tells us the relation is not a function, because it has two outputs for that input.
<95141404393>
Simplify each epression and state the domain restrictions for each expression. You
MUST show your work (either typing or attaching a file) for full credit.
1.
2.
9x+3
12x+4
2x²+10x
x²+10x+25
The answer and workout is provided in the attachment.
isaac is designing a circular table top that he plans to paint white. the table top has a circumference of 18.84 feet. using 3.14 for , what is the area of the table top rounded to the nearest hundredth?the area of the table top is
The area of the table top is approximately 28.27 square feet. To find the area of a circular table top with a given circumference, we can use the formula A = πr², where r is the radius.
To find the area of the table top, we need to use the formula for the area of a circle, which is:
A = πr²
We are given the circumference of the table top, which is:
C = 2πr
We can solve for r by dividing both sides by 2π:
r = C / (2π) = 18.84 / (2 * 3.14) = 3
Now we can substitute this value for r into the formula for the area of a circle:
A = π(3)² = 9π
Using 3.14 for π, we get:
A ≈ 28.26
Rounding to the nearest hundredth, the area of the table top is approximately 28.27 square feet.
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it is estimated that 45% of the senior class will go to prom this year. if you randomly choose 10 seniors and ask them if they are going to prom, would you use the normal approximation to predict these results?
Yes, we would use the normal approximation to predict these results.
When it comes to hypothesis testing and confidence intervals, the normal distribution plays a crucial role.
When sample sizes are large enough, the normal distribution can be used as a reasonable approximation for the binomial distribution.
This is because the binomial distribution approaches the normal distribution as sample size increases.
To calculate the normal approximation, you will need to determine the mean and standard deviation of the binomial distribution.
The mean is np and the standard deviation is the square root of np(1-p),
where n is the sample size and p is the probability of success.
The probability of success in this case is 45%, or 0.45.
Therefore, the mean is 10 * 0.45 = 4.5 and the standard deviation is the square root of 10 * 0.45 * (1 - 0.45) = 1.37.
Now that you have the mean and standard deviation, you can use the normal distribution to make predictions about the sample.
If you want to find the probability that exactly 5 students will go to prom, for example, you would use the formula for the normal distribution with a mean of 4.5 and a standard deviation of 1.37.
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