To graph a rational function on a graphing calculator, enter the equation into the Y= editor, then press the graph button. The calculator will display the graph of the rational function.
1. Enter the equation for the rational function into the Y= editor of your graphing calculator. Be sure to include all terms, coefficients, and operators.
2. Press the graph button. This will tell the calculator to generate the graph of the equation.
3. The calculator will display the graph of the rational function, including any asymptotes, zeroes, and intercepts.
4. Adjust the window settings as desired to get a better view of the graph. This can be done by pressing the WINDOW button, then setting the appropriate Xmin, Xmax, Ymin, and Ymax values.
5. Press the GRAPH button again to view the adjusted graph.
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PLEASE HELP I NEED IT ASAP
Which description of a figure and its image match the transformation described by (x,y) → (-x+1,y+1)
Answer:
the figue which is translated one unit up and one unit to the right
Step-by-step explanation:
Identify the measure of angle EHF:
Answer:
63
Step-by-step explanation:
h=90
90-27=63
ou are offered a free play at the following game: ten balls are numbered 1 through 10. three are selected at random (each combination equally likely). before balls are drawn, players try to guess which three numbers are drawn by filling out a ticket. neither the order that the player selects the numbers nor the order in which the balls are drawn matters. how many outcomes are in the sample space for this experim
The outcome in sample space is equal to the no. of ways of selecting 3 balls at random from 10 distinct balls. So, number of outcomes in sample space = ¹⁰C₃.
Permutation:
Permutations are different ways of arranging objects in a particular order. This can also be expressed as rearranging the elements in linear order of an already ordered set. The symbol are used to denote the number of permutations of n distinct objects obtained for each r. Block bus, train and plane timetables, postcode and phone number assignments. These are some situations where permutations are used.
Example: There are 5 chairs and 3 people need to sit on them. There are 5 ways to place the first person. 2nd person 4 seats, 3rd person 3 seats. So to find the number of ways to place her 3 on 5 chairs, multiply these ways. Make 5×4×3 streets. So we can do it 60 ways. 5 × 4 × 3 is written as (5!) / (2!) (or) (5!) / (5 - 3).
Combination:A combination is a selection of elements from a set with different members, so the order of selection does not matter (unlike a permutation). For example, if he is given three fruits, such as apples, oranges, and pears, he has three binary combinations that he can draw from this set. An apple and a pear. apples and oranges. Or pear and orange. More formally, a k-combination of a set S is a subset of the k distinct elements of S. Two combinations are identical only if each combination has the same members.
According to the Question:
The outcome in sample space is equal to the no. of ways of selecting 3 balls at random from 10 distinct balls. So, number of outcomes in sample space = ¹⁰C₃.
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A group of friends were hanging out discussing the movies. They discovered that altogether, they went to the movies 30 times last year. Clio went 5 times as often as alex. Bernice went 2 more times than alex. How many times did clio go to the movies last year?.
Clio went 20 times to the movies last year. This can be calculated using linear equations.
Given,
Number of times all together they went to movies = 30
Clio = 5 times more than Alex
Bernie = is 2 times more than Alex.
Let 'a' be the number of times Alex has gone to the movie:
Clio = 5a
Bernie = a + 2
So, we can calculate the number of times Clio went to the movies if we find out how many times Alex went. This can be calculated using the following linear equation:
Clio + Bernie + Alex = 30
5a + (a +2) + a = 30
7a + 2 = 30
7a = 30 - 2
7a = 28
a = 28 ÷ 7
a = 4 times
From solving the above equation, we got that Alex (a) went to the theatre 4 times last year. Now, substituting the value of 'a' we get:
Clio = 5a
Clio = 5*4 = 20 times
Bernie = a+2 = 4+2 = 6 times
So, we can conclude by saying that, Clio went 20 times to the movies last year.
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a biologist had mice and rats run through a maze and recorded the number that finished the maze successfully and the number that did not. the table below shows the results of the study: mice rats finished: 22 25 did not finish: 26 12 suppose we use this data along with a .05 significance level to test the claim that the rodent type and the success of finishing the maze are not related. what can we conclude?
Answer:3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
Step-by-step explanation:For each time that the rat goes through the maze, there are only two possible outcomes. Either he fails it, or he succeds. The trials are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution:The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.In which is the number of different combinations of x objects from a set of n elements, given by the following formula.And p is the probability of X happening.
What is the probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt?Missing on the first six, each with 70% probability(P(X = 6) when p = 0.7, n = 6).Succeeding on the 7th attempt, with p = 0.3. So 3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
1. The line parallel to y=2/3x+1
that passes through the point (3, 6)
The equation of the line is y = (2/3)x + 4
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line.
y = m(1)x + c
The line is parallel to y = (2/3)x + 1
It is in the form of y = m(2)x + c
This means,
m(1) = m(2)
m(1) = 2/3
Now,
The line passes through the point (3, 6).
(3, 6) = (x, y)
y = mx + c
6 = (2/3)3 + c
6 = 2 + c
c = 6 - 2
c = 4
The equation of the line.
y = (2/3)x + 4
Thus,
The equation of the line is y = (2/3)x + 4
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How do you get 1/2 of a number?
Answer: to get 1/2 of a number, simply divide it by 2
Step-by-step explanation: the denominator, or the second digit after the numerator, is the one you use to divide a number. for example 1/3 of 33 = 11, as you divide 33 by 3, or 1/2 of 500 = 250.
A set of magical wand prices are normally distributed with a mean of 505050 dollars and a standard deviation of 444 dollars. A blackthorn wand has a price of 45. 2045. 2045, point, 20 dollars. What proportion of wand prices are lower than the price of the blackthorn wand?.
The proportion of wand prices as per normal distribution are lower than the price of the blackthorn wand is equal to 0.1151.
As given in the question,
Mean of the set of magical wand price 'μ' = 50dollars
Standard deviation 'σ' for normal distribution = 4 dollars
Price of blackthorn wand 'X' = 45.20 dollars
z-score = (x - μ)/σ
Proportion of wand prices be 'x'
P(x < X)
=P( x< 45.20)
=P [(x - μ)/σ < (X - μ )/σ]
=P[ z < (45.20 - 50)/4]
=P( z < -1.2 )
= 0.11507
=0.1151
Therefore, the proportion of the wand prices which are lower than the price of blackthorn wand using normal distribution is equal to 0.1151.
The complete question is:
A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackthor wand has a price of 45.20 dollars. What proportion of wand prices are lower than the price of the blackthorn wand? You may round your answer to four decimal places.
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Help with question 13
The amount of stock that is wasted is given as follows:
1 - 21/64 inches.
How to obtain the amount of stock wasted?The total amount of stock is given as follows:
9 - 7/16 inches long = 144/16 - 7/16 = 137/16 inches long.
The total amount of stock used for the two punches is given by the sum of the two amounts, as follows:
4 - 1/64 + 4 - 3/32 = 8 - 7/64 = 505/64
Then the amount wasted is given by the subtraction of the total amount by the amount used, as follows:
137/16 - 505/64 = 548/64 - 505/64 = 43/64.
The decimal of this is of:
43/64 = 0.671875.
Hence the amount wasted is of:
1 - 43/64 = 64/64 - 43/64 = 21/64
Meaning that the third option is correct.
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Which of these relations is a function?
last question!!!!!!!!
Answer: the top left is a function
Lauren and Hazel's families provide money for their school lunch accounts. Hazel starts with $200 in her account. She spends $30 each week on lunches. Lauren starts with $50 in her account and does not spend any of it. Her family adds $20 each week to her account. Write an equation to represent how much money (y) Hazel has in her account after a number of weeks (x).
908 × 65 please help me with this question
Answer:
Step-by-step explanation:
59,020
Interest Earned over One Year
Answer: $300,000
Step-by-step explanation:
Translate a point (x,y) 3 units left and 5 units up. Then translate the image 5 units right and 2 units up. What are the coordinates of the point after the translations?
Answer:
[tex](x+2, y+7)[/tex]
Step-by-step explanation:
[tex](x,y) \longrightarrow (x-3, y+5) \longrightarrow (x+2, y+7)[/tex]
On the first day of a song's release, it had 20 million streams. If the number of streams increases by 10% per day, how many streams will there be on the seventh day? round to the nearest million.
Nearest Twenty-one million streams will be available on the seventh day of song's release day. So, the correct option is option(A).
As we know the formula for the increase of population for compond increasing rate
A = P(1 + r)ᵗ---(1)
where P --> the intial population
r --> rate in decimal
t --> the time
A --> final population after t years
We have given that,
On the first day the song's release , it streams around 20 million population.
Rate of increase= 10% per day
We have to find the number of streams on seventh day.
so, time is 6 for it.
we have , P= 20 million ; t= 6
r = 10% = 10/100 = 0.1
putting all values we get,
A = 20 ( 1 + 0.1 )⁶
=> A = 20(1.01)⁶
=> A = 21.23
so the numnber of stream is 21.23 million ~ 21 million on seventh day.
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Complete question:
On the first day of a song's release, it had 20 million streams. If the number of streams increases by 10% per day, how many streams will there be on the seventh day? Round to the nearest million.
a)21 million
b)35 million
c)37 million
d) 38 million
Can someone pls tell me how many boxes he can afford it’s due at 11:59 tonight!!
Answer:
You have chosen the correct answer
Step-by-step explanation:
He cannot spend more than 55. So the cost of the groceries has to be 55 or less.
He is only buying one package of eggs and the x represents how many packages of sugar he can purchase knowing that each box costs 11.50.
Help please.................
The solution to the expression ( √7 - √2 )² will be - 9 - 2√14. The value of the second part is 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is ( √7 - √2 )². The expression will be solved as below,
E = ( √7 - √2 )²
E = (√7)² + (√2)² - 2 x √7 x √2
E = 7 + 2 - 2√14
E = 9 - 2√14
The second part will be calculated as,
2/5√(25x3)+(2-√(2x2x6)
2/5 x 5√3 + 2 - 2√3
2√3 + 2 - 2√3
2
The value of the third part will be calculated as,
[tex]\dfrac{(2+\sqrt{2})(\sqrt(10-\sqrt{5}}{(15-10\sqrt{2}}[/tex]
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Pre-image ABCD was dilated to produce image A'B'C'D'.
What is the scale factor from the pre-image to the image?
Enter your answer in the box as a fraction in simplest form.
The scale factor from the pre-image to the image is 2/5.
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
let the scale factor be m, so that the scale factor multiplied by the dimension of pre-image should give dimension of image.
so that we have,
20 x m = 8
20m = 8
divide both sides by 20
m = 8/20
m = 2/5
In conclusion the dilation factor is 2/5
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Ann work in a upermarket for $10. 00 an hour. If her pay i increaed to $12. 00, then what i her percent increae in pay?
Her pay will increase by 20% as a result of the percentage being the difference from the original.
What is Percentage ?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 78% grade if you answered 78 of 100 questions correctly on a test (78/100).
According to the given Information
Another name for the percentage is the signifying hundredths. As a result, 2% is equal to two hundredths, or 2%=2/100=0.02.
According to what has been stated,
Original price: $10
Pay increase = $12
% growth = (10 x 100 - (12 - 10))
⇒ 20%
Hence
Her pay will increase by 20% as a result of the percentage being the difference from the original.
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Evaluate the expression for the given value of the variables.
0.7g - 2.7h
g= 17, h =2
Answer:
6.5
Step-by-step explanation:
Step 1: Plug in g = 17, h = 2
0.7 * 17 - 2.7 * 2
Step 2: Solve Using PEMDAS
11.9 - 2.7 * 2
11.9 - 5.4
6.5
Which of these fractions is equivalent to the fraction in this image?
1 of 3 slices of pizza
1) 4/12
2) 3/12
3) 2/12
4) None of these is correct.
Answer:
4/12
Step-by-step explanation:
What is quadrilateral with two distinct pairs of congruent and adjacent side?? a quadrilateral with two pairs of adjacent, congruent sides. it has perpendicular diagonals and one pair of opposite interior angles that are congruent. if you draw midsegments between adjacent sides of this quadrilateral, you form a parallelogram.
A quadrilateral with two distinct pairs of congruent and adjacent side is a kite.
A quadrilateral is a figure that has 4 sides and edges. Parallelogram, rectangle, square are all examples of quadrilateral.
Different quadrilaterals have different properties. A quadrilateral in which two distinct pairs of adjacent sides are congruent is termed as a kite.
Only kite is a quadrilateral which has the given property.
Some other properties of kite include-
1. diagonals of a kite are perpendicular to each other
2. along its main diagonal, a kite is symmetrical
3. one of the diagonals of the kite bisects the other
Thus, a quadrilateral with two distinct pairs of congruent and adjacent side is a kite.
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Is the coordinates of a point are 3 and 4?
The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)
The coordinates of point A = (-5, -4),
The coordinates of the point B = (-3, 3)
Let the point at the distance 3/4 from A to B = P
The coordinates of point 3/4 from A to B = P
At the x-coordinate, the distance from B to A is = -3-(-5) = 2 units.
At the y-coordinate, the distance from B to A is = 3-(-4) = 7 units.
Hence, the coordinates of P = (-5 + (3/4×(x-coordinate), -4 + 3/4×(y-coordinate)
P = (-5 + (3/4×(2), -4 + 3/4×(7))
P = (-3.5, 1.25)
Hence, the coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25).
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The complete question is -
What are the coordinates of the point 3/4 of the way from A to B?
Liam has a points card for a movie theater.
• He receives 50 rewards points just for signing up.
He earns 12.5 points for each visit to the movie theater.
He needs at least 160 points for a free movie ticket.
Write and solve an inequality which can be used to determine , the number of visits
Liam can make to earn his first free movie ticket.
Answer:
x >= 9.
Step-by-step explanation:
To earn a free movie ticket, Liam needs at least 160 points. He already has 50 points from signing up, so he needs 160 - 50 = <<160-50=110>>110 more points.
Each visit to the movie theater earns Liam 12.5 points, so the inequality representing the number of visits he needs to make is:
12.5 * x >= 110
To solve this inequality, we need to divide both sides by 12.5:
12.5 * x / 12.5 >= 110 / 12.5
This simplifies to:
x >= 8.8
Thus, Liam needs to make at least 9 visits to the movie theater to earn his first free movie ticket.
Therefore, the solution to the inequality is x >= 9.
Answer:
9 visits
Step-by-step explanation:
12.5 x 9 = 112.5
112.5 + 50 = 162.5
in last 20 years, 238 couples have divorced out of a random sample of 500 couples in a certain city. find a 95% confidence interval for the rate of couples who divorced in that city. find the upper bound of the confidence interval (round off to second decimal place).
The upper bound of the confidence interval is 0.52
What is confidence interval?
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
Out of 500 couples in a given city, 238 couples had divorced in the past 20 years. As a result, the sample proportion is calculated as follows:
[tex]P=238/500 = 0.476[/tex]
As a result, the following 95% confidence interval is calculated for the city's divorce rate: [tex]P +(Z_{a}*(\sqrt{\frac{P(1-P)}{y} } )[/tex]
[tex]Z_{a}= 1.96[/tex]
the upper bound of confidence interval = 0.0438 + 0.476
= 0.52
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Bill jumps off a diving board that is 12 feet above the surface of a swimming pool. Jumping upward and outward, he reaches a maximum height of 18 feet above the surface of the water when he has jumped outward 4 feet. Find f(x) an equation for his parabolic path and when he hits the water, how far out as he reached, to the nearest tenth of a foot.
The equation of the parabola is y = -0.25(x - 4)² + 16 and he reaches 12 feet outwards when he hits the water
How to determine the equation of the parabola?From the question, we have the following parameters that can be used in our computation:
Initial position = 12 feet above the surface
Maximum height = 18 feet at 4 feet outward
These parameters mean that
(h, k) = (4, 16) -- vertex
(x, y) = (0, 12)
A parabola is represented as
y = a(x - h)² + k
So, we have
y = a(x - 4)² + 16
Also, we have
12 = a(0 - 4)² + 16
This gives
12 = 16a + 16
So, we have
16a = -4
Divide
a = -0.25
Substitute a = -0.25 in y = a(x - 4)² + 16
y = -0.25(x - 4)² + 16
When it hits water, y = 0
So, we have
-0.25(x - 4)² + 16 = 0
This gives
0.25(x - 4)² = 16
So, we have
(x - 4)² = 64
Take square roots
x - 4 = 8
So, we have
x = 12
Hence, it is 12 feet outwards
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Find the value of x.
x=
Find the vector v with the given magnitude and the same direction as u. Magnitude ||v|| = 51 Direction u = ⟨-8,15
The vector [v] whose direction is same as that of vector [u] is given as -
[v] = -24i + 45j.
What is an expression? What is a expression? What is a mathematical equation? What is vector?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A vector quantity is a quantity that has both magnitude and direction.
We have the a vector [v] with the given magnitude and the same direction as u.
We can write vector [u] as -
[u] = - 8i + 15j
Unit vector {u} along vector [u] -
{u} = [u] / |u|
{u} = (- 8i + 15j)/17
We can write vector [v] as -
[v] = 51 x (- 8i + 15j)/17
[v] = 3(- 8i + 15j)
[v] = -24i + 45j
Therefore, the vector [v] is given by [v] = - 24i + 45j.
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In the month of March, the temperature at the
South Pole varies over the day in a periodic way
that can be modeled approximately by a
trigonometric function.
The highest temperature is about -50°C, and it is
reached around 2 p.m. The lowest temperature is
about -54°C and it is reached half a day a apart
from the highest temperature, at 2 a.m.
Find the formula of the trigonometric function
that models the temperature T in the South Pole
in March t hours after midnight. Define the
function using radians.
T(3) = - 50.59 is time period
What is Function using Radian ?A specific quantity is converted from degrees to radians using the RADIANS function. The supplied angle, which is in degrees, is translated into a roughly equivalent angle, which is in radians.
According to given information
Since maximum term is -50°C at 2 pm
So
We can start with cosine curve with maximum temperature -50°C at t = 0
Assuming 2 pm as starting point t = 0
Period = [tex]\frac{2\pi }{b}[/tex]
24 = [tex]\frac{2\pi }{b}[/tex]
b = [tex]\frac{\pi }{12}[/tex]
By using Formula
y = a cos(bx) + d
y = a cos([tex]\frac{\pi }{12}[/tex]t) - 52
At 5 pm , t = 3
T(3) = 2 cos([tex]\frac{\pi }{12}[/tex]×3) - 52
= 2 ×[tex]\frac{\sqrt{3} }{2}[/tex] - 52
T(3) = - 50.59 is time period
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