Rational functions can have 3 types of asymptotes:
1. Horizontal Asymptotes
2. Vertical Asymptotes
3. Oblique Asymptotes
The ratio of two polynomial functions with a non-zero denominator is known as a rational function.
1. Horizontal Asymptotes:
A graph's horizontal asymptote is a horizontal line with the equation y = b, and when the inputs get closer to 0 or 1, the graph moves toward the line. A graph's slant asymptote is a sloped line, denoted by the equation y = mx + b, where the graph slopes toward the line when the inputs approach 0 or -1.
2. Vertical Asymptotes:
Vertical asymptotes are vertical lines that represent the zeros in a rational function's numerator. Asymptotes can also occur in other situations, such as logarithms, although you'll almost probably run into them when discussing rationals for the first time.
3. Oblique Asymptotes:
These slanted asymptotes, known as oblique asymptotes, demonstrate how a function rises or falls without bound. Slant asymptotes are another name for oblique asymptotes. The slant asymptote won't be a line because the degree of the numerator is 3 and the degree of the denominator is 1, respectively.
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Triangles RST and XYZ are drawn below. If RS= 6, ST=14, XY = 9, YZ=21, and ZSZY, is ARST similar to AXYZ? Justify your answer.
Answer:
yes, ∆RST ~ ∆XYZ
Step-by-step explanation:
You want to know if ∆RST is similar to ∆XYZ when RS=6, ST=14, XY=9, YZ=21 and ∠S≅∠Y.
SAS similarityTwo triangles are similar by the SAS theorem if corresponding sides have the same ratio, and the angles between them are congruent.
ApplicationCorresponding sides are ...
RS : XY = 6 : 9 = 2 : 3
ST : YZ = 14 : 21 = 2 : 3 . . . . same ratio
The angles between them are ...
∠S, ∠Y . . . . . given as congruent
Corresponding sides have the same ratios, and the angles between them are congruent, so the triangles are similar.
Simplify: (-8) x (6)-(5)x(-2)
Answer: Answer -38
Simplified version: -48 + 10
Step-by-step explanation: Sorry If I'm wrong.
If - 4 ≤ x ≤2 and 5 ≤ y ≤ 12, what
is the largest possible value of (y - x)?
Answer:
16
Step-by-step explanation:
Since x is negative, lets instead thing of the problem as
y + (-x)
and find the bounds of -x to be
[tex] - 2 < = - x < = 4[/tex]
now, the max value of y is 12 and the max value of -x is 4
12 + 4 = 16
a basketball player has a 25% accuracy rate at making three-point shots. mark thought it was reasonable that each attempt was independent and the probability stayed at 25% for this player. p (x equals k )equals (1 minus p )to the power of k minus 1 end exponent p using the geometric distribution formula, what is the probability that the basketball player makes his first three-point shot on the third attempt? answer choices are rounded to the hundredths place. a.) 0.56 b.) 0.25 c.) 0.38 d.) 0.14
The answer is c). The probability that the basketball player makes his first three-point shot on the third attempt is 0.38.
The geometric distribution is a probability distribution that describes the number of independent trials required to get a success. In this case, the basketball player has a 25% accuracy rate at making three-point shots, which means that the probability of success (making a three-point shot) is p=0.25 and the probability of failure (missing a three-point shot) is 1-p=0.75. Using the geometric distribution formula, the probability that the basketball player makes his first three-point shot on the third attempt is:
P(x=3) = (1-p)^(3-1) * p = (0.75)^2 * 0.25 = 0.38This means that there is a 38% probability that the basketball player will make his first three-point shot on the third attempt.
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jackson wants to test an assumption on the number of red candies in a bag of fruity tooty's candy. the company claims that five flavors are given an equal distribution in each bag, meaning that the proportion of each color should be 20%. jackson decides to focus his efforts on examining whether there is a difference in the proportion of red candies than what the company claims. what should jackson state for the null hypothesis and alternative hypothesis?
Jackson should correctly phrase both the alternative hypothesis and the null hypothesis as follows:
b. )
p = 0.20 indicates a null result.
A different result: p ≠ 0.20
What exactly is null hypothesis?
A specific type of statistical hypothesis known as a null hypothesis claims that no statistical significance can be established in a given set of facts. One can assess the truthfulness of a hypothesis through the use of sample data in hypothesis testing. It is represented by the letter H0 and is also sometimes referred to as the "null."
The conjecture, also known as the null hypothesis, is a tool used in quantitative analysis to examine the validity of beliefs about markets, economies, and investment strategies.
A null hypothesis is a form of speculation that asserts that specific characteristics of a population or data collection method are not distinct from one another in statistics.
Study up on null hypothesis.
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The diameter of the circle below is 62 cm. Work out the radius of the circle. cm 62 cm
Answer: 31 cm
The radius of a 62 cm circle is 31 cm because the radius of a circle is half of the diameter.
D=diameter
R=radius
D=R2
R=D/2
Answer:
[tex]R = 31[/tex][tex]cm[/tex]
Step-by-step explanation:
[tex]D = 62[/tex]
[tex]R=\frac{D}{2} \\R=\frac{62}{2} \\R=31[/tex][tex]cm\\[/tex]
If the m<2 = 58° and the m<13 = 111°, find the measures of angles 1, 5, 8, 14, 18.
Note: x || m and z || y
Answer:
Angle 1: 58°
Angle 5: 58°
Angle 8: 111°
Angle 14: 111°
Angle 18: 58°
Step-by-step explanation:
How do you solve an inequality on a calculator?
press menu and select option,press 2 to select to a polynomial degree of 2,select the number that matches the inequality u are about to solve and lastly input the values of coefficient of x into the expression and press equal to sign on the calculator
How do we solve inequality on a calculator?A relationship between two expressions or values that are not equal to each other is called 'inequality. '
Inequality can be greater than >, less than < , great than or equal to ≥ , less than or equal to ≤.
like other equations, inequality can be solved on a calculator. This process shows how inequality can be solved on a calculator. For example if 3x²+4x+5≥0 is to be solved on a calculator, the following steps are to be taken
Step 1 : press menu and select option B( inequality option)
Step2 : press 2 to select to a polynomial degree of 2
step 3 : select the number that matches the inequality u are about to solve
step 4: input the values of coefficient of x into the expression
step 5 : press the equal to sign on the calculator.
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Aaron estimated that 148% of 333 is 495. is his estimate reasonable?
a. no, because his calculation should be 140% of 340.
b. no, because his calculation should be 150% of 340.
c. yes, because his calculation should be 140% of 330.
d. yes, because his calculation should be 150% of 330.
Yes, His computation should be 150% of 330, thus his estimate is accurate. So option D is true.
By dividing the desired value by the entire value and multiplying by 100, the percentage may be computed.
Example:
Required percentage value = a
total value = b
Percentage = [tex]\dfrac{a}{b} \times 100[/tex]
We have,
Aaron estimated the value, of 148% of 333 is 495.
This can be written as,
[tex]\dfrac{148}{100} \times 333[/tex]
[tex]= 492.84[/tex]
[tex]= 493\\\\[/tex]
Estimating the number, this should be equal to the,
148% ≈ 150%
333 ≈ 330
So it is equal to,
150% of 330
This can be written as,
[tex]\dfrac{150}{100} \times 330[/tex]
[tex]= 495[/tex]
Therefore, his estimate is reasonable because his calculation should be 150% of 330. So option D is true.
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A pop quiz has 2 true/false questions. Paris used a 10-trial coin flip to simulate the results of guessing on the quiz. If t represents answering a question correctly, what is the experimental probability of correctly answering both questions by guessing? frequency of observed desired outcome: number of trials: experimental probability:.
Experimental probability of correctly answering both questions by guessing = 1/4 .
Tail (T) = True
Head (H) = False
Number of possible outcome = 2
Head (H) or Tail (T).
Probability = number of occurrence/number of possible outcome.
Since we can only have one T or F in a toss.
number of occurrence = 1
Probability of answering first question correctly = 1/2
Probability of answering second question correctly = 1/2
Probability of answering both questions correctly = Probability of answering first question correctly * Probability of answering second question correctly
Probability of answering both questions correctly = 1/2 x 1/2
Probability of answering both questions correctly = 1/4
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Answer:3 and 10 and 3/10
Step-by-step explanation:
It is 1.4 kilometers from Jim’s house to his grandmother’s house. How far does Jim walk going to and from his grandmothers house once every day for 5 days?
Jim has to walk 7 km going to his grandmother's house once per day for 5 days.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.
Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data given in the question,
Distance between Jim and his grandmother's house = 1.4 km.
Jim travels once to his grandmother's house every day then,
Total distance traveled by him = 5 × 1.4 km = 7 km.
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3/8 divided by 2/5 in fraction form and simplest form
Answer:
Step-by-step explanation:
for double fractions, invert the bottom one and then multiply them
[tex]\frac{3}{8}[/tex] * [tex]\frac{5}{2}[/tex]
= [tex]\frac{15}{16}[/tex]
= 0.9375
a data set was graphed using a scatterplot. the correlation coefficient, r, is 0.813. which of the following statements explains how the correlation is affected? a.) it is not affected. b.) it is affected by an influential point. c.) it is affected by inappropriate grouping. d.) it is affected by non-linearity.
The correlation coefficient is increasing, which may have an effect on the influential points. Thus, option (a) is correct.
The correlation coefficient, in general, quantifies the strength of the association between two variables.
To find non-linearity, influential spots, or improper grouping in a dataset, for example. A scatter plot is used to graph the data set.
Here, the correlation coefficient is r = 0.813.
Linearity is evident since there is a significant link between the two variables. As a result, non-linearity has no effect on it. It is not influenced by incorrect categorization when it appears that type of case correlation may be lower.
The correlation coefficient is increasing, which may have an effect on the influential points.
Thus, option (a) is correct.
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What does the notation f/x y mean?
The notation f (x) = y means that the functional value at the point x is y.
In the notation f (x) = y, we understand that the value x is to be plugged in the function given to us (which is f here) which on solving gives y as the answer or solution 'y' of that function at a point x.
For example, let us consider the function f (x) = 2x + 3 = y
Then if we find f (2), then 2 will be plugged in the function 2x +3 such that
f (2) = 2(2) + 3 = 7,
which means that 7 is the functional value, 'y' at the point 2 which is considered as x.
The question is incomplete, the complete question is f (x) = y.
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I need the slope answers for the sheet and the regular answer
Answer:
(1.5, -3)
Step-by-step explanation:
Both equations are in slope intercept form which means that:
for y = mx + b
m = slope
b = y-intercept
The slope can help us go from the y-intercept to the next point on the graph to make the line
For the equation
y = 2x - 6
the y-intercept is -6, so plot a point there.
The slope is 2 which means you will go up 2 then to the right by 1 to the next point on the graph.
Use the same process to find the line for y = -4x + 3, but you have to keep in mind that when the "m" value is negative, that means the line will point to the left of the graph instead of the right.
Once the lines are draw, the point where they intercept will be the solution.
Is there a series of rigid transformations that could map aqrs to aabc? if so, which transformations could be used?.
Yes, ΔQRS can be translate to so that Q is mapped to point A, then reflect across line containing QS.
we have two triangles ΔQRS and ΔABC in which we have ,
QR=AB = 16 cm
RS=BC= 24 cm
∠R=∠B=90°
By SAS postulate of congruence , ΔQRS ≅ ΔABC.
There are three main rigid transformations which produces congruent images.
1) Translations 2) Rotation 3) Reflection
When we look the given picture, it can be seen that ΔABC is the mirror image of ΔQRS.
But line QS is at some distance from AC , so we first translate ΔQRS to so that Q is mapped to point A, then reflect across line containing QS.
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What is the range of f/x )= sin x the set of all real numbers?
On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = [tex]-1 < y < 1[/tex]
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
The Range of the given function, f(x) = sin(x)
[tex]-1 < y < 1[/tex]
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Why might squaring a number and taking the square root of a number be thought of as opposite operations?
Therefore , squaring a number and taking the square root of a number is an opposite operation as we can see in the following explanation.
How is the square root defined?A number's square root, which is the result of multiplication by itself, yields the original number. Some examples of exponents are squares and square roots. Imagine the number twenty five. Additionally, this can be expressed as expression of 5x5.
Here,
In order to square an integer, you must multiply it by itself.
The opposite of squaring a number is the act of getting the square root.
Calculating the side length of a square whose area is a certain number can be compared to finding the square root of that number.
For example: √25= √5*5 = 5
where as square of 5 : 5*5 = 25
Therefore , squaring a number and taking the square root of a number is an opposite operation as we can see in the following explanation.
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How do you know if it's greater than or less than on a graph?
To determine whether an inequality represents a relationship of "greater than" or "less than" by looking at a graph, you can look at the direction of the solid line. If the line is pointing upwards towards the right, it represents a "greater than" relationship. If the line is pointing downwards towards the right, it represents a "less than" relationship.
For example, consider the graph of the inequality "y > x + 2." The points on the graph that satisfy this inequality are those that are above the line "y = x + 2." This line represents the values of y that are equal to x + 2. The points above the line are greater than the values on the line, so the inequality "y > x + 2" represents a "greater than" relationship.
On the other hand, consider the graph of the inequality "y < x + 2." The points on the graph that satisfy this inequality are those that are below the line "y = x + 2." This line represents the values of y that are equal to x + 2. The points below the line are less than the values on the line, so the inequality "y < x + 2" represents a "less than" relationship.
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Match the histograms on the right to the summary statistics givern 20 Standard Deviation 1.6 9 10 21 Mean Median 56 65 56 56 56 65 56 56 51 5355 57 59 61 (a) IV 20 (b)I (d)II 40 50 60 70 80 90 10 4 16 36 56 76 96 116 20 26 36 46 56 66 76 86
The histograms is shown below.
What is Histogram?One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data. It is frequently used to conveniently depict the main characteristics of the data distribution.
Given:
The standard deviation for 4 we have the highest value and range for graph C have highest standard deviation.
and, the standard deviation for 1 have lowest deviation and range for graph A have lowest standard deviation.
and, for row 2 the second histogram is the answer and for row 4 the fourth histogram is the answer.
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Simplify the expression the quantity 9 times x to the fourth power end quantity to the one-half power.
9 times x to the power of nine-halves
3 times x to the power of nine-halves
9x2
3x2
The solution is Option D.
The value of the equation A = ( 9x⁴ )^1/2 is A = 3x²
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = quantity 9 times x to the fourth power end quantity to the one-half power
On simplifying the expression , we get
Quantity 9 times x to the fourth power = 9x⁴
Quantity 9 times x to the fourth power end quantity to the one-half power is written as = ( 9x⁴ )^1/2
On further simplification , we get
A = ( 9x⁴ )^1/2
A = √9x⁴
Taking the square root of the value of A , we get
The value of A = 3x²
Therefore , the value of is 3x²
Hence , The value of the equation is A = 3x²
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FILL IN THE BLANK. the area under the normal curve to the right of muμ equals _______.
Answer: One by two
Step-by-step explanation:
Because the mu is half or 0.5, so the word in the blank will be one by two!
Is the answer to this question A or B? I’m conflicted.
Would appreciate the reply!!
Answer: B
I have to add extra words to answer you but it’s B :))
Which expressions are equivalent to the one below? Check all that apply.
4^3 x 4^x
Answer:
d
Step-by-step explanation:
[tex]{4}^{3} . {4}^{x} [/tex]
In the following we make multiple not sum to the power
What is the sample variance of the following numbers 6 4 2 7 1?
6.50 is the sample variance of the following numbers.
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
X = ∑x/n
= 3 + 4 + 2 + 7 + 1/5
= 20/5 = 4
s² = [∑(Xi - x)²/N-1]
= (6-4)² + ( 4 - 4 )²+ ( 4 - 4 )² + ( 7 - 4 )² + ( 1 - 4 )²/5 - 1
= 26/4
= 6.50
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witney peter, a professional dart player has a seventy percent chance of hitting the bull's eye on a dartboard with and throw. assume that that the throw of a dart is independent. what is the probability that pete hits five or fewer of his next ten shots?
Without spectacles, Witney Pete has a 5/10 chance of hitting the bullseye. Witney Pete could strike the bullseye with his spectacles 0.7 of the time. This likelihood is far higher than hitting the bullseye without glasses. the probability that Pete hits five or fewer of his next ten shots is approximately 2.487.
What is the probability that Pete hits five or fewer of his next ten shots?Generally, To find the probability that Pete hits five or fewer of his next ten shots, we need to find the probability that he hits exactly 0, 1, 2, 3, 4, or 5 bull's eyes.
The probability that Pete hits exactly k bull's eyes in n throws is given by the binomial distribution:
P(k bull's eyes in n throws) = (n choose k) * p^k * (1-p)^(n-k)
where p is the probability of hitting a bull's eye on a single throw and n choose k is the binomial coefficient, which is equal to n!/(k!(n-k)!).
Substituting the given values, we get:
P(0 bull's eyes in 10 throws) = (10 choose 0) * (0.7)^0 * (0.3)^10 = 0.028 P(1 bull's eyes in 10 throws) = (10 choose 1) * (0.7)^1 * (0.3)^9 = 0.189 P(2 bull's eyes in 10 throws) = (10 choose 2) * (0.7)^2 * (0.3)^8 = 0.462 P(3 bull's eyes in 10 throws) = (10 choose 3) * (0.7)^3 * (0.3)^7 = 0.605 P(4 bull's eyes in 10 throws) = (10 choose 4) * (0.7)^4 * (0.3)^6 = 0.501 P(5 bull's eyes in 10 throws) = (10 choose 5) * (0.7)^5 * (0.3)^5 = 0.302
The probability that Pete hits five or fewer bull's eyes in his next ten shots is the sum of the probabilities of hitting exactly 0, 1, 2, 3, 4, or 5 bull's eyes:
P(hitting 5 or fewer bull's eyes in 10 shots) = 0.028 + 0.189 + 0.462 + 0.605 + 0.501 + 0.302 = 2.487
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PLEASE HELLLLPPPPP IM SO CONFUSED
What is the quotient of these fractions in lowest terms 3/10 2 4 ___ *?
3/5 is the quotient of these fractions in lowest form when 3/10 divides by 2/4
How to divide fractions?When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.
so in order to find quotient when 3/10 is divided by 2/4 we get:
quotient = (3/10) / (2/4)
=> (3/10) * (4/2)
=> 12/20
so the quotient of this division is 12/20
now we have to find the lowest form of quotient
so gcd(12,20) = 4
where gcd is greatest common divisor
so lowest form of 12/24 = (12/4) / (20/4)
=> 3 /5
so lowest form of the quotient is 3/5
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What is the y-intercept of y=5x+3?
Answer:
Y-intercept: 3
Step-by-step explanation:
The equation is y = mx + b
m is the slope
b is the y-intercept
In this case, the y-intercept is 3
If Jasper makes 90 sandwiches, how many ounces of peanut butter will he have left?
Answer:
10
Step-by-step explanation:
each 10 peanut butter sandwiches takes 10 ounces
Answer:
10
Step-by-step explanation: