find the range of the quadratic function write your answer as an inequality using x or y as appropriate. or you may instead click on empty set or all realsas the answer
Answers
The range of a function is a set composed of all of its output values. In this case this means all the possible y-values that the function can take. This is a cuadratic function which means that it has either a minimum or a maximum y-value that delimits its range. The sign of its leading coefficient is - which implies that this function has a maximum. This maximum is also known as the vertex of the function and if it's the point (h,k) then the range of this function can be described with this inequality:
\(y\leq k\)So if we find the y-value of the vertex we find the range. In order to find it we could find its x-value first. If the function has two x-intercepts then the x-value of the vertex is the midvalue of these two. Then we should find the x-intercepts so we find the x-value of the vertex and with it its y-value.
For any given quadratic equation of the form ax²+bx+c=0 its x-intercepts are given by:
\(r=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)In our case we have a=-3, b=30 and c=-72 so we get:
\(\begin{gathered} r=\frac{-30\pm\sqrt{30^2-4\cdot(-3)\cdot(-72)}}{2\cdot(-3)}=\frac{-30\pm\sqrt{36}}{-6}=\frac{-30\pm6}{-6} \\ r=\frac{-30+6}{-6}=4\text{ and }r=\frac{-30-6}{-6}=6 \end{gathered}\)So the x-values of the x-intercepts are 4 and 6. Then the x-value of the vertex (h) of this function is:
\(h=\frac{4+6}{2}=\frac{10}{2}=5\)Then the y-value of the vertex k is given by taking x=5 in the equation:
\(k=-3h^2+30h-72=-3\cdot5^2+30\cdot5-72=3\)AnswerThen the answer is:
\(y\leq3\)Related Questions
La distancia de la Tierra a Saturno es 5.95 x 108 y la distancia de la Tierra a Júpiter es 8.87 x 108. ¿Cuánto es la suma de las dos distancias en Notación Científica?
Answers
Answer:
no
Step-by-step explanation:
Your cousin renews his apartment lease and pays a new monthly rent his new rent is a calculated by applying a discount of $50 to his original rent and then applying at 10% increase to the discounted amount what was your cousins original monthly rent when his new rent is 5% greater
Answers
Answer:
10000000$
Step-by-step explanation:
gu kha le bhosadike duck you
Please help me I am confused
Answers
The answer is c...
y = mx + b is slope intercept form
This equation corresponds to that...
to be in slope intercept form:
y = mx + b is corresponded to y = 4x + 9
PLEASE HELP 50 POINTS!!
The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation:
2n + 1 = 157.
What is the first number?
A. 77
B. 78
C. 79
D. 80
Answers
If u add them n+(n+1) you get 157
So,
n+n+1=157
2n=156
n=78
What is an equation of the line that passes through the point ) (8,−5) and is parallel to the line
5x+4y=24?
Answers
By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.
The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.
To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.
Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.
Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.
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fill the table using this function rule
y=10x+1
Answers
The table with the numeric values of the function y = 10x + 1 is given by the image at the end of the answer.
How to calculate the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, each instance of the variable in the defined function or in the defined expression must be replaced by the value of the input variable at which the numeric value is to be found.
In this problem, the function is defined by the rule presented as follows:
y = 10x + 1.
The numeric values are found replacing the lone instance of x by the value that we want to find the output at, hence:
x = 1: y = 10(1) + 1 = 11.x = 2: y = 10(2) + 1 = 21.x = 3: y = 10(3) + 1 = 31.x = 5: y = 10(5) + 1 = 51.The table with these numeric values is given by the image at the end of the answer.
Missing InformationThe inputs are missing and are given by the table at the end of the answer.
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Katelyn had 2 dogs and 3 cats. Which of the following shows the ratio written correctly for the number of dogs to cats?
A) 3:2
B) 3-2
C) 2:3
D) 3 x 2
Answers
Answer:
2:3
Step-by-step explanation:
Ratio is indicated by :
Its dogs to cats, right so ratio is number of dogs:number of cats which is 2:3
Hope this helps plz mark brainliest if correct :D
Answer:
2:3
Step-by-step explanation:
2 is first and 3 is the second number so you put them in order
x^2 =1 how many solutions are there
Answers
Answer:
Answer:
x=1 or x=−1
Step-by-step explanation:
I think just 2
Answer:
x=1, x=-1
Step-by-step explanation:
x^2=1
x=sqrt(1)=+-1
Thus, there are 2 solutions: 1 and -1
4. A drawing of the top of a desk iS shown.
5 feet
2 feet
3feet ,2 feet. What is the area of the top of the desk?
Answers
The area of the top of a desk which is shown and the dimensions of the top is 5 feet and 2 feet, is 10 squared feet.
What is the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
\(A=a\times b\)
Here, (a)is the length of rectangle and (b) is the width of the rectangle
A drawing of the top of a desk is shown.
5 feet2 feetThe image of drawing ins not given in the problem. Here, the length of the desk is 5 feet and the width of the desk is 2 feet according to the data.
\(a=5\rm\; feet\\b=2\rm\; feet\)
Put the values in the above written formula as,
\(A=5\times 2A=10\rm\; ft^2\)
Thus, the area of the top of a desk which is shown and the dimensions of the top is 5 feet and 2 feet, is 10 squared feet.
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a library has 67,982 books. the children's section represents 1/3 of the total books. of the remaining books, 75% are fiction. how many books are in the non-fiction section?
Answers
Answer:
11331 non fiction books
Step-by-step explanation:
Given :
Total books = 67982
Childrens section = 1/3 of total
Number of children's books :
(1/3 * 67982) = 22660 books (approximately)
Books left :
67982 - 22660 = 45,322 books
Fiction books:
75% of remaining
0.75 * 45322
33991.5
= 33991 books
If the only section left is non - fiction, then
Non - fiction books = (45322 - 33991) = 11331
Explain how to determine whether two quantities are proportional.
please help :)
Answers
Answer:
* Ratios are proportional if they represent the same relationship.
*If the reduced fractions are the same, your ratios are proportional.
*If two ratios are proportional is to write them as fractions and then reduce them.
Hope its helpful
Thank you
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
Write F ∩ H and F ∩ H using interval notation. If the set is empty, write ∅.
Answers
The final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
What is the interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.
We have,
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
F is the set of all real numbers that are less than or equal to 4. H is the set of real numbers greater than 7.
F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:
F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets. Hence the answer is the empty set, Ø:
F ∩ H = Ø
F ∩ H = [7, 4]
F ∪ H = [-∞, ∞]
Hence, the final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
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What is the y-intercept of the
grouph of the line whose equation is
y = -2/5 x +4?
Answers
Answer:
b = 4
Step-by-step explanation:
y = mx + b represents the equation of a line
m represents the slope
b represents the y-intercept
Based on what we're given, we could determine that 4 is our y-intercept or b.
34 or 1777 please tell me hurry
Answers
Answer:
drum him list good drum karmic go insulin if drop off cool karmic chill of too so P well overboard
man I don't know
Step-by-step explanation:
october ovum kissel ovum Karl often oven Zen october get if if IC IC his Zeno Zeno if so is so is also do I have K do do do do do do do do do do do do do go go go go go go go go go go chi chi chi chi chi Karl user oxtail pixel pixel
Algebraic expression for 4less then 3x
Answers
When 'x' is 5, the Algebraic expression 3x - 4 evaluates to 11.
To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.
First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.
Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.
In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.
To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:
3(5) - 4
This simplifies to:
15 - 4 = 11
So, when 'x' is 5, the expression 3x - 4 evaluates to 11.
In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.
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Note the complete question:
Algebraic expression for 4 less than the product of 3 and some number
What is the algebraic expression for "4 less than the product of 3 and some number?
Please help me understand the meaning of how to calculate.
in a museum, a ratio of adults to Children is 12 to 9. If there are 252 people in the museum how many children are there?
Answers
Ratio of ADULT : CHILDREN =12:9
Total number of people = 252
Number of children:
\(\begin{gathered} \frac{9}{21}\times252 \\ \frac{2268}{21}\text{ = 108 children} \end{gathered}\)2. Determine the area of each composite figure below.
Answers
Answer:
\(6\pi\)
Step-by-step explanation:
There's two things to note here, we're dealing with a semi-circle and also a semi-circle that has some area taken out of it.
Area of a Circle:The area of a circle can be calculated using the formula: \(A=\pi r^2\) where "r" is the radius, equal to half the diameter.
Since we're dealing with the semi-circles, we can just divide this area by two to get: \(A=\frac{\pi r^2}{2}\)
Now as noted, we have some of the area taken out, but fortunately it's just another semi-circle. We can simply calculate the area of the entire semi-circle, and then calculate the area of the semi-circle inside and subtract them.
So the diameter of the entire thing is just 8 ft, so the radius is half of this, equal to 8 ft. That means the area is: \(A=\frac{\pi (4)^2}{2}=A = \frac{\pi * 16}{2} = 8\pi\)
One mistake that may be made here, is assuming the radius of the smaller semi-circle is just two, as provided in the image. It's actually the radius of the inner semi-circle plus two which gives us the radius of the outer circle, of 4 feet. Now luckily in this case, it actually still results in 2 ft (since 2 + 2 = 4), but in other examples, that may noe be the case.
So now let's calculate the area of the inner semi-circle: \(A=\frac{\pi (2)^2}{2}=2\pi\)
Now let's just subtract the areas: \(8\pi - 2\pi = 6\pi\), so the area is 6 pi
Object A is moving at 30 ft per sec. Object B is moving at 20 mph.
Answers
Answer:
what we have to find or to prove.
|2x-3|=2 what is the answer explanation if u can
Answers
Answer:
5/2 (2.5) --> 2
Step-by-step explanation:
2x-3=2
+3 +3
2x=5
/2 /2
x= 5/2 (2.5)
(You just get x alone like other problems, I think anyways.)
Describe,in words.the rule that is used to determine the time value from its position in the sequence
Answers
The rule used to determine the time value from its position in the sequence is discussed below.
In general, the rule could involve arithmetic progression (adding or subtracting a constant value at each step), geometric progression (multiplying or dividing by a constant value at each step), or a more complex pattern involving mathematical operations, functions, or other mathematical relationships.
To determine the time value, you would need to analyze the given sequence, identify the pattern or rule being followed, and then apply that rule to find the time value corresponding to a particular position in the sequence.
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1. Come up with an integer that is BIGGER than 10.
2. Come up with an integer that is SMALLER than 10.
3. Come up with an integer that is BIGGER than 0.
4. Come up with an integer that is SMALLER than 0.
I need help pleaseeee
Answers
Answer:
1) any number that is greater than ten is considered an integer bigger than ten: for example, 11, 12, 100, 1000000, etc.
2) any number that is smaller than ten is considered an integer smaller than ten: for example, 9, 8, 7, -100, -100000, etc.
3) any number that is bigger than zero is considered an integer bigger than ten: for example, 1, 2, 10, 100, 100000, etc.
4) any number that is smaller than zero is considered an integer smaller than zero: for example, -1, -2, -3, -10, -100000, etc.
Step-by-step explanation:
An integer is any whole number
Answer:
Step-by-step explanation:
integer bigger than 10 is 11
integer smaller than 10 is 9
integer greater than 0 is 1.
integer smaller than 0 is -1.
What is the slope and y-intercept? 20 points!!
Answers
Answer:
Slope = 2
Y-intercept = -4
Step-by-step explanation:
The slope of a function is found by finding the change in the y-values and dividing it in the change in x-values.
The change in y-values is 2 because that is the difference between each given data point. The change in x-values is 1 for the same reason.
The slope would be 2/1 which is just 2.
The y-intercept can be found by setting up the function in slope-intercept form (y=mx+b) and using the given data to solve for b. The point I chose to do this with was (2,0)
y=mx+b
y=2x+b
0=(2*2)+b
0=4+b
b=-4
So the slope is 2 and the y-intercept is -4.
what is the the answer of rounding .875 of hundreds
Answers
The dating web site oollama requires its users to create profiles based on a survey in which they rate their interest (on a scale from 0 to 3) in five categories: physical fitness, music, spirituality, education, and alcohol consumption. a new oollama customer, erin o'shaughnessy, has reviewed the profiles of 40 prospective dates and classified whether she is interested in learning more about them. based on erin's classification of these 40 profiles, oollama has applied a logistic regression to predict erin's interest in other profiles that she has not yet viewed. the resulting logistic regression model is as follows: for the 40 profiles (observations) on which erin classified her interest, this logistic regression model generates that following probability of interested. Probability of Probability ofObservation Interested Interested Observation Interested Interested35 1 1.000 13 1 0.41221 1 0.999 2 0 0.28529 1 0.999 3 0 0.21925 1 0.999 7 0 0.16839 1 0.999 9 0 0.16826 1 0.990 12 0 0.16823 1 0.981 18 0 0.16833 1 0.974 22 1 0.1681 0 0.882 31 1 0.16824 1 0.882 6 0 0.12828 1 0.882 20 0 0.12836 1 0.882 15 0 0.02916 0 0.791 5 0 0.02027 1 0.791 14 0 0.01530 1 0.791 19 0 0.01132 1 0.791 8 0 0.00834 1 0.791 10 0 0.00137 1 0.791 17 0 0.00140 1 0.791 4 0 0.00138 0 0.732 11 0 0.000(a) Using a cutoff value of 0.5 to classify a profile observation as Interested or not, construct the confusion matrix for this 40-observation training set.PredictedActual 0 10 1 Compute sensitivity, specificity, and precision measures and interpret them within the context of Erin's dating prospects.If required, round your answers to two decimal places. Do not round intermediate calculations.The sensitivity of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 6 at identifying the profiles that Erin is interested in.The specificity of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 8 at avoiding recommending profiles to Erin that she will not be interested in.The precision of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 10 at suggesting profiles of interest to Erin.(b) Oollama understands that its clients have a limited amount of time for dating and therefore use decile-wise lift charts to evaluate their classification models. For the training data, what is the first decile lift resulting from the logistic regression model? Interpret this value.The first decile lift of this classification is . It means that the first decile of the logistic regression model - Select your answer -halvesdoublestriplesdoes not changeItem 12 the number of profiles that Erin is interested in versus random selection.(c) A recently posted profile has values of Fitness = 3, Music = 1, Education = 2, and Alcohol = 1. Use the estimated logistic regression equation to compute the probability of Erin's interest in this profile.If required, round your answers to three decimal places. Do not round intermediate calculations.Log odds =Probability of Interest =(d) Now that Oollama has trained a logistic regression model based on Erin's initial evaluations of 40 profiles, what should its next steps be in the modeling process?Oollama should use their model to suggest profiles - Select your answer -of interestwith lack of interestof interest and with lack of interestItem 15 to Erin in order to compute classification accuracy measures on a validation set.
Answers
The dating web site Oollama.com requires its users to create pro les based on a survey in which they rate their interest (on a scale from 0 to 3) in positive categories: physical fitness, music, spirituality, education, and alcohol consumption.
A new Oollama customer, Erin O'Shaughnessy, has reviewed the pro les of 40 prospective dates and classi ed whether she is interested in learning more about them. Based on Erin's classi cation of these 40 pro les, Oollama has applied a logistic regression to predict Erin's interest in other pro les that she has not yet viewed. The resulting logistic regression model is as follows:
Log odds of Interested = −0.920 + 0.325 × Fitness − 3.611 × Music
+5.535 × Education − 2.927 × Alcohol
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A one-tailed hypothesis test with the t statistic Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions. Suppose you have a sample of 40 16-year-old children with antisocial tendencies and you are particularly interested in the emotion of disgust. The average 16-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed.
The null hypothesis is that your sample of children with antisocial tendencies would have no more difficulty recognizing emotion than the general population of 16-year-olds. Stated using symbols:_________. This is a __________ tailed test. Given what you know, you will evaluate this hypothesis using a________ statistic.
Answers
Step-by-step explanation
The answers in bold is what was required from the question.
the null hypothesis using symbol:-
H₀ : μ = 11.80
the alternative hypothesis using symbol:-
H₁: μ ≠ 11.80
This is a one tailed test. Given what you know, you will evaluate this hypothesis using a t test statistic.
Alpha level = 0.05
Sample size = n
Degree of freedom = n-1 = 40-1 = 39
To use the t distribution we will have to find the critical value from the t table this value is 1.685
But the question does not have sample mean and sample standard deviation. So I was unable to solve for the standard error
Compute the probability that a five-card poker hand is dealt to you that contains all hearts.
Answers
Answer:
the probability of this happening is 13 out of 52 chance.
A ladder is put against a building. The building is 25 feet tall. The ladder's base is 13.5 feet from the building. Find the angle which the ladder makes with the ground.
Answers
Answer:
correct me if i'm wrong but it's 57.32 degrees?
Geometry I need help
Answers
Figure O is reflected followed by a translation of 4 units in the left direction.
Given that:
Figure O and Figure P are shown on the graph.
The translation does not change the shape and size of the geometry. But changes the location.
Figure O is translated leftward by 4 units.
The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.
The translated figure O is reflected across the x-axis.
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B=4/(căn x +1) + 2/(1-căn x) - (căn x-5)/x-1
Answers
Answer:
what??? is this real????
Step-by-step explanation:
The collection of all equally likely outcomes is known as the
Answers
Answer:
The Sample space
Step-by-step explanation:
The collection of all equally likely outcomes is known as the- the sample space.