find the vertex, focus, and directrix of the parabola. x2 = 2y vertex (x, y) = focus (x, y) = directrix
Answers
The vertex, focus, and directrix of the parabola. x2 = 2y vertex (x, y) = focus (x, y) = directrix, is calculated to be the vertex, focus, and directrix of the parabola. x2 = 2y vertex (x, y) = focus (x, y) = directrix.
Given: x² = 2y We know that the standard form of a parabolic equation is : (x - h)² = 4a (y - k) where (h, k) is the vertex
To write the given equation in this form, we need to complete the square
.x² = 2yy = (x²)/2
Putting this value of y in the above equationx² = 2(x²)/2x² = x²
To complete the square, we need to add (2/2)² = 1 to both sides.x² - x² + 1 = 2(x²)/2 + 1(x - 0)² = 4(1/2)(y - 0) vertex (h, k) = (0, 0) focal length, f = a = 1/2 focus (h, k + a) = (0, 1/2) directrix y - k - a = 0 ⟹ y - 0 - 1/2 = 0 ⟹ y = 1/2
Answer: Vertex = (0,0)Focus = (0,1/2)Directrix = y = 1/2
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Related Questions
An expression is given. 26 , 091 ÷ 13 26,091÷13 What is the value of the expression?
Answers
1967.64 is the value of the given expression.
We must carry out the division operation in the following manner in order to assess the expression:
26,091 ÷ 13.26
= 1967.64
As a result, the expression has a value of 1967.64.
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Aaron is considering getting his car a new paint job. Doing so will have a total cost of $264.83. Can Aaron afford this? Explain a. Yes, he can make the purchase and still have money left over. b. Yes, but doing so will clear out his account. c. No, purchasing that would overdraw his account. d. No, he is overdrawn already.
Answers
Answer:
Yes, but doing so will clear out his account.
Step-by-step explanation:
CHECK THE COMPLETE QUESTION BELOW
Aaron's bank account has a balance of $1213.69 before he starts spending money. He makes the following transactions:
Transaction
Cost ($)
Car payment
260.16
Groceries
97.98
Parking ticket
75.00
DVD box set
115.35
Antique lamp
68.53
Suit
331.84
Aaron is considering getting his car a new paint job. Doing so will have a total cost of $264.83. Can Aaron afford this? Explain a. Yes, he can make the purchase and still have money left over. b. Yes, but doing so will clear out his account. c. No, purchasing that would overdraw his account. d. No, he is overdrawn already
Aaron's bank account balance=$1213.69
He made all this transactions below;
Car payment
260.16
Groceries
97.98
Parking ticket
75.00
DVD box set
115.35
Antique lamp
68.53
Suit
331.84
The summation of all his transactions is;260.16+97.98+75.00+115.35+68.53+
331.84= $948.86
Which means after performing those transactions above, he was left with $948.86.
We were informed that Aaron is considering getting his car a new paint job. Doing so will have a total cost of $264.83.
For him to paint his car now he will spend $264.83, if we add with the previous transactions it sum up to $1213.69 which was actual amount he has at hand. I.e ($264.83+$948.86)=
$1213.69
Therefore, the answer is Yes, but doing so will clear out his account.
Complete the frequency table: Method of Travel to School Walk/Bike Bus Car Row totals Under age 15 60 Age 15 and above 65 195 Column totals 152 110 98 360 How many students age 15 and above take a car to school? 18 38 50 87.
Answers
A total of 80 students aged 15 and above take a car to school
How many students age 15 and above take a car to school?From the question, we have the following parameters that can be used in our computation:
Method of Travel to School
Walk/Bike Bus Car Totals
Under age 15 60
Age 15+ 65 195
Totals 152 110 98 360
When completed, we have
Bus Age 15+ = 110 - 60 = 50
Total under age 15 = 360 - 195 = 165
Walk/Bike Under 15 = 152 - 65 =87
So, we have
Walk/Bike Bus Car Totals
Under age 15 87 60 18 165
Age 15+ 65 50 80 195
Totals 152 110 98 360
From the above, we can see that
80 students aged 15 and above take a car to school
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Question
Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Totals
Under age 15 60
Age 15+ 65 195
Totals 152 110 98 360
How many students age 15 and above take a car to school?
What is the result when the number 96 is increased by 86%?
Answers
Answer:
96.00 increased by 86% is 178.56
Step-by-step explanation:
Which of the following would show that the 4 points are the vertices of a parallelogram?
A. DA = AB = BC = CD =
B. AB = CD = ; DA = BC =
C. DB = ; AC =
D./
Answers
A parallelogram is a quadrilateral with opposite sides that are parallel. In order to determine if the given points form a parallelogram, None of the given options clearly demonstrate that the four points are the vertices of a parallelogram.
A parallelogram is a quadrilateral with opposite sides that are parallel. In order to determine if the given points form a parallelogram, we need to examine the relationships between the sides and diagonals.
Option A, which states that DA = AB = BC = CD, does not provide enough information about the relationship between opposite sides or diagonals. Similarly, Option B, which states that AB = CD = and DA = BC =, does not provide sufficient information.
Option C, which states that DB = and AC =, also does not provide enough information to establish the parallelism of opposite sides.
Option D, which is not provided, cannot be evaluated as it is missing the necessary information.
In conclusion, none of the given options demonstrate the properties required to establish that the four points are the vertices of a parallelogram. Additional information, such as the slopes or lengths of the sides, is needed to determine if the given points form a parallelogram.
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a diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the disease. also, if a person does not have the disease, the test will report that he or she does not have it with probability 0.9. only 3% of the population has the disease in question. if a person is chosen at random from the population and the diagnostic test indicates that she has the disease, what is the conditional probability that she does, in fact, have the disease? (round your answer to four decimal places.) are you surprised by the answer? would you call this diagnostic test reliable? this answer has not been graded yet.
Answers
The conditional probability that a person actually has the disease given a positive test result is approximately 0.0826 (rounded to four decimal places). This probability suggests that the test is not highly reliable.
To determine the conditional probability, we can use Bayes' theorem. Let's denote D as the event that a person has the disease and T as the event that the test result is positive. We are interested in finding P(D|T), the probability that a person has the disease given a positive test result.
According to the problem statement, P(D) = 0.03, which represents the probability that a person chosen at random from the population has the disease. The test has a sensitivity of 0.9, meaning that P(T|D) = 0.9, indicating that the test correctly detects the disease in 90% of individuals who actually have it.
Additionally, the test has a specificity of 0.9, implying that P(T|D') = 0.9, where D' represents the event that a person does not have the disease.
We can now apply Bayes' theorem:
P(D|T) = (P(D) * P(T|D)) / [P(D) * P(T|D) + P(D') * P(T|D')]
Substituting the known values:
P(D|T) = (0.03 * 0.9) / [(0.03 * 0.9) + (0.97 * 0.1)]
Calculating this expression yields P(D|T) ≈ 0.0826, or approximately 8.26%.
Given this result, it can be observed that the conditional probability of having the disease, given a positive test result, is relatively low. This suggests that the test is not highly reliable.
Although the test has a high accuracy in correctly identifying individuals without the disease, it has a significant false-positive rate when it comes to individuals who do have the disease. Therefore, it is important to consider other factors and confirmatory tests before reaching a conclusive diagnosis.
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4) Find the values of k for which the line y = 3x + 1 cuts the curve y = x² + kx + 2 in two distinct
points.
Answers
Answer:
\(k<1, k>5\)
Step-by-step explanation:
\(3x+1=x^2+kx+2 \\ \\ x^2+x(k-3)+1=0 \\ \\ \Delta>0 \implies (k-3)^2-4(1)(1)>0 \\ \\ (k-3)^2-2^2>0 \\ \\ (k-1)(k-5)>0 \\ \\ k<1, k>5\)
there are 80 people at the city swimming pool today. everyone in the park was wearing swimsuits and sunglasses; some people had both. how many people had swimsuits on but not sunglasses, if you know 68 people had swimsuits on and 39 had sunglasses?
Answers
Answer:
41 people
Step-by-step explanation:
If there are 68 people wearing swimsuits and 39 people are wearing sunglasses: 80 - 39 = 41. 41 people are wearing swimsuits but not sunglasses. This is only true aslong as everyone had to be wearing atleast a pair of sunglasses or a swimsuit.
miss austin gives her class 6 sets of data and asks them to identify which data set can most accurately be summarized by the mean. what topic is she covering?
Answers
Miss Austin is covering the topic of central tendency in statistics, specifically the mean. By giving her class 6 sets of data and asking them to identify which one can be most accurately summarized by the mean, she is testing their understanding of how the mean represents the average value of a set of data.
This also involves understanding how to calculate the mean and interpret its value in relation to the other values in the dataset. Therefore, Miss Austin is helping her class develop skills in data analysis and statistical reasoning. The use of the term "set" is not clear, but assuming it means "sets of data," it is relevant to the topic being covered.
Miss Austin is covering the topic of "Descriptive Statistics" in her class. Specifically, she is focusing on the concept of "mean" as a measure of central tendency to summarize data sets. By asking her students to identify which data set can most accurately be summarized by the mean, she is teaching them how to understand the appropriateness of using the mean for different sets of data.
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the radius of a sphere was measured and found to be 20 cm with a possible error in measurement of at most 0.05 cm. what is the maximum error in using this value of the radius to compute the volume of the sphere?
Answers
Using concepts of Errors and Measurement, we got 252cm³ will be the maximum error in volume of sphere.
We know that volume(V) of sphere is given by =\(\frac{4.\pi .r^{3} }{3}\),where r is the radius of the volume.
If the error in the measured value of r is denoted by then the corresponding error in the calculated value of Volume is , which can be approximated by the differentiating the volume with respect to radius.
When r = 20 and dr = 0.05, this becomes:
d(V)/dr = 4×π×r²
=>d(V)=(4×π×r²)×dr
On putting the values,
=>d(V)=4×π×(20²)×(0.05)
=>d(V)=4×3.14×400×0.05
=>d(V)=252
Hence, the maximum error is 252cm³ in calculating the volume of sphere if we use the given radius.
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Calculate the profits for company Econislife based on the figures in the table below. What is the profit-maximizing level of output? What is the profit at this quantity? Econislife Total Revenue and Total Cost Quantity (Q) Total Revenue (TR) Total Costs (TC) 1 $28 $40 2 $56 $45 3 $84 $55 4 $112 $72 5 $140 $120
Answers
Based on the given table, the profit-maximizing level of output for company Econislife is 4 units. At this quantity, the company's profit is $40.
To determine the profit-maximizing level of output, we need to analyze the relationship between total revenue (TR) and total costs (TC) for different quantities of output. The profit can be calculated as the difference between total revenue and total costs.
Looking at the table, we can see that as the quantity increases from 1 to 5, both total revenue and total costs increase. However, at a certain point, the increase in total costs outpaces the increase in total revenue, leading to a decrease in profit.
To find the profit-maximizing level of output, we compare the profits at different quantities.
Quantity 1: TR = $28, TC = $40, Profit = TR - TC = $28 - $40 = -$12
Quantity 2: TR = $56, TC = $45, Profit = TR - TC = $56 - $45 = $11
Quantity 3: TR = $84, TC = $55, Profit = TR - TC = $84 - $55 = $29
Quantity 4: TR = $112, TC = $72, Profit = TR - TC = $112 - $72 = $40
Quantity 5: TR = $140, TC = $120, Profit = TR - TC = $140 - $120 = $20
From the above calculations, it is evident that the profit is highest at Quantity 4. Therefore, the profit-maximizing level of output for company Econislife is 4 units. At this quantity, the company's profit is $40.
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what involves asking questions and answering those questions using statistical and quantitative tools for explanatory and predictive analysis?
Answers
A process of analysing, purifying, manipulating, and modelling data in order to find relevant information, come to conclusions, and enhance decision-making is known as data analytics.
It entails posing queries and providing answers utilising quantitative and statistical methods for explanatory and prescriptive analysis. Descriptive, diagnostic, predictive, and prescriptive analytics are the four basic categories of data analysis.
Diagnostic analytics is used to determine the reason why something occurred, whereas descriptive analytics is used to report what has already occurred.
The use of predictive analytics, on the other hand, enables the prediction of likely future events. Last but not least, prescriptive analytics is employed to decide what steps should be taken in order to accomplish a particular result or goal in light of the knowledge gleaned from descriptive, diagnostic, and predictive analytics.
By using these different types of analytics, individuals will be able to gather and analyze data to better understand trends, identify problems, and make informed decisions.
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a shipment of 13 televisions sets contains 6 defective sets. a hotel purchases 6 of these televisions sets. what is the probability that the hotel receives at least one of the defective sets?
Answers
The probability that the hotel receives at least one of the defective sets is 99.59%
To find the probability that the hotel receives at least one defective set, we can use the concept of complementary probability.
The probability of the hotel receiving at least one defective set is equal to 1 minus the probability of the hotel receiving no defective sets.
The probability of the hotel receiving no defective sets can be calculated as the ratio of the number of ways to choose 6 non-defective sets out of the total number of ways to choose any 6 sets.
The total number of ways to choose 6 sets from the shipment of 13 sets is given by the binomial coefficient C(13, 6).
The number of ways to choose 6 non-defective sets from the remaining 13 - 6 = 7 non-defective sets is given by the binomial coefficient C(7, 6).
Therefore, the probability of the hotel receiving no defective sets is:
P(no defective sets) = C(7, 6) / C(13, 6)
To find the probability of receiving at least one defective set, we subtract this probability from 1:
P(at least one defective set) = 1 - P(no defective sets)
Calculating the values:
C(7, 6) = 7
C(13, 6) = 1716
P(no defective sets) = 7 / 1716
P(at least one defective set) = 1 - 7 / 1716
Therefore, the probability that the hotel receives at least one defective set is approximately:
P(at least one defective set) ≈ 1 - 0.0041 ≈ 0.9959 or 99.59%
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pls say me the 12th qns
Answers
Answer:
Step-by-step explanation:
12) p & q are parallel lines , n is transversal
4z = 108 { corresponding angles are congruent}
Divide both sides by 4
z = 108/4
z = 27°
n & m are parallel lines , p is transversal
3y = 4z { corresponding angles are congruent}
3y = 4 * 27
y = \(\frac{4*27}{3}\)
y = 4*9
y = 36°
n & l are parallel lines, q is transversal
6x = 108 { corresponding angles are congruent}
x = 108/6
x = 18°
A rectangle has a perimeter of 45 feet and a base of 5.5 feet. What is the height?
Answers
The height of the rectangle will be 17 feet.
What is the perimeter of the rectangle?Let H be the height and W be the width of the rectangle.
Then the perimeter of the rectangle will be
Perimeter of the rectangle = 2(H + W) units
A rectangle has a perimeter of 45 feet and a base of 5.5 feet.
The sum of all the sides of the rectangle will be known as the perimeter of the rectangle.
Then the height of the rectangle will be
45 = 2(H + 5.5)
22.5 = H + 5.5
H = 22.5 - 5.5
H = 17 feet
Thus, the height of the rectangle will be 17 feet.
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Solve for y, Angle Q and Angle S
Answers
Answer:
hope
Step-by-step explanation:
2. Jodi works 51 hours one week. (Remember that 40 hours is a regular work
week) If she makes $25.50/hr., How much will she make that week?
Answers
Answer:
1300.5
51*25.5 = 1300.5
7 x ..... = 364 whats the missing number ?
Answers
To find the missing number divide 364 by 7
364 / 7 = 52
The missing number is 52
Answer:
52
Step-by-step explanation:
In this equation, you would have to use inverse operations.
Since this equation is a multiplication equation, you need to do the opposite, division. So, 364 ÷ 7 = 52
Hope this helps! :)
all else constant, which combination of factors would increase the width of a confidence interval most?
Answers
Factors that would definitely increase the width of a confidence interval is: Increase the sample mean and increase the percentage of confidence.
Which combination factors would increase width of confidence interval?
The width of the confidence interval decreases as the sample size increases. The width increases as the standard deviation increases. The width increases as the confidence level increases (0.5 towards 0.99999 - stronger).
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Please solve them I really need help
Answers
Answer:
Answers are below
Step-by-step explanation:
12) No because the scale factor is not the same between the two rectangles
13) Yes. TUV is congruent to XYZ. The scale factor is 3/4.
14) Yes. I used SAS to see whether or not the triangles were similar. PQR is congruent to UVW.
15) Yes. I used 14) Yes. I used SAS to see whether or not the triangles were similar. DGH is congruent to FEH.
The area of a circle is 23.79cm2.
Find the length of the radius rounded to 2 DP.
Answers
Answer:
2.75cm
Step-by-step explanation:
Given data
Area of circle= 23.79cm^2
We know that the formula for the area of a circle is
Area= πr^2
Substitute
23.79=3.142*r^2
23.79/3.142= r^2
7.57=r^2
Square roo both sides
r= √7.57
r= 2.75 cm
Hence the radius is 2.75cm
In AABC, if AC = CB, MZA = 3x + 18, m_B = 7x - 58, and mC = 2x - 8, find x and the
measure of each angle.
MZA =
mZB =
mZC =
Answers
The values of the angles of the triangle ABC is
∠A = 75, ∠B = 75 and ∠C = 30
Given, In ΔABC, AC = CB
∠A = 3x + 18, ∠B = 7x - 58 and ∠C = 2x - 8
Now, as AC = BC
∠A = ∠B
3x + 18 = 7x - 58
18 + 58 = 7x - 3x
76 = 4x
4x = 76
x = 19
So, the value of ∠A is 3x + 18 = 3(19) + 18
∠A = 75
the value of ∠B is 7x - 58 = 7(19) - 58
∠B = 75
also, the value of ∠C is 2x - 8 = 2(19) - 8
∠C = 30
Hence, the values of the angles of the triangle ABC is
∠A = 75, ∠B = 75 and ∠C = 30
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Evaluate (2x + 4) – (3x + 6) when x = 4.
Answers
Answer:
-6
Step-by-step explanation:
(2x + 4) – (3x + 6)
Distribute the minus sign
2x +4 -3x -6
-x -2
Let x = 4
-4-2
-6
Answer:
-6
Step-by-step explanation:
(2x + 4) – (3x + 6) =
= 2x + 4 - 3x - 6
= -x - 2
= -(4) 2
= -6
Given the following test scores, find a 95 percent confidence interval for the population mean: 148, 154, 158, 160, 161, 162, 166, 170, 182, 195, 236. Assume population normality
Answers
A 95% confidence interval for the population mean can be calculated by finding the sample mean and the margin of error for a given level of confidence.
To do this, we need to find the sample mean and standard deviation of the sample data and then use the standard error of the mean.
Here are the steps to calculate the 95% confidence interval:
Calculate the sample mean:
The sample mean is calculated by summing up all the sample data points and dividing by the total number of data points:
Sample mean = (148 + 154 + 158 + 160 + 161 + 162 + 166 + 170 + 182 + 195 + 236) / 11 = 167.36
Calculate the sample standard deviation:
The sample standard deviation is calculated as follows:
Sample standard deviation = sqrt(((148-167.36)^2 + (154-167.36)^2 + (158-167.36)^2 + (160-167.36)^2 + (161-167.36)^2 + (162-167.36)^2 + (166-167.36)^2 + (170-167.36)^2 + (182-167.36)^2 + (195-167.36)^2 + (236-167.36)^2) / 11-1) = 33.07
Calculate the standard error of the mean:
The standard error of the mean is calculated as follows:
Standard error of the mean = sample standard deviation / sqrt(sample size) = 33.07 / sqrt(11) = 11.11
Calculate the margin of error:
The margin of error is calculated as follows:
Margin of error = t-value * standard error of the mean
where t-value is the critical value from the t-distribution table for a given degree of freedom and level of confidence. For a 95% confidence level and 10 degrees of freedom, the t-value is approximately 1.833.
Margin of error = 1.833 * 11.11 = 20.53
Calculate the lower and upper bounds of the confidence interval:
The lower and upper bounds of the confidence interval are calculated as follows:
Lower bound = sample mean - margin of error = 167.36 - 20.53 = 146.83
Upper bound = sample mean + margin of error = 167.36 + 20.53 = 187.89
Therefore, the 95% confidence interval for the population mean is [146.83, 187.89]. This means that we are 95% confident that the true population mean lies between 146.83 and 187.89.
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What does the % error tell you about the accuracy of the measurements. Choose the letter corresponding to the explanation that bests fits your results.
Answers
The % error tells you about the accuracy of the measurements.
This is because it provides information about how close a measured or calculated value is to the true or accepted value.
The % error is expressed in percentage form.
It is computed as follows:
% Error = (|accepted value - experimental value|/accepted value) x 100
The % error can be used to determine the accuracy of measurements, and the higher the % error, the lower the accuracy.
A % error of 0% implies that the experimental value is the same as the accepted value, while a % error of 100% implies that the experimental value is two times greater than the accepted value.
Therefore, a small % error means that the measurements are accurate, while a large % error means that the measurements are inaccurate.
The % error may be used to identify the source of error in an experiment.
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Rewrite in simplest terms: -(3c - 8) - 3c
Answers
Answer:
3c -8 -3f = Kc-
Step-by-step explanation:
Answer:
did da work :)
Step-by-step explanation:
2(x+4)+2=5x+1 solve for x
Answers
Answer:
x = 3
Step-by-step explanation:
2(x+4) + 2 = 5x + 1
2x + 8 + 2 = 5x + 1
2x + 10 = 5x + 1
-3x + 10 = 1
-3x = -9
x = 3
To solve for x, we need to simplify the equation and isolate the variable. Let's proceed with the given equation:
2(x + 4) + 2 = 5x + 1
First, distribute the 2 to the terms inside the parentheses:
2x + 8 + 2 = 5x + 1
Combine like terms on the left side:
2x + 10 = 5x + 1
Next, let's move all terms containing x to one side of the equation and the constant terms to the other side. We can do this by subtracting 2x from both sides:
2x - 2x + 10 = 5x - 2x + 1
Simplifying further:
10 = 3x + 1
To isolate the x term, subtract 1 from both sides:
10 - 1 = 3x + 1 - 1
9 = 3x
Finally, divide both sides of the equation by 3 to solve for x:
9/3 = 3x/3
3 = ×
Therefore, the solution to the equation is x = 3.
Kindly Heart and 5 Star this answer and especially don't forgot to BRAINLIEST, thanks!find the expectation value of the position squared when the particle in the box is in its third excited state. answer this question with the correct coefficient of l2 for the expectation value.
Answers
The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.
The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),
where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to
\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).
This can be written as nine-eighths of the length of the box squared.
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A model plane is 1/48 the size of the actual plane. If the model plane is →28 inches long←, how long is the actual plane? Explain your reasoning to a classmate.
Answers
Answer: 112
Step-by-step explanation:
To change this into feet we need to determine how many lots of 12 inches we can fit into 1344 inches (12 inches = 1 foot). 1344 12 =112 feet
Translate the sentence into an equation.
Twice the difference of a number and 8 equals 6.
Answers
Answer:
2(n-8)=6
n = 11