The equation of the quadratic graph is: [tex]y = \frac{1}{8}(x - 3)^2 + 4[/tex]
In a quadratic graph, the focus and the directrix determine the shape and position of the parabola. The focus (3,4) represents the vertex of the parabola, and the directrix y=8 is a horizontal line.
To evaluate the equation of the quadratic graph, we use the vertex form of a quadratic equation, which is [tex]y = a(x - h)^2 + k[/tex], where (h,k) represents the vertex.
The focus coordinates indicate that the vertex is at (3,4). Thus, h = 3 and k = 4.
Since the directrix is a horizontal line, its equation takes the form y = c, where c is a constant. In this case, the directrix equation is y=8, meaning the distance from the vertex to the directrix is 4 units (8 - 4 = 4).
Using the formula [tex]a =\frac{1}{4p}[/tex], where p is the distance from the vertex to the focus (or directrix), we find that [tex]p = \frac{4}{2} = 2[/tex].
Substituting the values into the vertex form equation, we get:
[tex]y = a(x - 3)^2 + 4[/tex]
To evaluate the value of a, we use the formula a = 1 / (4p), where p = 2. Substituting this value, we have:
[tex]a = \frac{1}{4*2} = \frac{1}{8}[/tex]
Therefore, the equation of the quadratic graph is:
[tex]y = \frac{1}{8} (x - 3)^2 + 4[/tex]
Hence, the equation of the quadratic graph with a focus of (3,4) and a directrix of y=8 is [tex]y = \frac{1}{8} (x - 3)^2 + 4[/tex].
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a man sold an article at a gain of 5 percent if it had sold for rs 16.30 less he would have suffered a loss of 5 percent find the cost price?
Answer:
Step-by-step explanation:
let CP of the article = x
at 5% gain, SP of article = x + (5/100)x = 1.05x
at 5% loss, SP of article = x - (5/100)x = 0.95x
given that 1.05x - 0.95x = 16.5
⇒ 0.1x = 16.5
⇒ x = 16.5/0.1
⇒ x = Rs. 165.
The cost price of the article is Rs. 165.
A standard test of intelligence is scaled so that the mean IQ is 100, and the standard deviation is 15. If there are 40,00 people in a certain town , what is the percentage of people who have an IQ between 70 and 130 ?
a. 47.5%
b. 95%
c. 68 %
d. 99.7
The correct option to the sentence "The percentage of people who have an IQ between 70 and 130 ?" is:
b. 95%.
To solve for the percentage of people who have an IQ between 70 and 130, we will have to use the standard deviation and the mean IQ.
It is given that: Mean = 100, Standard deviation = 15
Now we will use these values to find the percentage of people who have an IQ between 70 and 130.
The first step to this process is to standardize the IQ scores by converting them to Z-scores.
The formula for Z-score is:
Z = (X - µ) / σ, where X represents the IQ score, µ represents the mean IQ, and σ represents the standard deviation.
IQ score of 70:
Z = (70 - 100) / 15
Z = -2
IQ score of 130:
Z = (130 - 100) / 15
Z = 2
Now that we have the Z-scores for IQ scores of 70 and 130, we can find the percentage of people who have an IQ between these two scores. We will use the Z-table to do this. The Z-table provides the area under the standard normal distribution curve for a given Z-score.
From the Z-table, we can find that the area under the curve between Z = -2 and Z = 2 is approximately 0.9545. This means that approximately 95.45% of people have an IQ between 70 and 130.
Therefore, the correct option is: b. 95%.
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I have an hour to do this please help
Answer:
6
Step-by-step explanation:
27/9 =3
now 18/3
=6
write both an explicit equation and recursive equation for the sequence 64,8,1,0,0.125..
HURRY PLEASE!!
Answer:
a(n) = n/8
Step-by-step explanation:
64/8 = 8, 8/8 = 1, 1/8 = 0.125.…
Explicit Equation: a(n) = n/8
Recursive Equation: a(1) = 64; a(n) = n/8
i dont know if this is correct or not but here you go!
If a researcher wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he makes on a simple test. The following data is recorded.
n = 4, Σx = 20, Σy = 25, Σxy = 144 & Σx² = 120.
Find the equation of the regression line:
y = a + bx. y = (a = ____) + (b = _____)x.
b = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²] = ____
a = [(Σy)(Σx²) - (Σx)(Σxy)] / [n(Σx²) - (Σx)²] = _____
The equation of the regression line is: y = 1.5 + 0.95x
How to find the equation of the regression lineTo find the equation of the regression line, we can use the formulas:
b = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²]
a = [(Σy)(Σx²) - (Σx)(Σxy)] / [n(Σx²) - (Σx)²]
Given the following data:
n = 4
Σx = 20
Σy = 25
Σxy = 144
Σx² = 120
Let's calculate the values step by step:
b = [4(144) - (20)(25)] / [4(120) - (20)²]
= (576 - 500) / (480 - 400)
= 76 / 80
= 0.95
a = [(25)(120) - (20)(144)] / [4(120) - (20)²]
= (3000 - 2880) / (480 - 400)
= 120 / 80
= 1.5
Therefore, the equation of the regression line is:
y = 1.5 + 0.95x
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Explain what you think that term dilation means.
Answer:
the action or condition of becoming or being made wider, larger, or more open.
Step-by-step explanation:
if the third term is 20 and 7th is 1.25, find the 11th term
Answer:
the 11th term is 0.0000488 or 4.88*10^-5.
Step-by-step explanation:
a3 = 20, a7 = 1.25
a7 = a3r^7-3
1.25 = 20r^4
r^4 = 0.0625
r = 4th root of 0.0625
r = 0.5
a3 = a1r^3-1
20 = a1(20)^2
400a1 = 20
a1 = 0.05
a11 = 0.05(0.5)^11-1 = 0.0000488 or 4.88*10^-5
HELPPP PLSSS Choose the most appropriate translation of the English sentence.
The radius of a balloon (which depends on the amount of air inside) is 3
inches.
Answer:
A radius(radius) = 3The radius of a balloon (which depends on the amount of air inside) is 3
inches
Let p(x)=x+3x²-4x-12 a) Find the x-intercepts of the graph of p(x) c) Sketch a graph of p(x) b) Find the y-intercept of the graph of p(x)
a) The x-intercepts of p(x) are x = 3 and x = -4/3. b) The y-intercept of p(x) is y = -12.
a) To find the x-intercepts, we set p(x) = 0 and solve for x:
x + 3x² - 4x - 12 = 0
Simplifying the equation, we get:
3x² - 3x - 12 = 0
Factoring, we have:
(x - 3)(3x + 4) = 0
Setting each factor equal to zero, we find the x-intercepts:
x = 3 and x = -4/3
b) The y-intercept is the value of p(0), so we substitute x = 0 into the equation:
p(0) = 0 + 3(0)² - 4(0) - 12 = -12
Therefore, the y-intercept is -12.
c) To sketch the graph, we plot the x-intercepts (x = 3 and x = -4/3) and the y-intercept (y = -12) on a coordinate plane.
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3. This spinner is divided into eight equal-sized sections. Each section is labeled with a number
Jake spins the arrow on the spinner once.
Drag and drop the events into the correct order from least likely to most likely.
Answer:
Least Likely: Arrow lands on a section labeled with an odd number.
_____: Arrow lands on a section labeled with the number 1.
Most Likely: Arrow lands on a section labeled with a number less than 4.
Step-by-step explanation:
The spinner:
There are 8 sections, 4 labeled with the number 1, 2 labeled with the number 3, 1 labeled with the number 3, and 1 labeled with the number 4.
Probabilities of the spinner:
Probability of landing on 1: 4/8 - 50%Probability of landing on 2: 1/8 - 12.5%Probability of landing on 3: 2/8 - 25%Probability of landing on 4: 1/8 - 12.5%The options:
A - Arrow lands on a section labeled with an odd number.
B - Arrow lands on a section labeled with the number 1.
C - Arrow lands on a section labeled with a number less than 4.
The least likely possibility out of the options would be B because, while a 50% chance sounds like a lot, it is the least of the three options.The mid possibility out of the options would be A. The odd numbers labeled on the spinner make up 75% of the whole. (1s and 3s - 50% + 25%)The most likely possibility out of the options is C because it accounts for every section except for the single section labeled with the number 4. (100% - 12.5%, 87.5%)Solve each inequality.
2s+5> 49
_
Answer: S > 22
Step-by-step explanation:
Answer:
s = 23 and above
Step-by-step explanation:
2s + 5 > 49
-5 -5
2s > 44
44/2
= 22
However, the answer for s is not 22
Since it has this sign > not ≥ then that means s = 23 and above
Check:
2(23) + 5 > 49
46 + 5 > 49
51 > 49
The blood results for a particular sample unknown test from ten finalists of a medical study were recorded for further analysis. Find the following quantities below.
Blood test results: {580, 610, 530, 530, 440, 670, 480, 540, 590, 490 }
(Use only 2 decimal places. Ex. if answer is 34.568, just write 34.56. If the answer is 321 just leave as 321, do not add any decimals)
a) Mean _______
(b) Median______
(c) Mode________
(d) Range________
(e) Variance ________
(f) Standard deviation_______
(g) IQR ______
(h) Upper fence ________
Answer:
(a) Mean = 541.00
(b) Median = 535.00
(c) Mode: 530
(d) Range = 230
(e) Variance = 5340.40
(f) Standard deviation = 73.10
(g) IQR = 100
(h) Upper fence = 740.00
Step-by-step explanation:
Which of these describe a unique polygon
Answer: d
Step-by-step explanation:
3 questions
4 is about what percent of 9?
About what percent of 7560 is 3000?
1.3 is about what percent of 27?
Please help me my teacher does not explain how to do this well..
 PLSSS HELP IMMEDIATELY!!!!! i’ll give brainiest, i’m not giving brainiest if u leave a link tho. (pls check whole picture!!) answer choices: (4,6) (0,1) (0,0) (5,4)
Answer:
(0, 1)
Step-by-step explanation:
All other choices do not match the two possible vertices of the square.
I need help on this question and answering it
Answer:
75 feet
Step-by-step explanation:
the shadow to the object would be a 4:5 ratio
since the shadow of the flagpole is 60 ft,
4x=60 so x would =15
then you multiply 15 by 5 and end up with 75
Answer: 75 feet
Step-by-step explanation: trust me
Are the ratios 18:6 and 3:1 equivalent?
Answer: no
Step-by-step explanation: here are all the ratios equivalent to 18:6 18 : 636 : 1254 : 1872 : 2490 : 30108 : 36126 : 42144 : 48162 : 54180 : 60198 : 66216 : 72234 : 78252 : 84270 : 90288 : 96306 : 102324 : 108342 : 114360 : 120378 : 126396 : 132414 : 138432 : 144450 : 150468 : 156486 : 162504 : 168522 : 174540 : 180558 : 186576 : 192594 : 198612 : 204630 : 210648 : 216666 : 222684 : 228702 : 234720 : 240738 : 246756 : 252774 : 258792 : 264810 : 270828 : 276846 : 282864 : 288882 : 294900 : 300918 : 306936 : 312954 : 318972 : 324990 : 3301008 : 3361026 : 3421044 : 3481062 : 3541080 : 3601098 : 3661116 : 3721134 : 3781152 : 3841170 : 3901188 : 3961206 : 4021224 : 4081242 : 4141260 : 4201278 : 4261296 : 4321314 : 4381332 : 4441350 : 4501368 : 4561386 : 4621404 : 4681422 : 4741440 : 4801458 : 4861476 : 4921494 : 4981512 : 5041530 : 5101548 : 5161566 : 5221584 : 5281602 : 5341620 : 5401638 : 5461656 : 5521674 : 5581692 : 5641710 : 5701728 : 5761746 : 5821764 : 5881782 : 5941800 : 600
https://goodcalculators.com/ratio-calculator/
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Answer:
yes
Step-by-step explanation:
18:6
18/6=3
6/6=1
3:1 is a simpler version of 18:6
What is the volume of a cone with a radius 3 cm and a height 6 cm?
Answer:
56.55
Step-by-step explanation:
Find the missing length.
= ✓ [?]
C =
с
6
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer:
Pythagoras theorem= 6 squared +11 squared
= 36 + 121
= 157
Step-by-step explanation:
9y8tyfstoylhlh
A company has dump trucks that repeatedly go through three activities: loading, weighing, and travelling. Assume that there are eight trucks and that, at time 0, all eight are at the loaders. Weighing time per truck on the single scale is uniformly distributed between 1 and 9 minutes, and travel time per truck is exponentially distributed with mean 85 minutes. An unlimited queue is allowed before the loader(s) and before the scale. All truck can be travelling at the same time. Management desires to compare one fast loader against the two slower loaders currently being used. Each of the slow loaders can fill a truck in from 1 to 27 minutes, uniformly distributed. The new fast loader can fill a truck in from 1 to 19 minutes, uniformly distributed. The basis for comparison is mean system response time over a 40 hour time horizon, where a response time is defined as the duration of time from a truck arrival at the loader queue to that truck's departure from the scale. Perform statistically valid comparison of the two options simulated using common random numbers. a
To perform a statistically valid comparison of the two loader options, we can use simulation and common random numbers. We simulate the process over a 40-hour time horizon and compare the mean system response times for each loader option.
For the two slower loaders, we generate random numbers uniformly distributed between 1 and 27 minutes to represent the time taken to fill a truck. For the fast loader, we generate random numbers uniformly distributed between 1 and 19 minutes.
By simulating the process multiple times using the same set of random numbers (common random numbers), we can compare the mean system response times between the two loader options.
After running the simulation, we calculate the mean system response time for each loader option by averaging the response times of all trucks. We repeat the simulation multiple times (e.g., 100 or more) to obtain reliable estimates of the mean system response times.
Once we have the mean system response times for each loader option from multiple simulation runs, we can perform a statistical analysis to determine if there is a significant difference between the two options.
This analysis can be done using a suitable statistical test, such as a t-test or confidence interval analysis, depending on the distribution of the response time data and the assumptions made.
The statistical analysis will provide insights into whether the fast loader option significantly reduces the mean system response time compared to the slower loader options. A lower mean system response time would indicate better performance in terms of faster truck processing.
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help ASAP! Ill mark brainliest!
Answer:
55 students
Step-by-step explanation:
Just write down the answer.
Answer:
Step-by-step explanation:
Football: 500(.38)= 190
Basketball: 500(.25)= 125
55 students (65 students)
please answer this i will mark brainliest
Answer:
The median is 2
Step-by-step explanation:
Arrange your numbers in numerical order.
0011112233445
Count how many numbers you have.
If you have an odd number, divide by 2 and round up to get the position of the median number.
If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.
PLEASE MARK ME BRAINLIEST
38 − 7x = −2(x − 29)
Answer:
x = -4Step-by-step explanation:
38 − 7x = −2(x − 29)
=> 38 - 7x = -2x + 58
=> 38 - 58 = 7x - 2x
=> -20 = 5x
[tex] = > x = \frac{ - 20}{5} [/tex]
=> x = -4 (Ans)
What does 1/3 represent for the picture below?
Answer:
c the ratio of the measure of arc QR and the circle
Step-by-step explanation:
i just took the quiz
hope this helps (:
A regular heptagon is shown below. What is the value of x?
Answer:
108+x=180
X=180-108
X=72
The value of the exterior angle (x) in a regular heptagon is approximately 51.43 degrees.
Given is a regular heptagon with one of the exterior angle be x we need to find the value of x
To find the value of the exterior angle of a regular heptagon, we can use the formula:
Exterior Angle = 360 degrees / Number of Sides
In this case, the heptagon has seven sides, so we can substitute the values into the formula:
Exterior Angle = 360 degrees / 7
Exterior Angle ≈ 51.43 degrees
Therefore, the value of the exterior angle (x) in a regular heptagon is approximately 51.43 degrees.
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how to read a q q q q q q q q q q q q q q q q q
Your read from left to right. Read intensively if you want to practice the fundamentals and learn vocabulary. Intensive reading is focused more on individual details of what you’re reading.
hope this helped <3
Answer:
This is how to read a
Pronounce it with your mouth open as in "ah" then smile with an "ee" sound. Say "Ay" and that's how you say A or "Ah"
How to read Q? Just pronounce it as "Kyuu" or when reading it say "Ck" with a sharper sound.
Hope this helped!
Write 0.4% in simplest form
Answer:
if simplest form by you mean fraction then the answer is 2/5
hope this is the answer you are looking for
Step-by-step explanation:
Which expression is equivalent to 36 + 24?
Answer:
60
Step-by-step explanation:
This trapezoid is made up of two right triangles and one rectangle.
Drag numbers to show the area of each triangle and the area of the rectangle. Then drag a number to show the total area of the trapezoid.
30 PIONT IF YOU ANSWER
9514 1404 393
Answer:
each triangle: 29.75 in²rectangle: 374 in²total area: 433.5 in²Step-by-step explanation:
The base of each triangle is half the difference between the bases of the trapezoid:
(29 in -22 in)/2 = 7 in/2 = 3.5 in
The area of the triangle is given by the formula ...
A = 1/2bh
A = 1/2(3.5 in)(17 in) = 29.75 in² . . . triangle area
__
The area of the central rectangle is the product of its base and height.
A = bh = (22 in)(17 in) = 374 in² . . . rectangle area
__
The total area of the trapezoid is the sum of the areas of the two triangles and the area of the rectangle.
total area = 2(29.75 in²) + 374 in² = 433.5 in² . . . total trapezoid area
You are a civil engineer designing a bridge. The walkway needs to be made of wooden planks. You are able to use either Sitka spruce planks (which weigh 3 pounds each), basswood planks (which weigh 4 pounds each), or a combination of both. The total weight of the planks must be between 600 and 900 pounds in order to meet safety code. If Sitka spruce planks cost $3.25 each and basswood planks cost $3.75 each, how many of each plank should you use to minimize cost while still meeting building code?
The optimal solution to minimize cost while meeting the building code is to use 0 Sitka spruce planks and 150 basswood planks.
How to Minimize Cost Using Function Equations?To minimize the cost while meeting the building code, let's assume we use x Sitka spruce planks and y basswood planks.
We want to minimize the cost, so our objective function is the cost of the planks. The cost is given by:
Cost = 3.25x + 3.75y
We also have the constraint that the total weight of the planks must be between 600 and 900 pounds:
3x + 4y ≥ 600
3x + 4y ≤ 900
To solve this optimization problem, we can use linear programming. We'll use the Simplex method to find the optimal solution.
Let's rewrite the constraints in standard form:
-3x - 4y ≤ -600
3x + 4y ≤ 900
Now we have the following system of equations:
-3x - 4y ≤ -600
3x + 4y ≤ 900
The feasible region is a quadrilateral with vertices at (0, 150), (0, 225), (300, 150), and (225, 0).
To minimize the cost, we need to find the corner point of the feasible region that lies on the cost line, which is given by 3.25x + 3.75y.
Let's evaluate the cost at each corner point:
Cost at (0, 150) = 3.25(0) + 3.75(150) = 562.50
Cost at (0, 225) = 3.25(0) + 3.75(225) = 843.75
Cost at (300, 150) = 3.25(300) + 3.75(150) = 1500.00
Cost at (225, 0) = 3.25(225) + 3.75(0) = 731.25
From the evaluations, we can see that the minimum cost is achieved at (0, 150), which means we should use 0 Sitka spruce planks and 150 basswood planks.
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