The fire department is setting off fireworks. they notice that the casing of the firework hits the ground 78 meters from where the firework was launched. the firework exploded at a maximum height of 760.5 meters.
Answers
The path of a firework can be modeled by a parabola. The standard form of a parabola is y = ax² + bx + c. The vertex form of a parabola is y = a (x - h)² + k where (h, k) is the vertex of the parabola.
The vertex of the parabola represents the maximum height of the firework. Since the firework exploded at a maximum height of 760.5 meters, we know that k = 760.5.
The x-intercepts represent the time when the firework hits the ground. Since the casings of the fireworks hit the ground 78 seconds after the firework was launched, we know that there are two x-intercepts: one at x = 0 and one at x = 78.
To find the y-intercept, we need to find the value of y when x = 0. Since we know that the vertex is (h, k) and that k = 760.5, we can substitute these values into the vertex form of the equation to get:
y = a(x - h)² + k y
= a(x - h)² + 760.5
Since we know that x = 0 when y is at its maximum value (the vertex), we can substitute x = 0 into this equation to get:
y = a(0 - h)² + 760.5 \
y = ah² + 760.5
Therefore, the y-intercept is (0, ah² + 760.5).
To find a and h, we need to use the information given in your question. We know that the vertex is (h, k) = (0, 760.5) and that there are two x-intercepts at x = 0 and x = 78.
We can use these three points to solve for a, b, and c in the standard form of the equation y = ax² + bx + c.
Substituting (0, 760.5) into y = ax² + bx + c gives:
760.5 = a(0)² + b(0) + c
c = 760.5
Substituting (0, ah² + 760.5) into y = ax² + bx + c gives:
ah² + 760.5 = a(0)² + b(0) + 760.5
ah² = 0 h = 0
Substituting (78, 0) into y = ax² + bx + c gives:
0 = a(78)² + b(78) + c
0 = 6084a + 78b + c
We have three equations with three unknowns:
c = 760.5 h = 0 6084a + 78b + c = 0
Solving for a, b, and c gives:
a ≈ -0.0198 b ≈ 1.0006 c ≈ 760.5
Therefore, the equation for this parabola is:
y ≈ -0.0198x² + 1.0006x + 760.5
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Complete question is:
The fire department is setting off fireworks. They notice that the casings of the fireworks hit the ground 78 seconds after the firework was launched. The firework exploded at a maximum height of 760.5 meters.
Identify how you see the x- and y-intercepts and vertex in the table, graph, and equation. (Hint: You may want to rewrite the equation in equivalent forms.)
(Refer the image also)
Related Questions
At a resort, the housekeeper and the concierge may have different levels of education and perform different tasks in their lines of work, but they both still work in the Lodging pathway of the Hospitality and Tourism cluster. Question 1 options: True False
Answers
Answer:
the answer is true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The test said it is right
HELP PLEAASE i need answer nowwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
Answers
Answer:Irrational,2/9,22/100 11/50, Irrational, No Fraction Given, Perfect Square, Non-Perfect Square
Step-by-step explanation:Best fit options for each question.
f(x) = 3x² + 5x – 2-g(x) = 5x³ - 4x² + 4Find (f + g)(x)O A. (f+g)(x) = -5x³ + 7x² + 5x - 6OB. (f+g)(x) = 8x³ + x + 2O C. (f+g)(x) = 5x³+3x²+x+2D. (f+g)(x) = 5x³ - x² + 5x+2
Answers
f(x) = 3x² + 5x – 2
g(x) = 5x³ - 4x² + 4
We want to find
(f+g)(x)
We need to add the two functions, making sure to line up the powers of x
f (x) = 3x² + 5x – 2
+g(x) = 5x³ - 4x² + 4
------------------------------
(f+g)(x) = 5x³ - x²+ 5x+2
The answer choice is choice D
D. (f+g)(x) = 5x³ - x² + 5x+2
2x+3y=8 (3/2)y+x=4 determine x and y and please show work!!
Answers
The system of equation has infinite many solutions
How to solve for x and y?The equations are given as:
2x+3y=8
(3/2)y+x=4
Multiply the second equation by 2
3y + 2x = 8
So, we have:
2x+3y=8 and 3y + 2x = 8
Both equations are the same
Hence, the system of equation has infinite many solutions
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I need to find 13 and 12
Answers
Values of 12 and 13 are 76° and 63° respectively.
What is triangle?A polygon with three sides and three angles is triangle.It is the simplest polygon and can be classified based on its sides and angles. Triangles are used in various fields, including mathematics, engineering, architecture, and art. They are also used to represent stability, strength, and balance in symbols and logos.
Given:-∠F = 104°
Let we assume ∠12 = x
therefore,
∠12 + ∠F = 180°
x + 104 = 180°
x = 180 - 104
x = 76°
therefore , ∠12 is 76°.
now ,
∠D = 41°
Sum of all angles of triangle is 180°
so,
∠D + ∠12 + ∠13= 180°
41 + 76 + ∠E = 180
117 + ∠E = 180
∠E = 180 - 117
∠E = 63°
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A fair 6-sided die is rolled 300 times. What is a reasonable prediction for the number of times the event of landing on an odd number will occur?
A. 150
B. 50
C. 175
D. 100
Answers
Answer:
A. 150
Step-by-step explanation:
Calculate the probability of landing on an odd number: 1/2.
Multiply the probability by the number of trials: (1/2) * 300.
Simplify the expression: 150.
Therefore, a reasonable prediction is that the event of landing on an odd number will occur 150 times out of the 300 rolls of the fair 6-sided die.
W + 14 = -8
What’s the value of w
Answers
W is equal to -22
W=22
Answer:
-22
Step-by-step explanation:
First, lets flip the equation so That we can find W
-8 - 14 = W
The rules of math state that a negative minus a positive can be equal to that negative turned positive plus that positive, the answer turned negative
For example
8+14 = 22
-8-14 =-22
So this means W is -22
Lets check our work
-22+ 14 =-8
So the answer is true
Hope this helps!^^
answerrrrrr plssss ill giveee brainliesttttt
Answers
\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)
plsssssssss help I really need to do this I will give brainliest to anyone who solves
Answers
Answer:
MSP: 6a/2
CUB: ab/2
ABC: 20 square centimeters
KDR: 5x cm * 3x cm / 2
Step-by-step explanation:
MSP: 6 x a divided by 2
CUB: a x b divided by 2
ABC: 8 x 5 divided by 2
KDR: 5xcm * 3xcm divided by 2
write 7.171717 as a mixed number
Answers
Answer:
7 17/99
Step-by-step explanation:
What would be the degree of financial leverage for Foggy Futures Weather Forecasters if the company has earnings before interest and taxes of $750,000, has a 4. 5% loan on $1,000,000, and is in the 38% tax bracket? The firm does not have any preferred stock outstanding. A. 1. 22 b. 0. 97 c. 1. 06 d. 1. 78
Answers
The degree of financial leverage for Foggy Futures Weather Forecasters
is 1.06
Degree of Financial leverage (DFL) = (EBIT) / (EBT)
Earnings Before Interest and Taxes (EBIT) = $750,000
Amount to be given as loan on $1000000
$1,000,000 x 4.5% = $1,000,000 x 4.5/100
= $45000
To find EBT ( Earnings Before Tax),
EBT = EBIT - 45000
= 750000 - 45000
EBT = 705000
∴ DFL = (EBIT) / (EBT)
= 750000/705000
DFL = 1.06
The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).
Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve
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I need help with this
Answers
1. Since triangle ABC and DEF are congruent, the value of x is -3
2. length AB = 24
length DE = 24
What are congruent triangles?If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE
therefore;
12- 4x = 15-3x
collect like terms
12 -15 = -3x +4x
x = -3
therefore the value of x is -3 and
AB = 12 - 4x
AB = 12 -4( -3)
AB = 12 +12 = 24
DE = 15-3x
= 15-3(-3)
= 15 + 9
= 24
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after analyzing their data with the correct statistical method, scientists produce a p-value of 0.02. they have a desired type i error rate of 0.05. since their p-value is less than 0.05, they reject their null hypothesis. based upon their decision, which type of error could the scientists be making?
Answers
Based on the information provided, if the scientists produce a p-value of 0.02 and reject their null hypothesis at a desired Type I error rate of 0.05, they could be making a Type I error.
Type I error, also known as a false positive, occurs when the null hypothesis is true, but it is mistakenly rejected based on the statistical analysis. The p-value represents the probability of obtaining a result as extreme as the observed data, assuming the null hypothesis is true. In this case, the p-value of 0.02 indicates that there is a 2% chance of observing such an extreme result if the null hypothesis were true.
By setting a Type I error rate of 0.05, the scientists have predetermined that they are willing to accept a 5% chance of making a Type I error in their hypothesis testing. If the p-value is less than or equal to the significance level (0.05), it falls into the critical region, leading to the rejection of the null hypothesis.
Therefore, since the scientists reject the null hypothesis based on the p-value of 0.02, which is less than the significance level of 0.05, they are choosing to reject the null hypothesis despite the possibility of it being true. This decision incurs a risk of a Type I error, where they conclude that there is a significant effect or difference when, in reality, there may not be one in the population being studied.
However, it's important to note that the possibility of a Type I error does not provide direct evidence that a Type I error has actually occurred. It only suggests that the scientists might be committing a Type I error by rejecting the null hypothesis.
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Solve for f(-1)
f(x)=-3x +3
f(-1)=?
Answers
Which sets of vectors are orthogonal? Check all that apply.
a = 〈–1, 0〉 and b = 〈1, 0〉
c = 〈1, 0〉 and d = 〈0, –1〉
e = 〈–4, –6〉 and f = 〈12, 8〉
g = 〈4, –6〉 and h = 〈12, 8〉
v = 〈10, –5〉 and w = 〈–10, –20〉
x = 〈10, –5〉 and y = 〈–10, –2〉
Answers
Answer:
B, D, and E
Step-by-step explanation:
Edge 2020
The sets of vectors are orthogonal and will be c-d,g-h, and v-w.
What exactly is a vector?A vector is a quantity with a magnitude, and direction that follows the law of vector addition.
Fo the orthogonal vector their dot product is equal to zero.
The dot product for the set are as follows;
a.b)〈–1, 0〉〈1, 0〉 = -1
c.d)〈1, 0〉 〈0, –1〉=0
e.f) 〈–4, –6〉 〈12, 8〉=-96
g.h)〈4, –6〉〈12, 8〉=0
v.w) 〈10, –5〉〈–10, –20〉=0
x.y)〈10, –5〉 〈–10, –2〉=-90
The sets of vectors are orthogonal are;
c-d ,g-h,v-w
Sets B, D, and E of vectors are orthogonal.
Hence the sets of vectors are orthogonal and will be c-d,g-h, and v-w.
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The wheel of the Singapore Flyer is a circle with a diameter of 150 metres. Calculate the circumference of the wheel. Give your answer correct to the nearest metre.
Answers
Answer:
circumference is given by πd, where d is the diameter of the circle.
This implies, the circumference= 22/7*150m
=3300/7=471.429m
A bridge, PR, across a river is 400 m long. Gabe is launching a canoe at point Q.
He will paddle in a diagonal line across the river to point P. He plans to return along a route beside the bridge from P to R, and then along the shore from R back to Q. How far will this be altogether?
Answers
Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.
To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.
First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.
The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.
Using the Pythagorean theorem, we have:
x^2 + (width of the river)^2 = PR^2
Since the width of the river is not given, we'll represent it as w. Therefore:
x^2 + w^2 = 400^2
Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.
Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.
To find the total distance, we add up the distances:
Total distance = QP + PR + RQ
= x + 400 + x
= 2x + 400
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HELP! QUICK!!!!!!!!!!!!!!!
Answers
Answer:
Q₃ = 185
Step-by-step explanation:
the first step is to find the median of the data set
the median is the middle value of the data arranged in ascending order
112 , 130 , 132 , 140 , 149 , 151 , 163 , 172 , 185 , 190 , 200
↑ middle value
median = 151
the upper quartile Q₃ is the middle value of the data to the right of the median
163 , 172 , 185 , 190 , 200
↑ middle value
upper quartile Q₃ = 185
What is the area of the trapezoid? 13 5t st st square feet
Answers
The formula for calculating the area of a trapezoid is given by;
\(A=\frac{a+b}{2}h\)where a and b are the base and h is the height
From the question,
a = 5
b= 13
h = 3
substitute the vakues into the formula
\(A=\frac{5+13}{2}(3)\)\(A=\text{ 9}\times3\)\(A=27ft^2\)Please help me with #3!!
Answers
Item 19 Your pump empties the water from a swimming pool in 6 hours. When your friend's pump is used together with your pump, the pool is emptied in 1.5 hours. How long (in hours) does it take your friend's pump to empty the pool when working alone
Answers
Answer:
0.75 hours
Step-by-step explanation:
Time taken by my pump = 6 hours
Time taken by friend's pump = x
Combined time = 1.5 hours
Rate :
my pump = 1/6
Combined rate = 1/1.5
Combinwd rate = 1/6 + 1/x
Hence :
1/6 + 1/x = 1/1.5
(x + 6) / 6x = 1.5
x + 6 = 9x
x - 9x = - 6
-8x = - 6
x = - 6 / - 8
x = 0.75 hours
how to determine if a relation is a function calculator
Answers
Answer:
A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.
Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).
To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:
1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.
2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.
3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.
Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.
Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.
Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.
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please help me with this precalc question
Answers
Answer:
the answer to this problem is (C)
The standard normal curve shown below is a probability density curve for a
continuous random variable. This means that the area underneath the entire
curve is 1. What is the area of the shaded region between the two z-scores
indicated in the diagram? z=-1.2 z=0.85
A.0.8937
B.0.6825
C.0.4263
D.0.6375
E.0.6872
Answers
Answer:
E
Step-by-step explanation:
Here, we want to find the area of the shaded portion on the graph.
That would be P(-1.2<z<0.85)
we complete this by checking these values on the standard score table as follows;
P( z< 0.85) - P(z<-1.2) = 0.68727
need help on this quick please
Answers
The most appropriate unit for expressing the distance between the two stars is the light-year. The stars are light-years apart.
What is the most appropiate unit for this case?Given that the distance between the two stars is 8.82 x 10¹⁴ miles, we need to determine which unit from the given list is the most appropriate.
A light-year is the distance that light travels in one year, and it is commonly used to measure astronomical distances. Since the given distance is already in miles, we can convert it to light-years.
To convert miles to light-years, we need to divide the distance in miles by the number of miles in a light-year. Using the given conversion factor that 1 light-year = 5.88 x 10¹² miles, we can perform the calculation:
Distance in light-years = (8.82 x 10¹⁴ miles) / (5.88 x 10¹² miles/light-year)Simplifying the expression, we can cancel out the units of miles:
Distance in light-years = (8.82 / 5.88) x 10¹⁴/10¹² light-yearsDistance in light-years = 1.5 x 10² light-yearsAccording to the information, the most appropriate unit for expressing the distance between the two stars is the light-year, and the stars are approximately 150 light-years apart.
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Tip is ___. * 1 point
an additional amount charged by the restaurant similar to sales tax
a percentage you may add to a restaurant bill for good service
a discount offered by restaurants
a set amount charged in addition to all other items at a restaurant
PLZ HURRY WILL GIVE BRAINEST
Answers
Answer:
Gratuity?
Step-by-step explanation:
A gratuity (normally called a tip) is a sum of money customarily given by a client or customer to certain service sector workers for the service they have performed, in addition to the basic price of the service.
Answer:
tip
Step-by-step explanation:
tip is a percentage you may add to a restaurant bill.
The percentage is usually based on your experience with the waiter and the total amount of your food costs.
Someone help? Im giving 20 points.
Use the diagram to answer the questions below. Note: This image is not drawn to scale.
Line l is parallel to line m and is cut by the transversal, t.
What is the measure of angle g?
What is the measure of angle h?
Answers
Answer:HOla
Step-by-step explanation:
Answer:
Angle g: 85 angle h: 95
Step-by-step explanation:
Derek can deposit $14,455.00 on each birthday beginning with his 27.00 th and ending with his 68.00 th. What will the rate on the retirement account need to be for him to have $3,793,695.00 in it when he retires? Answer format: Percentage Round to: 2 decimal places (Example: 9.24%,% sign required. Wil accept decimal format rounded to 4 decimal places (ex: 0.0924))
Answers
To have $3,793,695.00 in his retirement account when he retires, Derek would need the rate on the account to be approximately 5.89%.
To calculate the required rate on Derek's retirement account, we can use the formula for the future value (FV) of an annuity:
\(FV = P * [(1 + r)^n - 1] / r\)
Where:
FV is the desired future value
P is the amount deposited on each birthday
r is the interest rate per period
n is the total number of periods (number of birthdays)
In this case, the desired future value (FV) is $3,793,695.00, the amount deposited on each birthday (P) is $14,455.00, and the total number of periods (n) is the difference between Derek's final and initial birthday, which is 68 - 27 = 41.
We need to solve for the interest rate (r). Rearranging the formula:
\(r = [(FV / P) / [(1 + r)^n - 1]]\)
Substituting the given values, we have:
\(r = [(3,793,695.00 / 14,455.00) / [(1 + r)^{41} - 1]]\)
We can use numerical methods or trial and error to find the value of r that satisfies the equation. By using these methods, the approximate value of r is found to be 0.0589 or 5.89%.
Therefore, Derek would need the rate on his retirement account to be approximately 5.89% for him to have $3,793,695.00 in it when he retires.
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What is the midpoint of Line segment A B ?
Answers
Answer:
point g is the correct answer
Step-by-step explanation:
The midpoint of Line segment A B is Option B; Point G.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
Midpoint, means the point which lies in the middle of something.
Midpoint of a line segment means a point which lies in the mid of the given line segment.
Given the graph at the right, the midpoint of A and B
AB = 14 units (by counting).
The midpoint is 7 units from either endpoints.
Thus, the midpoint of Line segment A B is Option B; Point G.
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A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 6,193 with a standard deviation of 598. Of the 35 two-year colleges surveyed, the mean enrollment was 4,305 with a standard deviation of 572. Test the student's claim at the 0.01 significance level.
Answers
At a significance level of 0.01, we can confidently state that the student's claim is true.
The hypothesis in this question can be stated as follows:
Null Hypothesis: H0: μ1 = μ2 (There is no difference between the mean of four-year college enrollment and two-year college enrollment.)
Alternative Hypothesis: H1: μ1 > μ2 (Mean enrollment of four-year colleges is greater than the mean enrollment of two-year colleges in the United States.)
The significance level (α) is given as 0.01, which represents the probability of rejecting the null hypothesis when it is actually true.
To calculate the test statistic, we can use the formula:
z = ((X1 - X2) - (μ1 - μ2)) / √((σ1² / n1) + (σ2² / n2))
Substituting the given values:
z = ((6193 - 4305) - (0)) / √((598² / 35) + (572² / 35))
z = 10.33
Since this is a right-tailed test, we need to compare the test statistic with the critical value. At a significance level of 0.01, the critical value is 2.33.
The calculated test statistic (10.33) is greater than the critical value (2.33). Therefore, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the mean enrollment at four-year colleges is higher than at two-year colleges in the United States.
In conclusion, at a significance level of 0.01, we can confidently state that the student's claim is true. The mean enrollment at four-year colleges is higher than at two-year colleges in the United States.
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