The rocket reaches a maximum height of 1045.6 feet.
How to find the maximum height of a parabola by quadratic formula
The height of the rocket under free fall is described by a parabola and parabolas are explained by second order polynomials, whose form are:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficients.x - Time, in seconds.y - Height, in feet.The maximum height can be found by means of discriminant of the quadratic formula associated with following variant:
a · x² + b · x + (c - y) = 0
Discriminant
b² - 4 · a · (c - y) = 0
b² = 4 · a · (c - y)
b² / (4 · a) = c - y
y = c - b² / (4 · a)
If we know that a = - 16, b = 246 and c = 100, then the maximum height reached by the rocket is:
y = 100 - 246² / [4 · (- 16)]
y = 1045.563 ft
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Solutions greatest to smallest for function
=2+5−7
The greatest or maximum value for the given function = -8.25
The minimum or smallest value for the given function =-4
Calculation of greatest and smallest functionsThe maximum value of a function is the highest value of that function. To calculate the greatest function, the following equation is used,
Formula max = c - (b2 / 4a)
Where,
a = 2
b = 5
C = -7
Therefore maximum function
= -7 -(5*2/4*2)
= -7-(10/8)
= -7 - 1.25
= -8.25
The minimum value of a function is the least value of that function.
Formula for the minimum = c - b^2/4a.
= -7-5^2/4*2
= -32/8
= -4
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What is the standard form equation of an ellipse that has vertices (18,1) and (−10,1) and co-vertices (4,14) and (4,−12)?
Answer: [tex]\frac{(x-4)^2}{196} +\frac{(y-1)^1}{169} =1[/tex]
Step-by-step explanation:
You first need to determine if the ellipse is horizontal or vertical, which can be found by the length of the major axis.
The vertices are at (18,1) and (-10,1). The distance is 28 units. (horiz)
The co-vertices are at (4,14) and (4,-12) The distance 26 units (vert)
The major axis is horizontal, so the standard form of the ellipse is
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex] where (h,k) are the coordinates of the center.
To find the center, find the midpoint of the major axis [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
The center is at (4,1)
Since the major axis is 2a, a would be 28 divided by 2=14 squared : 196
The minor axis is 2b, so b would e 26/2=13 squared: 169
Inserting the center and a,b values into the standard form eq:
[tex]\frac{(x-4)^2}{196} +\frac{(y-1)^1}{169} =1[/tex]
hope this helps.
Type the correct answer In each box. Round your answers to the nearest tenth.
A ladder is placed 30 Inches from a wall. It touches the wall at a helght of 50 inches from the ground.
The angle made by the ladder with the ground is
(blank) degrees, and the ength of the ladder Is (blank)
Inches.
Answer:
Angle = 59.03 degrees
Length = 58.3 inches
Step-by-step explanation:
Sets A and I are defined as follows:
A = {-5, -2,0, 2, 5}
I = {−5, -1, 1, 5, 8}
Find the union of A and I.
Answer:
{-5,-2,0,2,5,-1,1,8}
Step-by-step explanation:
The union of two sets contains all elements that are in set A or in set B (possibly both).
{-5,-2,0,2,5} ∪ {-5,-1,1,5,8} = {-5,-2,0,2,5,-1,1,8}
For every 6,000 batches of 100 cards that are printed, she examines every 100th batch to make sure the logo is aligned and the magnetic strip works. Identify the population and the sample. a. population: 6,000 batches of 1000 cards sample: every 10,000 cards c. population: 6,000 batches of 1000 cards sample: every 100th batch b. population: 6,000 batches of 100 cards sample: every 10,000 cards. d. population: 6,000 batches of 100 cards sample: every 100th batch
Using sampling concepts, the population and the sample are given as follows:
d. population: 6,000 batches of 100 cards sample: every 100th batch.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and then:
The population is: All New York State residents.The sample is the 1000 randomly selected New York state residents.Hence, in the situation described the population is the 6,000 batches of 100 cards, while the sample is every 100th batch, hence option d is correct.
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Which mixed number is equivalent to the improper fraction 42/5?
4 2/5
7 4/5
8 2/5
9 3/5
40 points if answer is right
Answer:
8 2/5
Step-by-step explanation:
42/5
to find the improper fraction, divide the numerator by the denominator
and then find the remainder
42 / 5 = 8 ( 5*8) the remainder is 42-40 = 2
Put the remainder over the denominator
8 2/5
Hey there!
Question reads….
Which mixed number is equivalent to the improper fraction 42/5?
EQUATION:
42/5
The one that is equivalent to the fraction is:
8 2/5
Reason:
8 2/5
= 8 * 5 + 2 / 5
= 40 + 2 / 5
= 42 / 5
Therefore, your answer should be:
Option C. 8 2/5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Good recordkeeping helps protect assets and helps managers?
Answer:
yes i help yes of course he help
A class has $90 to spend on a field trip. The field trip costs $2.50 per person and there will be 5 chaperones on the trip. One student used the inequality 90 greater-than 2.50 (x + 5) to find x, the number of students that the field trip budget could accommodate. Which best describes the error in the student’s inequality?
Answer:
Step-by-step explanation:
x is the number of students
(x+5) is the number of students and chaperons
$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have
2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)
The inequality "90 greater-than 2.50 (x + 5) "
90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign
90 ≥ 2.50(x+5)
tephen uses \dfrac{2}{25}
25
2
start fraction, 2, divided by, 25, end fraction kilograms of tofu in each serving of his famous tofu dish. He has 1\dfrac{1}{10}1
10
1
1, start fraction, 1, divided by, 10, end fraction kilograms of tofu.
The total number of servings Stephen can achieve with 1/10 kilograms of tofu at 2/25 kilograms per serving is 5/4 servings
Unit rateTofu per serving = 2/25 kilogramsTotal tofu Stephen has = 1/10 kilogramsNumber of servings = Total tofu Stephen has ÷ Tofu per serving
= 1/10 ÷ 2/25
= 1/10 × 25/2
= (1×25) / (10 × 2)
= 25/20
= 5/4 servings
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If 1st and 4th term of G.P is 500 and 32 respectively ,its 2nd term is
The second term of sequence is 200
Geometric equationGeometric sequence are sequence that differs in their term by a common ratio. The nth term of a geometric sequence is expressed as:
Tn = ar^n-1
where
a is the first term
n is the number of term
If 1st and 4th term of G.P is 500 and 32 respectively, hence;
T1 = ar^0 = 500
T3 = ar^3 = 32
From both expressions, the first term a = 500
Substitute into equation 2
ar^3 = 32
500r^3 = 32
r^3 = 32/500
r = ∛32/500
r = 0.4
Determine the second term
T2 = 500(0.4)
T2 = 200
Hence the second term of sequence is 200
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A square lawn has area 98 ft². A sprinkler placed at the center of the lawn sprays water in a circular pattern as
shown in the figure. What is the radius of the circle?
The radius of the circle exists approximately 4.95 feet.
How to estimate the radius of the circle?Given the area of the square as A = 98 ft²
The side length of the square choice is equivalent to the diameter of the circle.
First, we must obtain the length of the square.
Area of a square [tex]= L^2[/tex]
98 = L²
L = √98
L = 9.89 ft
Thus the diameter of the circle exists at 9.89 ft
radius = diameter/2
radius = 9.89/2
radius ≈ 4.95 feet
Therefore the radius of the circle exists approximately 4.95 feet.
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Consider a situation that you might need to use your understanding of probability to make an informed
decision.
• What sorts of information would you collect?
How might you use what you have learned about probability to determine a course of action?
What are the possible benefits and limitations of this approach?
The information that can be collected to make an insurance policy will be information regarding the drivers.
How to illustrate the information?It should be noted that the probability simply means the likelihood of the occurence of an event.
In this case, when choosing a car insurance policy, we can use the probability to determine the likelihood for the need to file a claim.
The course of action is to survey a number of drivers to get information from them.
Also, the benefit of this approach is that the food drivers can pay less premium while the disadvantage can be the cost that's involved.
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1. A situation that can use probability to make an informed decision is when deciding on an insurance policy to take.
2. The information that you would collect for an insurance policy decision includes insurance:
PremiumPolicy coveragePolicy limitsDeductiblesDiscounts.3. An understanding of probability helps the policyholder to:
Analyze different insurance policies to determine the best plan to choose amid uncertainty.Measure the likelihood of an event occurring and its consequences.Determine the level of risk involved.4. Possible Benefits and Limitations of Probability:Using probability, the insurance policyholder enjoys these benefits:
Measure outcomesReduce uncertaintyOptimize policiesSpread risk coveragePredict future losses and events.However, the limitations of probability in measuring insurance risks become prominent under the following situations:
Presence of an infinite number of possible outcomes. Where the outcomes are not equally likely.Thus, probability analyzes insurance policies to determine the best plans and their deductible amounts.
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f(x) =4x2 + 8x -5 factor completely
The factors of 4x^2 +8x-5 are (2x-1) and (2x+5)
Find the standard deviation for the set of data. (17,26,28,9,30, 29,6,21,23}
Using it's concept, the standard deviation for the given data-set is of 8.22.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean for this problem is:
M = (17 + 26 + 28 + 9 + 30 + 29 + 6 + 21 + 23)/9 = 21
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(17-21)^2 + (26-21)^2 + (28-21)^2 + \cdots + (21-21)^2 + (23-21)^2}{9}} = 8.22[/tex]
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To what power must 10 be raised to give 10
The answer is 1
10¹ = 10
i hope it was helpful
5/9+ (-4/5)
A. 1/4
B. 11/45
C. -9/14
D. -11/45
PLEASE HELP ILL GIVE BRAINLIST
How much would you need to deposit in an account now in order to have $4000 in the account in 15 years? Assume the account earns 4% interest compounded monthly. Round to the nearest cent
Answer:
$2500
Step-by-step explanation:
CA=p(1+MR÷1200)
4000=p(1+180×4÷1200) 15 yrs =15×12=180 month
4000=1.6p
p=4000÷1.6
p=2500
please give me brainliest
Make sure the answer is 100% correct. Then circle the answer in a circle.
Answer:
False
Any integers that the numbers 5, 10 , 15 but 20 can be used as a counter argument against the statement.
Step-by-step explanation:
The claim is that A⊆B which stands for that A is a SUBSET in B, or that B contains A.
The truth is that B⊆A since 5 has more possible outcomes than 20 in the number of integers.
So the list of all possible answers are r5, r10, and r15 where N⊆Z.
For example I choose r=3 and r15, 3(15)= 45. I can use the number 45 as a counter argument that the statement of A⊆B is false.
483,800,000 place value of 4
Answer:
hundred million is the place value of 4 in 483800000
a map has a scale of 2in: 6mi. if a two twons on a map is 10 in apart then how far apart are the real twons
Answer:
Step-by-step explanation:
Suppose we want to choose 2 colors, without replacement from 3 colors red blue and green how many ways can this be done in the order of the choice is relevant and not relevant
The two colors can be chosen in 3 different ways.
In how many ways can we choose two colors?
If we have a set of N elements, the number of different sets of K elements (such that the order of the K elements does not matter) is:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
In this case, we have 3 colors, so N=3, and we want to choose 2, then K=2.
Replacing that we get:
[tex]C(3, 2) = \frac{3!}{(3- 2)!*2!} = \frac{3*2*1}{1*2*1} = 3[/tex]
The two colors can be chosen in 3 different ways.
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A committee of 6 members is to be selected from 8 senior and 10 junior. find how many ways can this be done if there is no restriction
Answer:
18564 ways
Step-by-step explanation:
The number of committees is equal to the number of combinations of 6 members that we can form out of 18 person :
then
This can be done in [tex]C^{6}_{18}[/tex] ways.
[tex]C^{6}_{18}=\frac{18!}{6!\left(18-6 \right)! } = 18564[/tex]
A tape manufacturer reduces the price of its Heavy Duty tape from $40 to $38 a reel and the price of Regular tape from $32 to $31 a reel. A computing center normally spends $1600 a month for tapes and 3/5 of this is for Heavy Duty tapes. How much will they save a month under the new prices?
Answer:
68
Step-by-step explanation:
Lets first find the quantity of tape the computing center is purchasing/month.
3/5 Of their 1600 dollar spending is on the heavy duty tapes, meaning they are spending 960 dollars/month on heavy duty tape, if we divide that by the original price, 40, it will give us the original quantity of heavy tape they are purchasing, 24/month.
The other 2/5 of their money, 640 dollars, are spent on regular tape, meaning they purchase 20 rolls of regular tape/month.
Given they are purchasing 24 rolls of heavy tape and 20 rolls of regular tape every month, we can simply multiple those by the new prices and sum the results.
24*38=912
20*31=620
912+620=1532
Then to find the money they are saving we subtract the new price from the original price.
1600-1532=68
find x and the length of each segment
s
13
T
6
U
2x-18
y
4x-29
Answer:
x = 15, UV = 12, SV = 31
Step-by-step explanation:
13 + 6 + (2x - 18) = 4x - 29
2x + 1 = 4x - 29
2x = 30
x = 15
UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12
SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31
Suppose you are looking to purchase a new TV. You are placing it in an opening that is 136 cm wide but want to leave at least 2 cm of room on either side of the TV. If the TV screen measures 86 cm high, what is the largest size TVin inches, that you can purchase? TV's are measured based on the diagonal measure. (1inch = 2.54cm) Write your answer as an integer.
Answer:
62 inches
Step-by-step explanation:
Since we need to leave 2 cm of room on both sides, the maximum width of TV is 136 - 2 - 2 = 132 cm. Next, use the Pythagorean Theorem, a^2 + b^2 = c^2, to find the diagonal.
132^2 + 86^2 = c^2
c^2 = 17424 + 7396
c^2 = 24820
c = 157.543644746 cm
Finally, convert the value to inches using the given conversion factor.
157.543644746/2.54 = 62.0250569868 inches
Which of the following is true about horizontal asymptotes?
a.) A function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ .
b.) All horizontal asymptotes describe what happens when x gets close to 0 .
c.) All rational functions have at least one horizontal asymptote.
d.) All horizontal asymptotes describe what happens when the denominator's value gets close to 0.
A function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ is the correct statement about horizontal asymptotes. Option A
What are horizontal asymptotes?A horizontal asymptote of a graph can be defined as a horizontal line at y = b where the graph tend to approach the line as an inputs approach to infinity ( ∞ or –∞).
A slant asymptote of a graph is known as a slanted line y = mx + b where the graph approaches the line as the inputs approach the positive infinity ∞ or to the infinity –∞.
Thus, a function has a horizontal asymptote at the value of y = a if the line y = a can be used to estimate the end behavior of a function and if f ( x ) → a as x → ∞ or x → − ∞ is the correct statement about horizontal asymptotes. Option A
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Chris bought a new car for 12,500 he made 3,000 down payment and financed the rest for 14.5% for 36 months for 3 years how much less would his total be for same loan 24 months 2 years
The difference in total loan repayments between the two mortgage payment option is 771.12
The requirement here is to determine the difference between total loan repayments when the period of loan is 36 months and the total repayments when the period of loan is 24 months instead.
Note the loan amount is the excess of purchase price over the down payment required.
loan amount=12,500-3,000
loan amount=9,500
The monthly payment in each case can be determined using the present value formula of an ordinary annuity.
PV=monthly payment*(1-(1+r)^-N/r
36-month loan month payment
PV=loan amount=9,500
monthly payment=X
r=monthly interest rate=14.5%/12=0.0120833333333333
N=number of monthly payments=36
9,500=X*(1-(1+0.0120833333333333)^-36/0.0120833333333333
9,500=X*(1-(1.0120833333333333)^-36/0.0120833333333333
9,500=X*(1-0.6489543809903260)/0.0120833333333333
9,500=X*0.3510456190096740/0.0120833333333333
9,500=X*29.0520512283869000
X=9,500/29.0520512283869000
X=327.00
Total month repayments=327.00*36
Total month repayments=11,772.00
24-month loan month payment
PV=loan amount=9,500
monthly payment=X
r=monthly interest rate=14.5%/12=0.0120833333333333
N=number of monthly payments=24
9,500=X*(1-(1+0.0120833333333333)^-24/0.0120833333333333
9,500=X*(1-(1.0120833333333333)^-24/0.0120833333333333
9,500=X*(1-0.7495652524008220/0.0120833333333333
9,500=X*0.2504347475991780/0.0120833333333333
9,500=X*20.7256342840700000
X=9,500/20.7256342840700000
X=458.37
Total month repayments=458.37*24
Total month repayments=11,000.88
Difference in total payments=11,772.00-11,000.88
Difference in total payments=771.12
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Answer:
just 771.21
Step-by-step explanation:
to make it shorter credits to the og person who said the awnser 771.21
on a number line, suppose point E has a quotient of -1, and EG = 12. what are the possible coordinates of point G?
-13, or +11, because they are both 12 places away from -1.
write the expression as the sine or cosine of an angle
pi/5 cos pi/2+sin pi/2\cos pi/5
The given expression as a sine function is [tex]sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
The addition formula for trigonometryThe given expression is:
[tex]sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )[/tex]
Note that:
[tex]sin(A+B)=sinAcosB+cosAsinB[/tex]
Applying the addition principle to the given expression, we have:
[tex]sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )=sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
Therefore, the given expression as a sine function is [tex]sin(\frac{\pi}{5} +\frac{\pi}{2} )[/tex]
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An 8ft length of 4 inch wide crown molding cost $13. How much it cost to buy 88ft of crow molding
The amount it costs to buy 88ft of crow molding is; $143.
How much does it cost to buy 88ft if crow molding?It follows from the task content that the cost for 8ft length of a specific width crown molding is; $13.
On this note, it follows that the cost of buying 88ft of the same kind of crow molding can be estimated as;
88 × ($13/8)
= $143.
Therefore, the cost of 88ft of crow molding is; $143.
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