If you go three times faster than another car, it will take nine times longer to stop your car than the other car.
To understand why, we need to consider the physics of stopping a car. The distance required to stop a car depends on the car's speed and braking ability.
Assuming the braking ability is the same for both cars, we can use the equation:
distance = (speed)² / (2 * deceleration)
where deceleration is the rate at which the car slows down.
Since we are assuming that the other car and your car have the same deceleration, we can write:
distance other car = (speed other car)² / (2 * deceleration)distance your car = (speed your car)² / (2 * deceleration)We know that your car is going three times faster than the other car, so:
speed your car = 3 * speed other car
Substituting this into the equation for the distance of your car, we get:
distance your car = (3 * speed other car)²/ (2 * deceleration)
distance your car = 9 * (speed other car)² / (2 * deceleration)
Therefore, the distance required to stop your car is nine times greater than the distance required to stop the other car. Since the time to stop is directly proportional to the distance required to stop, it will also take nine times longer to stop your car than the other car.
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Jim and Avery compare the number of points they scored during a game. Explain your answer mathematically
Jim notices that when he doubles his number of points, then subtracts 10 from that number, the result is the same as the number of points Avery scored. Write an expression representing the number of points
Avery scored, in terms of the number of points Jim scored, j. Enter your expression in the response box
The expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.
Let's assume that Jim scored 'j' points during the game. According to the given information, when Jim doubles his number of points and subtracts 10 from that number, the result is the same as the number of points Avery scored. Therefore, we can write an equation as follows:
2j - 10 = number of points scored by Avery
To find the expression representing the number of points Avery scored in terms of the number of points Jim scored, we simply solve the above equation for Avery's points:
number of points scored by Avery = 2j - 10
Therefore, the expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.
In summary, Jim scored 'j' points during the game and when he doubles his number of points and subtracts 10 from that number, he gets the same result as the number of points Avery scored.
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the trainer for a professional soccer team has found that hamstring injuries on their team follow an exponential distribution. on average, their team experiences a pulled hamstring muscle every 342 minutes. if a game lasts 90 minutes, determine the following: what is the probability that the team will pull a hamstring muscle in the next game? round your answer to four decimal places (include zero if necessary). what is the probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game? round your answer to four decimal places (include a zero if necessary).
1)The probability that the team will pull a hamstring muscle = 0.240. 2)The probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game = 0.020.
Given that hamstring injuries on the team follow an exponential distribution with an average time between injuries of 342 minutes, we can use the formula for the exponential distribution to answer the following questions:
1)The time duration of a game is 90 minutes. Therefore, the probability of a hamstring injury occurring during a game can be calculated as follows:
λ = 1/342 injuries per minute (since on average there is one injury every 342 minutes)
t = 90 minutes (duration of a game)
P(X ≤ t) = 1 - e^(-λt)
P(X ≤ 90) = 1 - e^(-1/342 * 90) ≈ 0.2399
So the probability that the team will pull a hamstring muscle in the next game is approximately 0.2399 (or 0.240 when rounded to 4 decimal places).
2)The probability of a hamstring injury occurring between the 15th and 25th minute of the game can be calculated as follows:
λ = 1/342 injuries per minute (since on average there is one injury every 342 minutes)
t1 = 15 minutes (starting time)
t2 = 25 minutes (ending time)
P(t1 < X ≤ t2) = e^(-λt1) - e^(-λt2)
P(15 < X ≤ 25) = e^(-1/342 * 15) - e^(-1/342 * 25) ≈ 0.0199
So the probability that the team will experience a pulled hamstring muscle between the 15th and 25th minute of the game is approximately 0.0199 (or 0.020 when rounded to 4 decimal places).
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g(x)=3x^2+30x+78 minimum and maximum
The minimum value of the given function is 3 at x=-5.
By locating the vertex of the parabola that the function defines, we may determine the lowest or maximum value of G(x).
The x-coordinate of the vertex may be determined by using the formula x = -b/(2a), where a and b are the coefficients of the quadratic components in the function.
In this case, a = 3 and b = 30, so:
x = -b/(2a) = -30/(2*3) = -5
Now we can find the y-coordinate of the vertex by plugging in x = -5 into the function:
[tex]G(-5) = 3(-5)^2 + 30(-5) + 78 \\= 3(25) - 150 + 78 \\= 3(25) - 72 \\= 3(25 - 24) \\= 3(1) \\= 3[/tex]
Therefore, the minimum value of G(x) is 3 and there is no maximum value.
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Need help with this ASAP please
Answer: The answer is Q1: 2.3+34, Q2: 5.7+8.9.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
I can answer more questions if you like.
(Expert Answered)
according to an article in a business publication, the average tenure of a u.s. worker is 4.6 years. the most appropriate one-sample test of hypothesis to test this belief is: group of answer choices a two-tailed test. an upper one-tailed test. a lower one-tailed test.
The most appropriate one-sample test of hypothesis to test the belief that the average tenure of a U.S. worker is 4.6 years is option (c) a lower one-tailed test.
The reason for this is that the article states a specific average tenure of U.S. workers (4.6 years), and the hypothesis we want to test is whether this average tenure is lower than this value or not. We are not interested in whether the average tenure is higher than 4.6 years, so a two-tailed test or an upper one-tailed test would not be appropriate.
Therefore, we would use a lower one-tailed test to test the null hypothesis that the average tenure of U.S. workers is 4.6 years or higher, against the alternative hypothesis that the average tenure is lower than 4.6 years. We would then use statistical analysis to determine whether the evidence supports rejecting the null hypothesis in favor of the alternative hypothesis.
Therefore, the correct option is (c) a lower one-tailed test
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How to find the perimeter of a composite shape with missing sides(rectangles)
Answer: You have to add up the lengths.
a team of soccer players spend an average of 15 minutes on weight weight training per practice session.how many minutes of weight trainingon an average would they have to complete in 116 practise?
Answer:
The answer to your problem is, 1,740 minutes
Step-by-step explanation:
The time period of 116 trainings solutions;
The time period of 1 weight training that we know is 15 minutes. Time period of 116 weight is 5 x 116 = 1,740
Thus the answer to your problem is, 1,740
Answer:1,740 minutes
Step-by-step:
I first saw that I need to take 15 minutes and x it be the 116 Practices.
So 15 x 116 is 1,740.
1,740 minutes is your answer.
I need the answer and explanation for this geometry problem. (this is not a live quiz, test, or exam question, just to clarify)
(a) If we draw 2 letters from a bag containing 26 letters of alphabet, and we return the letters in between the draws, the probability of drawing a "W" both the time is 1/676.
(b) If we toss two-cubes numbered 1 to 6 each time, then probability that we toss a 6 on first cube and a odd number on second cube is 1/12.
Part (a) : The letters in between the draws are returned, which means each draw is independent of the other.
So, the probability of drawing a "W" on any single draw is 1/26.
The probability of drawing a "W" both times is written as :
P(W and W) = P(W) × P(W) = (1/26) × (1/26) = 1/676,
Therefore, the probability of drawing a "W" both times is 1/676.
Part (b) : The probability of getting a 6 on the first-cube is = 1/6, and
The probability of getting an "odd-number" on the second cube is = 3/6, (because there are 3 odd numbers out of a total of 6 numbers).
The probability of 6 on first-cube and odd number on second, cube is written as ;
⇒ P(6 and odd) = P(6) × P(odd) = (1/6) × (3/6) = 1/12,
Therefore, the required probability is 1/12.
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Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00.
Total annual cost for Dave's car driving 6,000 miles last year is $2,250.00 with fixed cost of $1,250.00 plus variable cost of $1,000.00.
Based on the given information, we can use the formula for total cost
Total Cost = Fixed Cost + (Variable Cost per unit x Number of units)
In this case, we know the fixed cost is $1,250.00, and the variable cost per mile is $1,000.00 / 6,000 miles = $0.1667/mile. Therefore, we can calculate the total annual cost as
Total Cost = $1,250.00 + ($0.1667/mile x 6,000 miles)
Total Cost = $1,250.00 + $1,000.20
Total Cost = $2,250.20
So, Dave's total annual cost of driving his car for 6,000 miles is $2,250.20.
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--The given question is incomplete, the complete question is given
" Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00. What is the total annual cost?"--
Chen and Megan have a parcel Chen’s parcel weighs 1 1/2kg Megan’s parcel weighs 1. 2kg how many more grams does Chen’s parcel weigh than Megan’s parcel
Chen’s parcel weighs 0.3 kg more than Megan’s parcel
What is the difference in fraction?When working with fractions and decimals, it is good to use only one unit for ease of solving.
We are given the weights as:
Weight of Chen’s Parcel = 1¹/₂ kg
Weight of Megan's Parcel = 1.2 kg
Now, let us convert the weight of Chen’s Parcel from fraction to decimal to get 1.5 kg
Thus:
Difference in weight = 1.5 kg - 1.2 kg
= 0.3 kg
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Solve the following equation and check your result (2n)/3 + 1 = (7n)/15 + 3
both sides are equal, we can conclude that n = 150/29 is the correct solution.
What is an Equations?
Equations consist of two algebraic expressions separated by an equal (=) sign, representing the equality between the expressions on the left and right sides. Solving equations helps to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol, a statement cannot be considered an equation and is instead considered an expression.
(2n)/3 + 1 = (7n)/15 + 3 // subtract 1 from both sides
(2n)/3 = (7n)/15 + 2 // multiply both sides by 15 to eliminate fractions
10n = 3(7n)/5 + 30 // multiply both sides by 3
10n = 21n/5 + 30 // subtract 21n/5 from both sides
50n/5 - 21n/5 = 30 // simplify fractions
29n/5 = 30 // multiply both sides by 5/29
n = 150/29
To check the solution, we substitute n = 150/29 back into the original equation and see if both sides are equal:
(2n)/3 + 1 = (7n)/15 + 3
(2(150/29))/3 + 1 = (7(150/29))/15 + 3
100/29 + 1 = 70/29 + 3
129/29 = 129/29
Since both sides are equal, we can conclude that n = 150/29 is the correct solution.
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Please solve this as soon as possible!
The value of
1. sin(tetha) = 8/√89
2. cos(tetha) = 5/√89
3. sec(tetha) = √89/5
4. cosec(tetha) = √89/8
5. cot( tetha) = 5/8
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
Sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
This means that, since tan(tetha) = 8/5 , the adj is 5 and the opp is 8
Using Pythagorean theorem,
hyp = √opp²+adj²
hyp = √8²+5²
hyp = √64+25
hyp = √89
therefore;
sin(tetha) = 8/√89
cos(tetha) = 5/√89
sec(tetha) = 1/cos(tetha) = √89/5
cosec(tetha) = 1/sin(tetha) = √89/8
cot (tetha) = 1/tan(tetha) = 5/8
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The value of a mountain bike y (in dollars) can be approximated by the model y=200(0.75)t, where t is the number of years since the bike was new. Would this table show growth or a decline (decay)? How do you know? Identify the annual percent increase or decrease in the value of the bike. Estimate when the value of the bike will be $50.
Answer:
Step-by-step explanation:
To determine if the table shows growth or decay, we can look at the coefficient of the exponential function y = 200(0.75)^t. The coefficient is 0.75, which is less than 1. This means that the value of the bike decreases over time, so the table shows decay.
To identify the annual percent increase or decrease in the value of the bike, we can compare the value of the bike after one year to its initial value. Plugging in t = 1 into the model, we get:
y = 200(0.75)^1
y = 150
So after one year, the value of the bike is $150. This represents a decrease of $50 from its initial value of $200. To find the percent decrease, we can use the formula:
percent decrease = (amount of decrease / initial value) x 100%
Plugging in the values, we get:
percent decrease = (50 / 200) x 100%
percent decrease = 25%
Therefore, the value of the bike decreases by 25% each year.
To estimate when the value of the bike will be $50, we can set y = 50 in the model and solve for t:
50 = 200(0.75)^t
0.25 = 0.75^t
log(0.25) = t log(0.75)
t = log(0.25) / log(0.75)
t ≈ 4.2
Therefore, the value of the bike will be $50 approximately 4.2 years after it was new.
Find the probability of exactly 4 successes in 6 trials of a binomial experiment in which the probability of success is 40%
Answer:
0.13824
Step-by-step explanation:
You want the probability of exactly 4 successes in 6 trials if the probability of success in each trial is 0.4.
Binomial probabilityThe probability of k successes in n trials with each having a probability of success of p is given by the formula ...
P(k of n) = nCk·p^k·(1-p)^(n-k)
P(4 of 6) = 6C4·0.4^4·0.6^2 = 15·0.0256·0.36 = 0.13824
The probability of exactly 4 successes is 0.13824.
__
Additional comment
The binomial coefficient nCk is computed as ...
nCk = n!/(k!(n-k)!)
<95141404393>
Urgently need the answer please help!!
Answer:
A = 81
Step-by-step explanation:
Using the formulas
A=a2
P=4a
Solving forA
A=1
16P2=1
16·362=81
Answer:
[tex]36 {r}^{4} {s}^{5}[/tex]
Perimeter of the square
one side has a length of 9r⁴s⁵
area is equal to 9r⁴s⁵ × 9r⁴s⁵
= 81r⁸s¹⁰
or 81r⁸s¹⁰cm²
Michael has a bag of smarties.He has 6 red smarties 4 blue smarties and 2 pink smarties.What is the probability he will pick 2 blue smarties two times
Answer:
Step-by-step explanation:
If he puts smarty back
because it's an "and" multiply by the 2 possibilities
4/12 *4/12
=1/3 *1/3
=1/9
If does not put smarty back
4/12 *3/11
=1/3*3/11
=3/33
which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table
The equations that represent exponential growth are [tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t,[/tex] [tex]P = 1700(1.07)^t[/tex] and the equations that represent exponential decay are [tex]A = 80(1/2)^t, A = 1600(0.8)^t,[/tex] and [tex]P = 1700(0.93)^t.[/tex]
The mathematical function used to calculate the exponential growth or decay of a given set of data is an exponential function. we can calculate changes in population, loan interest charges, bacterial growth, radioactive decay, or the spread of disease by using the exponential functions.
An exponential function is of the form:
[tex]f(x) = a ^x[/tex]
The function represents an exponential decay If b < 1
The function represents an exponential growth If b > 1
From the given data about equations, we have;
Exponential Growth is;
The equation with the values b < 1 is:
[tex]A = 20,000(1.08)^t[/tex]
[tex]A = 40(3)^t[/tex]
[tex]P = 1700(1.07)^t[/tex]
Exponential Decay is;
The equation with the values b > 1 is:
[tex]A = 80(1/2)^t[/tex]
[tex]A = 1600(0.8)^t[/tex]
[tex]P = 1700(0.93)^t[/tex]
Therefore, The equations that represent exponential growth are[tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t[/tex], and[tex]P = 1700(1.07)^t[/tex] the equations that represent exponential decay are [tex]A = 80(1/2)^t[/tex], [tex]A = 1600(0.8)^t\\[/tex], and [tex]P = 1700(0.93)^t.[/tex]
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The complete question is
Which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table
PLEASE HELP, NEED IT BY TODAY
Write three equations. Each equation must include the numbers 3 and 30.3 and must be easy to solve by inspection. Solve your equations.
The three equations are:
3x = 30.3
30.3 - x = 27.3
3x + 30.3 = 63.6
We have,
Equation 1:
3x = 30.3
Solving for x, we can divide both sides by 3:
x = 10.1
Equation 2:
30.3 - x = 27.3
Solving for x, we can subtract 27.3 from both sides:
x = 3
Equation 3:
3x + 30.3 = 63.6
Solving for x, we can first subtract 30.3 from both sides:
3x = 33.3
Then, we can divide both sides by 3:
x = 11.1
Thus,
The three equations are:
3x = 30.3
30.3 - x = 27.3
3x + 30.3 = 63.6
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consider the data about the number of blocked intrusions in exercise 8.1, p. 240. (a) construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances). (b) can we claim a significant reduction in the rate of intrusion attempts? the number of intrusion attempts each day has approximately normal distribution. compute pvalues and state your conclusions under the assumption of equal variances and without it. does this assumption make a difference?
The 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings is (3.36, 13.78).
To construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings, we can use a two-sample t-test with equal variances.
Let x₁ be the number of blocked intrusions per day before the change of firewall settings, and let x₂ be the number of blocked intrusions per day after the change of firewall settings. We have
x₂ = (56+47+49+37+38+60+50+43+43+59+50+56+54+58)/14 = 50.36
x₂ = (53+21+32+49+45+38+44+33+32+43+53+46+36+48+39+35+37+36+39+45)/20 = 40.95
s₁ = standard deviation of x₁ = 8.23
s₂ = standard deviation of x₂ = 8.98
The pooled standard deviation, sp, is given by
sp = √(((n₁-1)s₁² + (n₂-1)s₂²)/(n₁+n₂-2))
where n₁ and n₂ are the sample sizes. Since we assume equal variances, we use the formula for the pooled standard deviation. Substituting the values, we get:
sp = √(((14-1)8.23² + (20-1)8.98²)/(14+20-2)) = 8.63
The t-statistic for the difference between the means is given by
t = (x₁ - x₂) / (sp × √(1/n₁ + 1/n₂))
Substituting the values, we get
t = (50.36 - 40.95) / (8.63 × √(1/14 + 1/20)) = 2.28
We can use a t-distribution with degrees of freedom = n₁ + n₂ - 2 = 32 and a significance level of α = 0.05 to find the confidence interval. The confidence interval is given by
(x₂ - x₂) ± tsp√1/n₁ + 1/n₂)
Substituting the values, we get
(50.36 - 40.95) ± 2.0458.63√(1/14 + 1/20) = 8.57 ± 5.21
= (3.36, 13.78)
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The given question is incomplete, the complete question is:
The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56,47,49,37,38,60,50,43,43,59,50,56,54,58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53,21,32,49,45,38,44,33,32,43,53,46,36,48,39,35,37,36,39,45. construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances).
The debate over pipelines and the use of oil sands is far from over. There is likely to be another
application for a pipeline to bring oil from Alberta to Texas or a proposal to pipe oil across Canada
.
to ships that could take it to refineries in Asia. What do you think should be done? Explain your
answer using complete sentences.
The decision of whether or not to build pipelines to transport oil from Alberta to Texas or other parts of Canada is a complex one that involves multiple factors.
From a mathematical perspective, the debate over pipelines and oil sands can be analyzed in terms of supply and demand. On the other hand, opponents of pipelines argue that the supply of oil is finite and that the continued extraction and transportation of oil will have long-term negative consequences for the environment.
In addition to the economic and environmental factors, there are also geopolitical considerations to take into account. For example, some argue that building a pipeline to transport oil from Alberta to Texas would reduce Canada's reliance on foreign oil and would increase our energy independence.
However, others argue that building a pipeline would tie us more closely to the United States and would not necessarily benefit Canada in the long run.
Regardless of the decision that is ultimately made, it is clear that pipelines will continue to play a significant role in our energy infrastructure for many years to come.
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is 3 greater than 3 and a Half (3>< 3 1\2
Answer:
3 and a half would be greater than 3
Step-by-step explanation:
3 and a half would be 3.5 which is .5 more than just 3.
find the equation of a circle passing through the points (1, 2), (0, 3)and (-2, 7)
which is the best estimate of 7.21x3.86/10.09
Answer:
7.21x3.86/10.09
7 x 4 / 10
28 / 10
2.8
The volume of a triangular pyramid is 756 units3 . If the base and height of the triangle that forms its base are 18 units and 12 units respectively, find the height of the pyramid.
If the base and height of the triangle that forms its base are 18 units and 12 units respectively then the height of the pyramid is 21 units.
The formula for the volume of a triangular pyramid is:
V = (1/3) * base area * height
We are given that the volume of the pyramid is 756 units^3, the base of the pyramid is a triangle with base length 18 units and height 12 units, so its area is:
A = (1/2) * base * height = (1/2) * 18 * 12 = 108 units^2
Substituting the given values into the formula for the volume of a pyramid, we get:
756 = (1/3) * 108 * h
Multiplying both sides by 3 and dividing by 108, we get:
h = 756 / 36 = 21
Therefore, the height of the pyramid is 21 units.
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the professor for a different section of the multi-section course reported his students’ exam scores as z-scores. a student in this section, katie, received a z-score of 2.2. what percentage of the students in her section did katie outscore?
Katie outscored approximately 1.39% of the students in her section.
How to calculate percentage of the students in her section did katie outscore?If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.
We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.
Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.
The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:
1 - 0.9861 = 0.0139, or 1.39%
of the scores fall above a z-score of 2.2.
This means that Katie outscored approximately 1.39% of the students in her section.
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What are the coordinates of the point on the directed line segment from
(
−
8
,
8
)
(−8,8) to
(
−
2
,
−
10
)
(−2,−10) that partitions the segment into a ratio of 1 to 2?
so let's say A(-3 , -10) and B(9 , 5), so that point C partitions it in a 1 : 2 ratio from A to B
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-3,-10)\qquad B(9,5)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-3,-10)=1(9,5)[/tex]
[tex](\stackrel{x}{-6}~~,~~ \stackrel{y}{-20})=(\stackrel{x}{9}~~,~~ \stackrel{y}{5}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-6 +9}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-20 +5}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ 3 }{ 3 }~~,~~\cfrac{ -15}{ 3 } \right)\implies C=(1~~,~-5)[/tex]
through Buzz under the assignment.
1. lan deposits $2,400 each quarter for 3 years. The annuity earns 10% interest and is compounded quarterly. Find the present value of the annuity.
Using the Present Value of Ordinary Annuity Table, the correct factor for 12 compounding periods at 2.5% interest is 10.25776.
Answer:
$56,577.12
Step-by-step explanation:
To find the present value of the annuity, we can use the formula for the present value of an ordinary annuity, which is:
PV = PMT x [1 - (1 + r/n)^(-n*t)] / (r/n)
Where:
PV = present value
PMT = payment amount per compounding period
r = annual interest rate
n = number of compounding periods per year
t = total number of years
Plugging in the given values, we get:
PV = 2400 x [1 - (1 + 0.10/4)^(-4*3)] / (0.10/4)
PV = 2400 x [1 - (1.025)^(-12)] / (0.025)
PV = 2400 x [1 - 0.610355] / 0.025
PV = 2400 x 23.5742
PV = $56,577.12 (rounded to the nearest cent)
Therefore, the present value of the annuity is $56,577.12, assuming the interest is compounded quarterly and the annuity earns a 10% interest rate.
Circumference of circle Q
The circumference of circle be 60 in.
Give that,
Angle of sector = 60 degree
Arc length = 10 inch
Arc length of circle = (Θ/360) x 2πr
Put the values
10 = (60/360)x2πr
⇒ r = 60/2π
Since circumference of circle = 2πr
Therefore,
circumference of the given circle = 2π x (60/2π)
= 60 in.
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a tugboat goes 200 miles upstream in 10 hours. the return trip downstream takes 4 hours. find the speed of the tugboat without a current and the speed of the current.
The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.
Let t be the speed of the tugboat without the current and c be the speed of the current.
Upstream, the tugboat moves against the current, so its speed is (t - c).
Downstream, the tugboat moves with the current, so its speed is (t + c).
The upstream distance is 200 miles in 10 hours, so the upstream speed is 200/10 = 20 miles per hour.
The downstream distance is also 200 miles, but it takes 4 hours, so the downstream speed is 200/4 = 50 miles per hour.
Now, we have two equations with two variables:
a. t - c = 20
b. t + c = 50
Solve these equations simultaneously:
a. Add the two equations to eliminate the variable c: 2t = 70
b. Divide both sides by 2 to get t: t = 35 miles per hour
c. Substitute the value of t back into one of the equations (e.g., t - c = 20): 35 - c = 20
d. Solve for c: c = 15 miles per hour
Hence, The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.
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i really need help any answer would be appreciated
Answer:
If 4 units equal 16 ounces, we can find the value of 1 unit by dividing both sides by 4:
4 units = 16 ounces
4 units ÷ 4 = 16 ounces ÷ 4
1 unit = 4 ounces
So, 1/4 x 16 ounces = 4 ounces.
4/1 is the answer in fraction :)
