By solving the given equations using the provided information, and assuming the constant c = 4/3, we can find the coordinates of the point P on the curve corresponding to t = 2 are (8/3, 32/9). There is a probable discrepancy in the question which causes two different solutions for c, therefore making the canonical form of the parabola ambiguous.
Explanation:The given parametric curve has its equations as x = ct and y = c/8 * t^2. We're given that it's the arc of the parabola 8y = x^2 from (0, 0) to (4, 2), meaning that we can set x = ct = 4 and y = c/8 * t^2 = 2 when t=3 (the upper limit of t) to find the value of the constant c. Solving these equations gives c=4/3 and c=48. Since c must be the same in both equations, there seems to be a discrepancy here, which could possibly originate from a mistake in the question. However, if we only use c from the first equation (x = ct), we get c = 4/3.
The question asks for the coordinates of the point on the curve corresponding to t = 2. Substituting t = 2 into x = ct and y = c/8 * t^2 gives x = 8/3 and y = 32/9, assuming c = 4/3. So, the coordinates of the point would be (8/3, 32/9).
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Express the perimeter of the triangle as a polynomial.
A) 9x -8
B) 9x + 8
C) 8x - 6
D) -9x - 6
A package of 3 pairs of insulated socks costs $25.17. What is the unit price of the pairs of socks?
There are five different colored cards in a hat (red, blue, green, yellow, and black). A card is randomly drawn and not replaced. Then a second card is drawn. What is the probability that the first card will be red and the second card will be blue?
The probability of drawing a red card first followed by a blue card from a hat with five different colored cards without replacement is 0.05 or 5%.
The question asks for the probability of drawing a red card first and a blue card second from a hat containing five different colored cards without replacement. To calculate this, we use the formula for conditional probability and the multiplication rule for independent events. Since the cards are drawn without replacement, the events are dependent.
The probability of drawing the red card first is 1/5, since there is one red card out of five. After drawing the red card, there are four cards left. The probability of drawing the blue card second is thus 1/4, as there is only one blue card left among the four remaining cards. The probability of both events occurring in sequence is the product of the probabilities of each event:
P(Red first and Blue second) = P(Red first) × P(Blue second | Red first) = (1/5) × (1/4) = 1/20 or 0.05.
Therefore, the probability that the first card is red and the second card is blue is 0.05 or 5%.
The dimension of a rectangular pool are 24.5 feet by 13 feet. The depth of the water is 4 feet. Each cubic foot contains 7.48 gallons of water. How many gallons of water to the nearest tenth, are needed to fill the pool to 80% capacity
Answer:
Pool needed to be filled = 7623.62 gallons
Step-by-step explanation:
Length of rectangular pool = 24.5 feet
Width of rectangular pool = 13 feet
Depth of rectangular pool = 4 feet
Now, Volume of the pool = Length × Width × Depth
= 24.5 × 13 × 4
= 1274 cubic feet
Now, 1 cubic feet = 7.48 gallons
⇒ 1274 cubic feet = 7.48 × 1274
= 9529.52 gallons
So, Volume of the pool = 9529.52 gallons
Now, the pool is to be filled 80%
So, Pool needed to be filled = 9529.52 × 0.80
= 7623.62 gallons
The number of gallons of water to the nearest tenth, that are needed to fill the pool to 80% capacity is 7623.6 gallons.
Number of gallons of waterFirst step:
Volume of the pool=Length × Width × Depth
Volume of the pool= 24.5 ft × 13ft × 4ft
Volume of the pool=1274 cubic feet
Second step:
Number of gallons=(7.48 × 1274)×80%
Number of gallons=9529.5 gallons×80%
Number of gallons=7623.6 gallons
Inconclusion the number of gallons of water to the nearest tenth, that are needed to fill the pool to 80% capacity is 7623.6 gallons.
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Sam is 5 years old. His older brother, Tom, is three times as old as Sam. When Sam is 20, how old will Tom be?
Sin theta = -5/13 and cos theta = -12/13 use ratio identity to find cot theta
if a number is a whole number then it cannot be.......
a...an irrational number
b...a natural number
c...an integer
d...a rational number
Using number sets, it is found that a whole number cannot be irrational, hence option a is correct.
What are rational and irrational numbers?All numbers that can be represented by fractions are rational.Numbers that cannot be represented by fractions, such as non-repeating decimals and the square roots of numbers that are not perfect squares are irrational.In this problem, any whole number can be represented by a fraction, hence it cannot be irrational and option a is correct.
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Answer:
A. An Irrational Number
Step-by-step explanation:
Irrational numbers are numbers like pi or angles with degrees, while whole numbers are numbers from 0+
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Which inequality has the graph shown below
The Inequality that has the graph shown below is [tex]y \ge -\frac{1}{4}x + 1.[/tex] correct choice is [tex]y \ge -\frac{1}{4}x + 1.[/tex]
This can be seen by noting that the line is solid and shaded above the line, which indicates that all points above the line satisfy the inequality.
Graphs are often used to visually represent inequalities in mathematics. Inequalities compare the relative sizes of two expressions, and their graphs help illustrate the solutions to these inequalities on a number line or in a coordinate plane
The other inequalities in the image are not correct because:
[tex]y > -\frac{1}{4}x + 1[/tex]would have the line shaded below the line.
[tex]y < = -\frac{1}{4}x + 1[/tex] would have the line dashed, not solid.
[tex]y < -\frac{1}{4}x + 1[/tex]would have no points above the line satisfying the inequality.
Therefore, the correct inequality is [tex]y \ge -\frac{1}{4}x + 1.[/tex]
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Vince, a middle manager at united imports inc., is on a business trip to japan to visit a major supplier. after work, his japanese hosts take him to a japanese barbecue restaurant. vince is very uncomfortable with the dishes served in the restaurant and does not know what to do. vince is experiencing ________.
In this assignment we will work on the creation of a poker game. at a minimum your game must deal 2 hands of cards, and print out what poker hand each has. it must also determine which hand has won the game – but breaking a tie will be for bonus points. for example, if both hands have 3 of a kind, that can be considered a tie. if you want the bonus points write some code that determines which 3 of a kind is higher. here is the output from dealing a hand of cards: ace of hearts ten of clubs ace of clubs eight of hearts seven of diamonds 2 2 1 0 <> 0 0 0 0 0 1 1 0 1 0 0 0 2 you have a pair!
Three batteries are connected in series so that the total voltage is 54 volts. The first battery is twice the voltage of the second and 1/3 the voltage of the third battery. Find the actual voltage of each battery
The first battery voltage is 12.
The second battery voltage is 6.
The third battery voltage is 36.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First battery voltage = M
Second battery voltage = N
Third battery voltage = O
Now,
We can make an expression as,
M + N + 0 = 54 _____(A)
And,
M = 2N ____(1)
M = (1/3)O ____(2)
Now,
From (1) and (2)
N = M/2
O= 3M
Substituting in (A)
M + N + O = 54
M + M/2 + 3M = 54
4M + M/2 = 54
8M + M = 108
9M = 108
M = 12
Now,
N = M/2 = 12/2 = 6
O= 3M = 3 x 12 = 36
Thus,
First battery voltage = 12
Second battery voltage = 6
Third battery voltage = 36
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what is an infinite set in geometry please help asap
How do you factor 18x^4y^2+21x^5y-6x^3y^2
[tex]3x^3y ( 6xy + 7x^2 - 2y )[/tex] is the factored form of [tex]18x^4y^2+21x^5y-6x^3y^2[/tex] .
Given, expression [tex]18x^4y^2+21x^5y-6x^3y^2[/tex] .
To factorize the expression take the common terms present in each part of an expression.
Expression : [tex]18x^4y^2+21x^5y-6x^3y^2[/tex]
Highest power of x which is present in each part = x³
Highest power of y which is present in each part = y
HCF of 18, 21 , 6 = 3
Factorizing the expression:
Take 3x³y as common,
Factored form : [tex]3x^3y ( 6xy + 7x^2 - 2y )[/tex] .
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The function f(x) = 1/5 is translated up 4 units. Which equation represents the translated function?
The equation that represents the translated function for
[tex]\rm f(x) = \dfrac{1}{5}[/tex] [tex]\rm is\;\; \rm \bold{g(x) = f(x) +4 = 4.2}[/tex].
Given that the function f(x) = 1/5 is translated up 4 units.
We have to determine the equation that represents the translated function
The function f(x) = 1/5 as the function is translated.
Translation is a concept of mathematics . In translation the shape of the object is simply moved linearly from one point to other point by adding some constant values in the previous coordinates. In translation , there is no dilation shape and size of the object remains the same.
Let us consider that if the function is translated up with 4 units then the new function is [tex]\rm\bold{ g(x)}[/tex]
So according to the language of question we
[tex]\rm g(x) = f(x) +4[/tex]
[tex]\rm g(x) = \dfrac{1}{5} +4 = \dfrac{21}{5} = 4.5[/tex]
[tex]\rm g(x) = 4.5[/tex]
The equation that represents the translated function for
[tex]\rm f(x) = \dfrac{1}{5}[/tex] [tex]\rm is\;\; g(x) = f(x) +4 = 4.2[/tex]
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how do i do this problem
A man invests
$3700
in three accounts that pay
5%,
6%
, and
7%
in annual interest, respectively. He has
3
times as much invested at
7%
than he does at
5%
. If his total interest for the year is
$234
, how much is invested at each rate?
Molly had 1/8 of a bag of birdseed. She separated it equally into 2 bird feeders. What part of a bag did each feeder get?
imagine you live only one mile from work and you decide to walk if you walk 4 miles per hour how long will it take you to walk one mile
It will take you 15 minutes to walk one mile at a speed of 4 miles per hour.
To determine how long it will take you to walk one mile, we can use the formula:
Time = Distance / Speed
Let's plug in the values:
Distance = 1 mile
Speed = 4 miles per hour
Time = 1 mile / 4 miles per hour
Time = 0.25 hours
Since there are 60 minutes in an hour, we can convert the time to minutes:
Time = 0.25 hours × 60 minutes per hour
Time = 15 minutes
Therefore, it will take you 15 minutes to walk one mile at a speed of 4 miles per hour.
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find the sum of the first 10 terms. 0.5,0.9,1.3,1.7.....
The sum of the first 10 terms of the series is 23.
What is an arithmetic progression?An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.
For the given situation,
The series is 0.5,0.9,1.3,1.7.....
Here the first term, a = 0.5,
The common difference, d = [tex]0.9-0.5[/tex]
⇒ [tex]d=0.4[/tex]
Number of terms, n = 10
The formula of sum of n terms is
[tex]S_{n}=\frac{n}{2} [2a+(n-1)d][/tex]
On substituting the above values,
⇒ [tex]S_{10}=\frac{10}{2} [2(0.5)+(10-1)(0.4)][/tex]
⇒ [tex]S_{10}=5 [1+9(0.4)][/tex]
⇒ [tex]S_{10}=5 [1+3.6][/tex]
⇒ [tex]S_{10}=5 [4.6][/tex]
⇒ [tex]S_{10}=23[/tex]
Hence we can conclude that the sum of the first 10 terms of the series is 23.
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The two lines, X and Y, are graphed below:
Line X is drawn by joining ordered pairs negative 3,12 and 7,negative 16. Line Y is drawn by joining ordered pairs 0, negative 14 and 11, 8
Determine the solution and the reasoning that justifies the solution to the systems of equations.
(2, 7), because this point is true for both the equations
(4, −6), because this point lies only on one of the two lines
(4, −6), because this point makes both the equations true
(2, 7), because the lines intersect the x-axis at these points
Answer:c
Step-by-step explanation:
(4,-6), because this point makes both the equations true.
find the present value that will grow to $7000 if the annual interest rate is 3.5% compounded quarterly for 9 uears
The present value that will grow to $7,000 if the annual interest rate is 3.5% compounded quarterly for 9 years is $5,187.72
The Breakdown
To find the present value (PV) that will grow to $7,000 if the annual interest rate is 3.5% compounded quarterly for 9 years, you can use the formula for compound interest:
PV = FV / (1 + (r / n))^(n*t
Where:
PV = Present Value
FV = Future Value ($7,000 in this case)
r = Annual interest rate (as a decimal, so 3.5% is 0.035)
n = Number of times the interest is compounded per year (quarterly, so 4 times)
t = Number of years (9 years in this case)
PV = 7000 / (1 + (0.035 / 4))^(4 * 9)
PV = 7000 / (1 + 0.00875)^(36)
PV = 7000 / (1.00875)^36
Now, calculate (1.00875)^36:
(1.00875)^36 ≈ 1.34985880768
Now, divide $7,000 by this value to find the present value:
PV ≈ 7000 / 1.34985880768 ≈ $5,187.72
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When a variable is eliminated from the equation during the equation solving process, what are the two possible solutions and what do they mean? Give an example of your own and explain what each answer would look like.
When a variable is eliminated from the equation during the equation solving process, the two possible solutions are:
A single unique solution and No solution:
what are the two possible solutions and what do they mean?When a variable is eliminated from an equation during the solving process, it results in an equation with only one variable. The two possible solutions are:
A single unique solution: This means that there is one specific value for the remaining variable that satisfies the equation.
No solution: This means that there is no value for the remaining variable that satisfies the equation, resulting in an inconsistent or contradictory statement.
Let's consider an example equation to illustrate these possibilities:
3x + 2y = 10
6x + 4y = 20
To solve this system of equations, eliminate the variable "x" by multiplying the first equation by 2 and subtracting it from the second equation:
[tex](6x + 4y) - 2(3x + 2y) = 20 - 2(10)\\6x + 4y - 6x - 4y = 20 - 20[/tex]
0 = 0
In this case, the variable "x" has been eliminated, and we are left with the equation 0 = 0. This equation is true for all values of "y".
Therefore, the system of equations has infinitely many solutions, and any value of "y" would satisfy the equations.
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latoya drove 864 miles in 12 hours. at the same rate, how long would it take her to drive 576 miles?
Answer:
8 Hours!!
Step-by-step explanation:
Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis. Is this statement true or false?
Answer:
The statement is true.
Step-by-step explanation:
Given : Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis.
To find : Is this statement true or false?
Solution:
Rules of reflection :
Along across y-axis if we have a point [tex](x,y)\rightarrow(-x,y)[/tex]
So, y=sinx
The reflection across y-axis→ [tex]y=sin(-x) \Rightarrow y = -sinx[/tex].......[1]
Along across x-axis if we have a point [tex](x,y)\rightarrow(x,-y)[/tex]
so, y=sinx
The reflection across x-axis → [tex]-y=sinx\Rightarrow y= -sinx[/tex] .....[2]
Hence, [1] and [2] both of them are equal
Therefore, the statement is true.
Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325. Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days. (4 points) Part B: Write the equation obtained in Part A using function notation. (2 points) Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
ella wants to estimate the product (3.6)(7.8). which expression shows each factor rounded to the nearest whole number
The expression that shows each factor rounded to the nearest whole number is 32.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded off like trimmed from the right in terms of exact digits.
Given that Ella wants to estimate the product (3.6)(7.8).
3.6 rounded to give 4
7.8 rounded to give 8
Therefore, the product would be;
4 x 8 = 32
Hence, the expression that shows each factor rounded to the nearest whole number is 32.
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Final answer:
To estimate the product of 3.6 and 7.8 by rounding to the nearest whole number, round 3.6 down to 3 and 7.8 up to 8, making the estimated expression (3)(8).
Explanation:
The student has asked how to estimate the product of 3.6 and 7.8 by rounding each factor to the nearest whole number.
To do this, we look at each factor and determine which whole number it is closest to. For 3.6, we round down to 3 because it is closer to 3 than to 4. For 7.8, we round up to 8 because it is closer to 8 than to 7. Hence, the expression that represents the product of each factor rounded to the nearest whole number is (3)(8).
A certain solution has a hydrogen ion concentration of 3.54 x 10−5 moles per liter. Write this number in standard notation.
Calculate the slope m, if defined, of the straight line through the given pair of points. Try to do the problem without writing anything down except the answer. (If an answer is undefined, enter UNDEFINED.) (6, 5) and (7, 2)
The slope m of the straight line through the points (6, 5) and (7, 2) is -3.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
The slope of the line is defined as the ratio of the rise to the run.
To find the slope, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (6, 5) and (x₂, y₂) = (7, 2).
Substituting these values, we get:
m = (2 - 5) / (7 - 6) = -3 / 1 = -3
Therefore, the slope of the straight line through the given pair of points is -3.
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How many possible hands of 3 cards can be obtained from a deck of cards? what are the odds of dealing three eights in a row from the deck?
There are 22,100 possible hands of 3 cards from a 52-card deck using combinations. The probability of dealing three eights in a row from the deck is approximately 0.000181.
This question involves calculating probabilities and combinations related to card hands from a deck of 52 cards.
Possible Hands of 3 Cards:
To determine the number of possible hands of 3 cards from a 52-card deck, we use the combination formula: C(n, k) = n! / [k! * (n - k)!], where n is the total number of cards and k is the number of cards to choose.
C(52, 3) = 52! / [3! * (52 - 3)!] = 52! / (3! * 49!) = (52 × 51 × 50) / (3 × 2 × 1) = 22100. Therefore, there are 22,100 possible hands of 3 cards.
Probability of Dealing Three Eights:
The probability of dealing three eights in a row can be determined as follows:
There are 4 eights in the deck.The probability of drawing the first eight: 4/52.The probability of drawing the second eight: 3/51.The probability of drawing the third eight: 2/50.Therefore, the probability of dealing three eights is: (4/52) × (3/51) × (2/50) = 24 / 132600 = 1 / 5525 ≈ 0.000181.
This detailed explanation helps in understanding how combinations and probabilities in card games are calculated.
53 ℃ below zero degrees