The relation is not an equivalence relation. (a) {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}:
Reflexive: (2,2), (3,3) are present, but (1,1) and (4,4) are not present. Hence, not reflexive.
Symmetric: (2,3) is present, but (3,2) is also present. Hence, not symmetric.
Transitive: No counterexample to transitivity exists. Hence, it is transitive.
Therefore, the relation is not an equivalence relation.
(b) {(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}:
Reflexive: (1,1), (2,2), (3,3), (4,4) are present. Hence, reflexive.
Symmetric: (1,2) is present, but (2,1) is also present. Hence, symmetric.
Transitive: No counterexample to transitivity exists. Hence, it is transitive.
Therefore, the relation is an equivalence relation.
(c) {(2,4),(4,2)}:
Reflexive: (2,2) and (4,4) are not present. Hence, not reflexive.
Symmetric: (2,4) is present, but (4,2) is not present. Hence, not symmetric.
Transitive: No counterexample to transitivity exists. Hence, it is transitive.
Therefore, the relation is not an equivalence relation.
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Every morning Jim runs for 15 minutes. If Jim runs 4 miles per hour, how far does Jim travel? Use the equation d=rt, where d is distance, r is rate, and t is time.
In △def, d = 20, e = 25, and f = 30. find m∠f to the nearest degree.
m∠f to the nearest degree is 83°.
The Law of Cosines is used to find an angle when all triangle sides are known.
f² = d² +e² -2de cos(F)
To find angle ∠F, we need to find the value of cos(∠F), which we can do by rearranging the Law of Cosines as follows:
cos(F) = (d² +e² -f²) / (2de)
cos(F) = (20² + 25² - 30²) / (2 × 20 × 25)
cos(F) = (400 + 625 - 900) / (1000)
cos(F) = 125/1000
∠F = arccos(1/8)
∠F = 82.8°
Rounding to the nearest degree
∠F = 83°
Hence, m∠f to the nearest degree is 83°.
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Select all the tables that show quadratic functions.
(select all that apply.)
To select all the tables that show quadratic functions, look for tables with a second-degree polynomial equation in the form of "y = ax² + bx + c".
Which of the following tables display a quadratic function in the form of "y = ax² + bx + c"?Tables that show quadratic functions:
(a).
x y
-2 8
-1 3
0 0
1 1
2 4
This table shows a quadratic function in the form of y = x² - 2x.
(b)
x y
-3 0
-2 1
-1 4
0 9
1 16
2 25
3 36
This table shows a quadratic function in the form of y = x².
A quadratic function is a second-degree polynomial function that can be expressed in the general form of "y = ax² + bx + c", where a, b, and c are constants.
In this form, the variable "x" is squared, and the coefficient "a" determines whether the parabola opens upward or downward.
To identify tables that show quadratic functions, we need to look for tables that display data points that follow a quadratic pattern.
That is, the dependent variable (y) changes in a way that corresponds to a quadratic equation.
In the first table, the values of y correspond to the quadratic equation y = x² - 2x. The second table shows a set of data points that corresponds to the quadratic function y = x².
Therefore, these two tables show quadratic functions.
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If a scale dilates a two dimensional object by factors of 2/3 it means that?
If a scale dilates a two-dimensional object by a factor of 2/3, it means that the image of the object will be reduced by a factor of 2/3. In other words, the length and width of the image will be 2/3 of the length and width of the original object.
For instance, consider a rectangle with length L and width W. If we dilate this rectangle by a factor of 2/3, the new length and width of the rectangle will be (2/3)L and (2/3)W, respectively. The area of the new rectangle will be (2/3)L x (2/3)W = (4/9)LW, which is 4/9 of the original area. This means that the image is smaller than the original rectangle, and this type of dilation is called a reduction.
Dilations can be used in different applications of mathematics, such as geometry, trigonometry, and algebra. They are useful for changing the scale or size of an object in a proportional way, without altering its basic shape or characteristics.
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two cards are drawn from a deck of 52 playing cards. the first card is not replace before the 2nd card is drawn. what is the probabilty of drawing a king and another king?
A. 3/676
B. 1/221
C. 1/169
D. 2/169
Answer:
1/221.
Step-by-step explanation:
Probability(first card is a King) = 4/52 = 1/13 (as there are 4 kings in the pack).
Now there are 51 cards left in the pack, 3 of which are Kings, so:
Probability(second card is a King) = 3/51 = 1/17.
These 2 events are independent so we multiply the probabilities:
Required probability =
1/13 * 1/17
= 1/221.
Identify the line of symmetry for the function below:
g(x) = |x +9|- 11
Answer:
x = -9
Step-by-step explanation:
As this is an absolute value function, the line of symmetry is the x-value of the maximum/minimum point. An absolute value function can be denoted as y = |x - h| + k, where (h, k) is the maximum/minimum point. We only need the x-value of the maximum/minimum point, so we only have to look at "h". Now, we can use y = |x - h| + k and turn it into g(x):
y = |x - h| + k
g(x) = |x - -9| + -11 --> this means h = -9, and the line of symmetry is at x = -9
g(x) = |x + 9| - 11
Answer:
I think x equals --9
1. Jason draws a rectangle in the coordinate plane at the right to represent his yard. To get from one corner of his yard to another, Jason travels 4 units down and then 6 units right. Draw arrows on the coordinate plane to show Jason’s path. Write the coordinates for his start and end points.
START:___ END:___
2. Use the coordinate plane in problem 1. What is the perimeter of rectangle YARD?
units
3. Mary models her rectangular room in the coordinate plane at the right. She plans to hang strings of lights on two perpendicular walls. What are the lengths of and ?
units units
4. Use the coordinate plane in problem 3. What is the area of Mary’s room?
square units
5. The coordinate plane at the right models the streets
of a city. The points A(3, 8), B(6, 3), and C(3, 3) are connected to form a park in the shape of a triangle. Connect the points to form the triangle. Which two sides of the park form a right angle?
and
6. Use the coordinate plane in problem 5. Tyler walks along the two sides of the park that form the right angle. How many blocks does he walk in all?
blocks
7. How can you find distances between points in a coordinate plane?
1. The coordinates are: START: (0,0) END: (6,-4), 2. The perimeter of rectangle YARD is 20 units,3. The lengths of YX and YZ are 4 units and 6 units, respectively, 4. The area of Mary's room is 24 square units,
1-To get from one corner of his yard to another, Jason travels 4 units down and then 6 units right. Starting from the origin, his starting point is (0,0). From there, he moves 4 units down to the point (0,-4), and then 6 units right to reach his endpoint, which is at (6,-4).
2-The rectangle has two sides of length 4 and two sides of length 6. The perimeter is the sum of the lengths of all sides, so it is equal to 2(4) + 2(6) = 8 + 12 = 20 units.
3-The coordinates of points Y, X, and Z are not given, so we cannot calculate the lengths directly. However, we know that the sides of a rectangle are perpendicular, so we can use the Pythagorean theorem to find the lengths. Let Y be the origin (0,0), and let X be the point (0, -4). Then YX has length 4 units. Similarly, let Z be the point (6, 0), so YZ has length 6 units.
4.To find the area of a rectangle, we can multiply the lengths of its sides. From problem 3, we know that the lengths of the sides are 4 and 6 units, so the area is 4 x 6 = 24 square units.
5. The sides AB and AC form a right angle.
To determine which sides of the triangle form a right angle, we need to find the slope of each side. The slope of AB is (3-8)/(6-3) = -5/3, and the slope of AC is (3-3)/(6-3) = 0. Since the product of the slopes of two perpendicular lines is -1, we can see that AB is perpendicular to AC. Therefore, sides AB and AC form a right angle.
6. Tyler walks 9 blocks in all.
To find the distance Tyler walks, we need to calculate the length of sides AB and AC. Using the distance formula, we can find that the length of AB is sqrt[(6-3)² + (3-8)²] =√[(34) units, and the length of AC is 3 units. Therefore, Tyler walks 3 + √[34 units along the two sides that form the right angle. This is approximately 9.4 blocks, so he walks 9 blocks in all.
7. The distance between two points in a coordinate plane can be found using the distance formula:
d = √[(x₂-x₁)² + (y₂-y₁)²]
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and d is the distance between them. The formula is derived from the Pythagorean theorem, which relates the sides of a right triangle.
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Evaluate JJ ) Ry0 +52, 15y52. (y + xy-2) dA; R= {(x,y): 0 < x
the evaluated double integral is approximately 14.25.
To evaluate the given double integral, we need to first understand the problem properly. We have the function f(x, y) = y + xy, and the region R is described by the inequalities: 0 < x < y^2, and 1 < y < 2.
Now we can set up the double integral:
∬(y + xy) dA over the region R.
Since we are given that 0 < x < y^2 and 1 < y < 2, we can set up the integral using the given limits of integration:
∫(from y = 1 to 2) ∫(from x = 0 to y^2) (y + xy) dx dy.
Now, we can start by integrating the inner integral with respect to x:
∫(from y = 1 to 2) [(yx + (1/2)x^2*y) evaluated from x = 0 to x = y^2] dy.
After evaluating the inner integral, we have:
∫(from y = 1 to 2) (y^3 + (1/2)(y^2)^2*y) dy.
Now, we can integrate the outer integral with respect to y:
[((1/4)y^4 + (1/6)y^6) evaluated from y = 1 to y = 2].
After evaluating the outer integral, we get:
[(1/4)(2^4) + (1/6)(2^6)] - [(1/4)(1^4) + (1/6)(1^6)].
Calculating the final result:
(4 + 10.6667) - (0.25 + 0.1667) = 14.6667 - 0.4167 ≈ 14.25.
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Garden plots in the Portland Community Garden are rectangles limited to 45 square meters. Christopher and his friends want a plot that has a width of 7.5 meters. What length will give a plot that has the maximum area allowed?
The length that will give a plot with the maximum area allowed is 6 meters.
To find the length that will give a plot with the maximum area, we need to use the formula for the area of a rectangle, which is A = lw, where A is the area, l is the length, and w is the width. In this case, we are given that the area is 45 square meters, and the width is 7.5 meters.
Substituting these values into the formula, we get:
45 = l(7.5)
To solve for l, we divide both sides by 7.5:
l = 45/7.5
Simplifying, we get:
l = 6
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A car is purchased for $35,000. The owner finances the car at an interest rate of 4.6%, continuously compounded, for 6 years. What is the monthly payment on the car? Group of answer choices $640.62 $46,124.68 $35,046.00 $743.95
The monthly payment on the car is approximately $640.62. The correct option is A
To solve this problemThe formula for the monthly payment on a continuously compounded loan can be expressed as:
P = (r * A) / (1 - (1 + r)^(-n))
Where
P is the monthly payment r is the yearly interest rateA is the principal (i.e., the original amount borrowed) n is the number of payments (i.e., the number of years multiplied by 12)r is the annual interest rate (stated as a decimal and constantly compounded)Plugging in the given values, we get:
P = (0.046 * 35000) / (1 - (1 + 0.046/12)^(-6*12))
P ≈ $640.62
Therefore, the monthly payment on the car is approximately $640.62.
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HELP!!
What will most likely happen in the absence of a vacuole?
Photosynthesis will not take place.
Genetic information will not be transmitted by the cell.
Energy will not be released during cellular respiration.
The cell will not store food, water, nutrients, and waste.
Answer:
if vacuole are absent in plant cell then there is no storage of food and ions in the process of and permeability of cell may be distorted
Find the measure of ZB 75° b
Answer: ∠b = 105°
Step-by-step explanation:
We know that a straight line is equal to 180 degrees. We will create an equation and solve for ∠b.
180° = ∠b + 75°
∠b = 180° - 75°
∠b = 105°
Of the money that was paid to a transportation company, 60\%60% went towards wages and 80\%80% of what was left went towards supplies.
If there was \$ 400$400 left after those two expenses, what was the original amount paid?
Amount paid = $
Answer is original amount paid to the transportation company was $800.
Let's work backwards from the final amount of $400 to find the original amount paid to the transportation company.
First, we know that percentage given is 80% of what was left after wages went towards supplies. So, if $400 was left after wages were paid, then:
0.8(400) = $320 went towards supplies.
Next, we know that 60% of the original amount went towards wages. So, if $320 went towards supplies, then the remaining amount that went towards wages was:
0.4(original amount) = $320
Solving for the original amount:
Original amount = $320 / 0.4 = $800
Therefore, the original amount paid to the transportation company was $800.
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For f(x)=1/x^2 show there is no c such that f(1)-f(-1)=f'(c)(2).
Explain why the mean value theorem doesnt apply over the interval
[-1,1]"
Prerequisites for the MVT are not met due to the discontinuity and non-differentiability of f(x) at x = 0 within the interval [-1, 1].
Let's first understand the Mean Value Theorem (MVT). The MVT states that if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:
f'(c) = (f(b) - f(a)) / (b - a)
Now, consider the function f(x) = 1/x^2. This function is continuous and differentiable for all x ≠ 0. However, in the interval [-1, 1], the function is not continuous nor differentiable at x = 0. Therefore, the Mean Value Theorem does not apply to this interval.
Since the MVT does not apply, we cannot say there exists a c in the interval (-1, 1) such that f'(c) = (f(1) - f(-1)) / (1 - (-1)). This is because the prerequisites for the MVT are not met due to the discontinuity and non-differentiability of f(x) at x = 0 within the interval [-1, 1].
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. let u = <4,8>, v = <-2, 6>. find u + v. (1 point)
how to find find u+v?
The sum of vectors u = <4,8>,and v = <-2, 6> i.e. (u+v) is <2, 14>
To find the sum of vectors u and v (u+v), you need to perform the following steps:
1. Identify the components of vectors u and v: u = <4, 8> and v = <-2, 6>.
2. Add the corresponding components of both vectors: To find the sum (u+v), add the x-components (4 and -2) and the y-components (8 and 6) separately.
3. Calculate the sum of the x-components: 4 + (-2) = 2.
4. Calculate the sum of the y-components: 8 + 6 = 14.
5. Combine the results to form the new vector (u+v): <2, 14>.
So, the sum of vectors u and v (u+v) is <2, 14>.
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Josh needs to save at least $100 to buy new shoes he wants. He makes $13 an hour working at Target and has already saved $35. How many hours does he need to work to have enough money to buy his shoes? Write an equation and solve the problem
Answer:
13×X + 35= 100 (equation)
X=(100-35)/13 = 5 hours
Answer:
13x+35=100
5 hours
Step-by-step explanation:
New shoes= $100
Hours he makes= $13
Hours he worked= unknown so its "x"
Now it's 5
He already has= $35
13 x 5 = 65) + 35 = 100
The housing market has been very intense since 2020 when the pandemic began. People in Southern California as well as across the USA wanted to buy homes away from cities with a prefence towards the suburbs and rural areas. Southern California homes experienced a 12. 6 % year over year increase in price gains since 2020 and this is still going on. Inventory is too low, that is the supply of homes is low. Home builders aren't able to build fast enough to keep up with demand, or won't. A: If a modest 2 bedroom 2 bathroom house in Santa Barbara county used to cost $567,000 in 2020, give the exponential formula that models the price of this house over time, assuming the percent appreciation sustains currently and into the future. Let P(t) be the "asking price" of the house. Let "r" be the rate of the appreciation value. Let t be time in years. Use decimals only. B: What would be the price of such a house in 2022? ( Round your answer to two places after the decimal, also known as the hundredths place).
A: P(t) [tex]= $567,000 * (1 + 0.126)^t[/tex]
B: [tex]567,000 * (1 + 0.126)^2 = $671,448.14[/tex]
How can we calculate the price of a 2 bedroom 2 bathroom house in Santa Barbara county in 2022, assuming the current rate of appreciation continues?A: To model the price of the house over time, we can use the exponential formula: P(t) = P₀ * (1 + r)^t, where P₀ is the initial price, r is the rate of appreciation, and t is the time in years.
In this case, the initial price (P₀) of the house is $567,000 and the rate of appreciation (r) is 12.6% expressed as a decimal, which is 0.126. Therefore, the exponential formula to model the price of the house over time would be: P(t) = 567,000 * (1 + 0.126)^t.
B: To find the price of the house in 2022, we substitute t = 2022 - 2020 = 2 into the exponential formula.
P(2) = 567,000 * (1 + 0.126)^2
P(2) = 567,000 * (1.126)^2
P(2) ≈ 567,000 * 1.268
P(2) ≈ $719,976.00
Therefore, the price of such a house in 2022 would be approximately $719,976.00
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The box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection. 4 8 12 16 20 24 28 32 36 40 44 48 speed of cars (miles per hour) a. What is the smallest value in the data set? 4 b. What is the largest value in the data set? 48 c. What is the median?â
a. The smallest value in the data set is 4 miles per hour. b. The largest value in the data set is 48 miles per hour. c. The median is 26 miles per hour.
a. The smallest value in the data set is 4 miles per hour.
b. The largest value in the data set is 48 miles per hour.
c. To find the median, we need to arrange the values in order from smallest to largest:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
The median is the middle value in this list. Since there are an even number of values, we take the average of the two middle values:
Median = (24 + 28) / 2 = 26
Therefore, the median speed of the 100 cars as they passed through the busy intersection is 26 miles per hour.
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The graph shows the salaries of 23 employees at a small company. Each bar spans a width of $50,000 and the height shows the number of people whose salaries fall into that interval.
The owner is looking to hire one more person and when interviewing candidates says that on average an employee makes at least $175,000.
How does the owner justify this claim?
Answer:
Based on the given graph, we can see that the bars representing salaries above $175,000 span a total of 7 employee salaries. Since each bar spans a width of $50,000, we can estimate that the total number of employees making at least $175,000 is approximately 7 multiplied by 50,000 divided by 10,000, which equals 35%. Therefore, the owner can justify the claim that on average an employee makes at least $175,000 by stating that approximately 35% of the current employees already make at least that amount. However, it's important to note that this calculation is based on estimates and assumptions and should not be used as a definitive answer.
Carla, the baker, worked for 5 hours to make cookies..
She ended with 380 cookies altogether. Write an
equation to express how many cookies Carla made
each hour.
Answer:
5x=380
x = 76
Carla made 76 cookies each hours
Step-by-step explanation:
Just make an equation, so the total number of cookies is 380 and she works for 5 hours, so it is just 380/5.
What is 30 players for 10 sports expressed as a rate
The rate can be expressed as "3 players per sport"
What is rate?A rate is a ratio that compares two quantities with different units. In this case, we have 30 players and 10 sports. To express this as a rate, we want to compare the number of players to the number of sports. We can write this as:
30 players / 10 sports
To simplify this ratio, we can divide both the numerator (30 players) and denominator (10 sports) by the same factor to get an equivalent ratio. In this case, we can divide both by 10:
(30 players / 10) / (10 sports / 10)
This simplifies to:
3 players / 1 sport
So the rate can be expressed as "3 players per sport" or "3:1" (read as "three to one"). This means that for every one sport, there are three players.
Alternatively, we can express the rate as a fraction or decimal by dividing the number of players by the number of sports:
30 players / 10 sports = 3 players/sport = 3/1 = 3 or 3.0 (as a decimal)
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Find f(a) if y = f(a) satisfies
dy/dx = 24yx³
and the y-intercept of the curve y = f(2) is 5. f(x) = ...
The solution to the differential equation is f(a) = 1/√(12a⁴/125 - 769/5000).
How to find the derivative of given equation?To find f(a), we need to solve the differential equation:
dy/dx = 24yx³
Separating variables, we get:
dy/y³ = 24x³ dx
Integrating both sides, we get:
-1/(2y²) = 6x⁴ + C
where C is the constant of integration.
To find the value of C, we use the fact that the y-intercept of the curve y = f(2) is 5. This means that when x = 2, y = 5. Substituting these values into the equation above, we get:
-1/(2(5)²) = 6(2)⁴ + C
Simplifying and solving for C, we get:
C = -1/(2(5)²) - 6(2)⁴
C = -769/125
So the solution to the differential equation is:
-1/(2y²) = 6x⁴ - 769/125
Solving for y, we get:
y = 1/√(12x⁴/125 - 769/5000)
Therefore, f(a) = 1/√(12a⁴/125 - 769/5000).
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A rectangular prism with a square base has a height of 17. 2 cm and a volume of 24. 768 cm3. What is the side length of its base?
The side length of the base of the rectangular prism is approximately 1.2 cm.
What is rectangular prism?The top, bottom, and lateral faces of a rectangular prism are all rectangles, and all the pairings of the opposing faces are congruent. A rectangular prism is a three-dimensional structure with six faces.
Let's denote the side length of the base of the rectangular prism as "x" cm.
We know that the volume of a rectangular prism is given by the formula:
Volume = Base Area x Height
In this case, the base is a square, so its area is given by:
Base Area = x²
We are given that the volume is 24.768 cm³ and the height is 17.2 cm.
Therefore, we can write the equation:
24.768 = x² * 17.2
To find the value of x, we can rearrange the equation:
x² = 24.768 / 17.2
x² = 1.4376
Taking the square root of both sides, we get:
x = √1.4376
x ≈ 1.2
Therefore, the side length of the base of the rectangular prism is approximately 1.2 cm.
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Question below, please help! this is part of my grade.. (30 points)
Answer:
y = 1 + 2√7 or y = 1 - 2√7
Step-by-step explanation:
To complete the square, you need to add and subtract the square of half of the coefficient of the y term.
First, you can factor out a 1 from the y^2 - 2y term:
y^2 - 2y - 27 = 0
y^2 - 2y = 27
Next, take half of the coefficient of the y term (-2/2 = -1) and square it (1):
y^2 - 2y + 1 - 1 = 27
The "+1 -1" doesn't change the value of the equation, it's just a way to add 0 to the equation so we can complete the square.
Now you can rewrite the left side as a perfect square:
(y - 1)^2 - 28 = 0
Add 28 to both sides:
(y - 1)^2 = 28
Take the square root of both sides (remembering to include both positive and negative square roots):
y - 1 = ±√28
y = 1 ± 2√7
So the solutions are:
y = 1 + 2√7
y = 1 - 2√7
Answer: y=± 2√7+1
6.29
Step-by-step explanation: Use the formula
(b/2)^2 in order to create a new term. Solve for y by using this term to complete the square.
A method for determining whether a critical point is a relative minimum or maximum using concavity.
To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.
If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.
On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.
If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.
Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.
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Complete question is:
What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.
plunk and ms. q run a $100$-meter race. plunk runs at $8$ meters per second, and ms. q runs at $5$ meters per second. because ms. q runs slower, she is given a $3$-second head start. plunk wins the race. how much time, in seconds, is it between the time plunk passes ms. q and the time that plunk finishes the race?
The seconds, is it between the time plunk passes Ms. q and the time that plunk finishes the race is 7.5 seconds..
Flow Distance In the Mathematics or Quants part of any competitive test, time is one of the most well-liked and significant topics. For inquiries about a variety of subjects, including motion in a straight line, circular motion, boats and streams, races, clocks, etc.
The notion of Speed, Time, and Distance is frequently employed. Candidates should make an effort to comprehend how the variables of speed, distance, and time interact.
Ms. q being slow will get a head start for the race so,
3 second head start = 3 x 5 = 15 meters
There difference in speed is 8- 5 = 3 m/s
Time required for the Plunk to catch up to Ms. q is:
15 / 3 = 5 seconds when P catches Q
(this is 8 seconds after Q starts the race)
In 5 seconds Plunk runs 5 x 8 = 40 meters this is when they are at the same point that is at time 8 seconds.
60 meters left in the race will take Plunk :
60 m / 8 m/s = 7.5 seconds to finish the race.
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Philip owns 100 shares of a stock that is trading at $97. 55 and pays an annual dividend of $2. 74. How much should he receive in quarterly dividends? What's the annual yield on this stock?
Philip should receive $68.50 in quarterly dividends and the annual yield on this stock is about 2.81%.
To calculate the quarterly dividend that Philip need to acquire, we need to first calculate the quarterly dividend per share:
Quarterly dividend in step with share = Annual dividend per percentage / 4
In this situation, the once a year dividend in line with proportion is $2.74, so the quarterly dividend per proportion is:
Quarterly dividend per proportion = $2.74 / 4 = $0.685
For the reason that Philip owns 100 shares, his quarterly dividend should be:
Quarterly dividend = Quarterly dividend per share * number of stocks
Quarterly dividend = $0.685 * 100 = $68.50
Therefore, Philip should receive $68.50 in quarterly dividends.
To calculate the once a year yield on this inventory, we want to divide the yearly dividend in line with proportion by the present day stock price, after which multiply by way of 100 to specific the result as a percentage:
Annual yield = (Annual dividend per share / inventory price) * 100
In this case, the annual dividend per percentage is $2.74, and the inventory charge is $97.55. Plugging those values into the components, we get:
Annual yield = ($2.74 / $97.55) * 100
Annual yield ≈ 2.81%
Therefore, the annual yield on this stock is about 2.81%.
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Patricia bought 4 apples and 9 bananas for $12. 70. Jose bought 8 apples and 11 bananas for $17. 70 at the same grocery store. What's the price of one apple?
The price of one apple is $0.70, obtained by solving the system of equations 4x + 9y = 12.70 and 8x + 11y = 17.70 using elimination.
How much would Patricia pay for each apples?Let's use a system of equations caculation the problem.
Let x be the price of one apple and y be the price of one banana.
From the first sentence, we know that:
4x + 9y = 12.70
From the second sentence, we know that:
8x + 11y = 17.70
Now we can solve for x by using either substitution or elimination.
Let's use elimination.
We can multiply the first equation by 11 and the second equation by -9, then add them together:
44x + 99y = 139.70
-72x - 99y = -159.30
-28x = -19.60
Dividing both sides by -28, we get:
x = 0.70
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A cylindrical swimming pool has a diameter of 12 feet and a height of 4 feet. How many gallons of water can the pool contain? Round your answer to the nearest whole number. (1 ft3 ≈ 7. 5 gal)
The number of gallons of water the pool can contain is approximately 3393 gallons.
To find the amount of water in gallons the pool can contain, we must find the volume of the cylindrical swimming pool, you can use the formula:
Volume = π * r² * h
Where r is the radius (half the diameter), and h is the height.
In this case, r = 12 feet / 2 = 6 feet, and h = 4 feet.
Volume = π * (6 ft)² * 4 ft ≈ 452.39 ft³
To convert cubic feet to gallons, use the given conversion factor (1 ft³ ≈ 7.5 gal).
Volume ≈ 452.39 ft³ * 7.5 gal/ft³ ≈ 3392.93 gal
Rounding to the nearest whole number, the pool can contain approximately 3393 gallons of water.
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A bag contains 5 red marbles, 6 blue marbles and 3 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be red?
Step-by-step explanation:
5 + 6 + 3 = 14 marbles 5 are red
1st marble red = 5 out of 14 = 5/14
now there are 13 marbles 4 are red
2nd marble red 4/13
and finally , 3rd marble red = 3/12
5/14 * 4/13 * 3/12 = 5/182 chance for three reds