The standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
What is conic?It is a type of curve with a curved line in the middle and two straight lines on the sides. Conic sections include circles, ellipses, parabolas, and hyperbolas.
The standard form of the equation of a conic is
Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F are constants.
In this case, the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
To derive this equation, we'll use the distance formula to calculate the distance between the vertices and the foci. The distance between the vertices and the foci is given by
d = √((x_1 - x_2)² + (y_1 - y_2)²)
where (x_1, y_1) is the coordinates of the first vertex and (x_2, y_2) is the coordinates of the first foci.
For the first vertex, (x_1, y_1) = (0, 8). For the first foci, (x_2, y_2) = (0, √48). Thus, the distance between the two points is
d = √((0 - 0)² + (8 - √48)² )
= √(0 + (-8 - √48)² )
= √(-16 - 2√48 + 48)
= √(32 -2√48)
= 2√(16 - √48)
= 2√(16 - 6.9)
= 2√(9)
= 2(3)
= 6
So, the distance between the vertices and the foci is 6.
The equation of the conic can then be written as x² + y² - 16x - 16y - (-8)² = 0, which simplifies to x² + y² - 16x - 16y - 192 = 0.
Thus, the standard form of the equation of the conic is x² + y² - 16x - 16y - 192 = 0.
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find the radius of a cylinder if the volume is 2,035.75 in^3 and the height is 3 times the radius. use the formula V= pi r^2h
The radius of the cylinder is approximately 6.75 inches.
How to calculate volume of cylinder?We can use the formula for the volume of a cylinder to solve this problem:
[tex]V = \pi r^2h[/tex]
We know that the volume V is 2,035.75 [tex]in^3[/tex], and the height h is 3 times the radius r. So we can write:
[tex]V = \pi r^2(3r)[/tex]
Simplifying this expression, we get:
V = 3π[tex]r^3[/tex]
To solve for r, we can divide both sides of the equation by 3π[tex]r^2[/tex]:
V/(3π[tex]r^2[/tex]) = r
Substituting the given value for V, we have:
2,035.75/(3π[tex]r^2[/tex]) = r
Multiplying both sides by 3πr^2, we get:
2,035.75 = 3π[tex]r^3[/tex]
Dividing both sides by 3π, we have:
[tex]r^3[/tex] = 2,035.75 / (3π)
Taking the cube root of both sides, we get:
r = [tex](2,035.75 / (3\pi ))^{1/3[/tex]
Using a calculator, we find that:
r ≈ 6.75 inches
Therefore, The cylinder has a radius of about 6.75 inches.
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The base of the right prism shown is a right triangle.
1. Name two lines parallel to AD.
2. Name a line skew to DE.
3. State the number of base edges.
4. State the number of lateral faces.
5. Find the base area,
6. Find the lateral area.
7. Find the volume.
Two lines parallel to AD are BF and CE.
Two lines skew to DE are EF and DF.
The number of base edges is three: DE, EF, and DF.
The number of lateral faces is three: ABDF, BCEF, and ACDE.
The base area is 6 square units.
The lateral area is 72 square units.
The volume is 36 cubic units.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
1. Name two lines parallel to AD.
BF, CE
2. Name a line skew to DE.
EF, DF
3. State the number of base edges.
DE, EF, DF
4. State the number of lateral faces.
3, Which are ABDF, BCEF, ACDE.
5. Find the base area,
the base of a prism is ΔDEF,
DE = AC = 3,
EF = BC = 4,
DF = 5
A = √(s(s-a)(s-b)(s-c))
s = (3 + 4 + 5)/2 = 6
A = √(s(s-a)(s-b)(s-c))
A = √(6(6-3)(6-4)(6-5))
A = √(6(3)(2)(1))
A = √36
A = 6
6. Find the lateral area.
the lateral area would be the sum of the area of the four rectangular faces.
A = lb
ABDF
A1 = 5* 6 = 30,
BCEF,
A2 = 4 * 6 = 24
ACDE
A3 = 3 *6 = 18
lateral area = 30 + 24 + 18
= 72
7. Find the volume.
The volume of a prism can be calculated by multiplying the area of the base by the height of the prism. Therefore, the formula for the volume of a prism is:
V = Bh
Where V is the volume, B is the area of the base, and h is the height of the prism.
V = 6 * 6 = 36
hence,
Two lines parallel to AD are BF and CE.
Two lines skew to DE are EF and DF.
The number of base edges is three: DE, EF, and DF.
The number of lateral faces is three: ABDF, BCEF, and ACDE.
The base area is 6 square units.
The lateral area is 72 square units.
The volume is 36 cubic units.
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La Suma delos cuadrados de dos números naturales consecutivos es 181 halla dichos numeros
The two consecutive natural numbers whose sum of squares is 181 are 9 and 10
Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:
x² + (x+1)² = 181
Expanding the equation:
x² + x² + 2x + 1 = 181
Combining like terms:
2x² + 2x - 180 = 0
Dividing both sides by 2:
x² + x - 90 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -90
x = (-1 ± √(1 + 360)) / 2
x = (-1 ± √(361)) / 2
x = (-1 ± 19) / 2
We discard the negative value, as it does not correspond to a natural number:
x = 9
Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.
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You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
Therefore, it will take 173 months to pay off the loan, or approximately 14 years and 5 months.
What is percentage?A percentage is a way of expressing a number as a fraction of 100. The symbol for a percentage is "%". For example, 50% is the same as 50/100 or 0.5 as a decimal. Percentages are often used to express a portion or share of a whole. For instance, if you scored 90% on a test, it means you got 90 out of 100 possible points. In finance, percentages are commonly used to express interest rates, returns on investments, or changes in stock prices.
First, we need to convert the monthly interest rate from a percentage to a decimal by dividing by 100.
0.25% / 100 = 0.0025
Now we can plug in the values into the formula:
N= (-log (1-0.0025*70000/250))/ (log (1+0.0025))
Simplifying the equation in the parentheses:
N= (-log (1-175))/ (log (1.0025))
N= (-log (0.9964))/ (0.002499)
N= 172.9
Rounding up to the nearest whole number since we can't make partial payments:
N= 173
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. Bert has a well-shuffled standard deck of 52 cards, from which he draws one card; Ernie has a 12-sided die, which he rolls at the same time Bert draws a card. Compute the probability that:
a. Bert gets a Jack and Ernie rolls a five.
b. Bert gets a heart and Ernie rolls a number less than six.
c. Bert gets a face card (Jack, Queen or King) and Ernie rolls an even number.
d. Bert gets a red card and Ernie rolls a fifteen.
e. Bert gets a card that is not a Jack and Ernie rolls a number that is not twelve.
Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.
What is probability, exactly?The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.
Here,
a.
P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)
= (4/52) * (1/12)
= 1/78
b.
P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)
= (13/52) * (5/12)
= 65/624
c.
P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)
= (12/52) * (6/12)
= 1/4
d.
P(Bert gets a red card and Ernie rolls a fifteen) = 0
e.
Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:
A regular 52-card deck contains 48 cards that are not Jacks,
so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.
On a 12-sided dice with 11 possible outcomes,
Ernie rolls a non-12th-number (1, 2, 3, etc.).
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KPI Payouts are: Prepaid Ring-out Only: $ 1.00 Prepaid Activation: $ 2.00 Accessories: 1.5 Equipment Protection: $ 1.00 You can make $ and ring it out at the POS. % when you activate a prepaid device with equipment protection
If no accessories are sold, $3 will be paid out. In the event that accessories are sold, the compensation is $2.00 plus $1.00 plus 1.5 percent of their worth.
Based on the information given, the KPI payouts are:
$1.00 for each Prepaid Ring-out Only
$2.00 for each Prepaid Activation
1.5% of the value of each Accessories sale
$1.00 for each Equipment Protection sale
We need to know the values of the prepaid activation and equipment protection in order to compute the payment for activating a prepaid device with equipment protection. Assume that the equipment protection is worth $Y and the prepaid activation is worth $X.
The following would be the total payment for activating a prepaid device with equipment protection:
Payout = $2.00 (for activation) + $1.00 (for equipment protection) + 1.5% (of the value of accessories sold)
If no accessories are sold, the payout would be:
Payout = $2.00 + $1.00
= $3.00
If accessories worth $Z are also sold, the payout would be:
Payout = $2.00 + $1.00 + 1.5% of $Z
= $2.00 + $1.00 + 0.015Z
So the payout for activating a prepaid device with equipment protection depends on the value of the accessories sold.
Therefore, If no accessories are sold, the payout is $3.00. If accessories are sold, the payout is $2.00 + $1.00 + 1.5% of the value of the accessories sold.
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 0 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 10. There are two dots above 1 and 4. There are three dots above 2 and 5. There are 4 dots above 3.
Which of the following is the best measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 9.
The range is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 9.
The range is the best measure of variability for this data, and its value is 4.
Which of the following is the best measure of variability for the data, and what is its value?The line plot displays the number of roses purchased per day at a grocery store, with the data values ranging from 0 to 4 (since there are no dots above 4).
The best measure of variability for this data is the range, which is the difference between the maximum and minimum values in the data set. In this case, the minimum value is 0 and the maximum value is 4, so the range is:
Range = Maximum value - Minimum value = 4 - 0 = 4
Therefore, the range is the best measure of variability for this data, and its value is 4.
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Last week, Kristen spent 4 hours gardening over a period of 7 days. She spent the same amount of time gardening each day.About how much time did she spend gardening each day last week?
A.less than 1 hour
B.between 1 and 2 hours
C.between 2 and 3 hours
D.between 4 and 7 hours
We can see that the choice falls within the range of (A) less than 1 hour. Therefore, the answer is (A), Kristen spends less than 1 hour .
What does "unitary method" mean?Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.
To find out approximately how much time Kristen spent gardening each day, we can divide the total time she spent gardening by the number of days she gardened.
Total time = 4 hours
Number of days = 7
So, Kristen spent approximately 4/7 = 0.57 hours or about 34 minutes each day gardening.
Since the answer choices are in ranges, we can see that this falls within the range of (A) less than 1 hour. Therefore, the answer is (A).
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0\left\{-10\le x\le10\right\}
Describe the transformations (vertical translation, horizontal translation, and dilation/reflection) from the parent function that happened to these formulas
The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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Which of these is a simplified form of the equation 6Y +4 equals 8+ 2Y plus 2Y
the simplified form of the equation 6Y + 4 = 8 + 2Y + 2Y is Y = 2.
How to solve the question ?
To simplify the equation 6Y + 4 = 8 + 2Y + 2Y, we can combine like terms. Like terms are terms that have the same variable and the same exponent. In this case, we have two terms with Y as the variable, so we can combine them.
First, let's add the 2Y terms on the right side of the equation: 6Y + 4 = 8 + 4Y
Next, we can subtract 4Y from both sides of the equation to isolate the variable on one side: 6Y - 4Y + 4 = 8
Simplifying further, we can combine the Y terms: 2Y + 4 = 8
Finally, we can subtract 4 from both sides to isolate the variable: 2Y = 4
And we can solve for Y by dividing both sides by 2: Y = 2
Therefore, the simplified form of the equation 6Y + 4 = 8 + 2Y + 2Y is Y = 2.
In summary, to simplify an equation, we want to combine like terms and isolate the variable on one side of the equation. Once we have the variable on one side, we can solve for its value.
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The count in a bateria culture was initially 300, and after 35 minutes the population had increased to 1600. Find the doubling period. Find the population after 70 minutes. When will the population reach 10000?
Factorize the following polynomials:
1) 54x²+42x³ - 30x4
100 POINTS
Answer this question for me please.
Answer: Rectangle
Step-by-step explanation: The shape created by the cross-section is a rectangle because the cross-section shows a 2-dimensional slice of a 3-dimensional rectangular prism. Since a rectangular prism has rectangular faces, any cross-section taken perpendicular to the length of the prism will be a rectangle.
What are answers to these questions?
1. f is concave up on the intervals = ?
2. f is concave down on the intervals = ?
3. The inflection points occur at x = ?
f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).
What is inflection Point?An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.
According to the given information:
To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.
First, we find the first derivative of f(x):
f'(x) = (14x)/(7x²+6)²
Then, we find the second derivative of f(x):
f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4
Simplifying the expression, we get:
f''(x) = 28(42x² - 72) / (7x^2+6)³
To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.
Setting f''(x) = 0, we get:
42x² - 72 = 0
Solving for x, we get:
x = ±√(6/7)
These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.
We can use a sign chart to determine the sign of f''(x) on each interval.
Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.
Here is the sign chart for f''(x):
x | -∞ | -√(6/7) | √(6/7) | ∞
f''(x)| - | + | - | +
From the sign chart, we can see that:
a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).
b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).
c) The inflection points occur at x = -√(6/7) and x = √(6/7).
Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).
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The f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞),f(x) is concave down on the interval (-√(6/7), √(6/7)) ,The inflection points occur at x = -√(6/7) and x = √(6/7).
What is inflection Point?
An inflection point is a point on a curve where the concavity changes, from concave up to concave down or vice versa, indicating a change in the curvature of the curve.
According to the given information:
To determine the intervals where f(x) is concave up or down, we need to find the second derivative of f(x) and determine its sign.
First, we find the first derivative of f(x):
f'(x) = (14x)/(7x²+6)²
Then, we find the second derivative of f(x):
f''(x) = [28(7x²+6)²- 28x(7x²+6)(4x)] / (7x²+6)^4
Simplifying the expression, we get:
f''(x) = 28(4x² - 72) / (7x^2+6)³
To determine where f(x) is concave up or down, we need to find the intervals where f''(x) is positive or negative, respectively.
Setting f''(x) = 0, we get:
42x² - 72 = 0
Solving for x, we get:
x = ±√(6/7)
These are the possible inflection points of f(x). To determine if they are inflection points, we need to check the sign of f''(x) on both sides of each point.
We can use a sign chart to determine the sign of f''(x) on each interval.
Intervals where f''(x) > 0 are where f(x) is concave up, and intervals where f''(x) < 0 are where f(x) is concave down.
Here is the sign chart for f''(x):
x | -∞ | -√(6/7) | √(6/7) | ∞
f''(x)| - | + | - | +
From the sign chart, we can see that:
a) f(x) is concave up on the interval (-∞, √(6/7)) U (√(6/7), ∞).
b) f(x) is concave down on the interval (-sqrt(6/7), √(6/7)).
c) The inflection points occur at x = -√(6/7) and x = √(6/7).
Therefore, the open intervals where f(x) is concave up are (-∞, -√(6/7)) and (√(6/7), ∞), and the open interval where f(x) is concave down is (-√(6/7), √(6/7)). The inflection points occur at x = -√(6/7) and x = √(6/7).
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PLEASE HELP DUE TODAY ASAP
im pretty sure the answer is B Please tell me if im correct ASAP!
Question 3(Multiple Choice Worth 1 points)
(08.07 LC)
The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 4 comma 3, a point at negative 6 comma 7, and a point at negative 2 comma 7.
What is the equation of g(x) in vertex form?
g(x) = (x − 4)2 − 3
g(x) = (x − 4)2 + 3
g(x) = (x + 4)2 − 3
g(x) = (x + 4)2 + 3
Step-by-step explanation:
Vertex at -4,3 would result in vertex form of parabola
g(x) = (x+4)^2 + 3
I need helppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
The distance formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
x1 is a,
x2 is 0,
y1 is 0 and
y2 is b. Fitting those into the formula where they belong:
[tex]d=\sqrt{(0-a)^2+(b-0)^2}[/tex] and
[tex]d=\sqrt{(-a)^2+(b)^2}[/tex]
Since a negative squared is a positive, then
[tex]d=\sqrt{a^2+b^2}[/tex]
which is the second choice down.
What kind of angle is
∠mah?
What is the value of x?
What is the measure of
∠mat ?
What is the measure of
∠tah ?
So according to the given figure ∠mah is right angle(90°), The value of x is 17, ∠mat is 38° and ∠tah is equal to 52°.
What is the source of this answer and define a graph?(A) ∠mah is right angle(90°) [GIVEN IN THE FIGURE]
(B) (2x+4)+(3x+1) = 90
5x+5 = 90
x= 17
(C) 2x+4 = 2×17 + 4 = 38°
(D) 3X + 1 = 3 × 17 + 1 = 52°
A graph is a visual representation or diagram that displays facts or values in an organised manner in mathematics. The points on a graph are typically used to depict the relationships between two or more things.
A graph in discrete mathematics is made up of vertices, which are groups of points, and edges, which are the connections between those vertices. There are numerous different types of graphs besides linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs.
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PLSS HELP IMMEDIATELY
The continuous compounding rate earned by the investment is given as follows:
8.022%.
How to model continuous compounding?The balance of an account after t years, using continuous compounding, is modeled by the equation presented as follows:
A(t) = A(0)e^{kt}.
In which:
A(0) is the initial amount.k is the continuous compounding rates.For this problem, the parameters are given as follows:
A(11) = 58, A(0) = 24, t = 11.
Hence the rate is obtained as follows:
24e^(11k) = 58
e^(11k) = 58/24
11k = ln(58/24)
k = ln(58/24)/11
k = 8.022%.
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what is 15 to the power of 12
Answer:
1.2974634e+14
Step-by-step explanation:
ye
7. A group of students wants to demonstrate that sunlight provides the energy for plants to grow. What is
the control group for the experiment?
A. Some plants will receive less water
B. Some plants will receive fertilizer
C. Some plants will receive no sunlight
D. Some plants will receive no water
I
The control group for the experiment would be option C: some plants will receive no sunlight.
What is control group for experiment ?The control group in an experiment is the group that does not receive the treatment or intervention being tested, so that the effects of the treatment can be compared to a baseline or reference point. In this experiment, the treatment being tested is the provision of sunlight as an energy source for plant growth.
Therefore, the control group should not receive sunlight, so that the effects of sunlight can be compared to the baseline of plant growth without sunlight.
Therefore, the control group for the experiment would be option C: some plants will receive no sunlight.
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Find the length of the triangle.
The length of the unknown side of the triangle is __________
Answer:
The answer is 2√10
Step-by-step explanation:
Hyp²=opp²+adj²
let hyp be x
x²=6²+2²
x²=36+4
x²=40
square root both sides
√x²=√40
x=2√10
positive.
an remove
3√5a-8√/35a2
Given F(x) = 4x - 8 and g(x) = -3x + 1, what is (f - g)(x)?
A) 7x-9
B) 7x - 7
C) x-9
D) x - 7
Therefore, the answer is (A) 7x-9 when it is given that function F(x) = 4x - 8 and g(x) = -3x + 1.
What is function?In mathematics, a function is a relationship between two sets of values, where each input (or domain element) is associated with a unique output (or range element). In other words, a function is a rule or a process that takes an input (or inputs) and produces a corresponding output. Functions can be expressed using various mathematical notations, such as algebraic formulas, graphs, tables, or even verbal descriptions. They are widely used in many fields of mathematics, science, engineering, economics, and computer science, to model and solve problems that involve relationships between variables or quantities.
Here,
To find (f - g)(x), we need to subtract g(x) from f(x), so we get:
(f - g)(x) = f(x) - g(x)
Substituting the given functions, we get:
(f - g)(x) = (4x - 8) - (-3x + 1)
Simplifying the expression by distributing the negative sign, we get:
(f - g)(x) = 4x - 8 + 3x - 1
Combining like terms, we get:
(f - g)(x) = 7x - 9
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Please help with #13!!
13.
m
mFP=
mPD=
Answer:
Step-by-step explanation:
36 26 so 36 +26 = 89
Find the final amount of a $750 investment after 15 years at 8% interest compounded semiannually, quarterly and daily.
With given compound interest, the final amount of the investment after 15 years at 8% interest compounded semiannually, quarterly and daily are $2,067.87, $2,094.28, and $2,101.62, respectively.
What is Compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or the interest earned on both the principal and any previously accrued interest. In other words, interest is computed not only on the original amount of money but also on any past interest gained. The interest generated on the cumulative interest can compound exponentially, resulting in enormous growth of an investment or loan sum over time. Compound interest is computed using a formula that takes the principle amount, interest rate, and compounding frequency into consideration.
Now,
To find the final amount of the investment, we can use the formula for compound interest:
A = P(1 + r/n)ⁿˣ
where:
A = final amount
P = principal (initial investment)
r = annual interest rate
n = times the interest is compounded per year
x = time in years
For semiannual compounding, n = 2 and x = 15:
A = 750(1 + 0.08/2)²*¹⁵= $2,067.87
For quarterly compounding, n = 4 and x = 15:
A = 750(1 + 0.08/4)⁴*¹⁵ = $2,094.28
For daily compounding, n = 365 (assuming no leap years) and x = 15:
A = 750(1 + 0.08/365)³⁶⁵*¹⁵ = $2,101.62
Therefore, the final amount of the investment after 15 years at 8% interest compounded semiannually, quarterly and daily are $2,067.87, $2,094.28, and $2,101.62, respectively.
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Find tan(Q).
A 1
3 9
"5
135°
P
para os a
was a s
Save and Exit
Next
Submit
Answer:
tanQ = 1
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ OPQ is an exterior angle of the triangle , then
∠ R + ∠ Q = 135°
90° + ∠ Q = 135° ( subtract 90° from both sides )
∠ Q = 45°
Then
tanQ = tan45° = 1
if k(x) =3x, then f'(x)=?
The five number summary of a dataset was found to be:
45, 52, 56, 63, 66
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
An observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.
Identifying the outliers in the summaryTo determine the outliers in a dataset using the five-number summary, we need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
IQR = Q3 - Q1
Where
Q1 = 52
Q3 = 63
So, we have
IQR = 63 - 52
IQR = 11
An observation is considered an outlier if it is:
Below Q1 - 1.5 × IQR
Above Q3 + 1.5 × IQR
Substituting the values, we get:
Below 52 - 1.5 × 11 = 35.5
Above 63 + 1.5 × 11 = 79.5
Therefore, an observation is considered an outlier if it is below 35.5 or above 79.5 in this dataset.
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taylor has enough money to buy either 90 granola bars or 78 pop tarts. After returning from the atore, taylor has no money, 75 granola bars and p pop tarts
Using equations, we can find that the number of pop tarts that Taylor has with him, p = 13.
Define equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others.
Let the cost of one granola bar = x.
Let the cost of one pop tart = y.
Now, assume Taylor had money, m.
So, as per the question:
90x = m
⇒ x = m/90
78y = m
⇒ y = m/78
75x + py = m
Substituting the values of x and y:
⇒ 75 × m/90 + p × m/78 = m
⇒ 75m/90 + pm/78 = m
⇒ (5850m + 90pm) / 7020 = m
⇒ 5850m + 90pm = 7020m
⇒ 90pm = 7020m - 5850m
⇒ 90pm = 1170m
⇒ p = 1170m/90m
⇒ p = 13.
Therefore, the number of pop tarts, p = 13.
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Is each number rounded correctly to the nearest hundred thousand?
yes is answer for all option .we can check it by rules of rounding off numbers .
what is rounding ?
Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.
In the given question,
Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.
To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).
If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.
If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.
Using these rules, we can see that:
350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.
792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.
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