Consequently, the loan's duration is roughly 0.6 years the loan's interest rate is roughly 22.5%And the investment's principal is roughly $6,387.
Define investement and interest?An asset or thing is considered an investment if it is bought with the expectation that it may one day produce income or increase in value. A purchase of commodities that are not used right now but will be utilised to generate wealth down the road is referred to as an investment in the economic sense. Stocks, bonds, properties, and mutual funds are a few types of investments.
On the other hand, interest is the fee associated with the right to borrow money. Usually, it is stated as an annual percentage rate. (APR). The percentage of ownership a stockholder has in a firm is another definition of interest.
1. Using the formula below, we can determine the term (period) of a simple interest loan with a $450 principal, a 1.4% annual interest rate, and interest earnings of $37.80.
I = Prt
where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.
Inputting the values provided yields:
37.80 = 450 * 0.014 * t
Simplifying this equation, we get:
t = 37.80 / (450 * 0.014)
(t 0.6 years)
2. Using the formula below, we can determine the interest rate for a simple interest loan with a $425.00 principal amount and $286.88 in interest accrued over three years:
I = Prt
where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.
Inputting the values provided yields:
286.88 = 425 * r * 3
When we simplify this equation, we obtain:
r = 286.88 / (425 * 3)
r ≈ 0.225 or 22.5%
3. Using the technique below, we can determine the principal of an investment with simple interest that generated $25.81 in interest over the course of 8 months at an interest rate of 3.2%:
I = Prt
where I stands for interest earned, P stands for the principal, r represents the yearly interest rate in decimal form, and t stands for the amount of time in years.
First, we must convert the seconds to years:
8 months equals 8/12 years.
Inputting the values provided yields:
25.81 = P * 0.032 * (8/12)
When we simplify this equation, we obtain:
P = 25.81 / (0.032 * (8/12))
P ≈ $6,387
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A point is moving on the graph of xy = 3. When the point is at (1, 3), its x-coordinate is increasing at a rate of 4 units per second. What is the speed of the y-coordinate at that moment and in which direction is it moving?
The speed of the y-coordinate at that moment is 12 units per second, and it is moving in the negative y-direction.
What is a graph?
In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).
We can start by taking the derivative of the equation xy = 3 with respect to time t:
x(dy/dt) + y(dx/dt) = 0
Now we can substitute the given information: when the point is at (1, 3), dx/dt = 4. Solving for dy/dt:
(1)(dy/dt) + (3)(4) = 0
dy/dt = -12/1 = -12 units per second
The negative sign indicates that the y-coordinate is decreasing.
So the speed of the y-coordinate at that moment is 12 units per second, and it is moving in the negative y-direction.
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What is the answer to this problem
The area of the composite figure in the diagram given is calculated as: C. 46 square inches.
How to Find the Area of a Composite Figure?In order to find the area of the composite figure given above, it can be decomposed into a parallelogram and a trapezoid.
Therefore:
Area of the composite figure = area of parallelogram + area of trapezoid
Area of parallelogram = base * height = 7 * 5 = 35 in.²
Area of trapezoid = 1/2 * (sum of the bases) * height = 1/2 * (3 + 8) * 2
= 1/2 * 22 = 11 in.²
Area of the composite figure = 35 + 11
= 46 square inches.
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10. [Ex 2E] If the points A, B and C have the coordinates A (5, 2), B (2, -3) and C (-8, 3) show that the triangle ABC is a right angled triangle.
The triangle ABC is a right-angled triangle.
What is the right-angled triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
Here, we have
Given: the points A, B, and C have the coordinates A (5, 2), B (2, -3), and C (-8, 3).
We have to show that the triangle ABC is a right-angled triangle.
Now, we find the vectors of AB, BC & AC:
AB = (2-5)i+(-3-2)j = -3i-5j
BC = (-8-2)i+(3-(-3))j = -10i+6j
AC = (-8-5)i+(3-2)j = -13i+j
Now if the dot product of two of these vectors results in zero, it means that those vectors (representing the triangle sides) are perpendicular to each other (which means triangle ABC is a right-angled triangle)
AB.BC = (-3)(-10)+(-5)(6) = 30-30 = 0
Hence, the triangle ABC is a right-angled triangle.
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The coordinates of the midpoint of GH are M (8, 0) and the coordinates of one endpoint are H (-2, 9).
Answer:
G(18 , -9)
Step-by-step explanation:
[tex]\boxed{\bf Midpoint = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]
H(-2 , 9) ⇒ [tex]x_1 = -2 \ & \ y_1=9[/tex]
[tex]\left(\dfrac{-2+y_1}{2},\dfrac{9+y_2}{2}\right)= \left(8,0 \right)[/tex]
Compare x and y co-ordiantes,
[tex]\dfrac{-2+x_2}{2}= 8 \ ; \ \dfrac{9+y_2}{2}=0[/tex]
Cross multiply,
-2 + x₂ = 16 ; 9 + y₂ = 0
x₂ = 16 +2 ; y₂ = -9
x₂ = 18
G(18 , -9)
whats a distribute property that equals seven
Answer: The distributive property of multiplication over addition that equals seven is:
2(3.5) + 2(0.5) = 7
Step-by-step explanation:
In a regression model, which of the following will be described using a binary variable?
Question 1 options:
a)
The volume of rainfall during a year
b)
The percentage of humidity in air on a particular day
c)
Whether it rained on a particular day or it did not
d)
The concentration of dust particles in air
Calcular la longitud del lado excentricidad y lado recto de la cónica 9x2 + 4y2 = 36.
The eccentricity (c) length is [tex]c = \sqrt{5}[/tex] and the length of the conic's straight side is 4.
What is the standard equation of an ellipse?[tex]\frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} } = 1[/tex]
We can begin by transforming the given conic equation into the standard form:
[tex]9x^2 + 4y^2 = 36[/tex]
When we divide both sides by 36, we get:
[tex]\frac{x^2}{4} + \frac{y^{2} }{9} = 1[/tex]
When we compare this to the standard form equation for an ellipse, we can see that the major axis is 2a = 6 (since [tex]a^{2}[/tex] = 9 and a = 3) and the minor axis is [tex]b^{2}[/tex] = 4 (because [tex]b^{2}[/tex] = 4 and b = 2). Thus, the eccentricity (c) length can be computed using the formula:
[tex]c^{2} = a^{2} - b^{2}[/tex]
[tex]c^{2} = 9 - 4[/tex]
c = [tex]\sqrt{5}[/tex]
To get the length of the conic's straight side, we must first determine the distance between the two vertices on the major axis. We can deduce from the equation [tex]\frac{x^2}{4} + \frac{y^{2} }{9} = 1[/tex] that We can see that the vertices' x-coordinates are 2, hence the distance between them is 4. As a result, the length of the conic's straight side is 4.
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Complete question:
Calculate the length of the eccentricity and straight side of the conic [tex]9x^{2} + 4y^{2} = 36.[/tex]
The Pythagorean theorem tells us how the what lengths of what triangles are related
The Pythagorean Theorem describes the relationship among the three sides of a right triangle. In any right triangle, the sum of the areas of the squares formed on the legs of the triangle equals the area of the square formed on the hypotenuse: a2 + b2 = c2.
Answer:
The answer to your problem is, Right Triangle
Step-by-step explanation:
If you remember the Pythagorean Theorem describes the relationship among the three sides of a right triangle
If we can consider a hypotenuse then using formula:
a2 + b2 = c2.
Our sum of the areas of the squares formed on the legs of the triangle equals the area of the square formed on the hypotenuse.
Thus the answer to your problem is, Right Triangle
helppppp with this pleaseee......
There are 3150 possible ways to answers the questions to the test by the student.
How to identify permutation notations?The expression for the number of ways to select 6 questions out of the first 10, and 4 questions out of the next 6, is given by the product of the number of permutations or combinations for each selection, since the selections are independent of each other. Therefore, the correct answer is either A or D, depending on whether we use permutations or combinations for each selection.
Option B gives the number of ways to select 4 questions out of the first 10 and 6 questions out of the next 6, which is not what the problem asks for.
Option C gives the sum of the number of ways to select 6 questions out of the first 10 and 4 questions out of the next 6, which counts the cases where some questions from the first set are answered correctly and some from the second set are answered incorrectly, which is not what the problem asks for.
Option E gives the number of ways to select 4 questions out of the first 10, which is not what the problem asks for.
Option F gives the number of ways to select 4 questions out of the first 10, which is not what the problem asks for.
Option G is not a valid expression for the solution, since it combines factorials and parentheses without using any valid operation.
Option H gives the sum of the number of permutations for each selection, which overcounts the cases where some questions from the first set are answered correctly and some from the second set are answered incorrectly.
Option I gives the product of the number of permutations for each selection, which is the correct expression for the solution.
Option J gives the sum of the number of ways to select 6 questions out of the first 10 and 4 questions out of the next 6, which counts the cases where some questions from the first set are answered correctly and some from the second set are answered incorrectly, which is not what the problem asks for.
Therefore, the correct answers are A and D. To evaluate, we can use the formulas:
nPk = n!/(n-k)!
nCk = n!/(k!(n-k)!)
Substituting the values:
A. 10P6 * 6P4 = 10!/(10-6)! * 6!/(6-4)! = 210 * 15 = 3150
D. 10C6 * 6C4 = 10!/(6!4!) * 6!/(4!2!) = 210 * 15 = 3150
Therefore, there are 3150 ways to answer the questions as required.
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Image transcribed:
Give an expression for the answer using permutation notation, combination notation, factorial notation, or other operations. Then evaluate.
Of the first 10 questions on a test, a student must answer 6. Of the second 6 questions, the student must answer 4. In how many ways can this be done?
Identify which notation properly depicts the solution to this problem. Select all that apply.
A. 10P6*6P4
B. 10!/(4!(10-4)!)
C. 10!/(6!(10-6)!) + 6!/(4!(6-4)!)
D. 10C6*6C4
E. 10!/(10-4)!
F. 10C4
G. 10! 6! (10-6)! (6-4)!
H. 10P6 +6P4
I. 10!/(6!(10-6)!) * 6!/(4!(6-4)!)
J. 10!/((10-6)!) + 6!/((6-4)!)
find three mixed numbers so that the sum is 18 and the difference between the greatest number and the least number is 5 1/5
Answer:
Step-by-step explanation:
Let's begin by assigning variables to represent the three mixed numbers. Let a be the greatest mixed number, b be the middle mixed number, and c be the least mixed number. Then we can write:
a + b + c = 18 (the sum of the three mixed numbers is 18)
a - c = 5 1/5 (the difference between the greatest and least mixed numbers is 5 1/5)
To solve for a, b, and c, we can use substitution. From the second equation, we can solve for a in terms of c:
a = c + 5 1/5
Substituting this expression for a into the first equation, we get:
(c + 5 1/5) + b + c = 18
Simplifying, we get:
2c + b = 12 4/5
Now we need to find three mixed numbers that satisfy this equation. We can start by choosing a value for c. Let's choose c = 2 1/2, which is the smallest possible value for c that will allow the mixed numbers to be non-negative. Then we can solve for b:
2c + b = 12 4/5
2(2 1/2) + b = 12 4/5
5 + b = 12 4/5
b = 7 4/5
Finally, we can solve for a using the equation a = c + 5 1/5:
a = c + 5 1/5
a = 2 1/2 + 5 1/5
a = 7 3/5
Therefore, three mixed numbers that satisfy the conditions of the problem are:
The greatest mixed number: 7 3/5
The middle mixed number: 7 4/5
The least mixed number: 2 1/2
And indeed, their sum is 18 and the difference between the greatest and least mixed numbers is 5 1/5.
The cost of buying different numbers of bagels is shown. Complete a true statement to describe the cost function.
The function is non-linear in the cost of buying different numbers of bagels shown.
What is non-linear function?A non-linear function is a mathematical function that doesn't follow a straight line or a constant rate of change. In other words, it's a function that does not have a constant slope. Non-linear functions are used in various fields such as physics, economics, engineering, and more. An example of a non-linear function is the quadratic function f(x) = x². As x increases, the rate of change of y increases as well, resulting in a curved graph. Non-linear functions can have different degrees, such as cubic or quartic functions, and they can be useful in modeling complex real-world phenomena where the relationship between variables is not linear.
Now
2.40 - 1.25 = 1.15
3.45 -2.40 = 1.05
so 1.15 ≠ 1.05
So the function is non-linear because there is not a constant rate of change.
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Determine the coordinates of polygon A'B'C'D' if polygon ABCD is rotated 180°.
OA'(0, 0), B'(-2, 5), C(5, 5), D'(3, 0)
OA(0, 0), B(2,-5), C(-5, -5), D'(-3,0)
O A'(0, 0), B(-5, -2), C'(5, -5), D'(3, 0)
O A'(0, 0), B'(-5, -2), C'(-5, 5), D'(0, 3)
The coordinates point of polygon A'B'C'D' are: A' (0, 0), B' (-2, 5), C' (-5, 5), and D' (-3, 0).
What is Polygon?A polygon is a two-dimensional geometric shape that is defined by a closed path consisting of three or more straight line segments. These line segments are called sides, and the points where they meet are called vertices. Polygons can have any number of sides, although the most common polygons are those with three (triangles), four (quadrilaterals), five (pentagons), six (hexagons), and eight (octagons) sides.
To find the coordinates of A', B', C', and D', we need to apply a 180° rotation to the coordinates of A, B, C, and D.
The general formula for a 180° rotation about the origin is:
(x', y') = (-x, -y)
Using this formula, we can find the coordinates of A', B', C', and D':
A' = (-0, -0) = (0, 0)
B' = (-2, -(-5)) = (-2, 5)
C' = (-5, -(-5)) = (-5, 5)
D' = (-3, -0) = (-3, 0)
Therefore, the coordinates of polygon A'B'C'D' are:
A' (0, 0), B' (-2, 5), C' (-5, 5), and D' (-3, 0).
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21 plus what equils 75
Brandon invests $5800 in two different accounts. The first account paid 3 %, the second account paid 8 % in interest. At the end of the first year he had earned $229 in interest. How much was in each account?
$ ___ at 3 %
$ ____ at 8 %
Brandon invested $4700 at 3% interest and $1100 at 8% interest using a linear equation.
In mathematics, what exactly is a linear equation?An algebraic equation of the form y=mx+b is a linear equation. m is the slant and b is the y-capture. A "linear equation in two variables" with y and x as variables is sometimes referred to as the one above.
A linear equation is one in which a variable is raised to its first power. One example of a one variable is ax+b = 0. x is a variable and an and b are genuine numbers.
Let x represent the amount invested in the first account, which earns interest at a rate of 3%, and let y represent the amount invested in the second account, which earns interest at a rate of 8%. Since the aggregate sum contributed is $5800, we have:
x + y = 5800 The first account has earned 0.03x in interest, while the second account has earned 0.08y in interest. After one year, we have earned $229 in total interest, so we have:
We now have two equations with two unknowns: 0.03x + 0.08y = 229
We can solve for x and y using either the elimination or substitution method. x + y = 5800. In this instance, we will employ substitution.
Find a solution to the first x-equation:
x = 5800 - y
Substitute this expression for x:
0.03(5800 - y) + 0.08y = 229
174 - 0.03y + 0.08y = 229
0.05y = 55
y = 1100
Now substitute this value of y into either equation to solve for x
x + 1100 = 5800
x = 4700
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When Amella started painting, the paint can had 7/8 gallon in it. She used 3/8 gallons How much paint is left in the can?
Answer: If Amella started with 7/8 gallon of paint in the can and used 3/8 gallons, then the amount of paint left in the can can be found by subtracting the amount used from the amount started with:
Amount left = Amount started with - Amount used
Amount left = 7/8 - 3/8
Amount left = 4/8 or 1/2 gallon
Therefore, Amella has 1/2 gallon of paint left in the can.
Step-by-step explanation:
n is inversely proportional to d²
n = 5 when d = 12
What is the value of n when d = 3?
Give answer to 1 d. p
Answer:
80
Step-by-step explanation:
To find the value of n when d = 3, we can use the given inverse proportionality relationship between n and d²:
n ∝ 1/d²
This can also be written as:
n = k / d²
where k is a constant of proportionality.
We are given that n = 5 when d = 12. Plugging in these values into the equation, we get:
5 = k / 12²
To solve for k, we can multiply both sides of the equation by 12²:
5 * 12² = k
k = 720
Now that we have the value of k, we can use it to find the value of n when d = 3:
n = k / d²
n = 720 / 3²
n = 720 / 9
n = 80
So, the value of n when d = 3 is 80.
Who can help me with this? I would really appreciate it
for example, let's find the 7.25% of "x"
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.25\% of x}}{\left( \cfrac{7.25}{100} \right)x}\implies \stackrel{ \textit{in decimal form} }{\text{\LARGE 0.0725}}\times x\implies 0.0725x[/tex]
Carlos puts $3 into his bank account, and it grows by 50% each year.
The perimeter of the quadrilateral is 39 centimeters. Find the length of each side.
x+6
x+2
2x-4
x²-2x
The length of each side include the following:
side one = 11 cm.
side two = 7 cm.
side three = 6 cm.
side four = 15 cm.
How to calculate the perimeter of a quadrilateral?In Mathematics and Geometry, the perimeter of a quadrilateral can be calculated by summing up all of its four (4) side lengths:
Perimeter of a quadrilateral, P = AB + BC + CD + AD
By substituting the given side lengths into the formula for the perimeter of a quadrilateral, we have the following;
39 = x + 2 + x + 6 + 2x - 4 + x² - 2x
39 = 2x + 4 + x²
x² + 2x - 39 + 4 = 0
x² + 2x - 35 = 0
x² + 7x - 5x - 35 = 0
x(x + 7) - 5(x + 7) = 0
(x + 7)(x - 5) = 0
x = 5 cm.
x+6; 5 + 6 = 11 cm.
x+2; 5 + 2 = 7 cm
2x-4; 2(5) - 4 = 6 cm.
x²-2x; 5²-2(5) = 15 cm.
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What is the surface area of a rectangular prism with a height of 5m, length of 5.5m , and width of 2.4 ?
Answer:
105.4 square meters
Step-by-step explanation:
The surface area of a rectangular prism can be calculated by adding the area of all six faces. The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height.
Substituting the given values, we get:
SA = 2(5.5)(2.4) + 2(5.5)(5) + 2(2.4)(5)
SA = 26.4 + 55 + 24
SA = 105.4 square meters
Therefore, the surface area of the rectangular prism is 105.4 square meters.
Answer:
105.4 m^2
Step-by-step explanation:
105.4 m^2
Using the surface area formula which is;
A = 2 (lh +wh + lw )
Brainliest?
I would appreciate it!
answer the following questions in the picture
a. The chart is prepared below.
b. At the end of 4 years, Ross still owes his parents $1,576.92.
How to calculate interest ?To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.
The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.
The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.
Here are the steps for calculating the balance for each year:
Year 1:
Beginning balance = $2,500.00
Interest for the year = $2,500.00 x 0.032 = $80.00
Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00
Year 2:
Beginning balance = $2,280.00
Interest for the year = $2,280.00 x 0.032 = $72.96
Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96
Year 3:
Beginning balance = $2,052.96
Interest for the year = $2,052.96 x 0.032 = $65.76
Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72
Year 4:
Beginning balance = $1,818.72
Interest for the year = $1,818.72 x 0.032 = $58.20
Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92
Here's a table that shows the details:
Year ,principal ,Interest rate, interest, Payment ,annual owing
1 $2,500.00 $80.00 $300.00 $2,280.00
2 $2,280.00 $72.96 $300.00 $2,052.96
3 $2,052.96 $65.76 $300.00 $1,818.72
4 $1,818.72 $58.20 $300.00 $1,576.92
b. At the end of 4 years, Ross still owes his parents $1,576.92.
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(lesson 4.2.5) Find g(-5) given g(x) = x³ - 2
Answer: g (-5)
-127
Step-by-step explanation:
Answer: 125 + 25 = 150 i think is the answer
Step-by-step explanation: To evaluate g(5), substitute x = 5 into g(x)
g
(
5
)
=
5
3
+
(
5
×
5
)
×
x
=
125
+
25
=
150
Somebody please help me ITS URGENT
Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.
What is the equation?Equation is a mathematical statement that expresses two expressions as equal. It consists of two expressions separated by an equal sign (=). An equation is used to solve for a unknown value by using known values and following the rules of algebra and arithmetic. Equations can be used to solve for a single unknown, multiple unknowns, and even non-numeric values.
Given that the total cost for parking and four tickets to a baseball game is $175.00.
$25 is the parking fee.
4 tickets cost $175 - $25.
Suppose that each ticket costs t.
t =($175 - $25)/4
Each ticket costs $37.5.
The equation follows.Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.
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Please give explanation too, not just answers <3
As x gets larger and larger, the value of y approaches zero.
The graph of [tex]y = (1/2)^x[/tex] does not have an x‑intercept.
The graph of [tex]y = (1/2)^x[/tex] does not have a vertical asymptote because there isn't a vertical line that the graph above approaches.
What is an exponential function?In Mathematics, an exponential function can be represented by using the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Based on the information provided about this graph, an exponential function which it models is given by;
[tex]y = (1/2)^x[/tex]
When x = 100, the value of y is given by;
[tex]y = (1/2)^{100}[/tex]
For the x-intercept when y = 0, we have:
[tex]0 = (1/2)^x[/tex]
By taking the ln of both sides, we have:
0 = 1 (false).
In conclusion, this exponential function [tex]y = (1/2)^x[/tex] does not have a vertical asymptote because its denominator can never be equal to zero.
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what is the answer to this question?
No, a continuous function function f(x) exits in (-2 , 3 ) .
What does continuous function mean?
In mathematics, a continuous function is a function without discontinuities, i.e. without unexpected changes in value.
A function is continuous if it can be guaranteed for arbitrarily small changes by limiting the changes in the input to be small enough.
A function f(x) such that
f(0) = -2, f(2) = 2
f'(x) ≤ 3 ∀ in (0,2)
If f'(x) ≤ 3
then f(x) decreasing on (-2, 3 )
But her f'(x) ≤ 3
So, f(x) is not continuous (-2, 3 )
So, No continuous function f(x) exits in (-2 , 3 ) .
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Me pueden ayudar porfavor
Answer:
C.
Step-by-step explanation:
3/8 × -7/6 × -2/5
a/b × c/d = ac/(bd)
-×- = +
+×+ = +
(a×b)×c = a×(b×c) = (a×c)×b ...
vamos começar com
(-7/6)(-2/5) = 7/6 × 2/5 = 2×7/(6×5) = 14/30
e agora
3/8 × 14/30 = 3×14/(8×30) = 42/240 = 7/40
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the value of p is 3/2, the value of q is 3t, and the value of r is 2/9.with the sum of the first n terms of the arithmetic series formula we are able to solve it
what is arithmetic series ?
An arithmetic series is a series of numbers in which each term is obtained by adding a fixed number to the preceding term (known as the common difference). The sum of the terms in an arithmetic series can be found by multiplying the average of the first and last
In the given question,
We know that the first term of the arithmetic series is given by (2t+1) and the common difference is 3. Therefore, the nth term can be written as:
aₙ = a_1 + (n-1)d
(14r - 5) = (2t + 1) + (n-1)3
14r - 5 = 2t + 1 + 3n - 3
14r - 4 = 2t + 3n
7r - 2 = t + (3/2)n --------(1)
Now, we need to find the values of p, q, and r for the sum of the first n terms of the series, which is given by:
Sₙ = (n/2)[2a_1 + (n-1)d]
Sₙ = (n/2)[2(2t+1) + (n-1)3]
Sₙ = n(3n+4t+2)/2
We can simplify this expression by factoring out a 2 from the numerator:
Sₙ = n(3n+4t+2)/2 = (2n/2)(3n+4t+2)/2
Sₙ = (n/2)(3n+4t+2) = (3/2)n² + 2tn + n
Now, we need to write this expression in the form p(qt-1). To do this, we need to factor out (3/2):
Sₙ = (3/2)(n² + 4/3 tₙ + 2/3 n)
Sₙ = (3/2)[n² + 4/3 tₙ + (2/9)(3n)]
Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n]
Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n + (4/9)t² - (4/3)tₙ + (4/3)tₙ]
Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n + (4/3)tₙ]
Sₙ = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)(3t*n)]
Now we can see that p=3/2, q=3t, and r=2/9. Therefore, the value of p is 3/2, the value of q is 3t, and the value of r is 2/9.
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If you have a quadratic equation in standard form and it has values of a=2, b = -16 and c = 15, what equation would represent a line that would be its axis of symmetry ? TIMED!!!
The equation of the line that represents the axis of symmetry of the quadratic function y = 2x² - 16x + 15 is x = 4.
What is quadratic equation?A quadratic equation is a second-degree polynomial equation in a single variable, where the variable is typically denoted by x.
According to question:The axis of symmetry of a quadratic function in standard form (y = ax² + bx + c) is a vertical line that passes through the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a, so the equation of the axis of symmetry can be written as x = -b/2a.
In this case, the values of a, b, and c are given as a = 2, b = -16, and c = 15. Substituting these values into the formula for the axis of symmetry, we get:
x = -b/2a
x = -(-16)/(2*2)
x = 4
Therefore, the equation of the line that represents the axis of symmetry of the quadratic function y = 2x² - 16x + 15 is:
x = 4.
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A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Tennis Soccer Baseball Basketball
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled tennis going to a value of 17, the second bar labeled soccer going to a value of 12, the third bar labeled baseball going to a value of 27, and the fourth bar labeled basketball going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled tennis going to a value of 17, the second bar labeled soccer going to a value of 12, the third bar labeled baseball going to a value of 27, and the fourth bar labeled basketball going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled soccer going to a value of 17, the second bar labeled tennis going to a value of 12, the third bar labeled basketball going to a value of 27, and the fourth bar labeled baseball going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled soccer going to a value of 17, the second bar labeled tennis going to a value of 12, the third bar labeled basketball going to a value of 27, and the fourth bar labeled baseball going to a value of 44
Question 12(Multiple Choice Worth 2 points)
After answering the presented question, we can conclude that baseball graphs going to a value of 27, and the fourth bar labelled basketball going to a value of 44.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle
The correct graph to display the given data is: a bar graph with the title favourite sport, an x axis labelled sport, and a y axis labelled number of students, with the first bar labelled tennis going to a value of 17, the second bar labelled soccer going to a value of 12, the third bar labelled baseball going to a value of 27, and the fourth bar labelled basketball going to a value of 44.
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Answer: A. tennis=17 , soccer= 12, baseball=27, basketball=44
BAR GRAPH make sure its not a histogram!!
Step-by-step explanation:
I took the test and got 100% on it!
You randomly draw a marble from a bag, record its color, and then replace it. You draw a red marble 17 out of 20 times. What is the experimental probability that the next marble will be red? Write your answer as a fraction, decimal, or percent.
If you randomly draw a marble from a bag, record its color, and then replace it. the experimental probability of drawing a red marble on the next trial is 17/20, 0.85.
What is the experimental probability ?The experimental probability of drawing a red marble on the next trial is equal to the number of times a red marble was drawn out of the total number of trials, assuming that each trial is independent and the probabilities do not change.
Since a red marble was drawn 17 out of 20 times, the experimental probability of drawing a red marble on the next trial is:
17/20 = 0.85 = 85%
Therefore, the experimental probability of drawing a red marble on the next trial is 17/20, 0.85, or 85%.
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