Answers
This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.
What are functions ?
In mathematics, a function is a rule that maps each element in a set (the domain) to a unique element in another set (the range). It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are commonly represented using function notation, where the symbol "f" is used to represent the function, and the input value is placed inside parentheses. For example, if the function takes the input "x" and returns the output "y"
According to the question:
To prove algebraically that g(x) = f(x), we need to show that the expressions for g(x) and f(x) are equivalent for all values of x. That is, we need to show that:
2x²+3x-1 = x²-3
We can start by simplifying both sides of the equation:
2x²+3x-1 - (x²-3) = 0
Simplifying the left side, we get:
2x²+3x-1 - x²+3 = x²+3x+2
Now we can simplify the right side:
x²+3x+2 = (x+1)(x+2)
Substituting this expression back into the equation, we get:
2x²+3x-1 - x²+3 = (x+1)(x+2)
Simplifying the left side again, we get:
x²+3x-4 = (x+1)(x-4)
Now we have:
(x+1)(x-4) = (x+1)(x+2)
We can cancel out the factor of (x+1) from both sides, since it is not equal to zero for any value of x:
x-4 = x+2
Subtracting x from both sides, we get:
-4 = 2
This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.
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Related Questions
a fourth grade class is hosting a pancake breakfast fundraiser adult tickets are $10 each and children tickets are$6 each the class sells a total of 105 the total amount raised is 870how many adult tickets and how many children tickets were sold
Answers
60 adult tickets and 45 children tickets were sold.
How to solve this problemLet's use algebra to solve the problem:
Let x be the number of adult tickets sold.
Let y be the number of children tickets sold.
From the problem, we know that:
x + y = 105 (total tickets sold)
10x + 6y = 870 (total amount raised)
We can solve this system of equations by using elimination:
Multiply the first equation by 6: 6x + 6y = 630
Subtract the second equation from the first: 4x = 240
Solve for x: x = 60
Now we can use x to find y:
x + y = 105
60 + y = 105
y = 45
Therefore, 60 adult tickets and 45 children tickets were sold.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the absolute value functions with their vertices.
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f(x)= |x-51+
f(x) = -2|2|-
-
f(x)= |x-1| +4
f(x)=x+11-4
Vertex
(-1,-4)
(5, 1)
(0, -1)
(2, 4)
f(x) = |z|-
f(2)=|z-|+{
Absolute Value Function
Answers
Answer:
[tex]\boxed {\left(-1, -\dfrac{3}{7}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{1}{2}\left|x\:+\:1\right|-\frac{3}{7}}[/tex]
[tex]\boxed{\left(5,\:\frac{2}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{3}{5}\left|x\:-\:5\right|+\:\frac{2}{3}}[/tex]
[tex]\boxed{\left(0,\:-\frac{4}{5}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{1}{2}\left|x\right|\:-\:\frac{4}{5}}[/tex]
[tex]\boxed{\left(\frac{2}{5},\:\frac{5}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{3}{2}\left|x-\frac{2}{5}\right|+\frac{5}{3}}[/tex]
Step-by-step explanation:
The vertex of an absolute function
y = f(x) = a|x - b| + c occurs at x - b = 0 or when x = b
Plugging this into the original equation will give the value for f(b) which will be f(b) = 0 + c which will be the y-value of the vertex
[tex]\text{Vertex of } f(x) = \dfrac{3}{5} |x - 5| + \dfrac{2}{3}\\\\ \longrightarrow x = 5, y = \dfrac{2}{3} \\\\\longrightarrow \left(5, \dfrac{2}{3} \right)[/tex]
You can do the others in a similar manner.
Here it is easier because the constant in f(x) corresponds to the y-coordinate of the vertex and they are different in the answer choices
Find the required information to fill out the missing words in the sentence
Answers
The perimeter is 14 x 6 = 84 inches .The area is (1/4) x 14 x 6²x cot(π/14) = 153.94 square inches.
What is perimeter?Perimeter is a measurement of the total length of the boundary of a two-dimensional shape, such as a polygon or a circle. It is the distance around the outside of a shape, and is usually measured in units such as centimeters, meters, or feet.
What is area?Area is a measurement of the amount of space enclosed by a two-dimensional shape, such as a polygon or a circle. It is usually measured in square units such as square centimeters, square meters, or square feet.
In the given question,
We can use the following formulas to find the measure of one interior angle, the perimeter, and the area of a regular polygon:
The measure of one interior angle of a regular polygon with n sides is given by:
(n-2) x 180 / n degrees.
The perimeter of a regular polygon with n sides and side length s is given by: P = n x s.
The area of a regular polygon with n sides and side length s is given by: A = (1/4) x n x s² x cot(π/n), where cot is the cotangent function.
Given that the polygon has 14 sides and one side is equal to 6 inches, we have:
The measure of one interior angle is (14-2) x 180 / 14 = 154.29 degrees (rounded to the nearest whole degree).
The perimeter is 14 x 6 = 84 inches (rounded to the nearest whole number).
The area is (1/4) x 14 x 6² x cot(π/14) = 153.94 square inches (rounded to the nearest hundredths place).
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can you solve this quesiton?
y'=?
Answers
The derivative οf [tex]y = e^{(-5tan(\sqrt{x}))[/tex] is [tex]-5/2x^{(1/2)[/tex] [tex]* sec^2(\sqrt{x}) * e^{(-5tan(\sqrt{x}))}).[/tex]
What is derivative?A functiοn's varied rate οf change with respect tο an independent variable is referred tο as a derivative. When there is a variable quantity and the rate οf change is irregular, the derivative is mοst frequently utilised.
The derivative is used tο assess hοw sensitive a dependent variable is tο an independent variable (independent variable). In mathematics, a quantity's instantaneοus rate οf change with respect tο anοther is referred tο as its derivative. Investigating the fluctuating nature οf an amοunt is beneficial.
[tex]dy/dx = d/dx (e^{(-5tan(\sqrt{x}))}) = e^{(-5tan(\sqrt{x}))} * d/dx (-5tan(\sqrt{x}))[/tex]
Next, we need tο find the derivative οf -5tan(√x) using the chain rule and the prοduct rule:
d/dx (-5tan(√x)) = -5 * d/dx (tan(√x)) = -5 * sec^2(√x) * d/dx (√x)
Tο find the derivative οf √x, we use the pοwer rule:
[tex]d/dx (√x) = 1/2x^{(1/2)[/tex]
Substituting this back intο the derivative οf -5tan(√x), we have:
[tex]d/dx (-5tan(\sqrt{x})) = -5 * sec^2(\sqrt{x}) * (1/2x^{(1/2)})[/tex]
Nοw we can substitute this back intο the derivative οf y:
[tex]dy/dx = e^{(-5tan(\sqrt{x}))} * (-5 * sec^2(\sqrt{x}) * (1/2x^{(1/2)}))[/tex]
Simplifying this, we get:
dy/dx = -5/2x^(1/2) * sec^2(√x) * e^(-5tan(√x))
Therefοre, the derivative of y = [tex]e^{(-5tan(\sqrt{x}))[/tex] is [tex]* sec^2(\sqrt{x}) * e^{(-5tan(\sqrt{x}))}).[/tex]
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Pudge has three times as many apples as Ace, and Ace has twice as many as Christi. How many apples does each
have if Pudge has 12 more than both Ace and Christi together?
Can you work the problem out please? I’m really having a hard time putting it into a formula.
Answers
Answer: Ace has 8 apples Christi has 4 and Pudge has 24
Step-by-step explanation:
Ace has 2 twice as much as Christi has, and 4 x 2 is 8. Pudge has 3 times more than Ace has and 8 x 3 is 24. Pudge has 12 more than Christi and Ace combined. 8 + 4 = 12. 12 + 12 = 24. I hope I explained it right.
Math
Unitary method
#Question
a) If a motor needs 25l pertol to travel 125 km, find the quantity of pertol to travel only 75 km by the same number.
b)If the cost of 32m clothing is Rs. 401.60,find the cost of 45m of the cloth.
c) If the cost of 5 shirt is Rs. 1125,find the cost of 75 such shirts
Note:-Any spam or Innaportiatre things will be reported
Ur help will be appcriated!
Answers
In the unitary method,
a) For 75km we need = 15 l
b) cost of 45m cloth is Rs 564.75
c) cost of 75 shirts is Rs 16875.
What is the unitary method?
The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
a) Here using unitary method , we need to find petrol for 1 km.
To travel 125 km we need 25 l pertrol. Then,
for to travel 1 km = [tex]\frac{25}{125} =\frac{1}{5} = 0.2 l[/tex]
Then to travel 75km we need = 0.2×75 = 15 l.
b) Cost of 32m cloth = Rs. 401.60
Then cost of 1m cloth is = [tex]\frac{401.60}{32}=Rs 12.55[/tex]
Now cost of 45m cloth is = 12.55×45 = Rs 564.75
c) Cost of 5 shirts = Rs 1125
Then cost of 1 shirt = [tex]\frac{1125}{5}=Rs 225[/tex]
Now cost of 75 shirts = [tex]225\times75[/tex] = Rs 16875.
Hence using unitary method the answers are,
a) For 75km we need = 15 l
b) cost of 45m cloth is Rs 564.75
c) cost of 75 shirts is Rs 16875.
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What is the solution set of √
x + 7 − 1 = x?
Answers
Answer:
x = 9
Step-by-step explanation:
Solving radical equations:√x + 7 - 1 = x
√x + 6 = x
Isolate √x,
√x = x - 6
Square both sides,
(√x)² = (x - 6)²
Use identity (a -b)² = a² - 2ab + b²
x = x² - 2*x*6 + 6²
x = x² - 12x + 36
x² - 12x + 36 - x = 0
x² - 13x + 36 = 0
We look for two integers which when added give (-13) and when multiplied gives 36.
So, the factors are (-9) and (-4).
-9 + (-4) = -13 & (-9)*(-4) = 36.
Rewrite the middle term using the factors.
x² - 13x + 36 = x² - 9x - 4x + 36
Take out the common factor 'x' from first and second term & take out the common factor (-4) from third and fourth term.
=x(x -9) -4(x - 9)
= (x -9)(x- 4)
x - 9 = 0 ; x - 4 = 0
x = 9 ; x = 4
But 4 doest not satisfy the equation. So, only 9 is the solution.
one integer is selected at random from integers 7 through 27. find the probabilty that the number is even
Answers
The probability of selecting an even integer is 1/2 or 0.5.
What exactly is probability?
Probability is a measure of an event's possibility or chance of occurring. It is a number between 0 and 1, with 0 indicating that the occurrence is improbable and 1 indicating that the event is unavoidable. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide variety of fields, including mathematics, statistics, economics, physics, engineering, and social sciences, to make predictions and informed decisions.
Now,
There are a total of 27 - 7 + 1 = 21 integers between 7 and 27, inclusive. Of these, half are even and half are odd, since consecutive integers alternate between even and odd.
Therefore, the probability of selecting an even integer is 1/2 or 0.5.
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Calculate the mean and median for the data given 8 1 5 8 0 5 8 2 5 5
Answers
Answer:
Mean is 5.5 and Median is 6.5
Write the following absolute value function as a piecewise function.
f(x) = |- x² - 8x - 7|
Answers
The absolute value function as a piecewise function f(x) = |- x² - 8x - 7| is
f(x) = { - (x² + 8x + 7) , x ≤ -7 or x ≥ -1
{ x² + 8x + 7 , -7 < x < -1
What is meant by absolute value?
Absolute value is a mathematical function that gives the distance of a number from zero on a number line. It is denoted by two vertical bars enclosing the number and always returns a non-negative value.
What is meant by piecewise function?
A piecewise function is a function that is defined by different expressions or rules on different parts or intervals of its domain. The domain is divided into pieces, and each piece has its own expression or rule.
According to the given information
When x² + 8x + 7 ≥ 0, we have:
f(x) = |-(x² + 8x + 7)| = -(x² + 8x + 7)
When x² + 8x + 7 < 0, we have:
f(x) = |x² + 8x + 7| = x² + 8x + 7
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highlight formation of linear programming model
Answers
Answer:
The formation of a linear programming model involves the following steps:
1. Define the objective: Determine what you want to optimize or minimize, such as maximizing profit or minimizing costs.
2. Identify the decision variables: Identify the variables that affect the objective, such as the number of units produced.
3. Formulate the constraints: Establish the limitations that the model needs to operate within, such as production capacity, labor availability, or budget constraints.
4. Write the mathematical equations: Use the identified decision variables, constraints and objective function to write a set of linear equations.
5. Test and solve the model: Test the model by solving the linear equations using mathematical techniques such as simplex method or graphical method.
6. Interpret the results: Analyze the results of the model to gain insights into the optimization of your objective and how changes in variables or constraints can affect the outcome.
What is the equation of the linear relationship that has a slope of 200 and a y-intercept of 100?
A. y = 100x + 200
B. y = 200x + 100
C. y = −200x + 100
D. y = −100x + 200
Answers
The solution is B. [tex]y = 200x + 100[/tex] is a linear equation with a slope-intercept form.
How do linear and nonlinear differ?When a function is displayed in a graph, a linear function makes a straight line, but a nonlinear function, which is bent in some way, does not. Whereas the slopes of a non - linear function is changing constantly, the slopes of a linear model remains constant.
Why is a function linear?The graph of a linear function is a direct line. One regression coefficient and one predictor variables make up a linear function. The variables that are both independent and dependent are X and Y, respectively. The y interception, often known as the constant term a.
The slope-intercept form of a linear equation is [tex]y = mx + b[/tex], where m is the slope and b is the y-intercept. Using the given values, we have:
slope [tex]= 200[/tex]
[tex]y-[/tex]intercept [tex]= 100[/tex]
So, the equation of the linear relationship is:
[tex]y = 200x + 100[/tex]
Therefore, the answer is B. [tex]y = 200x + 100[/tex].
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I need help with my iready assignment
Answers
The volume of the capsule is [tex]3052.08 mm^3[/tex]
What is volume of the hemisphere ?
The formula for the volume of a hemisphere is [tex]V = (2/3)\pi r^3[/tex], where r is the radius of the hemisphere.
The volume of a hemisphere is half of the volume of a full sphere with the same radius. This is because a sphere can be divided into two hemispheres of equal size. Therefore, we can use this formula to find the volume of a hemisphere:
[tex]V = (1/2) (4/3)\pi r^3[/tex]
Simplifying this expression, we get:
[tex]V = (2/3)\pi r^3[/tex]
So, the volume of a hemisphere is [tex](2/3)\pi r^3[/tex].
According to the question:
To find the volume of a capsule, we need to break it down into two parts: a cylinder and two hemispherical ends.
The formula for the volume of a cylinder is[tex]Vcylinder = \pi r^2h[/tex], where r is the radius of the cylinder and h is its height.
The formula for the volume of a sphere (or hemisphere) is[tex]Vsphere = (4/3)\pi r^3.[/tex]
Since the capsule is made up of two hemispheres and a cylinder, the total volume of the capsule is the sum of the volumes of these three parts:
[tex]Vcapsule = 2Vsphere + Vcylinder[/tex]
First, let's calculate the volume of the cylinder. We are given that the radius is 3mm and the height is 100mm, so we have:
[tex]Vcylinder = \pi r^2h = 3.14 x 3^2 x 100 = 2826 mm^3[/tex]
Next, let's calculate the volume of the hemispheres. Since the capsule has a radius of 3mm, each hemisphere has a radius of 3mm. So, we have:
[tex]Vsphere = (4/3)\pi r^3 = (4/3) ( 3.14) (3^3 )= 113.04 mm^3[/tex]
Finally, we can calculate the total volume of the capsule by adding the volume of the cylinder and the two hemispheres:
[tex]Vcapsule = 2Vsphere + Vcylinder = 2 *113.04 + 2826 = 3052.08 mm^3[/tex]
Therefore, the volume of the capsule is [tex]3052.08 mm^3[/tex].
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A capital is invested, at simple interest, at the rate of 4% per month. How long, at least, should it be applied, so that it is possible to redeem triple the amount applied? * 1 point a) 15 months b) 30 months c) 35 months d) 50 months.
Answers
The amount of time needed for this capital to triple would be 50 months, the letter "d" being correct. We arrive at this result using simple interest.
Simple interestSimple interest is a type of financial calculation that is used to calculate the amount of interest on borrowed or invested capital for a given period of time.
In order to find the amount of time required for the principal to be equal to three times the redemption, we have to note that the amount will be equal to three times the principal, using this information in the formula. Calculating, we have:
M = C * (1 + i * t)
3C = C * (1 + 0.04t)
3 = 1 + 0.04t
0.04t = 3 - 1
0.04t = 2
t = 2/0.04
t = 50
The radius of a cylindrical water tank is 4 ft, and its height is 6 ft. What is the volume of the tank?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
0
4 ft
6 ft
Answers
In response to the stated question, we may state that Therefore, the cylinder volume of the tank is approximately 301 cubic feet.
what is cylinder?A cylinder is a three-dimensional polyhedron made up of two congruent parallel circular bases but a curving surface linking the two bases. The bases of a cylinder are all equal to its axis, which is an artificial straight line across the centre of both bases. The volume of a cylinder is the composite of its base area and length. The volume of a cylinder is computed as V = r2h, where "V" represents the volumes, "r" represents the circle of the base, and "h" is the height of the cylinder. The formula to find the volume of a cylinder is:
[tex]V = \pir^2h[/tex]
Where V is the volume, r is the radius, h is the height, and π is a constant value that approximates to 3.14.
[tex]V = 3.14 * 4^2 * 6\\V = 3.14 * 16 * 6\\V = 301.44\\V = 301 ft^3[/tex]
Therefore, the volume of the tank is approximately 301 cubic feet.
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PLEASE HELP ME WITH THIS PLEASE!!
Answers
Answer:
Step-by-step explanation:
sto p cheating ur too bad
(btw its 1d * 4r pi / 28)
The figure below represents 17/36 of a full circle. Find the measure of the marked central angle.
Answers
The specified central angle is 170 degrees since the figure is 17/36 of a full circle.
A central angle is an angle with endpoints on the perimeter and a vertex in the centre of a circle. An arc is defined by the angle in the centre of a circle.
Since the figure represents 17/36 of a full circle, the central angle that it subtends is also equal to 17/36 of 360 degrees (the measure of a full circle).
We can calculate this as follows:
Central angle = (17/36) x 360 degrees
Central angle = 17 x 10 degrees
Central angle = 170 degrees
Therefore, the measure of the marked central angle is 170 degrees.
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Answer:
170°Step-by-step explanation:
To find:-
The measure of the marked Central angle.Answer:-
As we know that the measure of complete angle about any point is 360° = 2π rad .
Also we are given that the given circle is 17/36 of full circle. So the angle substended too be will be equal to 17/36 of the complete angle.
So that , we have;
==> Angle = 17/36 * 360°
==> Angle = 170°
Hence the value of central angle is 170° .
component of optimi
1. Jaden wanted to begin a career in marketing. He had his heart set on a marketing program at a
private university. However, the private university did not admit Jaden to the school. After finding
out he was not accepted, Jaden chose to apply to a nearby state school that also had a highly rated
marketing program. Jaden is now a marketing manager.
Answers
Answer:
you need to learn yo stuff
Step-by-step explanation:
bye
Express using algebra
Z increased by 16%
Answers
Answer:
Z(1.16)
Step-by-step explanation:
Let's start by expressing "Z increased by 16%" using algebra.
Let Z be the original value of some quantity.
To increase Z by 16%, we need to add 16% of Z to Z:
Z + 0.16Z
Simplifying this expression by factoring out Z, we get:
Z(1 + 0.16)
Combining like terms, we have:
Z(1.16)
Therefore, "Z increased by 16%" can be expressed algebraically as:
Z increased by 16% = Z(1.16)
A coach spent $975.84 on new uniforms for his team. If he bought uniforms for 16 players, how much did each uniform cost? Use r to represent the price of each uniform.
Answers
Answer: for each of the players' uniform it would be $60.99
Step-by-step explanation:
so here would be the equation written out.
975.84=16x
so, to get x by itself you would need to divide by 16.
x=60.99
Find an equation of the line described below. Write the equation in slope intercept form( solved for y) when possible through (8,5) and (5,8)
Answers
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}[/tex]
3. AABC has side lengths 15 cm, 20 cm, and 25 cm.
What could be the side lengths of a triangle
similar to AABC?
A. 7 m, 8 m, and 9 m
B. 6 m, 8 m, and 10 m
C. 5 cm, 10 cm, and 15 cm
D. 30 mm, 40 mm, and 55 mm
Answers
The side lengths of a triangle similar to AABC are B: 6 m, 8 m, and 10 m fοr triangle ABC.
What is triangle ?There are three straight sides and three angles in a triangle, which is a geοmetric shape. Having three sides, it is a plygοn. In mathematics, science, and engineering, triangles are οne οf the mοst fundamental and fundamental shapes in geοmetry.
The lengths and angles οf a triangle's sides can be used tο categοrise it. Triangles can be categοrised as scalene, isοsceles, οr equilateral based οn the lengths οf their sides. Triangles with equal sides are called equilateral triangles; thοse with twο equal sides are called isοsceles triangles; and triangles with different sides are called scalene triangles.
Accοrding tο the questiοn:
Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal. In this case, we knοw that AABC has side lengths οf 15 cm, 20 cm, and 25 cm.
Tο find a triangle that is similar tο AABC, we need tο find anοther set οf side lengths that have the same ratiοs as the side lengths οf AABC. We can dο this by dividing each side length οf AABC by a cοmmοn factοr tο οbtain a set οf new side lengths.
Let's try this with each answer chοice:
A. 7 m, 8 m, and 9 m
We can divide each side length οf AABC by 5 tο οbtain 3, 4, and 5, respectively. Hοwever, 3, 4, and 5 dο nοt match the side lengths given in chοice A. Therefοre, chοice A is nοt cοrrect.
B. 6 m, 8 m, and 10 m
We can divide each side length οf AABC by 5 tο οbtain 3, 4, and 5, respectively. These side lengths match the side lengths given in chοice B, sο chοice B cοuld be the cοrrect answer.
C. 5 cm, 10 cm, and 15 cm
We can divide each side length οf AABC by 5 tο οbtain 3, 4, and 5, respectively. Hοwever, 3, 4, and 5 dο nοt match the side lengths given in chοice C. Therefοre, chοice C is nοt cοrrect.
D. 30 mm, 40 mm, and 55 mm
We can divide each side length οf AABC by 5 tο οbtain 3, 4, and 5, respectively. Hοwever, 3, 4, and 5 dο nοt match the side lengths given in chοice D. Therefοre, chοice D is nοt cοrrect.
Therefοre, the answer is chοice B: 6 m, 8 m, and 10 m.
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PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
The notation Σ-2 (3η + 5) is incorrect for representing the arithmetic series 8 + 11+ ... + 29.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
The series has 11 terms, and each term can be found by adding 3 to the previous term, starting with the first term 8. Therefore, the general form of the series is 6i + 2, where i represents the index of the term in the series.
In contrast, the notation Σ-2 (3η + 5) appears to have multiple errors. The use of a negative index (-2) is not valid, as the index should start from 1 or 0. Also, the use of the Greek letter eta (η) instead of i as the index variable is unconventional and likely to cause confusion. Finally, the expression inside the parentheses does not appear to correspond to the terms of the arithmetic series.
The correct notation for the arithmetic series 8 + 11 + ... + 29 should be:
Σ_{i=1}^{11} (6i + 2)
To explain the error in the given notation Σ-2 (3η + 5), we can break it down as follows:
The use of a negative index (-2) is incorrect. The index of summation should always be a non-negative integer.
The use of the Greek letter eta (η) instead of i as the index variable is unconventional and may cause confusion or errors.
The expression inside the parentheses, 3η + 5, does not represent the terms of the arithmetic series. In particular, it does not involve the index variable i or the common difference 3.
Therefore, the correct notation for the given arithmetic series is Σ_{i=1}^{11} (6i + 2).
3^? x ?^4 = 9^20.What is the missing numerator and denominator? i don't have much time left so make it fast plez
Answers
The answer to the 1st power mark would be 36 if the 2nd power will be assumed as 3.
What is Power?
How many times a number should be multiplied depends on its power (or exponent).
It appears as a little number above and to the right of the basic number.
So according to the question,
3ˣ x ?⁴ = 9²⁰
3ˣ x 3⁴ = 9²⁰(let 2nd variable be 3)
3ˣ x 3⁴ = 3²⁰(a^m x a^n=a^(m+n))
3⁽ˣ⁺4⁾ = 3²⁰
So if bases equal powers get equal,
X+4=40
X=36
The above problem can only be proceeded as assumption because two variables cannot be obtained through one equation.
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What is the percent change from 310 to 155?
Answers
Answer: 50% decrease
Step-by-step explanation:
50% of 310 = 155
310-155=155
50% decrease :)
ANSWER: 50% decrease
SOLUTION:
50% of 310 = 155
310-155=155
So in all the answer is.......
50% decrease :)))))
-XOXOXO:)
Find the differance quotient of y=4x³-5x
Answers
Answer:
12x² + 12xh + 4h² - 5
Step-by-step explanation:
f(x + h) - f(x) / h
= [4(x + h)³ - 5(x + h)] - [4x³ - 5x] / h
= [4x³ + 12x²h + 12xh² + 4h³ - 5x - 5h] - [4x³ - 5x] / h
= 4x³ + 12x²h + 12xh² + 4h³ - 5x - 5h - 4x³ + 5x / h
= 12x²h + 12xh² + 4h³ - 5h / h
= 12x² + 12xh + 4h² - 5
Hope this helps :)
A carpenter attaches a brace to a rectangular picture frame. If the dimensions of the picture frame are 30 inches by 40 inches, what is the length of the
brace?
Answers
The brace measures 50 inches in length.
What is Pythagoras's Theorem?The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equals the sum of the squares on the legs of the triangle, a2 + b2 = c2.
The other two sides of the picture frame are its length and width. We thus have:
Length of the hypotenuse (brace)² = Length² of the picture frame + Width² of the picture frame
Let's enter the picture frame's specified dimensions:
Length of the brace² = 30² + 40²
Length of the brace² = 900 + 1600
Length of the brace² = 2500
Taking the square root of both sides, we get:
Length of the brace = √(2500)
Length of the brace = 50
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A primary credit card holder has a current APR of 14.75%. What is the monthly periodic interest rate, rounded to the nearest hundredth of a percent? 12.29% 14.75% 0.01% 1.23%
Answers
Answer:
12.29 I thin
Step-by-step explanation:
The monthly periodic interest rate is 0.01%.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
We are given that;
APR=14.75%
Now,
The monthly periodic interest rate is the annual interest rate divided by 12 months. According to 1, the formula is:
r = (1 + i/m)^(m/n) - 1
Where:
r = periodic interest rate
i = nominal annual rate
m = number of compounding periods per year
n = number of payments per year
In this case, i = 14.75%, m = 12 and n = 12. Plugging these values into the formula, we get:
r = (1 + 0.1475/12)^(12/12) - 1
r = (1 + 0.012292) - 1
r = 0.012292 or 1.23%
Therefore, by the given APR the interest rate will be 0.01%, rounded to the nearest hundredth of a percent.
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As part of a survey, 55 adults were asked if they had been abroad on holiday or visited somewhere in the UK. 25 people went
abroad and 15 people went on holiday in the UK. What is the probability that a randomly selected person actually went on holiday
that year? Round your answer to three decimals.
Answers
The probability that a randomly selected person actually went on holiday that year is 0.727
How to calculate the probability that a randomly selected person actually went on holiday that yearOut of the 55 adults surveyed, 25 went abroad and 15 went on holiday in the UK.
Therefore, the total number of people who went on holiday is 25 + 15 = 40
The probability of selecting a person who went on holiday is the number of people who went on holiday divided by the total number of people surveyed:
P(went on holiday) = 40/55
Simplifying the fraction, we get:
P(went on holiday) = 8/11
Rounding to three decimals, we get:
P(went on holiday) = 0.727
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3. A company developed a promising product and wants to make decisions. Based on the best available information, a decision tree is drawn.
a) Calculate expected value at every node. Show work.
b) What is the optimum decision and expected value?
c) What is the optimum decision and expected value if they are seeking at least $1.2M?
Answers
The greatest expected value of 1.2.
a) We multiply the value of each potential outcome by its likelihood, then add the resulting products to determine the expected value at each node.
Beginning with the first node on the right, we have:
"Invest" should return 0.7(2) + 0.3(-2) = 1.2.
Don't invest has an anticipated value of 0.5(0) + 0.5(1.5) = 0.75.
The centre node is next:
"Develop" should be expected to have a value of 0.6(1.2) + 0.4(0.75) = 1.05
"Do not develop" should have a value of 0.4(0) + 0.6(0) = 0.
Lastly, at the node on the left:
Market research should be worth 0.5(1.05) + 0.5(0) = 0.525.
In light of this, the anticipated value at each node is:
Spend: 1.2
1.05 Development
Market research: 0.525
b) Since "Invest" has the highest expected value of 1.2, it is the best course of action.
c) If they are looking for at least $1.2M, "Invest" is still the best course of action because it has the greatest expected value of 1.2, which is already above the desired level.
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