The sum of the first 11 terms of the geometric sequence aₙ = 2aⁿ - 1 with an initial value of a₁ = 1/8 is -10.71.
Therefore the answer is -10.71.
The geometric sequence aₙ = 2aⁿ - 1 with an initial value of a₁ = 1/8 represents the amount of money saved after n years of investing.
So sum of n terms
Sn = 2a - 1 + 2a² - 1 + ... + 2aⁿ - 1
Sn = 2( a + a² + ... + aⁿ) - n
The sum of the first n terms of a geometric sequence aₙ = arⁿ⁻¹ with first term a₁ and common ratio r is given by the formula:
Sn = a₁(1 - rⁿ)/ (1 - r), that is
[tex]S_{n} = a_{1}\frac{ (1 - r^n)}{1 - r}[/tex]
So a + a² + ... + aⁿ = a(1 - aⁿ)/ (1 - a)
Thus Sn = 2( a + a² + ... + aⁿ) - n
Sn = 2a(1 - aⁿ)/ (1 - a) - n
In this case, a₁ = a = 1/8 and n = 11
So the sum of the first 11 terms of the geometric sequence is:
Sn = 2×1/8×( 1 - (1/8)¹¹)/ (1 - 1/8) - 11
Sn = -10.71
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Write a linear equation and one variable that has infinitely many solutions. show the process of simplifying the equation to prove that it has infinitely many solutions.
Answer: 3x + 6 = 3x + 6
3x - 3x = 6 - 6
0 = 0
infinitely many solutions.
Step-by-step explanation: Little tip....if ur equation ends up like this : 0 = 0, or 2 = 2...or anything equal, it will have infinite solutions. If ur equation ends up like this : 2 = 4, or 5 = 7...or anything unequal, then it will have no solutions. If ur equation ends up like this : y = 2, or x = 10....then there will be one solution.
Find the measure of angle MKN.
Answer:
90°
Step-by-step explanation:
360÷4=90°
Each is 90°
How do you solve a 2 step equation 7th grade?
The Two steps equation in mathematics can be solved within exactly two steps by performing operation on both sides of the equation .
What is a Two Step Equation ?
The Two Step Equation can be defined as the equations that can be solved exactly within two steps.
When solving the two step equation, we have to perform the operation on both sides of equals to sign.
To solve the equation we need to perform same operation on both sides of equation.
For Example ⇒ Solve [tex]3x+3=12[/tex] ;
Step1 : we Subtract 3 from both sides to isolate the variable x.
⇒ [tex]3x + 3 - 3 = 12 - 3[/tex]
⇒ [tex]3x = 9[/tex]
Step2 : We Divide both the sides of equation by 3 and solve for x.
⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]
⇒ [tex]x = 3[/tex] ;
Therefore , the given equation is solved in two steps .
The given question is incomplete , the complete question is
How do you solve a 2 step equation ?
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Si 20 000 se invierten al 9% anual capitalizable semestralmente encuentra el minimo numero de semestres requeridos para que el capital exceda 25000 30000 40000
Answer:
Los resultados están abajo.
Step-by-step explanation:
Dada la siguiente información:
Inversión inicial (VP)= $20.000
Tsa de interés (i)= 0,09/2= 0,045
Para calcular la cantidad de semestres necesarios (n) para lograr el valor requerido, debemos usar la siguiente formula:
n= ln(VF/VP) / ln(1+i)
25.000:
n= ln(25.000/20.000) / ln(1,045)
n= 5,07 semestres
30.000:
n= ln(30000/20.000) / ln(1,045)
n= 9,21 semestres
40.000:
n= ln(40.000/20.000) / ln(1,045)
n= 15,75 semestres
please help this is due today!! :( find the constant rate of change in interpret meanings for both graphs
Answer:
2/3
Step-by-step explanation:
each point on the graph goes up 2 and over 3, and it's going in the positive direction. every 2/3 days the book sales go up 1,000 dollars
Evaluate the expression 4xy-yz
The expression 4xy-yz is an algebraic equation.
What is expression?Expression is defined as a way of conveying one's thoughts and feelings through spoken or written words, behavior, or art. It is a form of communication, which can be both verbal and non-verbal. Expression can also be used to show an emotion, opinion, or reaction. Expression is a way of expressing oneself, and it can be used to share ideas, feelings, and experiences with others.
To evaluate it, one must first substitute numerical values for the variables. For example, if x=2, y=3, and z=1, then the equation can be solved as follows: 4(2)(3) - (3)(1) = 12 - 3 = 9. Therefore, the expression 4xy-yz evaluates to 9.
The expression 4xy-yz can also be evaluated using the Order of Operations. This is the rule that states that multiplication and division should be done before addition and subtraction. In the equation 4xy-yz, the multiplication (4xy) should be done first, followed by the subtraction (-yz). This would yield an answer of 4x-z. Again, numerical values must be assigned to the variables in order to find the answer.
In conclusion, the expression 4xy-yz can be evaluated by either substituting numerical values for the variables or following the Order of Operations. The answer will depend on the values that are assigned to the variables.
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The expression 4xy-yz is an algebraic equation.
What is expression?Expression is defined as a way of conveying one's thoughts and feelings through spoken or written words, behavior, or art. It is a form of communication, which can be both verbal and non-verbal. Expression can also be used to show an emotion, opinion, or reaction. Expression is a way of expressing oneself, and it can be used to share ideas, feelings, and experiences with others.
To evaluate it, one must first substitute numerical values for the variables. For example, if x=2, y=3, and z=1, then the equation can be solved as follows: 4(2)(3) - (3)(1) = 12 - 3 = 9. Therefore, the expression 4xy-yz evaluates to 9.
The expression 4xy-yz can also be evaluated using the Order of Operations. This is the rule that states that multiplication and division should be done before addition and subtraction. In the equation 4xy-yz, the multiplication (4xy) should be done first, followed by the subtraction (-yz). This would yield an answer of 4x-z. Again, numerical values must be assigned to the variables in order to find the answer.
In conclusion, the expression 4xy-yz can be evaluated by either substituting numerical values for the variables or following the Order of Operations. The answer will depend on the values that are assigned to the variables.
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we the following mixed operations word problems
During a normal day, there are 782 passengers in average that
are late for their plane each day. However, during the
Christmas holidays, there are 1,835 passengers that are late for
their planes each day which caused delays of 14 planes. How
many more passengers are late for their planes in each day
during the Christmas holidays?
An average of 782 travelers miss their flight each day during a typical day. In contrast, 1,835 passengers are late for their flights every day over the Christmas holiday, which results in 14 planes being delayed.
1,053 travelers (2,835-782 = 1,053)
During the Christmas holidays, there are 1,053 extra passengers who are late for their flights.
How do you figure out the average number of days late?In order to compute WADO, we multiply the total amount of each overdue invoice by the number of days past due, then divide that total by the number of days past due. You may figure out your average daily sales by dividing your total sales over a certain period of time by the number of days in that same period.
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It takes a Kailtyn 1/8 of an hour to make a pair of earrings. How many pairs can Kailtyn make in 3 3/8 hours?
Answer:
I think the answer is 27 im not sure although i hope it is correct
Step-by-step explanation:
Good luck and have a good day
HELP me please
It is due in 10 minutes
Answer:
C, 8 hours
Why?
Because adding the given areas are 2 + 3 + 1 = 6 hours
Now we know that a given fact is that there are 60 minutes in 1 hour.
Let's add the minutes first, 45 + 45 + 30 = 120
120 divided by 60 = 2 hours
Now let's add ALL the areas:
6 hours + 2 hour = 8 hours.
A survey of 100 high school students provided this frequency table on how students get to school: Drive to Take the Grade Walk School bus Sophomore 2. 25 3 Junior 13 20 2. Senior 25 5 5 Find the probability that a randomly selected student drives to school.
The probability that a randomly selected student drives to school is [tex]\frac{2}{5}[/tex]
It is correct for Acellus 100%
Explanation: Trust me lol
2/5 is the probability that a randomly selected student drives to school.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that A survey of 100 high school students provided this frequency table on how students get to school.
The total number of students drive to school are 2+13+25
40 students drive to school.
The total number of students in school is 100.
We need to find the probability that a randomly selected student drives to school.
P(Drive to school)=40/100
=2/5
Hence, 2/5 is the probability that a randomly selected student drives to school.
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jace read 66 pages in 1 and 3/5 hours. if he continues reading at the same rate, how many pages will he read in an hour?
Answer:
156
Step-by-step explanation:
1 3/5 of an hour is 96 you get that by addind 60 mins with 36(3/5) then just add 60 mins
i believe this is right if you have any questions let me know
Paige has set a goal to earn at least $220 from her part time sales job this month. she earns $20 regardless of what she sells for the month and then 20% Commission on all product sales. Write inequalities that can be used to determine X the amount of product sales Paige needs to make her goal for the month.
Answer:
The required inequality is;
0.2·X + 20 > 220
Step-by-step explanation:
The parts of the required inequality are;
The goal amount Paige set to earn for the month = At least $220
The amount she earns regardless of what she sells = $20
The percentage commission she gets for all product sales = 20%
Given that 'X' represent the amount of product sales Paige makes, we have;
The amount Paige makes in a month, A = 20% × X + 20 = 0.2·X + 20
Therefore, given that Paige's goal is to earn at least $220 from her part time sales in the current month, we get the inequality that can be used to determine the value of 'X' Paige needs to make are goal as follows;
A = 0.2·X + 20 > 220
The required inequality = 0.2·X + 20 > 220
∴ X > (220 - 20)/0.2 = 1,000
From which we get;
The amount of product sales Paige needs to make her goal, X > 1,000.
-97.54 es racional o irracional
Respuesta: Racional
Explicación:
El número es racional ya que podemos representarlo como una fracción de enteros.
Más específicamente, -97.54 = -9754/100
-----------------------------------------------------------------------------
Translation to English:
Answer: Rational
Explanation:
The number is rational since we can represent it as a fraction of integers.
More specifically, -97.54 = -9754/100
In this course, we'll begin to
explore "opposite" function types. For example, think about
a quadratic function and its key features. What key features do you think its opposite
function will have? Why?
Answer:
Some key features quadratic functions have are:
Axis of symmetryx and y-interceptsZeroesvertexPoint symmetric to y-interceptStep-by-step explanation:
Answer: You could say something like this ''I think the opposite function of a quadratic function would have an inverted parabolic curve that always opens upwards, since a quadratic function can open upwards or downwards. It would also have a single maximum or minimum point, depending on the coefficient of the quadratic term, since a quadratic function has a single vertex. Finally, the opposite function would have either no real roots or two real roots with opposite signs, depending on the discriminant, since a quadratic function can have either two distinct real roots or two complex roots.''
Jamie is trying to work out the surface area of the cuboid below. Spot any mistakes and write the correct answer.
Step-by-step explanation:
The dimensions of the cuboid are 5 cm, 7 cm and 9 cm.
The formula for the surface area of the cuboid is as follows :
[tex]A=2(lb+bh+hl)[/tex]
We have,
b = 9 cm, l = 7 cm and h = 5 cm
So,
[tex]A=2(9\times 7+9\times 5+7\times 5)\\\\A=2\times 143\\\\A=286\ cm^2[/tex]
Jamie forgets to multiply 143 by 2 as the formula for surface area contains 2 as well.
what is the area of the shaded portion of the figure above
Answer:
i need help too
Step-by-step explanation:
plese
4t+6 evaluate the expression if t=1
Answer:
10
Step-by-step explanation:
You can replace t in the equation with 1 like so 4(1)+6 using pemdas first you'd multiply 4 by 1 which is 4 and then add 6 which is 10.
can somebody please help me solve this question:
you are going to climb the roof of your two-story house using a 15-foot ladder. If the safety directions say that you can put the ladder only 2 feet from the house, how far up will you be able to reach on your house?
thanks
Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet
What is Pythagoras TheoremPythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:
x² = y² + z²
where x is the hypothenuse and y, z are the legs of the right angle triangle.
To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.
x² = y² + z²
15² = 2² + z²
z² = 15² - 2²
z² = 221
z = √221
z = 14.87 feet
The height is 14.87 feet
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The probability of rolling a 4 on a number cube is 1/6. If you were to roll the cube 48 times, you would expect to get a 4 around 8 times
Answer: If you were to roll the cube 48 times, you would expect to get a 4 around 8 times.
Step-by-step explanation:
(1/6 - 48 = 8).
Answer:
yes
Step-by-step explanation:
1/6 X 48 times =8 times
I don´t understand the last one
The horizontal distance that the boat is from the lighthouse is 920.31 feet
What is an equation?An equation is used to show the relationship between numbers and variables.
Trigonometric ratio shows the relationship between the sides and angles of a right angled triangle.
A beacon light is 113 feet above the water. The angle of elevation to the beacon is 7 degrees.
Let d represent the horizontal distance from the house.
Using trig ration:
tanФ = opposite/adjacent
Substituting:
tan(7) = 113 / d
d = 920.31 feet
The horizontal distance is 920.31 feet
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What y-intercept means?
A line's x-intercept as well as y-intercept are the points at which the x- and y-axes, respectively, are crossed.
Now, According to the question:
Let's know:
Definition of Intercept
The term "intercept" refers to the location where a line and curve crosses an graph's axis. The x-intercept would be the point at which the x-axis gets crossed. The y-intercept would be the point at which the y-axis becomes crossed.
The x- as well as y-axis intersection point gets what is meant when a line has an intercept. The y-axis was often taken into account if indeed the axis is also not stated. The letter "b" can be typically used to represent it.
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links will be reported
what is the area of the figure
Answer:
Step-by-step explanation:
The figure is a combination of a triangle and a rectangle
Area of rectangle = bh = 15(5) = 75
We have no way of finding the height of the triangle, unless there is some information that I don't see with regard to the figure.
A. Encuentra el valor del tercer ángulo en un triángulo que tiene dos ángulos que miden 112º Y 52º B. Encuentra el valor del cuarto ángulo en un cuadrilátero que tiene los siguientes ángulos: 105º, 32º Y 10º
Answer:
El tercer ángulo en un triángulo será 16 ° si los otros dos ángulos son 112º y 52º.
El cuarto ángulo en un cuadrilátero será 213 ° si los otros tres ángulos son 105º, 32º y 10º.
Step-by-step explanation:
Spanish
La suma de los ángulos de un triángulo siempre es igual a 180 grados. Si conocemos dos de ellos, podemos encontrar el tercero. Dejemos que el tercero se denote por x entonces
112 ° + 52 ° + x = 180 °
x = 180 ° -112 ° -52 °
x = 16 °
El tercer ángulo en un triángulo será 16 ° si los otros dos ángulos son 112º y 52º.
La suma de los ángulos de un cuadrilátero siempre es igual a 360 grados. Si conocemos tres de ellos, podemos encontrar el cuarto. Dejemos que el cuarto se denote por y luego
105º + 32º + 10º + y = 360 °
o
y = 360 ° -105º- 32º- 10º
y = 213 °
El cuarto ángulo en un cuadrilátero será 213 ° si los otros tres ángulos son 105º, 32º y 10º.
English
The sum of angles in a triangle is always equal to 180 degrees. If we know any two of them we can find the third one. Let the third one be denoted by x then
112°+52°+x= 180°
x= 180°-112°-52°
x= 16°
The third angle in a triangle will be 16° if the other two angles are 112º and 52º.
The sum of angles in a quadrilateral is always equal to 360 degrees. If we know any three of them we can find the fourth one. Let the fourth one be denoted by y then
105º+ 32º+ 10º+y= 360°
or
y = 360°-105º- 32º- 10º
y= 213°
The fourth angle in a quadrilateral will be 213° if the other three angles are 105º, 32º and 10º.
What is the y value where the hole is located in this equation. Show your work. f(x)= (4x-4) x (x-12)/(x-12)
Answer:
y = 44
Step-by-step explanation:
Given
f(x) = [tex]\frac{(4x-4)(x-12)}{x-12}[/tex] ← cancel the factor (x - 12)
= 4x-4
Removing this factor creates a hole at
x - 12 = 0 ⇒ x = 12
Substitute x = 12 into the simplified f(x)
y = 4(12) - 4 = 48 - 4 = 44
That is hole at (12, 44 )
In which quadrant does θ lie if the following statements are true:
cosθ<0 and cscθ>0
Given:
[tex]\cos\theta <0[/tex] and [tex]\csc\theta >0[/tex]
To find:
The quadrant in which θ lie if the given statements are true.
Solution:
We know that,
All trigonometric ratios are positive in I quadrant.
Only sine and cosecant are positive in II quadrant and others are negative.
Only tangent and cotangent are positive in III quadrant and others are negative.
Only cosine and secant are positive in IV quadrant and others are negative.
We have,
[tex]\cos\theta <0[/tex] and [tex]\csc\theta >0[/tex]
Here, cosine is negative and cosecant is positive. It is only possible when [tex]\theta [/tex] lies in II quadrant.
Therefore, the [tex]\theta [/tex] lies in II quadrant.
janmilkzec whatever your name is post up
Big Ideas:
Explain your reasoning.
Answer:
Stretch the graph of f(x) = x + 3 vertically by a factor of 2.
The "same" transformations result in f(x) = 2x + 5
The "different" transformation results in f(x) = 2x + 6
Step-by-step explanation:
Transformation Rules
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
Carry out the given transformations.
Given function:
[tex]f(x) = 2x + 3[/tex]
Translation of 2 units up:
[tex]\begin{aligned}\implies f(x) + 2&= 2x + 3 + 2\\&=2x+5\end{aligned}[/tex]
Given function:
[tex]f(x) =x + 3[/tex]
Vertical stretch by a factor of 2:
[tex]\begin{aligned}\implies 2f(x)&=2(x+3)\\&=2x+6\end{aligned}[/tex]
Given function:
[tex]f(x) = x + 5[/tex]
Horizontal shrink by a factor of 1/2:
[tex]\implies f\left(\dfrac{1}{\frac{1}{2}}x\right)=f(2x)=2x+5[/tex]
Given function:
[tex]f(x) = 2x + 3[/tex]
Translation of 1 unit left:
[tex]\begin{aligned}\implies f(x+1) &= 2(x+1) + 3\\&=2x+5\end{aligned}[/tex]
Three of the transformations result in the same function f(x) = 2 + 5.
Therefore, the transformation that does not belong with the other three is:
Stretch the graph of f(x) = x + 3 vertically by a factor of 2.D t
-60 0
-56 10
-24 90
-20 100
-8 130
0 150
Choose the correct statement.
Select one:
a.
The function is
D(t)=52t−150
b.
The function is
D(t)=25t−150
c.
The function is
D(t)=52t−60
d.
The function is
D(t)=25t−60
Answer: To determine the correct statement, you need to find a pattern in the values of D(t). You can do this by finding the difference between consecutive values of D(t).
The difference between -60 and 0 is 60.
The difference between 0 and 10 is 10.
The difference between 10 and 90 is 80.
The difference between 90 and 100 is 10.
The difference between 100 and 130 is 30.
The difference between 130 and 150 is 20.
The pattern that emerges is that the difference between consecutive values of D(t) is always 25. This means that the correct statement is "The function is D(t)=25t−60". The correct answer is therefore d.
Step-by-step explanation:
Part A
What is the volume of the gift shown?
Part B
Which equation was used to find the volume in Part A?
Answer:
Part A:
1120 inches cubed
Part B:
Base X Height
Step-by-step explanation:
Jessi is making a clay tower for an art project. The tower has a rectangular base with an area of 36 cm2. She wants
to tower to be 10 cm high. What is the volume of clay that Jessi will use in her tower?
Answer:
360cm3
Step-by-step explanation:
To do this, you can multiply the base (l * w) by the height to determine the volume. This would be 36*10=360. Then remember that it is a 3 dimensional shape, so the valume is cubed.