Final answer obtained is 2/3
What is a geometric sequence?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54, etc. has a common ratio of 3. Similar to that, the geometric series 10, 5, 2.5, 1.25,... has a common ratio of 1/2.
Powers [tex]r^{k}[/tex] of a given non-zero number r, like [tex]2^{k}[/tex] and [tex]3^{k}[/tex], are examples of a geometric sequence. A geometric sequence's basic structure is
[tex]ar,ar^{2},ar^{3}.ar^{4},-----[/tex]
where a is not equal to 0 is a scale factor that is equal to the initial value of the series and r is not equal to 0 is the common ratio.
A series is a sum, whereas a progression is a sequence. This is the difference between the two.
∑[tex]_{i=0}^{n}[/tex] [tex]ar^{i}=\frac{a(1+r^{n+1})}{1-r}[/tex]
We see that n= 99, r= -1/2, a=1
∑[tex]_{i=0}^{99}[/tex] [tex](\frac{-1}{2}) i=[/tex] [tex]\frac{1-(\frac{-1}{2})^{99+1} }{1-\frac{1}{2} }=\frac{1-(\frac{-1}{2})^{100} }{1+\frac{1}{2} }=\frac{1-\frac{1}{2}^{100} }{\frac{3}{2} }[/tex]
[tex]=\frac{\frac{2^{100}}{2^{100}} -\frac{1}{2^{100}} }{\frac{3}{2} } =\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]
[tex]\frac{2*(2^{100}-1)}{3*2^{100}}[/tex]
To know more about geometric sequence, visit:
https://brainly.com/question/3985139
#SPJ4
What are the points of intersection between the graphs of the functions
f(x) = (x+3)(x − 1) and g(x) = (x + 1)(x − 3)
Step-by-step explanation:
THE POINT OF INTERSECTION IS WHERE F(x) = G(x)
[tex](x + 3)(x - 1) = (x + 1)(x - 3) \\ {x}^{2} + 2x - 3 = {x}^{2} - 2x - 3 \\ \\ {x}^{2} - {x}^{2} + 2x + 2x - 3 + 3 = 0 \\ 4x = 0 \\ \frac{4x}{4} = \frac{0}{4} \\ x = 0[/tex]
find the y coordinate by plugging in the value of c in any of the function.You will get thw same value
[tex]g(0) = (0 + 1)(0 - 3) \\ g(0) = 1( - 3) \\ g(0) = y = - 3[/tex]
The point of intersection is (0,-3)
Use the point slope form to write the equation of a line that passes through the point (1,-17) with slope 4
The equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .
What is the slope intercept form of a line ?
The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.
The equation of a line which is passing through point (1 , -17) with slope m = 4 can be found by using the slope intercept form which is given by :
y = mx + c
Here ; m is the slope and c is the y - intercept of the line.
So ;
The point given is (x , y) = (1, -17) and slope m = 4. Let's use these values to find out the equation of the line. But before that let's find out the value of y-intercept (c).
-17 = (4 × 1) + c
c = - 17 - 4
c = -21
Hence , the equation of line passing through (1, -17) will be :
y = 4 × x + (-21)
or
y = 4x - 21
Therefore , the equation of line passing through (1, -17) with slope 4 will be y = 4x - 21 .
Learn more about slope intercept form here :
brainly.com/question/18594541
#SPJ1
Geometry question!!
Please help i’ll give points!
Answer:
63°
Step-by-step explanation:
[tex]m\angle OZQ=m\angle OZP+m\angle PZQ \\ \\ 125^{\circ}=62^{\circ}+m\angle PZQ \\ \\ m\angle PZQ=63^{\circ}[/tex]
HELPPPPPPPPPPPPPPPPPPPPPPPPP! whats 1+1
What is the measure of XYZ?
V
33
Y
O D. 54°
N
X
75⁰
O A. 33°
OB. 75°
O C. 108°
Write an equation for a line that passes through the points (1, 2) and (11, 22). The form is your choice
Its too confusing pls help!
hello! please read the instructions in the picture :)))
made just for you <3
a pedometer treats walking 2,000 steps as walking 1 mile. it assumes that one step is a bit over 18 inches (1 mile
The required code for the pedometer is illustrated below:
steps_per_mile=2000
def steps_to_miles(steps, inches_per_step):
distance = steps * inches_per_step
miles = distance / (steps_per_mile * inches_per_step)
return miles
if __name__ == '__main__':
steps = int(input())
inches_per_step=float(input())
miles_in_pedometer = steps_to_miles(steps,inches_per_step)
print(f"You walked {steps} steps which are about {miles_in_pedometer:.2f} miles.")
what is a pedometer?
which will matter steps and decide the gap traveled, pedometers are made to apprehend vertical hip motionthey're not able to offer data at the multivariate framework of regular workout or the period of time spent carrying out numerous activities of various intensities.The required code for the pedometer is illustrated below:
steps_per_mile=2000
def steps_to_miles(steps, inches_per_step):
distance = steps * inches_per_step
miles = distance / (steps_per_mile * inches_per_step)
return miles
if __name__ == '__main__':
steps = int(input())
inches_per_step=float(input())
miles_in_pedometer = steps_to_miles(steps,inches_per_step)
print(f"You walked {steps} steps which are about {miles_in_pedometer:.2f} miles.")
Learn more about pedometers here:
https://brainly.com/question/9776399
#SPJ4
1.
Steve drew line segments ABCD, EFG, BF, and C
as shown in the diagram below. Scalene ABFC i
formed.
Which statement will allow Steve to prove
ABCD||EFG?
1) LCFG = LFCB
2) LABF = LBFC
3) ZEFB=LCFB
4) ZCBF = LGFC
Answer:
Choice 1: ∠CFG = ∠FCB
Step-by-step explanation:
∠CFG and ∠FCB are interior alternate angles and equal only if ABCD||EFG
Bella has a bag that contains pineapple chews, lemon chews, and watermelon chews. She performs an experiment. Bella randomly removes a chew from the bag, records the result, and returns the chew to the bag. Bella performs the experiment 58 times. The results are shown below:
A pineapple chew was selected 53 times.
A lemon chew was selected 2 times.
A watermelon chew was selected 3 times.
the probability is pinapple 53/58
lemon 2/58
watermelon 3/58
The given values are
A pineapple chew was selected 53 Times
A lemon chew was selected 2 times
A watermelon chew was selected 3 times
The probability that you Bella remove from the bag is pineapple chew.
Probability is which we can't predict actual it is usually about the prediction
As we know
Probability - expected outcome/total outcome
The question Bela perform experiment 58 times then the total outcome will be 58 if you pineapple was selected 53 times the probability of the chew Bella pick of pineapple is 53/58
The probability of Bella pick chew of lemon -2/58
The probability of Bella pick watermelon is - 3/58
To know more about probality click
https://brainly.com/question/25688842
#SPJ9
rolling a fair dice, what is the probability that before you getting an odd number, you have got all the even numbers
The probability is [tex]\frac{1}{2}[/tex].
To solve this problem we need to recognize the idea of probability.
To calculate the probability we need to divide the desired final results with the aid of the overall number of consequences.
here, it is asked to locate the chance of having all even numbers earlier than getting an strange variety.
We know that the whole number of results when we roll a dice is 6.
We realize there are three odds and three even in the cube. So, the required
probability of getting even = [tex]\frac{3}{6}[/tex]
= [tex]\frac{1}{2}[/tex]
The required probability is equals to [tex]\frac{1}{2}[/tex].
To learn more about the probability visit the link:
https://brainly.com/question/11234923
#SPJ4
Choose one value that is in the domain of both y(x) = x² and y² = x and that is greater than
0. Substitute that value into y(x) = x² and y² = x and then simplify. Explain how your answers
help to show that the graph on the left represents a function while the graph on the right
represents a relation. Show your work and use function notation where possible
I
We take the value 2 for which y(2)=4 and [tex]y^{2}[/tex]=2 and see that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a relation.
Domain is the set of values that a variable can take in an algebraic expression.For the equation y(x)=[tex]x^{2}[/tex], x can take any value from negative infinity to positive infinity so we can say that the domain for x is (-∞,∞). For the equation [tex]y^{2}[/tex]=x, x can take any value greater than or equal to zero. Since x=[tex]y^{2}[/tex] we can't take a negative value for x because squared numbers are always positive, so the domain of x will be [0,∞). The common domain for both the equations is [0,∞). Let us choose a value from this common domain,let's say 2. Then for
y(x)=[tex]x^{2}[/tex]⇒y(2)=4 ...(i)
[tex]y^{2} =x[/tex]=2 then y=±[tex]\sqrt{2}[/tex]...(ii)
A function always has an output variable and one or more input variables.For first equation, y is the output variable and x is the input variable. A relation states that two expressions are equal and one is not dependant on another. For equation (i) y is dependant on x but in equation (ii) both the variables are independant.
Thus we can conclude that y(x)=[tex]x^{2}[/tex] is a function and [tex]y^{2}[/tex]=x is a realtion.
Learn more about functions and realtions here:
https://brainly.com/question/2253924
#SPJ9
James, fay and sal share 160 apples. james got 1/4 of the apples. fay and sal shared the remainder in the ratio 3:2 respectively. 1) find how many oranges fay received 2) how many oranges did sal receive than james?
Using the ratio given in the question,
Apples received by Fay are 72.Apples received by James are 40.Apples received by Sal are 48.What is Ratio?The relation between the quantities of two or more objects—referred to as a ratio—indicates how much of one object is contained in the other. The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as, for any two quantities, let's assume a and b.
a:b = a/b
Given that James, Fay and Sal share 160 apples.
Total number of apples = 160
Hence, apples received by James = 1/4(160)
= 40 apples
Remaining apples = 160 - 40 = 120 apples
It is also given that the remainder is shared by Fay and Sal in the ratio 3:2.
Hence, the total share will be 3+2=5
So, we can write that Fay's share will be 3/5 of total apples and Sal's share will be 2/5 of the total apples.
Fay's share = 3/5(120)
=3(24)
=72 apples
Sal's share = 2/5(120)
=2(24)
=48 apples
Therefore, the number of apples with Fay is 72.
The number of apples with Sal is 48.
To learn more about ratio, visit:
https://brainly.com/question/16298679
#SPJ4
choose the equation that represents the line that passes through the point (6, −3) and has a slope of one half. (1 point)
The equation that represents the line that passes through the point (6, −3) and has a slope of one half is 2y - x = 13.
The equation of a line is represented as,
y = mx + c equation1
x and y are the coordinates of the point from where the line is passing and m is the slope of the line.
As per the question the line is passing from the point (6, -3). This means value of x = 6 and that of y = -3. The slope of line is (1/2), means m = (1/2).
The slope of the line through the point (-1,6) can also be written as (y - 6)/(x - (-1)) = (y-6)/(x+1).
i.e., m = (y-6)/(x+1)
On equating both the values of m, we will get
(y-6)/(x+1) = 1/2
On simplifying, we get
2y - 12 = x +1
or 2y - x = 13
The equation that represents the line that passes through the point (6, −3) and has a slope of one half is 2y - x = 13.
To know more about Straight Lines refer to the link:
https://brainly.com/question/25969846
#SPJ4
Kurt spent $96.39 over 414 months on movie streaming services. if he spent the same amount of money each month, how much money, in dollars, did kurt spend per month on movie streaming services?
Using proportions, it is found that Kurt spent $22.68 a month on movie streaming services.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, or operations such as multiplication and division.
These operations are used from the unit rates, as for example, when we have an amount over a period of time, the amount per unit of time is the total amount divided by the total time.
For this problem, we have that the important parameters are found as follows:
The total amount is of $96.39.The time is a mixed number, 4 and 1/4 months, hence it is of 4.25 months, as 4 + 1/4 = 4 + 0.25 = 4.25.Hence his monthly spending is given by the unit rate as follows:
96.39/4.25 = $22.68 a month.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Find the LCM of 34 ( use prime factorisation method
The LCM of 34 using prime factorisation method is 2 and 17
Simplify the fraction 24/56 until it is in simplest form.
explain
Answer: 3/7
Step-by-step explanation:
You would divide this by the number 8.
8*3 = 24
8*7 = 56
Therefore the answer is 3/7
Hey there!
24/56
= 24 ÷ 8 / 56 ÷ 8
= 3/7
Therefore, your answer should be:
3/7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the value of x and y.
circles with centers $(2,1)$ and $(8,9)$ have radii $1$ and $9,$ respectively. the equation of a common external tangent to the circles can be written in the form $y
The value of b in the equation of common external tangent to both the given circles is 3.75.
A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a particular point remains constant.The equation of a circle with a centre at (2,1) and a radius of 1 is : (x - 2)² + (y - 1)² - 1² = 0.The equation of a circle with a center at (8,9) and a radius of 9 is : (x - 8)² + (y - 9)² - 9² = 0.The equation of the common external tangent is :y = mx + b, where m < 0If m < 0, then the circles touch each other.We will get the equation of the common external tangent by equating the equations of both the circles.(x - 2)² + (y - 1)² - 1² = (x - 8)² + (y - 9)² - 9²(y - 1)² - (y - 9)² = (x - 8)² - (x - 2)² + 1² - 9²(2y -10)(8) = (2x - 10)(-6) + 1 - 8116y - 80 = -12x + 60 - 8016y = -12x + 60y = (-3/4)x + (15/4)y = -0.75x + 3.75y = mx + bOn comparison, we get b = 3.75.To learn more about tangent, visit :
https://brainly.com/question/2410166
#SPJ4
HELP- pleaseeee I’m beggginnngg
The ending number is related to the starting number by n + 9.
To start with this magic number puzzle, let us take a positive number and a negative number. After that we have to perform some simple mathematical operations,
Taking positive number as 10 and negative number as -8.
Now, performing the mathematical operations as described in the next steps.
First starting with positive number which is 10.
Step-1. Add 10
So, 10+10 = 20
Step-2. Multiply by 2
So, 20×2 = 40
Step-3. Subtract 2,
So, 40 - 2 = 38
Step-4. Divide by 2,
So, 38/2= 19
Number chosen in the starting was 10 and at the end it became 19. The number 9 got added to 10.
Now, performing the steps on our negative number which is -8,
Step-1. Add 10
So, 10-8=2
Step-2. Multiply by 2
So, 2×2 = 4
Step-3. Subtract 2
So, 4-2 = 2
Step-4. Divide by 2
So, 2/2 = 1.
Number chosen in the starting was -8 and after performing the steps it became 1.
Now, for any number 'n',
Step-1. Adding 10
So, n+10
Step-2. Multiply by 2
So, 2(n-10) = 2n+20
Step-3. Subtract 2
So, 2n+20-2 = 2n+18
Step-4. Divide by 2.
So, (2n+18)/2 = n+9
The number taken in the starting was n and now it became n+9.
So the ending number becomes 9 times more in the end then the starting number.
To know more about Mathematical operations, visit,
https://brainly.com/question/4721701
#SPJ9
1. 3x-2x² = 7
2. 5-2x² = 6x
3. (x+3)(x + 4) = 0
4. (2x+7)(x-1)=0
5. 2x(x-3) = 15
Answer:
No 3
2x+4x+3x+12=0
9x+12=0
9x=0_12
9x=-12
divide by 9
x=1.333
HI, I need help!! I'm so lost on how to solve this.
Answer:
3⁹
Step-by-step explanation:
you can use a calculater and it will give 19683 and 3⁹ gives 19683
martin s cat weighs 12.37 pounds. what is this weighs written as a mixed number
Answer:
your mixed fraction would be 12 37/100
Step-by-step explanation:
The number has two parts the whole number part is 12, and the decimal part is .37, 12 would be the whole number part of your mixed fraction and we will convert the .37 to become the fraction part of your mixed fraction.
You have to convert the decimal part into a fraction since there are two decimal places you will have 100 in the denominator .37 becomes 37/100 simplify this fraction if possible.
Area of Circles Area of Circles Area of Circles
The area of the circle with the radius is 192 square feet
How to calculate the area of the circle?The figure represents the given parameter
On the figure, we have the radius (r) to be
r = 8 ft
The area of a circle is calculated as
A = πr^2
Where π is given as
π = 3
So, we have
A = 3 * 8^2
Evaluate the exponent
A = 3 * 64
Evaluate the product
A = 192
Hence, the area of the circle with the radius is 192 square feet
Read more about areas at
https://brainly.com/question/22972014
#SPJ1
the area of the circle is 201.06
PLEASE HELP!!!
Solve.
-2x+3y-z=-2
3x + y = 4
-2y+2z=4
Enter your answer, in the form (x, y, z), in the boxes in simplest terms.
Step-by-step explanation:
the second equation gives us right away
y = 4 - 3x
we can use that now in the 3rd equation :
-2(4 - 3x) + 2z = 4
-8 + 6x + 2z = 4
6x + 2z = 12
3x + z = 6
z = 6 - 3x
now we use both in the 1st equation :
-2x + 3(4 - 3x) - (6 - 3x) = -2
-2x + 12 - 9x - 6 + 3x = -2
-8x + 6 = -2
-8x = -8
x = 1
y = 4 - 3x = 4 - 3×1 = 4 - 3 = 1
z = 6 - 3x = 6 - 3×1 = 6 - 3 = 3
so,
(1, 1, 3)
Help please. I cant figure this one out.
Answer:
x =52
Step-by-step explanation:
The angles shown are same side interior angles, and when the lines are parallel, same side interior angles add to 180 degrees
< 1 + <2 = 180
x+23 + x+53 = 180
Combine like terms
2x+ 76 = 180
Subtract 76 from each side
2x+76-76 = 180 -76
2x = 104
Divide by 2
2x/2 = 104/2
x =52
Answer:
x = 52
Step-by-step explanation:
Angle 1 and angle 2 are on the same side, and on the inside of the interior. This means that when added together they = 180
We can set up an equation
x+23+x+53 = 180
Simplify: 2x + 76 = 180
Subtract 76 from both sides
2x = 104
Now divide by 2
x = 52
•The total surface Areas of a cone of base radius r and perpendicular height h, his given by s=πr ² +πr√(r²+h²). iF r and h are each increasing at the rate of 0.5m/s and 0.2m/s respectively, find the rate at which s is increasing at the instant when r=3m and h =4m
The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.
What is the rate of change of the surface area of a cone?
In this question we find a formula for the surface area of a cone, of which we must estimate its rate of change by applying derivative rules and the concept of rate of change. The rate of change is the first derivative of the equation:
ds / dt = 2π · r · (dr / dt) + π · √(r² + h²) · (dr / dt) + π · r · [0.5 / √(r² + h²)] · [2 · r · (dr / dt) + 2 · h · (dh / dt)]
If we know that r = 3 m, h = 4 m, dr / dt = 0.5 m / s and dh / dt = 0.2 m / s, then the rate of change of the surface area of the cone is:
ds / dt = 2π · (3 m) · (0.5 m / s) + π · √[(3 m)² + (4 m)²] · (0.5 m / s) + π · (3 m) · [0.5 / √[(3 m)² + (4 m)²] · [2 · (3 m) · (0.5 m / s) + 2 · (4 m) · (0.2 m / s)]
ds / dt ≈ 18.473 m² /s
The rate of change of the surface area of the cylinder is approximately to 18.473 square meters per second.
To learn more on rates of change: https://brainly.com/question/12786410
#SPJ1
Question 2(Multiple Choice Worth 5 points)
(Irrational Numbers LC)
Describe in words where √60-11 would be plotted on a number line.
O Between -3 and -4, but closer to -3
O Between -3 and -4, but closer to -4
O Between 7 and 8, but closer to 8
O Between 7 and 8, but closer to 7
The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.
What is number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.Given: √60 - 11
The value of √60 - 11 is given as: √60 - 11 = 7.2 (approx.) - 11 = -3.2
Thus, as seen from the calculation of the value of the given number, √60 - 11 will lie between -3 and -4, but closer to -3 as -3.2 is closer to -3 than to -4.
Hence, The number √60 - 11 will be plotted between -3 and -4, but closer to -3 (Option A), as seen by number system.
To learn more about number system, refer to the link: https://brainly.com/question/13162939
#SPJ9
suppose that 10% of people are left handed. if you pick two people at random, what is the probability that they are both left handed? express your answer as a decimal rounded to three decimal places.
The probability that they are both left-handed is 0.01
Probability is the number of ways of achieving success.
the total number of possible outcomes.
Probability takes values between 0 (no chance) and 1 (certain) inclusive.
Complement Rule (probability that an event doesn't occur): P(A') = 1 - P(A) .
Addition rule: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .
Multiplication rule: P(A ∩ B) = P(A) × P(B) for independent events. P(A ∩ B)
For both, the persons selected at random are left-handed
10 % out of 100 % are left-handed.
Hence the probability that the person is left-handed
P(L) = 10 /100 = 1 / 10 = 0.1
where P(L) is the probability that the person is left-handed.
Therefore both the persons selected are left-handed
= 0.1 * 0.1
= (0.1)^2
= 0.01
Hence the probability that they are both left-handed is 0.01.
For more information on probability click on the link below:
https://brainly.com/question/24756209
#SPJ4
write the algebric expression two less than four times a number
PLEASE SHOW WORK
The expression two less than four times a number is represented as 4x - 2
Algebraic expressionsAn algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.
According to the question, we are to transform two less than four times a number into expression
Let the unknown number be x such that
four times a number = 4x
two less than four times a number = 4x - 2
Hence the expression two less than four times a number is represented as 4x - 2
Learn more on algebraic operation here; https://brainly.com/question/723406
#SPJ1
Avani is making smoothies. Each smoothie uses cup of yogurt. How many cups of
yogurt does she need to make 17 smoothies? Express your answer in simplest form.
5
16
Answer type: Mixed number
Submit Answer
Avani needs 6 cups of yogurt.
To find the amount of yogurt required for specified number of smoothies, simple multiplication operation needs to be performed.
For 1 smoothie, the required amount of yogurt = 3/8 cups
So, the required amount of yogurt for 17 smoothies = (3/8) × 17
Performing multiplication and division to find the amount of yogurt required
Amount of yogurt required = 51/8 cups
Converting the fraction into fraction into decimal -
Amount of yogurt required = 6.375 cups
Rounding off the number of cups to convert it in simplest form -
Number of cups of yogurt required = 6 cups
Hence, the amount of yogurt for making 17 smoothies is 6 cups.
Learn more about calculations on smoothie -
https://brainly.com/question/14387710
#SPJ4
The complete question is -
Avani is making smoothies. Each smoothie uses 3/8 cups of yogurt. How many cups of yogurt does she need to make 17 smoothies? Express your answer in simplest form.