Answers
The solution to the geometric progression are
a) The geometric progression converges , r = 0.1
b) The geometric progression converges , r = 0.2
c) The geometric progression diverges , r = 5
d) The geometric progression converges , r = 0.2
e) The geometric progression diverges , r = 5
f) The geometric progression converges , r = 0.2
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
A geometric progression is said to converge if the common ratio r lies between -1 < r < 1
So , If -1 < r < 1, the geometric sequence converges
a)
The geometric progression is A = 0.3 + 0.03 + 0.003 + ...
The common ratio r = second term / first term
The common ratio r = 0.03 / 0.3
The common ratio r = 0.1
So , -1 < r < 1 and the GP converges
b)
The geometric progression is A = 0.25 + 0.05 + 0.01 + ...
The common ratio r = second term / first term
The common ratio r = 0.05 / 0.25
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
c)
The geometric progression is A = 0.23 + 1.15 + 5.75 + ...
The common ratio r = second term / first term
The common ratio r = 1.15 / 0.23
The common ratio r = 5
So , r > 1 and the GP diverges
d)
The geometric progression is A = 0.75 + 0.15 + 0.03 + ...
The common ratio r = second term / first term
The common ratio r = 0.15 / 0.75
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
e)
The geometric progression is A = 0.00025 + 0.00125 + 0.00625 + ...
The common ratio r = second term / first term
The common ratio r = 0.00125 / 0.00025
The common ratio r = 5
So , r > 1 and the GP diverges
f)
The geometric progression is A = 128,750 + 25,750 + 5,150 + ...
The common ratio r = second term / first term
The common ratio r = 25,750 / 128,750
The common ratio r = 0.2
So , -1 < r < 1 and the GP converges
Hence , the geometric progression is solved
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Related Questions
Please help me
Rachel works for a clothing store. She is paid every week plus a 10% commission on any clothes that she sells. Which of the following is true in regards to Rachel's weekly paycheck? Chose three correct answers.
1. $100 in clothing sales gives Rachel a $250 paycheck
2. $1,100 in clothing sales gives Rachel a $260 paycheck
3 $.2,200 in clothing sales gives Rachel a $370 paycheck
4. $ 4,200 in clothing sales gives Rachel a $420 paycheck
5. $10,800 in clothing sales gives Rachel a 1,230 paycheck
6. $ 16,000 in clothing sales gives Rachel a 1,450 paycheck
Answers
Answer:
2. $1,100 in clothing sales gives Rachel a $260 paycheck
3 $.2,200 in clothing sales gives Rachel a $370 paycheck
5. $10,800 in clothing sales gives Rachel a 1,230 paycheck
Step-by-step explanation:
Here is the complete question :
Rachel works for a clothing store. She is $150 paid every week plus a 10% commission on any clothes that she sells. Which of the following is true in regards to Rachel's weekly paycheck? Chose three correct answers.
1. $100 in clothing sales gives Rachel a $250 paycheck
2. $1,100 in clothing sales gives Rachel a $260 paycheck
3 $.2,200 in clothing sales gives Rachel a $370 paycheck
4. $ 4,200 in clothing sales gives Rachel a $420 paycheck
5. $10,800 in clothing sales gives Rachel a 1,230 paycheck
6. $ 16,000 in clothing sales gives Rachel a 1,450 paycheck
The equation representing Rachel's paycheck = amount she earns every month + commission
If she makes $100 in clothing sales, her paycheck = $150 + (0.1 x 100) = $160
If she makes $1100 in clothing sales, her paycheck = $150 + (0.1 x 1100) = $260
If she makes $2200 in clothing sales, her paycheck = $150 + (0.1 x 2200) = $370
If she makes $4200 in clothing sales, her paycheck = $150 + (0.1 x 4200) = $570
If she makes $10800 in clothing sales, her paycheck = $150 + (0.1 x 10800) = $1230
If she makes $16000 in clothing sales, her paycheck = $150 + (0.1 x 16000) = $1750
thus the correct options are 2,3,5
Please help quickly! Due in 2 hours! 20pts
A line which is perpendicular to this line would have a slope of ___.
Write your answer as a whole number or simplified fraction or improper fraction (not a decimal or mixed number). Use a / for a fraction bar.
Answers
Answer:
1/2
Step-by-step explanation:
A line that is perpendicular to another has an opposite reciprocal slope. In this case, we can see that the slope of the given line is -2, so the perpendicular line would have a slope of 1/2.
Answer:
1/2
Step-by-step explanation:
The slope of a line perpendicular to any given line is the negative reciprocal of the given line's slope:
[tex]m_\perp = \dfrac{1}{m}[/tex]
In this problem, the slope of the given line is [tex]\dfrac{-2}{1}[/tex] (rise over run).
So, to find the slope of a line that is perpendicular to it, we simply flip the given line's slope and change its sign.
[tex]m_\perp = \dfrac{1}{2}[/tex]
So, a line which is perpendicular to the given line would have a slope of 1/2.
Twelve eggs cost $2.04. How much will 18 eggs cost
Answers
Answer: $3.06
Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.
if you do 44 push ups in 4 minutes how many will he do in 5 minutes
Answers
Answer:
55
Step-by-step explanation: i think
Answer:
Step-by-step explanation:
it would be 55 because he does 11 each minute.
Someone please help me
Answers
Because the line of the graph is only going on 3, they are all positive 3 and the equation what x = 3.which mean they are all equal.
-4x + 5 > -5 please help me
Answers
Answer:
x<5/2
Step-by-step explanation:
hope this helps :)
Answer:
[tex]x < \frac{5}{2} [/tex]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable. Hope it helps :)
PLEASE HELP ASAP. I WILL GIVE BRAINLIEST!!!
Which of the following is not an expression
A. 7 - 5x
B. 2 + 3x = 8
C. x/2 + 1
D. 2x + 6
Answers
Answer:
B) 2 + 3x = 8
Step-by-step explanation:
Option B is not an expression as expressions do not have equal signs.
help me i been stuck for like a good 20 min
Answers
[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]
notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.
The table shows the amount of certain school supplies left over in the school bookstore at the end of the year.
Item Total
Pens 36
Markers 48
Erasers 24
The bookstore manager will make packages of the remaining school supplies and sell them for $5 per package. Each package will be identical and contain the same number of items, and there will be none left over. The manager wants to create the greatest number of packages possible. How much will the bookstore earn if all of the packages of supplies are sold?
Multiple choice question.
Answers
The amount earned by the bookstore if all of the packages of supplies are sold is given as follows:
$60.
How to obtain the amount earned?Before obtaining the amount earned, we must obtain the number of packages, with is given by the greatest common factor of the amounts of each item.
The amounts of each item are given as follows:
36, 48 and 24.
Their greatest common factor is obtained factoring them simultaneously by the same prime factors as follows:
36 - 48 - 24|2
18 - 24 - 12|2
9 - 12 - 6|3
3 - 4 - 2
Hence:
gcf(36, 48, 24) = 2² x 3 = 12.
Which is the number of packages. As each package sells for $5, the amount earned is given as follows:
12 x 5 = $60.
Each package is composed by:
36/12 = 3 pens.48/12 = 4 markers.24/12 = 2 erasers.More can be learned about the greatest common factor at https://brainly.com/question/219464
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Is 2 a zero of the polynomial x³ 4x² 3x?
Answers
2 is not a polynomial root of [tex]x^{3} + 4x^{2} + 3x[/tex] . A polynomial is an equation that employs addition, subtraction .
what is polynomial ?A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients that uses solely the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that employs addition, subtraction, multiplication, and division of numbers to combine variables, constants, and exponents (No division operation by a variable).
given
[tex]x^{3} + 4x^{2} + 3x[/tex]
= [tex]2^{3} + 2^{2} + 3(2) = 0\\8 + 4 + 6 = 0 \\18= 0[/tex]
Consequently, 2 is not a polynomial root of [tex]x^{3} + 4x^{2} + 3x[/tex] .
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please answer asap if you know the answers
Answers
Step-by-step explanation:
there is nothing its just a dark screen?
NEED THIS ASAP!
(picture below)
is it
A
B
C
or D ?
(this is Fractions and Whole Numbers)
(100 Points)
Answers
Answer:
C) 4 2/3------------------------------
The product of 7/9 and 6 is:
7/9 × 6 = Simplify by cancelling 37/3 × 2 = Multiply 14/3 = Convert to mixed number4 2/3 AnswerAnswer:
[tex]\textsf{C)} \quad 4\frac{2}{3}[/tex]
Step-by-step explanation:
To find the product of two numbers, multiply them.
[tex]\implies \dfrac{7}{9} \times 6[/tex]
To multiply a fraction by a whole number, first rewrite the whole number as a fraction by dividing it by 1:
[tex]\implies \dfrac{7}{9} \times \dfrac{6}{1}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\times\dfrac{b}{d}=\dfrac{a \times b}{c \times d}[/tex]
[tex]\implies \dfrac{7 \times 6}{9 \times 1}[/tex]
Simplify:
[tex]\implies \dfrac{42}{9}[/tex]
Reduce the fraction by dividing the numerator and denominator by the common factor of 3:
[tex]\implies \dfrac{42 \div 3}{9 \div 3}[/tex]
[tex]\implies \dfrac{14}{3}[/tex]
Divide the numerator by the denominator:
[tex]\implies 14 \div 3=4\;\rm remainder\;2[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]\implies 4\frac{2}{3}[/tex]
3.
Write the linear inequality shown in the graph. The gray area represents the shaded region.
A. y ≤ –3x – 5
B. y ≤ –3x + 5
C. y ≥ –3x – 5
D. y ≥ –3x + 5
Answers
Answer:
B. y ≤ –3x + 5
Step-by-step explanation:
Its B, all y-values are less than -3x+5. also consider root by setting -3x+5=0
x=5/3 is positive so its the second one
...................................................................................................................................................
Answer:
Step-by-step explanation:
we know that
The solution of the inequality is the shaded area below the solid line (the gray area)
The slope of the solid line is negative
The y-intercept of the solid line is positive
The equation of the solid line is equal to
therefore
the equation of the inequality is equal to
Find the unit rate.
130 feet in 6.5 seconds
Answers
Answer:
20 feet per second
Step-by-step explanation:
130/6.5 = 20
You have inherited land that was purchased for $30,000 in 1960. The value of the
land increased by approximately 8% per year. What is the approximate value of
the land in the year 1995?
Hint: Use the formula A=P(1+r)
Answers
Answer:
the answer is 42,000
Step-by-step explanation:
obviously because if you carry the one and than divide by the denominator, you get four oranges. and when life gives you lemons, you give it back
based on the data provided, does this algorithm run in a reasonable or unreasonable time? explain your answer
Answers
As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.
What exactly is a linear equation?A linear equation is represented by the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "simple formula with 2 factors," where both y and x are variables, is what the previous sentence was referred to as. Calculations with two variables are referred to as "bivariate linear equations." Here are a few illustrations: 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3 are the results. A mathematical equation is considered to be linear if its solution has the format y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Based on how quickly iterations rise as input increases, fair and unreasonable algorithms can be distinguished. Since the algorithm does not grow exponentially, we can infer that it completes in an acceptable amount of time.
assessing the mathematical function that represents the algorithm's growth rate when input is added;
200 = 10k, where k is the proportionality constant.
k = 200/10
k = 20
The function that represents the number of iterations is as a result:
I = input size; n = 20i; represents the number of iterations.
As a result, the answer to the provided linear equation problem is that the iteration runs in an acceptable amount of time and does not rise exponentially.
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The correlation coefficient r between the size of a lake in square miles, x, and the yearly number of registered boaters, y, is 0.743. What percent of the variation in the number of yearly boaters can be explained by differences in lake sizes
Answers
Answer:
55.2049%
Step-by-step explanation:
R², the coefficient of determination, is the proportion of the variation in the dependent variable that is predictable from the independent variable.
In this case, if we square our correlation coefficent r=0.743, we get R²=0.552049, which means that 55.2049% of the variation in the number of yearly boaters can be explained by differences in lake sizes
Jack spent half of his weekly allowance on video games. To earn more money his parents let him wash the car for $6. What is his weekly allowance if he ended with $15? (do NOT use $ in your answer. Numbers only)
help please
Answers
Answer:
90 is your answer i hope this helps
Step-by-step explanation:
b) The graph of y = x2 – 2x + 5 is
drawn on the axes on the left.
Use the graph to estimate the
values of x when y = 6.
Give your answers to 1 decimal
place.
Please Help!!!!
Answers
Answer:
[tex]x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4[/tex]
Step-by-step explanation:
[tex]y = x^2-2x+5\\\\6=x^2-2x+5\\\\x^2-2x-1=0\\\\\\\frac{-b+-\sqrt{b^2-4ac} }{2a} = x\\a = 1, b = -2, c = -1\\\\\frac{2+-2\sqrt{2} }{2\\}\\\\x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4[/tex]
The value of the x is -0.4 when y = 6 and the graph is drawn on the left.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The quadratic equation,
y = x² – 2x + 5
To find the value of x:
When y = 6.
So,
x² – 2x + 5 = 6
x² – 2x - 1 = 0
Comparing the quadratic equation with standard quadratic equation,
ax²+ bx +c = 0
We get,
a = 1, b = -2 and c = -1
So,
x = {-b ±√(b²-4ac)}/2a
Substituting the values,
x = (2±√8)/2
x = 1 ± √2
x = 2.41421 and x = −0.414214
And the graph is drawn on the left so x = −0.414214 = -0.4 to one decimal place.
Therefore, the value of the x is -0.4.
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DE is parallel to AC. Find the lengths of AC and AD. FAST!!!
Answers
Answer:
we have:
∆BDE is similar to ∆BAC
so their side are proportional :
BD/BD=BE/BC
2/BD=4/(6+4)
BD=2×10/4
BD=5
again
BE/BC=DE/AC
4/10=5/AC
AC=5×10/4
AC=25/2
Now,
AC=25/2 or 12.5.
AD=BA-BD=5-2=3.
is your answer.
Answer:
AC = 12.5, AD = 3
Step-by-step explanation:
A line parallel to a side of a triangle and intersecting the other 2 sides, divides those sides proportionally, that is
[tex]\frac{BD}{BE}[/tex] = [tex]\frac{AD}{CE}[/tex] , substitute values
[tex]\frac{2}{4}[/tex] = [tex]\frac{AD}{6}[/tex] ( cross- multiply )
4 AD = 12 ( divide both sides by 4 )
AD = 3
-----------------------------------------
Δ BDE and Δ BAC are similar, so the ratios of corresponding sides are equal, that is
[tex]\frac{DE}{AC}[/tex] = [tex]\frac{BD}{BA}[/tex] , substitute values
[tex]\frac{5}{AC}[/tex] = [tex]\frac{2}{5}[/tex] ( cross- multiply )
2 AC = 25 ( divide oth sides by 2 )
AC = 12.5
After Myong's cylindrical birthday cake was sliced, she received the slice at right. If her birthday cake originally
had a diameter of 14 inches and a height of 6 inches, find the volume of her slice of cake.
Answers
Answer:
97.53 in³
Step-by-step explanation:
The cylindrical birthday cake has a diameter (d) of 14 inches and a height (h) of 6 inches.
The radius of the cake (r) = diameter / 2 = 14 inches / 2 = 7 inches.
The volume of the full cake = πr²h = π(7²)6 = 924 in³
Since only a part of the cake was cut and given to Myong. The total measure of the cake is 360°, but the part given to her was 38°. Hence the volume of her slice is given as:
Volume of her slice = (38 / 360) * volume of the full cake = (38 / 360) * 924 = 97.53 in³
Volume of her slice = 97.53 in³
Twelve less than 4 times a number is 20. What
is the number?
A. 2
B.4
C. 6
D.8
Answers
the correct answer is D, 8.
AJLK ~ APQR. Find the value of x.
L
5
8
K
10
X
4
20
5
Р
X=
Answers
Answer:
2.5
Step-by-step explanation:
Just if you divide any to congruent sides you will find the ratio to be 2
Solve for the missing side
What kind of triangle has sides 4 4 8?
Answers
Answer:
No triangle
Step-by-step explanation:
Since [tex]4+4=8[/tex], the side lengths fail to satisfy the triangle inequality theorem. Thus, no such triangle exists.
Find the area of the figure.
8ft
8ft
6 ft
12 ft
10 ft
Answers
Answer:
46080
Step-by-step explanation:
multiply all of them
Answer: might be 150 sq ft if the problem is of the irregular figure
someone help please
Answers
Answer:
A to #4
B to #3
C to #1
D to #2
Step-by-step explanation:
A. 7 + 3² = 16
B. 5 - 2²=1
C. 2 · 2³ = 2^4
D. 3^4/3^1=27
Find an ordered pair (x,y) that is a solution to the equation.
x-3y=9
(x,y)= ?
Answers
Answer:
(9,-3)
Step-by-step explanation:
The area of a carpet is 180 square feet. 25% of the carpet is blue. What is the area of the blue part of the carpet?
Answers
Answer:
45
Step-by-step explanation:
How can you use cause-and-effect relationships to explain how the difference in air pressure results in the wind direction that you saw in the photograph?
Answers
Answer: Hope This Helps!
Step-by-step explanation:
Changes in air pressure are determined by a variety of forces, including the density and temperature of air masses. When air moves from between areas of high pressure and low pressure, wind directions and speeds may change. The driving force behind changes in air pressure and therefore the creation of wind is gravity.
2. A computer valued at $6500 depreciates at the rate of 14.3% per year. a. Write a function that models the value of the computer. b. Find the value of the computer after 3 years
Answers
Answer:
$4088.5
Step-by-step explanation:
Given data
Price a = $6500
Rate of depreciation r= 14.3%
Time x= 3 years
The exponential function Decay is described as
y= ab^x
For decay
b= 1-r
a.
Hence the exponential function that model the value of the computer is
y=a(1-r)^x
b.
y= 6500(1-0.143)^3
y= 6500*(0.857)^3
y= 6500*0.629
y=$4088.5
Hence the value of the computer after 3 years is $4088.5