Second term of a geometric series is , the limiting sum is 9.
Get the values of first term a and common ratio r.
Answers
Answer:
The answer is below
Step-by-step explanation:
Second term of a geometric series is 2, the limiting sum is 9.
Get the values of first term a and common ratio r.
Solution:
A geometric series is in the form:
a + ar + ar² + ar³ + . . . + arⁿ ⁻ ¹
Where a is the first term, n is the nth term and r is the second ratio.
Since the second term of the series is 2, hence:
ar⁽² ⁻ ¹⁾ = 2
ar = 2 (1)
Also, the limiting sum is 9, hence:
a/ (1 - r) = 9
a = 9 - 9r (2)
Substitute a = 9 - 9r in eqn 1:
(9 - 9r)r = 2
9r - 9r² = 2
9r² - 9r + 2 = 0
9r² - 6r - 3r + 2 = 0
3r(3r - 2) -1(3r - 2) = 0
(3r - 1)(3r - 2) = 0
r = 1/3 or r = 2/3
When r = 1/3; a = 9 - 9r = 9 - 9(1/3) = 6
When r = 2/3; a = 9 - 9r = 9 - 9(2/3) = 3
Related Questions
45% of the students of a Padampur Shiksha Niketan School play basketball, 40% play cricket and 30% play both. If 360 students play neither basketball nor cricket, use Venn-diagram and find the number of students in the school. Also, find the number of students who play only basketball. Ans: 800, 120
Answers
Then we have:
n(B) = 45% of the total number of students
n(C) = 40% of the total number of students
n(B ∩ C) = 30% of the total number of students
n(Not B and Not C) = 360 students
We want to find the total number of students, which is given by the formula:
n(Total) = n(B) + n(C) - n(B ∩ C) + n(Not B and Not C)
Substituting the given values, we get:
n(Total) = 45% + 40% - 30% + 360
n(Total) = 55% + 360
n(Total) = 800
Therefore, the total number of students in the school is 800.
To find the number of students who play only basketball, we can use the formula:
n(B only) = n(B) - n(B ∩ C)
Substituting the given values, we get:
n(B only) = 45% - 30%
n(B only) = 15%
Since 15% of 800 is 120, we can conclude that 120 students play only basketball.
if James have 12 books and Jack has 15 who has more
Answers
Answer:
Jack
Step-by-step explanation:
Jack has more books because 15 is more than 12
lol
Need help!!!!!!!!!!!
Answers
Answer:
90°
-Sum of angles in a triangle= 180°
-angle C is 90°
-therefore angle A + angle B is,
180° - 90° = 90°
Han got $2 from Claire, but still has less than $20 as a inequality
Answers
Please re-phrase into a question.
Which expression is equivalent to 3x2+(5x−8x2)+4−(5x+2)
Answers
Answer: -5x^2 + 2
Step-by-step explanation:
If my savings of $x grows 10% each year. How much will I have in: 5 years
Answers
After 2 years=x1.1*1.1
………
After 5 years=x1.1*1.1*1.1*1.1*1.1=x1.61051
Answer:
See below
Step-by-step explanation:
Assuming the interest is compounded annually
x * (1 + .10)^5 = 1.61051 x
your final amount will be 1.61051 times bigger than the initial deposit
Which value is a solution to the inequality x 4
Answers
Answer:
0
Step-by-step explanation:
x < 4 means all numbers less than 4, excluding 4 itself.
4.5 > 4.
5 > 4.
so 0 is the solution
Answer:
4
Step-by-step explanation:
interval notation ( negative infinity, 4)
5
364,860
0/1 point
Camila has finally found a house she adores! The cost of the home is $210,000, which she intends to purchase on a 30-year fixed mortgage. Blinded by her adoration for the
property, she has agreed to a 5.5% interest rate. Round all answers to the nearest cent.
How much will Camila pay in interest over the lifetime of the mortgage?
Answers
The total interest on the mortgage loan is $219,249.60
What is a mortgage loan?
It is a loan taken in order to purchase a property that requires periodic repayments such as monthly repayment since most mortgages are repaid monthly.
Our first task is to determine the monthly repayment using the present value formula of an ordinary annuity because the monthly payment becomes due at the end of each month.
PV=monthly repayment*(1-(1+r)^-N/r
PV=loan amount=$210,000
monthly repayment=unknown(assume it is X)
r=monthly interest rate=5.5%/12=0.00458333333333333
N=number of monthly payments in 30 years=30*12=360
$210,000=X*(1-(1+0.00458333333333333)^-360/0.00458333333333333
$210,000=X*(1-(1.00458333333333333)^-360/0.00458333333333333
$210,000=X*(1-0.19277525234572900)/0.00458333333333333
$210,000=X*0.80722474765427100/0.00458333333333333
$210,000=X*176.12176312456800000
X=$210,000/176.12176312456800000
X=monthly payment=$1,192.36
total repayments(360 months)=$1,192.36*360
total repayments(360 months)=$429,249.60
Total interest=total repayments(360 months)-loan amount
Total interest=$429,249.60-$210,000
Total interest=$219,249.60
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Find the domain of the function:\(\frac{\sqrt{2-x} }{x-1}\)
Answers
1+2*5?
please answer
Answers
Answer:
11
Step-by-step explanation:
which ordered pair would form a proportional relationship with the point graphed below
A.(-10, 30)
B.(30, -15)
C.(-30, 10)
D.(80, -30)
Answers
Answer:
d
Step-by-step explanation:
i took the test
When I make two batches of cookies I need 4 cupsOf chocolate chips. How many chocolate chips would I need if I made 3 batches of cookies?
Answers
Answer:
it would be 6 cups I don't know how to explain though
Step-by-step explanation:
PLZ HELPPPPP WILL GIVE BRAINLIEST AND NO WRONG ANSWER PLZ
Answers
Answer:
D
Step-by-step explanation:
Answer:
D.
Step-by-step explanation:
D. because it has a proper domain and range and no other answer has correct domain/range. Therefore, D is the answer.
5) What is the solution to this equation?
x+ 20 + 10x=20+ 9x
A. x= 10
B.x=0
C. X = 20
D. x=2
Answers
Answer:
x=0
Step-by-step explanation:
11x-9x=20-20
2x=0
x=0
(Secx+1)/tanx - Sinx/1-cosx
Answers
Note that it is true to state that the expression (sec(x)+1)/tan(x) = (sin(x))/(1-cos(x)) is true for any known value of x except where cos(x) = 1 and x is an odd multiple of pi/2.
What is the rationale for the above response?We can start by manipulating the left-hand side of the equation using the trigonometric identities for secant, tangent, and Pythagorean identity for sine and cosine:
(sec(x) + 1) / tan(x)
= (1/cos(x) + 1) / (sin(x)/cos(x))
= ((1 + cos(x))/cos(x)) / (sin(x)/cos(x))
= (1 + cos(x)) / sin(x)
= [(1 + cos(x)) / sin(x)] * [(1 - cos(x)) / (1 - cos(x))]
= [(1 + cos(x)) * (1 - cos(x))] / [sin(x) * (1 - cos(x))]
= sin(x) / (1 - cos(x))
Therefore, we have shown that:
(sec(x) + 1) / tan(x) = sin(x) / (1 - cos(x))
Hence, the equation is true for any value of x, except where cos(x) = 1 and x is an odd multiple of pi/2.
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Full Question:
Note that the question seems incomplete. Thus, the rationale requirement here is to determine that the left side and the right side of the expression below are trully equal.
(sec(x)+1)/tan(x) = (sin(x))/(1-cos(x))
any help please - Simplify the expression 3(x + 2) –5(2x + 1). Factorise the expression 12x –18y and 2x2–5x –3. (3+6=9)
Answers
Simplifying the expression, the answer would be -7x+1
Solution
3 (x+2) - 5 (2x+1)
3x + 6 - 10x -5
COLLECT LIKE TERMS
3x - 10x + 6 - 5
= -7x+1
What interest is needed to earn $137.50 on a deposit of $500 for five years if it earns simple interest?
Answers
Answer:
5.5%
Step-by-step explanation:
Given data
Simple interest = $137.50
Principal= $500
time = 5 years
We want to find the rate R
Simple interest= PRT/100
137.50 = 500*R*5/100
137.50=2500R/100
cross multiply
137.5*100= 2500R
13750= 2500R
divide both sides by 2500
R= 13750/2500
R=5.5%
Hence the rate is 5.5%
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1900 seats. The students filled 44% of the seats in the theater. How many 6th graders went on the trip?
Answers
1900 * 0.44 = 836
Nora is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The labor and materials cost $150 for each phone manufactured, and the total cost of producing 8 phones in a day would be $2200. Write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
Answers
Answer:
C=150p+1000
Step-by-step explanation:
Solve for the y-intercept:
C=50p+b Slope intercept form of a line
2200=150(8)+b
Plug in known point
2200=1200+b Multiply
1000=b
Subtract 12001200
The equation is C = 1000 + 150p
The total cost of producing a phone is the sum of the fixed cost and the variable cost
Total cost = fixed cost + variable cost
Fixed cost is the cost of producing phone that remains constant regardless the quantity of phones produced. e.g. rent
Variable cost is the cost of producing phone that increases with the quantity of phones produced. e.g. labour cost
In order to write the equation, the fixed cost has to be determined.
Fixed cost = total cost - variable cost
Variable cost = $150 x 8 = $1200
2200 - 1200 = 1000
The equation is : C = 1000 + 150p
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What is 471,284 rounded to the nearest
thousands
Answers
Answer:
471,000
Step-by-step explanation:
The four points A(-1.0). B(3.b). C(a. 2) and D(-2.1) are the vertices of a parallelogram ABCD. find the value of a and b.
Answers
Answer:
Step-by-step explanation:
Question 2 help please
Answers
Answer:
The measure of the vertex angle is 94 degrees ⇒ A
Step-by-step explanation:
In any triangle, the sum of the measures of its interior angle is 180°In the isosceles triangle, the two base angles are equal in measures∵ In an isosceles triangle, the measure of the base angle = (2x + 5)
∵ The base angles of the isosceles triangles are equal in measures
∴ The measures of the base angles are (2x + 5), (2x + 5)
∵ The measure of the vertex angle = (5x - 1)
∵ The sum of the measure of the three angles = 180°
∴ (2x + 5) + (2x + 5) + (5x - 1) = 180
→ Add the like terms in the left side
∵ (2x + 2x + 5x) + (5 + 5 + -1) = 180
∴ 9x + 9 = 180
→ Subtract 9 from both sides
∴ 9x + 9 - 9 = 180 - 9
∴ 9x = 171
→ Divide both sides by 9 to find x
∴ x = 19
→ Substitute the value of x in the measure of the vertex angle to find it
∵ The measure of the vertex angle = 5x - 1
∴ The measure of the vertex angle = 5(19) - 1
∴ The measure of the vertex angle = 95 - 1
∴ The measure of the vertex angle = 94°
∴ The measure of the vertex angle is 94 degrees
Information
500 customers contacted a company today.
Phone
250 Customers
Webchat
4x Social Media
Email
III)
50% of Phone
Social Media
Question
Adjust the pie chart to represent the source of customer contacts.
G
Answers
Pie graphs can be used to display percentages of an entire group and depict percentages at a certain moment. Customers contacted via the web = x(let) then.as a result, customers contacted online (chart = x = 100), 25 customers were reached by social media, or x/4
What purpose does a pie chart serve?Pie charts can be used to show percentages for the whole group or for a specific time period.
In contrast to bar and line graphs, pie charts do not show changes over time.
The following pages provide descriptions of the various pie chart elements.
Since the slices of a pie chart represent different parts of the whole, their sum must always equal 100%.
Number of customers overall = 250 clients were contacted via email for every 500 customers contacted via phone, or 50% of phone contacts.
=(50÷100)×250
=125
Customers reached via social media
= total customers + 250 + 125 + x+1 = 500 x+1
=125 × 5
T=125
x=100.
Customers contacted via the web = x(let) then.
as a result, customers contacted online (chart = x = 100)
25 customers were reached by social media, or x/4
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A machine, when working properly, produces 5% or less defective items. Whenever the machine produces significantly greater than 5% defective items, it needs repair. A random sample of 300 items taken from the production line contained 27 defective items. Test at the 1% significance level if the percentage of defective items produced by this machine is greater than 5%.
Answers
Answer:
The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.
Step-by-step explanation:
A machine, when working properly, produces 5% or less defective items.
This means that the null hypothesis is:
\(H_0: p \leq 0.05\)
Test if the percentage of defective items produced by this machine is greater than 5%.
This means that the alternate hypothesis is:
\(H_a: p > 0.05\)
The test statistic is:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.
0.05 is tested at the null hypothesis:
This means that \(\mu = 0.05, \sigma = \sqrt{0.05*0.95}\)
A random sample of 300 items taken from the production line contained 27 defective items.
This means that \(n = 300, X = \frac{27}{300} = 0.09\)
Value of the test statistic:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z = \frac{0.09 - 0.05}{\frac{\sqrt{0.05*0.95}}{\sqrt{300}}}\)
\(z = 3.18\)
Pvalue of the test:
Testing if the mean is greater than a value, which means that the pvalue of the test is 1 subtracted by the pvalue of Z = 3.18, which is the probability of a finding a sample proportion of 0.09 or higher.
Looking at the Z-table, Z = 3.18 has a pvalue of 0.9993
1 - 0.9993 = 0.0007
The pvalue of the test is 0.0007 < 0.01, which means that we reject the null hypothesis and accept the alternate hypothesis that the percentage of defective items produced by this machine is greater than 5%.
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), what are the
coordinates of B?
Answers
The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).
To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.
Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).
Using the midpoint formula, we can set up the following equations:
(x1 + x2) / 2 = -4
(y1 + y2) / 2 = 2
Substituting the coordinates of point A (-7, 3), we have:
(-7 + x2) / 2 = -4
(3 + y2) / 2 = 2
Simplifying the equations:
-7 + x2 = -8
3 + y2 = 4
Solving for x2 and y2:
x2 = -8 + 7 = -1
y2 = 4 - 3 = 1
Therefore, the coordinates of point B are (-1, 1).
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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
Answers
The expression which shows the possible length of segment AB shows 27 < AB < 81.
Based on the diagram, the expression which shows the possible length of segment AB shows that 27 < AB < 81
A triangle that does not have equal sides and angles is known as a scalene triangle.
From the figure attached below, let's have a triangle ABC by using the parameter in the instructions given.
side |AC| = 27
side |CB| = 54
side |AB| = ???
We can use the Pythagoras rule to determine the side |AB|.
Pythagoras' rule states that the sum of the hypotenuse squared is equal to both the sum of the opposite squared and adjacent squared.
What is the Pythagoras' rule?
hyp² = opp² + adj²
AC² = AB² + CB²
54² = AB² + 27²
\(AB^2=54^2-27^2\\AB^2=2187\\AB=\sqrt{2187} \\AB=47\)
AB = 47
Therefore, we can conclude that the expression which shows the possible length of segment AB shows 27 < AB < 81.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The calculated scale factor from ABC to A'B'C is 1/3
Calculating the scale factor from ABC to DEF?From the question, we have the following parameters that can be used in our computation:
The triangles
From the triangles, we have the following parameters
A = (0, 3)
A' = (0, 1)
Using the above as a guide, we have the following:
Scale factor of the dilation = A'/A
So, we have
Scale factor of the dilation = (0, 1)/(0, 3)
Evaluate
Scale factor of the dilation = 1/3
Hence, the scale factor of the dilation is 1/3
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What is 4/9 as a decimal rounded to 3 decimal places? HELP ASAP
Answers
This Venn diagram shows sports played by 10 students.
Karl
Jada
Gabby
PLAYS
BASKETBALL
O A=0.50
OB. 0.29
OC. =0.40
D.
=0.20
Fran
Juan
lan
Ella
Let event A = The student plays basketball.
Let event B = The student plays soccer.
What is P(AB)?
PLAYS
SOCCER
Mickey
Mai
Marcus
Answers
The conditional probability for this problem is given as follows:
C. P(A|B) = 2/5 = 0.4 = 40%.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:
C. P(A|B) = 2/5 = 0.4 = 40%.
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I need help with this!
Answers
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
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