The sum of the second and third terms of a geometric sequence is 96. The sum to infinity of this sequence is 500. Find the possible values for the common ratio, r.
Answers
Let, first term be a and common ratio is r.
So, \(\dfrac{a}{r}+\dfrac{a}{r^2}=96\)
Sum of series, \(S = \dfrac{a}{1-r}=500\)
a = 500( 1 - r )
\(a( \dfrac{1}{r}+\dfrac{1}{r^2})=96\\\\r=0.916\)
Therefore, the value of common ratio is 0.916 .
Hence, this is the required solution.
Related Questions
What is the missing length? will mark brain list if correct
Answers
Answer:
5
Step-by-step explanation:
10*5/2=25
Using no other digits except 2 and 5 write down, if possible, a three-digit multiple of 6
Answers
Answer:
255
522
525
252
225
552
Step-by-step explanation:
IM NOT SURE
Answer:
A three-digit multiple of 6 that uses no other digits except 2 and 5 is 252.
Step-by-step explanation:
The question is basically asking a number that only uses 2 and 5 that is divisible by 6.
When you divide 252 by 6, you get 42, and this proves that 252 is a multiple of 6.
homework question . Some tutor said they couldn’t solve it ?
Answers
The points that will apply will be where x>1 and y>7
Relevant points: A, B and E
Students voted for a new class president and the results are shown in the table.
A 2-column table with 3 rows. Column 1 is labeled Candidate with entries Rosalia, Jocelyn, Danny. Column 2 is labeled Votes with entries 124, 109, 111.
Suppose four more people voted and they all voted for Jocelyn. What fraction of the votes would be for Jocelyn? I really need it thx
Answers
Answer:
113:348
Step-by-step explanation:
i got it wrong cause i only put 113 but it showed this is the answer
Answer:
its Jocelyn
Step-by-step explanation:
PLEASE HELP!!!
John and Chuck are building a new house. When finished, the house will cost $190,750. The price of the house is 9% higher than the price when the original plans were made. What was the price of the house when the original plans were made?
Answers
Answer:
190,750 decreased by 9% is 173,582.5
Step-by-step explanation:
Help me please and thank you..
Answers
Answer:
You will move each point of this shape 1 unit into the right. Then will move each point of this shape 2 units down. The draw line between each point.What is the factored form of 27d^6 + 8g^12
Answers
Answer:
(3d^2+2g^4) x (9d^4 - 6d^2 g^4 + 4g^8)
that is the factored form hope it helps
Answer:
Answer: B
Step-by-step explanation:
What is the difference of the given values to the correct level of precision?
22.108 L
– 5.80 L
Answers
22.108-(-5.80)
22.108+ 5.80= 27.908
Natalya designed a patio for her backyard. The two brick
sections will be the same size and concrete fills the rest of
the patio. Her design and the scale she will use to build
the patio are both shown below.
The concrete portion of the patio will cost $3 per square
foot to construct and the brick portion of the patio will
cost $6 per square foot to construct.
How much will Natalya spend constructing the patio with
concrete and brick?
Scale
1 cm = 4 ft.
A
B
6 cm
$432
$648
Brick
Concrete
6 cm
3 cm
Brick
3 cm
OPTIONS
A
$432
B
$648
C
$2,160
D
$3,024
Answers
The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.
We are given that;
The concrete portion of the patio cost=$3 per square
To construct and the brick portion of the patio cost= $6 per square
Now,
The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:
6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft
Therefore, the area of the concrete portion is:
24 ft x 12 ft = 288 ft^2
The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:
3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft
Therefore, the area of one brick rectangle is:
12 ft x 24 ft = 288 ft^2
Since there are two brick rectangles, the total area of the brick portion is:
2 x 288 ft^2 = 576 ft^2
Now we can multiply the areas by their costs per square foot to get the costs of each portion:
Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456
The total cost of constructing the patio is the sum of the costs of each portion:
Total cost = $864 + $3456 = $4320
Therefore, by area the answer will be $4320.
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A state lotto has a prize that pays $900 each week for 20 years.
Find the total value of the prize: $
If the state can earn 5% interest on investments, how much money will they need to put into an account
now to cover the weekly prize payments?
Reminder: There are 52 weeks in a year.
Answers
The total value of the prize is $936,000.
The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.
What is the total value of the prize?The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:
= $900/week x 52 weeks/year x 20 years
= $936,000.
How much money is needed to put into the account?We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r
Plugging in the values:
PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154
PV = $900 x 657.221075423
PV = $591,498.968.
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Arianys is going to invest $11,000 and leave it in an account for 9
years. Assuming the interest is compounded monthly, what interest
rate, to the nearest hundredth of a percent, would be required in order
for Arianys to end up with $20,000?
Answers
The compound interest rate of the investment is 1.10%
How to determine the compound interest rate?The given parameters about the compound interest are
Principal, P = $11,000
Amount, A = $20,000
Time, t = 9
Number of times, n = 12 i.e. monthly interest
To calculate the amount, we have:
A = P(1 + R/n)^nt
Substitute the known values in the above equation, so, we have the following representation
20000 = 11000 * (1 + r/12)^(12 * 9)
This gives
1.82 = (1 + r/12)^108
Take the 108th root of both sides
1 + r/2 = 1.0055
Subtract 1 from both sides
r/2 = 0.0055
Multiply by 2
r = 0.011
Express as percentage
r = 1.10%
Hence, the value of the interest rate is 1.10%
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Answer:
6.66%
Step-by-step explanation:
Compounded Monthly:
�
=
�
(
1
+
�
�
)
�
�
A=P(1+
n
r
)
nt
Compound interest formula
�
=
20000
�
=
11000
�
=
9
�
=
12
A=20000P=11000t=9n=12
Given values
20000
=
20000=
11000
(
1
+
�
12
)
12
(
9
)
11000(1+
12
r
)
12(9)
Plug in values
20000
=
20000=
11000
(
1
+
�
12
)
108
11000(1+
12
r
)
108
Multiply
20000
11000
=
11000
20000
=
11000
(
1
+
�
12
)
108
11000
11000
11000(1+
12
r
)
108
Divide by 11000
1.8181818
=
1.8181818=
(
1
+
�
12
)
108
(1+
12
r
)
108
(
1.8181818
)
1
/
108
=
(1.8181818)
1/108
=
[
(
1
+
�
12
)
108
]
1
/
108
[(1+
12
r
)
108
]
1/108
Raise both sides to 1/108 power
1.0055509
=
1.0055509=
1
+
�
12
1+
12
r
−
1
−1=
−
1
−1
Subtract 1
0.0055509
=
0.0055509=
�
12
12
r
12
(
0.0055509
)
=
12(0.0055509)=
(
�
12
)
12
(
12
r
)12
Multiply by 12
0.0666108
=
0.0666108=
�
r
6.66108
%
=
6.66108%=
�
r
Convert to percent (multiply by 100)
�
≈
r≈
6.66
%
6.66%
Round to the nearest hundredth of a percent
What is the first step in evaluating the expression shown below?
12
÷
(
7
.
4
−
3
.
6
)
+
8
−
2
Answers
Answer:
Step-by-step explanation:
The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.
Step 1: Evaluate the expression inside the parentheses.
7.4 - 3.6 = 3.8
After evaluating the expression inside the parentheses, the expression becomes:
12 ÷ 3.8 + 8 - 2
Step 2: Perform the division.
12 ÷ 3.8 = 3.158
After performing the division, the expression becomes:
3.158 + 8 - 2
Step 3: Perform the addition and subtraction from left to right.
3.158 + 8 = 11.158
11.158 - 2 = 9.158
Therefore, the value of the given expression is approximately 9.158.
The first step is:
⇨ parenthesesWork/explanation:
The expression is:
12 ÷ (7.4 − 3.6) + 8 − 2
Let's recall the order of operations first:
order of operations = PEMDASPEMDASParenthesesExponentsMultiplicationDivisionAdditionSubtractionSo we evaluate
\(\sf{12\div(7.4-3.6)+8-2}\)
\(\sf{12\div3.8+8-2}\)
Next, division:
\(\sf{3.158+8-2}\)
Next, addition & subtraction:
\(\sf{9.158}\)
Hence, the first step is to evaluate the parentheses.what is 39.5/4 if you tell me you get 45 points
Answers
Answer:
9.875
Step-by-step explanation:
Answer:
9.875
Step-by-step explanation:
get a calculator
Which expression shows the prime factorization of 30?
2 x 3 x 5
3 x 5 x 7
3 x 5 x 5
2 x 2 x 3
Answers
Hope I helped :)
Answer:
A
Step-by-step explanation:
because 2x3 equals 6
then 6x5 equals 30
( i did the math for the other ones and its a;)
Write an equation for the line parallel to the line -7x - 7y= 7 through the point (-1,2)
Answers
Answer:
\(y=-x+1\)
Step-by-step explanation:
Slope-Intercept Formula:It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:
\(-7x-7y=7\)
add 7x to both sides:
\(-7y=7x+7\)
Divide both sides by -7
\(y=-x-1\)
Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:
\(y=-x+b\text{ where b }\ne -1\)
We're given the point (-1, 2) and we can use it to solve for that "b" value.
We plug in -1 as x and 2 as y
\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)
Now we just plug this into the general equation to get: \(y=-x+1\)
the equation below represents the total price of Michigan State University per semester where c represents the number of classes and t represents the total cost for the semester including a one time fee for room and board
Answers
The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).
The equation captures the relationship between these variables and calculates the overall cost for a student attending the university. It is important to note that the equation provides a quantitative representation and does not take into account other factors such as scholarships, financial aid, or additional expenses. Therefore, the equation serves as a useful tool for estimating the total cost of attending Michigan State University, allowing students and their families to plan and budget accordingly for their education.For such more question on equation
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Use the graph of f(x) to find the solutions to the equation f(x)=0.
Answers
Answer:
x = -4, 7
Step-by-step explanation:
Pre-SolvingWe are given the graph of the function f(x), and we want to find the values that make the statement f(x) = 0.
f(x) = 0 means that there are certain values that make the value of f(x) (which can be considered as y) equal to 0.
SolvingWe can look to the graph to help us - we should look at where y is equal to 0, which is the x-axis.
On the x-axis, we can see that the function passes through both -4 and 7 (the graph goes up by 1) on that line.
As coordinate points, they are written as (-4,0) and (7,0).This means that when either -4 or 7 are substituted into the function (i.e. when they are equal to x), they will make the function equal 0.
So, it means that x = -4, 7.
Mike got 31 out of 50 for a test.
The pass mark is 60%.
Did Mike pass the test?
Answers
Answer:
Yes Mike passed the test.
Step-by-step explanation:
31/50 is equal to 62% which is higher than the needed mark to pass.
Answer:
Yes
Step-by-step explanation:
Change denominator to 100 by multiply both denominator and numerator by 2, so 31*2= 62, so he passed the test.
Maya’s unpaid balance is $205.16. Her APR is 14.4% and she has $82.10 in new transactions. What is her new balance? Responses $289.72 $289.72 $290.71 $290.71 $316.80 $316.80 $533.45
Answers
Based on the information given the new balance is $289.72.
New balanceFirst step is to calculate the finance charge
\(\text{Finance charge}=205.16\times(0.144\div12 \ \text{months})\)
\(\text{Finance charge}=205.16\times0.012\)
\(\text{Finance charge}=2.46\)
Second step is to calculate the New balance
\(\text{New balance}=205.16+2.46+82.10\)
\(\text{New balance}=\bold{\$289.72}\)
In conclusion, the new balance is $289.72.
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Please explain your answer to the question in the picture with steps
Answers
Answer:
x = 31.2
Step-by-step explanation:
You want the solution to the proportion 12/x = 5/13.
Rational equationYou can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...
\(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)
Now, the value of x is found by dividing both sides by its coefficient.
\(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)
__
Additional comment
The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.
Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.
You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.
Any proportion can be written 4 ways:
\(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)
These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.
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SOS PLS HELP
A machine that drills holes for wells drilled to a depth of
-72 feet in one day (24 hours).
At this rate, how many hours will it take until the drill
reaches its final depth of -132 feet?
Answers
Answer:
20 hours
Step-by-step explanation:
If the machine drilled 72 feet in 24 hours, we can divide 72 by 24 to find out that the machine drilled 3 feet in one hour.
Next, you must find the distance that must be traveled. You can do this by subtracting 72 from 132. You will get 60
So, if the machine drilled at 3 feet per hour, and it needs to drill 60 feet, it will take 20 hours because 60 divided by 3 is 20.
B
15x+7
6x+2y|
y +3
2y + 1
С
E
The triangles are congruent. Find the length of each hypotenuse.
A. 3
B. 5
C 17
Answers
Answer:
Hypothenus = 22
Step-by-step explanation:
From the question given above, we were told that the triangles are congruent (i.e same size). Thus,
AC = EF
BC = DE
To obtain the length of each Hypothenus, we shall determine the value of y and x. This can be obtained as follow:
For y:
AC = y + 3
EF = 2y + 1
AC = EF
y + 3 = 2y + 1
Collect like terms
3 – 1 = 2y – y
2 = y
y = 2
For x:
BC = 5x + 7
DE = 6x + 2y
y = 2
DE = 6x + 2(2)
DE = 6x + 4
BC = DE
5x + 7 = 6x + 4
Collect like terms
7 – 4 = 6x – 5x
3 = x
x = 3
Finally, we shall determine the length of each Hypothenus. This can be obtained as follow:
Hypothenus = BC
Hypothenus = 5x + 7
x = 3
Hypothenus = 5x + 7
Hypothenus = 5(3) + 7
Hypothenus = 15 + 7
Hypothenus = 22
OR
Hypothenus = DE
DE = 6x + 2y
y = 2
x = 3
Hypothenus = 6(3) + 2(2)
Hypothenus = 18 + 4
Hypothenus = 22
What is the x intercept of the graph of the inequality 2x + 3y > 12
Answers
Answer: x intercept = 6
This is the location (6,0)
===============================================================
Explanation:
I assume you're talking about the boundary line of the inequality. The boundary line equation is 2x + 3y = 12
To find the x intercept, plug in y = 0 and solve for x
2x + 3y = 12
2x + 3(0) = 12
2x = 12
x = 12/2
x = 6
The boundary line 2x+3y = 12 crosses the x axis at x = 6.
We can say the x intercept is x = 6. This is the location (6,0).
Side note: the y intercept is y = 4, which is found by plugging in x = 0 and solving for y.
The first term of an arithmetic sequence is 4. The common difference is 8. What is the 25th term of sequence
Answers
Answer:
196
Step-by-step explanation:
T25=4+(25-1)8
=4+192
T25=196
The 25th term of the arithmetic sequence is 196.
The formula that can be used in finding the nth term of an arithmetic sequence will be: = a + (n - 1)d
where,
a = first term = 4
d = common difference = 8
n = number of terms = 25
Therefore, the 25th term of the sequence will be:
= a + (n - 1)d
= 4 + [(25 - 1) × 8]
= 4 + (24 × 8)
= 4 + 192
= 196
The 25th term is 196.
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The bakery shop purchased 7 2/10 pounds of sugar and 7 5/10 pounds of flour. How much sugar and flour did they purchase in all?
Answers
Answer:
Sugar = 1-2/5 pounds, Flour = 3-1/2 pounds
Together = 5-9/10 pounds
Step-by-step explanation:
sugar = 7(2/10)
flour = 7(5/10)
sugar + flour = 7(2/10) + 7(5/10)
sugar = 14/10 or 1-2/5 pounds
flour = 35/10 or 3-1/2 pounds
solve ~
2x - 4 = 2 ( x + 2 )
thankyou ~
Answers
Distribute 2x-4=2(x+2) 2x-4=2x+4
add 4 to both sides of the equation
simplify subtract 2x from both sides
0 = 8
Step-by-step explanation:
Given that
2x - 4 = 2 ( x + 2 )
We need to determined the value of x and find the number of solution.
Expand the bracket
2x - 4 = 2x + 4
Collect like terms
2x - 2x = 4 + 4
0 = 8
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which equation represents exponential decay?
1.y=1/100 (31)^x
2.y = 1/10 (3.1)^x
3.y=10(0.13)^x
4.y=100(1.03)^x
in in a hurry. will give brianliest
Answers
Answer: The correct option is the third one; y=10(0.13)^x
The figure above shows a store's supply-demand graph for coffee makers. If the store sells $600 worth of coffee makers, which of the following is a valid possible price for them?
A. $15
B. $30
C. $40
D. $55
Answers
The possible price for the items if the store sells $600 is (c) $40
How to determine the possible price for the items?From the question, we have the following parameters that can be used in our computation:
The supply-demand graph
If the store sells $600, then there is a supply worth of $600
The equation of the supply line is calculated as
y = mx + c
Where
c = y = 0
i.e. c = 100
So, we have
y = mx + 100
Using another point on the graph, we have
30m + 10 = 400
So, we have
m = 13
This means that
y = 13x + 100
For a supply of 600, we have
13x + 100 = 600
So, we have
13x = 500
Divide by 13
x = 38.4
Approximate
x = 40
Hence, the possible price for the items is (c) $40
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Dee’s Catering Budget vs. Actual Comparison for December 2010
a. What is the variance (dollar and percent) in Dee’s total cost of sales for the month of December? Answer: $32,051 and 12.8%
b. To what do you attribute the variance in Dee’s total cost of sales for December?
c. What is the variance (dollar and percent) in Dee’s salaries and wages for the month of December? Answer: $6,100 and 15.7%
d. To what do you attribute the variance in Dee’s salaries and wages for December?
e. What is the variance (dollar and percent) in Dee’s marketing expenses for the month of December? Answer: $-1.050 and -87.5%
f. What advice would you give Dee regarding her marketing expense variance?
I need help with answering these questions. Letter B, D, and F.
Answers
Walton's actual check average is $9.52
The actual food cost is lower than the flexible budget by $5020
We have ,
Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.
The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.
Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.
Hence, Walton's actual check average is $9.52
The actual food cost is lower than the flexible budget by $5020
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complete question:
A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?
b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?
d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?
e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?
f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?
g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?
help!!!!!!!!!!!!!!!!!!!
Answers
Answer:
D. 1/5
Step-by-step explanation:
Because
0.2222...>0.2>0.12