Answers
The value of S₃ is 65/9.
what is a geometric series?A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. S= a + ar + ar² + ar³+ . . .
a=start term r =common ratio
Given here, the nth term is 5(1/3)ⁿ⁻¹
therefore the sum of the first 3 terms of the geometric series is
S₃ = 5(1/3⁰) +5(1/3)¹+5(1/3)²
= 1+ 5/3 + 5/9
= 65/9
Hence the final answer is 65/9
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Related Questions
whole numbers greater than 15 but less than 16
Answers
Answer:
There are no whole numbers greater than 15 but less than 16... I am pretty sure it cant be 15 1/2 or something like that...
Step-by-step explanation:
A wheel whose diameter is 3 feet rolls a distance of 45 feet without slipping. Through what radian angle did the wheel rotate? 1) 30 2) 25 3 30 pi 4) 12 pi
Answers
Answer:
1) 30
Step-by-step explanation:
We need the radius of the wheel, we know that the radius is half the diameter, therefore:
r = d / 2 = 3/2 = 1.5
the angle is equal to the distance traveled (s) divided by the radius, thus:
° A = s / r =
° A = 45 / 1.5
° A = 30 radians
Through the radiation angle of 30 radians the wheel turned
therefore the answer is 1) 30
The radian angle at which the wheel rotated is; 1: 30
What is the angle of rotation?
We are given;
Diameter of wheel; d = 3 ft
Radius; r = d/2 = 3/2 = 1.5 ft
Now, the formula for the radian angle at which the wheel rotated is;
θ = s/r =
where;
s is distance
r is radius
Thus;
θ = 45/1.5
θ = 30 radians
Thus the angle at which the wheel rotated is 30 radians
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120 inch board is cut into two pieces one piece is two times the length of the other find the length of the shorter piece
Answers
Answer: 30(short piece) 90(long piece)
Step-by-step explanation:
Maria has 14 pencils, Ted has 9 pencils, Tom has 12, pencils, Lucinda has 13 pencils, so that they all have the same amount? How many pencils should each person have?
Answers
Answer:
"If they add all of the pencils together and then divided by how many of them there, which is 60/5, we can that there will be 12 pencils given to each person."
"Sample Response: Maria should give away 2 pencils. Ted should get 3 pencils. Lucinda should give away 1 pencil. Everyone should have 12 pencils. "
Check all that you included in your response.
Maria should give away 2 pencils.
Ted should get 3 pencils.
Lucinda should give away 1 pencil.
Everyone should have 12 pencils.
Step-by-step explanation:
Mrs. Brown gives two tests to her class. 30% of the class passed both tests and 45% of the class passed the first test. What percent passed the second test given that they passed the first test?
Answers
66.67% of the students who passed the first test also passed the second test.
To find the percent of students who passed the second test given that they passed the first test, we need to calculate a conditional probability. Let's define the events:
A: Passing the first testB: Passing the second testWe are given:
Probability of both events happening (passing both tests), P(A ∩ B) = 30% or 0.30Probability of passing the first test, P(A) = 45% or 0.45The conditional probability P(B|A) can be calculated using the formula:
P(B|A) = P(A ∩ B) / P(A)
Substitute the given values into the formula:
P(B|A) = 0.30 / 0.45
When we divide 0.30 by 0.45, we get 0.6667 or approximately 66.67%.
Therefore, 66.67% of the students who passed the first test also passed the second test.
Help me answer this please : The new cost of an iPhone 11 is $700. You decide to put this on your credit
card that earns 9% (0.09). When the bill comes in you pay off $200,
meaning you still owe $500. How much interest will you be charged? And what will your new total bill be?
Answers
Answer:
No I will never ever help you
To calculate the interest charged on the credit card, subtract the amount paid off from the new cost of the iPhone 11 and multiply it by the interest rate and time. The interest charged is $45. The new total bill will be $545.
Explanation:To calculate the amount of interest charged on the credit card, we need to find the difference between the new cost of the iPhone 11 ($700) and the amount you paid off ($200). This difference will be the initial principal amount on which interest is charged.
Interest is calculated using the formula: interest = principal x rate x time. In this case, the principal is $500 (the remaining amount owed), the rate is 0.09 (9% as a decimal), and the time is 1 year since the interest is calculated annually for credit cards.
Using this information, we can calculate the interest charged: interest = $500 x 0.09 x 1 = $45.
To find the new total bill, we add the interest charged to the remaining amount owed: new total bill = $500 + $45 = $545.
Which transformations are needed to change the parent cosine function to the cosine function below?
vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up
vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down
vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down
vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down
Answers
Question:
1. vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up
2. vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down
3. vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down
4. vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down
Answer:
The correct option is;
4. Vertical stretch of 2, horizontal compression to a period of π/2, phase shift of π units to the right, vertical shift of 1 unit down
Step-by-step explanation:
Here, we have the parent cosine function given by y = cos(x)
A plot of the above function is attached
By comparison, it is observed that the transformation required to change the parent function includes;
1. Vertical stretch from the parent function of amplitude 1 to amplitude 2
2. A horizontal compression so that the period of one complete revolution is π/2 rather than 2·π in the parent cosine function
3. Phase shift of pi units to the right such that cos(π) = 1 rather than cos(2π) = 1 as it applies to the parent function
4. Shift of the y values from the symmetrical x-axis origin downwards by 1 unit such that the maximum y value of the doubly stretched transformation is 1 rather than 2
Kayla’s work to find the surface area of a composite solid formed when a rectangular prism and rectangular pyramid are joined at their bases is shown below. SA = 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) = 255.7 square units What statement best describes Kayla’s error? She used the wrong expression for the lateral faces of the solid. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)). She left out one of faces of the solid. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6). She used the wrong expression for the lateral faces of the solid and left out the base of the figure. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6). She included the face where the pyramid and prism are joined together. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) minus 2((5) (6)). SA = 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) = 255.7 square units
What statement best describes Kayla’s error?
She used the wrong expression for the lateral faces of the solid. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)).
She left out one of faces of the solid. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6).
She used the wrong expression for the lateral faces of the solid and left out the base of the figure. She should have simplified 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) + (5) (6).
She included the face where the pyramid and prism are joined together. She should have simplified 2 ((5) (7)) + 2 ((6) (7)) + 2 (one-half (5) (9.3)) + 2 (one-half (6) (9.2)) minus 2((5) (6))
Answers
Answer:
Option B
Step-by-step explanation:
The reason is because the surface area is not including the base of the pyramid and the top of the prism.
Option b. she left out one of the faces of the solid she should have simplified 2((5)(7))+2((6)(7))+2[1/2(5)(9.3)]+2[1/2(6)(9.2)]+(5)(6)
Step-by-step explanation:
we know that
The surface area of the composite figure is equal to the surface area of the pyramid not including the base plus the surface area of the prism not including the top
so
SA= 285.7 units squared
Answer:
B
Step-by-step explanation:
can someone help me with this question please
Answers
Answer:
C. the vertical scale does not start at zero.
Step-by-step explanation:
The bars should be longer than they are drawn because the scale does not start at zero. As it is visual comparisons of the different months is misleading.
For example, it looks like the sales for February are about twice the March sales but that is not true.
Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year’s value. At this rate, what can Dan expect the approximate value of the computer to be after 7 years?
Answers
Answer:
$120.14
Step-by-step explanation:
This question is an example of a compound percentage decrease.
To work this out you would first need to convert the percentage of 25 into a decimal. You can do this by dividing the percentage of 25 by 100, this gives you 0.25. This is because percentages are out of 100.
The next step is to minus 0.25 from 1, this gives you 0.75. This is because we are working out the percentage decrease.
The final step is to multiply the amount of 900 by 0.75 to the power of 7, this gives you $120.14.
1) Divide 25 by 100.
[tex]25/100=0.25[/tex]
2) Minus 0.25 from 1.
[tex]1-025=0.75[/tex]
3) Multiply 900 by 0.75 to the power of 7.
[tex]900*0.75^7=120.14[/tex]
Answer:
If you’re looking for the vale after 8 years, I got $90 but I’m not sure if I’m right .
Step-by-step explanation:
If you help me get this right i will give you brainly, and 5 stars!
Answers
Answer:
all 3 statements are true
Step-by-step explanation:
domain is the x value or the first number in the parentheses
range is the y value or the second number in the parentheses
Answer:
1. True.
2. True.
3. True.
Step-by-step explanation:
The domain contains X coordinates, and the range contains Y coordinates. From the given list of coordinates, the domain contains numbers 2, 3, 5, and 6.
The range contains numbers 1, 4, 5, and 7, making questions 1 and 2 true.
Both the domain and range contain the number 5, so question 3 is also true.
A three-dimensional model of Lucia’s apartment is shown. To cool the whole apartment, an air conditioner must provide 2.5 BTUs per cubic foot. How many BTUs are needed to cool Lucia’s apartment? 19,600 BTUs 19,800 BTUs 20,400 BTUs 24,000 BTUs
Answers
Answer: c
Step-by-step explanation:
20,400
The Smiths spend 7% of their budget on entertainment. Their total budget this year is $1,000 more than
last year, and this year they plan to spend $3,150 on entertainment. What was their total budget last year?
Their total budget last year was
Answers
Answer:
Their total budget last year = $44,000
Step-by-step explanation:
Let last year's budget be x
let total budget this year be y
we are given the following information
y = 1000 + x - - - (1) (Their total budget this year is $1,000 more than last year)
7% of y = $3,150
7/100 × y = 3,150
0.07y = 3,150
y = 3,150 ÷ 0.07 = $45,000
Therefore, budget this year = $45,000
from equation 1
y = 1000 + x - - - (1)
∴ x = y - 1000
x = 45,000 - 1000 = $44,000
Therefore their total budget last year = $44,000
Final answer:
To find the Smiths' total budget last year, divide the amount they plan to spend on entertainment this year ($3,150) by 7% to calculate this year's budget ($45,000), then subtract the $1,000 increase from last year to reach the total budget for last year ($44,000).
Explanation:
To determine the Smiths' total budget last year, we need to work backwards from the amount they plan to spend on entertainment this year, which is $3,150. Given that entertainment costs represent 7% of their total budget, we can calculate their total budget for this year by dividing the entertainment expenditure by 7% (or 0.07). Once we have their budget for this year, we can subtract the $1,000 increase to find their budget for last year.
Let's calculate the total budget for this year:
Total budget this year = $3,150 / 0.07 = $45,000
Now, to find last year's budget, we subtract the $1,000 increase:
Total budget last year = $45,000 - $1,000 = $44,000
Therefore, the Smiths' total budget last year was $44,000.
The first four terms of a sequence are shown below.
2,9,40.5,182.25 ...
what is the next number in the sequence?
Answers
Answer:
820.125
Step-by-step explanation:
2*4+2/2=9
9*4+9/2=40.5
40.5*4+40.5/2=182.25
182.25 * 4 + 182.25/2 = 820.125
In addition to the congruent supplements theorem and cpctc, what else is needed to justify the conclusion that ∠ptq ≅ ∠rtq by sas? given: ∆pst ≅ ∆rst the reflexive property of congruence the vertical angles theorem aas theorem sss postulate description
Answers
To justify the conclusion that ∠PTQ ≅ ∠RTQ by SAS, the congruent supplements theorem and CPCTC are needed.
Explanation:To justify the conclusion that ∠PTQ ≅ ∠RTQ by SAS (Side-Angle-Side) in the given triangles PST and RST, we need to use the following:
The congruent supplements theorem, which states that if two angles are supplements of congruent angles (in this case, the angles ∠PTS and ∠RTS) then the two angles are congruent.The CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem, which states that if two triangles are congruent, then their corresponding parts (in this case, the angles ∠PTQ and ∠RTQ) are congruent.Therefore, by using the congruent supplements theorem and the CPCTC theorem, we can conclude that ∠PTQ and ∠RTQ are congruent.
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78 is what percent of 450
Answers
Answer:
17.33
Step-by-step explanation:
plug 78/450 into your calculator
78 is 17.33% of percent of 450.
78 is what percent of 450?A percentage is defined as the ratio that can be expressed as a fraction of 100.
To calculate what percent of 450 is 78, we can use the following formula:
percent = (part / whole) * 100
In this case, the part is 78 and the whole is 450. Thus, we have:
percent = (78 / 450) * 100
percent = 17.33%
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Sylvia earns $7 per hour at her after school job. After working one week, she received a paycheck for $91.
a. Write and solve an equation to find the number of hours Sylvia worked to earn $91.
b. The greatest number of hours Sylvia can work in any week is 15. Write an inequality to represent this statement.
c. What is the greatest amount of money Sylvia can earn in one week?
please help
Answers
Answer:
a.) [tex]hours=13[/tex]
b.) [tex]h\leq 15[/tex]
c.) $[tex]$105[/tex]
Step-by-step explanation:
a.) If she earns $7 'per' hour, this multiplication. After a week, we need to see how many hours she worked to earn $91, so this goes behind the equal sign. Let h be the unknown number of hours:
[tex]7h=91[/tex]
Solve for h. Divide both sides by 7:
[tex]\frac{7h}{7}=\frac{91}{7}\\\\h=13[/tex]
Sylvia worked 13 hours at a rate of $7 an hour.
b.) She can work at most 15 hours a week. At 'most' can also mean less than or equal to. Let h be hours:
[tex]h\leq 15[/tex]
Sylvia can work less than or equal to 15 hours per week.
c.) If Sylvia can work 15 hours, plug in this value for h into an equation when she earns $7 per hour. Let the product of the hours and money equal t for total:
[tex]t=7(15)\\t=105[/tex]
The most money Sylvia can earn in a week is $105.
Finito.
can someone help me with this
Answers
Answer:
A) 24 ft³
Step-by-step explanation:
The area of the right triangle base is ...
A = (1/2)(3)(4) = 6 ft²
The volume of the triangular prism is the product of the area of its base (6 ft²) and its height (4 ft).
V = Bh = (6 ft²)(4 ft) = 24 ft³ . . . . matches choice A
_____
Comment on the triangle
You know the 3-4-5 triangle is a right triangle, because you have seen those numbers many times in relation to the Pythagorean theorem. If you don't know that, then you can check to see by using the Pythagorean theorem:
5² = 3² +4²
25 = 9 + 16 . . . . . true; so the triangle is a right triangle
In any event, there are other means for finding the area of the triangle based on the lengths of its sides. You will get the same area result.
Using Heron's formula, s = (a+b+c)/2 = (3+4+5)/2 = 6.
A = √(s(s -a)(s -b)(s -c)) = √(6(3)(2)(1)) = √36 = 6 . . . . area of base triangle
A small university enrolls in-state and out-of-state students. Enrolled in their most recent freshman class was 243. The school reported that it enrolled seven in-state students for every two out-of-state students. How many of each type of student was enrolled in the freshman class?
Answers
There were 189 in-state students and 54 out of state students.
Total number of students = 243
Number of In-state students will be:
= 7/(7+2) × 243
= 7/9 × 243
= 189
Number of Out of states students will be:
= 2/(7+2) × 243
= 2/9 × 243
= 54
Therefore, there were 189 in-state students and 54 out of state students.
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Which relation is NOT a function?
Help ASAP
Answers
Answer:b
b
Step-by-step explanation:
tell me if you got it right.
solve some algebra problems using the properties of equality...
pls help i’m horrifyingly bad a math i understand nothing :(((
Answers
Answer:
a. Property 1
b. Property 2
Step-by-step explanation:
In this case, what we will do is say the properties of the equations, which are 4, the following:
Property 1: When a number is added or subtracted to both sides of equality, equality remains.
Property 2: When multiplied or divided by the same number, other than zero, on both sides of equality, equality remains.
Property 3: When both members of equality are raised to a nonzero power, equality remains.
Property 4: When the same root is extracted, on both sides of the equality, equality remains.
In other words, property 1 is used in part a and property 2 is used in part b.
olve these story problems.
Mr. Wilcox drove 459 miles at the aver-
age speed of 51 miles per hour. How
many hours did it take him to reach his
destination?
Answers
Step-by-step explanation:
Simple
Speed of 1 hour = 51 miles
Total miles = 459
459 ÷ 51 = 9
It will take 9 hours for him to reach his destination
A sample of bacteria is growing at a rate of 8% per hour compound continuously. How many hours will it take for the sample to double? Round your answer up to the nearest whole number and do not include units
Answers
Answer:
The sample would double in 9 hours
Step-by-step explanation
The number of hours it will take for the sample to double can be found using the 72 rule.
The 72 rule is such that a growth rate would double itself by it is used in dividing the number 72 as shown below:
number of hours =72/8=9 hours
The number of hours it would take the sample to double is 9 hours as computed above.
If sin Θ = 2 over 3 and tan Θ < 0 , what is the value of cos Θ?
Answers
[tex]\sin \theta = \dfrac 2 3[/tex]
[tex]\tan \theta < 0[/tex]
Positive sine, negative tangent, means we have a negative cosine. We're talking about the second quadrant.
[tex]\cos^2 \theta + \sin ^2 \theta = 1[/tex]
[tex]\cos^2 \theta = 1 - \sin ^2\theta[/tex]
[tex]\cos \theta = \pm \sqrt{1 - \sin ^2\theta}[/tex]
We know it's negative,
[tex]\cos \theta = - \sqrt{1 - (2/3)^2} =-\sqrt{5/9} = - \dfrac 1 3 \sqrt{5}[/tex]
Answer: -(1/3)√5
which statement is true about the potential solutions to log3(2x^4 +8x^3) -3log3x =2log3x please help!
Answers
Answer:B
Step-by-step explanation:
Answer:
b. Only x = –2 is an extraneous solution.
Step-by-step explanation:
edge 2021
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AKS 18/19 A travel agent is arranging a private cruise. The agent can arrange for, at most, 40 people to go on the trip. The trip cannot be finalized unless there are at least 12 men and 15 women committed to the cruise. The agent will make $26 profit per man and $14 profit per woman. What are the constraints for this situation?
Answers
Answer:
M + W <= 40
M >= 12
M >= 15
Total profit = $26 * M + $14 * W
Step-by-step explanation:
Let the number of men be denoted by M
number of women be denoted by W
Maximum no of people that can go one trip = 40
Therefore representing it mathematically we have
M + W <= 40 -------------- CONSTRAINT 1
Minimum number of men needed on trip = 12
Therefore representing it mathematically we have
M >= 12 CONSTRAINT 2
Minimum number of women needed on trip = 15
Therefore representing it mathematically we have
M >= 15 CONSTRAINT 3
profit on 1 man = $26
profit on M men = $26 * M
profit on 1 woman = $14
profit on M men = $14 * W
Total profit combining for men and women =
$26 * M + $14 * W -------------CONSTRAINT 4
___________________________________________
writing together all the constraint
M + W <= 40
M >= 12
M >= 15
Total profit = $26 * M + $14 * W
if√y - 2 = 8 then y =
Answers
Answer:
100
I want brainliest
Step-by-step explanation:
sqareroot of y -2=8
10-2=8
sqare root 10^2-2=8
y=100
Answer:
y = 100
Step-by-step explanation:
Assuming you mean sqrt(y) - 2 = 8
Add 2 to each side
sqrt(y) - 2+2 = 8+2
sqrt(y) = 10
Square each side
y = 10^2
y = 100
Ulissa is making a birthday card and wants to put a border made of pink ribbon all the way around the front of the card. The card is a rectangle 7 inches long and 4 inches wide. How long will the pink border be?
Answers
Answer:
22 inches
Step-by-step explanation:
7 + 7 = 14
4 + 4 = 8
14 + 8 = 22
Tyler borrowed $2,000 at an 11.5% simple interest rate. What is the total amount Tyler will pay back at the end of 5 years?
Answers
Answer: $3,150.00
Step-by-step explanation:
[tex]Formula: A=P(1+rt)[/tex]
Where;
A = amount
P = principal ($2,000)
r = rate (11.5% or 0.115)
t = time (5 years)
Plug this into the formula
[tex]A=(2000)(1+(0.115)(5))\\A=(2000)(1+0.575)\\A=(2000)(1.575)\\A=3150[/tex]
A cube has an edge length of 2/3 inch . What is the volume of the cube ?
Answers
Answer:
The volume would be eight inches. I hope this helps.
Brainliest welcome
Step-by-step explanation:
Final answer:
The volume of a cube with an edge length of 2/3 inch is found by cubing the edge length, which results in a volume of 8/27 cubic inches.
Explanation:
To find the volume of a cube with an edge length of 2/3 inch, we use the formula for the volume of a cube, which is the edge length cubed (V = [tex]s^3[/tex]). Thus, the volume V is:
V = (2/3 inch) * (2/3 inch) * (2/3 inch)V = ([tex]2^3[/tex])/([tex]3^3[/tex]) cubic inchesV = 8/27 cubic inchesTherefore, the volume of the cube is 8/27 cubic inches.