Answer:
Choice 120 daysStep-by-step explanation:
You are being asked to compare the value of a growing infinite geometric series to a fixed constant. Such a series will always eventually have a sum that exceeds any given fixed constant.
__
a)Angelina will get more money from the Choice 1 method of payment. The sequence of payments is a (growing) geometric sequence, so the payments and their sum will eventually exceed the alternative.
__
c)For a first term of 1 and a common ratio of 2, the sum of n terms of the geometric series is given by ...
Sn = a1×(r^n -1)/(r -1) . . . . . . . . . . series with first term a1, common ratio r
We want to find n such that ...
Sn ≥ 1,000,000
1 × (2^n -1)/(2 -1) ≥ 1,000,000
2^n ≥ 1,000,001 . . . . add 1
n ≥ log(1,000,001)/log(2) . . . . . take the base-2 logarithm
n ≥ 19.93
The total Angelina receives from Choice 1 will exceed $1,000,000 after 20 days.
The table below shows Ashley's earnings on the job. Time (hours) Earnings (dollars) 18 $514.80 23 $657.80 31 $886.60 How much does she make in 11.25 hours
Answer:
$321.75
Step-by-step explanation:
k = y/x
514.80/18= 28.6
28.6 * 11.25 =321.75
Thus, Ashley will earn 321.75 in 11.25 Hours
~Lenvy~
Answer:
$321.75
Step-by-step explanation:
Formula ⇒ k = y/x
Dollar = y
x = Hour
Hence,
514.80/18= 28.6
28.6 × 11.25 =321.75
Therefore, Ashley will make $321.75 in 11.25 Hour
[RevyBreeze]
Here are clues for a puzzle involving two numbers.
Seven times the first number plus six times the second number equals 31.
Three times the first number minus ten times the second number is 29.
PART A
What are the two numbers?
Answer:
the first number is 5 1/2the second number is -1 1/8Step-by-step explanation:
The relations describing the two numbers can be written as equations. First, we need to assign variables: let x and y represent the first and second numbers, respectively.
The given relations are then ...
7x +6y = 31
3x -10y = 29
__
Such a system of equations can be solved many ways. One that is usually convenient is to use a graphing calculator. It tells us ...
the first number is 5 1/2the second number is -1 1/8Ms. Lee takes out a loan to start a business. She borrows $5,000 of a simple annual interest rate of 6. 5% for 5 years. What is the total amount of interest Ms Lee must pay
Answer:
A = $6,625.00
Step-by-step explanation:
A = P(1 + rt)
A = 5000(1 + (0.065 × 5)) = 6625
Consider a dust mite that measures 10−3 millimeters in length and a gecko that measures 10 centimeters long. How many orders of magnitude as long as the mite is the gecko?
The gecko is about 10⁵ times bigger than the mite in length.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
1 cm = 10 ml
The dust mite measures 10⁻³ ml. The gecko measures 10 cm
Length of gecko = 10 cm = 10 cm * 10 ml per cm = 100 ml
Magnitude of gecko to mite = 100 ml / 10⁻³ ml = 10⁵
The gecko is about 10⁵ times bigger than the mite in length.
Find out more on equation at: https://brainly.com/question/2972832
Answer:
it is 5
Step-by-step explanation:
Line of reflection
just the graph
rectangle GHIJ with vertices G(2,-1) H(7,-1) I(7,-4) J(2,-4)
Rectangle GHIJ with the vertices G(2,-1) H(7,-1) I(7,-4) J(2,-4) is reflected across the line y= -5 to give G'(2, 3) H'(7, 3) I'(7, -3) J'(2, -3)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Rectangle GHIJ with the vertices G(2,-1) H(7,-1) I(7,-4) J(2,-4) is reflected across the line y= -5 to give G'(2, 3) H'(7, 3) I'(7, -3) J'(2, -3)
Find out more on transformation at: https://brainly.com/question/4057530
WILL GIVE BRAINLIEST FOR THE CORRECT ANSWER
Answer:
(3,5)
Step-by-step explanation:
We first need to substitute x for 3 in the equation :)
y = 2(3) - 1
y = 6 - 1
y = 5
The cordinate will be (3,5)
Have an amazing day!!
Please rate and mark brainliest!!
Consider the equation - 3x2 + 27x - 63 = 0.
What is the discriminant of the equation?
Answer:
answer is 19/9.
Step-by-step explanation:
give me brielient.
Write the log equation as an exponential equation. You do not need to solve for x.
log 5 (5) = 3x
Answer:
[tex]5=5^{3x}[/tex]
Step-by-step explanation:
[tex]log_5(5)=3x\\\\5=5^{3x}[/tex]
A plane flies 100km north and then flies 400km south, what is its new position?
Answer:
300km south
Step-by-step explanation:
Go up once from original position then down four times
1. D=7.4 calculate the area of the circle
2. R=2.2 yd
Calculate the circumference of the circle
3. D=5 cm
Calculate the circumference of the circle
4. D=6 cm
Calculate the circumference of the circle
5. R=2.1 m
Calculate the area of the circle
6. R= 1.3 mm
Calculate the circumference of the circle
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
We need to know two formulas before we start ~
Area of circle = [tex]\sf \pi r² [/tex]Radius (r) = diameter (d) ÷ 2 Circumference = [tex]\sf 2\pi r \:\: or \;\;\pi d [/tex]Taking value of pi as 3.14
Let's solve ~
problem 1[tex]\qquad \sf \dashrightarrow \:d = 7.4[/tex]
[tex]\qquad \sf \dashrightarrow \:r = d \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:r = 7.4 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:r = 3.7 \: \: units[/tex]
now,[tex]\qquad \sf \dashrightarrow \:area = 3.14 \times (3.7) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:a = 42.9866 \approx43 \: \: unit {}^{2} [/tex]
problem 2[tex]\qquad \sf \dashrightarrow \:r = 2.2 \: yd[/tex]
[tex]\qquad \sf \dashrightarrow \: circumference = 2 \times 3.14 \times 2.2[/tex]
[tex]\qquad \sf \dashrightarrow \: c =13.816 \: yd[/tex]
problem 3[tex]\qquad \sf \dashrightarrow \:d = 5 \: cm[/tex]
[tex]\qquad \sf \dashrightarrow \:circumference = 3.14 \times 5[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 15.7 \: \: cm[/tex]
problem 4[tex]\qquad \sf \dashrightarrow \:d = 6 \: cm[/tex]
[tex]\qquad \sf \dashrightarrow \:circumference = 3.14 \times 6[/tex]
[tex]\qquad \sf \dashrightarrow \:c =18 .84 \: \: cm[/tex]
problem 5[tex]\qquad \sf \dashrightarrow \:r = 2.1 \: m[/tex]
[tex]\qquad \sf \dashrightarrow \:area = 3.14 \times (2.1) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:a = 3.14 \times 4.41[/tex]
[tex]\qquad \sf \dashrightarrow \:a \approx13.85 \: \: m {}^{2} [/tex]
problem 6[tex]\qquad \sf \dashrightarrow \:r = 1.3 \: mm[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 2 \times 3.14 \times 1.3[/tex]
[tex]\qquad \sf \dashrightarrow \:c = 8.16 \: \: mm[/tex]
What is 3/7 as a decimal rounded to 3 decimal places?
Instructions: Find the missing side. Round your answer to the nearest tenth.
Answer:
14.4
Step-by-step explanation:
We have hypotenuse so cannot use tangent. We have adjacent so we can't use sine, therefore, we have to use cosine.
x = cos(59) x 28
x = 14.4
Find the area of the unshaded region.
Answer: 21
Step-by-step explanation:
Find the distance between points A and B if A is point(-2, 12) and B is point (3, 0)
options:
11 units
18 units
15 units
13 units
Answer:
13 units is the answer to the questionWhich geometric figure would be the best to model a suitcase?
Answer:
A rectangular prism would be best to model a suitcase
Step-by-step explanation:
Hope that helps!
Answer:
Rectangular Prism
Step-by-step explanation:
If you look at a suitcase, it resembles a rectangular prism quite well.
What is the reciprocal of look at the attachment
Answer:
5/2
Step-by-step explanation:
to find the reciprocal you just flip the fraction.
Answer:
the answer is 5/2 because reciprocal means to flip the equation
Step-by-step explanation:
please no guessing (WILL GIVE BRAINILIST)
STATISTICS
Answer:
#2 mean is 90.3846154 and range is 40
#3 mean 91.9230769 and range is 20
(you might have mixed the second and third graph up)
Step-by-step explanation:
if there are 15 plane 2 crash 1 breakdown how many planes are left
Answer:
15 planes
Step-by-step explanation:
none disappear, just change shape/ability. its a riddle.
Answer:
15-2-1 = 15-3 = 12.
there are 12 planes left.
Step-by-step explanation:
hope this helped have a nice day
Which transformations are needed to change the parent cosine function to y = 0. 35 cosine (8 (x minus StartFraction pi Over 4 EndFraction))? vertical stretch of 0. 35, horizontal stretch to a period of 16 pi, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical compression of 0. 35, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 4 EndFraction units to the left vertical compression of 0. 35, horizontal compression to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical stretch of 0. 35, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right.
The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression of period of [tex]\pi/4[/tex]phase shift of [tex]\pi/4[/tex] to rightHow does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift): Left shift by c units: [tex]y = f(x+c)[/tex]earlier)Right shift by c units: [tex]y = f(x-c)[/tex]output, but c units late)Vertical shift:Up by d units: [tex]y = f(x) + d[/tex]Down by d units: [tex]y = f(x) - d[/tex]Stretching:Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to [tex]y = 0.35\cos(8(x-\pi/4))[/tex]
We can see its vertical stretch by 0.35, right shift by [tex]\pi/4[/tex]horizontal stretch by 1/8
Period of cos(x) is of [tex]2\pi[/tex] length. But 1.8 stretching makes its period shrink to [tex]2\pi/8 = \pi/4[/tex]
Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression to period of [tex]\pi/4[/tex] (which means period of cosine is shrunk to [tex]\pi/4[/tex] which originally was [tex]2\pi[/tex] )phase shift of [tex]\pi/4[/tex] to rightLearn more about transformation of functions here:
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To determine the number of rams in a conservation area, a researcher catches and marks 103 rams. Then the researcher releases them. Later, 89 rams are caught and it is found that 21 of them are tagged. About how many rams are in the conservation area?
There are about rams in the conservation area.
(Round your answer to the nearest whole number as needed.)
Answer:
19 the explanation is 19 46
Element X decays radioactively with a half life of 7 minutes. If there are 980 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 40 grams?
Answer:
32.3m
Step-by-step explanation:
Use equation A = Ao(0.5)^(t/t½)
Now input values: 40 = 980(0.5)^(t/7)
rearrange for t: t = [7ln(2/49)]/ / ln(0.5). Then from here, you can extract 32.3 as your answer
Answer:
t = 32.3 min
Step-by-step explanation:
This is an example of half-life exponential decay.
For situations like this we have a formula.
[tex]N = N_{0} * (\frac{1}{2})^n[/tex]
N represents the end amount of parent element, N (naught) represents the starting amount of the parent element, and n being the amount half-lifes that have occurred.
Now n, can be broken down further into t/p, which means the time elapsed (t) divided by time it takes for one decay period (p), which essentially gives you the amount of half-lifes that have occurred. So you can represent the formula as:
[tex]N = N_{0} * (\frac{1}{2})^{t/p}[/tex]
The question tells you you start off with 980 grams of Element x, so put that for N naught. [tex]N = 980g * (\frac{1}{2})^{t/p}[/tex]. Then it tells you half-life is 7 minutes, which means the period it takes for one half-life to occur is 7, which is p. [tex]N = 980g * (\frac{1}{2})^{t/7min}[/tex]. You are also told that you end up with 40 grams, so put that in for N. [tex]40g = 980g * (\frac{1}{2})^{t/7min}[/tex]. Now we solve for t, the time elapsed.
(This is the part where you use logs to solve, but if you are still rough on this, I'll walk you through it)
Start off by dividing on both sides.
[tex]\frac{40g}{980g} = (\frac{1}{2})^{t/7min} \\, \frac{2}{49} = (\frac{1}{2})^{t/7min}[/tex]
Take the log of both sides.
[tex]log(\frac{2}{49}) = log( (\frac{1}{2})^{t/7min})[/tex]
Now we gotta get t out of the exponent, we'll do this by using log laws. More specifically the exponent law for log laws which states. [tex]log(b^x) = x*log(b)[/tex]. If we apply that to our situation like so.. [tex]log((\frac{1}{2})^{t/7min}) = \frac{t}{7min} * log(\frac{1}{2})[/tex]
Now our whole equation now looks like this:
[tex]log(\frac{2}{49}) = \frac{t}{7min} * log( \frac{1}{2})[/tex]
keep simplifying,
[tex]\frac{log(\frac{2}{49}) }{log(\frac{1}{2}) } = \frac{t}{7min}[/tex]
[tex]7min *\frac{log(\frac{2}{49}) }{log(\frac{1}{2}) } = t\\\\t = 32.3min \\[/tex]
Now you have your answer!
Which statements are true regarding the regular dodecagon? Check all that apply
Answer:
A dodecagon is a shape with 12 sides
Step-by-step explanation:
Decagon is 10 and do is 2 so 12
Write the following as an inequality.
5 is greater than or equal to w, and -5 is less than or equal to w
use w only once in your inequality
Answer:
[tex]-5\leq w\leq 5[/tex]
[tex]\huge\underline\mathtt\red{Answer:}[/tex]
−5 ≤ w ≤ 5
The ratio of the number of boys to the number of girls in choir is 6 to 7. There are 70 girls in choir. How many boys are in choir?
Answer:
48
Step-by-step explanation:
Kaylee was out at a restaurant for dinner when the bill came. her dinner came to $24. after adding in a tip, before tax, she paid $28.08. find the percent tip.
Answer:
17%
Step-by-step explanation:
subtract/originial*100=lercent change
4.08/24=0.17*100=17
The answer is 17%
! PLEASE HELP!
A signal can be sent from one location to another by running different colored flags up a flagpole, one above the other. There are 15 different colored flags to choose from but only 4 flags will be flown. Find the number of different signals consisting of 4, if the first flag must be orange.
If the first flag is orange then the number of different signals consisting of 4 flags is ____
Using the combination formula, it is found that if the first flag is orange then the number of different signals consisting of 4 flags is 364.
The order in which the flags are chosen is not important, hence, the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, considering that the first flag is orange, 3 flags will be chosen from a set of the remaining 14, hence the number of signals is given by:
[tex]C_{14,3} = \frac{14!}{3!11!} = 364[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
Trina purchases 10 tickets from a charity raffle. Each ticket in the raffle has 6 different numbers between the numbers 1 and 20. If there is only one prize, what is the probability of Trina winning the prize? Express your solution as a fraction in reduced form.
The probability of winning when there is only one prize, is:
P = 1/2,790,720
How to find the probability?
Each ticket has 6 different numbers, in order, from 1 to 20.
The first number has 20 options.The second number has 19 options (because the numbers can't repeat).The third number has 18 options, and so on.The total number of possible combinations is given by the product between the numbers of options, so there are:
C = 20*19*18*17*16*15 = 27,907,200 possible tickets.
So, if Trina purchases 10 tickets, she has a probability of 10 out of 27,907,200 winning (when we assume that there is only one prize)
Then the probability is:
P = 10/27,907,200 = 1/2,790,720
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2. You bought 8 bags of gummy bears and they cost $2.79 each. How much did
the gummy bears cost after you included the 8% sales tax?
Your answer
Answer:
$24.11
Step-by-step explanation:
Find the total price of the gummy bears by multiplying the 2.79 each bag by the 8 bags. 2.79×8=22.32.Convert the percentage into a decimal. Move the decimal place that is after the 8% (same as 8.0% if you need to visualize the location of the decimal) to 2 places to the left. This means your decimal is 0.08.Multiply the decimal by the total untaxed cost from the first step. This will give you the tax. 22.32×0.08=1.7856, which rounds to currency of 1.79. Add the tax and the untaxed total together to get the grand total. 1.79+22.32=24.11Your answer is $24.11What is the approximate volume of the tube? round to the nearest whole cubic centimeter. 1,005 cm3 1,340 cm3 3,351 cm3 4,021 cm3
The approximate volume of the cylinderical tube is 1005 cm³ round to the nearest whole cubic centimeter.
What is of volume of cylinder?Volume of cylinder is the amount of quantity, which is obtained by the bylinder in the 3 dimensional space.
Volume of cylinder is the can be given as,
[tex]V=\pi r^2h[/tex]
Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.
A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift.
The diameter is 8 cm and the radius of a cylinder is half of its radius. Thus the radius of the cylinder is,
[tex]r=\dfrac{8}{2}\\r=4\rm\; cm[/tex]
Put the values in the above formula a,s
[tex]V=\pi (4)^2(20)\\V=320\pi\\V=1005.31\\V=\approx 1005\rm\;cm^3[/tex]
The approximate volume of the cylinderical tube is 1005 cm³ round to the nearest whole cubic centimeter.
Learn more about the volume of cylinder here;
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please help I'm trying to write this in scientific notation
will give brainliest
Answer:
8.0 * 10^4
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
8.0 x 10 4
Step-by-step explanation:
This is right