Answer:
S₄₀ = 2780
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
14 - 11 = 17 - 14 = 3
this indicates the sequence is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 11 and d = 3 , then
S₄₀ = [tex]\frac{40}{2}[/tex] [ (2 × 11) + (39 × 3) ]
= 20( 22 + 117)
= 20 × 139
= 2780
The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount. The half-life of the radioactive gas radon is approximately 2.8 days. The initial amount of radon used in an experiment is 74 grams. If N represents the number of grams of radon remaining t days after the start of the experiment,
a. Write an equation that gives Nin terms of t.
b. how much gas radon approximately remains after 2.8 days?
c. approximately when will the amount of radon remaining be 10 grams?
Step-by-step walkthrough:
a.
Well a standard half-life equation looks like this.
[tex]N = N_0 * (\frac{1}{2})^{t/p[/tex]
[tex]N_0[/tex] is the starting amount of parent element.
[tex]N[/tex] is the end amount of parent element
[tex]t[/tex] is the time elapsed
[tex]p[/tex] is a half-life decay period
We know that the starting amount is 74g, and the period for a half-life is 2.8 days.
Therefore you can create a function based off of the original equation, just sub in the values you already know.
[tex]N(t) = 74g * (\frac{1}{2})^{t/2.8days[/tex]
b.
This is easy now that we have already made the function. Here we just reuse it, but plug in 2.8 days.
[tex]N(t) = 74g * (\frac{1}{2})^{t/2.8days} = N(2.8days) = 74g * (\frac{1}{2})^{2.8days/2.8days}\\= 74g * \frac{1}{2} = 37g[/tex]
c.
Now we just gotta do some algebra. Use the original function but this time, replace [tex]N(t)[/tex] with 10g and solve algebraically.
[tex]10g = 74g * (\frac{1}{2})^{t/2.8days}\\\\\frac{10g}{74g} = (\frac{1}{2})^{t/2.8days}[/tex]
Take the log of both sides.
[tex]log(\frac{5}{37}) = log((\frac{1}{2})^{t/2.8days})[/tex]
Use the exponent rule for log laws that, [tex]log(b^x) = x*log(b)[/tex]
[tex]log(\frac{5}{37}) = \frac{t}{2.8days} * log(\frac{1}{2})[/tex]
[tex]\frac{log(\frac{5}{37})}{log(\frac{1}{2})} = \frac{t}{2.8days}[/tex]
[tex]2.8 * \frac{log(\frac{5}{37})}{log(\frac{1}{2})} = t[/tex]
slap that in your calculator and you get
[tex]t = 8.1 days[/tex]
The regular octagon shown is enlarged so that its side are 3 times
as large. What affect does this have on the perimeter?
Answer:
The perimeter is 2 times greater.
Step-by-step explanation:
What points should I circle and in which point do they intersect?
I WILL MARK BRAINLIEST AND GIVE THANKS
Answer:
[tex]\displaystyle [3, -2][/tex]
Explanation:
All you do is substitute three in for [tex]\displaystyle x[/tex]to get the y-coordinate of [tex]\displaystyle -2.[/tex]This means that these equations meet at the ordered pair of [tex]\displaystyle [3, -2].[/tex]
I am joyous to assist you at any time.
Select the set of equations that is NOT equivalent to 8k = 20
help me please!!!!!!!!!
Answer:
A = 5
I hope you have an amazing day!
can someone help me answer this
Answer:
sum the numbers of favorite food together.
pizza- 58.
hamburger- 36.
pasta- 14.
others- 17.
Addition of the favorite food will give us .
58+36+14+17=125.
pizza ..58/125 × 100 =46.4
HELP ASAP ILL MARK BRAINLIST
Describe the tangent ratio and solve. Show your work. Round your answer to the nearest thousandth.
Answer: 0.428
Step-by-step explanation:
[tex]\tan \theta=\frac{\text { side opposite to } \theta}{\text { side adjacent to } \theta}[/tex]
[tex]\begin{aligned}\tan \theta &=\frac{A B}{A C} \\\tan \theta &=\frac{6}{14} \\\tan \theta &=\mathbf{0 . 4 2 8}\end{aligned}[/tex]
You+deposit+$500+in+an+account+that+pays+5%+interest+compounded+yearly. +how+much+money+is+in+the+account+after+4+years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=500\left(1+\frac{0.05}{1}\right)^{1\cdot 4}\implies A=500(1.05)^4\implies A\approx 607.75[/tex]
The final amount will be $607.75 after 4 years if the principal amount is $500 and it compounded annually with interest rate of 5%
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+r)^t[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have in the problem:
P = $500, r = 5% = 0.05, and n = 4 years
[tex]\rm A = 500(1+0.05)^4[/tex]
A = $607.75
Thus, the final amount will be $607.75 after 4 years if the principal amount is $500 and it compounded annually with interest rate of 5%
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PLS HELP
WILL GIVE BRAINLIEST
answer:
(-7; -5)
step by step
I need help with this math question, please.
Sandra decides to alter the design of the rectangular lunch box so that one dimension of the bottom of the box is 1.25 times the height of the box, as shown in the diagram below. She still wants the volume of the box to be 355 in.^3. Write an equation in terms of W
The volume of the rectangular lunch box is the amount of space in it
The volume in terms of W is LW^2 = 443.75
How to determine the volume expression?The volume is given as:
V = 355
Let the width of the box be W, and the height be H; such that:
W = 1.25H
Make H the subject
H = W/1.25
The volume is calculated as:
V = LWH
So, we have:
355 = L * W * W/1.25
Multiply through by 1.25
443.75 = L * W * W
This gives
443.75 = LW^2
Rewrite as:
LW^2 = 443.75
The diagram is not given. So, the question cannot be solved further
Hence, the volume in terms of W is LW^2 = 443.75
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Shawna won 40 super bouncy balls playing
horseshoes at the county fair. At school she
gave three to every student in her math
class. She only has 1 remaining. How
many students are in her class?
Answer:
13 not including Shawna
Step-by-step explanation:
First, you have to take into account that the remainder is 1, so you must subtract 1 from 40, giving you 39. 39/3 is 13, so 13 is your final answer.
Answer:
13
Step-by-step explanation:
13 x 3=39. There is one remaing, +1 = 40.
Angelina’s family owns a mini-golf course. When discussing the business with a customer, she explains there is a relationship between the number of visitors and hole-in-one winners. If x is the number of visitors and y is the number of winners, which conclusion is correct?
The ordered pair (–3, 7) is viable.
The ordered pair (0, 4) is viable.
The ordered pair (7, 0) is non-viable.
The ordered pair (12, 3) is viable.
Answer:
D
Step-by-step explanation:
X must be positive as you cannot have a negative amount of people and neither X and Y could be 0. (In this case (7, 0) could have been viable but the choice says non-viable.) This means the answer is (12,3).
The ordered pair (12, 3) is viable is correct answer.
What is ordered pair?"Ordered pair is defined as the two numbers or variables which is written in form of pair using parenthesis."
According to the question,
Number of visitors = x
Number of winners = y
Relationship given,
Number of visitors and hole in one winners.
Negative value cannot be part of number of visitors or winners.
Therefore,
(-3,7) is not the correct ordered pair.
'x' and 'y' value cannot be equals to zero as per the condition given.
(7,0) is non viable.
Therefore,
(0,4) and (7,0) is not the correct ordered pair.
(12,3) represent both positive value as per the condition.
Hence, the ordered pair (12, 3) is viable is correct answer.
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A cupcake shop makes 25 dozen cupcakes in 2 days, how many cupcakes are made in 5 days at this rate
A 600
B 650
D 750
D 900
Answer:
D. 750
Step-by-step explanation:
if the shop makes 25 dozen in 2 days that means it makes 300 cupcakes in 2 days because 1 dozen is 12 cupcakes, so you will see that they make 50 dozen in 4 days which is 600 then you know she is only going to be making half of that 25 dozen on the 5th day so you just take half of 300 which is 150 and add it all up: 300+300+150=750
What is the volume of the square pyramid?
Answer:
v = 118.333333333
Step-by-step explanation:
formula: V=a^2h/3
The area is the base edge (so 5)
The height is the line going up the triangle (14.2)
Fill in:
v = 5^2(14.2/3)
Solve:
exponent first: 5^2 = 25
v = 25 (14.2/3)
divide/find out fraction: 14.2/3 = 4.73333333333
v = 23 x 4.73333333333
multiply: 23 x 4.73333333333 = 118.333333333
v = 118.333333333
you can also write as v = 118.3 with a line like “-“ over 3 to show the 3 is repeating:)
What is the slope of the line that passes through the points (2,8) and (12,20)?
Write your answer in simplest form.
The slope of the required line is [tex]\frac{6}{5}[/tex].
Thus, the slope of the line passing through (2,8) and (12,20) is [tex]\frac{6}{5}[/tex] .
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help please? requestig help to a smart person?
[tex] \frac{150}{10} = \frac{300}{20} = \frac{450}{30} = \frac{600}{40} = 15[/tex]
[tex]for \: x = 15y[/tex]
[tex]50x = 50(15) = 750.00[/tex]
Option B :)The table displays the scores of students on a recent exam. Find the mean of the scores to the nearest ioth. Score Number of Students 55 8 60 6 65 3 70 4 75 9 80 3 85 3 90 4
Answer:
38.75
Step-by-step explanation:
Not sure what you mean by ioth but when you add up all the numbers and divide by n, you get 38.75 (hopefully you can round it to whatever you want)
The first two terms of an arithmetic sequence are 7 and 11. Which of the following is the value
of its 30th term
Answer:
123
Step-by-step explanation:
Add 4 enough times to 11 and you will get there.
Number 3. (Look at the Image) Using the formula ū = ||T||(cos o 7 + sin 0 j) Il, find the magnitude and direction of ū= (3,-V3).
Magnitude should be written in simplified radical form.
ů= 11 ull (cosoit sin 63
ů
find magnitude and direction of
ů - <333)
Answer:
its 54
Step-by-step explanation:
1+2=3 3x5=15 15x2=30 30+16=46 46+8=54
I will mark brainliest for the first person to answer my question
Answer:
A. Line
<------------->
B. Angle
⦟
C. Line Segment
.___________.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
can some one answer this question please show work
When you reflect across the Y axis, the Y value remains the same and the x value becomes opposite.
Answer: (5,-3)
The unit rate of change of y with respect to r is the amount y changes for a change of one unit in I.
is the unit rate of change of y with respect to r greater in the equation y = 0.25% or in the graph below?
Choose 1 answer:
The graph
The unit rates are the same.
The equation
Answer:
(.8-.4)/(2-1) =.4
SLOPE IS THE RATE OF CHANGE Answer: A
Step-by-step explanation:
What is the area of the given quadrilateral?
Answer:
20 square units
Step-by-step explanation:
as its a square, we just add all the sides together. like a+b+c+d..
5+5+5+5=20 units
find the distance between the follwing points: (-4,11), (3,5)
Answer:
43
Step-by-step explanation:
equation= sqrt (x2-x1)^2 + (y2-y1)^2
PLEASE HELP
A shipping container is in the shape of a right rectangular prism with a length of 8. 5
feet, a width of 4 feet, and a height of 7 feet. The container is completely filled with
contents that weigh, on average, 0. 85 pound per cubic foot. What is the weight of the
contents in the container, to the nearest pound?
Answer:
14.875
Step-by-step explanation:
hope it helped
Solve by completing the Square
[tex]2x^{2} +3x=20[/tex]
Step-by-step explanation:
2x²+3x=20
2x²+3x=20
(√2x)²+2(√2x)(3/2√2)+(3/2√2)²-(3/2√2)²=20
(√2x+3/2√2)²=20+9/8
(√2x+3/2√2)²= 169/8
(√2x+3/2√2)= ±13/2√2
√2x=10/2√2 or -16/2√2
x= 10/4 or -16/4
x= 5/2 or -4
PLEASE HELP!!
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.
Answer:
40/41.
Step-by-step explanation:
sin Z = opposite side / hypotenuse
= 40/41
a rectangular painting is 24 inches wide and 20 inches tall without the frame. With the frame, it is 28 inches wide and 24 inches tall. What is the area of the frame not covered by the painting?
Answer:
191
Step-by-step explanation:
do the frame with the pic first that is
28*24=672
next just the pic
24*20=480
next subtract the pic from the frame
672-480=191
lily wants to find out how many students in her school enjoy pizza. describe a method she could use to get a representative sample without asking every single student in her school
Using sampling concepts, it is found that she could use systematic sampling, asking one out of every 10 students for example, as long as it involves students of all possible groups.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, the most viable type is a systematic sample, asking one out of every 10 students for example, as long as it involves students of all possible groups.
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HALP PLSSSSSSSS will give brainliset
Answer:
ezz multiply and see what it s if its wrong then txt me
Step-by-step explanation: