Step-by-step explanation:
Perimeter of a rectangle = 2(L+W)
L is the length of the rectangle:
W is the width of the rectangle.
Given
Perimeter = 214feet
If the length is 41 ft longer than the width, then L = 41+W
Substitute L = 41+W into the formula:
P = 2(L+W)
214 = 2(41+W+W)
214 = 2(41+2W)
214 = 82+4W
4W = 214-82
4W = 132
W = 132/4
W = 33 feet
Since L = 41+W
L = 41+33
L = 74 feet
Hence the dimension of the field is 74ft by 33ft
The width of the playing field is 33feet
the half life of c14 is 5730 years. Suppose that wood found at an archeological excavation site contains about 35% as much C14 as does living plant material. Determine when the wood was cut
Answer:
The wood was cut approximately 8679 years ago.
Step-by-step explanation:
At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:
[tex]\frac{dm}{dt} = -\frac{m}{\tau}[/tex] (Eq. 1)
Where:
[tex]\frac{dm}{dt}[/tex] - First derivative of mass in time, measured in miligrams per year.
[tex]\tau[/tex] - Time constant, measured in years.
[tex]m[/tex] - Mass of the radioactive isotope, measured in miligrams.
Now we obtain the solution of this differential equation:
[tex]\int {\frac{dm}{m} } = -\frac{1}{\tau}\int dt[/tex]
[tex]\ln m = -\frac{1}{\tau} + C[/tex]
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (Eq. 2)
Where:
[tex]m_{o}[/tex] - Initial mass of isotope, measured in miligrams.
[tex]t[/tex] - Time, measured in years.
And time is cleared within the equation:
[tex]t = -\tau \cdot \ln \left[\frac{m(t)}{m_{o}} \right][/tex]
Then, time constant can be found as a function of half-life:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (Eq. 3)
If we know that [tex]t_{1/2} = 5730\,yr[/tex] and [tex]\frac{m(t)}{m_{o}} = 0.35[/tex], then:
[tex]\tau = \frac{5730\,yr}{\ln 2}[/tex]
[tex]\tau \approx 8266.643\,yr[/tex]
[tex]t = -(8266.643\,yr)\cdot \ln 0.35[/tex]
[tex]t \approx 8678.505\,yr[/tex]
The wood was cut approximately 8679 years ago.
Its late and i need this pls
Gretchen made a paper cone to hold a gift for a friend. The paper cone was 11 inches high and had a radius of 4 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π.
The volume is ___in^3
Answer:
184.2 in^3
Step-by-step explanation:
vol of cone=
[tex]\pi {r}^{2} \frac{h}{3} [/tex]
[tex]3.14 \times 16 \times \frac{11}{3} [/tex]
=184.2
find the sum of 2x ÷ x-1 and x÷x-1
Answer with step-by-step explanation:
First of all, ORDER OF OPERATIONS!! 2x/x is 2/1, which is 2. Then, subtract 1, which is 1.
2x ÷ x - 1 = 1
Same thing: x/x = 1. Subtract 1 from 1, which is 0.
x ÷ x - 1 = 0
1 + 0 = 1
Hope this helped!
Michael exercises more than 35 minutes per day.
Use t to represent Michael's amount of exercise (in minutes per day).
Answer:
t>35
Step-by-step explanation:
Since Michael exercises more than 35 days, t is greater than 35. To express that in an inequality, the answer is t>35. Hope this helped!
the first number in the pattern is 32 the rule is to add 27
Answer:
59
Step-by-step explanation:
I need help the instructions say go left to right
SOMEONE PLEASE HELP ILL GIVE BRAINLIEST
Answer:
A.
Step-by-step explanation:
A square patio has an area of 135 square feet. How long is each side of the patio to the nearest tenth?
Each side of the patio is approximately
feet long.
Seventeen less than a number
is negative two. What is that
number?
Answer:15
Step-by-step explanation:
15-17=-2
Answer:
15
Step-by-step explanation:
15
I need help please thanks
find x when y = 18, if y = 9 when x = 8
ASAP PLEASE
so
y=9 -> y=18
*2
x=8 -> x=16
*2
so x = 16
Answer:
the only logical way solving this question is:
if y=9 then x=8
if y=18 then x should be 16
Step-by-step explanation:
I cant find any other way to solve
QUICK
solve this equation
a^n+b^n=
If a roof has a pitch of 5 to 11, how high will the roof rise over a 33-foot run?
a.
3
C.
2
72 feet
1 feet
b. 15 feet
d.
20 feet
The answer is b. 15ft
your job requires that you work at least 40 hours a week you have already worked 15 and there are 4 more days left in the week how many hours do you have to work each day to get at least 40 hours: inequality and solution
Answer:
6.25 hours
Step-by-step explanation:
this is rather simple really,
first, you have to work 40 hours a week
you have already worked 15 so now you can subtract that
40-15= 25hrs
if you have 4 more days of the week you divide the remaining hours by the days left
25/4= 6.25hrs
that would be the bare minimum of hours for you to work a 40 hour week.
7th grade math help me plzzzz
Answer:
a. -14
b. -13
c. -5
d. -3
e. -12
f. 0
Step-by-step explanation:
hope it helps
Answer:
A is -14.
B is -13
C is -5
D is -3
E is -12
F is 0
Step-by-step explanation:
A, B, E both numbers are negative so you just add them together and add a negative sign.
C would read 4-9
D 10-7 and add a - to the answer
F is 6-6
A newspaper is launching a new advertising campaign in order to increase the number of daily subscribers. The newspaper currently (t0) has 26,000 daily subscribers and management expects that number, S(t), to grow at the rate of subscribers per day, where t is the number of days since the campaign began. How long (to the nearest day) should the campaign last if the newspaper wants the number of daily subscribers to grow to 49,000?
Answer:
57 days
Step-by-step explanation:
Given that:
t(0) = 26000
Growth rate (S'(t)) = 80t^1/2
Targeted number of subscribers = 49000
Take the integral of the growth rate :
∫80t^1/2dt = [(80t^(1/2 + 1)) / 1/2 + 1] + C
[(80t^(1/2 + 1)) / 1/2 + 1] + C = (80t^3/2) / 3/2 + C
(80t^3/2) * 3/2 + C = (160/3)t^3/2 + C
(160/3)t^3/2 + C
Let C = t(0)
(160/3)t^3/2 + 26000 = 49000
(160/3)t^3/2 = 49000 - 26000
(160/3)t^3/2 = 23000
Multiply both sides by 3/160
t^3/2 = 23000* 3/160
t^3/2 = 69000/160
t^3/2 = 431.25
t^(3/2 * 2/3) = 431.25^2/3
t = 57.080277
t = 57 days (approx.)
Toby works at an amusement park. He loads 10 new passengers onto the roller coaster every
3/4
of a minute. At what rate does Toby load passengers?
Pleaseeee
Answer:
13 1/3
Step-by-step explanation:
im sure this is right btw
In a certain state's lottery, 45 balls numbered 1 through 45 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order in which the numbers are drawn does not matter.
Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.
P
(win) =
A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.
Answer: $
A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar.
Answer: $
Step-by-step explanation:
The order of the numbers doesn't matter, so we'll use combinations instead of permutations. The number of combinations is:
₄₅C₈ = 215,553,195
So the probability of a ticket having the winning combination is 1 / 215,553,195.
The expected value to the state is:
E(X) = 10,000 (1) ($2) + 10,000 (1 / 215,553,195) (-$1,000,000)
E(X) = $19954
The expected value to you is:
E(X) = 10,000 (1) (-$2) + 10,000 (1 / 215,553,195) ($1,000,000)
E(X) = -$19954
If b^2 = 25 then b= Answer it please
Answer:
b = 5
mark me as brainliest plz!! :DD
You have 8 donuts and you want to give 1/4 of them to a friend. How many donuts would your friend get?
Answer: pretty sure the friend would get 2 donuts
Step-by-step explanation:
A gallon of gas costs an average of two dollars is Betty spends $144 a month on gas determine how many gallons of gas she uses a month
Answer:
she uses 72 gallons
Step-by-step explanation:
just do 144/2 and the answer is 72
if you wanna check your answer just do 72x2 and it equals 144
estimate the answer for 1 2/3 x 5 1/10 (type a whole number
Answer:
Exact Form:
17/2
Decimal Form:
8.5
Mixed Number Form:
8 1/2
Question:
7x^2 + 8x = x^2
Answer:
x1= -4/3 and x2= 0
Step-by-step explanation:
Xis normally distributed with mean 1,000 and standard deviation 250. What is the probability that X lies between 800 and 1, 100?
Answer:
0.4435
Step-by-step explanation:
Given that :
X is normally distributed:
mean(m) = 1,000
standard deviation (s) = 250
probability that X lies between 800 and 1,100?
Using the relation :
X = 800
Zscore = (x - m) / s
Zscore = (800 - 1000) / 250
Zscore = - 200 / 250
Zscore = - 0.8
P(Z ≤ - 0.8) = 0.2119
X = 1100
Zscore = (x - m) / s
Zscore = (1100 - 1000) / 250
Zscore = 100 / 250
Zscore = 0.4
P(Z ≤ 0.4) = 0.6554
P(Z ≤ 0.4) - P(Z ≤ - 0.8)
0.6554 - 0.2119
= 0.4435
Write an equation in the line in slope intercept form
Answer:
Y=2x-1
Step-by-step explanation:
In order to find the slope, its rise over run. So you would move from (0,-1) to the next point it intercepts, (1,1) and find it from there
As for the Y-Intercept, it would just be wherever the line connects with the Y axis, which happens to be (0,-1) or Negative 1.
I thought of a two-digit number. The unit digit of my number is 7 more than the tens digit cubed. What is my number?
Answer:
18
Step-by-step explanation:
The tens digit a is cubed (a³ ) still less than the biggest possible 1 -digit number . It can be only 0 or 1 , so even 2³ =8 ( in such case the unit digit is 15,- that's not possible) .
0 can not be the the first digit in 2 digit number. So the only possible tens digit is 1. So the unit number is 1+7=8.
Answer 18
Answer:
18
Step-by-step explanation:
B^2 + 11b + 18 ( Factor the question)
Help please!
Answer:
=b^2+(9+2)b+18
=b^2+9b+2b+18
=b(b+9)+2(b+9)
=(b+9)(b+2)
Translate the sentence into an equation.
Seven times the sum of a number and 2 is 6.
Use the variable y for the unknown number.
Answer:
7(y+2)=6
Step-by-step explanation:
its right
The table shows the unit prices (per pound) of tomatoes
at different stores.
Store
Tomato Unit Prices
Jamal needs to buy 3.25 lb of tomatoes. If Jamal only
has $10, from which store(s) could he purchase his
tomatoes? Check all that apply.
Store A
Store B
Store C
Store D
Store E
A
$3.10 per pound
B
$3.02 per pound
с
$2.97 per pound
D
$3.07 per pound
E
$3.09 per pound
Answer:
store B, C, and D
Step-by-step explanation:
8 tomatoes for $2 unit rate
I don't have much so please 17
anyone in flvs? we should find each other in live lessons lol
Answer:
nope
Step-by-step explanation: