Answer:
18.85
Step-by-step explanation:
C=2πr=2·π·3≈18.84956
The circumference of this pool is 6π feet.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
Given:
The radius of a small wading pool is 3 feet.
r = 3 feet
And the pool is circular.
So,
circumference of circle = 2πr
Circumference of circle = 2π(3)
Circumference of circle = 6π feet
Therefore, 6π feet is the circumference of the pool.
To learn more about the circle;
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Is 18.52 irrational or rational
how to write 1/4z-1/3-1/7z^2 in az^2+bz
Answer:
huh?nani?
ksjn
lsjsmskkks
A biologist wants to compare the proportions of rainbow trout infected with whirling disease (an illness of
trout and salmon caused by a microscopic parasite) coming from two separate watersheds. For each
watershed, the biologist will collect a random sample of trout and record the proportion infected in the
sample. The biologist intends to estimate the difference for all trout in the two watersheds. Assuming all
conditions for inference are met, which of the following is the most appropriate method for the biologist to
use to analyze the results?
A
A one-sample z-interval for a population proportion
B
A one-sample z-interval for a sample proportion
с
A one-sample z-interval for a difference in sample proportions
D
A two-sample z-interval for a difference in population proportions
E
A two-sample z-interval for a difference in sample proportions
Answer:
D
Step-by-step explanation:
Because, the biologist wants to find the difference between the population of trouts from two watershed,
A biologist wants to compare the proportions of rainbow trout infected with whirling disease (an illness of trout and salmon caused by a microscopic parasite) coming from two separate watersheds.
The biologist will collect a random sample of trout and record the proportion infected in the sample The biologist intends to estimate the difference for all trout in the two watersheds
According to the given question, the most appropriate method for the biologist will be -A two-sample z-interval for a difference in population proportions
Because,Biologist wants to compare the proportions of rainbow trout infected with whirling disease and find the difference between the population of the trouts from two watershed .
Therefore , Statement D is the Correct
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what slope equation is parallel to y=5x-10
Answer:
y = 5x + (anything except negative 10)
For example:
y = 5x + 5
Step-by-step explanation:
A parallel equation is any equation with the same slope, but a different y intercept. As long as your y intercept isn't - 10, your answer will be parallel.
A fish tank is initially filled with 400 liters of water containing 1 g/liter of dissolved oxygen. At noon, oxygenated water containing 10g/liter of oxygen flows in at a rate of 5 liters per minute and the well-mixed water is pumped out at a rate of 7 liters per minute.Let A(t) represent the amount of dissolved oxygen in the tank at time t. a) Write the differential equation that represents the problem.b) Solve the differential equation. c) At 1 p.m., what is the amount of dissolve oxygen in the fish tank
Answer:
a. [tex]dA(t)/dt = 50 - \frac{7A(t)}{400} where A(0) = 400[/tex]
b. [tex]A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}[/tex]
c. 3.717 kg
Step-by-step explanation:
a) Write the differential equation that represents the problem.
Let A(t) be the amount of dissolved oxygen in the tank at any time, t.
The net flow rate dA(t)/dt = mass flow in - mass flow out
Since 10 g/l of oxygen flows in at a rate of 5 l/min, the mass flow in is 10 g/l × 5 l/min = 50 g/min
Since A(t) is the amount of oxygen present in the tank at time, t, and the volume of the tank is 400 liters. The concentration of oxygen in the tank is thus A(t)/400 g/l.
Also, water is being pumped out at a rate of 7 l/min. So, the mass flow out is thus concentration × flow rate out = A(t)/400 g/l × 7 l/min = 7A(t)/400 g/min
So, dA(t)/dt = mass flow in - mass flow out
dA(t)/dt = 50 - 7A(t)/400 with A(0) = 400 l × 1 g/l = 400 g since the tank initially contains 1 g/l of dissolved oxygen and has a volume of 400 l
So, the differential equation is
dA(t)/dt = 50 - 7A(t)/400 where A(0) = 400 g
[tex]dA(t)/dt = 50 - \frac{7A(t)}{400} where A(0) = 400[/tex]
b) Solve the differential equation
To solve the equation, we use separation of variables, so
dA(t)/dt = 50 - 7A(t)/400 where A(0) = 400 g
dA(t)/(50 - 7A(t)/400) = dt
Integrating both sides, we have
∫dA(t)/(50 - 7A(t)/400) = ∫dt
-7/400 ÷ -7/400∫dA(t)/(50 - 7A(t)/400) = ∫dt
1/ (-7/400)∫-7/400dA(t)/(50 - 7A(t)/400) = ∫dt
(-400/7)㏑(50 - 7A(t)/400) = t + C
㏑(50 - 7A(t)/400) = -7t/400 + (-7/400)C
㏑(50 - 7A(t)/400) = -7t/400 + C' (C' = (-7/400)C)
taking exponents of both sides, we have
50 - 7A(t)/400 = exp[(-7t/400) + C']
50 - 7A(t)/400 = exp(-7t/400)expC'
[tex]50 - \frac{7A(t)}{400} = e^{-7t/400}e^{C'} \\50 - \frac{7A(t)}{400} = Ae^{-7t/400} A = e^{C'}\\ \frac{7A(t)}{400} = 50 - Ae^{-7t/400} \\A(t) = \frac{400}{7} X 50 - \frac{400}{7} Ae^{-7t/400} \\A(t) = \frac{20000}{7} - \frac{400}{7} Ae^{-7t/400}[/tex]
when t = 0 , A(0) = 400. So,
[tex]A(t) = \frac{20000}{7} - \frac{400}{7} Ae^{-7t/400} \\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{-7(0)/400}\\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{0/400}\\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{0}\\A(0) = \frac{20000}{7} - \frac{400}{7} A\\400 = \frac{20000}{7} - \frac{400}{7} A\\\frac{400}{7} A = 400 - \frac{20000}{7}\\\frac{400}{7} A = \frac{2800}{7} - \frac{20000}{7}\\\frac{400}{7} A = -\frac{17200}{7}\\\\A = -\frac{17200}{7} X \frac{7}{400} \\A = -43[/tex]
So,
[tex]A(t) = \frac{20000}{7} - \frac{400}{7} X -43e^{-7t/400} \\A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}[/tex]
c) At 1 p.m., what is the amount of dissolve oxygen in the fish tank.
At 1 p.m, t = 60 min
So, the amount of dissolved oxygen in the fish tank is A(60)
So,
[tex]A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-7X60/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-420/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-1.05}\\A(60) = \frac{20000}{7} + \frac{17200}{7} X 0.3499\\A(60) = \frac{20000}{7} + \frac{6018.93}{7} \\A(60) = \frac{26018.93}{7} \\A(60) = 3716.99 g[/tex]
A(60) ≅ 3717 g
A(60) ≅ 3.717 kg
the Rangers played 40 games. They won 18 more games then they lost. How many games did they win?
9514 1404 393
Answer:
29
Step-by-step explanation:
Let w represent the number of wins. Then the number of losses is w-18. The total number of games played is ...
wins + losses = 40
w + (w-18) = 40
2w = 58
w = 29
The Rangers won 29 games.
Nancy borrowed $150 from her parents to buy a video game system. She has agreed to pay them back $25 each week Which equation represents the amount of money
Nancy still owes her parents, P. after w weeks?
Answer:
P = 150 - 25w
Step-by-step explanation:
Amount borrowed = $150
Repayment amount = $25 each week
P = amount Nancy owes
w = number of weeks
Amount Nancy owes = amount borrowed - repayment plan per week
P = 150 - 25w
During the first week of repayment: when w = 1
P = 150 - 25w
P = 150 - 25(1)
= 150 - 25
= 125
P = $125
Which point is a solution to the following inequality? y<2x+2
Answer:
Y<2x
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
a
Step-by-step explanation:
the answer is a
Find the equation of the line that contains the given point and with the given slope. Write the equation in slope-intercept form, if possible, and graph the line (2,1); slope =3
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the straight lines.
y-y1 = m(x-x1) + C
====> y - 1 = 3(x - 2)
====> y-1 = 3x -6
====> y = 3x - 5
hence the equation is y = 3x - 5
There are 9 movies ranked on the summer's "must see movie list." What is the probability that you guess the summer's top two must see movies if you randomly guess?
Answer:
1/36 = 0.0278 = 2.78% probability that you guess the summer's top two must see movies if you randomly guess
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the movies are chosen is not important, which means that we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
Top two movies, so only one outcome, which means that [tex]D = 1[/tex]
Total outcomes:
Two movies from a set of 1. So
[tex]T = C_{9,2} = \frac{9!}{2!(9-2)!} = 36[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{1}{36} = 0.0278[/tex]
1/36 = 0.0278 = 2.78% probability that you guess the summer's top two must see movies if you randomly guess
Answer:
1.39%
Step-by-step explanation:
This is a permutation problem because order matters.
There are 9! ways to rank the summer's must-see movies.
There are (9−2)!=7! ways to choose two movies as the top two must-see movies.
P = 7!/9! = 1/72 = 0.0139
To express our answer as a percent, we multiply by 100:
0.0139 x 100 = 1.39%
The measure of angle A in ABC is twice the measure of angle B and the measure of angle C is 20° less than the measure
of angle B. What are the measures of the angles in ABC?
Answer:
m∡A = 100°
m∡B = 50°
m∡C = 30°
Step-by-step explanation:
let 'x' = m∡B; 50°
let '2x' = m∡A; 100°
let 'x-20' = m∡C; 30°
x + 2x + x - 20 = 180
4x - 20 = 180
4x = 200
x = 50
I am not usre what the answer could be
Answer:
[tex]x \le 5[/tex]
Step-by-step explanation:
Given
Shape: Cube
Dimensions: x, 3x and 2x
[tex]Volume < 900[/tex]
Required
Show that [tex]x \le 5[/tex]
First, calculate the volume
[tex]Volume = x * 3x * 2x[/tex]
[tex]Volume = 6x^3[/tex]
[tex]Volume < 900[/tex] becomes
[tex]6x^3 < 900[/tex]
Divide both sides by 9
[tex]x^3 < 150[/tex]
For [tex]x^3 < 150[/tex], the value of x as to be: 1, 2, 3, 4 or 5
Hence:
[tex]x \le 5[/tex]
Write this number in scientific notation 56,023,987
Find the missing angle
Answer:
x=21
Step-by-step explanation:
69+90= 159
180-159=21
find the component equation of the plane which is normal to the vector -2i+5j+k and which contains the point (-10;7;5).
Given:
A plane is normal to the vector = -2i+5j+k
It contains the point (-10,7,5).
To find:
The component equation of the plane.
Solution:
The equation of plane is
[tex]a(x-x_0)+b(y-y_0)+c(z-z_0)=0[/tex]
Where, [tex](x_0,y_0,z_0)[/tex] is the point on the plane and [tex]\left< a,b,c\right>[/tex] is normal vector.
Normal vector is -2i+5j+k and plane passes through (-10,7,5). So, the equation of the plane is
[tex]-2(x-(-10))+5(y-7)+1(z-5)=0[/tex]
[tex]-2(x+10)+5y-35+z-5=0[/tex]
[tex]-2x-20+5y-35+z-5=0[/tex]
[tex]-2x+5y+z-60=0[/tex]
[tex]-2x+5y+z=60[/tex]
Therefore, the equation of the plane is [tex]-2x+5y+z=60[/tex].
The H.C.F of 42,70 and 56
Answer: 14
Step-by-step explanation
Do the prime factorization & it will give you 14
I need to find the x of the triangle.
Find the missing number:
Answer:
20%
Step-by-step explanation:
Not sure if this is exactly correct, but let's say we start with 1 unit. If it increased by 25%, we get:
1 × 1.25 = 1.25 units.
Now, to get back to 1 unit, we need to find:
1.25 × ? = 1
? = [tex]\frac{1}{1.25}[/tex] = 0.80
So, 100% - 80 % = 20%
A 20% decrease.
Not completely sure though.
Proszę o jak najszybszą odpowiedź
Answer:sorry I don’t speak proeze najsztbsza but do you know the way
Step-by-step explanation:
Please help! Due soon!
Answer:
a/..the first is 3/8
b/ 84/280
Answer:
a) 3/8
b) 3/10
Step-by-step explanation:
multiply the numerators and the denominators and then simplify.
a) is just 3*1 divided by 4*2, no simplification possible
b) is 4*21 divided by 7*40 is 84/280 and simplifies to 3/10 (divide by 28)
Elmer is purchasing 2 4/5 pounds of candy that cost $1.85 per pound.
If he pays with $10, how much will he get in change? HELP I WILL MARK BRAINIEST
Answer:
hi
Step-by-step explanation:
Daniel bought 1 pound of jelly beans and 2 pounds of chocolates for $2.00. ... for $1.50. How much would he have to pay on his next trip to the candy store if he bought 1 pound of each of the 4 kinds ... How many are there? Assign ... Multiply each equation by a factor, so that all equations will have the same total price: 3(1j +.
In ΔRST, the measure of ∠T=90°, the measure of ∠S=16°, and ST = 2.9 feet. Find the length of TR to the nearest tenth of a foot.
Answer:
0.8
Step-by-step explanation:
A computer game originally sold for $40 but is now on sale for 30% off. What is the sale price of the computer game?
Answer:
28
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
30% of 40 is 12, 40-12=28, the answer is 28.
Someone pls answer this!! 10
POINTSSSSSSSS
Answer:
perimeter of square = 4×side.
36cm=4×side.
36/4=side.
9cm=side
What is the slope of a line that passes through the following points (-2,-5) and (2, 5)?
a.-4/10
b.4/10
c.-10/4
d.10/4
Select all ratios equivalent to 4:3.
Answer:
8:6 and 16:12
Step-by-step explanation:
If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b?
2
4
9
10
Answer:
A: 2
Step-by-step explanation:
EDGE 2021
Considering that the magnitude of the complex number x is of 13, a possible value of b is of 2.
What is a complex number?A complex number is modeled by:
z = a + bi.
In which:
a is the real part.b is the imaginary part.In this problem, the number is:
x = 3 + bi.
It's magnitude is given by:
[tex]|x| = \sqrt{3^2 + b^2}[/tex]
Then:
[tex]\sqrt{3^2 + b^2} = \sqrt{13}[/tex]
[tex]3^2 + b^2 = 13[/tex]
[tex]b = \pm \sqrt{4}[/tex]
[tex]b = \pm 2[/tex]
A possible value of b is of 2.
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What is the solution to the system of equations below?
s 2y = x + 6
1 3.x = y +7
(20, 13)
(13, 20)
(5, 4)
(4, 5)
Answer:
(4,5)
Step-by-step explanation:
For Problems 2-5, use the thermometer to the right,
Each sentence is stated incorrectly, Rewrite the sentence to correctly describe each
situation
The temperature is 10 degrees Fahrenheit below zero,
b. The temperature is –22 degrees Celsius below zero,
