Given :
The population of fish in a pond from 2001 to 2014 is modeled by the function below where t is the years since 2001.
[tex]p(t) = \dfrac{1125}{1+12e^{-0.17t}}[/tex] ...1)
To Find :
Find the number of fish is the pond in 2014.
Solution :
Number of years, t = 2014 - 2001 = 13.
Putting value of t in equation 1), we get :
[tex]p(t) = \dfrac{1125}{1+12e^{-0.17\times 13}}\\\\p(t) = 485.67[/tex]
p(t) ≈ 486
Therefore, number of fish in the pond in 2014 is 486.
Hence, this is the required solution.
Express the following ratios in simplest form: 20:40
Answer:
1:2
Step-by-step explanation:
By dividing both sides by 20 you will get 1:2 which is the same thing as 20:40 if you multiply 1:2 on both sides by 20
Answer:
1 : 2
Step-by-step explanation:
20 : 40
20/10 : 4/10
2 : 4
2/2 : 4/2
1 : 2
Tommy bought a total of 30 apples and oranges for a classic picnic. Apple's cost $3 per pound and oranges cost $4 per pound. Tommy spent $100 total. How many apples and oranges did Tommy buy?
Answer:
20 apples and 10 orangesStep-by-step explanation:
Let amount of apples be x and oranges be y
Then we have:
x + y = 303x + 4y = 100Subtract triple of the first equation from the second one:
3x + 4y - 3(x + y) = 100 - 3*303x - 3x + 4y - 3y - 10y = 10Then finding x
x = 30 - 10 = 20So apples = 20, Oranges = 10
you have 50$ and want to buy some shoes that cost $45. the tax rate for the shoes is 7%. do you have enough money to buy the shoes?
Please answer questions answer don't write a random word I will report and get banned from the site
Answer:
Yes, you have enought money
Step-by-step explanation:
45 times 107% (100 for the total cost and and 7 for the tax) is equal to 48.15. You have 50 dollars, therefore you can buy your shoes.
which expression is equal to 5/2? Write a situation that could represent the fraction above.
Answer:
3/2 + 2/2. A teacher has to give 2 pencils to one student. 1 student gives him 3 pencils, another student give him 2 pencils. How much pencils does the teacher have?
Step-by-step explanation:
All you do is you find a problem that would give you 5/2 then create a word problem.
Maria's plant grew 3 1/4 inches every month for 2 1/2 months. How many inches did Maria's plant grow during that time?
Answer: 8.125 inches
Step-by-step explanation: Ok so if the plant grew 3.25 inches every month, and there were 2.5 months, you need to multiply 3.25 by 2.5 to get the total amount of growth. So that would be 8.125
Which angles are adjacent angles?
Answer:
<stv and <stq
Step-by-step explanation:
adjacent angles have the same vertex and are side by side.
i need the answers for the seven angels
Answer:
<1=83
<2=97
<3= 83 (given)
<4=97
<5=83
<6=97
<7=83
<8=97
Step-by-step explanation:
They give you the angle for 3 which is 83, so from there all you have to do is find the equivalent angles which are angle 1,5,7. Then for angles 2,4,6,8 you subtract 83 from 180 and you get 97.
Can someone explain how to solve this?
Answer:
here you go. hope this helps!
Kevin wants to buy 2.5 pounds of chicken at $6.49 per pound. How
much will he pay?
Answer:
16.225
just times 2.5 times 6.49
Find the length of side x in simplest radical form with a rational denominator
Answer:
The length of x=3/1
Step-by-step explanation:
Given the right triangle
Ф = 30
We know that
sin Ф = opposite/hypotenuse
The opposite of angle 30° = x
The hypotenuse is = 6
so
sin 30 = opposite/hypotenuse
1/2 = x/6 ∵ sin 30 = 1/2
1/2 × 6 = x
6/2 = x
3/1 = x
Therefore, the length of x=3/1
isolate the variable on the following problem. show your work.
11=c/5
15.5 divided by 33.17
Answer: 15.5 divided by 33.17 would be 0.46728972
Make sure you put your decimal point
What is the percent change from 9,000 to 900?
Answer:
-90%
Step-by-step explanation:
Change/ original x 100
9000-900= 8100
8100/9000= 0.9
0.9 x 100 = 90
Show work thanks please help me
Answer:
∠ JKL = 32°
Step-by-step explanation:
Since KN bisects ∠ LKM , then
∠ LKN = ∠ NKM = 35°
Thus
∠ JKL = ∠ JKM - ∠ LKN - ∠ NKM
= 102° - 35° - 35°
= 102° - 70°
= 32°
There are 5 less oranges on the tree today than there was yesterday
Plz help
The no. of apples on the tree today
= The no. of apples on the tree yesterday - 5
Let us take 'the no. of apples on the tree today' as 'x'
and 'the no. of apples on the tree today' as 'y'
Therefore, x = y - 5
Hope this is the thing u are looking for
evaluate the expression 8/d + 3 when d=4
Answer: 5,
Step-by-step explanation: I got it right, and I hope this helps you! ✨
Answer:
the evaluation of the equation is 5
Step-by-step explanation:
To add fractions, find the LCD and then combine.
solve : 3 under root a/b
Given x:y:z = 7:2:5 and the value of
x - z =18. Find the value of x+y+z.
Diberi x:y:z = 7:2:5 dan nilai x - 2 =18.
Cari nilai bagi x+y+z
A 14
B. 126
C. 210
D. 232
Answer:
x + y + z = 123
Step-by-step explanation:
x:y:z = 7:2:5
Let x = 7a, y = 2a, z = 5a
Since x - z = 18
Therefore,
7a - 5a = 18
2a + 18
a = 18/2
a = 9
7a = 7*9 = 63
2a = 2*9= 15
5a = 5*9 = 45
x + y + z = 63 + 15 + 45
x + y + z = 123
Write the equation of the line y=(5)/(6)x+(7)/(6) perpendicular to
that passes through the point (-8,7)
Answer:
6x + 5y + 13 = 0.
Step-by-step explanation:
y = 5/6x + 7/6
Gradient = 5/6
Since the line is perpendicular to y = 5/6x + 7/6
then its gradient is -6/5.
Hence its equation is: point (-8,7).
y - 7 = -6/5(x -(-8))
multiplying through by 5 we get;
5y - 35 = -6(x + 8)
5y - 35 = -6x - 48
6x + 5y + 13 = 0
A rhombus is graphed
on the set of axes below.
Answer:
Step-by-step explanation:
reflection over y-axis
Option A is correct, 180 degree rotation counter clockwise about the origin is transformation which would carry the rhombus onto itself.
We need to consider the properties of a rhombus and how each transformation affects its shape and orientation.
A rhombus is a quadrilateral with all four sides of equal length. It also has opposite angles that are congruent. Based on this information, we can analyze each transformation option:
180-degree rotation counterclockwise about the origin is a transformation would preserve the shape and size of the rhombus since a 180-degree rotation does not change the lengths of the sides or the angles.
Therefore, it is a possible transformation that carries the rhombus onto itself.
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Find the value of x. The diagram is not to scale.
a. x = 40
b. x = 23
c.x= 13
d. none of these
Answer:
d. none of these
Step-by-step explanation:
PLEASE PLEASE HELP.
Answer:
120 square feet
Step-by-step explanation:
they are similar so they are in a ratio 20/10=2 so smaller triangle is twice the larger one 6×2=12ft
area of triangle =1/2×base×height
=1/2×20×12
=120 square feet
pls help on these two math questions ill give brainlyest to first correct answer
Answer:
#1: Dillon, Harry, Paul, Winston #2: B
Step-by-step explanation:
#1: Absolute value is the opposite of the negative number, so it's just 2, 8, 10, and 13.
#2: Count by 10's, it's on the 50 line
Answer:
1)Dillon, Harry, Paul and Winston
2) C
How to do this question plz answer
Answer:
a. 9 sides
b. 18 sides
c. 24 sides
d. 30 sides
Step-by-step explanation:
We can use the equation 180(n-2), which n is the number of sides to find the answer.
a. 180(n-2)=1260
n-2=7
n=9
b. 180(n-2)=2880
n-2=16
n=18
c. 180(n-2)=3960
n-2=22
n=24
d. 180(n-2)=5040
n-2=28
n=30
Answer:
a) 9 sides
b) 18 sides
c) 24 sides
d) 30 sides
Step-by-step explanation:
sum of interior angles = (n - 2) * 180
where n is the number of sides
a) 1260
(n - 2) * 180 = 1260
(n - 2) = 1260/180
(n - 2) = 7
n = 7 + 2
n = 9
b) 2880
(n - 2) * 180 = 2880
(n - 2) = 2880/180
(n - 2) = 16
n = 16 + 2
n = 18
c) 3960
(n - 2) * 180 = 3960
(n - 2) = 3960/180
(n - 2) = 22
n = 22 + 2
n = 24
d) 5040
(n - 2) * 180 = 5040
(n - 2) = 5040/180
(n - 2) = 28
n = 28 + 2
n = 30
In the equation a= 3/b is a positive, real number. As the
value of b is increased so it becomes closer and closer to
infinity, what happens to the value of a ?
Answer:
The value of a tends to zeroStep-by-step explanation:
Given the expression a = 3/b
as the denominator of the of the expression b increases the value of the output is known to be decreasing. if the value of b now goes so large to become an infinite, value then the value of a will goes to zero as shown;
If b = ∞
a = 3/∞
a = 0
Note that for any constant value a, the ratio a/∞ will always tends to zero
Plz help btw the second one has the same options .
−3x+8<15 please help
Answer:x<-7/3
Step-by-step explanation:
Answer: X > -7/3
Step-by-step explanation:
-3x + 8 < 15
subtract 8 from both sides
-3x < 7
divide by negative 3
Also, when dividing or multiplying by a negative you flip the sign.
x > -7/3
Answer :)
Type only a number for your answer
Answer:
x = 80
Step-by-step explanation:
x + 30 = 110 (opposite sides are congruent/equal)
x = 110 - 30 (subtract the 30 from both sides to get X by itself)
x = 80 (simplify)
What is the rate of change of y with respect to x for 25x - 4y = 50 ?
Answer:
25/4Step-by-step explanation:
The change of y with respect to x is known as the slope of the line. The standard form of the equation is y = mx+c where m is the slope.
Given the equation 25x - 4y = 50, we need to make y the subject of the formula before we get the slope as shown;
25x - 4y = 50
-4y = -25x+50
Divide through b y -4
-4y/-4 = -25x/-4 + 50/-4
y = 25/4 x - 25/2
Comparing with y = mx+c
mx = 25/4 x
m = 25/4
Hence the rate of change of y with respect to x is 25/4
The rate of change of y with respect of x for the given equation is [tex]\frac{25}{4}[/tex].
Given the equation:
[tex]25x - 4y = 50[/tex]
The rate of change = the slope of the line
To determine the slope of 25x - 4y = 50, rewrite the equation in slope-intercept form. i.e. [tex]y = mx + b[/tex]Where, slope = mThus,[tex]25x - 4y = 50[/tex]
Add 25x to both sides of the equation[tex]25x -25x - 4y = - 25x + 50\\\\-4y = - 25x + 50[/tex]
Divide both sides by -4[tex]\frac{-4y}{-4} = \frac{-25x}{-4}+ \frac{50}{-4}\\\\y = \frac{25}{4}x - \frac{25}{2}[/tex]
Therefore, the rate of change of y with respect of x for the given equation is [tex]\frac{25}{4}[/tex].
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Giovanni justifies whether the expression -4x-8 is equivalent to -2(x+1)-2(x+3) by letting x=3 in both expressions. What is the value of each expression when x=3.
3 and -20
4 and 4
-20 and -20
3 and 4
Answer:
The value of each expression when x=3 will be -20 and -20.
Step-by-step explanation:
Given the expression
-4x-8
setting x=3
= -4(3)-8
=-12-8
=-20
Given the expression
-2(x+1)-2(x+3)
setting x=3
=-2(3+1)-2(3+3)
=-2(4)-2(6)
=-8-12
=-20
so we conclude that the value of both the expressions was -20 when we substituted the value x=3.
Therefore, the value of each expression when x=3 will be -20 and -20.