Answer:
The initial population is 200
The population after 10 years is 687
Step-by-step explanation:
Given
[tex]P(t) =\frac{800}{1+ 3e^{-0.29t.}}[/tex]
Solving (a): The initial population
Here:
[tex]t = 0[/tex]
Substitute 0 for t in P(t)
[tex]P(0) =\frac{800}{1+ 3e^{-0.29*0}}[/tex]
[tex]P(0) =\frac{800}{1+ 3e^{0}}[/tex]
[tex]P(0) =\frac{800}{1+ 3*1}[/tex]
[tex]P(0) =\frac{800}{1+ 3}[/tex]
[tex]P(0) =\frac{800}{4}[/tex]
[tex]P(0) =200[/tex]
The initial population is 200
Solving (b): Population after 10 years.
Here
[tex]t = 10[/tex]
Substitute 10 for t in P(t)
[tex]P(10) =\frac{800}{1+ 3e^{-0.29*10}}[/tex]
[tex]P(10) =\frac{800}{1+ 3e^{-2.9}}[/tex]
[tex]P(10) =\frac{800}{1+ 3*0.055}[/tex]
[tex]P(10) =\frac{800}{1+ 0.165}[/tex]
[tex]P(10) =\frac{800}{1.165}[/tex]
[tex]P(10) =687[/tex] -- approximated.
The population after 10 years is 687
Someone please help!!
Answer:
A
Step-by-step explanation:
Hi! I think the answer is gonna be B! I could be wrong but that’s what I worked it out to! Good luck on the edge thing!!
9x+ 5 = 14x — 4
I need help with this I have to solve for x
Answer:
here u go
Step-by-step explanation:
its 9/5 or 1.8. Also 1 to 4/5
math Finding the root (30points!!!!!)
Answer:
p = [tex]\frac{12}{7}[/tex]
Step-by-step explanation:
let the root be α then the other root is 3α
The sum of the roots of a quadratic equation is
α + 3α = - [tex]\frac{b}{a}[/tex] = - [tex]\frac{-8}{7}[/tex] = [tex]\frac{8}{7}[/tex]
Thus 4α = [tex]\frac{8}{7}[/tex] ( divide both sides by 4 )
α = [tex]\frac{2}{7}[/tex]
The product of the roots of a quadratic equation are
α × 3α = [tex]\frac{c}{a}[/tex] = [tex]\frac{p}{7}[/tex], that is
3α² = [tex]\frac{p}{7}[/tex] ← substitute value of α
3 × ([tex]\frac{2}{7}[/tex] )² = [tex]\frac{p}{7}[/tex]
3 × [tex]\frac{4}{49}[/tex] = [tex]\frac{p}{7}[/tex]
[tex]\frac{12}{49}[/tex] = [tex]\frac{p}{7}[/tex] ( cross- multiply )
49p = 84 ( divide both sides by 49 )
p = [tex]\frac{84}{49}[/tex] = [tex]\frac{12}{7}[/tex]
Please help...........
Answer:
x = 59.4°
Step-by-step explanation:
Reference angle = x
Side opposite to x° = 22
Adjacent side = 13
To find x, apply trigonometric ratio formula. Thus:
[tex] tan(x) = \frac{22}{13} [/tex]
[tex] x = tan^{-1}(\frac{22}{13}) [/tex]
[tex] x = 59.4 [/tex] (nearest tenth of degree)
A circle has radius 50 cm. Find the area of the circle to the nearest hundredth.
What is the result when 9r^3 + 27x^2 + 11x +1 is divided by 3x + 1?
Answer:
the answer is 3x^2 + 8x + 1
Step-by-step explanation:
(I used x as the variable due to the invalid difference of variables in your question )
To find the correct answer, I had to use polynomial division.
(9 x 3 + 27 x 2 + 11 x + 1) / (3 x + 1)
= ( 3 x + 1 ) ( 3 x 2 + 8 x + 1 ) / (3 x + 1)
= 3 x 2 + 8 x + 1
Each number line is shaded to represent a percent drag a percent to each number line that represents a percent.
Answer:
Step-by-step explanation:
The first one is 20%
The second one is 95%
(Can you take another picture so I can see the rest)
Leslie paid $12 for 4 books. What is the unit rate of the book purchase?
Answer: 3 dollars for a book.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Find the sum of 2x2 – 8x — 6 and 9x2 – 8.
Answer:
Submit Answer
Answer:f
( x ) = x , g ( x ) = x 3 − 1 f ( x ) = x 4 + x 3 − 11 x 2 − 5 x + 30 , g ( x ) = 2 x − 2 f ( x ) = x 2 , g ( x ) = 7 x − 1
in short ways the answer is 7 x − 1
Hence , the sum is [tex]11x^2-8x-14[/tex].
WHAT IS A POLYNOMIALIn mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
How to Solve?Given , we need to add [tex]2x^2-8x-6[/tex] and [tex]9x^2-8[/tex].
So, we can write it as :
[tex]2x^2 -8x-6+9x^2-8[/tex]
Writing like terms together:
[tex]= 2x^2+9x^2-8x-6-8[/tex]
[tex]=11x^2-8x-14[/tex]
Hence , the answer is [tex]11x^2-8x-14[/tex].
Learn more about Algebraic expressions :
https://brainly.com/question/395066
#SPJ2
Find the missing side or angle.
Round to the nearest tenth.
A=18°
B= 28°
b=100
a=[ ?]
Answer:
a = c2 +b2
Step-by-step explanation:
18=10000 + 784
10784 ÷ 18
599.111111 BUT ROUNDED WOULD BE 600.00
Is 5/9 closer to 1, 1/2, or 1?
Answer:
Closer to 1/2
Step-by-step explanation:
Half of 9 is 4.5 and 5 is .5 away from half and to make this 1 it needs to be 9/9 which is 4 away.
Answer:
1/2
Step-by-step explanation:
Half of 9 is 4.5/9, and 5/9 is closer to 4.5/9 than 9/9(or 1)
The length of a rectangle is 4 cm less than 3 times its width. If the width is x cm, then the length is
a. 3x - 4
b. 4 - 3x
c. 4x - 3
d. 3x + 4
e. 3 - 4x
Find the area of the shaded region. All angles are right angles.
URGENT!!!! The area of a rectangular floor is 80 square feet. The length of the floor is 2 feet less than the width of the floor.
What is the width of the floor?
Drag the answers into the boxes to correctly complete the statements.
The equation Response area , where w is the width of the floor in feet, can be used to solve this problem. The width of the floor is Response area feet.
Answer:
Width of the floor = 10 feet
Step-by-step explanation:
Given that:
Area of rectangular floor = 80 square feet
Width of rectangular floor = w
Length of rectangular floor = w - 2
Now,
Area = Length * Width
80 = w(w-2)
[tex]80=w^2-2w\\w^2-2w-80=0\\[/tex]
Factorizing the equation,
[tex]w^2+8w-10w-80=0\\w(w+8)-10(w+10)=0\\(w+8)(w-10)=0[/tex]
Either,
w+8 = 0
w = -8
Or,
w-10 = 0
w=10
As width cannot be negative,
width = 10 feet
Hence,
Width of the floor = 10 feet
Tristan can walk 3 miles in one hour. At this rate, how far will Tristan walk in 4 hours?
Answer:
12 miles
Step-by-step explanation:
sometimes looking at the units is helpful.
How far Tristan will walk is measured in miles.
3 miles/hour * 4 hours has a unit of miles * hour/hour = miles
3*4 = 12
Answer:
12 Miles
Step-by-step explanation:
Multiply 3 by 4
Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.4 millimeters (mm) and a standard deviation of 0.8 mm. For a randomly found shard, find the following probabilities.
a. the thickness is less than 3.0 mm
b. the thickness is more than 7.0 mm
c. the thickness is between 3.0 mm and 7.0 mm
Answer:
a) the required probability is 0.0013
b) the required probability is 0.0288
c) the required probability is 0.9759
Step-by-step explanation:
Given the data in the question;
let x be the thickness measurements
Given that X follows a Normal distribution with mean μ = 5.4
standard deviation σ = 0.8
then z = x-μ / σ = x-5.4 / 0.8 follows standard Normal
a) probability that the thickness is less than 3.0 mm
P( x<3 ) = P( x-5.4 / 0.8 < 3-5.4 / 0.8 ) = P( Z < -3.00 ) = 0.0013
Therefore, the required probability is 0.0013
b) the thickness is more than 7.0 mm
P( x>7 ) = P( x-5.4 / 0.8 > 7-5.4 / 0.8 ) = P( Z > 2.00)
= 1 - P( Z ≤ 2)
= 1 - 0.9772
= 0.0288
Therefore, the required probability is 0.0288
c) the thickness is between 3.0 mm and 7.0 mm
P(3< x<7 ) = P( x<7) - P(x<3)
= P( x-5.4 / 0.8 > 7-5.4 / 0.8 ) - P( x-5.4 / 0.8 < 3-5.4 / 0.8 )
= P( Z< 2 ) - P( Z < -3)
= 0.9772 - 0.0013
= 0.9759
Therefore, the required probability is 0.9759
The average of three test scores is 82. The scores on the first test and the third test are the same. The score on the second test is 6 less than the score on the first test. What is the score on the first test?
Answer:
84
Step-by-step explanation:
Let x = the test
(x + x + ( x - 6))/3=82
((3x - 6)/3) • 3= 82 • 3
3x - 6 + 6 = 246 + 6
3x = 252
3 3
x = 84
b. (1-4) Name two obtuse
angles in the shape
below:
Answer
ADC and BDC
Explain:
Answer:
Same like other users
What’s the answer to this problem
Answer:
1.2075
Step-by-step explanation:
Multiply the speed of the turtle ( 0.69 miles per hour) by the number of hours it takes ( 1.75 hours)
Answer: 1.2075
Step-by-step explanation:
multiply 0.69*1.75 and u will get 1.2075
In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=60°, and JH = 80 feet. Find the length of IJ to the nearest foot.
Answer:
46.2
Step-by-step explanation:
46.188= 46.2
I will give brainiest to whoever answers correctly !!
Answer:
34.5%
I'm not sure.
but I'm quite sure.
Answer:
The percent markup is 300%
Step-by-step explanation:
15.75 = 1575%
18.75 = 1875%
1875% - 1575% = 300%
Your friend has created a dice game where the probability of winning is 0.45. If you win at least 60% in a series of n games you win the grand prize. You may choose to play a series of n = 10, 20, or 50 games. Which value of n should you choose to get the best chances of winning the grand prize?
A. n = 10
B. n = 20
C. n = 50
D. n = 10 or 20; they have the same probability
E. All three have the same probability.
Answer:
D. n = 10 or 20 they have the same probability
Victor knows that 2 + 7 = 7 + 2 and 2.7= 7.2.
He wonders if 27 = 72.
Fill in the blanks to explain whether 2 = 72.
Answer:
No 27 does not equal 72
Step-by-step explanation:27 is not even an even number but 72 is
Factor 24x – 18 using the GCF
Answer:
24x – 18
6(4x-3)is required factor.
Will mark brainliest!!Solve for x and round to nearest tenth
Answer:
ok we know the box means 90 degrees and one corner is 63 degrees so in order to get 180 degrees we add 90+63 which is 153 then we take that away from 180 so the answer is 17
You are driving up a mountain. At the base of the mountain you see a sign that states the elevation above sea level is 3,720 feet at this point. You then travel a horizontal distance of 5 miles to the top of the mountain, and see another sign that states the elevation is 4,215 feet above sea level. What was the average slope of the mountain you just climbed in feet/mile?
A) 843 ft/mi
B) 744 ft/mi
C) 99 ft/mi
D) 0.0188 ft/mi
Step-by-step explanation:
Slope of the mountain
= Rise in height / Run in distance
= (4215ft - 3720ft) / 5 mi
= 495ft / 5mi
= 99ft/mi. (C)
Please solve the question below 5
Answer:
Answer is B
Step-by-step explanation:
P(x<2) - P(x<-2) = .9772 - .0228 = .9544
= 95%
PLEASE HELP DUE SOON FIRST GOOD ANSWER GETS BRAINLIEST
show that x^2 + y^2 + z^2 = 3(2x-y) -1 is a sphere
Step-by-step explanation:
x² + y² + z² = 3(2x - y) - 1
x² + y² + z² = 6x - 3y - 1
x² - 6x + y² + 3y + z² = -1
(x - 3)² + (y + 1.5)² + z² = -12.25
(x - 3)² + (y + 1.5)² + z² = -(3.5)²
Since it follows the general equation form, it is a sphere.
Tell whether each angle is acute, right, obtuse, or straight.
Answer:
Right
Straight
Obtuse
Acute
IN THE ORDER YOU PUT THE PICTURE!!
Step-by-step explanation:
Answer:
The First is right, Second is Straight, Third is Obtuse and, Forth is Acute
Step-by-step explanation:
I am smart
Josie packed unit cubes into a prism, as shown. Which statement about the volume of the box is true?
Also so, the answer to this is; The volume of the prism is less than 72 cubic units.
Why is this the answer?
The actually cubic units for that is actually 54 cube units which if you think is; 54 < 72
So I hope this helps. I wasn´t able to see the image but according to what I know, I think it is in one of the imagine math or something else lessons. If what im telling has nothing to do with your question, I am sorry and- I guess thats that. I really hope this helps. Bye!! ^m^
Answer:
The volume of the prism is less than 72 cubic units.
Here's what I did:
6x3x3
Which is length x height x width or it can be the other way around it really doesn't matter I think