Answer:
In 59 days, the number of bacteria reaches 1000.
Step-by-step explanation:
Given the data in the question;
by placing 100 spores of the bacteria at the start of the project,
p(0) = 100
dP over dt equals the product of 0.05 times P and the quantity 1 minus P over 2000
dp/dt = 0.05p( 1 - p/200 )
2000dp / p( 2000 - p ) = 0.05dt
[1 / p + 1 / 200-p ]dp = 0.05 dt
Now, we integrate
∫[1 / p + 1 / 200-p ]dp = ∫ 0.05 dt
ln p - ln [2000 - p ] = 0.05 + c'
ln[ p / 2000 - p ] = 0.05 + c'
p / 2000 - p = [tex]e^{0.05t + c'[/tex]
p / 2000 - p = k[tex]e^{0.05t[/tex]
Now, since p(0) = 100, we substitute
100 / (2000 - 100) = k[tex]e^{0.05(0)[/tex]
100 / 1900 = k × [tex]e^{0[/tex]
100 / 1900 = k × 1
k = 1 / 19
Therefore,
p / 2000 - p = k[tex]e^{0.05t[/tex]
p / 2000 - p = (1/19)[tex]e^{0.05t[/tex]
when p( t ) = 1000, then t will be;
1000 / (2000 - 1000) = (1/19)[tex]e^{0.05t[/tex]
1000 / 1000 = (1/19)[tex]e^{0.05t[/tex]
1 = (1/19 ) × [tex]e^{0.05t[/tex]
1/(1/19 ) = [tex]e^{0.05t[/tex]
(1 × 19)/1 = [tex]e^{0.05t[/tex]
[tex]e^{0.05t[/tex] = 19
0.05t = ln( 19 )
0.05t = 2.9444
t = 2.9444 / 0.05
t = 58.888 ≈ 59 days
Therefore, In 59 days, the number of bacteria reaches 1000.
4. A zoo is open for 10 1/2 hours every day. There
are two security guards on duty at a time and each
shift is 3 1/2 hours. How many shifts are there per
day?
A. 1 shift
B. 2 shifts
C. 3 shifts
D. 4 shifts
Answer:
C
Step-by-step explanation:
This can come from process of elimination, 1 shift is not enough. 2 shifts, 3 1/2 + 3 1/2 is 7, meaning it still isn't enough. 4 shifts 7 + 7 is 14, making it to much.
Please answer the question correctly with factual information for brainliest.
Juan Hernandez, a Cuban athlete who visits the United States and Europe frequently, is allowed to return with a limited number of consumer items not generally available in Cuba. The items, which are carried in a duffel bag, cannot exceed a weight of 5 pounds. Once Juan is in Cuba, he sells the items at highly inflated prices. The three most popular items in Cuba are denim jeans, CD players, and CDs of U.S. rock groups. The weight and profit (in U.S. dollars) of each item are as follows:
Item Weight (lb.) Profit
Denim jeans 2.1 $40
CD players 3.2 48
Compact discs 0.8 16
uan wants to determine the combination of items he should pack in his duffel bag to maximize his profit. This problem is an example of a type of integer programming problem known as a "knapsack" problem. Formulate and solve the problem.
Answer:
z (max) = 96
x₁ = 2
x₂ = 0
x₃ = 1
Step-by-step explanation:
Fromproblem statement:
weight (lb) . Profit $
Denim jeans 2.1 40
CD players 3.2 48
Compact Discs 0.8 16
Objective Function z is:
z = 40*x₁ + 48*x₂ + 16*x₃ to maximize
Subject to:
Weight constrain: 5 lb
2.1*x₁ + 3.2*x₂ + 0.8*x₃
x₁≥ 0 x₂ ≥ 0 x₃ ≥ 0 All integers
Using AtomZmath on-line solver and after 2 iterations
Solution:
z (max) = 96
x₁ = 2
x₂ = 0
x₃ = 1
The maximized profit is the highest profit Juan can get by selling his items.
The maximized profit is $96
Let x represents the Denim jeans, y represents the CD players and z represent the compact discs.
So, we have the following parameters
Weights
[tex]x = 2.1[/tex]
[tex]y = 3.2[/tex]
[tex]z = 0.8[/tex]
The weight cannot exceed 5 pounds.
So, the constraint is
[tex]2.1x + 3.2y + 0.8z \le 5[/tex]
The profit is given as:
[tex]x = 40[/tex]
[tex]y = 48[/tex]
[tex]z = 16[/tex]
So, the objective function to maximize is
[tex]Max\ Z = 40x + 48y + 16z[/tex]
The integer programming model is then represented as:
[tex]Max\ Z = 40x + 48y + 16z[/tex]
Subject to:
[tex]2.1x + 3.2y + 0.8z \le 5[/tex]
[tex]x,y,z \ge 0[/tex]
Using a graphing calculator, the values that maximize the objective function are:
[tex]x = 2[/tex]
[tex]y = 0[/tex]
[tex]z = 1[/tex]
Substitute these values in the objective function
[tex]Max\ Z = 40x + 48y + 16z[/tex]
[tex]Z = 40 \times 2 + 48 \times 0 + 16 \times 1[/tex]
[tex]Z = 80 + 0 + 16[/tex]
[tex]Z = 96[/tex]
Hence, the maximized profit is $96
Read more about integer programming at:
https://brainly.com/question/13841397
Suppose Hailey has taken four exams and made 86, 94, 76, and 81. If each exam counts equally, what does Hailey need to make on her fifth test to have an overall average of 85?
Answer:
She has to get a score of 88 on that test
Step-by-step explanation:
Take the average of the other grades, and that gives you 84.25. So she has to think about what rating she gives it is 85, and the rating is 88.
Hailey needs to score an 88 on the last exam in order to get an average of 85.
The overall average is the mean and the mean is calculated by adding up all the scores and then dividing by the number of exams.
There are 5 exams but only 4 scores. The 5th score will be denoted, "x" and the average we are looking for is 85.
The fifth score should therefore be:
Overall score = Sum of 5 exams / 5
85 = (86 + 94 + 76 + 81 + x) / 5
85 x 5 = 337 + x
425 = 337 + x
x = 425 - 337
= 88
In conclusion, Hailey needs a score of 88 on the fifth exam.
Find out more at https://brainly.com/question/17031271.
Rayann has 4 bracelets, Jennifer has 8 bracelets, June has 3 bracelets, and Tammy has 5 bracelets. They want to redistribute the bracelets so that each girl has the same number of bracelets. If the bracelets are redistributed, how many should each girl get?
A balance diagram going from 1 to 9. 1 circle is above 3, 4, 5, and 8.
4
5
6
7
Answer:
they will each get 45 bracelets
Step-by-step explanation:
add all the bracelets then divide by the number of girls
Answer:
B= 5
Step-by-step explanation:
took the test
Plz help I've been crying about this question about number 8 plz help with number 8 I'll give brainiest.
Answer: I got ~17% (It's 17% as the problem asked for the answer to be rounded)
Step-by-step explanation:
I added the 12 possible chances from the spinner with the 6 sided die chances. This gets me 18. Since the problem is asking the probability of rolling an 8 or 10 alongside a 3, I did 3/18 and got 16.66% (repeating). I'm not entirely sure if I did this right, but I hope this helped somehow. Let me know if it's not the correct answer.
Find the midpoint of line segment
Step-by-step explanation:
[tex]midpoint = ( \frac{4.9 + - 5.2}{2} , \: \frac{ - 1.3 + - 0.6}{2} ) \\ = ( - 0.15, \: - 0.95)[/tex]
I need help plz I don’t know how to do this
Answer:
(2,4)
Step-by-step explanation:
3x-2(-2)=x
3x-4=x
-4= -2x
x=2
y=3(2)-2
y=6-2
y=4
(2,4)
Find the volume of this sphere.
Use 3 for TT.
V
3
જ
V ~ [?]cm
V = Tr3
10 cm
Enter
9514 1404 393
Answer:
500 cm³
Step-by-step explanation:
The diameter of the sphere is shown as 10 cm, so its radius is 5 cm. Using the given numbers in the given formula, you find the volume to be ...
V = (4/3)(3)(5 cm)³ = 4(125 cm³) = 500 cm³
1
32. A friend plans to purchase a mattress that sells for $1200 at a particular store. The store
is offering 15% off any one mattress. He also has an internet coupon for an additional
10% off any discounted price. How much will your friend save (a) in dollar amount and
(b) in percent
Answer:
(A) Your friend will save $282.
(B) Your friend will get 23.5% off the original price of the mattress.
Step-by-step explanation:
We first need to find out the price of the mattress after the 15% discount. Our first step is to find what 15% of 1,200 is. We can do this by multiplying the two numbers.
1,200 x 15% -----> 1,200 x 0.15= 180.
15% of $1,200 is $180.
Next subtract $180 from $1,200, which equals $1,020. We can now apply the 10% off internet coupon.
1,020 x 10% ------> 1,020 x 0.10= 102.
10% of $1,020 is $102.
Next we subtract $102 from $1,020 and we get $918, the final price of the discounted mattress.
We subtract to see how much money the friend saved.
$1,200 - $918= $282.
We can get the percentage by dividing $282 by $1,200.
282 / 1200= 0.235 decimal form ----> 23.5%
Q.Jason has 3 red pencils and 6 yellow pencils. Which statement is true?
•The number of red pencils is 1/2 times the number of yellow pencils
•The number of red pencils is 2 times the number of yellow pencils
•The number of yellow pencils is 1/2 times the number of red pencils
•The number of red pencils is 3 more than the number of yellow pencils
Answer:
The number of red pencils is 2 times the number of yellow pencils
Please help me with this it is very important to my grade
Answer:
Option B is correct
Step-by-step explanation:
[tex] \sf \longmapsto \: \frac{{x}^{3} - {y}^{3} }{4} \\ \sf \longmapsto \: \frac{ {4}^{3} - {2}^{3} }{4} \\ \sf \longmapsto \: \frac{64 - 8}{4} \\ \sf \longmapsto \: \frac{56}{4} \: \: \: \: \: \: \: \: \\ \sf \longmapsto \: 14[/tex]
What is the equation of a circle with center (-2,3) and radius 4?
A. (x + 2)^2 +(y-3)^2 = 4
B. (x-2)^2 +(y +3)^2= 16
C. (x + 2)^2 + (y - 3)^2 = 16
D. (x+2)^2- (y - 3)^2 - 16
Find the surface area of a triangular pyramid.
Answer:
91in^2
Step-by-step explanation:
SA of base = 7x7 = 49in^2
SA of each triangle = 1/2 x 7 x 3 = 10.5in^2
SA of all 4 triangles = 10.5 x 4 = 42in^2
SA Total = 49 + 42.= 91inch^2
What is the area help fast
Answer:
142.5 cm2
Step-by-step explanation:
The small markings create a new height, so that would be 9.5 cm.
Multiply:
9.5x15=142.5
Therefore, the area is 142.5 cm2
Azul spun a tri-color spinner twice. What is the probability that the spinner landed on the colors blue and green in any order? BB, BG, BY, GB, GG, GY, YB, YG, YY 2 ON 3 Acvate Win Gettings to
Answer:
The Probability that the spinner landed on the colors blue and green in any order = 2/9
Step-by-step explanation:
Given - Azul spun a tri-color spinner twice.
To find - What is the probability that the spinner landed on the colors blue and green in any order?
Solution -
Given that,
A tri-color spinner spun twice
So,
The Sample Space, S = {BB, BG, BY, GB, GG, GY, YB, YG, YY}
⇒n(S) = 9
Now,
Let A be an event that the spinner landed on the colors blue and green
So,
A = {BG, GB}
⇒n(A) = 2
Now,
Probability that the spinner landed on the colors blue and green in any order = n(A) ÷ n(S)
= 2 ÷ 9
∴ we get
The Probability that the spinner landed on the colors blue and green in any order = 2/9
Does anyone know
How to do probability?
Probability is simply how likely something is to happen.
Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
The best example for understanding probability is flipping a coin:
There are two possible outcomes—heads or tails.
What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?P(H)=?P, left parenthesis, H, right parenthesis, equals, question mark.You might intuitively know that the likelihood is half/half, or 50%.
Tips
The probability of an event can only be between 0 and 1 and can also be written as a percentage.
What is −y+9z−16y−25z+4 written in simplest form?
Answer:
[tex] - 17y−16z+4[/tex]
Step-by-step explanation:
[tex] - y+9z−16y−25z+4[/tex]
[tex] - 17y+9z−25z+4[/tex]
[tex] - 17y−16z+4[/tex]
Hope it is helpful....The heights of 4 different people are: 1.55m, 1.52m, 1.81m, and 1.91m. The range of these
heights is:
Miguel makes bags. He can make 8 bags with 2 yards of fabric. Write an equation to represent the yards of
fabric, x, needed to make a certain numbers of bags, y.
2yrds/8= 9 inches
9 inches are needed to make 1 bag
:)
The equation represents the yards of fabric, x, needed to make a certain number of bags, y will be y = 4x.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
2 yards of fabric for 8 bags,
y/x = 8/2 = 4
y = 4x
Hence "The equation represents the yards of fabric, x, needed to make a certain number of bags, y will be y = 4x".
For more information about ratios and proportions,
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Tessellations
Determine whether the given figure tessellates the plane.
a. yes
b. no
Please select the best answer from the choices provided
Answer:
B. No
Step-by-step explanation:
I calculated it logically
Two window washers, Tori and Nathan, lean a ladder against the side of a building so that Tori can wash a window while Nathan holds the ladder. The top of the ladder reaches the window, which is 12 feet off the ground. The base of the ladder is 5 feet away from the building. How long is the ladder?
Answer:
13 feet
Step-by-step explanation:
This is a right triangle problem
Use the Pythagorean Theorem
c² = a² + b²
c² = 12² + 5²
c² = 144 + 25
c² = 169
Take the square root of both sides
c = 13
Select the correct answer. Simplify the following expression. 3^2/5 * 3^-7/5
Answer:
1/6075
Step-by-step explanation:
A circle has an equation (x+2)2+(y−5)2=64. What is 34 of its area.
Answer:
3/4 of the area of the circle is of [tex]48\pi[/tex] squared units.
Step-by-step explanation:
Equation of a circle:
The equation of a circle has the following format:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In which the center is [tex](x_0,y_0)[/tex] and r is the radius.
Area of a circle:
The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
Circle (x+2)² + (y-5)² = 64
Comparing with the standard equation, we have that:
[tex]r^2 = 64[/tex]
Area of the circle:
[tex]A = \pi r^2 = 64\pi[/tex]
What is 3/4 of its area?
[tex]\frac{3A}{4} = \frac{3*64\pi}{4} = 3*16\pi = 48\pi[/tex]
3/4 of the area of the circle is of [tex]48\pi[/tex] squared units.
Presume we have this sack of marbles. There are 4 green marbles, 3 red marbles, 2 blue marbles, and 1 yellow marble.
What is the probability of pulling a red marble, given a blue marble was pulled before without replacement?
Answer:
There is a 33.3% chance you will pull a red marble after pulling a blue one.
Step-by-step explanation:
There are a total of 10 marbles in the sack. A blue marble is removed from the bag without being replaced, leaving 9 in the sack. 3 of the marbles left are red. To find the probability of pulling a red marble, we divide the number of red marbles by the number of total marbles.
3/9 = 1/3 = 0.333 = 33.3%
Chris drops an egg with a parachute from the top of a building. The height, h, in feet, of the egg above the ground after t seconds is given
by h (t) = 100 - 16t2
After how many seconds does the egg hit the ground?
I
Answer:
The egg hits the ground after 2.5 seconds.
Step-by-step explanation:
Height of the egg:
The height of the egg after t seconds is given by:
[tex]h(t) = 100 - 16t^2[/tex]
After how many seconds does the egg hit the ground?
This is t for which [tex]h(t) = 0[/tex]. So
[tex]h(t) = 100 - 16t^2[/tex]
[tex]16t^2 - 100 = 0[/tex]
[tex]16t^2 = 100[/tex]
[tex]t^2 = \frac{100}{16}[/tex]
[tex]t = \sqrt{\frac{100}{16}}[/tex]
[tex]t = \frac{10}{4}[/tex]
[tex]t = 2.5[/tex]
The egg hits the ground after 2.5 seconds.
Please help me!!! I'm being timed right now do please help me!!!
Answer:
The answer would be 2. Which means that your answer would be option 1 I believe.
Step-by-step explanation:
Find the measures of the angles given
Answer:
BCD = 60
ABD - 90
Step-by-step explanation:
BCD)
BC and CD are the same length on in the circle, they are the radius. Therefor, all angles will be the same at 60
ABD)
All angles together are 180
You know 2 Angles, A at 30 and D at 60
180 - 30 - 60 = Angle B
90 = Angle B
Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form.
D
45
53
28
sin D=
sin E=
COS DE
COS E =
Answer:
sin D = 28/53
sin E =45/53
cos D =45/53
cos E =28/53
Mike drinks 2/5 of a litre of juice each day.Juice costs £4.40 for a 2 litre carton and £2.60 for a 1 litre carton.Mike buys enough juice to last for 7 days.What is the lowest price Mike can pay for this juice?Show how you decide.