Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Hoped this helped!
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MCR3U1 Culminating 2021.pdf
#7.
A colony of bacteria is introduced into a growth medium. Its initial population
size is 350 thousand. 12 hours later, the colony has grown to a size of
800 thousand. If its population size increases exponentially, determine:
(a)
the exponential growth model for the size of the population Alt), after
t hours.
(b)
the population size after (i) 8 hours and (ii) 24 hours.
(c)
the rate of increase in the population size as a %/hour
(d)
the doubling time of the bacteria population.
Answer:
(a) [tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is 607,325
(ii) The population after 24 hours is 1,828,643
(c) The rate of increase of the population as a percentage per hour is 7.132%
(d) The doubling time of the population is approximately, 10.06 hours
Step-by-step explanation:
(a) The initial population of the bacteria, y₁ = a = 350,000
The time the colony grows, t = 12 hours
The final population of bacteria in the colony, y₂ = 800,000
The exponential growth model, can be written as follows;
[tex]y = a \cdot (1 + r)^t[/tex]
Plugging in the values, we get;
[tex]800,000 = 350,000 \times (1 + r)^{12}[/tex]
Therefore;
(1 + r)¹² = 800,000/350,000 = 16/7
12·㏑(1 + r) = ㏑(16/7)
㏑(1 + r) = (㏑(16/7))/12
r = e^((㏑(16/7))/12) - 1 ≈ 0.07132
The model is therefore;
[tex]y = 350,000 \times (1 + 0.07132)^t[/tex]
(b) (i) The population after 8 hours is given as follows;
y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82
By rounding down, we have;
The population after 8 hours, y = 607,325
(ii) The population after 24 hours is given as follows;
y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571
By rounding down, we have;
The population after 24 hours, y = 1,828,643
(c) The rate of increase of the population as a percentage per hour = r × 100
∴ The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%
(d) The doubling time of the population is the time it takes the population to double, which is given as follows;
Initial population = y
Final population = 2·y
The doubling time of the population is therefore;
[tex]2 \cdot y = y \times (1 + 0.07132)^t[/tex]
Therefore, we have;
2·y/y =2 = [tex](1 + 0.07132)^t[/tex]
t = ln2/(ln(1 + 0.07132)) ≈ 10.06
The doubling time of the population is approximately, 10.06 hours.
Using the diagram below, which of the following parts of the triangles are
congruent?
Answer:
C.
Step-by-step explanation:
ACE is a straight line that connects to line AB and line DE.
AB & ED have same gradient which mean that it is parallel.
The parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)
What is congruent triangle?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the otherCongruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles.How to solve this problem?The steps are as follow:
As ACE is a straight line which connects to line AB and DEAlso the line AB and ED are parallel because their gradient are sameSo from above mention two reasons we can say that their is congruence between angle A and angle ESo the parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)
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The probability that a newborn baby at a certain hospital is male is 50%. What is the probability that exactly 2 out of 3 babies born in the hospital on any given day are male?
Answer:
50/50 bc you dont know until he/she is born
The requried probability that exactly 2 out of 3 babies born in the hospital on any given day are male is 0.375 or 37.5%.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
This is a binomial probability problem with n = 3 (three babies) and p = 0.5 (probability of a baby being male).
The probability of exactly 2 out of 3 babies being male can be calculated using the binomial probability formula:
[tex]P(X = 2) = (n choose X) * p^X * (1 - p)^{(n - X)}[/tex]
where "n choose X" is the binomial coefficient, equal to n! / (X! * (n - X)!) and X is the number of successes (in this case, 2).
Substituting the values, we get:
[tex]P(X = 2) = (3 choose 2) * 0.5^2 * (1 - 0.5)^{(3 - 2)}[/tex]
= 3 * 0.25 * 0.5
= 0.375
Therefore, the probability that exactly 2 out of 3 babies born in the hospital on any given day are male is 0.375 or 37.5%.
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the volume of a cuboid is 480cm cube,it's breadth and height are 8cm are 6cm respectively find its length
Avery goes out to lunch. The bill, before tax and tip, was $9.80. A sales tax of 6% was added on. Avery tipped 19% on the amount after the sales tax was added. What was the total cost of the meal, plus tax and tip? Round to the nearest cent.
Answer:
12.36
Step-by-step explanation:
price x sales tax rate =sales tax
9.80 x .06=sales tax
.59=sales tax
price + sales tax=price with sales tax included
9.80+.59=10.39
price with sales tax x tip percentage=tip amount
10.39 x .19=1.97
price with sales tax + tip = total amount
10.39+1.97=12.36
the sum of a number and 12 is 31. Inches hat is the number?
Answer:
n+12=31
n=31-12
n=19
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
if the angle of elevation of the sun is 40 degrees, and is decreasing 1/3 radians/hour how fast is the shadow of a 35m tall pole lengthening?
[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr}[/tex]
Step-by-step explanation:
Let y = height of the pole = 35 m (constant)
x = length of the shadow
They are related as
[tex] \tan \theta = \frac{y}{x} [/tex]
or
[tex]x = \frac{y}{ \tan\theta } = y \cot \theta[/tex]
Taking the time derivative of the above expression and keeping in mind that y is constant, we get
[tex] \frac{dx}{dt} = y( - \csc^{2} \theta) \frac{d \theta}{dt} [/tex]
Before we plug in the numbers, let's convert the degree unit into radians:
[tex]40° \times ( \frac{\pi \: rad}{180°}) = \frac{2\pi}{9} \: radians[/tex]
Since the angle is decreasing, then d(theta)/dt is negative. Therefore, the rate at which the shadow is lengthening is
[tex] \frac{dx}{dt} = (35 \: m)( - \csc^{2} \frac{2\pi}{9} )( - \frac{1}{3} \frac{rad}{hr} )[/tex]
or
[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr} [/tex]
Factor the common factor out of each expression: 30+6k+18k^5
Round the answer to the nearest hundredth
tan= opp/adjacent
tan= 9/3
tan^-1 (9/3) =72°
A total of 937 people attended the play.
Admission was $2.00 for adults and $0.75
for students. The total ticket sales
amounted to $1,109. How many students
and adults attended the school play?
Answer:
612 adults & 361 students
Step-by-step explanation:
The batting averages for five baseball players are listed below.
0.125, 0.312, 0.256, 0.287, 0.193
What is the mean absolute deviation of the batting averages?
OA
0.2346
OB. 0.256
C. 0.06048
D. 0.187
Reset
Next Question
Answer:
A. 0.2346
Step-by-step explanation:
add all of the batting averages and divide by 5 (bc there are 5 of them)
Choose the number sentence that illustrates the distributive property of multiplication over addition.
a.) 3 × (4 + 6) = (3 × 4) + (3 × 6)
b.) 3 × (4 + 6) = (3 + 4) × (3 + 6)
c.) 3 × (4 + 6) = (3 × 4) + 6
Answer:
A. LHS,
3×(4+6)
3×10
30
NOW,
RHS,
(3×4)+(3×6)
12+18
30
Therefore, A is ans
Can someone help please ?!
Step-by-step explanation:
53 is the correct answer
can someone please help for brainlest
Answer:
3:1
Step-by-step explanation:
It’s three times the original
Which of the equations below could be the equation of this parabola?
Answer:
D
Step-by-step explanation:
The parabola opens to the right
therefor it will be of the form x = +y^2
Consider the diagram.
What is the length of segment AB?
9
16
ОООО
18
B)
9
С
Answer:its 9
Step-by-step explanation: got it right on edge
what is the value of b
Answer:
Step-by-step explanation:
b is an inscribed angle. The rule for this is that the measure of an inscribed angle is half the measure of the arc it intercepts. The arc it intercepts is 56 degrees, so the measure of angle b is half of that at 28
QUESTION 2
Simplify the following
a5×a7
Answer:
[tex]a^{12}[/tex]
Step-by-step explanation:
Identity Used : [tex]a^x \times a^y = a^{x+ y}[/tex]
[tex]a^5 \times a^7 = a^{5 + 7} = a^{12}[/tex]
The incubation time for hummingbird eggs is approximately normal and has a mean of 16 days and standard deviation of 2 days. Let x = the length of hatching times find p(1518days)
Answer:
0.5328 = 53.28% probability that the length of hatching times is between 15 and 18 days.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 16 days and standard deviation of 2 days.
This means that [tex]\mu = 16, \sigma = 2[/tex]
Probability that the length of hatching times is between 15 and 18 days.
This is the p-value of Z when X = 18 subtracted by the p-value of Z when X = 15. So
X = 18
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 16}{2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413
X = 15
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 16}{2}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085
0.8413 - 0.3085 = 0.5328
0.5328 = 53.28% probability that the length of hatching times is between 15 and 18 days.
4. There are 10 people in a room. If everyone high fives everyone else exactly once, how many hig flves took place in the room?
Answer:
45
Step-by-step explanation:
Let's do it for smaller numbers first.
0 people -> 0 high fives
1 people -> 0 high fives
2 people -> 1 high fives
3 people -> person 1 high fives 2 then 3
And person 2 high fives 3
->2+1= 3 high fives
4 people -> person 1 high fives 2,3, then 4
And person 2 high fives 3 then 4
And 3 high fives 4
->3+2+1=6
5 people -> person 1 high fives 2,3,4, then 5
And person 2 high fives 3,4, 5
And 3 high fives 4,5
And 4 high fives 5
-> 4+3+2+1=10
So for n people there would be (n-1)+(n-2)+....+3+2+1 high fives or (n-1)n/2 people.
Test:
3 people -> (3-1)3/2=(2)3/2=3
4 people -> (4-1)4/2=(3)4/2=6
5 people -> (5-1)5/2=(4)5/2=10
10 people-> (10-1)10/2=(9)10/2=90/2=45
or you could do 9+8+7+6+5+4+3+2+1 which also gives 45.
The other person has a great answer. Here's another approach.
Let's say we're selecting 2 people to fill slots A and B.
Slot A has 10 choices and slot B has 9 choices (since we can't pick the same person again to fill both slots simultaneously).
We have 10*9 = 90 ways to do this if order mattered.
However, we don't care about the order so we actually have 90/2 = 45 ways
---------------------------
Put another way: we can form a table that has 10 rows and 10 columns.
This table has 10*10 = 100 cells inside it.
Cross off the main diagonal that runs from the upper left corner to the bottom right corner. Any of these cells represent a certain person handshaking with themself, which we don't consider.
We cross of 10 items along this diagonal so we have 100-10 = 90 cells leftover.
Now consider that person A shaking with B can be notated as AB. This is identical to BA because the order doesn't matter. So we have twice as many handshakes counted.
That's why we divide by 2 to go from 90 to 90/2 = 45
-----------------------------
Another way to find the answer is to use the nCr combination formula with n = 10 and r = 2.
Yet another way to find the answer is look at Pascal's triangle. Find the row that has 1,10,45... in it at the start. These values correspond to r = 0, 1 and 2 respectively. We can see that 45 is when r = 2, which means we have 2 people shaking hands and there are 45 ways to have ten people shake hands.
So there are many approaches you can take with this problem.
39.76÷7.94
use compatible numbers and estimate
Answer:
5
Step-by-step explanation:
As for estimation, you may round 39.76 to the whole number, resulting in 40.
7.94 to 8
40 / 8 = 5
5 is your answer for the result of estimation
for the following right triangle find the side length 19,12 x. Round the nearest hundredth
Answer:
Step-by-step explanation:
c^2 - a^2 = b^2
19^2 - 12^2 = b^2
361 - 144 = 217
[tex]\sqrt{217\\}[/tex] = 14.7309198627
Round to the nearest hundredth = 14.73
Hope this helps!
Point A is located at (−4,2) and point B is located at (0,5).Find AB to the nearest tenth.
Answer:
The length of line segment AB is 5.
Step-by-step explanation:
Envision a right triangle that has one acute vertex at (-4, 2) and the other at (0, 5). The horizontal distance from the first to the second vertex is 0 - (-4) = 4, and the vertical distance is 5 - 2 = 3.
Then the length of the hypotenuse, according to the Pythagorean Theorem, is
d = √(4² + 3²) = 5
The length of line segment AB is 5. Note that this is a 3-4-5 triangle, and so 3² + 4² = 5²
Enter the slope-intercept equation of the line that has slope 12 and yintercept (0, 3).
Answer:
y= 12x+3
Step-by-step explanation:
The slope-intercept equation is basically y=mx+b
m is the slope and b is the intercept.
Plug the numbers in for those 2 and there's your answer :)
Answer:
y = 12x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 12 and c = 3 , then
y = 12x + 3
helppp plzzzz i need this asap!!!!!! i need the domain and range
WILL GIVE BRANLIEST! pls help ty! ( ignore the selected answer i just pressed one on accident )
Answer: It's C basically they just have to mirror each other, i hope i helped
Step-by-step explanation:
Answer: I believe the answer is D.
Step-by-step explanation:
Which of the following expressions is undefined
cot180°
sec0°
csc(-90°)
Answer:
Step-by-step explanation:
cot x = adjacent side / opposite side
So cot 180 = x / 0 which is undefined.
Question
Lila has $40 in a savings account that earns 10% interest, compounded annually.
To the nearest cent, how much interest will she earn in 2 years?
Answer:
$40.8
Step-by-step explanation:
Use the formula
n(1+percentage given/100)[tex]x^{of the given year}[/tex]
PS: the x means nothing just wanted to show you it is an indices
40(1+10/100)^2
40x1.01^2=$40.80
Kendra is saving to buy a new computer write an expression to represent them out of money she will have if she has a dollar saved and adds D dollar per week for the next 12 weeks
A and B can fill a cistern in 4 hours. A and C can fill
the same cistern in 5 hours. B can fill twice as fast as
C. Find how long C would take to fill the cistern.
Step by step explanation please.
Answer:
20 hours
Step-by-step explanation:
We can work easier if we think in terms of an hour
the first equation that we can write is
A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)
the second equation we can write is
A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)
the third equation that we can write is
B = 2C (its meaning is that in an hour B fill 2 times C the cistern)
now we can substitute the value of B in the first two equations
A + 2C = 1/4
A + C = 1/5
A = 1/5 - C
1/5 - C + 2C = 1/4
C = 1/4 -1/5
C = (5-4)/20
C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)
A = 1/5 - 1/20
A = (4-1)/20 = 3/20
B = 1/20 *2 = 1/10
A and B can fill a cistern in 4 hours. A and C can fill the same cistern in 5 hours and C would take to fill the cistern 20 hours
We can work easier if we think in terms of an hour
The first equation that we can write is
What is the first equation?A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)
The second equation we can write is
A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)
The third equation that we can write is
B = 2C (its meaning is that in an hour B fill 2 times C the cistern)
now we can substitute the value of B in the first two equations
A + 2C = 1/4
A + C = 1/5
A = 1/5 - C
1/5 - C + 2C = 1/4
C = 1/4 -1/5
C = (5-4)/20
C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)
A = 1/5 - 1/20
A = (4-1)/20 = 3/20
B = 1/20 *2 = 1/10
A and B can fill a cistern in 4 hours. A and C can fill the same cistern in 5 hours and C would take to fill the cistern 20 hours.
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