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.​

Answers

Answer 1

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.


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 can someone pls help for brainlest

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Answer:

[tex]surface \: area = area \: of \: base + area \: of \: the \: 4 \: triangular \: faces \\ = (l \times w) + 8 \times ( \frac{1}{2} \times base \times height) \\ = (4 \times 4) + 8 \times ( \frac{1}{2} \times 2 \times 7) \\ = 16 + 56 \\ = { \boxed{72}} \: square \: millimeters[/tex]

The answer is 73 i think

Mr. Dominguez wrote the formula below to calculate o, the acceleration of his motor.
V-S
а
t-b
Solve Mr. Dominguez's formula for t, the final time.

Answers

Answer:

t = {(v - s) + ab} / a

Step-by-step explanation:

a = (v - s) / (t - b)

Make t the subject of the equation

a = (v - s) / (t - b)

Cross product

a * (t - b) = (v - s)

at - ab = (v - s)

Add ab to both sides

at = (v - s) + ab

t = {(v - s) + ab} / a

A 200 foot long zipline cable is attached to the top of a tree and extends to an anchor on the ground. The cable makes an angle of 61º with the ground. Calculate how far away the foot of the cable is to the base of the tree.

Answers

Answer:

~ 97 ft

Step-by-step explanation:

cos = adj/hyp

cos61 = adj/200

200 * cos61 = adj

adj = 96.961924049267406

~ 97 ft

The foot of the cable is 95 feet away from the base of the tree.

What is Trigonometric Function?

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of the sides of the triangle.

We have,

The angle between the ground and the cable is given as 61º.

In a right triangle, the side opposite the angle (in this case, the height of the tree) is related to the hypotenuse (the length of the cable) and the adjacent side (the distance from the foot of the cable to the base of the tree) by the trigonometric function cosine.

Cosine(angle) = adjacent/hypotenuse

Cos(61º) = adjacent/200 ft

adjacent = Cos(61º)x200 ft

adjacent ≈ 0.475 x 200 ft

adjacent ≈ 95 ft

Therefore, the foot of the cable is 95 feet away from the base of the tree.

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Which line is the correct graph for y = -3/4x
A/ blue line
B/ purple line
C/ green line
D/ red line

Answers

Answer:D

Step-by-step explanation:

Which scenario could be represented by the algebraic expression n minus 13?

Answers

I don’t. Know either

The vertices of quadrilateral DEFG are D(-2, 6), E(-4, 6), F(-6, 9), and G(-1, 9). Find the coordinates of the image of quadrilateral DEFG after a translation using the rule (x, y) → (x + 1, y - 6), a reflection over the x-axis, and a reflection over the y-axis

Answers

Answer:

the coordinates from all of the transformations are (1,0) (3,0) (5,-3) (0,-3)

Step-by-step explanation:

after using the first rule the coordinates were (-1,0)(-3,0)(-5,3)(0,3)

after reflectiong it over the x-axis (-1,0)(-3,0)(-5,-3)(0,-3)

after reflecting it over the y-axis it gave the final answer of (1,0) (3,0) (5,-3) (0,-3)

The expression 2x+(x-7)^2 is equivalent to x^2+bx+49 for all values of x.
what is the value of b?
A. 12
B. -12
C. 14
D. -14

Answers

The answer is option B

The expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].

Then Value of b is - 12.

Option(B) is correct answer.

What is an expression?

An expression is a mathematical phrase combining numbers and/or variables using mathematical operations. Both sides of an equation are expressions.

According to the question,

The expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].

[tex]2x+(x-7)^{2}=x^{2} +bx+49[/tex]

[tex]2x+(x-7)^{2}=x^{2} +bx+49[/tex]

[tex]2x+x^{2} -14x+49=x^{2} +bx+49[/tex]

[tex]x^{2} -12x+49=x^{2} +bx+49[/tex]

[tex]-12x=bx[/tex]

[tex]b=-12[/tex]

∴  [tex]b=-12[/tex]

Hence, the expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].

Then Value of b is - 12.

Option(B) is correct answer.

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Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

Answers

56.7!!!!!!!!!!!!!!!!!!!!

if CH CD and DG CD, then CH ? DG.

Answers

Answer:

The answer is A

Step-by-step explanation:

If two lines are perpendicular to that same line, then they are parallell.

A is the answer to your question.

Twins Isaac and Isaiah were just born. Isaac weighs 666 pounds 222 ounces and Isaiah weighs 555 pounds 444 ounces.
How many ounces do Isaac and Isaiah weigh together

Answers

The answer is 666 because when you add them together it comes up as 666

Allison measured her rectangular deck and found that it has dimensions of 512 yards by 8 yards. Both the length and the width may have a measurement error of up to 15%. What is the maximum possible area of Allison’s deck, rounded to the nearest thousandth of a square yard?

Answers

Answer:

5416.96 square yards

Step-by-step explanation:

To find the maximum possible area, increase the dimensions by 15%, since the measurement error may be up to 15%.

512(1.15) = 588.8

8(1.15) = 9.2

Find the area using the area formula, A = lw

Plug in the length and width:

A = lw

A = (588.8)(9.2)

A = 5416.96

So, the maximum possible area is 5416.96 square yards

Find the lateral area of a cone with a diameter of 10 centimeters and a slant height of 9 centimeters round to the nearest tenth

Answers

Answer:

The lateral area of a cone is 141.4 square centimeters

Step-by-step explanation:

Mathematically, we have the formula for the lateral area of a cone as;

A = pi * r * l

where r is the radius of the cone and l

is the slant height of the cone

Mathematically, the radius is simply half the measure of the diameter

we have that as 10/2 = 5 cm

So substituting these values;

A = 22/7 * 9 * 5

A = 141.4 square centimeters

can someone please help me with this?? please please please help me

Answers

Step-by-step explanation:

base is 12, hypotenuse is 20

so X² is h²-b²

so X=16

after reading the directions to paint,on the paint drum, the information indicated two coats of paints is required when using the 5 liter paint and one coat with the 20 liter drum. With both paints 1 litre of paint covers 9 meter squared.

There are 28 rooms to be painted.Show with calculations which will be cheaper paint to buy​

Answers

29 rooms left to uncover the paint from the 9 meter squared rooms


Dan sells beaded necklaces. Each large necklace sells for $6.40 and each small necklace sells for $4.80. How much will he earn from selling 7 large necklaces
and 1 small necklace?

Answers

Step-by-step explanation:

my horses are working and in the image above

help please fast 10min left :(

Answers

Answer:

The angle corresponding to angle 4 is angle 8

The cost of 5 kg of mangoes is rupees 147. At what rate per kg are the mangoes
being sold.​

Answers

Step-by-step explanation:

the cost of 1 kg mangoes = 147/ 5

= Rs. 29.40

mark me as brainliest

Answer:

cost of 1 kg mango = rupees 29.4

Step-by-step explanation:

cost of 5 kg mangoes =rupees 147

cost of 1 kg mango =?

Now, lets find cost of 1 kg mangoes

CP od 1 kg mangoes = cost of 5 kg mangoes/5 kg

=rupees 147/5

=rupees 29.4

For the Transformation T write the T-1
T: (x, y) = (x + 4, y + 3)
Т-1 (x, y) -
(x+3, y + 2)
(x-4, y-3)
(x+, y + 3)

Answers

Answer:

(T - 1)(x, y) = (x - 4, y - 3)

Step-by-step explanation:

For a given transformation:

T(x, y) = (x', y')

the inverse transformation is defined by:

(T - 1)(x', y') = (x, y)

So, if our transformation is:

T(x, y) = (x + 4, y + 3)

Then for the inverse transformation, we should have:

(T - 1)(x + 4, y + 3) = (x, y)

So the inverse transformation reduces the x-value by 4, and reduces the y-value by 3.

Writing the inverse transformation for a generic (x, y) point, we get:

(T - 1)(x, y) = (x - 4, y - 3)

100 POINTS HELP! THIS IS A PROJECT. BUT AN ANSWER TOMORROW OR TODAY IS OKAY!


Describe how to find the terms mean, median, mode, and range of a group of numbers then, give examples. Make sure you include the data set (the group of numbers) you will be working with.

Answers

Answer: We will be working with the numbers 1-4, you can change the numbers to anything, just change the math.

The mean is the "average" of a set of numbers. Add up ALL the numbers, and then divide by how many numbers there are.

Ex. 1+2+3+4 then, 10/4 =2.5

The mode is the number that occurs most frequently in a set of numbers.

Ex. 1, 2, 2, 2, 3, 4, 2, 2, 4, : The mode would be 2.

The range is the difference between the smallest and highest numbers.

Ex. 1, 2, 3, 4, ,3, 2, 3, 4, : Put all the numbers in order, then subtract highest from lowest.

1,2,2,3,3,3,4,4

4-3=1 The range would be 1.

Answer:

The median is the middle. You add and divide for the mean. The mode is the one that appears the most. And the range is the difference in between. For example, the median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above. The mean is the average of the numbers.  It is easy to calculate: add up all the numbers, then divide by how many numbers there are.  In other words it is the sum divided by the count. The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode! The difference between the highest and the lowest values in a set. Interval, also called range, a set of real numbers that includes all numbers between any two numbers in the set.

The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2.50 each and bottles of water sell for $1.25 each. The club needs to raise at least $600 to cover the cost of renting costumes. The students can accept a maximum of 460 cans and bottles.

Write a system of inequalities that can be used to represent this situation.

The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer.

Answers

Answer:

Step-by-step explanation:

The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2.50 each and bottles of water sell for $1.25 each. The club needs to raise at least $600 to cover the cost of renting costumes. The students can accept a maximum of 460 cans and bottles.

Write a system of inequalities that can be used to represent this situation.

The club sells 144 cans of lemonade. What is the least number of bottles of water that must be sold to cover the cost of renting costumes? Justify your answer

The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water is the pool?

Answers

Answer:

The height of the water increases 2 inches per minute. Or A

Step-by-step explanation:

Edge

Answer: A ( The height of the water increases 2 inches per minute)


Pls help I have to find the area

Answers

Answer:

28 square units

Step-by-step explanation:

The area of a rectangle is A = l x w.

The length of this rectangle is 7 square units.

The width is 4 square units.

7 x 4 = 28 square units

The equation SA = 6s can be used to calculate the surface area, SA, of a cube with side length S. What is the
surface area, in square meters, of a cube with a side length of 0.5 meter?

Answers

6a2
=6 • 6 = 36
36 sq ft.

y=2x+5
how do i find the x and y coordinates?

Answers

Answer:

for each x, the difference in the y value it has an origin at (0,5)

Step-by-step explanation:

if x equals 0, y equals 5.

if x equals 1, y equals 7 and so on

if x equals -1, y equals -5 and so on.

Answer:

I dont know to be honest I dont remember so yeahmmmm ummmmm

Brainliest goes to whoever answers correctly

Answers

Answer:

The answer is C.

it definitely c because your trying to find what they had spent

Given: m∠ELG = 124°

Prove: x = 28

3 lines are shown. A line with points D, L, G intersects a line with points E, L, H at point L. Another line extends from point L to point F between angle E L G. Angle D L E is (2 x) degrees.
Complete the steps in the two-column proof.

♣:

♦:

Answers

Answer:

clover

Step-by-step explanation:

because

The measure of angle ∠x = 28°.

We have a geometrical figure [Refer to the image attached in the end].

We have to prove that x = 28°.

What is the measure of a Straight angle.

The measure of straight angle is 180°.

According to the question -

Line DLG is a Straight line. Therefore -

2∠x + 124° = 180°

2∠x = 56°

∠x = 28°

Hence Proved.

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determine whether the given lines are parallel or not right with the reason ​

Answers

Answer:

[tex]AB[/tex] is parallel to [tex]CD[/tex] ([tex]AB ||CD[/tex])

Step-by-step explanation:

In a set of parallel lines cut by the traversal, [tex]\angle AHG[/tex] and [tex]\angle DGH[/tex] are alternate interior angles. In a set of parallel lines cut by a traversal, alternate interior angles are always equal. Therefore, since [tex]\angle AHG=\angle DGH=115^{\circ}[/tex] (they are equal), the lines AB and CD must be parallel.

*A set of parallel lines proves that alternate interior angles are always equal, but the converse is also true in that equal alternate interior angles proves a set of parallel lines. This is because if you changed the angle measure of either of the angles, the relative slope of the lines must change and they would no longer be parallel.

Darryl was shopping for a new camera. He found one with an original price of $125.00 and is marked 45% off. Sales tax for the item is 5.2%. What is the final price of the camera, including tax?

Answers

Answer:

$75.25

Step-by-step explanation:

Given data

Original price =$125

Discount =45%

Tax=5.2%

Let us find the discount

45/100*125

0.45*125

56.25

Let us find the tax

5.2/100*125

0.052*125

6.5

Hence the amount is

125-56.25+6.5

=$75.25

PLS ANSWER ASAP PLS DUE AT 9:35

Answers

Answer:

your answer is option B

Answer:

Your answer came out to be B.

christian has a collection of 18 shark teeth he has 6 tiger shark what precentage is tiger​

Answers

Answer:

33.3% I think lpl

Step-by-step explanation:

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