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For the image below, which action below allows the scale to be balanced?


A) Add 3 blocks to the right side

B) Add 4 blocks to the right side

C) Take away 3 blocks to the left side

D) Take away 5 blocks to the left side

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.

[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]

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

tan= opp/adjacent

tan= 9/3

tan^-1 (9/3) =72°

Answer:

3:1

Step-by-step explanation:

It’s three times the original

Answer:

A. LHS,

3×(4+6)

3×10

30

NOW,

RHS,

(3×4)+(3×6)

12+18

30

Therefore, A is ans

Step-by-step explanation:

53 is the correct answer

Answer:

D

Step-by-step explanation:

The parabola opens to the right

therefor it will be of the form x = +y^2

Answer:

A. 0.2346

Step-by-step explanation:

add all of the batting averages and divide by 5 (bc there are 5 of them)

Answer:

Step-by-step explanation:

cot x = adjacent side / opposite side

So cot 180 = x / 0 which is undefined.

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)

The steps are as follow:

So the parts of triangles which are congruent is ∠A ≅ ∠E which is option (C)

Learn more about Congruent triangle here:

https://brainly.com/question/1675117

#SPJ2

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:

Step-by-step explanation:   6  22  22  51

one orange box is 10  the other box looks like 15

the scale factor is 15/10  or 1.5

the smaller triangle blue box is a 4

multiply 4 by the scale factor  1.5

  4 × 1.5  = 6

Answer:its 9

Step-by-step explanation: got it right on edge

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

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

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%.

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%.

Learn more about probability here:

brainly.com/question/14290572

#SPJ3

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.

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.

Answer:

A, c, d

Step-by-step explanation:

Answer:

C & D

Step-by-step explanation:

In order to find the perimeter, we would need to add all the sides. w+L+w+L would be adding the lengths and the widths. Simplifying this, we would get 2w, because there are 2 sides that are the same width, and 2 sides that are 2 lengths.

w+L+w+L or w+w+L+L or 2w+2L

Hope this helps!

--Applepi101

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!

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

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]

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

Answer:

612 adults & 361 students

Step-by-step explanation:

Answer:

n+12=31

n=31-12

n=19

Step-by-step explanation:

Answer:

19

Step-by-step explanation: