the number of bacteria in a culture is increasing according to the law of exponential growth. after 3 hours, there are 400 bacteria, and after 6 hours, there are 3,200 bacteria. write an equation that can be used to determine the number of bacteria y in the culture after t hours.

The addition of 113 and -56 using the number line gives the answer as 57.

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The value of the c is obtained as; c = ac/(b + a - 4ab).

A mathematical equation can be defined in a variety of ways. In its most basic form, an equation is a statement that demonstrates that two formulas are equal.

Now, for the given equation in three variables;

(1/a)+(1/b)-(1/c) = 4

Bring the quantity to be find on one side and others on the other side.

1/a + 1/b - 4 = 1/c

Taking LCM on the left hand side.

(b + a - 4ab)/ab = 1/c

Taking the reciprocal on the both side.

c = ac / (b + a - 4ab)

Thus, the solution of the given equation in the terms of the c is;

c = ac / (b + a - 4ab).

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For the given data set the lower quartile is 12 , the median is 15 and the upper quartile is 19 .

In the question ,

the data det is given as {11, 12, 12, 13, 14, 15, 16, 18, 19, 19, 20}

the median is the central value , that is 15.

For lower and upper quartile ,

the set is divided into two halves ,

the lower half is {11,12,12,13,14}

the median of the lower half (lower quartile) = 12

the upper half is {16,18,19,19,20}

the median of the upper half(upper quartile) = 19.

Therefore , for the given data set {11, 12, 12, 13, 14, 15, 16, 18, 19, 19, 20},  the lower quartile is 12 , the median is 15 and the upper quartile is 19 .

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Answer:

44

Step-by-step explanation:

Answer:

k = -1/3

Step-by-step explanation:

1. Simplify by distributing

3k + 15 = -6k + 12

Move -6 onto the left side by adding 6k onto both sides =

9k + 15 = 12

Now subtract 15 on both sides=

9k = -3

Now divide both sides by 9=

k = -1/3

Answer:

k=-1/3

Step-by-step explanation:

3k+15=-6k+12

15-12=-6k-3k

3=-9k

k=-1/3

Permutation P-values should never be zero: calculating exact P-values when permutations are randomly drawn

This is a research paper whose authors are Belinda Phipson , Gordon K Smyth,

Abstract:

Conclusions:

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Quadratic equation for stream of water; (x-6)² = -36/5(y-5)

Using symmetry;

if (0,0) is taken as origin and maximum height is reached by stream at (6,5); the stream will strike the ground at (12,0);

Equation of a parabola whose mouth is open toward negative y- axis;

x² = -4ay

Parabola vertex shifted from (0,0) to (6,5);

(x-6)² = -4a(y-5);

Put x = 0, y = 0, as it lies on parabola;

36 = -4a(-5);

36 = 20a;

a = 36/20;

Quadratic equation for stream of water; (x-6)² = -36/5(y-5);

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The required equation of the line is y = 7x–27.

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The mean will increase by 1.6 miles.

It should be noted that from the information, in two weeks he plans on increasing the distance he runs on Monday and Tuesday by 1 mile, and the amount he runs on Friday, Saturday and Sunday by 2 miles.

The mean will be:

= (1 × 2) + (2 ×3) / 5

= (2 + 6)/5

= 8/5

= 1.6

The mean will increase by 1.6 miles.

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He can make 5 pots of  macaroni and cheese.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Jason uses 3 1/2 cups of uncooked pasta.

He has= 18 1/2 cup of pasta

So, the numbers pots he can make

=18 1/2 ÷ 3 1/2

=37/2 ÷ 7/2

=37/2*2/7

=37/7

=5.28

= 5 pots

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The confidence interval lies between (0.827754, and 1.77225).

What is confidence interval ?

Here, sample mean x = 1.3

sample standard deviation s = 0.45

and sample size n = 6

The 95% confidence interval for the mean waste recycled

= 1.3 - [tex]\frac{0.45}{\sqrt{6} }[/tex] X  [tex]t_{0.025'}[/tex] 1.3 +[tex]\frac{0.45}{\sqrt{6} }[/tex] X [tex]t_{0.025'}[/tex]

= 1.3 - [tex]\frac{0.45}{\sqrt{6} }[/tex] X 2.57058 , 1.3 +[tex]\frac{0.45}{\sqrt{6} }[/tex]X  2.57058

= (0.827754, 1.77225)

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Julie will make 3.5 litres of punch

Julie is making a punch for her birthday

She first pours 2 litres if ginger ale

She then adds 750 millilitres of grape juice

Convert 750 millilitres to litres

750/1000

= 0.75 × 2

= 1.5

Total number of litres= 1.5 + 2

= 3.5 litres

Hence Julie makes 3.5 litres of punch

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Answer:729

Step-by-step explanation:someone else said it

Answer:

plug in the 2 for x so its 2^2+6 2^2 is 4 plus 6 is 10

Step-by-step explanation:

Considering the probabilities of each outcome, it is much more likely that Janet wins than David, hence this is not a fair method.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The 36 total outcomes for the roll of two dice are given as follows:

The number of outcomes in which the sum is less than 6 is:

10.

Hence the probability that David wins is:

p = 10/36.

Janet winning is complementary to David, hence the probability she wins is:

p = 26/36.

From the probabilities, it is much more likely that Janet wins than David, hence this is not a fair method.

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Check the picture below.

The dimensions of the rug which Abdul would use in discuss as described in the task content are; 21.84 ft by 21.84 ft.

It follows from the task content that the dimensions of the rug which Abdul would use in the room in discuss are to be determined.

Since the room Abdul wants to put a rug on is; 775 ft² and the room is a square room.

It follows that all sides of the room are equal and the length of each side can be determined as;

s = √Area; since Area = s².

s = √775

s = 27.839 ft.

Hence, the dimensions of the room is; 27.839 ft by 27.839 ft.

However, since he wants to leave a 3-foot border of bare floor on each side, it follows that the dimensions of the rug on each axis would be;

= 27.839 - 3 -3 = 21.839 ft on all sides.

Consequently, the dimensions of the rug rounded to the nearest hundredth are; 21.84 ft by 21.84 ft.

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Height of the tree is 16ft

There is a tree and a wall.

height of the wall = 4ft

Base of the wall = 6ft

tanθ for wall = height of the wall/Base of the wall

                     =  4/6

                     = 2/3

Height of the tree be h

base of the tree = 24ft

tanθ for tree= h/24

tanθ for wall = tanθ for tree

2/3 = h/24

h=(2/3)(24)

 = 16ft

Height of the tree is 16ft.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or between a base and something above it. Height is something measured vertically, whether it is high or low.

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The slope of the line is: 1.

Slope of a line (m) = rise of the line / run of the line.

Given the line in the diagram, the image attached below shows the run of the line, which is the blue line, and the rise of the line, which is the red line.

Rise of the line = 2 units

Run of the line = 2 units

Slope of the line = 2/2

Slope of the line = 1

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Value of cos(x+π) = [tex]\bold{\frac{\sqrt{3} }{2}}[/tex]

Given cosine of x = [tex]-\frac{\sqrt{3} }{2}[/tex]

i.e., cos(x) =  [tex]-\frac{\sqrt{3} }{2}[/tex]

Also cos([tex]\frac{\pi}{6}[/tex]) =  [tex]\frac{\sqrt{3} }{2}[/tex]. So x = [tex]\frac{\pi}{6}[/tex].

We need to find cos(x+π) = cos([tex]\frac{7\pi}{6}[/tex]).

But its value is not easy to find. So we use trigonometric formulas.

We have the trigonometric formula, cos (x+π) = - cos(x) = -  [tex]-\frac{\sqrt{3} }{2}[/tex] =  [tex]\bold{\frac{\sqrt{3} }{2}}[/tex]

Cos(x+π) lies in the 3rd quadrant. So there cosine has negative values. That is why, cos (x+π) = - cos(x).

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Step-by-step explanation:

[tex] = \sqrt{a} \times \sqrt[3]{a} \\ = {a}^{ \frac{1}{2} } \times {a}^{ \frac{1}{3} } \\ = {a}^{ \frac{1}{3} + \frac{1}{2} } \\ = {a}^{ \frac{5}{6} } [/tex]

I CONVERTED THE TERMS TO BE IN A POWER FORM TO SOLVE THIS EASILY

AND USED THE LAW OF EXPONENT..MULTIPLYING POWERS OF THE SAME BASE WE KEEP ONE BASE AND ADD THE EXPONENTS.

The fraction of his salary  he does save is 3/10, on the basis that Mr. Sid spends 2/5 of his salary on food and 3 10 of the remaining on house rent

What fraction of total salary is saved?

The fraction of the salary saved means the proportion of total salary that is neither spent on food nor on house rent, it can determined as the total salary minus the fractions spent on food and house rent respectively

If assume that the total salary is 1, when deducting 2/5 and 3/10 from 1 we can determine the part that is saved

savings=1-(2/5)-(3/10)

if lcm is 50, we would have the below

savings=(50-20-15)/50

savings=15/50

savings=3/10

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1) 72 + 18 =90. Therefore the angles are complementary angles

2) Angles one and two are a pair of opposite angles made by two intersecting lines. Those are called vertical angles.

3) Those two are right angles, and two right angles add up to 180. So they are right angles and supplementary angles.

4) Adjacent angles

5) Vertical angles and supplementary (because both are right angles)

6) Right angles, supplementary, linear, adjacent angles.

7) Complementary and adjacent angles.

8) Angle of a straight line is 180. So 180-21 should equal x. x=159

9) As stated in number 2, vertical angles are congruent. x=129

10) 38 and x are complementary angles. (it shows a box on the angle formed by both of them, which means it is a right angle.) 90-38 = 52

11) Vertical angle rule. y = 93. The sum of 93, y, x, and z is 360, because the degree of a full circle is 360 degrees. so, 360-93-93 is 174. However, because of the vertical angle rule we will know that x=z. so 174/2 is 87.

x=87 and z=87

12) If you read the question, it states m∠PQR is 147, and ∠PQR is consisted of 119 and x. So, 147-119 is x. x=28

13) W and 34 are linear angles. Linear angles add up to 180 degrees. So, 180-34. w=146. Angle x is labeled with a box at the vertex of the angle. That indicates it is a right angle. x=90. The angle formed with 34 and z is labeled with a box at the vertex, indicating 34+z is 90. Therefore, 90-34=z. z=56. Finally, because angle x is linear with angle (y+z), we will know that y+z is equal to 90. Therefore, y+z=90, y+56=90, y=90-56, y=34

14) We are given that m∠AEC is 41. ∠AEC and ∠AED are linear angles. So, m∠AED = 180-41. m∠AEC=139

15) ∠DEF is a right angle, indicated by the box label at the vertex. ∠DEF and ∠CEF are linear angles, therefore m∠CEF = 180-90. m∠CEF=90

16) ∠DEB and ∠AEC are vertical angles. Therefore m∠AEC and m∠DEB are equal. ∠DEB=41

17) ∠DEB and ∠BEF form a right angle together. In question 16 we confirmed that m∠DEB is 41. Therefore m∠BEF is equal to 90-41.

m∠BEF=49

18) In question 15 we confirmed that m∠CEF is 90, and in question 17 we confirmed that m∠BEF is 49. So m∠CEB must be 90+49. m∠CEB=139

19) In question 15 we confirmed that m∠CEF is 90, and the direction states m∠AEC is 41. Therefore m∠AEF is 90+41. m∠AEF=131

20) Vertical angles are congruent. Therefore ∠PQR is the same degree measure as ∠SQT. m∠PQR=109

21) Complementary angles add up to 90. Therefore ∠2+∠3 = 90. And it is given that ∠2=24. Therefore ∠3 = 90-24.  ∠3=66

22) Supplementary angles add up to 180. Therefore ∠K+∠L= 180. And it is given that ∠K=56. Therefore ∠L = 180-56.  ∠L=124

The sum of the radii of the two circles C₁ and C₂ is 4 units

Given data

Two circles C₁ and C₂ have their centres at the point (3,4)

The centre of C3 is at the point (0,0) and its radius is 2

And C1 and C2 is touching C3

Since the two circles have same centre and touch a third circle at same point, The two circles have equal radius r

The distance, d from the origin using point x and y given is solved for as follows:

d^2 = x^2 + y^2

d^2 = 3^2 + 4^2

d^2 = 9 + 16

d^2 = 25

d = √25

d = 5

Radius if the two circles is 5 - 3 = 2

One of the radius is 2 hence sum of the two radii

= 2 + 2

= 4 units

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Answer:

m = - 1 and b = - 4

Step-by-step explanation:

the equation of a line in slope= intercept form is

y = mx + b (m is the slope and b the y- intercept )

here slope m = - 1 , then

y = - x + b ←  is the partial equation

to find b substitute (- 3, - 1 ) into the partial equation

- 1 = 3 + b ⇒ b = - 1 - 3 = - 4

y = - x - 4 ← equation of line

with m = - 1 and b = - 4

Answer:

d-7 would be the equation. If you don't know what D is, use the variable "D"