Please help simplify the expression

Answer:

k=.25068

Step-by-step explanation:

450 = 100 [tex]e^{6k}[/tex]

4.5 =   [tex]e^{6k}[/tex]

ln(4.5) = 6k

k= ln(4.5)/6

k=.25068

The number of bacteria after 13 hours will be 2579.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

Given that a biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favourable growth medium. Six hours later, he measures 450 bacteria.

The bacteria after 13 hours will be calculated as,

[tex]N=100(e)^{13\times 0.25)[/tex]

[tex]N = 100\times e^{3.25}[/tex]

N = 2579.

Therefore, the number of bacteria after 13 hours will be 2579.

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Answer:  Choice C) integers from 1 to 10 inclusive

==============================================================

Explanation:

The "U" means "set union". We form a larger set that contains any number that's in set A, set B, or both.

So,

A U B = {stuff from set A,  stuff from set B}

A U B = {1,3,5,7,9,       2,4,6,8,10}

A U B = {1,2,3,4,5,6,7,8,9,10}

A U B = set of integers from 1 and 10 inclusive

That makes choice C the final answer.

Choice B is very close to it, but that verbally describes the set {2,3,4,5,6,7,8,9} which leaves out 1 and 10. The "inclusive" makes sure to involve the endpoints 1 and 10, as well as everything in between.

Given:

The expressions are [tex](x+1),\ (x-1)[/tex] and [tex](x^2-1)[/tex].

To find:

The least common multiple of given expressions.

Solution:

The expressions are [tex](x+1),\ (x-1)[/tex] and [tex](x^2-1)[/tex]. The factor forms of these expressions are:

[tex](x+1)=1\times (x+1)[/tex]

[tex](x-1)=1\times (x-1)[/tex]

[tex](x^2-1)=(x-1)(x+1)[/tex]                 [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

The least common multiple is the product of all distinct factors with its highest degree. So,

[tex]L.C.M.=1\times (x+1)\times (x-1)[/tex]

[tex]L.C.M.=(x+1)(x-1)[/tex]

[tex]L.C.M.=x^2-1^2[/tex]                [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]L.C.M.=x^2-1[/tex]

Therefore, the least common multiple of given expressions is [tex]x^2-1[/tex].

Answer:

6

Step-by-step explanation:

sqrt(36)

sqrt(6^2)

6

Answer:

6

Step-by-step explanation:

18 * 2 = 64

√64 = 6

Answer:

[tex]{ \tt{ = 2 \frac{1}{2} }} \\ \\ = \frac{5}{2} \\ \\ { \tt{ = 2.5}}[/tex]

Option c is correct formula

Answer:

Yes they are congruent and it is explained below

Step-by-step explanation:

There are 5 postulates when testing for congruency and they are;

SSS, SAS, ASA, AAS and HL.

S represents side

A represents angle

H represents hypotenuse

L represents leg

Now, in this our question, we can see that the 3 angles and the three sides of both triangles are equal to each other.

Thus, we can make use of SSS postulate whereby we say the 3 sides of the first triangle are equal to the 3 sides of the second triangle.

Thus, they are congruent.

Answer:

3.3 m

Step-by-step explanation:

the height = 2/3 × 5 = 10/3 = 3.3 m

Please delete my answer. I made a mistake

Answer:

X'(-3, -2), Y'(-5, 1), and Z'(2, -3)

Answer: 13 dots

Step-by-step explanation:

You're basically adding 4 each time around, so number 1 is 1 dot, then number 2 is 5 dots because you added 4, number 3 is 9 dots because you added 4, etc.

Answer:

T4 = 13

Step-by-step explanation:

Using arithmetic progression

Tn = a + (n - 1)d

Where a - first term

n - n^th term

d - common difference

Answer:

28 days = 4 weeks

339 days = 11 month

14 months = 420 days

8 weeks = 56 days

90 days = 3 months

3 minutes = 90 seconds

3 days = 72 hours

48 days = 48 days

5 minutes = 300 seconds

Answer:

The angle measurement is 61.218°

Step-by-step explanation:

I used a triangle calculator

Answer:

x = 14

Step-by-step explanation:

Triagle GIA and Triangle GNT are congruent.

Answer:

1. (4,1,2,3,5)

Step-by-step explanation:

Since all the members of set A are present in "1"

B : 7.9......................

Answer:

7.9

Step-by-step explanation:

15 + 12 + 5 + 9 + 7 + 2 + 5

55

55 ÷ 7

[tex]\frac{55}{7}= 7\frac{6}{7}=7.85714285714[/tex]

7.85714285714 rounds to 7.9

Answer:

smaller piece is 65cm

larger piece is 115cm

Step-by-step explanation:

let 's' = smaller piece

let '180-s' = larger piece

3(180-s) = 85 + 4s

540 - 3s = 85 + 4s

540 = 85 + 7s

455 = 7s

s = 455/7 which is 65cm

larger piece = 180-65 or 115cm

Step-by-step explanation:

a. increased b. discreased c. increased d. decreased

Answer:

3000

Step-by-step explanation:

30%×100=3000

then the profit is=

4200-3000=1200

Answer:

12/25 = 48/100 = .48 = 48%

Step-by-step explanation:

The sum of two numbers and their difference is 30.

Answer:

y = 1/2x - 3

Step-by-step explanation:

The line intercepts with the y-axis at -3 and its pattern is going right two and up one.

Step-by-step explanation:

my answer is an image above

Answer:

1  11/21

Step-by-step explanation:

Use common denominator of 3 * 7 = 21

2/3 * 7/7 = 14/21

6/7 * 3/3 = 18/21

-------------------------

14/21 + 18/21 = 32/21

Reduce

32/21 = 1  11/21

Answer: 1 11/21

Step-by-step explanation:

Data: 2/3+6/7=x

Step one, Find the common denominator

(2/3)x7(for each number)=14/21

(6/7)x3(for each number)=18/21

Reason: To add fractions, you always have to find the common denominator(so you can make the denominator the same for each fraction). The common denominator of 3 and 7 is 21 and since what you do to the bottom has to be done to the top, you multiply 2 by 7 and 6 by 3 to end up with 14/21 and 18/21.

Step two, add

14/21+18/21=32/21=1 11/21

Reason: Since we have our common denominators, we just have to add and, with fractions, you only add the top(numerator) and not the bottom(denominator) you end up with 32/14 but when made into a mixed fraction(by dividing the bottom into the top and leaving the remainder on the top) you get 1 11/21 which can't be simplified.

So since it can't be simplified, it's your answer

I hope this helps!

Answer:

(2,0)

x-value: [1+3]/2 = 4/2 = 2

y-value: [2+-2]/2 = 0/2 = 0

Step-by-step explanation:

Given:

Total bill = $67.65

Mr. Scott paid with four $20 bills.

To find:

The amount of change he have received.

Solution:

It is given that, Mr. Scott paid with four $20 bills. So, the total amount paid by him is:

[tex]\$20\times 4=\$80[/tex]

Total bill = $67.65

Now,

Amount of change = Total amount paid - Total bill

                               = $80 - $67.65

                               = $12.35

Therefore, he should have received $12.35.

Answer:

Surface area = 6.92 cm²

Step-by-step explanation:

Given the following data;

Surface area = 692 cm²

To convert the area in cm² to mm²;

Conversion:

10 mm to cm = 10/10 = 1 cm

1 mm² to cm² = 1/100 = 0.01 cm²

692 mm² to cm² = 692 * 0.01 = 6.92 cm²

Therefore;

692 mm² = 6.92 cm²

In conclusion, the surface area of the piece of paper is 6.92 square centimeters.

Answer:

x=-3×-5×-7

-3×-5=15

15×-7=-105

=-105

Answer:

50 boys

Step-by-step explanation:

The number of groups = 24

The average number of children = 16

The new average number of children when one group is added = 18

The ratio of boys to girls in the group that just joined = 5:6

The initial number of boys = 220

Let the initial number of children

The initial total number of children = 24 × 16 = 384

The initial number of girls = 384 - 220 = 164

The final number of children = 25 × 18 = 450

The number of children in the group that joined in the game = 450 - 384 = 66

The ratio of boys to girls in the group = 5:6

Therefore, we get;

The number of boys = 66 × 5/11 = 30

The number of girls = 66 - 30 = 36

The number of boys at the end = 220 + 30 = 250

The number of girls at the end = 164 + 36 = 200

The number of more boys than girls at the end = 250 - 200 = 50

The number of more boys than girls at the end = 50 boys

Answer:

a) 5x - 9 = 3x + 3

5x - 3x = 3 + 9

2x = 12

x = 12 / 2

x = 6

b) x + 6 = 34 - x

x + x = 34 - 6

2x = 28

x = 28 / 2

x = 14

[tex] \: (a)5x - 9 = 3x + 3 \\ 5x - 9 - 3x = 3 \\ 2x - 9 = 3 \\ 2x = 3 + 9 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6 \\ (b) \: x + 6 = 34 - x \\ x + 6 + x = 34 \\ 2x + 6 = 34 \\ 2x = 34 - 6 \\ 2x = 28 \\ x = \frac{28}{2} \\ x = 14[/tex]