What is the true solution to the equation below? 2 lne^ln2x-lne^ln10x=ln30

Answer:

106 people.

Step-by-step explanation:

Logistic equation:

The logistic equation is given by:

[tex]P(t) = \frac{K}{1+Ae^{-kt}}[/tex]

In which

[tex]A = \frac{K - P_0}{P_0}[/tex]

K is the carrying capacity, k is the growth/decay rate, t is the time and P_0 is the initial value.

Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor.

This means that [tex]K = 191, P_0 = 38[/tex], so:

[tex]A = \frac{191 - 38}{38} = 4.03[/tex]

Then

[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]

3 days later 68 people have heard it.

This means that [tex]P(3) = 68[/tex]. We use this to find k.

[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]

[tex]68 = \frac{191}{1+4.03e^{-3k}}[/tex]

[tex]68 + 274.04e^{-3k} = 191[/tex]

[tex]e^{-3k} = \frac{191-68}{274.04}[/tex]

[tex]e^{-3k} = 0.4484[/tex]

[tex]\ln{e^{-3k}} = \ln{0.4484}[/tex]

[tex]-3k = \ln{0.4484}[/tex]

[tex]k = -\frac{\ln{0.4484}}{3}[/tex]

[tex]k = 0.2674[/tex]

Then

[tex]P(t) = \frac{191}{1+4.03e^{-0.2674t}}[/tex]

How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?

This is P(6). So

[tex]P(6) = \frac{191}{1+4.03e^{-0.2674*6}} = 105.52[/tex]

Rounding to the nearest whole number, 106 people.

Answer:

f

Step-by-step explanation:

Answer:

S = 62.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan S = opp side / adj side

tan S = sqrt(42)/ sqrt (11)

tan S = sqrt(42/11)

Taking the inverse tan of each side

tan ^ -1( tan S) =  tan ^-1(sqrt(42/11))

S=62.89816

Rounding to the nearest tenth

S = 62.9

Let x, y, and z be the amounts (in liters, L) of the 25%, 35%, and 55% solutions that the chemist used.

She ended up with 120 L of solution, so

x + y + z = 120 … … … [1]

x L of 25% acid solution contains 0.25x L of acid. Similarly, y L of 35% solution contains 0.35y L of acid, and z L of 55% solution contains 0.55z L of acid. The concentration of the new solution is 40%, so that it contains 0.40 (120 L) = 48 L of acid, which means

0.25x + 0.35y + 0.55z = 48 … … … [2]

Lastly,

z = 3y … … … [3]

since the chemist used 3 times as much of the 55% solution as she did the 35% solution.

Substitute equation [3] into equations [1] and [2] to eliminate z :

x + y + 3y = 120

x + 4y = 120 … … … [4]

0.25x + 0.35y + 0.55 (3y) = 48

0.25x + 2y = 48 … … … [5]

Multiply through equation [5] by -2 and add that to [4] to eliminate y and solve for x :

(x + 4y) - 2 (0.25x + 2y) = 120 - 2 (48)

0.5x = 24

x = 48

Solve for y :

x + 4y = 120

4y = 72

y = 18

Solve for z :

z = 3y

z = 54

Answer:

5 ≤ x ≤ 10             5 ≤ y ≥ -1

Step-by-step explanation:

9514 1404 393

Answer:

  a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22

  b) 30

  c) 6

  d) yes; no

Step-by-step explanation:

a) The values are read from the graph.

__

b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest

__

c) -2 -(-8) = -2 +8 = 6 . . . positive difference

(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)

__

d) -2 + 5 < 5 . . . . true

  -2 + 5 < -2 . . . . false

Answer:

101 cm

Step-by-step explanation:

Add all the side lengths up to get 101 cm.

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Answer:

  x = 10/3 = 3 1/3 ≈ 3.33

Step-by-step explanation:

Triangles ABC and ADE are similar, so corresponding sides are proportional.

  DE/DA = BC/BA

  x/(4+6) = 2/6

  x = 10(2/6) = 10/3 = 3 1/3

Answer:

cos theta  = adj / hyp is positive (+/+)

Step-by-step explanation:

In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.

in this interval:

sin theta = opp / hyp is neg (-/+)

cos theta  = adj / hyp is positive (+/+)

tan theta = opp / adj = (-/+) :  negative

9514 1404 393

Answer:

  4x+10

Step-by-step explanation:

For parallelogram adjacent sides a and b, the perimeter is ...

  P = 2(a +b)

For the given sides, the perimeter is ...

  P = 2((x +3) +(x +2)) = 2(2x +5)

  P = 4x +10 . . . perimeter of the parallelogram

Answer:

im not too sure but try using a cartesuan plane and measure it precisely using a protractor then key in the measurements. Im not entirely sure its the correct method tho

Answer:

2 pages per minute

Step-by-step explanation:

Take the number of pages and divide by the number of minutes

46 pages / 23 minutes

2 pages per minute

2 Pages per Minute

46 ÷ 23 = 2

Anthony can read 2 pages per minute.

Answer:

B

Step-by-step explanation:

substitute the values in the eq. Ot is also arithmetic progression.

Answer:

30 clocks

Step-by-step explanation:

Set up an equation:

Variable x = number of clocks

1200 + 20x = 60x

Isolate variable x:

1200 = 60x - 20x

1200 = 40x

Divide both sides by 40:

30 = x

Check your work:

1200 + 20(30) = 60(30)

1200 + 600 = 1800

1800 = 1800

Correct!

Answer:

Z =  -1.60

it is low ... it appears that for this problem 2 standard deviations below must be reached to be considered "unusual"

Step-by-step explanation:

Answer:

The answer is "0.7794".

Step-by-step explanation:

Please find the complete question in the attached file.

Given:

[tex]\to n_{1}=n_{2}=25\\\\[/tex]

Hypotheses:

[tex]\to H_{0}:\mu_{B}-\mu_{A}\geq 0\\\\\to H_{a}:\mu_{B}-\mu_{A}< 0\\\\[/tex]

Testing statistics:

[tex]\to z=\frac{(\bar{x}_{B}-\bar{x}_{A})-(\mu_{B}-\mu_{A})}{\sqrt{\frac{\sigma^{2}_{B}}{n_{1}}+\frac{\sigma^{2}_{A}}{n_{2}}}}=\frac{3.5-(0)}{\sqrt{\frac{16^{2}}{25}+\frac{16^{2}}{25}}}=0.77[/tex]

The test is done just so the p-value of a test is

[tex]\to p-value = P(z < 0.77) = 0.7794[/tex]

Because the p-value of the management is large, type B can take it.

Answer:

Hello

Step-by-step explanation:

The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1

and the disk ? (inside of a circle) of center (0,0) and radius 2

[tex]dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\[/tex]

Answer:

(7x + 18) or 60 Mangoes

Step-by-step explanation:

Let the no. of mangoes Kubie possesses be x

So,

Cyril has mangoes = 2x + 6  ...(i)

So,

Maxine has = 2 * (2x + 6)

= 4x + 12

Given that,

Kubie has mangoes = 6

∵ The combined mangoes they have in terms of x,

= Cyril + Kubie + Maxine

= (2x + 6) + x + (4x + 12)

= 7x + 18

A.T.Q.

Cyril has = 2x + 6

∵ Cyril has mangoes = 2 * (6) + 6

= 18 mangoes

∵ Maxine has = 2 * Cyril's mangoes

= 2 * 18

= 36

Thus,

Total mangoes = Cyril + Kubie + Maxine

= 18 + 6 + 36

= 60 Mangoes

Answer:

Amount gained = $900

Step-by-step explanation:

Let the cost price be = x

Given selling price = 8400

And profit% = 12%

Profit = selling price - cost price

        = 8400 - x

[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]

Therefore , cost price of the radio $7500

The amount she gained = 8400 - 7500 = $ 900

Answer:

khai niem hinh cat don gian?

"RS tangent to circle a..." is first statement          Reason: Given

Second Reason: "Radius perpendicular to tangent"

Second Statement: "AR is parrallel to BS"      Reason: "2 lines perpendicular..."

Answer:

(1238.845 ;1285.376)

Step-by-step explanation:

Conditions for constructing a confidence interval :

Data must be random

Distribution should be normal and independent ;

Based on the conditions above ; data meets initial conditions ;

C. I = sample mean ± margin of error

Given the data :

1241 1210 1267 1314 1211 1299 1246 1280 1291

Mean, xbar = Σx / n = 11359 / 9 = 1262.11

The standard deviation, s = [√Σ(x - xbar)²/n - 1]

Using a calculator ; s = 37.525

The confidence interval :

C.I = xbar ± [Tcritical * s/√n]

Tcritical(0.10 ; df = n - 1 = 9 - 1 = 8)

Tcritical at 90% = 1.860

C. I = 1262.11 ± [1.860 * 37.525/√9]

C.I = 1262.11 ± 23.266

(1238.845 ;1285.376)

± 23.266

The margin of error :

[Tcritical * s/√n]

[1.860 * 37.525/√9]

C.I = ± 23.266

Answer:

1/4

Step-by-step explanation:

White = w

Black = B

Blue = b1

Tan = t

Wb1

Wt

Bbi

Bt

The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.

Answer:

1/4

Step-by-step explanation:

it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.

If 6ˣ = 5, then

(6ˣ)³ = 6³ˣ = 5³ = 125,

and

6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500

Answer:

Angle A = Angle D = 69° 30'

Angle B = Angle C = 110° 30'

Step-by-step explanation:

     B ___ C

    /              \

  /                  \

A ________ D

AB and CD are 10

BC is 6

AD is 14

If we divide the trapezoid, we can imagine a line.

     B_ F_C

    /      |      \

  /        |         \

A ___E____ D

AE = ED = 7 (14/2)

BF = FC = 3

So now, we draw another line from B or C to AE or ED

     B_ F_ C

    /      |     | \

  /        |     |    \

A ___E_ G_ D

EG = GD = 3.5 (7/2)

There is a right triangle now, GCD

GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:

CD is H, and GD is A

cos D = A/H

cos D = 3.5/10 → 0.35

angle D = 69° 30'

By theory, we know that angle D and angle A, are the same so:

Angle D = Angle A = 69° 30'

Angle B = Angle C

We also make a cuadrilateral, which is EFCD.

Angle D is 69° 30', Angle E is 90°, Angle F is also 90°

Sum of angles in cuadrilateral is 360°

360° - 69° 30' - 90° - 90° = Angle C = Angle B

Angle C = Angle B = 110° 30'

Let's confirm the angles in the trapezoid:

69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°

A + B + C + D

Step-by-step explanation:

Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t

Now, we are given that the savings is =Rs 500

So, According to our assumption, 2t=500

⇒t=250

Hence, the income of the family is =7×250=Rs 1750

And the expenditure is =Income−Savings

=Rs 1750−Rs 500

=Rs 1250

The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.

Option D is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The rate of change of a linear function is also known as the slope of the function.

To determine the slope of the function represented by the given table, we need to calculate the change in Y for a unit change in X.

Using the values given in the table, we can calculate the slope as follows:

Slope = (Change in Y) / (Change in X)

So,

(a - 27) / (11 - 10) = (11 - 27) / (12 - 10) = -8

Setting this equation equal to -8, we get:

= (a - 27) / 1

= -8

Simplifying the equation, we get:

a - 27 = -8

a = 19

Therefore,

The value of a that would make the data in the table represent a linear function with a rate of change of -8 is a = 19.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ7

The statement is totally false.

[tex]\neg P\lor\neg Q \equiv \neg(P \land Q) \not\equiv P\land Q[/tex]

because (P and ¬P) is a contradiction.

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Answer:

  (d)  -1/32

Step-by-step explanation:

It may be easier to rearrange the expression so it has positive exponents.

  [tex]\dfrac{1}{2^{-2}x^{-3}y^5}=\dfrac{2^2x^3}{y^5}=\dfrac{4(2)^3}{(-4)^5}=-\dfrac{4\cdot8}{1024}=\boxed{-\dfrac{1}{32}}[/tex]