3x +2 = 9x + 20 for x

The null hypothesis is that there is no discernible difference among the 5 treatments. The alternative hypothesis is that there is a discernible difference among the 5 treatments

Degree of freedom between groups is nothing but the number of treatments-1 i.e. 5-1=4 and degree of freedom within groups is nothing but total number of subjects- number of treatments i.e. 5*10-5=50-5=45

Mean squares between groups is calculated as follows:

Mean squares between groups= Sum of squares between groups/degrees of freedom between groups= 232/4=58

Mean squares within groups is calculated as follows:

Mean squares within groups= Sum of squares within groups/degrees of freedom within groups= 400/45= 8.89 rounded off to two decimal places

F ratio is calculated as follows:

F= Mean squares between groups/Mean squares within groups

= 58/8.89

= 6.524184477

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Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and

after 11 steps, the mixture contains less than 9% vinegar.

What is concentration?

Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.

a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:

\(C(1) = C(0) * \frac{1 - 0.14}{1}\)

where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:

C(2) = C(1) * \(\frac{1 - 0.14}{1}\)

Substituting the formula for C(1), we get:

C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)

or, more generally:

\(C(n) = C(0) * (0.86)^n\)

b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:

\(C(0) * (0.86)^n < 0.09\)

Dividing both sides by C(0), we get:

\((0.86)^n < 0.09\)

Taking the natural logarithm of both sides, we get:

n * ln(0.86) < ln(0.09)

Dividing both sides by ln(0.86), we get:

n > ln(0.09) / ln(0.86)

Using a calculator, we get:

n > 10.7

Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.

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Answer:

x = {2, 5 , -2}

Step-by-step explanation:

See photo for explanation:

Answer:

it is 237

Step-by-step explanation:

Answer: 237

Step-by-step explanation:

You do not to do order of operations for this problem

2 x 100 = 200

200 + 18 = 218

218 - 1 = 217

217 + 20 = 237

Hope it helps!

Answer:

See below

Step-by-step explanation:

sf = s0 + v0 t  + 1/2 at^2

        1  + (-3)t + 1/2 (.2t) t^2           ( weird acceleration value)

s =  1 -3t + .1 t^3           You will need a 't' value to determine the position

you can find some if you scroll down on the page we're on.

They should kinda look like questions in little boxes.

They'll be under the header "New Questions in Mathematics"

don't feel bad, it took me a while too, they kinda blend in & no one would scroll down that far. I hoped this help you or someone else

have a great day :D

Step-by-step explanation:

option B is correct

as,

3x² × 2x³y = 6x⁵y

and

3x² × 5xy⁴ = 15x³y⁴

so,

6x⁵y + 15x³y⁴.

hope this answer helps you dear and may u have a great day ahead! take care

Answer:

Lol, thank you for telling me this information..

To find arcsin, we need to use the identity:

sin(arcsin(x)) = x

Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:

sin(arcsin) = -sqrt(1 - (cos)^2)

where (cos)^2 = 8/17

Substituting, we get:

sin(arcsin) = -sqrt(1 - (8/17))

Simplifying, we get:

sin(arcsin) = -sqrt(17/17 - 8/17)

Simplifying further, we get:

sin(arcsin) = -sqrt(9/17)

Therefore, arcsin = -sqrt(9/17)

To find arctan, we need to use the identity:

tan(arctan(x)) = x

Substituting, we get:

tan(arctan) = -8/17

Therefore, arctan = -8/17

So, arcsin is -sqrt(9/17) and arctan is -8/17.

The given differential equation:

y''' − 2y'' + y' = 2 − 24ex + 40e5x,

y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2

Therefore, the next solution is 13/2

Differential Equation:

In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.

Now,

Given differential equation is

y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ                 ------------ (1)

Auxiliary equation is m³ - 2m² +2m = 0

Now,

   m(m² - 2m +2) = 0

⇒ m(m-1)² = 0

Therefore, m = 0,1,1

Therefore,

\(y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}\)

Now, we have to find the particular solution by method of undetermined coefficient.

   \(y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}\)

⇒ \(y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}\)

⇒ \(y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}\)

⇒ \(y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}\)

Putting these values in differential equation (1), we get:

y'''(0) = 13/2

Complete Question:

Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2

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The probability that exactly 20 out of 30 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately 0.0802.

To find the probability that exactly 20 out of 30 randomly selected adult smartphone users use their smartphones in meetings or classes, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting exactly k successes

n is the total number of trials (sample size)

k is the number of desired successes

p is the probability of success on a single trial

In this case:

n = 30 (number of adult smartphone users randomly selected)

k = 20 (number of users who use smartphones in meetings or classes)

p = 0.42 (probability of using smartphones in meetings or classes)

Plugging in the values into the formula:

P(X = 20) = C(30, 20) * (0.42)^20 * (1-0.42)^(30-20)

Calculating the values:

C(30, 20) = 30! / (20! * (30-20)!) = 30! / (20! * 10!) = 30,045

P(X = 20) = 30,045 * (0.42)^20 * (0.58)^10

Calculating the final result:

P(X = 20) ≈ 0.0802

Therefore, the probability is approximately 0.0802.

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Answer:

-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,

By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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Answer:

6.2 approx i believe

Step-by-step explanation:

Answer:

5x<30

Open circle.

5x<30

Divide by 5

x < 6

Open circle, arrow to the left. Answer is H

The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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Answer:

120 children and 388 adults bought tickets for the swimming pool. Explanation: Create two simultanous equations:.

Answer:

The cahier earns 7.25 an hour

and in three hours she will have 21.75

Answer:

Step-by-step explanation: IT Is The cashirs earns $7.25 each hour.She will have 21.7$

Answer:

75

Step-by-step explanation:

Use the arithmetic progression formula:  S =n/2(2a + (n-1)d)

a = 5, d = 5, n = 5

S = 5/2((2(5) + (5-1)(5)) = 75

your answer is 3.375

Answer:

61 hot dogs

122 sodas

Step-by-step explanation:

x+x2=183

3x=183

183÷3=

61

Answer:

E $10240.00

Step-by-step explanation:

The total amount of money is x.

3/8 × x = 3840

Multiply both sides by the reciprocal of 3/8 which is 8/3.

x = 3840 × 8/3

x = 10240

Answer: E $10240.00

Answer:

E. $10240.00

Step-by-step explanation:

$3840.00 is 3/8

so 3 ---> $3840

     1 ---> $3840/3

     1 ---> 1280

Then total money you had is ( 1280 * 8 ) = $10240

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer: 400

Step-by-step explanation:

Answers:

10.

B: Austin did not combine -3 and -9 correctly.

11.

x=8.5

12.

2r-4s

13.

10x+3y

14.

k=2

(4,-8)

Step-by-step explanation:

from -5 to -1 you would have to count from 1 to 4. and do the same for -8 to -16

Answer:

57 minutes

Step-by-step explanation:

Simply what is %5 of 60.

%5 of 60 can be found by multiplication by 0.05 x 60 giving you 3.

Answer:

\(SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 \)  

\(SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =6750\)  

\(SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8000\)  

And we have this property  

\(SST=SS_{between}+SS_{within}=6750+8000=14750\)  

The degrees of freedom for the numerator on this case is given by \(df_{num}=k-1=4-1=3\) where k =4 represent the number of groups.  

The degrees of freedom for the denominator on this case is given by \(df_{den}=df_{between}=N-K=20-4=16\).  

And the total degrees of freedom would be \(df=N-1=20 -1 =19\)  

We can find the \(MSTR=\frac{6750}{3}=2250\)

And \(MSE=\frac{8000}{16}=500\)

And the best answer would be:

d. 2,250

Step-by-step explanation:

We want to test the following null hypothesis:

\(  H0: \mu_1 =\mu_2 =\mu_3 =\mu_4\)

If we assume that we have \(4\) groups and on each group from \(j=1,\dots,k\) we have \(k\) individuals on each group we can define the following formulas of variation:  

\(SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 \)  

\(SS_{between=Treatment}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =6750\)  

\(SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8000\)  

And we have this property  

\(SST=SS_{between}+SS_{within}=6750+8000=14750\)  

The degrees of freedom for the numerator on this case is given by \(df_{num}=k-1=4-1=3\) where k =4 represent the number of groups.  

The degrees of freedom for the denominator on this case is given by \(df_{den}=df_{between}=N-K=20-4=16\).  

And the total degrees of freedom would be \(df=N-1=20 -1 =19\)  

We can find the \(MSTR=\frac{6750}{3}=2250\)

And \(MSE=\frac{8000}{16}=500\)

And the best answer would be:

d. 2,250