4x=x+18 solve for x

Answer:

[tex] a_n = 16(\frac{1}{4})^{n - 1} [/tex]

Step-by-step explanation:

Given:

Fifth term of a geometric sequence = [tex] \frac{1}{16} [/tex]

Common ratio (r) = ¼

Required:

Formula for the nth term of the geometric sequence

Solution:

Step 1: find the first term of the sequence

Formula for nth term of a geometric sequence = [tex] ar^{n - 1} [/tex], where:

a = first term

r = common ratio = ¼

Thus, we are given the 5th term to be ¹/16, so n here = 5.

Input all these values into the formula to find a, the first term.

[tex] \frac{1}{16} = a*\frac{1}{4}^{5 - 1} [/tex]

[tex] \frac{1}{16} = a*\frac{1}{4}^{4} [/tex]

[tex] \frac{1}{16} = a*\frac{1}{256} [/tex]

[tex] \frac{1}{16} = \frac{a}{256} [/tex]

Cross multiply

[tex] 1*256 = a*16 [/tex]

Divide both sides by 16

[tex] \frac{256}{16} = \frac{16a}{16} [/tex]

[tex] 16 = a [/tex]

[tex] a = 16 [/tex]

Step 2: input the value of a and r to find the nth term formula of the sequence

nth term = [tex] ar^{n - 1} [/tex]

nth term = [tex] 16*\frac{1}{4}^{n - 1} [/tex]

[tex] a_n = 16(\frac{1}{4})^{n - 1} [/tex]

Answer:1760

Step-by-step explanation:

Answer:

please mark my answer brainliest

Step-by-step explanation:

A.....will be the answer....

(4×10)+(7×1\100) = 40+7/100 =4007/100

4007/100= 40,07

40,07 = 40,070

just add 0 to right side

(40,0700 also = 40,070)

Hope this helps ^-^

Answer:

60 ; 20

B.) 1 hour working on problems, 3 hours reading

Step-by-step explanation:

Given the information :

Time - - - Total problems Answered

8am: - - - - 0

9am: - - - - 80

10am: - - - - 140

11am: - - - - -180

noon: - - - - 200

The marginal, or additional, gain from Ana’s second hour of work, from 9:00 AM to 10:00 AM, is ?

(Total problem answered at 10 a.m - Total problems Answered at 9a.m)

(140 - 80) = 60

The marginal gain from Ana’s fourth hour of work, from 11:00 AM to noon, is ?

(Total problem answered at Noon - Total problems Answered at 11a.m)

(200 - 180) = 20

In other to get the best possible exam score,

Since it is assumed that

Solving 70 problems is equivalent to 1 hour of reading in terms of score improvement

Also, it is assumed that the same number of pages is covered for every hour spent whine reading.

Hence it is only during the first hour, that is (8:00 - 9:00) that she was able to solve above 70 questions (80 - 0). Number of questions solved during subsequent hours were not up to 70, hence it would have been more rewarding if they had been used for reading.

Hence, she should have spent 1 hour working on problems and 3 hours reading

Answer:

y+2x = 3

Step-by-step explanation:

The formula for finding the equation of a tangent line is expressed using the point slope equation y-y0 = m(x-x0) where:

m is the slope of the line and (x0, y0) is a point on the line.

m = dy/dx = dy/dt ÷ dx/dt

dy/dt = 2(t-1)

dx/dt = e^t

m = 2(t-1)/e^t

If x = e^t, and x = 1

1 = e^t

Taking ln of both sides

ln1 = lne^t

t = ln1

t = 0

Substituting t = 0 into the slope formula:

m = 2(t-1)/e^t

m = 2(0-1)/e^0

m = 2(-1)/1

m = -2/1

m = -2

Substituting the slope m= -2 and the given point (1,1) into the formula for calculating the equation of tangent line we will have;

y-1 = -2(x-1)

y-1 = -2x+2

y+2x = 2+1

y+2x = 3

Hence the equation of the tangent line in Cartesian coordinates for the given parameter t is y+2x = 3

Answer:

.4 is in the 10th place in a number so .4 is one tenth of 1

The given decimal is equivalent to the one tenth of 4.

A decimal number is the representation of a number in whole and a part. The whole is represented by an integer while the part is equivalent to a number divided by the order of 10.

The given number in decimal form is 0.4.

In order to convert it in fraction, it can be written in the form of p/q as follows,

0.4 = 0.4/1

Multiply the numerator and denominator by 10 to obtain,

(0.4 × 10)/(1 × 10) = 4/10      

Hence, the given number is one tenth of 4.

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Answer:

x = 5

Step-by-step explanation:

4|0.5x - 2.5| = 0

|0.5x - 2.5|  = 0 / 4

0.5x - 2.5 = 0

0.5x = 2.5

x = 2.5 / 0.5

x = 5

Answer:

42

Step-by-step explanation:

12880000/140900=94.41

Therefore there is 1 teacher in every 94.41 people so

3860/94.41=42.2

So we would find around 42 teachers in Marshall, IL

Answer:

Step-by-step explanation:

Hello,

We will prove it by induction.

Step 1 - for n=2

2!=2*1=2

2^2=4

and 2 < 4 so this is true for n=2

Step2 - We assume that this is true for k and we have to prove it for k+1.

Induction hypothesis is [tex]k!<k^k[/tex]

[tex](k+1)!=(k+1)k![/tex]

We use the induction hypothesis and we we can write that

[tex](k+1)!=(k+1)k!<(k+1)k^k<=(k+1)(k+1)^k=(k+1)^{k+1}\\\\\text{As }k <= k+1[/tex]

so, we prove it for k+1

Step 3- conclusion

for n >= 2 we just proved that [tex]n!<n^n[/tex]

Answer:

Patient A receives 150 milligrams and Patient B receives 50 milligrams

Step-by-step explanation:

Patient A = 3x

Patient B = x

200 milligrams = 3x + x

200 milligrams = 4x

x = 50

Patient A = 3(50) = 150

Patient B = 50

I hope this helps!

-TheBusinessMan

Let the medicine received by patient B be x.

According to the question patient A receives 3 times as much,

The total amount of medicine administered to the two patients equals to 200 milligrams.

We can write the relation as ,

[tex]:\implies \sf \ \ \ x + 3x = 200 \\ \\ \\ [/tex]

[tex]:\implies \sf \ \ \ 4x = 200 \\ \\ \\ [/tex]

[tex]:\implies \sf \ \ \ x = \dfrac{200}{4} \\ \\ \\ [/tex]

[tex]:\implies \sf \ \ \ { \underline{ \boxed{ \bf{ \blue{x = 50}}}}} \ \bigstar \\ \\ [/tex]

Therefore,

Answer: 22

Step-by-step explanation: The range is the difference between the greatest number in the data set and the least numbe rin the data set.

In this case, thats 30 - 8 or 22.

Answer:

22

Step-by-step explanation:

30 - 8 = 22

highest number - lowest number

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Normal distribution :

Mean (m) = 1049

Standard deviation (sd) = 189

Number of samples (n) = 16

A) What is the probability that one randomly selected student scores above 1100 on the GRE?

Obtain the z score

Zscore = (x - m) / sd

Zscore = (1100 - 1049) / 189

Zscore = 51 / 189 = 0.2698412 = 0.27

Using the z-table

P(X > 100) = 1 - P(X < 100) = 1 - 0.6064 = 0.3936

B) The sample mean = population mean

Hence sample mean = 1049

The sample standard deviation = standard error

Standard Error (SE) = sd / sqrt(n)

SE = 189/4 = 47.25

Hence shape = normal, standard deviation = 47.25, mean = 1049

C.) P(X < 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 47.25

Zscore = 51 / 47.25 = 1.0793650 = 1.08

Using the z-table :

P(X < 1100) = 0.8599

D.) P(X > 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 47.25

Zscore = 51 / 47.25 = 1.0793650 = 1.08

Using the z-table :

P(X > 1100) = 1 - P(X < 1100) = (1 - 0.8599) = 0.1401

E) if n = 64

SE = 189 / sqrt(64) = 189 / 8 = 23.625

P(X > 1100)

Zscore = (x - m) / SE

Zscore = (1100 - 1049) / 23.625

Zscore = 51 / 47.25 = 2.1587301 = 2.16

Using the z-table :

P(X > 1100) = 1 - P(X < 1100) = (1 - 0.9846) = 0.0154

The probability decreases as the same distribution hinges towards a Boal distribution with increasing sample size.

Answer:

a. cosθ = ¹/₂[e^jθ + e^(-jθ)] b. sinθ = ¹/₂[e^jθ - e^(-jθ)]

Step-by-step explanation:

a.We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Adding both equations, we have

e^jθ = cosθ + jsinθ

+

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ + cosθ + jsinθ - jsinθ

Simplifying, we have

e^jθ + e^(-jθ) = 2cosθ

dividing through by 2 we have

cosθ = ¹/₂[e^jθ + e^(-jθ)]

b. We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Subtracting both equations, we have

e^jθ = cosθ + jsinθ

-

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ - cosθ + jsinθ - (-jsinθ)

Simplifying, we have

e^jθ - e^(-jθ) = 2jsinθ

dividing through by 2 we have

sinθ = ¹/₂[e^jθ - e^(-jθ)]

Answer:

For every 72 eggs, 32 omelets can be made.

Step-by-step explanation:

The ratio for eggs to omelets is 9:4. Or 9/4 in fraction form. (Note that the ratio can be written interchangeable such as 4:9).

The ratio says for every 9 eggs, it makes 4 omelets.

72 can be multiplied by 9. (9*8=72).

If we multiply the "top" and the "bottom" of the ratio by 8/8 (8/8=1. We must multiply this way so the ratio will remain the same when reduced.)

We will get 72:32.

For every 72 eggs, 32 omelets can be made.

Answer:

We use the rule of three !

9 eggs ------------> 4 omoletes

72 eggs -----------> x

So x= (72 eggs × 4 omoletes ) / 9 eggs

We simplify by 《eggs 》 because it is in the numerator and the denominator.

So x=(72×4 omoletes) / 9

x =288 omoletes /9

x = 32 omoletes

So we can made 32 omeletes with 72 eggs !!

4mn. You are multiplying them all together.

Answer:

4mn

Step-by-step explanation:

you would multiply the 2s then the m and n cant multiply so they would stay beside eachother so it would be 4mn

Complete question:

Please find the attached file for task table

Answer:

The minimum cycle time is 50 s

The maximum  cycle time is 50.4 s

Step-by-step explanation:

Given;

production time, t = 7 hours

desired output = demand, D =  500 units

The minimum cycle Time is given by;

Minimum cycle time = maximum task time, from the table the maximum task time is 50 seconds.

Thus, Minimum cycle time = 50 s

The maximum cycle Time is given by;

[tex]CT = \frac{Production \ time}{D} \\\\CT = \frac{7*3600 s}{500 \ units} \\\\CT = 50.4 \ s[/tex]

Thus, Maximum cycle time = 50.4 s

Answer:

C. 2.937

Step-by-step explanation:

Given the following :

H0 : p = 0.25

H1 : p > 0.25

Number of observations (n) = 647

p' = 30% = 0.3

SD = sqrt[(p(1 - p) / n)]

1 - p = 1 - 0.25 = 0.75

SD = sqrt[(0.25 * 0.75) / 647]

SD = sqrt[0.0002897]

SD = 0.0170234

Z = (p' - p) / SD

Z = (0.3 - 0.25) / 0.0170234

Z = 0.05 / 0.0170234

Z = 2.9371187 = 2.937

Answer:

Slope= 2.0003.000=1.500

x−intercept=−312​=−4

y−intercept= 12/2=6

Hoped I helped

Answer:

[tex]\huge\boxed{a = 10 \ , \ b = 0}[/tex]

Step-by-step explanation:

Conjugate of -1 + 3i = -1 - 3i

Their Product:

[tex]=(-1+3i)(-1-3i)\\Using \ Formula : (a+b)(a-b) = a^2-b^2\\=(-1)^2 - (3i)^2\\=1 - 9i^2\\We \ know \ that \ i^2 = -1\\=1 - 9(-1)\\=1 + 9\\=10[/tex]

Since the answer is 10, It seems like:

a + bi = 10

So, This means that:

a = 10

b = 0

Answer:

x = 5

Step-by-step explanation:

To find the value of x make sure to get it on one side

First subtract 3x from each side. This makes the equation now

3x + 2 = -8 + 25

Now see what 25 subtract by 8 is (17)

3x + 2 = 17

Next subtract 2 from both sides

3x = 15

Lastly, divide 15 by 3, making x equal 5

x = 5

Step-by-step explanation:

Remember: Coplanar definition: In the same plane.

Here, we can see that points G, N, and M make up the intersection of plane K and plane L, so that means our answers are: G, N, and M because we were looking forth e points that are on planes K and L. The other points are not the answer because they are either on only one of the planes or not on any of them at all.

I hope this helps! :)

Answer:

I THINK it is M,N,G they are coplanar and they intersect, hope i helped

Answer:  A) sin 59° = cos 31°

Step-by-step explanation:

Based on the angle and the sides provided, we can establish that

tan 31° = 17/x

Since no hypotenuse is provided and we cannot solve for it, we can rule out options B, C, and D.

We know that the sum of the angles of a triangle is 180°. In a right triangle, we know that one of the angles is 90°, so the other two angles are complimentary  -->   sin Ф = cos (90 - Ф).

Therefore, option A is true.

Answer:

Step-by-step explanation:

Given: AC is angle bisector of <BAD.

=> So, <BAC = <CAD

30° = x-1 °

30 +1 = x

31 = x

Then, X = 31

Hope this helps.. Good luck :)

Answer:

  see below

Step-by-step explanation:

The result of the expression is P∨Q, since the P∧¬R term is subsumed by the P term. That is, ..

  (P∨Q) ∨ (P∧¬R) = Q ∨ (P ∨ P∧¬R) = Q∨P

4*3

12

12*6

72

hope it help

The surface area of the given box is 108 square inches.

The surface area of a box is the sum of the areas of its six faces. We can find the surface area of the given box by using the formula:

Surface Area = 2lw + 2lh + 2wh

where "l" is the length, "w" is the width, and "h" is the height of the box.

As per the question, we have

l = 3 inches, w = 3 inches, and h = 6 inches

Substituting the given values, we get:

Surface Area = 2(4 x 3) + 2(4 x 6) + 2(3 x 6)

Surface Area = 24 + 48 + 36

Surface Area = 108 square inches

Therefore, the surface area of the given box is 108 square inches.

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