Prove that :-

[tex] \quad \leadsto \quad \bf \zeta ( z ) = \displaystyle \bf \sum_{\bf n=1}^{\infty} \bf \dfrac{1}{n^x} \cdot e^{-iy \cdot log ( n )} [/tex]

Where , z = x + yi

Riemann Hypothesis :) ​

Answer: The answer for 9 is 50 miles per hour and the one who drove farthest is is ben because at 5 hours he drove already 250 miles. And for number 9 according to the table she is driving 15 miles per hour because on the bottom it always adds up by 15 miles.

Step-by-step explanation: So first to figure out 9 I used y2-y1/x2-x1 to figure out the rate of change and got 50 miles per hour and the point I used were (5,100) and (5,250). Then According to Ben's graph it shows that he drove 250 miles at 5 hours while sally was at 100 miles for 5 hours. So Ben drove the farthest. Then finally for number 9 I concluded that sally is driving 15 miles per hour because distance always adds up by 15 miles.

Hope this Helps :D

Answer: 252

Step-by-step explanation:

Answer:

12, 24, 36, 48, 60, 72, 84, 96

Step-by-step explanation:

The smallest natural number that is a common multiple of 3 and 4 is 12. The answer is all multiples of 12 less than 100.

Answer: 12, 24, 36, 48, 60, 72, 84, 96

Answer:

x= 8

Step-by-step explanation:

Sum of the two angles = 90

12x - 30 + 3x = 90

15x -30 = 90

15x = 90 + 30

15x = 120

x = 120/15 = 8

The solution to the given inequality -3(x - 2) ≤ 1/3 is x ≤ 17/9

-3(x - 2) ≤ 1/3

-3x + 6 ≤ 1/3

-3x ≤ 1/3 - 6

-3x ≤ (1-18) / 3

-3x ≤ -17/3

x ≤ -17 /3 ÷ -3

x ≤ -17/3 × 1/-3

x ≤ -17/-9

x ≤ 17/9

A verbal statement describing the solution to the inequality is x is less than equal to 17 over 9

Verifying the solution of the inequality:

-3(x - 2) ≤ 1/3

-3x + 6 ≤ 1/3

-3(17/9) + 6 ≤ 1/3

-51/9 + 6 ≤ 1/3

(-51+54) / 9 ≤ 1/3

3/9 ≤ 1/3

1/3 ≤ 1/3

Therefore, the -3(x - 2) ≤ 1/3 to the inequality -3(x - 2) ≤ 1/3 in verbal statement is x is less than equal to 17 over 9.

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The missing part from this problem for you to solve it is that the total marbles Sara had.

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

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have been given that Mahad had no marbles, so Sara gave ⅓ of her marbles to Mahad.

Here we can see that this problem cannot be solved due to a lack of information. we need the total marbles Sara had.

If we are given the total marbles Sara had, then we can just simply divide the amount by the denominator.

Therefore, the missing part from this problem for you to solve it is that the total marbles Sara had.

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The volume of a cuboid or box is the multiplication of length, width, and height by that expression the width of the given cuboid box is 10 inches.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

The volume of cuboid = length × height × width.

Given that,

Height (H) = 9 inches.

The length is three inches more than the width.

So,

L = 3 + W

Now,

Volume of box = 1170 inches³

Now,

The volume of the cuboid is given as

V = L×W×H

1170 = (3 + W) × W×9

W² + 3W - 130 = 0

W² + 13W - 10W - 130 = 0

W(W + 13) - 10(W + 13) = 0

(W + 13)(W - 10) = 0

W = 10,-13 since the length can never be negative so 10 inches will be right.

Hence "The width of the given cuboid box is 10 inches".

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Step-by-step explanation:

f(x) = x³ + 2x² - 3x - 6

f(-2) = (-2)³ + 2(-2)² - 3(-2) - 6

= -8 + 8 + 6 - 6

= 0

Answer:

The answer is in the attached screenshot.

The Three solutions for the linear equation are: (0, -0.333), (1,1) and (3, 3.667).

According to the statement

We have to find that the solution of the linear equation.

So, For this purpose, we know that the

A linear equation is defined as an equation that is written in the form of Ax+By=C.

From the given information:

The three solutions for the linear equation 4x-3y = 1.

Then

The given equation is :

4x-3y = 1

Slope intercept form is

y = 4/3x - 1/3.

Then

For x = 0, we have that

y = 4/3x - 1/3.

y = 4/3(0) - 1/3.

y =  - 1/3.

y = -0.334

Then

For x = 1, we have that

y = 4/3x - 1/3.

y = 4/3(1) - 1/3.

y =  3/3.

y = 1.

Then

For x = 3, we have that

y = 4/3x - 1/3.

y = 4/3(3) - 1/3.

y =  11/3.

y = 3.67.

So, The Three solutions for the linear equation are: (0, -0.333), (1,1) and (3, 3.667).

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The interest earned in next 90 days is  $390.6.

The amount of money earned, in compound interest, after t years, is given by:

A= P[tex]( 1+ r/n)^{(nt)}[/tex]

Given:

A = Amount

P = Principal = $28,214.35

r = rate = 0.055

n = number of periods=365

t = time in years=3/12= 1/4

Using compound interest formula

A= P[tex]( 1+ r/n)^{(nt)}[/tex]

A(90)=  28,604.95[tex]( 1 + 0.055/365)^{(365 * 1/4)}[/tex]

A(90)=28241.35 [tex](1.00015)^{(91.25)}[/tex]

A(90)=  $28,604.95

So, the interest earned in next 90 days is

=28,604.95 - 28,604.95

= $390.6

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Step-by-step explanation:

and ... ? what do we need to do ?

I guess finding the number of quarters and dimes.

x = number of quarters

y = number of dimes

x + y = 185

x = 185 - y

0.25×x + 0.1×y = 26.75

after all, a quarter has a value of $0.25, and a dime of $0.10.

let's use the identity of the first equation in the second equation :

0.25×(185 - y) + 0.1×y = 26.75

to make is simpler to see let's multiply the whole thing by 100 :

25×(185 - y) + 10y = 2675

4625 - 25y + 10y = 2675

4625 - 15y = 2675

1950 = 15y

y = 130

x = 185 - y = 185 - 130 = 55

there are 55 quarters and 130 dimes in the bag.

Answer:

Step-by-step explanation:

Background: f(x) is the same thing as y but represents the value of x in parentheses.

Ej: f(2)=3x+2, this solution would be "8" because the value in the parentheses represents the value of x. (if the parentheses have an "x" then the value of x is unknown.

1.

f(x)=5x+8   g(x)=(x-8)/5

f(g(x))=?, 5((x-8)/5)+8

f(g(x))=x-8+8

f(g(x))=x

g(f(x))=5x+8-8/5

g(f(x))=5x/5

g(f(x))=x

g(f(x))=f(g(x)) because they both equal x proving they are inverses

Sorry, I don't have time to answer the rest of the steps (I will give the answers to check the work).

All of them are x=x because they are all inverse functions.

The value of g(4) is 7 when given function is g(x)= 4x-9 .

By considering the given function

g(x)= 4x-9

g(4)=4(4)-9

g(4)=16-9

g(4)=7

A function in mathematics that goes from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are referred to as the function's domain and codomain, respectively.

a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are everywhere in mathematics, and they are essential for constructing physical relationships in the sciences.

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Answer:

a) 28

Step-by-step explanation:

Given information,

→ w = 5

→ x = 9

→ y = 2

The given expression is,

→ x + 20 - 1

Let's solve the expression,

→ x + 20 - 1

→ 9 + 20 - 1

→ 29 - 1

→ 28

Hence, the answer is 28.

The table of the function y = (1/2)x + 3 is when (x = 4, y = 5), (x = 6, y = 6),

( x = 9, y = 15/2), ( x = 11, y = 17/3).

An expression represents that two different forms of numerical and variables are the same.

Given an expression y = (1/2)x + 3 we have to determine the range of this function corresponding to the domain { 4, 6, 9, 11 }.

For x = 4,

y = (1/2).4 + 3.

y = 2 + 3.

y = 5.

For x = 6,

y = (1/2).6 + 3.

y = 3 + 3.

y = 6.

For x = 9,

y = (1/2).9 + 3.

y = 9/2 + 3.

y = 15/2.

For x = 11,

y = (1/2).11 + 3.

y = 11/2 + 3.

y = 17/3.

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According to this formula, the time when the world population reach 8 billion is D. 2026.

From the information given, the capita growth rate of the world population continues to be what it was in the year 2016, the world population t years after July 1, 2016, will be 7.4 ✕ 1.011t billion.

Therefore, the year when the world population reach 8 billion will be:

80 billion = 7.4 × 1.011t billion

1.011t = 80/7.4

1.011t = 10.8

t = 10.8/1.011

t = 10

Therefore, the number of years will be added. This will be:

= 2016 + 10

= 2026

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The measurement of the angle X is 60 degrees.

Angles L and X are the highest angles according to the diagram. They line up to have an angle of L = X = 60 degrees.

However, because the figures in a diagram could be oddly arranged, you shouldn't rely exclusively on it. A more effective strategy is to consider the letter combinations JKLMN and VWXYZ.

Observe how the third letters of JKLMN and VWXYZ, respectively, are L and X. This indicates that the letters are congruent angles and couple up (since the polygons are similar). Thus, this is a non-visual method of understanding how angle L = angle X = 60.

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The solution to the linear equation given as 2.4 (x - 6) = 0.4 (x + 8) + 12 is  x = 14.8

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The linear equation is given as

2.4 (x - 6) = 0.4 (x + 8) + 12

Open the brackets

So, we have

2.4x - 14.4 = 0.4x + 3.2 + 12

Collect the like terms in the above expression

So, we have

2.4x - 0.4x = 14.4 + 3.2 + 12

Evaluate the like terms in the above expression

So, we have

2.0x = 29.6

Evaluate the quotient in the above expression

So, we have

x = 14.8

Hence the solution to the linear equation given as 2.4 (x - 6) = 0.4 (x + 8) + 12 is  x = 14.8

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The equation of the line in standard form is 12x-2y=13.

Given that line that is the perpendicular bisector of the segment whose endpoints are R(-1, 6) and S(5, 5).

R≡(-1,6) and S≡(5,5)

The perpendicular bisector of the line segment joining R and S will pass through the midpoint M.

coordinate of M is =((-1+5)/2,(6+5)/2)

coordinate of M is=(2,11/2)

Slope of the line joining R and S is

m₁=(6-5)/(-1-5)

m₁=-1/6

We know that for two perpendicular lines having slope m₁ and m₂,

m₁m₂=-1

Here, m₁=-1/6

Let m₂ be the slope of the perpendicular bisector

(-1/6)m₂=-1

m₂=6

Equation of the perpendicular bisector will be,

(y-yₙ)/(x-xₙ)=m₂   [(xₙ,yₙ) is the coordinate of M]

(y-11/2)/(x-2)=6

(2y-11)/2=6(x-2)

2y-11=12x-24

12x-2y=13

Hence, the equation of the given line in standard form when ine that is perpendicular bisector of the segment whose endpoints are R(-1, 6) and S(5, 5) is 12x-2y=13.

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Answer:

Solution:

So answer is 12 inches

Answer: 1/6

Step-by-step explanation:

Based on the given equation, the solution to x is -32.

The formula given is:

x / -2² = 4 (-2)

To solve for x, solve for the exponents:

x / -2² = 4 (-2)

x / 4 = 4 (-2)

Then solve the brackets:

x / 4 = 4 (-2)

x / 4 = -8

Then solve for x:

x / 4 = -8

x = -8 x 4

x = -32

In conclusion, based on the equation of x given, the value of x can be found to be -32.

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Answer:

yes

Step-by-step explanation:

you can classify people into categories by name, state, and age. Hope this helps!

Strategy 2 will generate higher expected profit and the company should invest k 8000 for market research to determine with certainty whether demand will be strong or weak.

                                       →Strong demand (P= 0.6) k12000 outflow

                                   →|

                                       →Weak demand (P=0.4) k30000 outflow

New product launch   ║

                                       →Strong demand (P= 0.6) k80000 outflow

                                    →|

                                       →Weak demand (P=0.4) k20000 outflow

Expected market value in strategy 1 is

= - 120000 x 0.6 + (-30000) x 0.4

= -k 84000

Expected market value in strategy 2 is

= - 80000 x 0.6 + 20000) x 0.4

= k 56000

Therefore strategy 2 will generate higher expected profit

In strategy 2

Expected value in strong demand is 80000 x 0.6 = k 48000

Expected value of weak demand is 20000 x 0.4 = k 8000

Thus the company should invest k 8000 for market research to determine with certainty whether demand will be strong or weak

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Step-by-step explanation:

0.25(x+10) = 2+0.5(x-1)

0.25 * x + 0.25 * 10 = 2.05 * x - 2.05 * 1

0.25x + 2.5 = 2.05x - 2.05

0.25x - 2.05x = -2.05 - 2.5

-1.8x = - 4.55

x = -4.55/-1.8

x = 2.53777777778

Work Shown:

[tex](x_1,y_1) = (7,-6) \text{ and } (x_2,y_2) = (6,-6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-6 - (-6)}{6 - 7}\\\\m = \frac{-6 + 6}{6 - 7}\\\\m = \frac{0}{-1}\\\\m = 0\\\\[/tex]

Lines with slope of 0 are always horizontal. The y coordinates are the same value.

The net pay of the individual after having deducted total deductions is $166.54

How do we determine the amount of each deduction?

The amount of each deduction is based on the gross pay of $351.00, as a result, we simply multiply the percentage of deduction by the gross pay to determine the dollar amount of each deduction.

the gross pay=$351

federal tax (assuming 20% of gross earnings)=$351*20%=$70.20

state tax (assuming 6% of gross earnings)=$351*6%=$21.06

social security deductions (assuming 7.05% of gross earnings)=$351*7.05%=$24.75

group health insurance (assuming 13% of gross earnings)=$351*13%=$45.63

pension deduction (assuming 6.5% of gross earnings)=$351*6.5%=$22.82

total deductions=$70.20+$21.06+$24.75+$45.63+$22.82

total deductions=$184.46

net pay=$351-$184.46

net pay=$166.54

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