The average income,I, in dollars, of a lawyer with an age of x years is modeled with the following function:

 z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]   is the value of z in linear equation.

What in mathematics is a linear equation?

a ) Simplify using exponent rule with same base  = a[tex]a^{n} . a^{m} = a^{n + m}[/tex]

Based on the given conditions, corresponding exponents are equal                                                                              = [tex]3^{2 + x} = 3^{7}[/tex]

Rearrange unknown terms to the left side of the equation                                                                           = 2 + x = 7

 Calculate the sum or difference                                                                               x = 5

b) Calculate the power 5764801 + [tex]7^{y}[/tex] = 117649

Rearrange unknown terms to the left side of the equation

         7^{y} = 117649 - 5764801

The equation is not defined.

c)  the equations  z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]

   answer    z =  3  or z = [tex]\frac{In q^{12} }{In q^{4} }[/tex]

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The surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches

The given parameters are

Height, h = 8 inches

Diameter, d = 6 inches

The radius is calculated as

r = d/2

So, we have

r = 6/2

r = 3

The surface area of a cylinder is calculated as

S = 2πr(r + h)

So, we have

S = 2 * 3.14 * 3 * (3 + 8)

Evaluate

S = 207.24

Hence, the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches

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Answer:   [tex]q=\frac{112}{501}[/tex]

Step-by-step explanation:

1) Add similar elements: 11q < 512q - 112

2) Subtract 512q from both sides: 11q - 512q < 512q - 112 - 512q

3) Simplify: -501q < -112

4) Multiply both sides by -1 to reverse the inequality: (-501q)(-1) > (-112)(-1)

5) Simplify: 501q > 112

6) Divide both sides by 501: [tex]\frac{501q}{501} > \frac{112}{501}[/tex]

7) Simplify: [tex]q=\frac{112}{501}[/tex]

Answer:

-0.2667

Step-by-step explanation:

m =y2 - y1

x2 - x1

=14 - (10)

-7 - (8)

=14 - 10

-7 - 8

=4

-15

The electric potential energy is 5.0 × 10^(-9) J

The formula to calculate the electric potential energy in a capacitor is;

E = 1/2 * C * V²

Where;

E = electric potential energy

C = capacitance = charge

V = voltage applied

We are given;

Voltage applied; V = 100 V

Capacitance (Charge) = 1 × 10⁻¹⁰ C

Plugging in the relevant values gives

E = 1/2  * 1 × 10⁻¹⁰ *  100

E = 1/2 * 1 × 10⁻⁸

E = 0.5  × 0⁻⁸ volts

E = 5.0 × 10^(-9) J

Thus, we conclude that the electric potential energy is 5.0 × 10^(-9) J

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Answer:

7y + 13x

Step-by-step explanation:

Let's simplify step-by-step.

7y+5x+8x

Combine Like Terms:

=7y+5x+8x

=(5x+8x)+(7y)

=13x+7y

The expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x which is correct answer would be option (B).

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction rule is abbreviated as PEMDAS. This rule is used to answer the problem correctly and properly.

⇒ (7y + 5x) + 8x

Open parenthesis and combine like terms to get the solution,

⇒ 7y + 5x + 8x

⇒ (5x + 8x) + (7y)

⇒ 13x + 7y or

⇒ 7y + 13x

Therefore, the expression 7y + 13x is equivalent to given expression (7y + 5x) + 8x.

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Answer:

$18.95

Step-by-step explanation:

The number of ice creams according to the probability,  Neither contain nuts nor are fat free is 6.

According to the statement

We have to find that the ice creams that neither are fat-free nor contain nuts.

So, For this purpose, we know that the

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.

From the given information:

There are 35 flavors of ice cream at an ice cream parlor, 25 flavors contained ice creams.

Contain nuts = 25

Are fat free = 12

Are both = 8

Then

Contain nuts or are fat free = 25+12-8 = 29

Total = 35

Neither contain nuts nor are fat free = 35-29 = 6.

So, The number of ice creams according to the probability,  Neither contain nuts nor are fat free is 6.

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Answer:

190

Step-by-step explanation:

(120*2) - 10 = 190

hope this helped !!

researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. c. naturalistic observation

A study technique called naturalistic observation includes watching participants in their natural settings. Many psychologists and other social scientists employ this strategy. It is an approach to qualitative research that emphasizes gathering, analyzing, and describing non-numerical data.

When performing lab research would be impractical, expensive, or would adversely influence the subject's behavior, it may be helpful. Naturalistic observation is to capture behavior as it happens in its natural environment without intervention or efforts to change any of the factors. In a lab context, people frequently act differently than they would in the wild. Sometimes, researchers wish to watch their subject's behavior "in the wild".

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Answer:

8

Step-by-step explanation:

$ 42 / 5.25 $ / box = x  = 8 boxes

Answer:

Step-by-step explanation:

i know

If x is near but not equal​ to, the value an is that f(a) then the function will not continue.

Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.

In another word, limit is a mathematical concept in which we find out the value of any function at a point by its adjacent very close point.

If a function f(x) is defined near to x = a but not a then there will be no continuity of that function at that point.

To exist a limit at x = a

LHL = RHL

But for continuity

LHL = RHL = f(a)

Hence "If x is near but not equal​ to, the value an is that f(a) then the function will not continue".

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Answer:

0.20 hours

Step-by-step explanation:

Bike rental is $46 for 9 hours.

We want to find hours per dollar, so divide time by cost:

9 hours / 46 dollars = 0.19565217... hours/dollar

Rounded to nearest hundredth:

0.20 hours

The value of x for f(x) = 2 (3-x) -2x at f(x) = -10 is 4.

To find the value of f(x) when f(x) equals -10, we substitute -10 into the equation and solve for x.

Given:

f(x) = 2(3 - x) - 2x, we have:

-10 = 2(3 - x) - 2x

Let's simplify the equation step by step:

-10 = 6 - 2x - 2x

-10 = 6 - 4x

-10 - 6 = -4x

-16 = -4x

To solve for x, divide both sides by -4:

x = (-16) / (-4)

x = 4

Therefore, when f(x) = -10, the value of x is 4.

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Answer:

See proof below

Step-by-step explanation:

If B is the midpoint of AC, then AB = BC

If C is the midpoint of BD then BC = CD

Using the transitive property of equality, if a = b and  b = c  then a =c

We apply this to the above line segments and get

If AB = BC and BC = CD then AB=CD
For two line segments to be congruent they must have the same length

So AB is congruent to CD

Answer:   Let the length and breadth of a rectangle are x and y units , its area is x.y units^2

Step-by-step explanation: sorry no explanation

Vernon put 16 liters of gas in his tank. 21 miles per gallons of gas are consumed each mile that is driven.

Given that,

Vernon put 16 liters of gas in his tank.

The table depicts the linear relationship between the mileage driven and the amount of gas in his tank.

We have to find how many gallons of gas are consumed each mile that is driven.

From the table we can say

The total Distance is 336

The total gallons of gas is 16

Rate= Total distance/Total gallons

Rate=336/16

Rate=21 miles per gallons

Therefore, 21 miles per gallons of gas are consumed each mile that is driven.

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Answer: 5.218*10^8 ==> Option 4

Step-by-step explanation:

(5.3 x 10^8) − (8.2 x 10^6)=

(5.3*10^2 x 10^6) − (8.2 x 10^6)=

(5.3*100*10^6)-(8.2*10^6)=

(530*10^6)-(8.2*10^6)=

(530-8.2)*10^6=

(530.0-8.2)*10^6=

521.8*10^6=5.218*10^8 ==> Option 4

The following ingredients are needed to make 6 brownies:

Cups of butter needed  is 1/4 cups

Ounces of chocolate needed is 1 7/8

Cups of sugar needed is 9/16

Ounces of vanilla needed is 3/4

Integers are whole numbers. It is a number without a fraction or decimal component. Integers can either be positive, negative or zero. An example of an integer is -1.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a fraction is which the numerator is less than the denominator.

Cups of butter needed = (2/3 x 6) / 16

4 / 16 = 1/4 cups

Ounces of chocolate needed = (5 x 6) / 16

= 30 / 16 = 1 14/16 = 1 7/8

Cups of sugar needed = ( 1 1/2 x 6) / 16

(3/2 x 6) / 16 = 9/16

Ounces of vanilla needed = ( 2 x 6) / 16

= 12 / 16 = 3/4

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The value of m∠1 is 158° as the two line x and y are parallel.

Two lines are said to be parallel if they do not meet at any point and the perpendicular distance between them is always the same.

In the given figure it is given that x║y and m∠2 = 22°.

Now let us use the above principles to solve the value of the other angles.

m∠2+m∠1 = 180°(linear pair)

or, m∠1= 180°-22°

or, m∠1=158°

m∠2+m∠3 = 180°(co-interior angles are supplementary)

or,m∠3=158°

m∠2=m∠4(Corresponding angles are equal)

or, m∠4=22°

m∠2=m∠5 (vertically opposite angles are equal)

or, m∠5=22°

m∠6=m∠1 (vertically opposite angles are equal)

or, m∠6=158°

m∠2=m∠7(alternate angles are equal)

or, m∠7=22°

m∠3=m∠8 (vertically opposite angles are equal)

or, m∠8=158°

Hence all the above angles are calculated using the properties of parallel lines.

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Answer:

7 months to pay it off.

Step-by-step explanation:

see attached for details.

200 gallons of regular gas and 80 gallons of premium gas were sold.

Let the amount of regular gas sold be x gallons. So, the amount of premium gas sold will be (280 - x).

Now, forming the equation using the given information, to find the amount of each type of gallon.

Equation -

2.10x + 2.90(280 - x) = 652

Performing multiplication with values inside bracket in Left Hand Side

2.10x + 812 - 2.90x = 652

Rewriting the equation -

812 - 652 = 2.90x - 2.10x

Performing subtraction

160  = 0.8x

Rewriting the equation according to x

x = 160÷0.8

Performing division to find the value of x

x = 200

So, 200 gallons of regular gas was sold.

Amount of premium gas sold = 280 - 200

Performing subtraction

Amount of premium gas sold = 80 gallons

Hence, 200 gallons of regular gas and 80 gallons of premium gas was sold.

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The system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30

The given parameters are

Length = Not more than 12 inches

Perimeter = Less than 30 inches

"Not more than" means less than or equal to

So, we have

l ≤ 12

The perimeter of a rectangle is

P = 2l + 2w

So, we have

2l + 2w = Less than 30 inches

"Less than" is represented with <

So, we have

2l + 2w < 30

Hence, the system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30

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Answer:

a. I ≤ 12
    2l + 2w < 30

Step-by-step explanation:

i got it right on edge.

The value of z-score for James is 0.2

Step-by-step explanation:

From the formula of z-score we know that

z-score = individual score - mean / standard deviation

Given

James score = 40

Mean = 38

Standard deviation = 10 (missing in question)

To find

z-score =?

Let's put the values in the formula

z-score = 40-38/ 10

z-score = 0.2

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Answer:  Choice C

This is the result of subtracting 3x from both sides. The inequality sign does not flip. It only flips if we multiply or divide both sides by a negative number.

Answer:

rise = 4, run = 5. The slope would be 4/5

Step-by-step explanation:

You go up by four then right by 5

Answer:

48

because. Of the time