The average income,I, in dollars, of a lawyer with an age of x years is modeled with the following function:
Answers
Solving a quadratic equation, the youngest age for which the average income of the lawyer is of $250,000 is of 26 years.
What is a quadratic function?A quadratic function is given according to the following rule:
y = ax² + bx + c
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation that models the income as function of age is given by:
I(x) = -425x² + 45500x - 650000.
The income is of 250,000 when I(x) = 250000, hence:
250000 = -425x² + 45500x - 650000.
425x² - 45500x + 900000 = 0.
Hence the coefficients are a = 425, b = -45500 and c = 900000, then:
[tex]\Delta = (-45500)^2 - 4(425)(900000) = 540250000[/tex][tex]x_1 = \frac{45500 + \sqrt{540250000}}{2(425)} = 80.87[/tex][tex]x_2 = \frac{45500 - \sqrt{540250000}}{2(425)} = 26.18[/tex]The youngest age for which the average income of the lawyer is of $250,000 is of 26 years. (the oldest is of 81 years).
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Related Questions
for #13-14 determine if the lines are parallel, perpendicular or neither 10x +5y=-5 and y=-2x+6
Answers
Answer:
48
because. Of the time
The list of ingredients for chocolate
brownies given at right will make 16
brownies.
Use the list to decide how much of
each ingredient is needed to make 6
brownies.
2
3
5 ounces unsweetened chocolate
1/2 cups sugar
cup butter
2 teaspoons vanilla
2 eggs
1 cup flour
www
cup(s) of butter is needed.
(Simplify your answer. Type an integer, simplified fraction, or mixed number.)
ounce(s) of chocolate are needed
(Simplify your answer. Type an integer, simplified fraction, or mixed number.)
Answers
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
How much ingredients are needed?
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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Please help due tonight.
Answers
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.
How many boxes of cereal can you buy with $42 if one box costs $5.25? As Equation Review
Answers
Answer:
8
Step-by-step explanation:
$ 42 / 5.25 $ / box = x = 8 boxes
a gas station sells regular gas for $2.10 per gallon and premium gas for $2.90 a gallon. at the end of a business day 280 gallons of gas had been sold, and receipts totaled $652. how many gallons of each type of gas had been sold?
Answers
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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Help with all answers
Answers
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.
A straight line intersecting both the parallel lines is called a transversal.The alternate interior or exterior angles formed are always equal.The corresponding angles are equal.The co-interior angles are supplementary.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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Amys weight this year is 50 pounds lessthan twice her weight from last year. if she weighs 120 pounds this year, what equation can be used to find her weight from last year?
Answers
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. the researchers attend political debates and record how frequently each candidate displays positive facial expressions. which research method are the researchers using? a. random sample b. case study c. naturalistic observation d. survey
Answers
researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. c. naturalistic observation
What is 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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7. Vernon filled his gas tank with 16 gallons of
gas. The table shows the linear relationship
between the amount of gas remaining in his
tank and the miles driven. What is the rate of
change of gallons of gas per mile driven?
Miles Driven
Gas (gal)
0,16
84,12
105,11
336,0
* coordinates is a chart x representing miles driven y representing gas(gal)
Answers
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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If the length of a certain rectangle is increased by 1, then the area of the rectangle is increased by 12. If instead, the width is increased by 2, then the area of the rectangle is increased by 42. What is the area of the original rectangle?
Answers
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
what are corresponding angles
Answers
a) 3² x 3* = 37
Find the value of x.
b) 78 + 7 = 76
Find the value of y.
c) (q¹)² = q¹²
12
Find the value of z.
Marks
Answers
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?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.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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What is the measure of x?
Answers
Mrs. Figueroa made a spaghetti dinner for the cheerleaders after practice. She purchased four and three fourths pounds of beef for $3.99 per pound. How much money did she spend on the beef for the spaghetti?
$7.25
$8.87
$9.98
$18.95
Answers
Step by step
4 3/4 pounds x $3.99 per pound
Change your fraction into a decimal and multiply
4.75 x 3.99 = 18.95
Or
4 3/4 x 3.99
Change to improper fraction
19/4 x 3.99
Multiply across
75.81/4
Divide = $18.95
Problem solved!!
Answer:
$18.95
Step-by-step explanation:
Calculate the electric potential energy in a capacitor that stores 1.0 x 10^-10 C
of charge at 100.0 V. Use PE = 1/2QAV.
OA. 1.0 x 10-8 J
OB. 1.0 x 102 J
O C. 5.0 × 10¹ J
OD. 5.0 × 10-9 J
Answers
The electric potential energy is 5.0 × 10^(-9) J
How to calculate the electric potential energy?
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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Tallie wants to buy a new iPhone. The iPhone costs
$850. She has saved $325 to put down as an initial
payment and will pay another $75 each month until
the phone is paid off. How many months will it take
for Tallie to pay for her new iPhone?
Answers
Answer:
7 months to pay it off.
Step-by-step explanation:
see attached for details.
At Cheng's Bike Rentals, it costs $46 to rent a bike for 9 hours. How many hours of bike use does a customer get per dollar? Answer each part. If necessary, round your answers to the nearest hundredth.
Answers
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
is james scored a 40 on a test with a mean of 38 and the standard deviation was for whataburger z-score be
Answers
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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finding the rise and the run on the graph
Answers
Answer:
rise = 4, run = 5. The slope would be 4/5
Step-by-step explanation:
You go up by four then right by 5
Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?
l ≤ 12
2l + 2w < 30
l > 12
2l + 2w < 30
l ≤ 12
l + w < 30
l > 12
l + w < 30
Answers
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
How to determine the system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?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.
What is the slope of the line that passes through the points (10, 8) and (7, 14)?
Write your answer in simplest form.
Answers
Answer:
-0.2667
Step-by-step explanation:
m =y2 - y1
x2 - x1
=14 - (10)
-7 - (8)
=14 - 10
-7 - 8
=4
-15
Subtract (5.3 x 108) − (8.2 x 106).
2.9 x 102
5.218 x 102
2.9 x 108
5.218 x 108
Answers
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
Given f(x) = 2(3 - x) - 2x, what is the value of f(x) = -10?
Answers
2(3- - 10) - 2 (-10)
2*(26) - 20
52 -20= 32
So f(-10)= 32
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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Which of the following is equivalent to (7y + 5x) + 8x?
35xy + 8y
7y + 13x
8x(7y + 5x)
7y + 40x
Answers
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).
What is algebra?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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Solve the inequality 34q−23q<512q−112 and write the solution in interval notation.
Answers
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]
Use the distributive property to solve the equation. 5x/2-x=x/6-8/3.
Answers
Answer:
Step-by-step explanation:
i know
the limit of f(x) as xa describes what happens to f(x) when x is near, but not equal to, the value a.
Answers
If x is near but not equal to, the value an is that f(a) then the function will not continue.
What is the limit?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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of the 35 flavors of ice cream at an ice cream parlor, 25 flavors contain some sort of nuts, 12 are fat-free, and 8 both fat-free and contain nuts. how many of the flavors at the ice cream parlor neither are fat-free nor contain nuts?
Answers
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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Find the surface area of a cylinder with a height of 8 inches and base diameyer of 6 inches i need help badly
Answers
The surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches
How to find the surface area of a cylinder with a height of 8 inches and base diameter of 6 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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Given: B is midpoint if AC
C is the midpoint if BD
Prove: AB is congruent to CD
Answers
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