We are given
The average income, I, in dollars is
[tex]I=-425x^2+45500x-650000[/tex]
(a)
now, we are given
average income is $275000
so, [tex]I=275000[/tex]
now, we can set them equal
and then we can solve for x
[tex]275000=-425x^2+45500x-650000[/tex]
[tex]-425x^2+45500x-925000=0[/tex]
we will have to use quadratic formula
[tex]x=\frac{-45500+\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{-\sqrt{45500^2-1572500000}+45500}{850}[/tex]
[tex]x=\frac{-45500-\sqrt{45500^2-4\left(-425\right)\left(-925000\right)}}{2\left(-425\right)}:\quad \frac{\sqrt{45500^2-1572500000}+45500}{850}[/tex]
we get
[tex]x=27.28199[/tex]
[tex]x=79.776[/tex]
we need to find youngest age
It means that we need to choose smallest value
so,
[tex]x=27[/tex]............Answer
(b)
we are given
x=40
so, we can plug it and find I
[tex]I=-425(40)^2+45500(40)-650000[/tex]
[tex]I=490000[/tex]..............Answer
To find the youngest age for an average income of $275,000 for a lawyer, one would solve the quadratic equation formed by setting the income function equal to $275,000 and choosing the positive solution. The predicted average annual income of a 40-year-old lawyer is calculated by plugging 40 into the income function and rounding to the nearest dollar.
The student asked two questions about a quadratic function representing the average income of a lawyer by age.
Finding the youngest age for a certain average income
To find the youngest age at which the average income of a lawyer is $275,000, we set the quadratic income function I = -425x^2 + 45,500x – 650,000 equal to $275,000 and solve for x. After simplifying, we get a quadratic equation that can be solved using factorization, completing the square, or applying the quadratic formula. Once we find the values for x, we select the positive solution since age cannot be negative, and round it to the nearest year.
Predicted average annual income for a 40-year-old lawyer
To determine the average income for a 40-year-old lawyer, we substitute x = 40 into the given income model and calculate the value of I. The result will be the predicted average annual income of a 40-year-old lawyer, rounded to the nearest whole dollar.
what is the radius of a circle with circumference 56 in?
the radius is 8.917197452 in
Select ALL the correct answers.
Todd is at the grocery store purchasing ingredients for homemade granola. He needs x ounces of almonds, which are priced at m dollars per ounce in the baking section. The total cost of the other ingredients is b dollars. The following expression represents the total amount of money that Todd will spend on all of the granola ingredients.
Todd later finds almonds in the bulk section that are half the price of those in the baking section. If he purchases the almonds in the bulk section, which of the following statements are true about the given expression?
The value of x will change because that is the price of the almonds
Therefore mx will change
And the value of mx+b will decrease because the price is cheaper
Answer:
The correct statements are :
1. The value of mx will change.
2. The value of m will change.
3. The value of mx+b will decrease.
Step-by-step explanation:
Todd needs x ounces of almonds, which are priced at m dollars per ounce in the baking section. So, price of x ounces becomes = mx
The total cost of the other ingredients is b dollars.
Hence, total cost is given as = [tex]mx+b[/tex]
Now, Todd later finds almonds in the bulk section that are half the price of those in the baking section.
So, now price is :[tex]\frac{m}{2}[/tex]
And total price for 'x' ounce will become: [tex]\frac{mx}{2}+b[/tex] dollars.
Therefore, if Todd purchases the almonds in the bulk section, the total cost will decrease.
The correct statements are :
1. The value of mx will change.
2. The value of m will change.
3. The value of mx+b will decrease.
Can you help me find the side??? It's trigonometry!!
Answer: 5.6
===================================
Work Shown:
cos(angle) = adjacent/hypotenuse
cos(B) = AB/BC
cos(62) = AB/12
12*cos(62) = AB
AB = 12*cos(62)
AB = 5.63365875
AB = 5.6
20 points if right.
Answers:
A. continuous data, graph B
B. discrete data, graph B
C. discrete data, graph A
D. continuous data, graph A
The answer is option A
I'm not sure how to get the answer can you help me?
Suppose △PKN≅△BGH.
Which other congruency statements are correct?
Select each correct answer.
A △NKP≅△HBG
B △KPN≅△BHG
C △NPK≅△HBG
D △KNP≅△GHB
C and D are correct. Look how the letters correspond to each other.
You are making balloons arrangements for a brithday party. There are 16 white balloons and 24 red balloons each arrangement must be identical what is the greatest number of arrangements you can make using every ballon
Answer: 8
Step-by-step explanation:
Find the GCF of 16 and 24
16: 2 x 2 x 2 x 2
24: 2 x 2 x 2 x 3
GCF = 8
NOTE: Each basket will contain 2 white and 3 red ballons.
A fair was attended by 834,009 people. Round the number to the nearest ten thousand.
A fair was attended by 834,009 people
Rounding up this number of people to nearest ten thousand.
9 has a 'ones' value
Going to the right from left:
Second last zero has a 'tens' value.
Third from last zero has a 'thousands' value
4 has 'ten thousands' value
Round up 4 and because it is less than five it converts to zero
This gives an answer of 830,000.
Ira writes that the sum of a+b is a number that is located a distance of [b] units from a on the number line. Choose four values for a and b and show that this is true. Use the four number lines on the right to show your work and support your answer
Answer:
1. Take a=4, b=6
a+b
=4+6
=10( Both are positive integers)
2. a=4 , b= -6
then 4 + (- 6)
= 4 - 6
= -2 [Smaller is positive integer and larger is negative integer , So subtract smaller from larger and apply the sign possessed by larger integer]
3. a = -4, b= -6
a+ b
= -4 -6
=-10 [ Both are negative integers add them apply - sign before the number.]
4. a = -4, b=6
a +b
= -4+ 6
= 2 [one is positive and other is negative subtract smaller from larger and apply positive sign before the number.]
A babysitter is trying to determine the ages of three children: Jerome, Keenan, and Leitha. She knows the following facts about their ages: the sum of Jerome’s and Keenan’s ages is 18 years; the sum of Jerome’s and Leitha’s ages is 19 years; and the sum of Keenan’s and Leitha’s ages is 21 years. How old is Keenan?
Answer:
10 years.
Step-by-step explanation:
Let Jerome, Keenan, and Leitha have ages of x,y and z respectively,.
Then given that x+y =18 ... i
x+z =19 ... ii
y+z = 21 ... iii
From the above information we are to find out y and i.e.Keenan age.
Add all the 3 equations
Left side becomes x+y+y+z+z+x = 2(x+y+z)
and right side becomes = 18+19+21 = 58
In other words, 2(x+y+z) = 58
Divide by 2
x+y+z =29 ... iv
From the equation iv subtract ii
x+z =19
We get y = 10
Hence Kennan age = 10 years
Get-down electronics buys mp3 players with an invoice date of june 29, and terms of sale of 4/20 eom. Calculate the discount date.
Answer:
August 20.
Step-by-step explanation:
1. The problem says that the invoice date is June 29 and terms of sale of [tex]\frac{4}{20}[/tex] EOM. This means that if the payment is made 20 days from the end of the month, a percent of 4% may be taken as cash discount.
2. If the number of days in that month is greater than 25, you must add another month. Therefore, you must add July and 20 days of August.
3. Therefore, the discount date is August 20.
-9 - 4b = 3 + 8b how do you solve this?
Have all the terms containing the variable on one side of the equation and the rest of the terms on the other side of the equation.
I will put all terms containing the variable b on the left side of the equation and the rest on the right side of the equation.
Subtract 8b from both sides of the equation.
-9 -12b = 3
Add 9 to both sides of the equation to isolate the term with the variable b.
-12b = 12
Divide both sides of the equation by -12 to solve for b.
b = -1
Danny poured 78 liters of water into containers x, y, and z. The ratio of the volume of water in container x to the volume of water in container y is 5:2. The ratio of the volume of water in container y to the volume of water in container z is 8:11.
a) how much water was poured into container s?
b) how much more water was poured into container x than container z?
a) Container z: 22 liters. b) Container x has 18 liters more than container z.
To solve this problem, let's first find the volumes of water in containers x, y, and z.
Let's represent the volume of water in container x as 5x liters and the volume of water in container y as 2x liters, based on the ratio given.
Then, according to the ratio of y to z, if the volume of water in container y is 2x, the volume of water in container z is (11/8) × 2x liters.
Now, we can set up an equation to find the value of x.
5x (container x) + 2x (container y) + (11/8 × 2x) (container z) = 78 liters
5x + 2x + (11/8 × 2x) = 78
5x + 2x + (11/4 × x) = 78
Multiplying through by 4 to clear the fraction:
20x + 8x + 11x = 312
39x = 312
x = 312 / 39
x = 8
Now, we can find the volumes of water in each container:
Container x = 5x = 5 × 8 = 40 liters
Container y = 2x = 2 × 8 = 16 liters
Container z = (11/8) × 2x = (11/8) × 16 = 22 liters
a) The amount of water poured into container s (assuming it was meant instead of "s" since "s" wasn't mentioned in the problem) is the volume of water in container z, which is 22 liters.
b) The difference in the amount of water poured into containers x and z:
Volume in container x - Volume in container z = 40 liters - 22 liters = 18 liters.
So, 22 liters of water was poured into container s, and 18 liters more water was poured into container x than into container z.
Jason and his 3 roommates share the cost of the electric bill ece
What is the result of dividing x^3−7 by x + 2?
x^2−2x+4− 15/x+2
x^2−2x+4− 1/x+2
x^2−2x+4+ 1/x+2
x^2−2x+4+ 15/x+2
Answer:
Choice A: x^2−2x+4− 15/x+2
Step-by-step explanation:
The result of the division of the cubic polynomial x^3-7 by the binomial [tex]x+2 is x^2-2x+4 - 15/(x+2)[/tex], as obtained by carrying out the process of polynomial division.
Explanation:The student is asking for the result of dividing a cubic polynomial, x^3-7, by a binomial, x+2. To do this, we need to perform polynomial division. The result of this division is [tex]x^2-2x+4 - 15/(x+2)[/tex]. We get this by setting up and performing the division, which operates similarly to long division, except that you are working with polynomials instead of numbers. The steps involved are too complicated to list here, but involve repeatedly subtracting multiples of x+2 from x^3-7 until the remainder is less than x+2, at which point you can't subtract more multiples of x+2.
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Solve the systems by eliminations 3x-3y+4z=11
More than one quarter of the netherlands lies below sea level.Lucas visits a museum located at an elevation of 7m and bicyclesto the neighborhood of purmerend which has an elevation of -16m. What is the change of elevation for his trip?
Elisa withdrew $20 at a time from her bank account and withdrew a total of $140.Francis withdrew $45 at a time from his bank account and withdrew a total of $270.Who made the greater number of withdrawals?Justify you answer
Divide the total amount withdrawn by the amount of each withdrawal for both people.
Elisa : 140 / 20 = 7 withdrawals.
Francis : 270 / 45 = 6 withdrawals.
Elisa made the most withdrawals because seven is greater than six.
Expand by using the distributive property: (a + bc)2x
2xa + 2xbc (just multiply both units in the paranthesis by whats on the outside.)
(a + bc)2x
= 2x*a + bc*2x
= 2ax + 2bcx
The fare for a taxi cab is a $2 flat fee plus an additional $1.50 for each mile. Which equation represents the total cab fare in dollars?
The hottest temperature recorder in the world and degrees fahrenheit can be found by multiplying 13.46 x 10 finest temperature justify your pod seizur the hottest temperature recorded in the world and degrees fahrenheit can be found by multiplying 13.46 x 10 finest temperature justify your producer
The hottest temperature ever recorded on Earth was 134°F in Death Valley, California. If you were to multiply this temperature by 13.46, then the result would not provide a realistic temperature on Earth. This is due to the non-linear relationship of Fahrenheit or any temperature scale with its multiples.
Explanation:The question seems to be asking whether, if the hottest recorded temperature in the world in degrees Fahrenheit is multiplied by 13.46, the result would be equal to ten times that same temperature. This arithmetic operation would not, in reality, be accurate in defining the world's hottest temperature. This is because Fahrenheit temperatures don't have a linear relationship with its multiples. For example, if the highest recorded temperature is 120°F, 10 times that would be 1200 and this temperature is not realistic on earth.
The hottest temperature ever recorded on Earth was 134°F (56.7°C) in Furnace Creek Ranch, Death Valley, California, USA on July 10, 1913. This temperature was recorded using a standard thermometer in a ventilated, shaded structure 1.5 meters above the ground, which is the standard method for measuring ambient temperature. Doubling or multiplying this figure as suggested wouldn't produce a viable result in real-world physics or climatology.
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7 1/8 is equal to greater than or less than 7.025
Maria buys a dress that is 15% off. She then uses a coupon to get an additional 10% off the sale price. She pays $91.80 for the dress. What was the original price of the dress? PLZ INCLUDE STEPS SO I KNOW HOW TO DO IT!!
Answer:
$120
Step-by-step explanation:
First add the 10% back, to do so make it a decimal by moving the . over to the left twice.
Now setup the equation OP= New price/(1-discount)
91.80/(1-.10)=102
So the price before the 10% discount is $102
Now set it up again with the new numbers.
102/(1-.15)=120
So the original price before all discounts was $120
*Let p = original price
So firstly, how would we get the price when it's 15% off? You would find multiply the price by 0.15 (15% in decimal form) and then subtract the product from the original price. This can be represented as [tex](p-p\times0.15)[/tex]
Next, we would have to use the 10% off when the dress is already 15% off. The process is similar: Multiply 0.10 (10% in decimal form) with 15% off dress, then subtract the product from the 15% off price. This can be represented as [tex](p-p\times0.15)-0.10(p-p\times0.15)[/tex]
Now since the price is equal to $91.80, we would equal the prior expression to 91.80 as such: [tex](p-p\times0.15)-0.10(p-p\times0.15)=91.80[/tex] From here we can solve for p.
Firstly, solve the multiplication inside of the parentheses:
[tex](p-0.15p)-0.10(p-0.15p)=91.80[/tex]
Next, distribute -0.10 to (p - 0.15p):
[tex]p-0.15p-0.10p+0.015p=91.80[/tex]
Next, combine like terms:
[tex]0.765p=91.80[/tex]
Lastly, divide both sides by 0.765:
[tex]p=120[/tex]
Answer:The original price of the dress was $120.
Factor the expression completely over the complex numbers.
x^4 + 10x^2 + 25
Enter your answer in the box.
Answer:
Step-by-step explanation:
I would say
(x+5)(x-5)(x+5i)(x-5i)
The factor of the expression x⁴ + 10x² + 25 is (x + √5i)(x - √5i) after using the factor method.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
It is given that:
The expression is:
= x⁴ + 10x² + 25
Let t = x²
= t² + 10t + 25
= (t + 5)²
= (x² + 5)²
x² = -5
x = ±√5i
(x + √5i)(x - √5i)
Thus, the factor of the expression x⁴ + 10x² + 25 is (x + √5i)(x - √5i) after using the factor method.
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If three hats cost 24.30 how much is 1 hat
Determine if the rates $24 for 6 hours of work and $36 for 8 hours of work are equivalent. Explain your reasoning
Solve m=h-w/8 for the variable hsolve the above equation for w
[tex]\dfrac{h-w}{8}=m\ \ \ \ |\cdot8\\\\h-w=8m\ \ \ \ |-h\\\\-w=-h+8m\ \ \ |\text{change the signs}\\\\\boxed{w=h-8m}\\--------------------------\\h-\dfrac{w}{8}=m\ \ \ \ |-h\\\\-\dfrac{w}{8}=-h+m\ \ \ \ |\cdot(-8)\\\\\boxed{w=8h-8m}[/tex]
The sides of a ladder are parallel. Since the rungs are perpendicular to one side of the ladder, what conclusion can be made?
- The sides are parallel to the rungs.
- The rungs are parallel to the sides.
- The sides are perpendicular to each other.
- The rungs are perpendicular to the other side.
- The rungs are perpendicular to the other side.
Answer:
The rungs are perpendicular to the other side.
Step-by-step explanation:
Given
The sides of ladder are parallel.Rungs is perpendicular to one side of the ladder.
Let [tex]a\parallel b[/tex]
[tex]a\perp c[/tex]
When two lines are parallel then the slopes of two lines are equal.
We can say [tex]m_1=m_2[/tex]
Where [tex]m_1[/tex]= slope of line a( side of ladder)
[tex]m_2[/tex]= solpe of line b( side of ladder)
When two lines are perpendicular then slopes of two lines are opposite reciprocal to each other.
We can say [tex]m_2=-\frac{1}{m_3}[/tex]
Where [tex]m_2[/tex]= Slope of line b
[tex]m_3 [/tex]=Slope of line c (rung)
By transitive property of equality we get
[tex]m_1=-\frac{1}{m_3}[/tex]
Hence, the slope of side of ladder a and rung c are opposite reciprocal to each other.Therefore , the rungs are perpendicular to the other side.
Which expression is equal to 7/√5?
7√5/25
35√5
49/√35
7√5/5
[tex]Solution, \frac{7}{\sqrt{5}}=\frac{7\sqrt{5}}{5}\quad \left(\mathrm{Decimal:\quad }\:3.13050\dots \right)[/tex]
Answer Choice A. [tex]7\cdot \frac{\sqrt{5}}{25}=\frac{7\sqrt{5}}{25}\quad \left(\mathrm{Decimal:\quad }\:0.62610\dots \right)[/tex]
Answer Choice B. [tex]35\sqrt{5}=78.26238\dots[/tex]
Answer Choice C. [tex]\frac{49}{\sqrt{35}}=\frac{7\sqrt{35}}{5}\quad \left(\mathrm{Decimal:\quad }\:8.28251\dots \right)[/tex]
Answer Choice D. [tex]7\cdot \frac{\sqrt{5}}{5}=\frac{7\sqrt{5}}{5}\quad \left(\mathrm{Decimal:\quad }\:3.13050\dots \right)[/tex]
The correct answer is D. 7√5/5
Hope This Helps!!!
The expression that is equal to the equation 7/√5 is 7√5/5. The fourth option is correct.
[tex]\mathbf{\dfrac{7}{\sqrt{5}}}[/tex]
In the given mathematical expression, fractions containing square roots are known as surds. They are usually no longer further simplified but they can be converted to decimal numbers with the use of calculators. Surds are commonly known as irrational numbers.
From the given expression, we are going to convert it to decimal numbers to determine the options that correspond to it.
[tex]\mathbf{\dfrac{7}{\sqrt{5}} = 3.1305}[/tex]
From the given options:
[tex]\mathbf{\dfrac{7 \sqrt{5}}{25} = 0.6261 }[/tex]
[tex]\mathbf{35 \sqrt{5} = 78.26}[/tex]
[tex]\mathbf{\dfrac{49}{\sqrt{35}} = 8.2825}[/tex]
[tex]\mathbf{\dfrac{7\sqrt{5}}{5} = 3.1305}[/tex]
Therefore, from the above solution, the fourth option correctly corresponds and is equal to the expression 7/√5
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which expression is equivalent to the expression below? (m+3/m^2-16)/(m^2-9/m+4)
Answer:
B. 1/(m-4)(m-3)
Answer:
[tex]\frac{1}{(m-3)(m-4)}[/tex]
Step-by-step explanation:
(m+3/m^2-16)/(m^2-9/m+4)
Lets factor the numerator and denominator
use identity a^2 - b^2 = (a+b)(a-b)
[tex]m^2 - 16= m^2 - 4^2 = (m+4)(m-4)[/tex]
[tex]m^2 - 9= m^2 - 3^2 = (m+3)(m-3)[/tex]
we have divisiion sign in between, change the division symbol in to multiplication symbol by flipping the fraction in the denominator
(m+3/m^2-16)*(m+4/m^2-9)
[tex]\frac{m+3}{(m+4)(m-4)} * \frac{m+4}{(m+3)(m-3)}[/tex]
Cancel put m+3 and m+4 at the top and botom
[tex]\frac{1}{(m-3)(m-4)}[/tex]
Your total restaurant bill for food and drinks is $63.57. What is a good estimated cost for just the food and drinks
To estimate the cost of just the food and drinks, subtract the cost of other items from the total bill.
Explanation:To estimate the cost of just the food and drinks, we need to subtract the cost of other items from the total bill. If we assume that the bill includes a fixed cost of $25 for other items such as taxes and service charges, we can subtract this amount from the total bill to get an estimate for just the food and drinks. So, the estimated cost for just the food and drinks would be $63.57 - $25 = $38.57.
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The estimated cost for just the food and drinks is $63.57.
Explanation:To find the estimated cost for just the food and drinks, you need to subtract any other expenses from the total bill.
For example, if there were additional charges for tax, service fees, or tips included in the total bill, you would subtract those amounts.
Let's assume there are no additional charges, so the estimated cost for just the food and drinks would be equal to the total bill amount of $63.57.
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