given f(x) = 4x+1
evaluate f(2)
f(2) = ?
evaluate f(-3)
f(-3)= ?
The value of the functions are:
f(2) = 9
f(2) = -11
Use the concept of fucntion defined as:
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
The given function is,
f(x) = 4x+1
Put x = 2 in the given fucntion,
f(2) = 4(2) + 1
f(2) = 9
Put x = -3 in the given fucntion,
f(2) = 4(-3) + 1
f(2) = -11
Hence, The functions,
f(2) = 9
f(2) = -11
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12y + 48 - 4y= 8(y - 6)
Shirley and Pam, working together, can mow the lawn in 6
6
hours. Working alone, Pam takes three times as long as Shirley. How long does it take Shirley to mow the lawn alone?
Answer:
each takes 3 together 3x3=9
Chef Smith will be serving a breakfast banquet for 300 guests. Each guest will be served a two-egg
omelet. How many dozen eggs should Chef Smith order?
Answer: 50
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
300(2) bcuz 300 guests and each person gets 2
600(12) bcuz 300(2) is 600 and a dozen is 12
=50
Convert the following metric units of length.
100 kilometers to meters
a 100,000 m
b 10,000 m
c 108,076 m
d 109,076 m
The conversion of 100 kilometers to meters would be,
100 kilometers = 100,000 meters
The correct answer is an option (a)
In this question we need to convert the metric units of length.
We need to convert 100 kilometers to meters.
We know that, 1 kilometer = 1000 meters
Let 100 kilometers = p meters
So, we get an expression,
p × 1 = 100 × 1000
From this expression we get,
p = 100,000 meters
This means, 100 kilometers = 100,000 meters
Therefore, the conversion of 100 kilometers to meters would be,
100 kilometers = 100,000 meters
The correct answer is an option (a)
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How many points are represented in the graph below? Enter a number or 'oo' if there are an infinite number
of points.
There are how many
points on the graph?
Answer:
Infinite
Step-by-step explanation:
The graph is continuous, so it passes through infinitely many points.
Prove that for all integers a, b, n, if n = a + b, then a ≤ n/2 or b ≤ n/2 using proof by contradiction.
From the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that all integers a, b, and n, if n = a + b, then a ≤ n/2 or b ≤ n/2. Let the value of a = 3 and b = 3 now the value of n will be:-
n = a + b
n = 3 + 3 = 6
a = 3, n = 6 then a ≤ n/2.
b = 3, n = 6 then b ≤ n/2.
Therefore, the example that if a = 3 and b = 3 so the value of n = 6. It means that a ≤ n/2 and b ≤ n/2.
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Find AB→+BC→+CD→+DE→+EF→
Answer:
34 I plus the word like in number it self
Chika's uncle makes perfect brownies. Chika noted how much sugar he uses based on how many batches
he makes:
Answer:
7.5 batches
Step-by-step explanation:
if he uses 0.6kg of sugar per 2 batches, it's 0.3kg per batch.
2.25kg would let us make
2.25kg / 0.3kg = 2.25 / 0.3 = 7.5 batches
Kubin Company’s relevant range of production is 12,000 to 16,000 units. When it produces and sells 14,000 units, its average costs per unit are as follows:
Average Cost per Unit
Direct materials $ 7.30
Direct labor $ 4.30
Variable manufacturing overhead $ 1.80
Fixed manufacturing overhead $ 5.30
Fixed selling expense $ 3.80
Fixed administrative expense $ 2.80
Sales commissions $ 1.30
Variable administrative expense $ 0.80
Required:
1. Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 14,000 units?
b. What is the total indirect manufacturing cost incurred to make 14,000 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 14,000 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the Manufacturing Department?
3. Assume the cost object is the company’s various sales representatives. Furthermore, assume that the company spent $39,200 of its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives’ compensation.
a. When the company sells 14,000 units, what is the total direct selling expense that can be readily traced to individual sales representatives?
b. When the company sells 14,000 units, what is the total indirect selling expense that cannot be readily traced to individual sales representatives?
Show less
3. Assume the cost object is the company’s various sales representatives. Furthermore, assume that the company spent $39,200 of its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives’ compensation.
a. When the company sells 14,000 units, what is the total direct selling expense that can be readily traced to individual sales representatives? (Round per unit value to 2 decimal places.)
b. When the company sells 14,000 units, what is the total indirect selling expense that cannot be readily traced to individual sales representatives?
3a. Sales commissions per unit
3a. Number of units sold
3a. Total sales commission $0
3a. Fixed portion of sales representatives’ compensation
3a. Total direct selling expense $0
3b. The total indirect selling expense
1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600.
1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200.
2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600.
2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200.
3a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.
3b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.
4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.
4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.
3a. Sales commissions per unit is $1.30.
3a. The number of units sold is 14,000 units.
3a. Total sales commission is $18,200.
3a. Fixed portion of sales representatives’ compensation is $14,000.
3a. Total direct selling expense is $18,200.
3b. The total indirect selling expense is $14,000.
Data and Calculations:Relevant production range = 12,000 to 16,000 units
Production and sales units = 14,000 units
Average Cost
per Unit
Direct materials $ 7.30
Direct labor $ 4.30
Variable manufacturing overhead $ 1.80
Direct cost per unit $13.40
Fixed manufacturing overhead $ 5.30
Total manufacturing cost per unit $18.70
Fixed selling expense $ 3.80 $53,200 ($3.80 x 14,000)
Fixed administrative expense $ 2.80 $39,200 ($2.80 x 14,000)
Total fixed costs per unit $6.60 $92,400 ($6.60 x 14,000)
Variable selling and admin:
Sales commissions $ 1.30
Variable administrative expense $ 0.80
Total variable selling and admin per unit = $2.10
1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600 ($13.40 x 14,000).
1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200 ($5.30 x 14,000).
2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600 ($13.40 x 14,000).
2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200 ($5.30 x 14,000).
3) Fixed selling expenses = $53,200 ($3.80 x 14,000)
Advertising expenses = $39,200
Sales Compensation = $14,000 ($53,200 - $39,200)
Sales Commission = $18,200 ($1.30 x 14,000)
Total Salespersons' compensation = $32,200
a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.
b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.
4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.
4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.
3a. Sales commissions per unit is $1.30.
3a. The number of units sold is 14,000 units.
3a. Total sales commission is $18,200 (14,000 x $1.30)
3a. Fixed portion of sales representatives’ compensation is $14,000.
3a. Total direct selling expense is $18,200.
3b. The total indirect selling expense is $14,000.
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Select the expression that has a quotient greater than 1. Explain your reasoning PLEASE ANSWER THIS
1. 4 2/3 ÷ 5 1/4
2. 3 1/8 ÷ 2 2/5
3. 1 6/7 ÷ 2 1/3
4. 5 3/4 ÷ 7 3/8
The expression involving fractions that have a quotient less than 1 is: 2. 3 ⅛ ÷ 2 ⅖
How to Solve Fractions?To solve each of the expressions involving fractions, convert mixed fractions into improper fractions before finding the quotient of each.
1. 4 ⅔ ÷ 5 ¼
Convert to improper fractions
14/3 ÷ 21/4
14/3 × 4/21
= 56/63 (less than 1)
2. 3 ⅛ ÷ 2 ⅖
Convert to improper fractions
25/8 ÷ 12/5
25/8 × 5/12
125/96 (greater than 1)
3. 1 6/7 ÷ 2 1/3
13/7 ÷ 7/3
13/7 × 3/7
= 39/49 (less than 1)
4. 5 3/4 ÷ 7 ⅜
23/4 ÷ 59/8
23/4 × 8/59
= 184/236 (less than 1)
Therefore, the expression involving fractions that have a quotient less than 1 is: 2. 3 ⅛ ÷ 2 ⅖
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Copy and complete the table of values for
y = -2x² + 4x + 9.
What numbers replace A and B?
Answer:
Below in bold.
Step-by-step explanation:
A = value of y when x = -1:
A = -2(-1)^2 + 4(-1) + 9
= -2*1 - 4 + 9
= -2 - 4 + 9
= 3.
B = value of y when x = 2:
B = -2(2)^2 + 4(2) + 9
= -2*4 + 8 + 9
= - 8 + 8 + 9
= 9.
AP Calculus ab question: what is the derivative function, f'(x), using the definition of derivative for : f(x) = 3/(x+1)
Answer:
Solved using 2 different methods, used the definition of derivative aswell.
Kelsey made cupcakes to sell as a fundraiser for her trip to Washington DC.
She purchased one cupcake pan for $12. She calculated that the ingredients
cost her $0.25 per cupcake. She plans to sell the cupcakes for $0.75 each.
a. Write an equation that could be used to find the number of cupcakes
(x) she will need to sell to break even.
b. Solve the equation from part a. Explain how you know
is correct.
c. If she sold 184 cupcakes, what was her profit?
your answer
Answer:
a. 12= 0.50x
b. x=24 because if 0.5 times x is 12 then 12 *2 is x
c. 80$
Step-by-step explanation:
Its above.
Suppose a charity received a donation of $23.3 million. If this represents 58% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Step-by-step explanation:
23.3 million = 58%
1% = 58%/58 = 23.3 mil. / 58
100% = 1%×100 = 100×23.3 mil./58 =
= 2,330,000,000/58 = 40,172,413.79... ≈
≈ $40 millions
Question:
Given the demand equation p=190/q+10 where 10<0<85, for what value of q is | n | a maximum? For what value is it minimum?
The maximum and minimum value of η at q = 10 and q = 85 respectively.
The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.
η is the elasticity of demand.
Then, the elasticity of demand is given as:
η = ( dq/ dp) × ( p / q )
Now, we have p = 190/ (q + 10)
Therefore,
p ( q + 10 ) = 190
pq + 10p = 190
q = ( 190 - 10p ) / p
Now,
dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )
dq / dp = ( -190/ p² )
Substituting these values in the elasticity demand,
η = ( dq/ dp) × ( p / q )
η = ( -190/ p² ) × ( p / q )
η = ( -190/ pq )
η = ( -190/ [190 / (q + 10 ) ]q )
η = [ - ( q + 10 ) / q ]
| η | = | - ( q + 10 ) / q |
η = ( q + 10 ) / q = 1 + 10/q
The critical point is when | η' | = 0.
η' = ( d / dq ) ( 1 + 10/q )
η' = - 10/ q²
- 10/ q² = 0
Hence, - 10/ q² is not defined.
Therefore, the function is not defined at q = 0.
Therefore, q = 0 is not a solution.
We have 10 ≤ q ≤ 85
The value of functions at the endpoint,
At q = 10,
η = ( 1 + 10/q )
η = ( 1 + 10/10 )
η = 1 + 1 = 2
At q = 85,
η = ( 1 + 10/q )
η = ( 1 + 10/85 )
η = 1.11764
Therefore, the absolute value of the elasticity of demand is maximum at q = 10.
The absolute value of the elasticity of demand is minimum at q = 85.
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What are the solutions of this quadratic equation?
x² - 6x+2=0
OA.
O B.
OC.
2-3 ± √7
CD. 2-3 ± √11
-6 ± √7
x=3+√7
2.21x10^3= convert the expression to decimal form
2210
Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
Expanding the term,
2.21 x 1000 = 2210
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Suppose you start at the origin, move along the x-axis a distance of 2 units in the positive direction, and then move downward a distance of 9 units. What are the coordinates of your position?
The coordinates of our position after moving up and down will be (0, -7)
We are given a coordinate plane and we are standing at the origin of the plane.
That is, our position is (0, 0).
Now, we move 2 units in the positive direction.
So, now our position will be:
(0, 2)
Then, we move downward a distance of 9 units.
So, our position will now become:
(0, 2 - 9)
(0, -7)
Therefore, the coordinates of our position after moving up and down will be (0, -7)
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Let f(x)=12x+7. Use algebra to find the inverse function f^-1(x).
Step-by-step explanation:
Replace x with y and y with x.
Then, try to isolate the y.
x=12y+7
x-7=12y
(x-7)/12=y
f^-1(x)=(x-7)/12
QUESTION 4
Which of these is not a very good example of a command economy?
a.)China
b.)Soviet Union
c.)United States during WWII
d.)United States today
(d) the Present United States is not a good example of a command economy.
A command economy is a crucial component of a political system in the economy in which the degree of output that is permitted and the prices that may be paid for goods and services are set by a central governing body. Most industries are owned by the public.
The principal alternative to a command economy is a free market b where supply and demand determine prices and output.
A communist political system includes a command economy, whereas capitalist countries have a free market.
Cuba, North Korea, and the former Soviet Union all have command economies. Up until 1978, when it started to shift to a mixed economy that combines communist and capitalist features, China maintained a command economy. A socialist market economy has been used to characterize its existing setup.
The central government of a country must possess and manage the means of production in a command economy, commonly referred to as a planned economy.
There is no private ownership of land or capital, or it is very restricted. Prices are determined by central planners, who also manage production levels and restrict or forbid competition in the private sector. There is no private sector in a command economy because all companies are owned by or under the supervision of the central government.
Government officials establish national economic priorities in a command economy, such as when and how to promote economic growth, how to share resources, and how to disperse the produce. This frequently takes the shape of a long-term plan.
Hence, the United States today is not a very good example of a command economy.
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f is the function (x)-2x+5.
(a) Find (3)
(6) Express the inverse function f' in the form f'(x)-
g is the function g(x)-²-25.
(c) Find g(-3).
(d) (1) Find gfx)
r'(x)-
Give your answer as simply as possible.
(ii) Solve g(x)-0.
gf(x) -
(1)
8
e
(5)
The given functions can be solved using composition functions.
What is a composition function?Function composition is a mathematical procedure where two functions, f and g, are taken and a function, h = g f, is produced such that h(x) = g(f(x)). The function g is applied in this operation on the outcome of applying the function f to x.
function (x)-2x+5.
(a) f(3) = 2(3) + 5
= 11
(b) f'(x)
y = 2x + 5
y - 5 = 2x
x = y - 5 / 2
f'(x) = x - 5 / 2
g is the function g(x)-²-25.
(c) g(x)-²-25
g(-3) = (-3)² - 25
g(-3) = -16
(d) g(f(x)) = g(2x + 5)² - 25
= 4x² + 25 + 20x - 25
⇒ 4x² + 20x
r'(x) = 2x + 5
(ii) g(x) - 0
⇒ g(x)
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Whats (500 x 2) divided by 2?
Answer:
500
Step-by-step explanation:
500*2=1000
1000/2=500
find the distance between the two points in simplest radical form. (1,-7) and (7,0)
Step-by-step explanation:
Answer:
The distance between the two given points is equal to √85.
Step-by-step explanation:
Let's recall what the distance formula is:
\displaystyle \huge\math\boxed{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }\math
d= (x 1 −x2 ) 2 +(y 1 −y 2) 2
We are defined our two points as:
(x₁, y₁) → (1, -7)
(x₂, y₂) → (7, 0)
We can rewrite this into our different "variables":
x₁ = 1
y₁ = -7
x₂ = 7
y₂ = 0
Now given our distance formula and our variables, we can find the distance between the two points:
\begin{gathered}\displaystyle\huge\begin{aligned}d & = \sqrt{(1 - 7)^2 + (7 - 0)^2} \\& = \sqrt{(-6)^2 + (7)^2} \\& = \sqrt{36 + 49} \\& = \math\boxed{\sqrt{85}} \\\end{aligned}\end{gathered}
d= (1−7) 2+(7−0) 2= (−6) 2+(7) 2 = 36+49=\math 85
∴ since the radical is already in its simplest form, our distance between the two points is equal to √85.
Hope this helps!
a solid is 5.0cm tall, 3.0cm wide and 2.0cm thick. it has a mass of 387g. What is the density?
Answer: 12.9
Step-by-step explanation:
5 x 3 x 2= 30
5 x 3= 15
15 x 2= 30
D= M/V -> Try to remember the DMV
387 / 30= 12.9
30 x 10= 300
30 x 2= 60
30 x 1= 30
30 x .9= 27
10 + 2 + .9= 12.9
300 + 60 + 27= 387
If a ball is thrown upward at 96 feet per second from a height of 12 feet, the height of the ball can be modeled by S=12+96t- 16t² feet,
where t is the number of seconds after the ball is thrown. How long after the ball is thrown is the height 152 feet?
It takes seconds for the ball to reach the height 152 feet.
Answer:
2.5 & 3.5
Step-by-step explanation:
152 = 12+96t- 16t²
140+96t- 16t²=0
152 = 12+96t- 16t²
4t²-24t+35=0
(2t-7)(2t-5)=0
t = 2.5 & 3.5
A taxi ride for the airport to your hotel costs a flat fee of $10 the moment you sit in the back seat plus $0.75 each mile plus a tip of $5 to the driver at the end of the ride. Your hotel is 24 miles from the airport and you have $30 in your pocket. Do you have enough money to make it to your hotel in the taxi, including the tip? Declare what your variable represents, write the equation or inequality that models the situation, solve for the variable showing your steps, and answer the question.
Greetings from Brasil...
We have 2 fixed fees:
→ $10 when you sit on the bench
→ $5 tip
So, fixed fees = $10 + $5 = $15
The rate that varies would be the distance traveled. The fee will be $0.75 per mile moved. In this case we can write that:
C = 0.75M + fees
C = 0.75M + 15let
C = cost
M = mile(s)
for 24 miles, M = 24, then
C = 0.75M + 15
C = 0.75 · 24 + 15
C = 18 + 15
C = $33
With $30 it will not be possible to make this trip, as the total cost would be $33
One solution or alternative would be to reduce the tip amount. Instead of $5, pay only $2 of tip.
We can rewrite the cost expression involving a variable for the tip:
C = 0.75M + T + 10
let T = tip
For the exercise example.... The distance (M) its 24 miles and the value of C has to be what I have in my pocket: 30.... then M=24 and C=30
C = 0.75M + T + 10
30 = 0.75 · 24 + T + 10
30 = 18 + T + 10
30 - 18 - 10 = T
T = 2
Is it possible to do this ride if you pay only $2 tip
sam had a yard sale. the next day he made a deposit with no cash back. he deposited 28 twenties, 18 tens, 32 fives, 20 ones, 18 quarters and checks for $22, $18.18 and $67.04. what was the amount of his deposit?
The total amount of money Sam deposited is $1,031.72.
Given that, Sam deposited 28 twenties, 18 tens, 32 fives, 20 ones, 18 quarters and checks for $22, $18.18 and $67.04.
We need to find out what was the amount Sam deposited.
What is the sale?Add the rate to the purchase price to determine the discount. Subtract the discount from the original price to arrive at the sale price.
The discounted price at which products or services are being sold is known as a sale price.
Now, total money = 28×20+18×10+32×5+20×1+18×0.25+22+18.18+67.04
=560+180+160+20+4.5+22+18.18+67.04
=1,031.72
Therefore, the total amount of money Sam deposited is $1,031.72.
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A small pizza has an area of
730
730730 square centimeters.
Write an inequality that describes
p
pp, the area of a pizza that is larger than a small pizza.
The inequality that describes p, the area of a pizza that is larger than a small pizza 730(seven hundred thirty) < p
What is inequality?
Inequality refers to the miracle of unstable and/ or unjust distribution of coffers and openings among members of a given society. The term inequality may mean different effects on different people and in different surroundings. The major exemplifications of social inequality include income gap, gender inequality, health care, and social class. In health care, some individuals admit better and further professional care compared to others.
From the information given, we have that;
Area of the small pizza = 730(seven hundred thirty) square centimeters
p = area of the larger pizza
In writing inequality, we have to use the signs
< less than
> greater than
Since p has a greater area, we have
730(seven hundred thirty) < p
Thus, the inequality that describes p, the area of a pizza that is larger than a small pizza 730(seven hundred thirty) < p
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Help me plsss this is my last oneeeree
Answer:
For the first question:
The fraction that comes after 0/3 is 1/3The fraction that comes after 1/3 is 2/3For the second question:
The fraction that comes after 0/6 is 1/6The fraction that comes after 1/6 is 2/6The fraction that comes after 2/6 is 3/6The fraction that comes after 3/6 is 4/6The fraction that comes after 4/6 is 5/6Step-by-step explanation:
Hope it helps! =D