The commission when the salesman earns 40% commission on all the merchandise that he sells is $320.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the salesman earns 40% commission on all the merchandise that he sells and last month he sold $800 worth of merchandise.
The amount in commission will be:
= Commission percentage × Sales
= 40% × $800
= $320
The commission is $320.
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A scientist places 20 mg of bacteria in a culture for an experiment and he finds that the mass of the bacteria triples every day.
a.)Each day that passes, the mass of bacteria in the culture changes by what percent?
Answer: 300%
Step-by-step explanation:
Multiplying something by 3 is the same as 300% of that number
20 x 3 = 60
60 = 300% x 20
In all the cases shown below, the velocity vectors v₁ and v₂ have the same length.
a)
b)
c)
d)
In which case does Δv=v₂-v₁ have the largest absolute value?
A. a
B. b
C. c
D. d
The case of the velocity vectors, v₁ and v₂ that yield the largest absolute value of Δv = v₂ - v₁ is the case of option B. b
What is a velocity vector?A velocity vector provides an indication of s particle's speed and direction of motion.
The vectors in the question can be expressed using vector notation as follows;
a) [tex]\vec{v_1}[/tex] = i + j
[tex]\vec{v_2}[/tex] = i + j
Δv = v₂ - v₁ is therefore;
v₂ - v₁ = i - i + j - j = 0
Δv = 0
b) [tex]\vec{v_1}[/tex] = i + j
[tex]\vec{v_2}[/tex] = -i - j
Δv = v₂ - v₁ is therefore;
v₂ - v₁ = i - (-i) + j - (-j) = 2·i + 2·j
Δv = 2·i + 2·j
c) [tex]\vec{v_1}[/tex] = i + j
[tex]\vec{v_2}[/tex] = i - j
Δv = v₂ - v₁ is therefore;
v₂ - v₁ = i - i + j - (-j) = 2·j
Δv = 2·j
d) [tex]\vec{v_1}[/tex] = i + j
Comparing the vertical and horizontal lengths of the arrows, indicates;
[tex]\vec{v_2}[/tex] ≈ -1.2·i - 0.5·j
Δv = v₂ - v₁ is therefore;
v₂ - v₁ = i - (-1.2·i) + j - (-0.5·j) = 2.2·i + 1.5·j
Δv = 2,2·j + 1,5·j
Option (b) and (d) have the largest values, however, their magnitudes are;
b) |Δv| = √(2² + 2²) = 2·√2 ≈ 2.83
d) |Δv| = √(2.2² + 1.5²) ≈ 2.66
Therefore, option b has the largest absolute value for Δv = v₂ - v₁
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What is the solution to the following inequality?
X/-3≤ 3
O A. x ≤ 1
OB. x ≤-9
OC. x≤-9
D. x ≤ 6
The solution to the x/-3≤ 3 inequality is x ≤ -9.
Define inequality.In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. In mathematics, an inequality is a relationship between two numbers or other mathematical expressions that results in an unequal comparison. Inequalities are the name given to certain algebraic mathematical expressions.
Given,
Inequality:
x/-3 ≤ 3
Cross multiplying:
x ≤ 3× -3
x ≤ -9
The solution to the x/-3≤ 3 inequality is x ≤ -9.
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2500 dollars is placed in an account with an annual interest rate of 9%. To the nearest year, how long will it take for the account value to reach 7500 dollars?
It will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.
According to the question,
We have the following information:
2500 dollars is placed in an account with an annual interest rate of 9%.
We know that following formula is used to find simple interest:
Simple interest = principal*rate*time/100
Now, the simple interest on any amount will be equal to the total amount after interest minus the principal amount:
7500-2500
5000
So, we have the following expression:
(2500*9*t)/100 = 5000
Now, using cross multiplication method:
t = (5000*100)/(2500*9)
t = 200/9 years
t = 22.2 years
Now, the nearest year will be 22 years.
Hence, it will take 22 years for the account value to reach $7500 with an annual interest rate of 9% per year.
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Jacob has a coin collection. He keeps 5 of the coins in his box, which is 10% of the collection. How many total coins are in his collection?
The number of coins that are in Jacob's collection is 50
How to find the number of coinsinformation from the problem
Jacob has a coin collection
He keeps 5 of the coins in his box, which is 10% of the collection
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
10%
= 10 percent
= 10 / 100
= 0.1
The factor 0.1 of the total number of coin is 5
let the total number be x
0.1 * x = 5
0.1x = 5
x = 5 / 0.1
x = 50
The total number of coins is 50
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Angela meets with a new couple to determine their needs for a new home and how large a home they can afford. What is Angela’s profession?
A.
financial services sales agent
B.
insurance sales agent
C.
real estate broker
D.
tax accountant
E.
personal finance manager
Angela is a real estate broker option c.
Real Estate Broker;
A real estate broker represents the buyer or seller when looking for the appropriate home. A broker often works for a larger company that helps home sellers and home purchasers select the best and most affordable housing alternative.
A real estate broker is a licenced real estate professional in their own right, as opposed to only being a licenced real estate agent. Like an agent, a real estate broker possesses knowledge that can assist clients with real estate transactions and the sale or acquisition of real estate.
Here,
Angela works as a real estate broker. In order to ascertain the couple's demands for a new home and the size of a property they can afford, Angela meets with them. As a result, choice C is accurate.
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Which of the j-values satisfy the following nequality?
10 ≥j +5
Choose all answers that apply:
A j = 3
B j=4
C j = 5
Answer:
j=5
10
[tex] 10 \geqslant j + 5[/tex]
10-5=j
j=5
c
order from greasest to least ; 3.84,3.789,3,3 41/50
Answer: 3.84 , 3 41/50 , 3.789 , 3
Subtract the expressions. (9.12n − 4.3) − (8 + 13.6n)
The expression (9.12n 4.3) (8 + 13.6n) are subtracted to yield (12.3 + 4.48n).
What is an algebraic expression?
An algebraic expression is a type of mathematical expression that uses variables and constants.
Algebraic expressions are evaluated by changing the variables to numbers or values.
What in mathematics is a polynomial?
Sums of terms of the form k⋅xⁿ, when k is any variable and n is a positive number, compensate polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.
Detailed explanation:
We begin by solving the equation = 9.12n - 4.3 - 8 - 13.6n. Next, we remove the comparable terms using the formula = - 12.3 - 4.48n.
Therefore, the simple answer to the formula is -(12.3 + 4.48n).
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help please. what are these? thank you.
8. The value of x is 9
9. The value of x is 9
10. The value of x is 36
11. The value of x is 8
Calculating the value of xFrom the question, we are to determine the value of x in the given diagram.
8.
2x + 12 = 5x - 15
Collect like terms
12 + 15 = 5x - 2x
27 = 3x
3x = 27
Divide both sides by 3
3x/x = 27/3
x = 9
9.
8x - 63 = 4x - 27
Collect like terms
8x - 4x = -27 + 63
4x = 36
Divide both sides by 4
4x/4 = 36/4
x = 9
10.
(3x - 18)° = 90°
3x - 18 = 90
Add 18 to both sides
3x - 18 + 18 = 90 + 18
3x = 108
Divide both sides by 3
3x/3 = 108/3
x = 36
11.
Since the angles are complementary, we can write that
(3x)° + (8x + 2)° = 90°
3x + 8x + 2 = 90
11x + 2 = 90
Subtract 2 from both sides of the equation
11x + 2 - 2 = 90 -2
11x = 88
Divide both sides by 11
11x/11 = 88/11
x = 8
Hence, the value of x is 8
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Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
The parabola equation in its vertex form is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?From the question, we have the function to be
f(x) = 3x²
Also, we have the vertex to be given as
Vertex = (5, 9)
A quadratic function takes the form:
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
So, we can rewrite f(x) = 3x² as follows
f(x) = 3(x - 0)² + 0
By comparing the equations, we have
a = 3
Also, by comparison, we have
(h, k) = (5, 9)
Substitute a = 3 and (h, k) = (5, 9) in f(x) = a(x - h)² + k
So, we have
f(x) = 3(x - 5)² + 9
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
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Damari needs to paint the circular concrete mural at the
park. The mural has a diameter of 45 feet. A gallon of
paint covers approximately 300 square feet. Each
gallon is $18.99. How much will Damari spend in order
to paint the mural? Use 3.14 to approximate I and
round your answer to two decimal places.
The total spent to paint the mural which is circular with a diameter of 45 feet will be $100.67.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The longest line which can be drawn inside the circle will be the diameter.
The perimeter of the circle = 2πr where r is the radius of the circle.
As per the given,
Diameter = 45 feet so radius 45/2 = 22.5 feet
Area of circle = πr² = π(22.5)² = 1590.43 feet²
Since one gallon covers 300 square feet.
Number of gallons needed to cover the whole area,
1590.43/300 = 5.30
Cost of one gallon = $18.99
Total spend = 5.30 × 18.99 = $100.67
Hence "The total spent to paint the mural which is circular with a diameter of 45 feet will be $100.67".
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Which expression is equivalent to N/4+n/4+n/4+n/4
Answer: 4[tex]\frac{n}{4}[/tex]
Step-by-step explanation:
An airliner passes over an airport at noon traveling 520 mi/hr due east. At 1:00 p.m., another airliner passes over the
same airport at the same elevation traveling due south at 560 mi/hr. Assuming both airliners maintain their (equal)
elevations, how fast is the distance between them changing at 3:00 p.m.?
The distance between the two airlines changing at 3:00 p.m is 374mi/hr
Here, the trajectory of the 2 planes will form a right angle at the airport.
Let 'a' be the distance of the east bound plane travelled past the airport and b be the distance of the south bound plane travelled past the airport and c is the horizontal distance between the two planes
a² + b² = c²
differentiating both sides with respect to time
2a da/dt + 2b db/dt = 2c dc/dt
The speed of both airlines is given,
da/dt = 520mi/hr and db/dt = 560mi/hr
At 12 pm the east bound plane has been flying post airport
at 3 pm, the distance = 3 x da/dt = 2(520) = 1560
At 1 pm the east bound plane has been flying post airport
at 3 pm, the distance = 2 x db/dt = 2(560) = 1120
c = √(a² + b²)
c = √(1560² + 1120²)
c = 1920.41
fast is the distance between them changing dc/dt
dc/dt = (3a da/dt + 2b db/dt)/2c
= (1560 x 520+ 1120x560)/1920
dc/dt = 374
Therefore, the distance between them changing at 3:00 p.m is 374mi/hr
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Use the diagram to answer both questions.
The value of x : 56
What is Angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
Given,
∠A = (2x - 6)°
∠B = 74°
Since, we have to find the value of x
we have to find it by Linear equation
∠A + ∠B = 180°
Substituting the values we have
(2x - 6)° + 74° = 180°
2x - 6 + 74 = 180
2x + 68 = 180
2x = 180 - 68
2x = 112
x = 112/2
x = 56
The value of ∠A = 56 - 6 = 60°
Hence, The value of x = 56
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True or false
A credit union is an example of a service cooperative.
Answer:
false
Step-by-step explanation:
Credit Unions are not-for-profit financial service cooperatives
The equation of the line that passes through the given points (4,6) and (4.2)
Answer: ___________________________________________________
x = 4
simplify (8.1)(8.1²)⁴
(8.1)6
(8.1)7
(8.1)8
(8.1)9
The indices (8.1)(8.1²)⁴ simplifies to 8.1⁹
How to simply indices?
Index is the power or exponent which is raised to a number or a variable. For example, in number 3², 2 is the index of 3. The plural form of index is indices
Given: (8.1)(8.1²)⁴
To simplify these indices, we are going to apply one of the indices, which is expressed below: (4³)² = 4³ ˣ ² = 4⁶. We basically multiply the powers
We also need another law which is expressed below:
3⁶ x 3⁴ = 3⁶⁺⁴ = 3¹⁰
If two indices with the same base (in case 3) are being multiplied, you can simplify by taking one of the bases and then add the powers
Thus, to simplify (8.1)(8.1²)⁴:
(8.1)(8.1²)⁴ = (8.1)(8.1)²ˣ⁴
= (8.1)(8.1)⁸
= 8.1¹ × 8.1⁸
= 8.1¹⁺⁸
= 8.1⁹
Therefore, (8.1)(8.1²)⁴ simplifies to 8.1⁹. The 4th option is the answer
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A boat sail is a right triangle. The length of one side of the sail is 7 feet more than the other side. The hypotenuse is 13 feet find the length of two sides of the sail.
Base of the Sail is 12 feet and Height of the Sail is 5 feet
What is Right Angle Triangle?
A right triangle or right-angled triangle, or more technically an orthogonal triangle, historically known as a rectangled triangle, is a triangle with one right angle (that is, a 90-degree angle) and two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
Solution:
Accroding to the Question,
Let, Base = x and Height = y
x = 7 + y
Using the Pythagorous Theorem
[tex]Base^{2} + Perpendicular^{2} = Hypotenuse^{2}[/tex]
[tex]x^{2} + y^{2} = 13^{2}[/tex]
Using the above mentioned relation
49 + y^2 + 14y + y^2 = 169
2y^2 + 14y - 120 = 0
Discriminant = 34
y = 5, -12
The length of a sail can not be neegative, therefore y = 5
From the equation 1, x = 12
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Factor the polynomial completely.
x4 + 2x2 - 35
Answer:
[tex](x^2+7)(x^2-5)[/tex]
Part A
3
A model car is for sale online. Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day th
If the original price of the model car was $40, how much did the car sell for to the nearest cent?
The car selling price is $34.30
From the question, we have
Selling price = 40* 95/100*95/100*95/100
=$34.30
The car selling price is $34.30
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Write and solve the equation for the following questions:
Leo ordered 4 large popcorn and soda combos. Each combo cost the same amount. With a $5
movie membership fee, the total cost was $68.96. How much did each popcorn and soda combo cost?
Answer:
$15.99
Step-by-step explanation:
Let y = the total cost
Let x = the cost of the combo
4x + 5 = 68.96 Subtract 5 from both sides
4x = 63.96 Divide both sides by 4
x = 15.99
A male elephant at the city zoo weighs 8,000 pounds, which is the same as 4 tons. The female elephant weighs 7,000 pounds. How many tons does she weigh?
Answer:
3.5 tons
Step-by-step explanation:
We can use the information we already have to figure out how much 1 ton is. In the equation: 8,000/4 will give us how many pounds per ton. The answer to that is 2,000 pounds per ton. So, if we divide the number of tons the female elephant is by how many pounds a ton is, we use the equation: 7,000/2,000, which equals 3.5 tons.
A student earns $13 per hour for tutoring and $8 per hour as a teacher's aid. Let x = the number of hours each week spent tutoring and y= the number of hours each week
spent as a teacher's aid.
Complete parts (a) through (e).
a. Write the objective function that describes total weekly earnings.
b. The student is bound by the following
three constraints:
1. To have enough time for studies, the
student can work no more than 23 hours
per week.
2. The tutoring center requires that each
tutor spend at least three hours r week
tutoring.
3. The tutoring center requires that each
tutor spend no more than eight hours per
week tutoring.
Write an inequality for each of
these constraints.
Submit test
...
c. Graph the system of inequalities from part (b). Use only the first quadrant and its boundary, because x and y are nonnegative. Select the correct graph.
OA.
O B.
O C.
O D.
Next
The objective function is z = 13x+8y
From the question, we have
A student earns $13 per hour for tutoring and $8 per hour as a teacher's aid.
x = the number of hours each week spent tutoring and
y= the number of hours each week spent as a teacher's aid.
the objective function is z = 13x+8y
Addition:
Addition is the process of combining two or more things. In mathematics, adding is the process of calculating the sum of two or more numbers. It is a basic mathematical operation that is applied frequently in daily life. We regularly use addition when dealing with money, calculating our food expenses, or calculating the time. However, for larger numbers, we divide the numbers into columns using their respective place values, such as ones, tens, hundreds, thousands, and so on. One-digit numbers can be added simply to solve addition issues.
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y+2=4/5(x+7) in stander form
Answer:
4x - 5y = -18
Step-by-step explanation:
y+2=4/5(x+7)
5(y + 2) = 5 × 4/5(x + 7)
5y + 10 = 4x + 28
5y = 4x + 18
4x - 5y = -18
(a) Find the derivative of f(x)=(x2+2)(4x−3) by first expanding the polynomials.
Enter the fully simplified expression for f(x) after expanding the polynomials.
f(x)=
Enter the derivative of f(x).
f'(x)=
(b) Find the derivative of f(x)=(x2+2)(4x−3) by using the product rule. Let g(x)=x2+2 and h(x)=4x−3 .
g'(x)=
h'(x)=
f'(x)=
(c) Are the expressions for the derivative in (a) and (b) the same?
(a) By expanding, the derivative of the polynomial is f'(x) = 12x² - 6x + 8
(b) Using the product rule, the derivative of the polynomial is f'(x) = 12x² - 6x + 8
(c) The expressions for the derivative in (a) and (b) are the same
Determining the derivative of polynomialsFrom the question, we are to determine the derivative of the given polynomial.
The given polynomial is f(x) = (x² + 2)(4x - 3)
(a) By expanding the polynomial, we get
f(x) = (x² + 2)(4x - 3)
f(x) = x²(4x - 3) +2(4x - 3)
f(x) = 4x³ - 3x² + 8x - 6
∴ f'(x) = 12x² - 6x + 8
(b) By using the product rule
f(x) = (x² + 2)(4x - 3)
g(x) = x² + 2
and
h(x) = 4x - 3
Thus,
g'(x) = 2x
h'(x) = 4
From the product rule
f'(x) = g(x).h'(x) + h(x).g'(x)
f'(x) = (x² + 2)(4) + (4x - 3)(2x)
f'(x) = 4x² + 8 + 8x² - 6x
Collect like terms
f'(x) = 4x² + 8x² - 6x + 8
∴ f'(x) = 12x² - 6x + 8
(c) The expressions are the same
Hence,
The derivative is f'(x) = 12x² - 6x + 8
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What is the slope of the
function below?
(3, 10)
(0, 1)
Slope = [?]
Simplify your answer.
Answer:
slope is 3
If you need the formula lmk
Answer: 3
Step-by-step explanation:
calculate the slope by subtracting the y coordinates, subtracting the corresponding x coordinates, then dividing y by x.
(10-1)/(3-0)=9/3=3
Answer the questions below! Thank you^^
a) The Factor of -4x² + 12x is 4x( -x +3)
b) The multiplication of (4.8x)(4x) is 19.2x²
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
-4x² + 12x
Now, factorizing
4x²= 2 x 2× x × x
12x = 2 ×2× 3 × x
So, the factor can be
-4x² + 12x
= -2 x 2× x × x + 2 ×2× 3 × x
= 4x( -x +3)
and, (4.8x) ×4x
= 4.8 × 4 × x × x
= 19.2x²
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Juan works 40 hours per week. He earns $9 per hours. How much does Juan earn in one week?
Answer:
2,500
Step-by-step explanation:
40 × 7 × 9
=2,500d dollars
Classify the polynomial by its name: 3
A) monomial
B) binomial
C) trinomial
D) other polynomial
