Rob is a tractor salesman last week his total sales amounted to 38,642.00 and he received 2,704.94 in commission what is his rate of commission
Maggs invests $10,250 at a rate of 9%, compounded weekly. To the nearest whole dollar, find the value of the investment after 7 years. $10,375 $11,208 $18,737 $19,230
Answer:
the correct answer is 19,230
Step-by-step explanation:
Please help!:
Charlie built a toy using a rectangular prism and cubes as shown below.
What is the surface area of the toy Charlie built?
A.650 sq cm
B.350 sq cm
C.550 sq cm
D.400 sq cm
PLZ HELP ASAP IF YOU KNOW THE ANSWER!!
Determine whether a triangle with the given side lengths is a right triangle angle: 15 cm, 17 cm and 19 cm
Yes or No_________
Show your work to prove your answer:
Find the absolute maximum and minimum values of f on the set
d. f(x, y) = xy2 + 2, d = {(x, y) | x ≥ 0, y ≥ 0, x2 + y2 ≤ 3}
The absolute minimum and maximum values of a function are the least and highest values, the function can take.
The absolute maximum and minimum values of f are 4 and 2, respectively.
The function is given as:
[tex]\mathbf{f(x,y) = xy^2 + 2}[/tex]
First, we determine the partial derivatives of f(x,y)
[tex]\mathbf{f_x(x,y) = y^2}[/tex]
[tex]\mathbf{f_y(x,y) = 2xy}[/tex]
Substitute 0 for y in the first equation.
So, we have:
[tex]\mathbf{x = 0}[/tex]
This means that:
[tex]\mathbf{Critical\ Point = f(0,0) = 0}[/tex]
Next, we calculate the extreme values.
We have:
[tex]\mathbf{x^2 + y^2 \le 3}[/tex]
Express as an equation
[tex]\mathbf{x^2 + y^2 = 3}[/tex]
Make y the subject
[tex]\mathbf{y^2 = 3 - x^2}[/tex]
Take square roots
[tex]\mathbf{y = \sqrt{3 - x^2}}[/tex]
Substitute [tex]\mathbf{y = \sqrt{3 - x^2}}[/tex] in [tex]\mathbf{f(x,y) = xy^2 + 2}[/tex]
So, we have:
[tex]\mathbf{f(x) = x(3 -x^2) + 2}[/tex]
Open brackets
[tex]\mathbf{f(x) = 3x -x^3 + 2}[/tex]
Differentiate
[tex]\mathbf{f(x) = 3 -3x^2 }[/tex]
Set to 0
[tex]\mathbf{3 -3x^2 =0}[/tex]
Collect like terms
[tex]\mathbf{3x^2 =3}[/tex]
Divide through by 3
[tex]\mathbf{x^2 =1}[/tex]
Take square roots of both sides
[tex]\mathbf{x =\±\sqrt1}[/tex]
[tex]\mathbf{x =\±1}[/tex]
The domain is given as:
[tex]\mathbf{x \ge 1}[/tex]
So, the possible value of x is:
[tex]\mathbf{x =1}[/tex]
Substitute 1 for x in [tex]\mathbf{y = \sqrt{3 - x^2}}[/tex]
[tex]\mathbf{y = \sqrt{3 - 1^2}}[/tex]
[tex]\mathbf{y = \sqrt{3 - 1}}[/tex]
[tex]\mathbf{y = \sqrt{2}}[/tex]
So, we have:
[tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex]
This means that, the absolute maximum is at: [tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex], while the absolute minimum is at [tex]\mathbf{(x,y) = (0,0) }[/tex]
Substitute these values in f(x,y)
[tex]\mathbf{(x,y) = (0,0) }[/tex]
[tex]\mathbf{f(0,0) = 0 \times 0^2 + 2 = 2}[/tex]
[tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex]
[tex]\mathbf{f(1,\sqrt 2) = 1 \times (\sqrt 2)^2 + 2 = 4}[/tex]
Hence, the absolute maximum and minimum values of f are 4 and 2, respectively.
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you invest $2,000 in a stock plan and another $2,000 in a savings account the stock plan decreases 7% the first year and gains 10% the second-year the savings account earns 3.7 APR and compounds annually what's the difference in earnings between the stock and savings account in the end of the second year
The difference in earnings between the stock and savings account in the end of the second year is $104.74.
What is the difference between the stock and savings account?The value of the stock plan at the end of the first year = (100 - 7) x 2000
0.93 x 2000 = $1860
The value of the stock plan at the end of the second year = (100 + 10) x 1860 = $2046
The future value of the savings account = 2000(1.037^2) = $2150.74
Difference = $2150.74 - $2046 = $104.74
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The sum of a number and its square is 2. Find the number(s).
The number 'x' that satisfies the condition of the sum of a number and its square equaling 2 are 1 and -2. This is determined by setting up a quadratic equation and solving for 'x'.
Explanation:To solve this problem, let's start by defining the unknown number we are looking for as 'x'. According to the problem, the sum of a number (x) and its square (x²) equals 2. As a mathematical equation, this would be written as x + x² = 2.
Once this equation is set up, we can solve for x. However, the equation is quadratic, which means it may have two solutions. Anyway, the equation can be rearranged into the standard quadratic format as x² + x - 2 = 0. It can be factored into (x - 1)(x + 2) = 0. This gives us two potential solutions for x: x = 1 and x = -2.
To verify if these solutions are valid, we can substitute them back into the original equation: 1 + 1² = 2 is true, and -2 + (-2)² = 2 is also true. Thus, both of these numbers, 1 and -2, are solutions to the original problem.
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kyle bought 28 feet of wire at the handware store. the wire cost was $2.79per foot, including sales tax. if kyle paid with a $100 bill, how much change should he have received?
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 16 cm2. (let x, y, and z be the dimensions of the rectangular box.) (x, y, z) =
Final answer:
Finding the exact dimensions of a rectangular box with the largest volume from a given surface area of 16 cm2 requires additional constraints. For illustrative purposes, in the case of a cube with equal sides, the side length can be found using the formula for surface area, showing how such a problem might be approached.
Explanation:
To find the dimensions of a rectangular box with the largest volume given a total surface area of 16 cm2, we can use the method of Lagrange multipliers or understand the principle that for a given surface area, the box which is closest to a cube will have the largest volume. However, without additional constraints, like a relation between the dimensions (x, y, z), solving for specific x, y, z values directly from just the surface area constraint alone leads to an infinite number of solutions. For simplicity, we'll consider a problem where symmetry is involved, as in the case of a cube, to illustrate how one might approach it.
Surface area of a rectangular box is given by 2(xy + xz + yz) = 16 cm2. To simplify and directly answer based on the data given would require additional constraints, such as assuming all sides are equal. For a cube, with all sides equal (let’s call each side 'a'), the surface area would be 6a^2. Solving 6a^2 = 16 gives a = sqrt(16/6) ≈ 1.633. This illustrates a scenario under specific conditions but doesn't directly solve the original question without additional constraints.
Find two numbers, if Their sum is −7 and their difference is 14
Answer:
3.5 and -10.5
Step-by-step explanation:
i checked, its correct
Deandres coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Deandre $5.95 per pound, and type B coffee costs $4.50 per pound. This month, Deandre made 136 pounds of the blend, for a total cost of $684.50. How many pounds of type B coffee did he use?
Emily buys the cage and two bowls for $54 the cage cost $40 each for cost the same amount what is the price of one bowl
Find two numbers, if their sum is (−1/3) and their difference is 18. PLEASE HELP
The two numbers are 53/6 and -55/6.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Let x and y be the two numbers.
We have sum of them is -1/3
x + y = -1/3 [Equation 1]
The difference of two numbers is 18.
x - y = 18 [Equation 2]
Adding equations 1 and 2,
x + y + x - y = -1/3 + 18
2x = 18 - [tex]\frac{1}{3}[/tex]
2x = 53/3
x = 53/6
Substituting the value in equation 1,
53/6 + y = -1/3
y = -1/3 - 53/6
= -55/6
Hence the numbers are 53/6 and -55/6.
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A ballroom in a hotel has the shape shown in the diagram. The hotel manager needs to determine how much carpet is needed to recarpet this area. All angles are right angles. The area of the ballroom is
Answer:
126 square yards
Step-by-step explanation:
When constructing inscribed polygons and perpendicular lines, how are the steps similar? -
A. For right angles are created
B. A protractor and ruler are used to take accurate measurements.
C. Intersecting arcs are created and connected
D. There are no similarities
((((( SIDE NOTE ::: I LOOKED IT UP AND PEOPLE ARE SAYING ITS D, AND THEN THE OTHER HALF OF PEOPLE ARE SAYING D IS WRONG......HELP )))))
C is Correct answer.
Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem. A cube-shaped container has an edge length of 23 feet. What is the volume of the container? Enter your answer, as a fraction in simplest form, in the box. ft³
in a gift store the ratio of cards to flowers was 8 to 7 if there were 56 cards how many flowers were there show how you got your answer please
What is the surface area of this right rectangular prism? Enter your answer in the box. in² A rectangular prism with a length of 3 inches, a width of 1 inch, and a height of 2 inches.
Answer:
Surface Area of Rectangular Prism is 22 [tex]in^2[/tex]
Step-by-step explanation:
Given: Dimensions of Rectangular prism are Length = 3 inches, width = 1 inch and height = 2 inches.
To find: Surface Area of Rectangular Prism
Formula Used for Surface Area of Rectangualr Prism
= 2 × ( Lenght × Width + Width × Height + Height × Length )
⇒ Surface Area = 2 × ( 3 × 1 + 1 × 2 + 2 × 3 )
= 2 × ( 3 + 2 + 6 )
= 2 × ( 11 )
= 22 [tex]in^2[/tex]
Therefore, Surface Area of Rectangular Prism is 22 [tex]in^2[/tex]
Answer:
22 inches
Step-by-step explanation:
Crystal's mud mask costs $23 for a 0.45 oz jar. She found the same mud mask online for $72. What is the size of the jar Crystal found online? (Round your answer to the nearest tenth)
Consider the graph of the linear equation 2x-5y=10. What is the x-intercept? What is the y-intercept? What is the slope?
n operator in the plant has a monthly salary of $3,200. Thirty-three percent (33%) of her salary is deducted for income tax. How much money is deducted from her salary for income tax each month? $736.00 $960.00 $1,056.00 $2,144.00
In the morning,a farm worker packed 3 pints of strawberries every 4 minutes.In the after afternoon,she packed 2 pints of strawberries every 3 minutes.What was the difference between her morning and afternoon packing rates in pints per hour?
What are the coordinates of the image produced by applying the composition / to the point (–3, –6)?
A.
(–6, –3)
B.
(3, –6)
C.
(3, 6)
D.
(6, 3)
Answer:
b
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
determine whether each set of side lengths could be the sides of a right triangle Drag and drop each set of side lengths to the correct box right triangle not a right triangle 8 in 15 in 17 in. 4 in 15 in 17 in
Answer:
8 in 15 in 17 in.--- form a right angled triangle.
4 in 15 in 17 in.---- do not form a right angled triangle.
Step-by-step explanation:
We know that according to the PYTHAGOREAN THEOREM of right triangles we have:
[tex]c^2=a^2+b^2[/tex]
where c is the hypotenuse or the largest side of a triangle and a and b are other two legs of a right triangle,.
1)
8 in 15 in 17 in.
[tex]17^2=15^2+8^2\\\\289=225+64\\\\289=289[/tex]
Hence, the given measure of sides form a side of a right angled triangle.
2)
4 in 15 in 17 in.
Since,
[tex]17^2\neq 15^2+4^2[/tex]
Hence, the given measure of sides do not form a side of a right angled triangle.
Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down. f left parenthesis x right parenthesisf(x)equals=3 x cubed minus 36 x minus 73x3−36x−7
a person travels 640 mi in 10 hours. What is the rate in miles per hour?
Nadiya determines that there are no fractions equivalent to 2/10 with a denominator greater than 10, but less than 20, that have a whole number numerator and denominator. Is Nadiya correct?
Yes, Nadiya is correct. By multiplying the numerator and denominator by 2, the first fraction equivalent to 2/10 is 4/20.
Yes, Nadiya is correct. By multiplying the whole fraction by any whole number, each equivalent fraction will continue to have a denominator of 10.
No, Nadiya is incorrect. She could multiply both the numerator and denominator of the unit fraction equivalent to 2/10 by 3 and arrive at the equivalent fraction 3/15.
No, Nadiya is incorrect. She could add any number between 1 and 8 to the numerator and denominator and arrive at an equivalent fraction with a denominator greater than 10 but less than 20.
No, Nadiya is incorrect. There is a fraction equivalent to 2/10 with a denominator greater than 10 but less than 20, which is 3/15.
Explanation:No, Nadiya is incorrect. She could multiply both the numerator and denominator of the unit fraction equivalent to 2/10 by 3 and arrive at the equivalent fraction 3/15.
When multiplying a fraction by a whole number, both the numerator and the denominator are multiplied by that number. By multiplying 2/10 by 3, we get (2 * 3)/(10 * 3) = 6/30, which can be simplified to 3/15.
Therefore, there is a fraction equivalent to 2/10 with a denominator greater than 10 but less than 20, and it is 3/15.
what is 2/3 × 5 in simplest form
What expression represents "eight more than a number cubed and 2"?
Possible Answers:
(x+6)(x-2)(x-1)=60 write a polynomial