\(-7(x-13) =-98\\\\\implies x -13 = \dfrac{-98}{-7} =14\\\\\implies x = 14 +13 = 27\)
Leo buys 6L cola £8 400ml each glass 80p what’s the prercentage profit
The percentage profit of Leo buys 6L cola £8 400ml each glass 80p is
900%.
Solutions for Linear EquationTo find the percentage profit, we need to know the cost of the 6L cola and the revenue generated from selling the cola.
The cost of the 6L cola is calculated as follows:6L = 6000 ml
6000 ml / 400 ml/glass = 15 glasses
Cost of 15 glasses = 15 x £0.80 = £12
So Leo spent £12 on the cola.
The revenue generated from selling the cola is calculated as follows:6L = 6000 ml
6000 ml / 400 ml/glass = 15 glasses
Revenue from selling 15 glasses = 15 x £8 = £120
Leo earned £120 from selling the cola.
The profit is the difference between the revenue and the cost:Profit = Revenue - Cost
Profit = £120 - £12
Profit = £108
To calculate the percentage profit, we divide the profit by the cost and multiply by 100:
Percentage profit = (Profit / Cost) x 100
Percentage profit = (£108 / £12) x 100
Percentage profit = 900%
So the percentage profit is 900%. This means that Leo earned 9 times the amount he spent on the cola.
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A square tile measures 16 inches on each side. If 1 inch = 2. 54 centimeters, determine the area of the tile in square centimeters. Round the answer to the nearest square centimeter.
Square tile with measure of each side is 16inches have area equals to 1652 centimeters( round off to nearest square centimeters).
As given in the question,
Measure of each side length of a square tile = 16 inches
Conversion
1 inch = 2.54 centimeters
16 inches = ( 16 × 2.54 )centimeters
= 40.64centimeters
Area of a square tile is :
= ( Side length ) × ( Side length)
= (40.64) × (40.64)
= 1651.6096 centimeters
= 1652 centimeters ( round off to nearest square centimeters)
Therefore, the area of a square tile with given measure of each side is equal to 1652 centimeters ( round off to nearest square centimeters).
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What ia the Lcm of 99 and 24
Step-by-step explanation:
792
........
........
........
.......
........
...
The LCM of 24 and 99 is 794
Part B
Here’s a different way to partition the same function. Write a description of the partitioned function using known function types. Include function transformations in your description
With a negative leading coefficient, quadratic polynomials, and the horizontal offset for a scaled 1/x function.
Section 1's wiggles might be attributed to a variety of distinct purposes. A fourth-degree polynomial is maybe the simplest. It would have to have a negative leading coefficient in order to have downward-trending end behavior.
The curve in section 2 appears to represent either an exponential function or a scaled and translated version of 1/x. We prefer a version of 1/x because the latter is anticipated to approach the horizontal asymptote more quickly than is depicted above.
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what is the answer for 2(5/3+3/4)-4/3s
Find the areas of the composite figure.
Answer:
Step-by-step explanation:
The figure below is a net for the box to the right. What is the surface area of the box?
1.5 feet
lid
1.5 feet
2 feet
2 feet
1.5 feet
bottom
1.5 feet
1.5 feet
2 feet
2 feet
2 feet
4 feet
4 feet
Answer:
24 feet
Step-by-step explanation:
(1 point) a pilot flies in a straight path for 1 hour and 30 min. she then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 hours in the new direction. if she maintains a constant speed of 620 miles per hour, how far is she from her starting position? answer: miles
The pilot is approximately 1145.47 miles from her starting position.
For the first part of the flight, the pilot covers a distance
Distance = Speed x Time
Distance = 620 miles/hour x 1.5 hours
Distance = 930 miles
Now, let's consider the second part of the flight. The pilot changes direction by 10 degrees to the right. This means that she will not be flying directly away from her starting position, but at an angle to it. To calculate the distance she travels during this part of the flight, we need to use some trigonometry.
We can use the following formula to calculate the distance the pilot travels at an angle
Distance = (sin(angle) x Hypotenuse)
In this case, the angle is 10 degrees, and the hypotenuse is the distance the pilot travels in the second part of the flight. To find the hypotenuse, we can use the formula
Hypotenuse = Speed x Time
Hypotenuse = 620 miles/hour x 2 hours
Hypotenuse = 1240 miles
Now we can use the formula to find the distance the pilot travels at an angle
Distance = (sin(10) x 1240)
Distance = 215.47 miles (rounded to two decimal places)
Therefore, the total distance the pilot is from her starting position is the sum of the distance she traveled in the first part of the flight and the distance she traveled at an angle in the second part of the flight
Total distance = 930 + 215.47
Total distance = 1145.47 miles
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David is working two summer jobs, making $13 per hour landscaping and making $8 per hour clearing tables. In a given week, he can work no more than 16 total hours and must earn no less than $160. Also, he must work at most 13 hours landscaping. If
� x represents the number of hours landscaping and �y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer: One possible solution is to work 12.3 hours landscaping and 3.7 hours clearing tables, earning approximately $167.1.
Step-by-step explanation:
Let x be the number of hours landscaping and y be the number of hours clearing tables.
The system of inequalities can be written as:
x ≤ 13 (maximum of 13 hours landscaping)
x + y ≤ 16 (maximum of 16 hours total)
13x + 8y ≥ 160 (minimum earnings of $160)
To graph this system of inequalities, we can start by graphing the boundary lines of each inequality as follows:
x = 13 (vertical line at x = 13)
x + y = 16 (line with intercepts at (0, 16) and (16, 0))
13x + 8y = 160 (line with intercepts at (0, 20) and (12.3, 0))
Note that we only need to graph the portion of the lines that are in the feasible region (i.e. where x and y are non-negative).
The feasible region is the triangle formed by the intersection of the three boundary lines, as shown below:
|
20 --|--------------------------
| /|
| / |
| / |
| / |
16 --|------------------
| / |
|/ |
-------------------------
13 12.3
Let x be the number of hours landscaping and y be the number of hours clearing tables.
The system of inequalities can be written as:
x ≤ 13 (maximum of 13 hours landscaping)
x + y ≤ 16 (maximum of 16 hours total)
13x + 8y ≥ 160 (minimum earnings of $160)
To graph this system of inequalities, we can start by graphing the boundary lines of each inequality as follows:
x = 13 (vertical line at x = 13)
x + y = 16 (line with intercepts at (0, 16) and (16, 0))
13x + 8y = 160 (line with intercepts at (0, 20) and (12.3, 0))
Note that we only need to graph the portion of the lines that are in the feasible region (i.e. where x and y are non-negative).
The feasible region is the triangle formed by the intersection of the three boundary lines, as shown below:
lua
Copy code
|
20 --|--------------------------
| /|
| / |
| / |
| / |
16 --|------------------
| / |
|/ |
-------------------------
13 12.3
The vertices of the feasible region are (0, 16), (12.3, 3.7), and (13, 0).
To determine one possible solution, we can evaluate the objective function (total earnings) at each vertex:
(0, 16): 13(0) + 8(16) = $128
(12.3, 3.7): 13(12.3) + 8(3.7) ≈ $167.1
(13, 0): 13(13) + 8(0) = $169
Therefore, one possible solution is to work 12.3 hours landscaping and 3.7 hours clearing tables, earning approximately $167.1.
For the given function, identify the x- and y-intercepts if any, the vertex, the axis of symmetry, and the maximum or minimum value. f(x)=−x2+25 A) There are no x-intercepts. The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is y=0. The maximum value of the function is 25. B) The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25. C) The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,−25). The vertex is (0,−25). The axis of symmetry is x=0. The minimum value of the function is −25. D) The x-intercepts are (−25,0) and (25,0). The y-intercept is (0,5). The vertex is (0,5). The axis of symmetry is x=0. The maximum value of the function is 5.
Answer:
B) The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25.
Step-by-step explanation:
Given that the function is:
\(y=f(x)=-x^2+25\)
It is quadratic equation, therefore we can observe that it is a parabola.
The coefficient of \(x^{2}\) is negative, therefore it opens downwards.
That means it will have a maximum value.
This maximum value is at the vertex and where x = 0.
Also, vertex is at x intercept.
x intercept is the value of x where we have y = 0 and
y intercept is the value of y where we have x = 0
So, let us put y = 0 first.
\(0=-x^2+25\\ \Rightarrow x^{2} =25\\\Rightarrow x =5, -5\)
Therefore x intercepts are at (5, 0) and (-5, 0)
Now, let us put x = 0,
\(y=0+25\\\Rightarrow y =25\)
Therefore y intercept is at (0, 25).
It is the point of maximum value (which is 25) and vertex of parabola as explained above.
Kindly refer to the attached image for the graph of given function.
Therefore, correct option is:
B) The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25.
Answer:
Vertex = (3,–4), y-intercept = (0,5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = 3
Step-by-step explanation:
what's the pattern? 7,11,19,35
The pattern of each number changes.. they are all factors of 4, the 4 turns into 8, than the 4 or 8 turns into 16.
7+4=11
11+8=19
19+16=35
[4×2=8, 8×2=16]
. Assume that the annual percentage rate increases by 5%, 10%, 20%, 40%, and 60%. [30 marks] a. Calculate the approximate doubling time (Dappx) b. Calculate the exact doubling time (Dexact) c. Calculate the percentage error in calculating the doubling time for each case.
a) Approximate Doubling Time Dappx = 70/r, where r is the annual interest rate in percentage terms.Assuming that r = 5%, 10%, 20%, 40%, and 60%Doubling time for 5% = 70/5 = 14 yearsDoubling time for 10% = 70/10 = 7 yearsDoubling time for 20% = 70/20 = 3.5 yearsDoubling time for 40% = 70/40 = 1.75 yearsDoubling time for 60% = 70/60 = 1.1667 yearsb) Exact Doubling Time Dexact = ln2/r where r is the annual interest rate in decimal terms.
Assuming that r = 5%, 10%, 20%, 40%, and 60%For 5%: ln2/0.05 ≈ 13.86 yearsFor 10%: ln2/0.1 ≈ 6.93 yearsFor 20%: ln2/0.2 ≈ 3.47 yearsFor 40%: ln2/0.4 ≈ 1.73 yearsFor 60%: ln2/0.6 ≈ 1.16 yearsc)
The percentage error is given by:(Dexact − Dappx)/Dexact × 100%For 5%: (13.86 - 14)/13.86 x 100% ≈ 1.18%For 10%: (6.93 - 7)/6.93 x 100%
≈ 1.15%For 20%: (3.47 - 3.5)/3.47 x 100%
≈ -0.86%For 40%: (1.73 - 1.75)/1.73 x 100%
≈ -1.15%For 60%: (1.16 - 1.1667)/1.16 x 100%
≈ -0.60%Note that the percentage error is small for lower values of interest rates but increases as the interest rate increases.
Also, the percentage error is negative for 20%, 40%, and 60%, which means that the approximate doubling time is actually larger than the exact doubling time.
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Choose the correct simplification of (7x3y3)2.
\(answer = {7x}^{6} {y}^{6} \\ solution \\ ( {7x}^{3} {y}^{3} ) ^{2} \\ = {7x}^{3 \times 2} {y}^{3 \times 2} \\ = {7x}^{6} {y}^{6} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment\)
Answer:
\(49 {x}^{6} {y}^{6} \\ \)
Step-by-step explanation:
\( {(7 {x}^{3} {y}^{3}) }^{2} \\ {7}^{2} {x}^{3 \times 2} {y}^{3 \times 2} \\ = 49 {x}^{6} {y}^{6}\)
hope this helps
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good luck! have a nice day!
What are the (x, y) coordinates of
the midpoint of the line segment
whose endpoints are (5, 1) and
(2, -3)?
A. (3.5, -1)
B. (3,-0.5)
C. (1, 1.15)
D. (5,-3)
E. (1, 2)
Answer: The midpoint of the line segment with endpoints (5, 1) and (2, -3) is (3.5, -1).
Step-by-step explanation:
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are:
((x1 + x2) / 2, (y1 + y2) / 2)
In this case, (x1, y1) = (5, 1) and (x2, y2) = (2, -3). Substituting these values into the formula, we get:
((5 + 2) / 2, (1 - 3) / 2) = (3.5, -1)
Therefore, the midpoint of the line segment with endpoints (5, 1) and (2, -3) is (3.5, -1). The correct answer is A. (3.5, -1).
Set up an algebraic equation and solve for the variable. Justify your answer by stating the angle relationship.
Answer:
x=103°
Step-by-step explanation:
x+x-26=180
2x=180+26
2x=206
x=206/2=103°
Find the percentage error if 3,750 is used as an approximation to 3,754.
Give the answer rounded to four decimal places.
A. 1066 %
B. 0. 1066 %
C. 0011 %
D. 0. 1067 %
0.1066% percentage error occurs when 3,750 is used as a rough approximation to 3,754.
Given that,
When 3,750 is used as a rough approximation to 3,754.
We have to find what percentage error occurs.
We know that,
What is percentage error?The absolute error, which is just the difference between the observed and the real value, is used to calculate percentage error. The relative error is then multiplied by 100 to produce the percentage error after the absolute error has been divided by the real number. For explanation, see the equations below.
Percentage error = |Vobserved – Vtrue|/ Vtrue× 100%
Percentage error = 3754 - 3750/3750= 4/3750=0.1066%
Therefore, 0.1066% percentage error occurs when 3,750 is used as a rough approximation to 3,754.
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Emily needs 12 cups of fruit juice for a punch recipe. The juice comes in quart bottles. How many bottles of juice should Emily buy?
Answer: She should buy 3 bottles
Step-by-step explanation: 1 quart = 4 cups. 4x3=12
Simplify the following expression:
2y-7x + 4x² + 3y + 7x
A. 4x214x + 5y
B. 4x² - 14x
C. 4x² + 14x + 5y
D. 4x² + 5y
The simplified expression for the expression 2y - 7x + 4x² + 3y + 7x is
D. 5y + 4x²
Option D is the correct answer.
We have,
To simplify the expression 2y - 7x + 4x² + 3y + 7x, we combine like terms:
The like terms are:
2y and 3y
-7x and 7x
Group the terms with "y" together: 2y + 3y = 5y
Group the terms with "x" together: -7x + 7x = 0
Combining (1) and (2) for the expression.
Now the expression becomes:
5y + 4x²
Thus,
The simplified expression for the expression 2y - 7x + 4x² + 3y + 7x is
D. 5y + 4x²
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Suppose you are interested in testing whether the mean earning of men in California differs significantly from the mean earning of men in New York. If the number of men from California in the sample is 123 and the number of men from New York in the sample is 88, how many degrees of freedom are there?
Answer:
(123+88)-2= 209
Step-by-step explanation:
The functions f(x)=−34x+214 and g(x)=(12)x+1 are shown in the graph. What are the solutions to −34x+214=(12)x+1? Select each correct answer.
The graphs cross at x=-1 and x=1. Those are the solutions to to the equation
How to explain the graphWe know that, If two functions are equal then there solution is the intersection point of the curves.
When we determine the graph the intersection points are (0,2) and (1,1.25).
The values of x of the intersection points are the solutions of the system
Using a graphing tool, there are two intersection points and therefore the solutions are x = -1 and x [ 1.
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4.2
The solid was created by connecting two congruent square pyramids to a rectangular prism.
18 in
x
15
1
15 in.
What is the surface area of this solid?
square inches
Answer:
The answer is "\(\bold{1920 \ in^2}\)".
Step-by-step explanation:
Please find the graph file.
Rectangular solid area:
Its region comprises four rectangles, each 15 for each case 14 in each.
The rectangle field is the formula \(A = lw\)
The four rectangles are therefore covered by a zone: \(\to A = 4lw = 4 \times 15 \ in \times 14 \ in = 840 \ in^2.\)
square Pyramids area:
The pyramids in both squares have 8 triangular facets.
Each triangle has a 15-inch basis with a 14-inch base.
The triangle zone formulation is \(A = \frac{1}{2}bh\)
That's it. The 8 triangles area is \(\to A = 8 \times \frac{1}{2}bh = 4bh = 4 \times 15 \ in \times 18 \ in = 1080 \ in^2\)
Total field surface:
Strong rectangular\(= 840 \ in^2\)
Pyramids in the Square\(= 1080\)
Overall area \(= 1920 \ in^2\)
The number is \(1920\ in^2\) for a total area.
2 2.1 Mathematical intro show that there is another form for spherical harmonics: 1 3 3 Y₁ x iy 1/√√2 (²-1) 2πT 2π 1 3 3 z YO 2 2π π r 1 3 x iy Y₁¹ 3 2π - - 12 √ √ 2² (²+²) 2 2π
Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:
Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)
Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:
Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)
Y1,0 = 1/2 √(3/π)cosθ
Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)
Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ
Y2,0 = 1/4 √(5/π)(3cos²θ-1)
Y0,0 = 1/√(4π)
The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.
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y= − 7x y= 4x+22 Solve the system by substitution
Answer:
x = -2 u got this
Step-by-step explanation:
-7x = 4x + 22
-11x = 22
x = -2
Easy bro
What are the coordinates of the point on the directed line segment from K (-5, -4) to L (5,1) that partitions the segment into a ratio of 3 to 2.
Answer:
i think its d
Step-by-step explanation:
On Monday, Takira counted 75 splatters of bird droppings on her car. On Tuesday afternoon, she counted 21 more. What is the percent change in the number of bird droppings on Takira's car from Monday to Tuesday?
Answer:
28%
Step-by-step explanation:
percent change in the number of bird droppings = increase in splatters / splatters counted on Monday x 100
\(\frac{21}{75}\) x 100 = 28%
Consider four finalists in a treasure hunt who are brought to the center of a large, flat field. Each is given a meterstick, a compass, a calculator, a shovel, and (in a different order for each contestant) these three displacements: 72.4 m,32.0
∘
east of north; 57.3 m,36.0
∘
south of west; 17.8 m straidint south. The three displacements lead to the point where the keys to a new Porsche are buried. The finder gets the Porsche. Three of the four contestants start measuring immediately, but the winner first calculates where to go. What does he calculate? Figure In a second contest, the three displacements given are 90.5 m,30.0
∘
west of north; 15.8 m straight north; and 80.9 m,42.0
∘
south of east. What magnitude does the winner calculate for the displacement to find the keys to the Porsche? Express your answer in meters. X Incorrect; Try Again; 5 attempts remaining Part B - Practice Problem: What direction does the winner calculate for the displacement to find the keys to the Porsche? Express your answer in degrees.
The winner of the treasure hunt calculates the resultant displacement by using vector addition. They add the three given displacements together to determine the net displacement needed to find the buried keys to the Porsche. This involves both magnitude and direction calculations.
In the first contest, the winner calculates the magnitude of the resultant displacement by adding the magnitudes of the three given displacements: 72.4 m, 57.3 m, and 17.8 m. The sum of these magnitudes gives the total distance that needs to be covered to reach the buried keys.
In the second contest, the winner calculates the direction of the resultant displacement by considering the angles associated with each given displacement. They take into account the directions mentioned, such as east, north, south, and west. By using trigonometric principles and vector addition, the winner determines the overall direction in which they should proceed to locate the buried keys.
By calculating both the magnitude and direction of the resultant displacement, the winner maximizes their chances of reaching the treasure efficiently and accurately.
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Saturn is about 1.427 x 10^12 miles from the sun. Light travels at approximately 3 x 10^8 miles/second. How long does it take for suns light to reach Saturn
Answer:
4,756.66 seconds or 1.321 hours
Here's how I got that:
- Simply use time formula and plug in what you know -
t = distance/speed
↓
1,427,000,000,000/300000000
↓
t = 4,756.66
~That's all folks~
-Siascon
which ordered pairs in the form (x, y) are solutions to the equation 4x−5y=24
Answer:
\(\(\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{1000000pt}}\)
19/23 as a decimal rounded to the nearest tenth
i need the answer for aleks
Answer:
0.8
Step-by-step explanation:we just need to divided 19 by 23
and rounded to the nearest tenth it’s .8
Hopes this helps please mark brainliest
a clydes dale drinks about 120 gallons of every 4 days at this rate how many gallons of water does a clydsdale drink in 28 days
The gallons of water that a clydsdale drink in 28 days will be 840 gallons.
How to calculate the gallons?It should be noted that Clyde's dale drinks about 120 gallons of every 4 days. Therefore, the gallons Frank in a day will be:
= 120 / 4
= 30 gallons
Therefore, the gallons drank for 28 days will be:
= 30 × 28
= 840 gallons.
Therefore, the gallons of water that a clydsdale drink in 28 days will be 840 gallons.
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