Answer:7 21/100
Step-by-step explanation: We will covert 7.21 into a fraction. .21 = 21/100. Since 21 can only be divided by 3 and 7, the simplest form of 21/100 is 21/100. So, the mixed number is 7 and 21/100
Answer:
7 and 21/100
Step-by-step explanation:
Since .01 is 1/100, 7.21 will be 7 and 21/100. There is no way to further simplify this, therefore, it is our final answer. Hope this helps! :)
Factor the GCF:-12x4y - 9x³y² + 3x²y³ (5 points)
O-3x²y(4x2 + 3xy - y²)
O 3x²y(-4x² + 3xy - y²)
O-3(4x²y + 3x³y² - x²y³)
O-3x²y(-4x2-3xy + y²)
Answer:
A. 3x^2y(4x2 + 3xy - y^2)
Step-by-step explanation:
-12(x^4)y - 9x³y² + 3x²y³
-3x²y(4x² + 3xy - y²)
A gardener uses 1/3 of a liter of water to water 2/7 of a garden.
1 1 / 6 litres of water is needed to watering the entire garden at the given rate.
How to find the amount of water using rate?We need to find how many litres of water is needed to watering the entire garden at this rate.
Let the total garden be x parts then,
Therefore,
2 / 7 x = 1 / 3
cross multiply
2x × 3 = 7
6x = 7
divide both sides by 6
6x / 6 = 7 / 6
x = 1 1 / 6
Therefore, Thus, 1 1 / 6 litres of water is needed to watering the entire garden at the given rate.
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1. In an auditorium, there are 22 seats in the first row and 28 seats in the second row. The number of seats in a row continues to increase by 6 with each additional row.
(a) Write an iterative rule to model the sequence formed by the number of seats in each row. Show your work.
(b) Use the rule to determine which row has 100 seats. Show your work.
Step-by-step explanation:
a) We can find the iterative rule by first making a table of values.
n -> [tex]a_n[/tex]
1 -> 22
2 -> 28
3 -> 34
We see that [tex]a_n[/tex] increases by 6 each time. Hence, the iterative rule should have the term 6n. However, if we put 1 in for n, we get 6. We want 22-6=16 more than this, or [tex]6n+16[/tex]. This would work for any seat row we give.
b) Our iterative rule to get the number of seats is [tex]6n+16[/tex]. Since we know that this value is 100, we can put both equal to each other.
[tex]6n+16=100\\6n=84\\n=14[/tex]
Thus, the 14th row has 100 seats.
Answer:
(a) S_n = S_1 + 6 (n - 1)
(b) Row 14 has 100 seats
Step-by-step explanation:
(a) The arithmetic sequence would follow the iterative rule,
S_n = S_1 + 6 (n - 1) where S is the number of seats in row n, n is the row number, and S is the number of seats in row 1.
Row 1 = S_1 = 22
2 = S_2 = 28
3 = S_3 = 34
4 = S_4 = 40
|| || = 46
|| || = 52
|| || = 58
|| || = 64
|| || = 70
|| || = 76
|| || = 82
|| || = 88
|| || = 94
Row 14 = S_14 = 100
(b) 100=22+6(n-1) solve for n after setting S_n = 100
100 = 22 + 6_n - 6
84/6 = 6n/6 Row 14 has 100 seats
14 = n
please say thanks!
Identify the expression equivalent to 2x 8 by substituting x = 7 and x = 5. a. 2x 10 10 b. 2(x 2) c. (x 4) (x 4) d. (x 4) e. 2(2x 4)
the expression equivalent to 2x + 8 is (x+4) + (x+4)
using the commutative property we can say that
2x +8 = x + x + 8
also 2x + 8 = x + 4 + x + 4
hence 2x + 8 = (x+4) + (x+4)
What is an expression?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both.Addition, subtraction, multiplication, and division are all possible mathematical operations.There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.In a mathematical expression, the following terms are used:An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.a number that is multiplied by a variable is referred to as a coefficient.To know more about variable with the given
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The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the horizontal distance in feet.
1) Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. Record each representation and clearly label which player the information belongs to.
2) Supposed there were no obstacles.
a. Whose ball would travel the greatest distance before hitting the ground?
b. Whose ball would travel the shortest distance before hitting the ground?
3) Suppose the fence was 350 ft from home plate. At what height was each ball when it passed over the fence?
The heights the balls hit a fence at 350 ft distance are 65 feet, 38 feet and 30 feet, respectively
Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph.Juan
Juan's equation is given as:
h = -0.001d^2 + 0.5d + 2.5
h =
Set d to multiples of 50 from 0 to 400.
So, the table of values of Juan's function is:
d (ft) h(ft)
0 2.5
50 25
100 42.5
150 55
200 62.5
250 65
300 62.5
350 65
400 42.5
See attachment for the graph of Juan's function
Mark
A quadratic function is represented as:
h = ad^2 + bd + c
Using the values on the table of values, we have:
c = 3 -- the constant value
So, the equation becomes
h = ad^2 + bd + 3
Using the two other values on the table of values, we have:
23 = a(50)^2 + b(50) + 3
38 = a(100)^2 + b(100) + 3
Using a graphing tool, we have:
a = -0.001
b = 0.45
So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3
See attachment for Mark's graph.
Barry
From the graph, we have the table of values of Barry's function to be:
d (ft) h(ft)
0 2.5
50 21
100 35
150 44
200 48
250 46
300 41
350 30
400 14
450 0
Using a graphing tool, we have the quadratic function to be:
y = -0.001x^2 +0.4x +2.5
The shortest and the greatest distance before hitting the groundFrom the graphs, equations and tables, the distance travelled by the balls are:
Juan = 505 feet
Mark = 457 feet
Barry = 450 feet
This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.
The height the balls hit a fence at 350 ft distanceTo do this, we set d = 350
From the graphs, equations and tables, the height at 350 ft by the balls are:
Juan = 65 feet
Mark = 38 feet
Barry = 30 feet
The above represents the height the balls hit the fence
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Selim is ordering concrete spheres to place as barriers in the city park. The spheres cost $2 per square foot, and Selim can spend $20 per sphere. What is the maximum diameter of the spheres he can purchase?
Answer:
1.78 feet.
Step-by-step explanation:
If they cost $20 each and its $2 per square foot, the area of the spheres
is 20 / 2 = 10 ft^2.
Area of sphere = 4 π r^2 = 10 (where r = the radius)
---> r^2 = 10 / 4π
= 0.796
---> r = 0.892 ft
So the diameter = 2 * r
= 1.78 feet to nearest hundredth.
The coordinates of point T are (0,2). The midpoint of ST is (5,-3). Find the coordinates of point S.
The other endpoint is
(Type an ordered pair.)
Step-by-step explanation:
the midpoint is exactly halfway in each coordinate direction.
so, whatever we have to add ti or subtract from the coordinates of T to get to the midpoint, we have to add to or subtract from the midpoint to get to S.
for x we get
0 + 5 = 5
so, we need to add another 5 to get the x coordinate of S.
that is then 5 + 5 = 10
for y we get
2 - 5 = -3
so, we need to subtract another 5 to get the y coordinate of S.
that is then
-3 - 5 = -8
S = (10, -8)
How long does it take for millions of dollars worth of emerald transactions to occur in bogota? a year three months a day a week
Answer: It will be A Day
Step-by-step explanation:
On June 10, Bertha Wooten deposited $8,241.78 in a savings account that pays 5.5% interest compounded
daily. How much interest will the money earn in 31 days?
The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.
What is the future value?The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.
The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.
Where:
A = future value
P = Present value of investment
i = interest rate
n = number of periods.
The future value of the investment can also be determined using an online finance calculator, as follows.
Then the interest is the difference between the future value and the present value.
Data and Calculations:Initial deposit = $8,241.78
Interest rate = 5.5% compounded daily
Investment period = 31 days
N (# of periods) = 31 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $8,241.78
PMT (Periodic Payment) = $0
Results:
FV = $8,280.37
Total Interest $38.59 ($8,280.37 - $8,241.78)
Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.
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The slope of the line below is -3 which of the following point-slope form of the line?
Answer:
The "point-slope" form of the equation of a straight line is:
\begin{gathered}y-y_1=m(x-x_1)\\\\(x_1;\ y_1)\ is\ a\ known\ point\\\\m\ is\ the\ slope\ of\ the\ line\end{gathered}y−y1=m(x−x1)(x1; y1) is a known pointm is the slope of the line
We have:
m=-3;\ (x_1;\ y_1)=(2;-2)m=−3; (x1; y1)=(2;−2)
Substitute
\begin{gathered}y-(-2)=-3(x-2)\\\\y+2=-3(x-2)\end{gathered}y−(−2)=−3(x−2)y+2=−3(x−2)
Answer: B. y + 2 = -3(x - 2
If i throw 20 knifes what is the probability that i will hit my assistant exactly 3 out of those twenty times?
The probability that knife will hit assistant exactly 3 out of 20 times is 0.001425.
According to the given question.
Number of times a kinfe is thrown = 20
Let p denotes the probability that knife will hits the assistant. And q denotes the probability that knife will not hit the assistant.
so,
p = 1/20
q = 1 - 1/20 = 19/20
Therefore,
The probability that knife will hit assiant exactly 3 out of 20 times
[tex]= ^{20}C_{3} ( \frac{1}{20}) ^{3} (\frac{1}{19} )^{17}[/tex]
= [tex]\frac{20!}{3!17!} (0.05)^{3} (0.0526)^{17}[/tex]
=
Hence, the probability that knife will hit assistant exactly 3 out of 20 times is 0.001425.
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Which expression is equal to
CSC X
- cOs x cot x
using identities?
Step-by-step explanation:
Because the two sides have been shown to be equivalent, the equation is an identity.
A pizza has a radius of 10 inches. A slice is removed. The length of the crust of the missing slice is 3 inches. What is the area of the missing slice?
The area of the missing slice is 15 inches ²
How to determine the area
From the information given, we can see that the pizza takes the form of a circle;
Area of the missing slice takes the shape of a triangle
Area of a triangle = 1/ 2 base × height
base = 10 inches
height = 3 inches
Area of missing slice = 1/ 2 × 10 × 3
Area = 1/ 2 × 30
Area = 15 inches ²
Thus, the area of the missing slice is 15 inches ²
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Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the
nearest hundredth.
The answer is 48π units³ or 150.72 units³.
To find the volume of the cone, use the formula : 1/3 × πr²h
We are given that r = 6 and h = 4.
Solving :
V = 1/3 × π × 6² × 4V = 12 × 4 × πV = 48π units³ (in terms of π)V = 150.72 units³Given the line segment CD = 30 cm and a point E on directed line segment CD that partitions CD into the ratio 4 to 1, find the lengths of line segments CE and ED.CE = 6 cm, ED = 24 cm
CE = 25 cm, ED = 5 cm
CE = 24 cm, ED = 6 cm
CE = 5 cm, ED = 25 cm
we can simply take the whole amount of 30 and divide it by (4 + 1), then distribute to each side accordingly, since they're in a 4 to 1 ratio.
[tex]\underset{\hspace{5em}4~\hfill to~\hfill 1\qquad }{\stackrel{\text{\LARGE 30}}{C\rule[0.35em]{18em}{0.25pt}E\rule[0.35em]{10em}{0.25pt}D}} \\\\\\ \stackrel{CE}{4\left( \frac{30}{4+1} \right)} ~~ : ~~ \stackrel{ED}{1\left( \frac{30}{4+1} \right)}\implies \stackrel{CE}{4\left( 6 \right)} ~~ : ~~ \stackrel{ED}{1\left( 6 \right)}\implies \stackrel{CE}{\text{\LARGE 24}} ~~ : ~~ \stackrel{ED}{\text{\LARGE 6}}[/tex]
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
The transformations that would be used on the blue segment CD to get it to match with the red segment C2D2 is to effect a 180° clockwise rotation, so that C remains at (3, -10) and D assumes (3, -11). Recall that original coordinates were: C (3, -10); D (5, -10).
What is transformation in math?A transformation is a broad phrase covering four distinct methods of changing the shape and/or location of a point, line, or geometric figure.
The pre-Image is the original shape of the item, and the Image during the transformation is the final shape and location of the object. The following are different types of transformation in math:
TranslationRotationReflection; and Dilation.What transformations would you use on the blue triangle to get it to match with the red triangle?The type of transformation that will be used here is called reflection.
D retains it's original coordinates of (5, -10); E goes to (6, -11) and F (6, -10).
Which line segments on the boat are parallel?The line with the coordinates [(4, -11) and (4, -10) that is EF is parallel to [(3,-11) and (3, -10).
Parallel lines are lines that are always the same width apart in a plane. Parallel lines never cross.
Which line segments on the boat are perpendicular?The lines that are perpendicular are: AB with coordinates A(3, -9) & B(3, -11) and CD with coordinates (3, -10) and (5, -10). Lines that intersect each other forming a right angle are called perpendicular lines.
The line segments on the boat that have a slope of zero are:
EF, AB AC, BC. A line with zero slope is one that has a constant value shown along the y-axis that does not vary over the line's points.
The line segments on the boat that are undefined are:
CD, CF, and DF. The gradient or slope of any vertical line that travels up or down is the undefined slope.
The slope (m) is calculated as:
(Y2-Y1)/(X2 - X1)
Given that:
Y1 = 5
Y2 = 4
X1 = -10
X2 = -11
Hence,
m = (5-4)/(-11 -10)
m = -0.048
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A circle is shown. The shelf is represented by a chord and the brace goes from the chord to to a point on the circle. The brace line is extended up to form a diameter.
Custom drapes are being fitted for a large circular window. It is difficult to get these measurements, but the window has an 8 ft horizontal shelf with a 2 ft brace that sits in the frame. If the brace is extended upward, it would go through the center of the shelf and the circle. What is the diameter of the window?
Diameter = feet
The length of the diameter formed is in the image given is: 10 ft.
What is a Diameter of a Circle?The diameter of a circle is the line segment that divides the circle into two equal halves. The diameter divides the circle into semicircles. Also, the diameter of a circle is twice the length of the radius of a circle.
If we know the length of the radius, we can determine the length of the diameter of a circle by multiplying the radius by two. On the other hand, if we know the length of the diameter, to find the length of the radius, divide the diameter by 2.
The image of the circle showing the shelf and the brace line, which is the diameter are shown below.
To find the diameter of the window, add the length of the horizontal shelf and length of the brace. Thus:
Length of the diameter of the window = 8 + 2
Length of the diameter of the window = 10 ft
Thus, the length of the diameter formed is: 10 ft.
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Answer:
10 ft
Step-by-step explanation:
DIVINE TOK A MATH TEST AND GOT 36 CORRCET AND 9 INCORRECT WHAT WAS THE PERCANTHGE OF CORRECT ANSWERS
Answer: 80% correct
Step-by-step explanation:
If Divine got 36 correct and 9 incorrect, then we can find the total number of questions.
36 + 9 = 45 questions
Now, we will divide the number of questions answered correctly by the total number of questions.
[tex]\displaystyle \frac{36}{45} =0.8[/tex]
Lastly, we will multiply it by 100 to find the percentage.
0.8 * 100 = 80%
Answer:
80% was correct.
Step-by-step explanation:
The total number of questions is 45 (36 + 9). The percentage is the part correct over the total.
36/45 = .8. The answer is given in the decimal form. To change a decimal to a percent, move the decimal two places to the right.
Consider a rectangle of perimeter 12 cm. form a cylinder by revolving this rectangle about one of its edges. what dimensions of the rectangle can give us a cylinder of maximum volume?
Answer:
Dimensions will be 4 * 2 cm.
Step-by-step explanation:
l = length of rectangle and w = width
Perimeter = 2l + 2w = 12
l + w = 6.
---> l = 6 - w
Volume of the cylinder
V = πr^2l
w = 2πr
--> r = w/2π
l = 6 - w so
V = π(w/2π)^ 2 * (6 - w)
---> V = w^2/4π (6- w)
---> V = 3w^2/ 2π - w^3/4π
Differentiating:
dV/ dw = 6w/ 2π - 3w^2 / 4π
= - 3(w - 4)w / 4π
This equals 0 for maximum volume
- 3(w - 4)w / 4π = 0
w = 0 or w = 4
Describe what a line with zero rate of change looks like.
Answer:
Step-by-step explanation:
rate of change = change in y/ change in x
The rate of change is 0 if the change in y = 0
0 = 0 / change in x
The graph is a horizontal line since the y values do not change.
The total surface area if a cylindrical can, whose height is equal to the radius of the base is 2464 cm^2, find its volume.
Step-by-step explanation:
TSA of cylinder = 2πr (h + r)
according to the question
height = radius
then,
TSA = 2πr (r + r)
2464=2 × 3.1415×r ×2r
2464/4 ×3.1415 = r×r
196.08 = r^2
r = 14.00
r = 1 4 cm
We know,
volume = 2πr ^2 ×h
=2×3.1415×14×14×14 (h=r)
=17240.552 cm^3
Answer:
8620.5 cm³
Step-by-step explanation:
h = r
SA = 2πrh + 2πr²
Since h = r, we can substitute h with r.
SA = 2πr² + 2πr² = 4πr²
4πr² = 2464 cm²
r = 14 cm
V = πr²h
r = h = 14 cm
V = π(14 cm)²(14 cm)
V = 8620.5 cm³
A horizontally thrown dart falls 5 cm before it travels 2. 5 m to hit the dart board. how fast was it thrown?
The dart player throws a dart horizontally at a speed of 24.75 m/s.
In this question,
The horizontal distance traveled by the dart, x = 2.5 m
The dart hits the board 5 cm below the height from which it was thrown.
⇒ 5 cm = 0.05 m
Let the time taken by the dart to hit the board is t.
The time taken can be calculated using the Newton's second law of motion,
[tex]y = ut+\frac{1}{2}at^{2}[/tex]
Put, u = 0, a = -g and g = 9.8
On substituting the above values, we get
⇒ [tex]-0.05 = 0-\frac{1}{2}(9.8)t^{2}[/tex]
⇒ [tex]0.05(\frac{2}{9.8}) = t^{2}[/tex]
⇒ [tex]t^{2} =0.0102[/tex]
⇒ [tex]t=\sqrt{0.0102}[/tex]
⇒ t = 0.1010 s
Now, the velocity (speed) can be calculated as
displacement = speed × time
⇒ 2.5 = speed × 0.1010
⇒ speed = [tex]\frac{2.5}{0.1010}[/tex]
⇒ speed = 24.7524 m/s
Hence we can conclude that the dart player throws a dart horizontally at a speed of 24.75 m/s.
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If 12 men are needed to run 4 machines. How many men are needed to run 20
Answer:
60Step-by-step explanation:
If 12 men are needed to run 4 machines. How many men are needed to run 20
we can solve with an equation
12 : 4 = x : 20
x = 12 * 20 : 4
x = 240 : 4
x = 60
----------------------------
check
12 : 4 = 60 : 20
3 = 3
the answer is good
what is the measure of an angle if it is 660 less than 6 times its own supplement
Answer:
60
Step-by-step explanation:
Since this angle is unknown, let's just represent it with the variable "x". So the supplement angle of "x" is essentially, the value of the angle that we need to add to "x" to get 180. In other words let's just say that the supplement angle is "y". This means that: [tex]x+y=180[/tex]. If we subtract x from both sides we can represent "y" or the supplement angle as: [tex](180-x)[/tex].
Since it's 660 less than 6 times it's own supplement let's first multiply the supplement by 6
[tex]6(180-x) = 1,080-6x[/tex]
Now let's subtract 660 from it, since it's 660 less
[tex](1,080 - 6x) - (660) = 420 - 6x[/tex]
This value should be equal to the angle, which is represented as "x". So let's set it equal to x
[tex]420-6x=x[/tex]
Add 6x to both sides
[tex]420=7x[/tex]
Divide both sides by 7
[tex]60 = x[/tex]
What is [tex]\frac{a+3}{8}[/tex] x [tex]\frac{2}{a}[/tex]
Answer: [tex]\frac{2a+6}{8a}[/tex]
Step-by-step explanation:
[tex]\frac{2(a+3)}{8a}=\frac{2a+6}{8a}[/tex]
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
C (Third option)
Step-by-step explanation:
The prime factorization of 675 is 5*5*3*3*3 or 5^2*3^3. With the square root, we take out all square integers, leaving (5*3)(sqrt3). The answer is 15(sqrt3) or C.
Break
√225×3√225√3√15²√315√3Option C
Consider a single spin of the spinner. A spinner contains 4 equal sections: 1, 2, 4 and 3. Sections 1 and 4 are shaded. The spinner is pointed at number 2. Which events are mutually exclusive
Answer:
Events that mutually exclusive are 1. Landing on a shaded portion and landing on a 3.2. Landing on an unshaded portion and landing on a number less than 2.
How many ways can a 2 person subcommittee be selected from a comittee of 6 people?
Answer: 15 ways
Step-by-step explanation: 5+4+3+2 + 1 = 15
Answer:
15.
Step-by-step explanation:
That would be the number of combinations of 2 from 6.
6C2
= 6! /4!2!
= 6*5/2*1
= 15.
Stuck on this problem. Help is needed please!
Step-by-step explanation:
A.
the height, the 17cm leg and half of the baseline (16/2 = 8cm) create a right-angled triangle.
so, Pythagoras applies.
c² = a² + b²
c being the Hypotenuse (side opposite of the 90° angle).
so, we get
17² = height² + 8²
289 = height² + 64
225 = height²
height = sqrt(225) = 15cm
B.
the answer to this is the surface area of the whole box.
it has 5 sides :
bottom : 20×16 rectangle = 320 cm²
left and right : 20×17 rectangles = 340×2 = 680 cm²
front and back : 16×15/2 triangles = 120×2 = 240 cm²
in total that is
320 + 680 + 240 = 1,240 cm² of cardboard
Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? explain why this is true.
The desired minimum revenue is $130.
What is revenue?
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.
The money received from routine business activities is referred to as revenue, sales, or the top line.Revenue (from the sale of goods or services) less operational expenses equals operating income.Non-operating income is irregular or irregular money that comes from other sources (e.g., lawsuit proceeds).Governments, nonprofit organizations, and private persons are examples of non-business entities that also declare revenue, albeit their methods and resources vary.Let us assume,
charge = b
customer= c
revenue= r
We know that,
r= bc
⇒ [tex]r=16\times 10[/tex]
⇒ [tex]r=\ 160[/tex]
Also,
[tex]b+1[/tex] ⇒ [tex]c-2[/tex]
with a target of [tex]r \geq 130[/tex]
Therefore,
[tex]b=10+x[/tex] ⇒ [tex]c=16-2x[/tex]
[tex](10+x)(16-2x)\geq 130\\160-20x+16x-2x^2 \geq 130\\-2x^2 -4x+30\geq 0\\x^2+2x-15\leq 0\\(x+1)^2 \leq 4^2\\x+1 \leq 4[/tex]
as negative value is not considered.
[tex]x\leq 3[/tex]
We get the result that [tex]\[/tex]3 is the maximum increase amount.
Therefore, revenue will be:
[tex](10+3)(16-3\times2)=13\times 10\\[/tex]
revenue = [tex]\[/tex]130
Full Question: Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour. Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions. Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.
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Answer:
The desired minimum revenue is $130.
What is revenue?
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.
Step-by-step explanation:
Worked out for me :)