The length of the apothem of the pentagon is 12.96 meters .
What is apothem ?
In geometry, the apothem of a polygon is the distance from the center of the polygon to the midpoint of one of its sides. For a regular polygon (a polygon with all sides and angles equal), the apothem is the perpendicular distance from the center of the polygon to one of its sides.
Explanation:
The formula for the area of a regular pentagon is:
A = (1/2)P × a
where A is the area, P is the perimeter, and a is the apothem.
To solve for the apothem, we need to rearrange the formula and solve for a:
a = (2A) / P
The perimeter of a regular pentagon is given by:
P = 5s
where s is the length of each side.
Substituting the given values, we get:
P = 5s = 5(9.7) = 48.5
A = 315.25
a = (2A) / P = (2 × 315.25) / 48.5 = 12.96
Therefore, the length of the apothem of the pentagon is 12.96 meters (rounded to two decimal places).
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Answer:
Step-by-step explanation:
its 13
To find the volume of a prism, Frank multiplies the area of the base by the height. Frank finds the area of the base of a rectangular prism is 24 square inches.
How many inch cubes are needed to fill the bottom layer of the prism?
Answer:
24 inch cubes are needed to fill the bottom layer of the prism.
Use a definition, postulate, or theorem to find the value of x in this figure described.
Y is the midpoint of XZ. If XZ = 6x-2 and YZ = 2x + 2, find x.
Select each definition, postulate, or theorem you will use.
A Segment Addition Postulate
B definition of segment bisector
C Linear Pair Theorem
D definition of a midpoint
The solution is x =__?
Thus, the value of x is 1.
What is midpoint ?The description that will be used to break this problem is D description of a midpoint.
By description, a midpoint is a point on a line member that divides it into two equal corridor. thus, Y is the midpoint of XZ, which means that XY is equal in length to YZ.
Using the Member Addition hypothetical( A), we can write
XZ = XY YZ
Substituting the values given in the problem, we get
x- 2 = XY 2x 2
Simplifying this equation, we get
x- 2 = XY 2x 2
4x = 4
x = 1
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Embassy Motorcycles (EM) manufacturers two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders. Embassy produces the engines for both models at its Des Moines, Iowa, plant. Each EZ-Rider engine requires 6 hours of manufacturing time and each Lady-Sport engine requires 3 hours of manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy's motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex and the supplier can only provide up to 280 Lady-Sport frames for the next production period. Final assembly and testing requires 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maximum of 1000 hours of assembly and testing time are available for the next production period. The company's accounting department projects a profit contribution of $2400 for each EZ-Rider produced and $1800 for each Lady-Sport produced. a) Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution to profit. c)Which constraints are binding? Use Excel and include the relevant Solver Answer Report with answers. I need help on putting this in Excel.
The linear programming model that can be used to determine the number of units of each model in order to maximize the profit is x2 <= 280 (Lady-Sport Frames), 2 x1 + 2.5 x2 <= 1000 (Assembly & Test).
What is linear programming model?When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
A linear programming problem can be solved by determining the best value.
a)Let x1 be number of EZ-Riders produced.
Let x2 be number of Lady-Sports produced.
The Objective is to maximize the profit contribution:
Max 2,400 x1 + 1,800 x 2
The Constraints are: Engine Manufacturing Time <= 2100 hours
Lady-Sport Frames <= 280 frames
Assembly & Test <= 1000 hours
6 x1 + 3 x2 <= 2100 (Engine Manufacturing)
x2 <= 280 (Lady-Sport Frames)
2 x1 + 2.5 x2 <= 1000 (Assembly & Test)
We also need bounds x1 and x2 => 0.
So the full model is:
Max 2,400 x1 + 1,800 x2
Subject to 6 x1 + 3 x2 <= 2100 (Engine Manufacturing)
x2 <= 280 (Lady-Sport Frames)
2 x1 + 2.5 x2 <= 1000 (Assembly & Test)
x1 => 0, x2 => 0
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If you invest $9,500 per period for the following number of periods, how much would you have?
13 years at 10 percent.
50 years at 9 percent.
The accrued amounts are $32,796.58 and $706,396.44.
Compound interest is computed as interest on the principle of an account plus any accrued interest.
Compound interest can be calculated using the following formula:
x = P (1+r/n[tex])^{rt}[/tex]
,where x = compound interest
P = principal (the initial deposit or loan amount)
r = annual interest rate
n = the number of compounding periods per unit of time
t = the number of time units the money is invested or borrowed for
(a) If you invest $9,500 per period for 13 years at 10 percent.
First, convert R as a percent to r as a decimal
r = R/100
r = 10/100
r = 0.1 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 9,500.00(1 + 0.1/1[tex])^{13}[/tex]
A = 9,500.00(1 + 0.1[tex])^{13}[/tex]
A = $32,796.58
(b). If you invest $9,500 per period for 50 years at 9 percent,
First, convert R as a percent to r as a decimal
r = R/100
r = 9/100
r = 0.09 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 9,500.00(1 + 0.09/1[tex])^{50}[/tex]
A = $706,396.44
Therefore, the amounts are$32,796.58 and $706,396.44.
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Morgan has 46 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 130 square meters. Solve for the dimensions (length and width) of the field.
Answer:
So we have two possible values for the width: W = 16 or W = 7.5.
If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.
If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.
Step-by-step explanation:
Let the length of the rectangular plot be L, and let the width be W. Then we have:
The perimeter of the plot is 2L + 2W, and this must equal the length of fencing that Morgan has, which is 46 m. So we have the equation:
2L + 2W = 46
The area of the plot is LW, and we know that this equals 130 square meters. So we have the equation:
LW = 130
We can solve for one variable in terms of the other from the second equation, so let's solve for L:
L = 130/W
Now we can substitute this expression for L into the first equation:
2(130/W) + 2W = 46
Simplifying this equation, we get:
260/W + 2W = 46
260 + 2W^2 = 46W
2W^2 - 46W + 260 = 0
Dividing by 2, we get:
W^2 - 23W + 130 = 0
This is a quadratic equation that we can solve using the quadratic formula:
W = [23 ± √(23^2 - 4(1)(130))] / (2(1))
W = [23 ± 9] / 2
So we have two possible values for the width: W = 16 or W = 7.5.
If W = 16, then L = 130/16 ≈ 8.125. This gives us a perimeter of 2(8.125) + 2(16) = 48.25, which is too much fencing.
If W = 7.5, then L = 130/7.5 ≈ 17.333. This gives us a perimeter of 2(17.333) + 2(7.5) ≈ 46.666, which is close enough to 46. Therefore, the dimensions of the field are approximately L = 17.333 m and W = 7.5 m.
Answer:
Length = 13
Width = 10
Step-by-step explanation:
Let L = length and W = width of the plot
The area is given by LW and is given as 130 square meters
LW = 130 (1)
The perimeter = 2(L + W) and given as 46 meters(length of fencing)
2(L + W) = 46
L+W = 23 (2)
In equation 1, isolate L by dividing both sides by W
LW/W = 130/W
L = 130/W
Substitute this value for L in equation (2)
L + W = 23
130/W + W = 23
Multiply throughout by W:
130/W x W + W x W = 23x W
130 + W² = 23W
Subtract 130W from both sides:
130 + W² - 23W= 0
Rewrite as
W² - 23W + 130 = 0
This is a quadratic equation which can be solved by factoring
Factoring W² - 23W + 130 = 0
(W - 13)(W-10) = 0
This means W = 13 or W = 10
If W = 13, L = 130/W = 120/13 = 10
If W = 10, L = 130/W= 130/10 = 13
So the possible values for L, W are
L = 13, W = 10
or
L = 10, W =13
Choosing the larger value for L gives us:
L = 13, W = 10
1) Ryan buys a sofa for £2500 plus VAT at 20%
a) What is the total price of the sofa?
The total price of the sofa is £3000.
Step-by-step explanation:1. Calculate the amount to pay for VAT.To calculate this, multiply the given amount by "0.2", which equals "20%".
[tex]2500*0.2=500[/tex]
2. Add up the two number to find the total amount due.[tex]2500+500=3000[/tex]
3. Conclude.The total price of the sofa is £3000.
-------------------------------------------------------------------------------------------------------
Alternative (and also easier) method.So if we want to add 20% of any amount to said amount, we may multiply it by (1+0.2), which equals "1.20", and it'll give us the result immediately:
[tex]2500*(1+0.2)\\ \\2500*1.2=3000[/tex]
Now, working on the opposite way, let's say we want to reduce that same number (2500) by 25%, maybe because there's a discount on the product. In that case, we must multiply by (1-0.25), which equals 0.75:
[tex]2500*(1-0.25)\\ \\2500*(0.75)=1875.[/tex]
Given :-
Ryan buys a sofa for £2500 .VAT is 20% .To Find:-
Total price of the sofa.Solution:-
Here we are given that Ryan purchases a sofa for £2500 . In order to find the cost of sofa after VAT , find 20% of the price of the sofa,
20% of £2500
20/100 * £2500
£500
Now add this to the original price of the sofa,
£2500 + £500
£3000
Hence the cost of the sofa after VAT is £3000 .
In a research study on multitasking, 8 students were
asked to play a video game. They were then asked to
record the number of minutes they played the video
game. Could this be a graph of the results? Explain
how you know.
Step-by-step explanation:
study by the University of London found that participants who multitasked during cognitive tasks, experienced an IQ score decline similar to those who have stayed up all night. Some of the multitasking men had their IQ drop 15 points, leaving them with the average IQ of an 8-year-old chil
let $pqr$ be an equilateral triangle, centered at $o.$ a point $x$ is chosen at random inside the triangle. find the probability that $x$ is closer to $o$ than to any of the vertices. (in other words, find the probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$)
The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,
⇒ 1/3
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
Let $pqr$ be an equilateral triangle, centered at $o$ a point $x$ is chosen at random inside the triangle.
Hence, The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,
⇒ 1/3
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point slope form holt mcdougal practice B lesson 5-8 answer key??
The point slope form of a linear equation is an equation that describes the relationship between two variables, x and y, in terms of their linear relationship.
What is the point slope form?It takes the form:.y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and m is the slope of the line.
In this form, you can find the equation of a line if you know a point on the line and the slope of the line. You can also use this form to find the equation of a line if you are given two points on the line, by first finding the slope using the two points, and then plugging in one of the points and the slope into the equation.
The point slope form can be useful in a variety of contexts, such as in graphing and in solving problems involving rates of change.
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Brian b has a box of 96 forks for $4.98. what is the unit price for each brand?
Answer: To find the unit price for each fork, we need to divide the total cost of the box by the number of forks in the box.
The cost of the box is $4.98, and the box contains 96 forks. So the unit price for each fork is:
$4.98 ÷ 96 = $0.051875
Rounding to the nearest cent, the unit price for each fork is $0.05.
Step-by-step explanation:
Using the unitary method, we found that the cost of one fork of brand B is $0.051.
What is meant by the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. We typically utilise this technique for maths computations. This method allows us to calculate both the value of many units from the value of one unit and the value of many units from the value of one unit.
The worth of many things is supplied in the unitary technique, and we must either determine the value of more or fewer items. To do that, we must first determine the value of a single item by division and then determine the value of further or more items by multiplication.
Given,
The number of forks in a box of brand B = 96
Price of 96 forks = $4.98
The unit price of brand B = Cost of one fork
Using the unitary method,
96 forks = $4.98
1 fork = $4.98 / 96 = $0.051
Therefore using the unitary method, we found that the cost of one fork of brand B is $0.051.
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PLEASE HELP!
Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
Answer:picture is not clear on my side, please re-upload thx!
Step-by-step explanation:
(-2, 5) and (-4,-5).
Answer: the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.
Step-by-step explanation:
(-2, 5) and (-4,-5) are two points in the coordinate plane.
The first point (-2, 5) has an x-coordinate of -2 and a y-coordinate of 5. This point is 2 units to the left of the y-axis and 5 units above the x-axis.
The second point (-4, -5) has an x-coordinate of -4 and a y-coordinate of -5. This point is 4 units to the left of the y-axis and 5 units below the x-axis.
To find the distance between these two points, we can use the distance formula:
distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the coordinates of the two points, we get:
distance = sqrt[(-4 - (-2))^2 + (-5 - 5)^2] = sqrt[(-2)^2 + (-10)^2] = sqrt[104]
So the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.
5. Luis has three different rectangular prisms below.
4 cm
Prism A
5 cm
6 cm
3 cm
Prism B
8 cm
4 см
5 cm
Select all the true statements below.
A. Prism A and C have the same volume.
B. Prism B has a greater volume than Prism C.
C. Prism B has the least volume.
D. The volume of Prism A is 120 cubic centimeters.
E. The volume of Prism C is less than the volume of Prism A.
Prism C
7 cm
3 cm
6. Select all measurements that show equivalent volume to the rectangular prism
shown below.
Statements B , D and E are True.
Statements A and C are False.
What is Volume ?The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
A. Prism A and C have the same volume. - False
The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.
B. Prism B has a greater volume than Prism C. - True
The volume of Prism B is 8 x 4 x 3 = 96 cubic cm, while the volume of Prism C is 7 x 3 x 5 = 105 cubic cm.
C. Prism B has the least volume. - False
The volume of Prism A is 5 x 6 x 4 = 120 cubic cm, which is greater than the volume of Prism B.
D. The volume of Prism A is 120 cubic centimeters. - True
As calculated above, the volume of Prism A is 120 cubic cm.
E. The volume of Prism C is less than the volume of Prism A. - True
As calculated above, the volume of Prism C is 105 cubic cm, which is less than the volume of Prism A.
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My teacher gave me an extra credit assignment with 25 minutes left of class. It is extra credit, not a timed assessment.
need done as soon as possible
Answer: it will be square or rhombus
Step-by-step explanation:
Can someone please check my answers?
Answer:
answer is mentioned in the pdf .Your answer is incorrectAnswer:
See attached image and explanation below
Step-by-step explanation:
For the first table:
The cumulative frequency for each class interval is obtained by adding that class frequency to the sum of all frequencies less than that class interval
So the table will look as in the first image attached
The second table talks about cumulative relative frequency and it uses the same technique as above but we are dealing with relative rather than absolute frequencies
The second image shows the correct values
Your relative frequency table (the third image you posted) is correct
PLEASE HELPPP!!!! DUE IN 2 HOURSS!!!!!
The current population of Algeria is 38 million
How to determine the current population of AlgeriaFrom the question, we have the following parameters that can be used in our computation:
P = 38(1 + r)^t
In the initial year, we have
t = 0
Substitute the known values in the above equation, so, we have the following representation
P = 38(1 + r)^0
Evaluate
P = 38
Hence, the population is 38 million
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Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) cos(x) + sin(x) 9 dx sin(2x)
Value of integral ∫cos(x) + sin(x) 9 dx sin(2x) is
-9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x)
What is integral?In mathematics, integrals are the continuous analogues of sums and are used to calculate areas, volumes, and their generalizations. Integration (the process of computing an integral) is one of the two basic operations in calculus, the other being differentiation.
Given,
∫(cos(x) + sin(x).9)dx . sin2x
simplifying
sin(2x) ∫(9sinx + cosx)dx
sin(2x) (9∫sin(x)dx+∫cos(x)dx)
sin(2x) (-9cos(x) + sin(x) + c)
Using distributive law
= sin(2x)(-9cos(x)) + sin(2x)sin(x) + sin(2x).c
= -9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x)
Hence, -9cos(x)sin(2x) + sin(2x)sin(x) + c.sin(2x) is the value of integral
∫(cos(x) + sin(x) . 9)dx sin(2x)
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Mrs. Grady surveyed 30 students, 13 of which said they liked basketball, 18 of which said they liked hockey, and 4 of which said they liked both sports.
(a) How many students did not like either sport?
(b) How many students liked exactly one of the sports?
Answer:
Step-by-step explanation:
(a) To find the number of students who did not like either sport, we can use the formula:
Total students = Students who like basketball + Students who like hockey - Students who like both sports + Students who like neither sport
We know that the total number of students surveyed is 30, and we also know the number of students who like basketball, hockey, and both sports. We can use this information to solve for the number of students who like neither sport:
30 = 13 + 18 - 4 + Students who like neither sport
Simplifying this equation, we get:
3 = Students who like neither sport
Therefore, there were 3 students who did not like either sport.
(b) To find the number of students who liked exactly one of the sports, we can subtract the number of students who liked both sports from the total number of students who liked at least one of the sports. We know that 13 students liked basketball, 18 students liked hockey, and 4 students liked both sports. To find the number of students who liked at least one sport, we can add the number of students who liked basketball and the number of students who liked hockey, but we need to make sure we don't count the 4 students who liked both sports twice:
Number of students who liked at least one sport = Students who like basketball + Students who like hockey - Students who like both sports
Number of students who liked at least one sport = 13 + 18 - 4 = 27
Therefore, the number of students who liked exactly one sport is:
Number of students who liked exactly one sport = Number of students who liked at least one sport - Number of students who liked both sports
Number of students who liked exactly one sport = 27 - 4 = 23
So there were 23 students who liked exactly one of the sports.
You insure your home for $125,000. You want to be safe and add coverage on the contents, so you take 55% on the contents. How much coverage will you have on the contents of your home?
The amount of coverage that you will have on the contents of your home would be = $68,750
How to calculate the amount of coverage for contents of your home?The total amount of money that was insured for the house = $125,000
The percentage of insurance that was left for the contents of the house = 55% of insurance.
That is;
= 55/100 × $125,000
= 6875000/100
= $68,750.
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The quotient of a number and 7 is 8. Use n to represent “a number”.
Answer:
Step-by-step explanation:
n+7=8
n=1
Find the area of the blue-shaded region. Please help I need it asap. The answer is 20.0m squared I cannot figure out the work for it
The area of the blue-shaded region is 19.95 m²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,
Using the Pythagoras theorem,
15.5² = 14²+w² [width]
w² = 240.25-196
w² = 44.25
w = 6.65
Therefore, the width of the rectangle is 6.65 m
That mean, the height of the parallelogram is 6.65 m,
The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,
Area of the remaining region = 14×6.65-11×6.65
= 6.65(14-11) = 6.65×3
= 19.95 m²
Hence, the area of the blue-shaded region is 19.95 m²
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Somebody help me please!!!!
Point F is on the line segment EG. Given EG=5x+7, EF=5x, and FG=2x-7, determine the numerical length of FG.
Answer:
[tex]\text{Numerical length of $\overline{FG}$ = 7}[/tex]
Step-by-step explanation:
We are given the following data:
[tex]EG = 5x + 7\\EF = 5x\\FG=2x-7\\[/tex]
Point F is the line segment [tex]\overline{EG}[/tex]
So F is between E and G
We get the relationship
EG = EF + FG
→ 5x + 7 = 5x + (2x - 7)
→ 5x + 7 = 5x + 2x - 7
→ 5x + 7 = 7x - 7
Moving x terms to the left and the constant 7 from left to the right gives
→ 5x - 7x = -7 +(-7)
→ -2x = -14
→ x = -14/-2 = 7
Therefore length of FG = 2x - 7
= 2(7) - 7
= 14 - 7
= 7
6/cm
4 cm
Find the value of x.
X
x = [?]up
The measurement of x, in the given circle, is 5 cm.
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
Given is a circle with a tangent of 6 cm and a secant of length 4+x, we need to find the measurement of x,
Using properties of circle,
6² = 4·(4+x)
36/4 = 4+x
9 = 4+x
x = 5
Hence, the measurement of x, in the given circle, is 5 cm.
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Follow these steps to graph this parabola:
y = x
Plot the y-intercept
2
1. Find/Plot the vertex
2.
3. Find/plot one more point
4. Reflect #2 and #3 over the axis of symmetry
-10-9-8-7 -6 -5 -4 -3 -2
7
10
9
8
7
6
54
3
2
1
0 1 2 3 4 5 6 7 8 9 10
-1
2
4x + 4
-3
-4
-5
-6
-7
-8
-9
X
Please find attached the graph of the parabola, y = x² - 4·x + 4, created with MS Excel, showing the points;
The vertex, (2, 0)Y-intercept; (0, 4)One more point; (1, 1)What is a parabola?A parabola is the locus of a point that moves such that its distance from a point (known as the focus) and a line (known as the directrix), are the same.
1. The quadratic function is; y = x² - 4·x + 4
The x-coordinates of the vertex of the quadratic function, f(x) = a·x² + b·x + c, can be found using the formula;
x = -b/(2·a)
The x-coordinates of the graph of the equation, y = x² - 4·x + 4, is the point;
x = -(-4)/(2 × 1) = 2
The y-value of the vertex is therefore;
y = 2² - 4 × 2 + 4 = 0
The coordinates of the vertex is therefore; (2, 0)
2. The y-intercept is the point the graph intersects the y-axis, which is the point the x-value is zero, therefore;
The coordinate of the y-value of the y-intercept is therefore;
y = 0² - 4 × 0 + 4 = 4
The y-intercept is therefore; (0, 4)
3. A point on a function can be plugging a value of the input as follows;
The point at x = 1 is; y = 1² - 4×1 + 4 = 1
Therefore, another point on the graph is; (1, 1)
4. The axis of symmetry is the vertical line passing through the vertex, with an equation which is the x-value of the vertex
The x-value of the vertex is; x = 2, therefore, the axis of symmetry is the line; x = 2
The reflection of a point (x, y) about the vertical y-axis is the point (-x, y)
Therefore, the image of the reflection of the y-intercept, (0, 4) about the line x = 2 will be the point (4, 4)
The reflection of the point (1, 1), about the line x = 2 is the point (3, 1)
The above points can be used to graph the parabola, y = x² - 4·x + 4.
Please find attached the graph of the parabola created with MS Excel.
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Can you please solve and see which one is a function and which one is not a function
For each relation, we would determine whether or not it is a function as follows;
Relation 1 is: B. not a function
Relation 2 is: B. not a function.
Relation 3 is: B. not a function
Relation 4 is: A. a function.
How to determine the relations that represent functions?In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).
This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.
Based on relations 1, 2, and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).
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In a population of 6000 cave-dwelling fish, eyesight is under selection. Fish that are homozygous for allele A1 have good eyesight, fish that are homozygous for A2 are blind and fish that are heterozygous have poor eyesight. In the dark caves that these fish live in, the cost of good eyesight is higher than the benefits and having good eyesight is thus deleterious. Blind fish have a selective advantage of 0.25, fish with poor eyesight have a selection coefficient of 0.05. Which statement is true?
I. Fish with good eyesight have a fitness W = 0
II. The trait blindness is likely to increase in this population
I
II
Both are false
Both are true
Answer: I am in high school so this may not be the best answer, but I would say that eventually eye sight would simply become useless to the fish because they live in a cave and don’t really need to see, there for I would say that the second answer is correct.
GROUP 'D' (4×5=20) A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S. At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000. If the price of land increases at the rate of 20% per annum and the price of house depreciates at the rate 20% per annum. After how many years the price of land and the price of house will be equal? Find it. combined solid is formed with the combination of hemisphere and cone having radius
After 2.5 years the price of land and the price of house will be equal.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S.
And, At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000.
Since, The price of land increases at the rate of 20% per annum.
Hence, We get;
A = 80,00,000 (1 + 20/100)ⁿ
And, The price of house depreciates at the rate 20% per annum.
Hence, We get;
A = 2,70,00,000 (1 - 20/100)ⁿ
Let after n years the price of land and the price of house will be equal.
Thus, We get;
80,00,000 (1 + 20/100)ⁿ = 2,70,00,000 (1 - 20/100)ⁿ
8 (120/100)ⁿ = 27 (80/100)ⁿ
8 (6/5)ⁿ = 27 (4/5)ⁿ
Take log both side,
log 8 + n (log 6 - log 5) = log 27 + n (log 4 - log 5)
0.9 + n × 0.8 = 1.4 + n × 0.6
0.9 + 0.8n = 1.4 + 0.6n
0.2n = 0.5
n = 2.5 years
Therefore, After 2.5 years the price of land and the price of house will be equal.
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let x be a random variable taking values [0, 1, 2, 3] with respective probabilities [0.2, 0.5, 0.2, 0.1] (a) determine the expectation of x. (show work)
A total of 23800 cubes can fit inside the box of the given dimensions.
What is the volume of cube?The volume of a cube is given by -
Volume = a x a x a = a³
Given is that a box has a length of 10 inches, a width of 8[tex]\frac{3}{4}[/tex] inches, and a height of 4[tex]\frac{1}{4}[/tex] inches.
The volume of the box would be -
V = 10 x 8[tex]\frac{3}{4}[/tex] x 4[tex]\frac{1}{4}[/tex]
V = 10 x 35/4 x 17/4
V = 371.875 inches³
The volume of cube -
v = 1/4 x 1/4 x 1/4
v = 0.015625 inches³
Number of cubes that will fill the box would be -
n = V/v
n = 371.875/0.015625
n = 23800
Therefore, a total of 23800 cubes can fit inside the box of the given dimensions.
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Use the diagram to complete the statement.
The length of CF is solved to be 12
How to find CFIn the figure the value of CF is solved using the vertical angle theorem and sum of angles in a triangle
In triangle GBC
angle C = 180 - 90 - 45
angle C = 45
Using vertical angle theorem
angle DCB = angle DCF
Using trigonometry relation we have
cos 45 = CF / 12√2
CF = cos 45 * 12√2
CF = 12
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Just need help with this question..
Graph appears to intersect the X axis in between 20 and 22 and algebraically the estimate of zero is 21.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given a linear function which represents the profit of Bethany, y after x hours of dog walking.
(a) From the graph, we have to estimate the zero.
The graph seems to intersect the X axis in between 20 and 22, approximately 21.
(b) To solve this algebraically, we have the profit function,
y = 23x - 480
When y = 0,
23x - 480 = 0
23x = 480
x = 20.87 ≈ 21
Hence the graphical method gives the same estimate as the algebraic method.
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