Using the normal vector of the parallel plane <7, -1, -1>. By Substituting the given points (9, -9, -6) in the plane equation and got the new plane equation: 7x - y - z = 69.
To find an equation of the plane passing through a given point and parallel to another plane, we need to use the normal vector of the parallel plane and substitute the given point in the equation of the plane.
A plane is defined by a point and a normal vector perpendicular to it. Therefore, to find an equation of the plane passing through the point (9, −9, −6), we need to determine its normal vector.
The given plane 7x − y − z = 1 can be written in the form Ax + By + Cz = D, where A = 7, B = -1, C = -1 and D = 1. The coefficients of x, y, and z in this equation give the components of the normal vector to the plane. Thus, the normal vector is N = (7, -1, -1).
Since the plane we want to find is parallel to the given plane, it has the same normal vector. Therefore, we can write its equation as 7x - y - z = D, where D is a constant. To determine D, we substitute the coordinates of the given point into the equation:
7(9) - (-9) - (-6) = 69
Thus, the equation of the plane passing through the point (9, −9, −6) and parallel to the plane 7x − y − z = 1 is 7x - y - z = 69.
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Find the measure of the arc or angle indicated
In the given circle, the measure of arc SM is 106°
Calculating the measure of an arc in the circleFrom the question, we are to determine the measure of arc SM.
First, we will determine the measure of angle QSM
m ∠QSM = 37° (Angles in the same segment)
Now,
Let the center of the circle be O
Thus,
OS and OM are radii
Therefore,
m ∠OSM = m ∠OMS
m ∠OSM = 37°
But,
Measure of arc SM = m ∠SOM
Now, we will determine the measure of angle SOM
m ∠SOM = 180° - 37° - 37°
m ∠SOM = 106°
Hence, measure of arc SM is 106°
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Choose the function whose graph is given by
Answer:
B
Step-by-step explanation:
Line ST and point V are shown on the graph.
On a coordinate plane, line S T goes through (negative 5, 0) and (5, 2). Point V is at (0, negative 2).
Line VW is to be drawn on the graph such that it is perpendicular to line ST. If the coordinates of point W are (−1, y), what is the value of y?
−7
−5
2
3
Answer:
3
Step-by-step explanation:
y + 2 = -5x
Substituting x = -1, we get:
y + 2 = 5
y = 5 - 2 = 3
Therefore, the value of y is 3. Answer: 3.
in a sample of 30 people, the average cost of a latte is $3.55. the standard deviation for the sample is $1.46. what is the margin of error for a 99% confidence interval?
In this case, the margin of error for a 99% confidence interval is $0.814.
To calculate the margin of error for a 99% confidence interval, we need to use the formula:
Margin of error = Z × (standard deviation / sqrt(sample size))
where Z is the z-score for the desired confidence level. For a 99% confidence interval, the z-score is 2.576.
Plugging in the given values, we get:
The margin of error = 2.576 × (1.46 / √(30))
Simplifying this expression, we get:
Margin of error = 0.814
Therefore, in this case, the margin of error for a 99% confidence interval is $0.814. This means that we can be 99% confident that the true average cost of a latte in the population falls within $3.55 ± $0.814. In other words, the true average cost of a latte in the population could be as low as $2.736 or as high as $4.364, based on the sample data.
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The perimeter of a rectangular farm is 1800 m and its length is 140 m longer than its breadth. Find the area of the farm.
Simultaneous equation
The area of the rectangular farm is 197,600 square meters.
Let's assume the breadth of the rectangular farm is x meters. According to the given information, the length of the farm is 140 meters longer than its breadth, so the length would be (x + 140) meters.
The perimeter of a rectangle is given by the formula P = 2(length + breadth). We can set up the equation as follows:
2(length + breadth) = 1800
Substituting the values, we get:
2((x + 140) + x) = 1800
Simplifying the equation:
2(2x + 140) = 1800
4x + 280 = 1800
4x = 1800 - 280
4x = 1520
x = 1520 / 4
x = 380
Therefore, the breadth of the farm is 380 meters.
Using this value, we can find the length:
Length = x + 140 = 380 + 140 = 520 meters.
The area of a rectangle is given by the formula A = length * breadth. Substituting the values, we have:
Area = 520 * 380 = 197,600 square meters.
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16. A cylindrical solid metal is 3m long and has a mass of 4kg. if its density is 5.6g/cm³, find the (3mks radius of its end. (take л=3.142)
After considering all the details we conclude that the radius at the end of the cylinder is 9.2 ×10⁻⁴ m, under the condition that a cylindrical solid metal is 3m long and has a mass of 4kg.
The formula for the volume of a cylinder is
[tex]V = \pi r^2h[/tex]
Here,
V = volume,
r = radius
h = height.
The formula for density is density = mass/volume.
It is known to us that the mass of the cylindrical solid metal is 4kg and its density is 5.6g/cm³, we can evaluate its volume as follows:
Density = mass/volume
Volume = mass/density
Volume = 4/(5.6/1000) m³
Volume = 0.000714 m³
Since the metal cylinder is 3m long, we can evaluate its height as follows:
Height = 3m
Now we can evaluate the radius of the cylinder as follows:
[tex]V = \pi r^2h[/tex]
0.000714 m³ = πr²(3m)
r² = (0.000714 m³)/(π*3m)
r² = 0.0000758 m²
r = √(0.0000758) m
r ≈ 0.0092 m
r = 9.2 ×10⁻⁴ m
Therefore, the radius of the end of the cylindrical solid metal is 9.2 ×10⁻⁴ m .
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Question 1 (1 point) Which of the following numbers would be considered a rational number? -03/2 -Both 0.7 and 3/2 -0.7 -√2 -pie -All of the above
The numbers that would be considered rational are -0.3/2, 0.7 and 3/2. The correct option is B.
We are given that;
The four options
Now,
A rational number is a number that can be written as a fraction of two integers. For example, 3/2 and 0.7 are rational numbers because they can be written as 3/2 and 7/10 respectively. However, √2 and pi are not rational numbers because they cannot be written as fractions of integers. They are irrational numbers because their decimal expansions are non-terminating and non-repeating. You can write your answer as:
Therefore, by the given fraction the answer will be -0.3/2, 0.7 and 3/2.
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.15 and the probability that the flight will be delayed is 0.14. The probability that it will rain and the flight will be delayed is 0.12. What is the probability that it is not raining and the flight leaves on time? Round your answer to the nearest thousandth.
The probability that it is not raining and the flight leaves on time is 0.83 rounded to the nearest thousandth.
Let's use the formula for the probability of the intersection of two events to find the probability that it will rain and the flight will be delayed:
P(rain and delay) = 0.12
The probability of either rain or delay or both by using the formula for the probability of the union of two events:
P(rain or delay) = P(rain) + P(delay) - P(rain and delay)
Substituting the given probabilities, we get:
P(rain or delay) = 0.15 + 0.14 - 0.12
P(rain or delay) = 0.17
The probabilities of rain or delay or both add up to 0.17 can find the probability that it is not raining and the flight leaves on time by subtracting this value from 1:
P(not rain and on time) = 1 - P(rain or delay)
P(not rain and on time) = 1 - 0.17
P(not rain and on time) = 0.83
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PLEASE HELP IM LITERALLY GONNA DIE
Rewrite the expression (27 [tex]x^{6}[/tex])[tex]^{\frac{2}{3} }[/tex] in radical form and simplify.
You launch a water balloon. The function h=-0.08t^2+1.6t+2 models the height h (in feet) of the water balloon after t seconds. After how many seconds does the water balloon hit the ground?
Find and simplify the function values.f(x,y) = 4 - x2 - 4y2(a) (0,0) (b) (0,1) (c) (2,3) (d) (1,y) (e) (x, 0) (f)(t,1)
The given f(x,y) is to be evaluated at 6 different points. At (0,0), the f(x,y) is 4, at (0,1)= -1, (2,3)= -37. When evaluated at (1,y), the f(x,y) simplifies to f(1,y) = 3 - 4y^2, at (x,0), the f(x,y) simplifies to f(x,0) = 4 - x^2. Finally, when evaluated at (t,1), the f(x,y) simplifies to f(t,1) = 3 - t^2 - 4.
Explanation:
To evaluate the function f(x,y) = 4 - x^2 - 4y^2 at point (0,0), we simply substitute x=0 and y=0 in the function. Thus, f(0,0) = 4 - 0^2 - 4(0)^2 = 4.
Similarly, to evaluate the function at point (0,1), we substitute x=0 and y=1 in the function. Thus, f(0,1) = 4 - 0^2 - 4(1)^2 = -1.
To evaluate the function at point (2,3), we substitute x=2 and y=3 in the function. Thus, f(2,3) = 4 - (2)^2 - 4(3)^2 = -37.
When we substitute x=1 in the function f(x,y), we get f(1,y) = 4 - 1^2 - 4y^2 = 3 - 4y^2. Hence, the function simplifies to f(1,y) = 3 - 4y^2 when evaluated at point (1,y).
Similarly, when we substitute y=0 in the function f(x,y), we get f(x,0) = 4 - x^2. Hence, the function simplifies to f(x,0) = 4 - x^2 when evaluated at point (x,0).
Finally, when we substitute y=1 in the function f(x,y), we get f(t,1) = 4 - t^2 - 4(1)^2 = 3 - t^2 - 4. Hence, the function simplifies to f(t,1) = 3 - t^2 - 4 when evaluated at point (t,1).
Therefore, the function values at the given points are 4, -1, -37, 3 - 4y^2, 4 - x^2, and 3 - t^2 - 4 for points (0,0), (0,1), (2,3), (1,y), (x,0), and (t,1), respectively.
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sjf incorporated, which has its corporate offices in boise, idaho, conducts business in idaho, oregon, california, and british columbia, canada. which of the following statements is true?
The true statement is that SJF Incorporated conducts business in multiple states and a foreign country. This means that the company is subject to different laws, regulations, and taxes in each jurisdiction, and must comply with the requirements of each. This can create complex legal and financial challenges for the company, as it must navigate the different legal systems and business environments of each region.
In particular, SJF Incorporated must be aware of the laws and regulations governing its operations in each jurisdiction. This includes corporate governance requirements, tax laws, labor laws, and environmental regulations, among others. Failure to comply with these requirements can result in legal liabilities, fines, and reputational damage for the company. Therefore, it is important for SJF Incorporated to maintain a strong compliance program that takes into account the differences between the jurisdictions in which it operates.
In addition, SJF Incorporated must also consider the cultural differences and business practices in each region. This includes understanding the local customs, language, and business etiquette, as well as building relationships with local stakeholders and partners. By adapting to the unique characteristics of each region, SJF Incorporated can build a successful and sustainable business across multiple jurisdictions.
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find the x coordinate of the point of maximum curvature (call it x0 ) on the curve y=3ex and find the maximum curvature, κ(x0).
There is no maximum value of κ on the curve y=3e^x.
To find the point of maximum curvature on the curve y=3e^x, we need to first find the second derivative of y with respect to x, which will give us the curvature of the curve:
y = 3e^x
y' = 3e^x (since the derivative of e^x is e^x)
y'' = 3e^x (since the second derivative of e^x is also e^x)
Now, to find the point of maximum curvature, we need to set y'' equal to zero and solve for x:
y'' = 3e^x = 0
e^x = 0
This equation has no real solutions, which means that there is no point of maximum curvature on the curve y=3e^x.
To find the maximum curvature, we can use the formula:
κ = |y''| / (1 + y'^2)^(3/2)
Since we know that y'' = 3e^x, we can simplify this formula to:
κ = 3e^x / (1 + (3e^x)^2)^(3/2)
To find the maximum value of κ, we can take the derivative of κ with respect to x and set it equal to zero:
dκ/dx = 3e^x (9e^2x - 2) / (1 + 9e^2x)^(5/2) = 0
This equation has no real solutions, which means that there is no maximum value of κ on the curve y=3e^x.
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On his recent free-throw attempts, Lamar made 4 shots and missed 6 shots. Considering this data, how many of his next 20 free-throw attempts would you expect Lamar to miss?Of the last 18 trains to pull into Castroville Station, 12 were full. Considering this data, how many of the next 12 trains would you expect to be full?
For Lamar's free-throw attempts, we can find the proportion of shots he made as 4/10 or 0.4. We can use this proportion to estimate how many of his next 20 free-throw attempts he would expect to make by multiplying the proportion by the number of attempts:
Expected number of missed free-throws = (1 - 0.4) x 20 = 12
Therefore, we would expect Lamar to miss 12 of his next 20 free-throw attempts based on his recent performance.
For the trains at Castroville Station, we can find the proportion of trains that were full as 12/18 or 0.67. We can use this proportion to estimate how many of the next 12 trains we would expect to be full by multiplying the proportion by the number of trains:
Expected number of full trains = 0.67 x 12 = 8
Therefore, we would expect 8 of the next 12 trains to be full based on the recent pattern of trains at Castroville Station.
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PLSSS HELPPPP I NEEED THIS
Answer:
6. Inverse
7. Direct
8.
a. 21
b. '10, '12
c. Inverse
9.
a. 3000
b. 6000
c. Month 9 (January)
Step-by-step explanation:
The figure above shows one of the Seven Wonders of the World, the Great Lighthouse at Alexandria, Egypt, whose construction started in 290 B.C. The platform on which the lighthouse stands is about 100 m wide, and the angle of elevation from the corner of the platform to the top of the lighthouse is 67°. To the nearest meter, how high is the lighthouse?
The required height of the lighthouse is 117.8 meters, as per the given condition
The angle of elevation in this case is given as 67°, and we know that the distance from the observer to the base of the lighthouse is 50 meters. Using these values, we can set up the following equation:
tan(67°) = k/50
This equation relates the height of the lighthouse, represented by "k", to the angle of elevation and the distance between the observer and the base of the lighthouse.
To solve for the height of the lighthouse, we can use algebra to isolate the variable "k". Multiplying both sides of the equation by 50, we get:
k = 50tan(67°)
k = 117.8 meters
Therefore, to the nearest meter, the height of the lighthouse is 117.8 meters.
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Find the volume of a cube whose side measures 9cm. [ V = e³ ]
The volume of a cube is given by the formula V = e³, where e represents the length of the side of the cube. In this case, the length of the side is 9cm. Therefore, the volume of the cube is V = 9³ = 729 cubic centimeters.
To find the volume of the cube, we need to raise the length of one side to the power of 3 since the volume of a cube is given by V = e³. In this case, the side of the cube measures 9cm, so we have e = 9.
Substituting this value into the formula, we get V = 9³ = 729 cubic centimeters. Therefore, the volume of the cube is 729 cubic centimeters. This means that the cube could hold 729 cubic
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OAB is a minor sector of the circle below.
The area of the circle is 54 m².
2
Calculate the area of OAB.
Give your answer in m² and give any
decimal answers to 1 d.p.
B
A
60°
O
in the given diagram, the area of minor sector OAB is 9 m²
Calculating the area of sectorFrom the question, we are to calculate the area of the minor sector of the circle shown in the diagram.
The area of a sector is given by the formula
A = θ/360° × πr²
Where A is the area of the sector
θ is the angle subtended at the center of the circle
and r is the radius of the circle
NOTE: The area of a circle is given by the formula,
Area of a circle = πr²
Thus,
Area of a sector = θ/360° × Area of the circle
From the given information,
Area of the circle = 54 m²
and θ = 60°
Thus,
Area of the sector = 60°/360° × 54
Area of the sector = 1/6 × 54
Area of the sector = 9 m²
Hence, the area of the minor sector is 9 m²
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Kiera is a hairdresser. Before her lunch break, she gave 3 haircuts and coloured the hair of 4 clients in 263 minutes. After lunch, she gave 1 haircut and coloured the hair of 1 client in 71 minutes. How long does it take for Kiera to perform each type of service, assuming the amount of time doesn't vary from client to client?
The time taken by her for haircut is 21 minutes and to color is 50 minutes.
Assume that
Haircut takes = x minutes
To Color takes = y minutes
According to the question
The expression for time be,
3x + 4y = 263 ...(i)
The expression for time be,
x + y = 71 ...(ii)
Apply elimination method to solve it,
After equation(i) - 3x(ii) we get,
y = 50 minutes
Now plug it into (ii) we get,
x = 21 minutes.
Hence,
Haircut takes = 21 minutes
To Color takes = 50 minutes
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helpppppp pls show work
For each of the functions, the roots are;'
1. -1/4 (twice)
2. -2/5 and -4
3. -1/4 and 5
What are the roots of a quadratic function?The roots of the functions can be obtained when we factor the expressions as given.
When we factor the expression;
16x^2 + 8x + 1 we get (4x + 1) (4x + 1)
Thus the zeros of the function are -1/4 (twice)
When we factor the expression;
-5x^2 - 22x - 8 we get (-5x - 2) (x + 4)
Thus the zeros are;
-2/5 and -4
When we factor the expression;
4x^2 - 19x -5 we get (4x + 1) ( x - 5)
The zeros are;
-1/4 and 5
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lena is going to rent a truck for one day. there are two companies she can choose from, and they have the following prices. company a charges and allows unlimited mileage. company b has an initial fee of and charges an additional for every mile driven. for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality for .
Therefore, company A will charge less than company B for any mileage greater than 65 miles.
To help you with your question, I need the specific prices for both companies, as well as any additional information you can provide about the charges.
To solve for the mileages at which company A will charge less than company B, we can set up the following inequality:
A < B
where A is the cost of renting from company A and B is the cost of renting from company B. We can plug in the given information to get:
x ≤ A
x > B = y + 40z
where x is the number of miles driven, y is the initial fee for company B, and z is the additional cost per mile for company B.
Now we can substitute the given values to get:
x ≤ A
x > y + 40z
For company A, the cost is a flat rate with unlimited mileage, so A is just the cost listed for one day of rental. Let's say that cost is $100.
For company B, the initial fee is $50 and the additional cost per mile is $0.25. So:
y = 50
z = 0.25
Now we can plug in these values and solve for x:
x ≤ 100
x > 50 + 40(0.25)
x > 65
Therefore, company A will charge less than company B for any mileage greater than 65 miles.
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Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)f ''(x) = 7/8x7/8
Thus, to find f from the given second-order differential equation, we integrated it twice to get the general solution, f(x) = (7/8)x^3/6 + (7/8)x^2/2 + Cx + D, where C and D are constants.
To find f from the given second-order differential equation, we need to integrate it twice.
The first integration will give us the first antiderivative of f, denoted by C, and the second integration will give us the second antiderivative of f, denoted by D. Then, we can solve for the constants C and D using the initial or boundary conditions if given.
Starting with f ''(x) = 7/8x + 7/8, we can integrate both sides with respect to x to get f '(x) = (7/8)x^2/2 + (7/8)x + C, where C is the constant of integration.
Then, we integrate again to get f(x) = (7/8)x^3/6 + (7/8)x^2/2 + Cx + D, where D is the constant of integration.
Therefore, the general solution of the differential equation is f(x) = (7/8)x^3/6 + (7/8)x^2/2 + Cx + D, where C and D are arbitrary constants.
We can determine the values of C and D by using the initial or boundary conditions given in the problem.
In summary, The values of C and D can be determined using the initial or boundary conditions provided.
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Your teacher states that your model will meet the state regulations. Clearly show that your teacher s correct including calculations and explanations. Pls help me im stuck :)
The length of the hypotenuse is approximately 50.16.
For the slope of the given triangle,
In general slope = Δy(horizontal)/Δx(verticle)
The slope = 4/50 = 1/12.5
This slope is under state regulation since it falls between the standard ratio.
As we can see in the given right angle triangle that is made in the given model,
the base is 50 and the height is 4, so for the hypotenuse,
Let's label the hypotenuse as 'c.'
We have:
[tex]y^2 = 50^2 + 4^2\\\\y^2 = 2500 + 16\\\\y^2 = 2516[/tex]
To find the value of 'y,' we take the square root of both sides:
y ≈ √(2516)
y ≈ 50.16
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write the ratio 4 : 3/6 in terms of 1 : n
Answer:
1:1/8
Step-by-step explanation:
we can see that 4 went down to 1, it must have been divided by 4 therefore we also ivide 3/6 by 4 which gives us the answer
a bag contains 6 black marbles and 4 blue marbles. two marbles are drawn from the bag, without replacement. what is the proba
To find the probability of certain events, we can use the concept of combinations. Let's calculate the probabilities for the given scenario:
1. Probability of drawing two black marbles:
There are 6 black marbles in the bag, so the probability of drawing one black marble on the first draw is 6/10. After removing one black marble, there are 5 black marbles left out of 9 total marbles. So, the probability of drawing a second black marble is 5/9. Since these events occur consecutively, we multiply the probabilities: (6/10) * (5/9) = 1/3.
2. Probability of drawing one black marble and one blue marble:
Similar to the previous case, the probability of drawing a black marble on the first draw is 6/10. After removing one black marble, there are 4 blue marbles left out of 9 total marbles. So, the probability of drawing a blue marble is 4/9. Since there are two possible orders in which the marbles can be drawn (black first, blue second, or blue first, black second), we multiply the probabilities by 2: 2 * (6/10) * (4/9) = 8/15.
Please note that these probabilities assume that each marble has an equal chance of being drawn and that there is no bias in the selection process.
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list all the elements of each set. (Note that sometimes you will have to put three dots at the end because the set is infinite.) E={All possible remainders from dividing a natural number by 6}.
PLEASE HELP I GIVE BRAINLIEST :D
[tex]E=\{0,1,2,3,4,5\}[/tex]
The remainders from dividing a natural number by a natural number [tex]n[/tex] are [tex]0,1,2,3,\ldots,n-1[/tex].
Two angles are supplementary. One angle measures 45 degrees. Find the measure of the other angle.
Answer:
The measure of the other angle is 135 degrees.
Step-by-step explanation:
If two angles are supplementary, then their sum is 180 degrees.
Let x be the measure of the other angle.
We have:
x + 45 = 180
Subtracting 45 from both sides:
x = 180 - 45
x = 135
Therefore, the measure of the other angle is 135 degrees.
Answer: x = 135
Step-by-step explanation:Supplementary angles are two angles that add up to 180 degrees. Given that one angle measures 45 degrees, we can use the fact that supplementary angles add up to 180 degrees to find the measure of the other angle.
Let x be the measure of the other angle. Then we have:
x + 45 = 180
Subtracting 45 from both sides, we get :
x=135
given the image above,describe the relationship of the angles A and C compared to angle D
leo invests 3500 into an account with a 5.2% interest rate that is compounded quarterly. how much will he have in the account at the end of eight years? round to the nearest penny. fv pv i n t
Answer:
$Amount in account in 8 years = $5291.40
Step-by-step explanation:
The compound interest formula is
[tex]A(t)=P(1+r/n)^n^t[/tex], where
A(t) is the amount, P is the principal (amount invested),r is the interest rate (converted to a decimal),n is the number of compounding periods,and t is the time in yearsWe know from the problem that:
P = $3500r = 0.052n = 4 (compound interest is always out of a year and quarterly implies 4)t = 8Now, we can simply plug everything into the problem and round to the nearest penny (hundredths place)
[tex]A(8)=3500(1+0.052/4)^(^4^*^8^)\\A(8)=3500(1.013)^3^2\\A(8)=5291.39638\\A(8)=5291.40[/tex]
A soccer player kicked a ball across the field. The graph shows the height in feet of the ball above the ground as a quadratic function of x, the horizontal distance in feet from the soccer player. What is the domain and range of the function for this situation?
Write the correct answer in each box. Answers may be used more than once. Not all answers will be used.
The domain and the range of the graph given will be 0 ≤ x ≤ 95 and 0 ≤ y ≤ 20.
Given is a graph, we need to find the domain and the range of the graph given,
So,
The domain is all the input values that mean all the values of x,
Here we see the values of x are lies between 0 to 95, so the domain is 0 ≤ x ≤ 95
And the range is all the output values that mean all the values of y,
Here we see the values of y are lies between 0 to 20, so the range is 0 ≤ x ≤ 20.
Hence the domain and the range of the graph given will be 0 ≤ x ≤ 95 and 0 ≤ y ≤ 20.
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