To solve the problem, we first need to graph the equation y = 3 / (√36-9x^2) and find the points where it intersects the x-axis and y-axis.
To find the x-intercept, we set y = 0 and solve for x:
0 = 3 / (√36-9x^2)
0 = 3
This has no solution, which means that the graph does not intersect the x-axis.
To find the y-intercept, we set x = 0 and solve for y:
y = 3 / (√36-9(0)^2)
y = 3 / 6
y = 1/2
So the graph intersects the y-axis at (0, 1/2).
Next, we need to find the point where the graph intersects the vertical line x = 3. To do this, we substitute x = 3 into the equation y = 3 / (√36-9x^2):
y = 3 / (√36-9(3)^2)
y = 3 / (√-243)
This is undefined, which means that the graph does not intersect the line x = 3.
Now we can draw a rough sketch of the graph and the region bounded by the x-axis, the line x = 0, and the curve y = 3 / (√36-9x^2):
|
_______|
/ |
/ |
/ |
/_________|
| |
The area we want to find is the shaded region, which is bounded by the x-axis, the line x = 0, and the curve y = 3 / (√36-9x^2). To find the area, we need to integrate the equation y = 3 / (√36-9x^2) with respect to x from x = 0 to x = 3:
A = ∫(0 to 3) 3 / (√36-9x^2) dx
We can simplify this integral by using the substitution u = 3x, du/dx = 3, dx = du/3:
A = ∫(0 to 9) 1 / (u^2 - 36) du/3
Next, we use partial fractions to break up the integrand into simpler terms:
1 / (u^2 - 36) = 1 / (6(u - 3)) - 1 / (6(u + 3))
So we have:
A = ∫(0 to 9) (1 / (6(u - 3))) - (1 / (6(u + 3))) du/3
A = (1/6) [ln|u - 3| - ln|u + 3|] from 0 to 9
A = (1/6) [ln(6) - ln(12) - ln(6) + ln(6)]
A = (1/6) [ln(1/2)]
A = (-1/6) ln(2)
Therefore, the exact area bounded by y = 3 / (√36-9x^2), x = 0, y = 0, and x = 3 is (-1/6) ln(2).
To find the area bounded by y = 3 / (√36-9x^2), x = 0, y = 0, and x = 3, we can set up an integral to compute the definite integral of the function over the given interval [0, 3]. The integral will represent the area under the curve:
Area = ∫[0, 3] (3 / (√(36-9x^2))) dx
To solve the integral, perform a substitution:
Let u = 36 - 9x^2
Then, du = -18x dx
Now, we can rewrite the integral:
Area = ∫[-√36, 0] (-1/6) (3/u) du
Solve the integral:
Area = -1/2 [ln|u|] evaluated from -√36 to 0
Area = -1/2 [ln|0| - ln|-√36|]
Area = -1/2 [ln|-√36|]
Since the natural logarithm of a negative number is undefined, there's an error in the original problem. Check the problem's constraints and the given function to ensure accuracy before proceeding.
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Find the mean absolute deviation (MAD) of the data in the pictograph below. Baskets
The key says one basketball picture equals two baskets. The key says one basketball picture equals two baskets. A picture graph labeled Baskets each student made. The vertical axis is labeled Baskets made. The horizontal axis is labeled Student. The names from left to right on the horizontal axis are Reynaldo, Marcelle, Allie, and Fernando. There are two basketball pictures above Reynaldo. There are four basketball pictures above Marcelle. There are three basketball pictures above Allie. There are five basketball pictures above Fernando
The mean absolute deviation (MAD) of the data in the pictograph is equals to the one basketball.
We have a data in the pictograph. In mathematics, a pictograph is a pictorial representation of data using images, icons. It is also known as a pictogram. We have a pictograph, in which the vertical axis is labeled Baskets made and the horizontal axis is labeled Student. Here, one basketball picture equals two baskets. Mean absolute deviation (MAD) is a statistical measure of the average absolute distance between each data value and the mean of a data set. It is a parameter or statistic that measures the spread, or variation, in data.
Mean is defined as the sum of data values divided by number of values.
Sum of data values = 4 + 4×2 + 3×2 + 5×2
= 28
So, mean = 28/4 = 7
Now, | 4 - 7| + |8 - 7| + |6 -7 | + | 10 - 7|
= 3 + 1 + 1 + 3 = 8
So,, mean absolute deviation (MAD) of the data = 8/7 = 1.1 ~ 1. Hence, required value is 1.
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Complete question :
Find the mean absolute deviation (MAD) of the data in the pictograph below. Baskets
The key says one basketball picture equals two baskets. The key says one basketball picture equals two baskets. A picture graph labeled Baskets each student made. The vertical axis is labeled Baskets made. The horizontal axis is labeled Student. The names from left to right on the horizontal axis are Reynaldo, Marcelle, Allie, and Fernando. There are two basketball pictures above Reynaldo. There are four basketball pictures above Marcelle. There are three basketball pictures above Allie. There are five basketball pictures above Fernando
Learn with an example
or
Watc
4) Graph this line using intercepts:
3x + y = -6
Answer:
Step-by-step explanation:
3x+y = -6
y=-3x-6
The Y-intercept is -6, therefore there is one point (0,-6)
Now go 3 down and one right, so there is your second point (1,-9)
a population of maned wolves has 246 individuals and over a year 83 individuals were born and 42 died. what is the per capita birth rate for this population? enter the value below rounding your answer to the hundredths place. for example, in the number 12.345, 4 is located in the hudredths place.
The per capita birth rate of the given population of manned wolves 246 with number of birth as 83 is equals to 0.34 births per individual per year.
Number of births = 83
Initial population = 246
Time period = 1 year
Number of deaths = 42
The per capita birth rate is calculated as the number of births per individual in the population.
Typically expressed as a rate per unit time.
Per capita birth rate as follows,
Per capita birth rate
= (Number of births / Initial population) × (Time period / 1 year)
Substituting these values into the formula, we get,
Per capita birth rate
= (83 / 246) × (1 / 1)
= 0.3374
Rounding this to the hundredths place, we get,
Per capita birth rate = 0.34
Therefore, the per capita birth rate for this population of maned wolves is 0.34 births per individual per year.
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if you increase your reading speed so that each page takes you 30 seconds less than it did before, and you begin reading 20 minutes per day, how many 200 page books can you now read in a year
We can read 91 books in a year if you increase your reading speed so that each page takes you 30 seconds less than it did before.
How is the number of books calculated?Now If each page now takes 30 seconds less to read than before,
then you will save 30*200 = 6000 seconds (or 100 minutes) on each book.
So, the time it will take you to read a 200-page book will be
20 minutes - 100 minutes = -80 minutes,
which means you will finish a 200-page book in 80 minutes (or 1 hour and 20 minutes).
In a year, there are 365 days. If you read for 20 minutes per day, then you will read for a total of
365 * 20 = 7300 minutes (or 121.67 hours) in a year.
Since you can finish a 200-page book in 80 minutes, you can read 7300/80 = 91.25 books in a year.
However, since you cannot read a fraction of a book, the maximum number of 200-page books you can read in a year is 91 books.
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Complete question is :
If you increase your reading speed so that each page takes you 30 seconds less than it did before,
and you begin reading 20 minutes per day,
How many 200 page books can you now read in a year?
Refer to the diagram. 115° (2x + 5)° Write an equation that can be used to find the value of x. What is the value of x
If measure of two "vertically-opposite-angles" are 115° and (2x + 5)°, then the equation to find value of "x" is 115° = (2x + 5)°,and value of "x" is 55.
The Vertically opposite angles are defined as a pair of non-adjacent angles formed by the intersection of two lines. and if the two angles are vertically opposite then their measures are equal, so, to find the value of "x", we equate the measure of both the angles,
The measure of the two angles are 115° and (2x + 5)°,
So, on equating,
We get,
⇒ 115° = (2x + 5)°,
⇒ 110° = 2x,
⇒ x = 55,
Therefore, the value of x is 55.
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The given question is incomplete, the complete question is
The measure of the two vertically opposite angles are 115° and (2x + 5)°, Write an equation that can be used to find the value of x. What is the value of x?
PLS HELP! URGENT!!!! A circular flower bed is 20 m in diameter and has a circular sidewalk around it that is 3 m wide. Find the area of the sidewalk in square meters. Use 3. 14 for pi
The area of the sidewalk in square meters is 69π.
To find the area of the sidewalk, we need to subtract the area of the flower bed from the area of the outer circle formed by the sidewalk.
First, we need to find the area of the flower bed. We know that the diameter of the flower bed is 20 m, so the radius is half of that, which is 10 m. We can use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.
Area of flower bed = π(10m)^2 = 100π square meters
Next, we need to find the area of the outer circle formed by the sidewalk. Since the sidewalk is 3 m wide, the radius of the outer circle will be 10 + 3 = 13 m (10 m for the flower bed radius plus 3 m for the width of the sidewalk).
Area of outer circle = π(13m)^2 = 169π square meters
Finally, we can find the area of the sidewalk by subtracting the area of the flower bed from the area of the outer circle:
Area of sidewalk = Area of outer circle - Area of flower bed
Area of sidewalk = (169π) - (100π)
Area of sidewalk = 69π square meters
Therefore, the area of the sidewalk in square meters is 69π, or approximately 216.6 square meters (if we use 3.14 for π).
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Point EE is located at (-6,1)(−6,1) on the coordinate plane. Point EE is reflected over the yy-axis to create point E'E
′
. Point E'E
′
is then reflected over the xx-axis to create point E''E
′′
. What ordered pair describes the location of E''?E
′′
?
E= ?, ?
The ordered pair that describes the location of E'' is (6, -1).
The initial location of Point EE is (-6, 1). To reflect Point EE over the yy-axis, we will change the sign of the x-coordinate while keeping the y-coordinate the same.
Step 1: Reflect Point EE over the yy-axis to create Point E'.
E' = (6, 1)
Next, to reflect Point E' over the xx-axis, you'll change the sign of the y-coordinate while keeping the x-coordinate the same.
Step 2: Reflect Point E' over the xx-axis to create Point E''.
E'' = (6, -1)
Therefore, the ordered pair that describes the location of E'' is (6, -1).
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its on the screenshot
The missing values can be found by setting up proportions for each of the ratios whose values are given. The completed table is shown below:
x 17 1/3 11
y 5.67 3.67 1.21
Ratio y/x 3.67 1/3 0.11
How do we calculate?In order to find the missing values of y, we can use the given ratios to set up proportions:
For the first ratio:
y/x = 5.67/17
y = (5.67/17) * x
y = (5.67/17) * 11
y = 3.67
So the first missing value of y is 3.67.
For the second ratio:
y/x = 1/3
y = (1/3) * x
y = (1/3) * 1/3
y = 0.11
Therefore, the second missing value of y is found as 0.11.
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Christian is rewriting an expression of the form y = ax2 bx c in the form y = a(x – h)2 k. which of the following must be true? h and k cannot both equal zero k and c have the same value the value of a remains the same h is equal to one half –b
The value of 'a' remains the same, 'h' is equal to -b/(2a), and 'h' and 'k' cannot both equal zero.
When rewriting a quadratic expression of the form y = ax^2 + bx + c into the vertex form y = a(x - h)^2 + k, the following must be true:
1. The value of 'a' remains the same in both expressions, as it represents the parabola's vertical stretch or compression.
2. 'h' is equal to -b/(2a), which is derived from completing the square to transform the standard form into the vertex form.
3. 'k' and 'c' do not necessarily have the same value. 'k' is the value of the quadratic function when 'x' equals 'h', which can be found by substituting 'h' back into the original equation and solving for 'y'.
4. 'h' and 'k' cannot both equal zero, unless the vertex of the parabola is at the origin (0,0).
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The guidance department has reported that of the senior class 2. 3% are members of key club 8. 6% are enrolled in AP physics and 1. 9% are in both
The percentage is 9.0% of the senior class are either members of the Key Club, enrolled in AP Physics, or both.
We need to find the percentage of seniors who are either members of the Key Club, enrolled in AP Physics, or both. We can use the formula:
Total percentage = Key Club percentage + AP Physics percentage - Both percentage
Step 1: Identify the given percentages
Key Club percentage = 2.3%
AP Physics percentage = 8.6%
Both percentage = 1.9%
Step 2: Apply the formula
Total percentage = 2.3% + 8.6% - 1.9%
Step 3: Calculate the result
Total percentage = 9.0%
So, 9.0% of the senior class are either members of the Key Club, enrolled in AP Physics, or both.
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The equation y=mx+b
is used to express the equation of a line. Which solution is a correct way to solve this equation for m
in terms of y
?
The correct way to solve this equation for m in terms of y is m = b - y/x
How to determine the valueIt is important to note that subject of formula is the variable that is made to stand alone in an equation.
It is described as the variable that is being worked out in an equation.
The subject of formula in an equation is worked to stand alone on on end of the equality sign.
Example of equations
x = y - 2
The variable 'x' is the subject of formula
From the information given, we have that;
y= mx+b
collect the terms
mx = b - y
Divide by the coefficient
m = b - y/x
The equation for m is m = b - y/x
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The complete question:
The equation y=mx+b is used to express the equation of a line. Which solution is a correct way to solve this equation for m in terms of y?
Two terms of a geometric sequence are a5=2500 and a8=312,500 Write an explicit rule for the nth term
Answer:
Step-by-step explanation:
You are ChatGPT, a large language model trained by OpenAI.
Knowledge cutoff: 2021-09
Current date: 2023-04-275-1)
2500 = a1 * r^4
a8 = a1 * r^(8-1)
312500 = a1 * r^7
We can divide the second equation by the first equation to eliminate a1:
312500 / 2500 = (a1 * r^7) / (a1 * r^4)
125 = r^3
Taking the cube root of both sides gives us:
r = 5
Now that we know the common ratio, we can use either of the two original equations to find the first term, a1. Using the first equation:
250
Copy and complete the equation of line B below. y = — 84 NWPца - 0 7- 6+ 5- 4- 3- 2- 1/ -11 -2- -8-7-6-5-4-3-2-10 1 2 3 4 5 6 7 8 ܢܐ ܚ ܩ ܘ ܘ ܢ -3 -4- -5 -6 x +_ -7 -8- Line B 19
The equation of the line passing through the given points is y = 3x-1.
Given that is a line passing through two points (0, 2) and (-1, -1) we need to find the equation of the line using them,
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (0, 2) and (-1, -1),
Therefore, the required equation is =
y+1 = -1-2/-1 (x-0)
y+1 = 3x
y = 3x-1
Hence, the equation of the line passing through the given points is y = 3x-1.
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Question
Write the product using exponents.
(−13)⋅(−13)⋅(−13)
Answer:
(-13)^3
Step-by-step explanation:
Exponents can be used for repeated multiplication.
In this case, the number "negative 13" is repeated several times, all connected with multiplication.
There are a total of three "negative 13"s being multiplied together ("negative 13" appears three times on the page).
To rewrite using exponents, we would write one of the following:
(-13)^3
[tex](-13)^3[/tex]
in KLMO, OM-25. What are the coordinates of M and K?
L(2b+4c4d)
ㅁ
M
The value of coordinate M and K are,
M = (25, 0)
K = (2b + 4c - 25, 2d)
Given that;
In KLMO,
OM = 25
L = (2b + 4c , 4d)
Hence, We can formulate;
The value of coordinate of M is,
M = (25, 0)
Since, M lies on x - axis.
Let the coordinate of K is,
K = (x, y)
Hence, Midpoint of LO is same as midpoint of KM.
Midpoint of LO is,
(0 + 2b + 4c / 2, 4d/2)
(b + 2c, 2d)
Midpoint of KM is
(x + 25/2, y + 0/2)
(x + 25/2 , y/2)
By comparing,
x + 25/2 = b + 2c
x + 25 = 2b + 4c
x = 2b + 4c - 25
y/2 = 2d
y = 2d
Thus, the coordinate of K is,
K = (2b + 4c - 25, 2d)
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Kristin made a scatter plot to represent the relationship between the temperature and the number of bottles of water sold at her concession stand at a soccer tournament. Which is a description of the location of the point Kristin will add to represent the 13 bottles of water that were sold when the temperature was 39 degrees Fahrenheit? Select one:
O Top left of the scatter plot
OBottom right of the scatter plot
O Top right of the scatter plot
OBottom left of the scatter plotâ
The location of the point Kristin will add to represent the 13 bottles of water sold at 39 degrees Fahrenheit is the bottom left of the scatter plot.
A scatter plot represents the relationship between two variables. In this case, the temperature (independent variable) is plotted along the x-axis, while the number of bottles of water sold (dependent variable) is plotted along the y-axis. As the temperature increases, it is expected that more bottles of water would be sold.
The bottom left area of the scatter plot is where lower values of both temperature and the number of bottles sold would be found. Since 39 degrees Fahrenheit is relatively low and 13 bottles of water is a lower quantity, the point representing this data will be in the bottom left quadrant of the scatter plot.
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Complete question:
Kristin made a scatter plot to represent the relationship between the temperature and the number of bottles of water sold at her concession stand at a soccer tournament. Which is a description of the location of the point Kristin will add to represent the 13 bottles of water that were sold when the temperature was 39 degrees Fahrenheit? Select one:
O Top left of the scatter plot
O Bottom right of the scatter plot
O Top right of the scatter plot
O Bottom left of the scatter plotâ
At her job, Avery earns $120 per week plus a one-time $300 bonus. Janelle teaches art lessons and earns $24 per week plus a $60 art supply fee for each student she teaches. a. System of equations:
The system of equations to describe the earnings by Avery and Janelle would be:
Avery's earnings: y = 120x + 300
Janelle's earnings: y = 24x + 60s
How to find the system of equations ?The problem provides two scenarios with different methods for earning money. Avery earns a fixed amount of $120 each week, in addition to a one-time bonus of $300. To represent this situation as an equation, we can use the formula:
y = 120x + 300
where y is Avery's total earnings, x is the number of weeks she works, and 300 is the one-time bonus she receives.
For Janelle, her earnings consist of a fixed weekly rate of $24 plus a variable amount based on the number of students she teaches.
We can represent Janelle's earnings as an equation using the formula:
y = 24x + 60s
where y is Janelle's total earnings, x is the number of weeks she works, and s is the number of students she teaches.
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Penny needs 12 ounces of a snack mix that is made up of chocolate and almonds. Chocolate cost $3. 50 per ounce and almonds cost $4. 50 per ounce. Penny has $50 to spend and plans to sell it all. X the amount of chocolate and Y is the amount of almonds. Determine which equations you are used to form a system of equations for the scenario
The two equations which can be used to form a system of equations for the scenario are X + Y = 12 and 3.50X + 4.50Y = 50
To solve this problem, we need to form a system of equations. Let X be the amount of chocolate and Y be the amount of almonds. The first equation we can form is based on the total amount of snack mix that Penny needs, which is 12 ounces:
X + Y = 12
The second equation we can form is based on the cost of the ingredients. We know that chocolate costs $3.50 per ounce and almonds cost $4.50 per ounce. If X is the amount of chocolate and Y is the amount of almonds, then the total cost of the snack mix will be:
3.50X + 4.50Y = 50
This equation represents the fact that Penny has $50 to spend on the snack mix. Now we have a system of two equations that we can use to solve for X and Y. We can use substitution or elimination to solve the system and find the values of X and Y that satisfy both equations.
Once we have those values, we can check that they add up to 12 and that the total cost is $50. This system of equations allows us to calculate the amount of chocolate and almonds Penny needs to make the snack mix within her budget.
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HELP ME PLEASE I WILL GIVR BRAINLIEST TO THE FASTED CORRECT ANSWER PLEASE HELP ME FAST AND TY
answer options:
x= 3, -4
x= 5, -1
x= 0, 5
x= 1, 5
From the given graph, the roots of the quadratic equation, 0 = x² - 6x + 5, is 1 and 5. The correct option is the last option x= 1, 5
Determining the roots of a quadratic function from the graphFrom the question, we are to determine the roots of the quadratic equation from the provided graph.
From the given information,
The given quadratic equation is
0 = x² - 6x + 5
The roots of a quadratic function are the values of x where the function equals zero. On a graph, this corresponds to the points where the graph intersects the x-axis.
From the graph, we will read the x-coordinates of the points where the graph intersects the x-axis.
From the given graph, the x-coordinates of the points where the graph intersects the x-axis are 1 and 5
Hence, the roots of the quadratic equation is 1 and 5
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Helppppppppppppppppp
find the next two terms in sequence?
Answer:
83 and 99 The sequence is going in +16 so the answer is 83 and 99 sorry if I am a bad explainer I’m new to this app :(
Step-by-step explanation:
Find the work done by the force field F(x,y) = x^2i – ryj in moving a particle along the F semicircle y = Sqrt(4 – x^2) from P(2,0) to Q(-2,0) and then back along the line segment from Q to P.
The work done by the force field F along the semicircle and the line segment is 32/3.
The work done by a force field F along a curve C from point A to point B is given by the line integral:
W = ∫ F dot dr
where dot represents the dot product and dr is the differential displacement vector along the curve C.
Let's divide the curve C into two parts: the semicircle from P to Q, denoted by C1, and the line segment from Q to P, denoted by C2.
For C1, the curve can be parameterized as x = 2cos(t) and y = 2sin(t) for t in [0, pi]. The differential displacement vector is then given by:
dr = (-2sin(t) dt)i + (2cos(t) dt)j
The force field F(x,y) = x^2i - ryj, so we have:
F(x,y) = (2cos^2(t))i - (2rsin(t))j
The dot product F dot dr is then:
F dot dr = (2cos^2(t))(-2sin(t) dt) + (2rsin(t))(2cos(t) dt)
= -4cos^2(t)sin(t) dt + 4rcos(t)sin(t) dt
= 4sin(t)cos(t)(r - cos(t)) dt
Therefore, the work done along C1 is:
W1 = ∫ C1 F dot dr
= ∫[0, pi] 4sin(t)cos(t)(r - cos(t)) dt
This integral can be evaluated using the substitution u = cos(t), du = -sin(t) dt:
W1 = -∫[1, -1] 4u(r - u) du
= 4r∫[1, -1] u du - 4∫[1, -1] u^2 du
= 0
Hence, the work done along C1 is 0.
For C2, the curve is simply the line segment from Q(-2,0) to P(2,0), which is parallel to the x-axis. Therefore, the differential displacement vector is given by:
dr = dx i
where i is the unit vector in the x-direction. The force field is the same as before, F(x,y) = x^2i - ryj. Along C2, y = 0, so the force field reduces to:
F(x,y) = x^2i
The dot product F dot dr is then:
F dot dr = x^2 dx
Therefore, the work done along C2 is:
W2 = ∫ C2 F dot dr
= ∫[-2, 2] x^2 dx
= 32/3
Hence, the work done along C2 is 32/3.
The total work done along the curve C is the sum of the work done along C1 and C2:
W = W1 + W2 = 0 + 32/3 = 32/3
Therefore, the work done by the force field F along the semicircle and the line segment is 32/3.
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A family spends $550 every month on food. if the family's income is $2,200 each month, what percent of the income is spent on food?
The percentage of the family's income that is spent on food is 25%.
Firstly, noting down the family's monthly spend on food ($550) and their total monthly income ($2,200).
Next, dividing the amount spent on food by the total income to find the ratio of the spend to income: $550 / $2,200.
Now, calculating this division: 550 ÷ 2,200 = 0.25.
Finally, finding the percentage, multiply the ratio (0.25) by 100: 0.25 x 100 = 25%.
So, the family spends 25% of their monthly income on food.
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I need help with this real quick please
First, using the Pythagorean theorem, we get the hypotenuse = 12.
sin = opposite/hypotenuse = [tex]\frac{6\sqrt{3} }{12} = \frac{\sqrt{3} }{2}[/tex]
cos = adjacent/hypotenuse = [tex]\frac{6}{12} =\frac{1}{2}[/tex]
tan = opposite/adjacent = [tex]\frac{6\sqrt{3} }{6} = \sqrt{3}[/tex]
csc = hypotenuse/opposite = [tex]\frac{12}{6\sqrt{3} } =\frac{2}{\sqrt{3} }[/tex]
sec = hypotenuse/adjacent = [tex]\frac{12}{6} =2[/tex]
cot = adjacent/opposite = [tex]\frac{6}{6\sqrt{3} } = \frac{1}{\sqrt{3} }[/tex]
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer:
Here we try the method of trial and error to find out if the equations have a common answer as zero
Step-by-step explanation:
Now,
(a) x²-4=0
(b) x²=-4
(c) 3x²+12=0
(d) 4x²=16
(e) 2(x-2)2=0
Here if we check the first equation i.e x²-4=0
Equating - 2²-4=4-4
=0
2²-4= 4-4
=0
So option (a) is true
Now x²=-4
Substituting, - 2²=4 & 2²=4
So here we get 4≠-4
Therefore, (b) is not true
Now 3x²+12=0
3(-2)²+12= 3(4)+12
=12+12= 24
3(2)²+12= 12+12
= 24
4x²=16
Substituting, 4(-2)²= 4(4)= 16
4(2)²= 4(4)= 16
So option (d) is also true
Now, 2(x-2)2=0
Substituting, 2(-2-2)2= 2(-4)2
4(-4)= - 16
2(2-2)2= 2(0)2
=4(0)=0
Here when we put x=-2, we get - 16
when we put x=2, we get 0
So the following equation is true only for x=2 and not x=-2
I hope this helps ;)
What would cause a discontinuity on a rational function (a polynomial divided by another polynomial)?
The function has a horizontal asymptote at y = 3. Other types of discontinuities can also occur in rational functions
What are polynomials ?A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.
A rational function can have a discontinuity at any point where the denominator of the function becomes zero since division by zero is undefined. These points are called "vertical asymptotes."
For example, consider the rational function f(x) = (x² - 1) / (x - 1). The denominator becomes zero when x = 1, which causes a vertical asymptote at x = 1. At x = 1, the function approaches positive infinity from the left-hand side and negative infinity from the right-hand side. This creates a "hole" or a "removable discontinuity" in the graph of the function.
Another type of discontinuity that can occur in a rational function is a "horizontal asymptote." This occurs when the degree of the numerator is less than the degree of the denominator. In this case, the function approaches a horizontal line (the horizontal asymptote) as x approaches infinity or negative infinity.
For example, consider the rational function f(x) = (3x² - 2x + 1) / (x² + 1). As x approaches infinity or negative infinity, the function approaches the horizontal line y = 3.
Therefore, the function has a horizontal asymptote at y = 3.
Other types of discontinuities can also occur in rational functions, such as "slant asymptotes" or "oscillating behavior," but these are less common and typically require more advanced techniques to identify.
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Suppose $40,000 is deposited into an account paying 2. 5% interest, compounded continuously.
How much money is in the account after eight years if no withdrawals or additional deposits are made?
The formula for calculating the amount of money in an account with continuous compounding is:
[tex]A = Pe^{(rt)}[/tex]
where A is the amount of money in the account, P is the principal (initial deposit), e is the mathematical constant e (approximately equal to 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).
Plugging in the given values, we get:
A =[tex]40000 * e^{(0.025 * 8)[/tex]
Using a calculator, we find that [tex]e^{(0.025 * 8)[/tex] is approximately 1.2214, so:
A = 40000 * 1.2214 = $48,856.12
Therefore, the amount of money in the account after eight years with continuous compounding is $48,856.12.
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he figure below is a net for a rectangular prism. Side a = 62 centimeters, side b = 21 centimeters, and side c = 16 centimeters. What is the surface area of this figure?
The surface area of the rectangular prism is 4960 cm².
The rectangular prism can be divided into six rectangular faces, with opposite faces having the same area. To find the surface area, we need to calculate the area of each face and add them up.
The net shows three rectangles with dimensions of 62 cm x 21 cm, 62 cm x 16 cm, and 21 cm x 16 cm.
Therefore, the surface area of the rectangular prism is:
Area of the first rectangle = 62 cm x 21 cm = 1302 cm²
Area of the second rectangle = 62 cm x 16 cm = 992 cm²
Area of the third rectangle = 21 cm x 16 cm = 336 cm²
Total surface area = 2(Area of first rectangle) + 2(Area of second rectangle) + 2(Area of third rectangle)
= 2(1302) + 2(992) + 2(336)
= 2604 + 1984 + 672
= 4960 cm²
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Why do you think that credit cards tend to be the entry point for establishing credit for so many consumers?
I believe credit cards tend to be the entry point for establishing credit for so many consumers because they provide an easy and accessible way for individuals to begin building their credit history. Credit card companies report to credit bureaus on a regular basis, which helps establish a credit score and credit history.
Additionally, credit cards offer a convenient way for individuals to make purchases and build their credit at the same time. However, it is important for individuals to use their credit cards responsibly and make timely payments in order to maintain good credit standing.
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