Answer:
The average absolute deviation (or mean absolute deviation (MAD)) about any certain point (or 'avg. absolute deviation' only) of a data set is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values). It is a summary statistic of statistical dispersion or variability. In the general form, the central point can be the mean, median, mode, or the result of any other measure of central tendency or any random data point related to the given data set. The absolute values of the difference, between the data points and their central tendency, are totaled and divided by the number of data points.
Measures of dispersion
Edit
Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. Unfortunately, the statistical literature has not yet adopted a standard notation, as both the mean absolute deviation around the mean and the median absolute deviation around the median have been denoted by their initials "MAD" in the literature, which may lead to confusion, since in general, they may have values considerably different from each other.
Mean absolute deviation around a central point
Edit
For arbitrary differences (not around a central point), see Mean absolute difference.
The mean absolute deviation of a set {x1, x2, ..., xn} is
{\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}|x_{i}-m(X)|.} \frac{1}{n}\sum_{i=1}^n |x_i-m(X)|.
The choice of measure of central tendency, {\displaystyle m(X)} m(X), has a marked effect on the value of the mean deviation. For example, for the data set {2, 2, 3, 4, 14}:
Mean Absolute Deviation (MAD) is a measure of the average distance between each data point and the mean of the dataset. It is calculated by finding the absolute value of the difference between each data point and the mean, and then averaging those differences. MAD is a robust statistic, less sensitive to outliers compared to standard deviation.
Mean Absolute Deviation (MAD) is a statistical measure used to quantify the average deviation of data points from the mean or average of the dataset. To calculate MAD, you follow these steps:
Compute the mean (average) of the dataset by adding up all the data points and dividing by the number of points.Find the absolute differences between each data point and the mean. 'Absolute' means you consider only the magnitude of the differences, not whether they are above or below the mean.Calculate the average of these absolute differences which gives you the MAD.The mean is the sum of all data divided by the number of data points, while the median is the middle value of an ordered dataset. MAD is more robust than standard deviation as it is not affected as much by extreme values. For example, if we have a dataset of exam scores, the standard deviation tells us how scores are spread out from the mean, which could be influenced by extremely high or low scores. On the other hand, MAD gives us a measure of spread that is more resilient to outliers in the data.
Relative Average Deviation (RAD) is similar to MAD, but it expresses the deviation as a percentage of the mean and hence provides a relative measure of spread.
Find the vertices and foci of the hyperbola with equation x^2/4 - y^2/60 = 1
Answer:
Vertices of hyperbola: (2,0) and (-2,0)
Foci of hyperbola: (8,0) and (-8,0)
Step-by-step explanation:
The given equation is:
[tex]\frac{x^2}{4}-\frac{y^2}{60}=1[/tex]
The standard form of equation of hyperbola is:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]
Center of hyperbola is (h,k)
Comparing given equation with standard equation
h=0, k=0
so, Center of hyperbola is (0,0)
Vertices of Hyperbola
Vertices of hyperbola can be found as:
The first vertex can be found by adding h to a
a^2 - 4 => a=2, h=0 and k=0
So, first vertex is (h+a,k) = (2,0)
The second vertex can be found by subtracting a from h
so, second vertex is ( h-a,k) = (-2,0)
Foci of Hyperbola
Foci of hyperbola can be found as
The first focus of hyperbola can be found by adding c to h
Finding c (distance from center to focus):
[tex]c=\sqrt{a^2+b^2} \\c=\sqrt{(2)^2+(2\sqrt{15})^2}\\c=8[/tex]
So, c=8 , h=0 and k=0
The first focus is (h+c,k) = (8,0)
The second focus is (h-c,k) = (-8,0)
Select the correct answer from each drop-down menu.
A rope is cut into three pieces. The lengths are given as 2ab(a − b), 3a2(a + 2b), and b2(2a − b).
The expression representing the total length of the rope is .
If a = 2 inches and b = 3 inches, the total length of the rope is inches.
math
Answer:
1) [tex]3 a^3 + 8 a^2 b - b^3[/tex]
2) 93 inches
Step-by-step explanation:
1) We know that the lenghts are given by these expressions:
[tex]2ab(a - b)\\\\3a^2(a + 2b)\\\\b^2(2a - b)[/tex]
Then, we need to add them in order to find the expression that represents the total length of the rope:
- Apply Distributive property.
- Add the like terms.
Then:
[tex]=2ba^2-2ab^2+3a^3+6ba^2+2ab^2-b^3\\\\=3 a^3 + 8 a^2 b - b^3[/tex]
2) Knowing that:
[tex]a=2in\\\\b=3in[/tex]
We must substitute these values into [tex]3 a^3 + 8 a^2 b - b^3[/tex] in order to caculate the total lenght of the rope. This is:
[tex]3 (2in)^3 + 8 (2in)^2 (3in) - (3in)^3=93in[/tex]
Which of the following reveals the minimum value for the equation 2x2 − 4x − 2 = 0?
2(x − 1)2 = 4
2(x − 1)2 = −4
2(x − 2)2 = 4
2(x − 2)2 = −4
Answer:
[tex]2(x-1)^{2}=4[/tex]
Step-by-step explanation:
we have
[tex]2x^{2} -4x-2=0[/tex]
This is the equation of a vertical parabola open upward
The vertex is a minimum
Convert the equation into vertex form
Group terms that contain the same variable and move the constant to the other side
[tex]2x^{2} -4x=2[/tex]
Factor the leading coefficient
[tex]2(x^{2} -2x)=2[/tex]
[tex]2(x^{2} -2x+1)=2+2[/tex]
[tex]2(x^{2} -2x+1)=4[/tex]
Rewrite as perfect squares
[tex]2(x-1)^{2}=4[/tex] -----> this is the answer
The vertex is the point (1,-4)
if the translation T maps point A(-3,1) onto point A'(5,5), what is he translation T?
Answer:
< 8, 4 >
Step-by-step explanation:
Consider the coordinates
x- coordinate A - 3 → A' 5 → that is + 8
y- coordinate A 1 → A' 5 → that is + 4
Hence T = < 8, 4 >
or (x, y) → (x + 8, y + 4)
The translation T is given by:
T(x,y)=(x+8,y+4)
i.e. it shifts the point 8 units to the right and 4 units up.
Step-by-step explanation:The translation is the transformation that changes the location of points of the figure but there is no change in the shape as well as size of the original figure.
It is given that:
The translation T maps point A(-3,1) onto point A'(5,5).
so, if the translation rule that is used is:
(x,y) → (x+h,y+k)
Here
(-3,1) → (5,5)
i.e.
-3+h=5 and 1+k=5
i.e.
h=5+3 and k=5-1
i.e.
h=8 and k=4
Hence, the translation is 8 units to the right and 4 units up.
Which expression is equivalent to ((2a^-3 b^4)^2/(3a^5 b) ^-2)^-1
Answer:
[tex]\large\boxed{\dfrac{1}{36a^4b^{10}}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{\left(2a^{-3}b^4\right)^2}{\left(3a^5b\right)^{-2}}\right)^{-1}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\=\dfrac{\left(3a^5b\right)^{-2}}{\left(2a^{-3}b^4\right)^2}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\dfrac{3^{-2}(a^5)^{-2}b^{-2}}{2^2(a^{-3})^2(b^4)^2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{3^{-2}a^{(5)(-2)}b^{-2}}{4a^{(-3)(2)}b^{(4)(2)}}=\dfrac{3^{-2}a^{-10}b^{-2}}{4a^{-6}b^8}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}[/tex]
[tex]=\dfrac{3^{-2}}{4}a^{-10-(-6)}b^{-2-8}=\dfrac{3^{-2}}{4}a^{-4}b^{-10}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{1}{3^2}\cdot\dfrac{1}{4}\cdot\dfrac{1}{a^4}\cdot\dfrac{1}{b^{10}}=\dfrac{1}{36a^4b^{10}}[/tex]
Answer:
1 / 36a^4 b^10
Step-by-step explanation:
Which is the graph of the equation y = -3x- 1
Neither of those two graphs do the trick, but if I saw the rest of the answer choices, then I would be happy to assist you.
Which of the following lists of ordered pairs is a function
Answer:
A
Step-by-step explanation:
A function can't have the same number more than once, so the answer is A since there are no repeating numbers.
can someone help me pls?
Answer:
graph c
Step-by-step explanation:
there is no slope since it doesn't go up/down by anything or over by anything. meaning there is no increase or decrease.
(07.03 MC)
Choose the correct simplification of the expression (3xy4)2(y2)3.
6x2y14
9x2y14
9x3y11
6x3y11
Answer:
9x²y¹⁴
Step-by-step explanation:
[tex]\tt (3xy^4)^2(y^2)^3\\\\=3^2x^2y^{4\cdot2}\cdot y^{2\cdot3}\\\\=9x^2y^{8}\cdot y^{6}\\\\= 9x^2y^{8+6}\\\\= 9x^2y^{14}[/tex]
alpha and beta are the zeros of the polynomial x^2 -(k +6)x +2(2k -1). Find the value of k if alpha + beta = 1/2 alpha beta(ITS URGENT)
Answer:
[tex]k=\frac{-11}{2}[/tex].
Step-by-step explanation:
We are given [tex]\alpha[/tex] and [tex]\beta[/tex] are zeros of the polynomial [tex]x^2-(k+6)x+2(2k-1)[/tex].
We want to find the value of [tex]k[/tex] if [tex]\alpha+\beta=\frac{1}{2}[/tex].
Lets use veita's formula.
By that formula we have the following equations:
[tex]\alpha+\beta=\frac{-(-(k+6))}{1}[/tex] (-b/a where the quadratic is ax^2+bx+c)
[tex]\alpha \cdot \beta=\frac{2(2k-1)}{1}[/tex] (c/a)
Let's simplify those equations:
[tex]\alpha+\beta=k+6[/tex]
[tex]\alpha \cdot \beta=4k-2[/tex]
If [tex]\alpha+\beta=k+6[/tex] and [tex]\alpha+\beta=\frac{1}{2}[/tex], then [tex]k+6=\frac{1}{2}[/tex].
Let's solve this for k:
Subtract 6 on both sides:
[tex]k=\frac{1}{2}-6[/tex]
Find a common denominator:
[tex]k=\frac{1}{2}-\frac{12}{2}[/tex]
Simplify:
[tex]k=\frac{-11}{2}[/tex].
Which functions has the graph shown?
Answer:
C.
Step-by-step explanation:
Let's identify some points here that are on the graph:
(0,0), (pi/2,-1), (pi,0).
Let's see if this is enough.
We want to see which equation holds for these points.
Let's try A.
(0,0)?
y=cos(x-pi/2)
0=cos(0-pi/2)
0=cos(-pi/2)
0=0 is true so (0,0) is on A.
(pi/2,-1)?
y=cos(x-pi/2)
-1=cos(pi/2-pi/2)
-1=cos(0)
-1=1 is false so (pi/2,-1) is not on A.
The answer is not A.
Let's try B.
(0,0)?
y=cos(x)
0=cos(0)
0=1 is false so (0,0) is not on B.
The answer is not B.
Let's try C.
(0,0)?
y=sin(-x)
0=sin(-0)
0=sin(0)
0=0 is true so (0,0) is on C.
(pi/2,-1)?
y=sin(-x)
-1=sin(-pi/2)
-1=-1 is true so (pi/2,-1) is on C.
(pi,0)?
y=sin(-x)
0=sin(-pi)
0=0 is true so (pi,0) is on C.
So far C is winning!
Let's try D.
(0,0)?
y=-cos(x)
0=-cos(0)
0=-(1)
0=-1 is not true so (0,0) is not on D.
So D is wrong.
Okay if you do look at the curve it does appear to be a reflection of the sine function.
Make y the subject of:
X=5y+4/2y-3
Step-by-step explanation:
I have answered ur question
To make y the subject, distribute and simplify the equation, then isolate y on one side by performing the necessary operations.
Explanation:To make y the subject of the equation X = 5y + 4/2y - 3, we need to isolate y on one side of the equation.
Distribute the 5 to both terms within the parentheses: X = 5y + 2 - 3.Combine the constants: X = 5y - 1.Move the constant term to the other side of the equation by subtracting 1 from both sides: X + 1 = 5y.Divide both sides of the equation by 5: (X + 1)/5 = y.Therefore, y = (X + 1)/5 is the solution.
Learn more about Solving for a Variable here:https://brainly.com/question/35263223
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how many solutions does the following equation have?
13 - |3x-9| = 2
It has _____ solutions
[tex]13 - |3x-9| = 2\\|3x-9|=11\\3x-9=11\vee 3x-9=-11\\3x=20 \vee 3x=-2\\x=\dfrac{20}{3} \vee x=-\dfrac{2}{3}[/tex]
TWO
Answer:
2
Step-by-step explanation:
[tex]13-|3x-9|=2[/tex]
Subtract 13 on both sides.
[tex]-|3x-9|=2-13[/tex]
Simplify right hand side.
[tex]-|3x-9|=-11[/tex]
Take the opposite of both sides (also known as multiply both sides by -1).
[tex]|3x-9|=11[/tex].
Let u=3x-9.
Since we have |u|=positive, we will have two solutions for x.
If we had |u|=negative, we will have no solutions for x.
If we had |u|=0, we would have one solution for x.
John was 40 years old in 1995 while his father was 65.In what year was John exactly half his father's age?
Answer:
1980.
Step-by-step explanation:
John was born in 1995 - 40 = 1955.
His father was born in 1995 - 65 = 1930.
Let x be Johns age and his father 2x
1955 + x = 1930 + 2x
1955 - 1930 = 2x - x
x = 25
So the year is 1955 + 25 = 1980..
In that year John was 25 and his father was 50.
A bank features a savings account that has an annual percentage rate of r=5.2% with interest compounded quarterly. Marcus deposits $8,500 into the account.
The account balance can be modeled by the exponential formula S(t)=P(1+rn)^nt, where S is the future value, P is the present value, r is the annual percentage rate written as a decimal, n is the number of times each year that the interest is compounded, and t is the time in years.
(A) What values should be used for P, r, and n?
P= _____ , r=______ , n=________
(B) How much money will Marcus have in the account in 7 years?
Answer = $______ .
Round answer to the nearest penny.
Answer:
Part A)
[tex]P=\$8,500\\ r=0.052\\n=4[/tex]
Part B) [tex]S(7)=\$12,203.47[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]S(t)=P(1+\frac{r}{n})^{nt}[/tex]
where
S is the Future Value
P is the Present Value
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part A)
in this problem we have
[tex]P=\$8,500\\ r=5.2\%=5.2/100=0.052\\n=4[/tex]
Part B) How much money will Marcus have in the account in 7 years?
we have
[tex]t=7\ years\\ P=\$8,500\\ r=0.052\\n=4[/tex]
substitute in the formula above
[tex]S(7)=8,500(1+\frac{0.052}{4})^{4*7}[/tex]
[tex]S(7)=8,500(1.013)^{28}[/tex]
[tex]S(7)=\$12,203.47[/tex]
In this problem, we find that Marcus should use the values P = $8,500, r = 0.052 and n = 4 for the given savings account. After calculating, we conclude that Marcus would have approximately $11,713.69 in the account after 7 years.
Explanation:This problem involves the concept of compound interest in mathematics. Let's break it down:
For part (A), we are given that the initial deposit or the present value P is $8,500, the annual percentage rate, r, is 5.2% (but for the formula we need to use this as a decimal, so divide by 100: r = 0.052), and the interest is compounded quarterly, or 4 times a year so n = 4.For part (B), we need to find out the future value S of the deposit after 7 years.We use the formula S(t)=P(1+rn)^(nt):
S(7) = 8500(1 + 0.052/4)^(4*7)
By calculating the above, we find the balance after seven years to be approximately $11,713.69 when rounded to the nearest penny.
Learn more about Compound Interest here:https://brainly.com/question/14295570
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what is the area of a rectangle that is 3/5 of a meter long and 7/12 of a meter long
Answer:
7/20 m^2
Step-by-step explanation:
A = l*w
=3/5 * 7/12
Multiplying the numerators
3*7 =21
Multiplying the denominators
5*12= 60
Putting the numerator over the denominator
21/60
Divide the top and bottom by 3
7/20
Answer:
7/20
Step-by-step explanation:
The graph below shows a system of equations: Draw a line labeled y equals minus x plus 5 by joining the ordered pairs 0, 5 and 5, 0. Draw a line labeled y equals x minus 1 The x-coordinate of the solution to the system of equations is ___ . (5 points)
Answer:
The x-coordinate of the solution is x=3
Step-by-step explanation:
we have
[tex]y=-x+5[/tex] ------> equation A
[tex]y=x-1[/tex] ------> equation B
Solve the system of equations by substitution
Substitute equation B in equation A and solve for x
[tex]x-1=-x+5[/tex]
[tex]x+x=5+1[/tex]
[tex]2x=6[/tex]
[tex]x=3[/tex]
Find the value of y
[tex]y=x-1[/tex] ------> [tex]y=3-1=2[/tex]
The solution of the system of equations is the point (3,2)
therefore
The x-coordinate of the solution is x=3
Answer:
x = 3
Step-by-step explanation:
i did the same test and got it right
Which graph shows the solution to the inequality |x+3| >2
Answer:
The answer is B, given the module of a number has always a positive value
Answer:
Answer is B.
SECOND NUMBER LINE
Step-by-step explanation:
Today, Jana picked 15 flowers from her garden. This is 5 more than what she picked yesterday. How many flowers did Jana pick yesterday? F. 10. G. 20. H. 25. I. 30.
Answer:
F. 10
Step-by-step explanation:
She had 15 flowers today
So if she had 5 more than yesterday
You subtract the 5 to get how much she had yesterday
15-5=10
Answer:
F. 10
Step-by-step explanation:
Today: 15 flowers
: 5 more than yesterday
more than means add
15 = 5+ yesterday
Subtract 5 from each side
15-5 = 5+ yesterday -5
10 = yesterday
if you can buy 1/4 pizza for 5 dollars, how much can you purchase for 8 dollars? write your answer as a fraction
Step-by-step explanation:
¼ pizza is to 5 dollars as x pizza is to 8 dollars.
¼ / 5 = x / 8
Cross multiply:
5x = 2
Divide:
x = ⅖
You can buy ⅖ of a pizza.
Trey is a car salesman who earned a base pay of $47,300 and was paid
commission of 15% for each car he sold. If x represents total sales in dollars,
then which of the following equations best represents Trey's total pay in
dollars?
Answer:
Trey earns a base pay of $47,300 plus 15% for each car sold.
The equation that represets Trey's total pay in dollars is:
y = $47,300 + 0.15x
Where $47,300 represents the base pay, and 0.15x represents the money he earn for the total cars sold.
Answer:
[tex]y=47,300+0.15x[/tex]
Step-by-step explanation:
Let x represent total sales in dollars.
We have been given that Trey earns base pay of $47,300 and was paid commission of 15% for each car he sold.
Since Trey is paid 15% for each car he sold and total sales were x dollars, this means his commission would be 15% of x that is [tex]\frac{15}{100}x=0.15x[/tex].
The total salary of Trey would be base salary plus commission: [tex]y=47,300+0.15x[/tex]
Therefore, the equation [tex]y=47,300+0.15x[/tex] represents Trey's total pay in dollars.
10 points for this! btw it’s really easy to some people so yea
Answer:
C
step-by-step explanation:
you just have to subtract them 9/16-1/4=8/12
Audrey has .x pounds of red grapes and y pounds of
green grapes. She has less than 5 pounds of grapes in
Which are reasonable solutions for this situation?
Check all that apply.
(-1,2)
(1.3.5)
(2, 2)
(4.5, 0.5)
(5,0)
Answer: (1,3,5) & (2,2)
Step-by-step explanation:
A garden has an area of 240 ft. Its length is 8 ft more than its width. What are the dimensions of the
garden?
Answer:
w=12
l=20
Step-by-step explanation:
The area can be found using the following equation:
[tex]A=lw[/tex]
Given the information provided, we are also told the following:
[tex]l=w+8[/tex]
Therefore, we can plug in our length and our area:
[tex]240=w(w+8)\\240=w^2+8w\\\\w^2+8w-240=0[/tex]
We can solve by using the quadratic formula.
[tex]w=\frac{-8+\sqrt{8^2-4(1)(-240)} }{2(1)}=12 \\\\[/tex]
w=12, so w+8=20.
Multiply (9-4i)(2+5i)
(9 - 4i)(2 + 5i)
To solve this question you must FOIL (First, Outside, Inside, Last) like so
First:
(9 - 4i)(2 + 5i)
9 * 2
18
Outside:
(9 - 4i)(2 + 5i)
9 * 5i
45i
Inside:
(9 - 4i)(2 + 5i)
-4i * 2
-8i
Last:
(9 - 4i)(2 + 5i)
-4i * 5i
-20i²
Now combine all the products of the FOIL together like so...
18 + 45i - 8i - 20i²
***Note that i² = -1; In this case that means -20i² = 20
18 + 45i - 8i + 20
Combine like terms:
38 - 37i
^^^This is your answer
Hope this helped!
~Just a girl in love with Shawn Mendes
Which statements about the graph of the function Fx=-x2-4x+2 are true check all that apply
Step-by-step explanation:
Just graph it and see if the descriptions fit the graph
(see attached)
A. We can see from the graph that the possible x-values are -∞ ≤ x ≤ +∞ . Hence limiting to domain to x≤ -2 this is obviously not true.
B. We can see from the graph that the vertex is y = 6 and that the entirety of the graph is under this point, hence range y<6 is true
C. We can see that the vertex is located at x=-2. Every part of the graph to the left of this point has a positive slope, hence the function is increasing for negative infinity to this point x=-2 is true
D) We can see that for the interval -4<x<∞, the graph actually increases between -4<x<-2, and then decreases after that. Hence this statement is not true.
E. it is obvious that the y intercept is y=2 which is positive. Hence this is true.
The graph of F(x)=-x^2-4x+2 is a downward-opening parabola with its vertex serving as the local and global maximum. There are no asymptotes for this quadratic function. The shape of the graph is best understood by examining its behavior over a range of x-values and by sketching it with the vertex and axis of symmetry.
The graph of the function F(x) = -x^2 - 4x + 2 represents a parabola opening downward because the coefficient of x^2 is negative. To understand the nature of the graph, we evaluate its characteristics by identifying the vertex, the axis of symmetry, and whether it has local or global extrema. The vertex of this parabola can be found using the formula -b/2a, which gives us the x-coordinate, and by substituting that back into the function for the y-coordinate. The axis of symmetry will be a vertical line passing through the vertex's x-coordinate.
Since this is a quadratic function, it does not have asymptotes because it extends indefinitely in both the positive and negative directions of the y-axis. Instead, the parabola will have a maximum point at the vertex, which is a local and global maximum because the parabola opens downward. Moreover, we should evaluate the function for a range of x-values to understand its behavior for large negative x, small negative x, small positive x, and large positive x.
Sketching the graph of this function would involve plotting the vertex, drawing the axis of symmetry, and selecting a few points around the vertex to determine the shape of the parabola.
can someone plz help me plz
Answer:
[tex]\large\boxed{C.\ y=2+x^4}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of linear function:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
============================
[tex]A.\\\\9y+3=0\qquad\text{subtract 3 from both sides}\\\\9y=-3\qquad\text{divide both sides by 9}\\\\y=-\dfrac{3}{9}\\\\y=-\dfrac{1}{3}\to m=0,\ b=-\dfrac{1}{3}[/tex]
[tex]B.\\\\y-4x=1\qquad\text{add}\ 4x\ \text{to both sides}\\\\y=4x+1\to m=4,\ b=1[/tex]
[tex]C.\\\\y=2+x^4\qquad\text{nonlinear, because}\ x\ \text{is in fourth power}[/tex]
[tex]D.\\\\x-2y=7\qquad\text{subtract}\ x\ \text{from both sides}\\\\-2y=-x+7\qquad\text{divide both sides by (-2)}\\\\y=\dfrac{1}{2}x-\dfrac{7}{2}\to m=\dfrac{1}{2},\ b=-\dfrac{7}{2}[/tex]
[tex]E.\\\\\dfrac{x}{y}+1=2\qquad\text{subtract 1 from both sides}\\\\\dfrac{x}{y}=1\to y=x\to m=1,\ b=0[/tex]
Mark is playing soccer. He is 150 yards from the center goal. When he kicks the ball it goes 145 yards at an angle of 2 degrees off to the right. How far is the ball from the goal?
Answer:
8 yards
Step-by-step explanation:
This can be illustrated from drawing it. (Attachment)
Scale- Real : Map
10 yard : 1 cm
150 yard : 15 cm
145 yard : 14.5 cm
Step 1: Draw a 7.5 cm line from origin to Point A
Step 2: Form a 2 degree angle from the origin
Step 3: Draw a 7.25 cm line 2 degree angle from the origin to Point B
Step 4: Measure the distance in cm from Point A to Point B
Step 5: Convert the distance from Point A to Point B in yards.
Therefore, the ball is 8 yards far from the goal.
!!
Answer:
The ball is 7.176 yards away from the center of the goal.
Step-by-step explanation:
Given distance between the center goal and Mark is AB = 150 yards
Distance traveled by ball at angle 2 degree off to the right from Mark is
AC = 145 yards
We have to find the distance BC in triangle ABC
Using cosine rule
[tex]BC^{2}=AB^{2}+AC^{2}-2AB\times AC\times \cos \Theta[/tex]
=>[tex]BC^{2}=[150^{2}+145^{2}-2\times 150\times 145\times \cos (2^{\circ})] yards^{2}[/tex]
=>BC^{2}=51.5 yards^{2}
=>[tex]BC=\sqrt{(51.5 yards^{2})}=7.176yards[/tex]
Thus the ball is 7.176 yards away from the center of the goal.
Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Check all that apply.
+ 8r2s4 – 3r3s3
s5
3r4s5
–r4s6
–6rs5
Answer:
[tex]3r^{4}s^{5}\\-r^{4}s^{6}[/tex]
Step-by-step explanation:
The standard form of a polynomial is when its term of highest degree is at first place.
In this case, we have two variables. The grade of each term is formed by the sum of its exponents. That means both given terms have a degree of six. So, the right answers must have a higher degree.
Therefore, the right answers are the second and third choice, because their degrees are 9 and 10 respectively.
identify the transformation taking place in this function. y = x^2 +8. a. translation down 8 units. b. translation left 8 units. c. translation right four units. d. translation up 8 units.
Answer:
D. if we are describing how to get from y=x^2 to y=x^2+8.
Step-by-step explanation:
If we are describing how to get from y=x^2 to y=x^2+8, then the transformation is just a translation of 8 units up.
If the equation was y=x^2-8, it would have been down 8 units.
If the equation was y=(x-8)^2, it would have been right 8 units.
If the equation was y=(x+8)^2, it would have been left 8 units.