Replace n in the equation with each given value and solve for m.
You are given n = {-2, 1, 4}
When n = -2:
3m = -2-7
3m = -9
m = -9/3
m = -3
When n = 1:
3m = 1-7
3m = -6
m = -6 /3
m=-2
When n = 4:
3m = 4-7
3m = -3
m = -3/3
m = -1
m = {-3, -2, -1}
The coordinate plane below represents a city.
Points A through F are schools in the city. graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at
The coordinate plane is below
Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.
Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A.
Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.
Answer:
Part A) The system of inequalities is
[tex]x\geq2[/tex] and [tex]y\geq2[/tex]
Part B) In the procedure
Part C) The schools that Natalie is allowed to attend are A,B and D
Step-by-step explanation:
Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions
we have
Points C(2,2), F(3,4)
The system of inequalities could be
[tex]x\geq2[/tex] -----> inequality A
The solution of the inequality A is the shaded area at the right of the solid line x=2
[tex]y\geq2[/tex] -----> inequality B
The solution of the inequality B is the shaded area above of the solid line y=2
see the attached figure N 1
Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities
Verify point C
C(2,2)
Inequality A
[tex]x\geq2[/tex] -----> [tex]2\geq2[/tex] ----> is true
Inequality B
[tex]y\geq2[/tex] ------> [tex]2\geq2[/tex] ----> is true
therefore
Point C is a solution of the system of inequalities
Verify point D
F(3,4)
Inequality A
[tex]x\geq2[/tex] -----> [tex]3\geq2[/tex] ----> is true
Inequality B
[tex]y\geq2[/tex] ------> [tex]4\geq2[/tex] ----> is true
therefore
Point D is a solution of the system of inequalities
Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.
we have
[tex]y < -2x+2[/tex]
The solution of the inequality is the shaded area below the dotted line [tex]y=-2x+2[/tex]
The y-intercept of the dotted line is the point (0,2)
The x-intercept of the dotted line is the point (1,0)
To graph the inequality, plot the intercepts and shade the area below the dotted line
see the attached figure N 2
therefore
The schools that Natalie is allowed to attend are A,B and D
A triangle has vertices at F (−7, 3), G (2, 6), and H (3, 5). What are the coordinates of each vertex if the triangle is reflected over the x axis?
Answer:
F(-7,3) -> F'(-7,-3)
G(2,6) -> G'(2,-6)
H(3,5) ->H'(3,-5)
Step-by-step explanation:
If you are taking point (a,b) and reflecting it across the x-axis (the horizontal axis), your x value is going to stay the same because you want the point on the same vertical line as (a,b). The y-coordinate is going to be opposite because you want a reflection and the opposite of b will this give you the same distance from the x-axis as b.
So the transformation is this: (a,b) -> (a,-b).
All this means is leave x the same and take the opposite of y.
F(-7,3) -> F'(-7,-3)
G(2,6) -> G'(2,-6)
H(3,5) ->H'(3,-5)
The coordinates of each vertex if the triangle is reflected over the x-axis are [tex]F'(-7,-3),G'(2,-6),H'(3,-5)[/tex].
Given:
The vertices of a triangle are [tex]F(-7,3),G(2,6),H(3,5)[/tex].
To find:
The coordinates of each vertex if the triangle is reflected over the x-axis.
Explanation:
If a triangle is reflected over the x-axis, then the rule of reflection is defined as:
[tex](x,y)\to (x,-y)[/tex]
Using this rule, we get
[tex]F(-7,3)\to F'(-7,-3)[/tex]
[tex]G(2,6)\to G'(2,-6)[/tex]
[tex]H(3,5)\to H'(3,-5)[/tex]
Therefore, the coordinates of each vertex if the triangle is reflected over the x-axis are [tex]F'(-7,-3),G'(2,-6),H'(3,-5)[/tex].
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find the real numbers that satisfy the equation
x=35.3
Answer:
35.3
Step-by-step explanation:
Actually, there are none but 35.3. Here you have already defined x as 35.3. 35.3 satisfies the given equation.
The solution to the given equation x = 35.3 is simply x equals 35.3. There are no further calculations required for this straightforward linear equation.
Explanation:The equation given, x = 35.3, is a simple linear equation where the variable x is already isolated on one side of the equation. The solution to this equation is straightforward: x equals 35.3. There is no need for further calculation or iterative numerical methods, as this is not a quadratic equation nor does it require techniques such as least squares to find a solution. The equation simply states that x is equal to the real number 35.3.
However, if you are given a quadratic equation or more complex equations, there can be different methods to solve for x. For example, the quadratic formula, iterative methods, or writing computer programs for finding least squares solutions in systems of equations with multiple variables.
Make n the subject of the formula t= square root of n+3/n
Step-by-step explanation:
hi I have answered ur question
To make n the subject of the formula t = square root of n+3/n, we can isolate the square root term by squaring both sides of the equation and rearranging the equation to make n the subject.
Explanation:To make n the subject of the formula t = √(n+3)/n, we can start by isolating the square root term. To do this, we square both sides of the equation:
t2 = √(n+3)/n2
Next, we can multiply both sides by n2 to get rid of the denominator:
t2n2 = n + 3
Finally, we can rearrange the equation to make n the subject:
n = (t2n2 - 3)/t2
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Match each expression to its equivalent standard form.
Answer:
(x+1+i)(x+1-i) goes with x^2+2x+2
(x+2i)(x-2i) goes with x^2+4
(x-2+2i)(x-2-2i) goes with x^2-4x+8
Step-by-step explanation:
(x+1+i)(x+1-i)
(x+[1+i])(x+[1-i])
Use foil.
First: x(x)=x^2
Outer: x(1+i)=x+ix
Inner: x(1-i)=x-ix
Last: (1+i)(1-i)=1-i^2 since 1+i and 1-i are conjugates
__Add together to get: x^2+2x+1-i^2
We can actually simplify this because i^2=-1
So x^2+2x+1-i^2=x^2+2x+1-(-1)=x^2+2x+2
(x+2i)(x-2i)
These are conjugates so just do first and last of foil.
First: x(x)=x^2
Last: 2i(-2i)=-4i^2=-4(-1)=4
==Adding together gives x^2+4
(x-2+2i)(x-2-2i)
(x+[-2+2i])(x+[-2-2i])
This is similar to first.
Foil time!
First: x(x)=x^2
Outer: x(-2-2i)=-2x-2ix
Inner: x(-2+2i)=-2x+2ix
Last: (-2-2i)(-2+2i)=4-4i^2 (multiplying conjugates again)
==Add together giving us x^2-4x+4-4i^2
This can be simplified since i^2=-1.
So applying this gives us x^2-4x+4-4(-1)
=x^2-4x+4+4
=x^2-4x+8
Answer:
1. The first expression is equivalent to [tex]x^2+2x+2[/tex].
2. The second expression is equivalent to [tex]x^2+4[/tex].
3. The third expression is equivalent to [tex]x^2-4x+8[/tex].
Step-by-step explanation:
(1).
The given expression is
[tex](x+1+i)(x+1-i)[/tex]
[tex][(x+1)+i][(x+1)-i][/tex]
Using the algebraic properties, we get
[tex](x+1)^2-(i)^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]x^2+2x+1-(i)^2[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]x^2+2x+1-(-1)[/tex] [tex][\because i^2=-1][/tex]
[tex]x^2+2x+2[/tex]
Therefore the first expression is equivalent to [tex]x^2+2x+2[/tex].
(2).
The given expression is
[tex](x+2i)(x-2i)[/tex]
Using the algebraic properties, we get
[tex](x)^2-(2i)^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]x^2-4i^2[/tex]
[tex]x^2-4(-1)[/tex] [tex][\because i^2=-1][/tex
[tex]x^2+4[/tex]
Therefore the second expression is equivalent to
[tex]x^2+4[/tex].
(3)
The given expression is
[tex](x-2+2i)(x-2-2i)[/tex]
[tex][(x-2)+2i][(x-2)-2i][/tex]
Using the algebraic properties, we get
[tex](x-2)^2-(2i)^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]x^2-4x+4-4i^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]x^2-4x+4-4(-1)[/tex] [tex][\because i^2=-1][/tex]
[tex]x^2-4x+4+4[/tex]
[tex]x^2-4x+8[/tex]
Therefore the third expression is equivalent to [tex]x^2-4x+8[/tex].
factor this polynomial expression 10x^2-7x-12
[tex]10x^2-7x-12=\\10x^2-15x+8x-12=\\5x(2x-3)+4(2x-3)=\\(5x+4)(2x-3)[/tex]
Answer:
(2x - 3)(5x + 4)
Step-by-step explanation:
Given
10x² - 7x - 12
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 10 × - 12 = - 120 and sum = - 7
The factors are - 15 and + 8
Use these factors to split the x- term
10x² - 15x + 8x - 12 ( factor the first/second and third/fourth terms )
= 5x(2x - 3) + 4(2x - 3) ← factor out (2x - 3) from each term
= (2x - 3)(5x + 4) ← in factored form
g(x) = x4 − 3x2 + 4x − 5
Let's solve for g.
gx=x4−3x2+4x−5
Step 1: Divide both sides by x.
gx
x
=
x4−3x2+4x−5
x
g=
x4−3x2+4x−5
x
Answer:
g=
x4−3x2+4x−5
x
What is the measure of PQR
Answer:
C. 86°
Step-by-step explanation:
I just did it on A p 3 x
What percent is 48cm of 1.5 m
First of all, recall that 1.5m is the same as 150cm.
Now, we simply build a proportion where we consider 48 to be 100, and wonder what 150 will be:
[tex]48\div 100 = 150 \div x[/tex]
Solving for x, we have
[tex]x = \dfrac{150\cdot 100}{48}=\dfrac{15000}{48} = 312.5[/tex]
Which actually makes sense, because we're stating that 1.5m is about 300% of 48cm, which means three times as much. Which is true, because three times 48cm means 144cm, which is about 1.5m
Answer:
32%Step-by-step explanation:
To solve this problem, you must first have the numbers in the same units, that is, convert the meters to centimeters and operate with them or transform to meters and work with them, therefore, I decide to work with centimeters, like this:
1.5 meters = 150 centimeters (each meter equals 100 centimeters)Then, you can make a simple rule of three, where 150 centimeters corresponds to 100% and you look for the percentage of 48 centimeters:
150 cm = 100% 48 cm = XSo:
X = (48 * 100) / 150 X = 4800/150 X = 32Therefore, the percentage of 48 centimeters is equal to 32%.
Suppose that g(x) = f(x) - 3. Which statement best compares the graph of
g(x) with the graph of Rx)?
Answer:
The graph of g(x) is a translation of f(x) 3 units down.
Step-by-step explanation:
The given function is
[tex]g(x) = f(x) - 3[/tex]
The parent function now is f(x).
The -3 tells us that there is a vertical translation of the parent function 3 units down.
Therefore the graph of g(x) is obtained by translating the graph of f(x) down by 3 units.
The picture shows the arrangement of balls in a game of boccie. The object of the game is to throw your ball closest to the small, white ball, which is called the pallino The green ball is the midpoint between the red ball and the pallino. The distance between the green ball and the red ball is 10 inches. The distance between the yellow
ball and the pallino is 8 inches. Which ball is closer to the pallino, the green ball or the yellow ball? Explain.
Answer:
Step-by-step explanation:
Distance of yellow to white = 8 inches which is given
The green ball is at the midpoint of red to white.
Since the green ball is 10 inches to the red ball, the green ball is also 10 inches from the white ball. That's what a midpoint is.
The yellow ball is closer.
In the diagram below, Pis circumscribed about quadrilateral ABCD. What is
the value of x?
A. 60°
B. 100°
C. 80°
D. 120°
Answer:
c
Step-by-step explanation:
x=180-100=80
The value of x is [tex]80^{o}[/tex].
What are the opposite angle of a quadrilateral?The opposite angles in a quadrilateral are those angles that are located diagonally opposite to each other.
What is the sum of the opposite angles of a quadrilateral?The sum of the opposite angles of a cyclic quadrilateral is 180 degrees.
According to the given question.
We have a quadrilateral ABCD which is inscribed in a circle.
Also, m ∠ABC = 100 degrees
Since, we know that the sum of the opposite angles of a cyclic quadrilateral is 180 degrees.
Therefore,
[tex]m\angle ABC +m\angle CDA = 180^{o} \\\implies 100^{o} + x = 180^{o} \\\implies x = 180^{o} -100^{o} \\\implies x = 80^{o}[/tex]
Hence, the value of x is [tex]80^{o}[/tex].
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State the degree: 11m^3n^2p
Explanation:
Using the rule that x = x^1, we can rewrite the p as p^1
So 11m^3n^2p is the same as 11m^3n^2p^1
The exponents are: 3, 2, 1
Those exponents add up to 3+2+1 = 6
The degree of a monomial like this is simply equal to the sum of the exponents.
Answer:
6
Step-by-step explanation:
Help pleaseeeeee!
State the various transformations applied to the base function ƒ(x) = |x| to obtain a graph of the function g(x) = 3[|x − 1| + 2].
Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3.
Horizontal shift of 3 units to the right, a vertical shift downward of 2 units, and a vertical stretch by a factor of 3.
Horizontal shift of 3 units to the left, a vertical shift upward of 2 units, and a vertical stretch by a factor of 3.
Horizontal shift of 1 unit to the left, a vertical shift downward of 6 units, and a vertical stretch by a factor of 3.
Answer:
Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..
Step-by-step explanation:
Given function is:
3[|x-1|+2]
Can also be written as:
3|x-1|+6
As we can see that the -1 is grouped with x which means it is a horizontal shift of 1 unit to the right.
Now, 6 is added to the function and it is not grouped with x which means that there is a vertical shift of 6 units upward.
Lastly, 3 is multiplied with the term containing x which means that there is a vertical stretch of 3 units.
Hence, the correct option is:
Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..
Answer:
Horizontal shift of [tex]1[/tex] unit to the right, a vertical shift upward of [tex]6[/tex] units, and a vertical stretch by a factor of [tex]3[/tex].
Step-by-step explanation:
First we re write the equation by multiplying the number [tex]3[/tex] in this way we will see much better the solution
[tex]g(x)=3[|x-1|+2]=3|x-1|+6[/tex]
we will start from the inside to the outside
[tex]|x-1|[/tex] this [tex]-1[/tex]is grouped with the x and this means there is a horizontal shift of [tex]1[/tex] unit to the right (because of the sign)
[tex]3|x-1|[/tex] this [tex]3[/tex] is multiplying the x which means the function will be stretching by a factor of [tex]3[/tex] ([tex]g(x)[/tex] will be [tex]3[/tex] times bigger)
[tex]3|x-1|+6[/tex] this [tex]6[/tex] is not goruped with x and moves the entire function 6 units upwards.
We can see it more clearly in the graph attached.
Sheila is looking at some information for the obstacle course she is interested in completing. The x-coordinate is the number of the obstacle, while the y-coordinate is the average time to complete the obstacle, measured in minutes. (1, 8.25), (2, 9.075), (3, 9.9825), (4, 10.98075) Help Sheila use an explicit formula to find the average time she will need for the 8th obstacle.
A. f(8) = 8.25(1.1)^8; f(8) = 17.685
B. f(8) = 8.25(1.1)^7; f(8) = 16.077
C. f(8) = 1.1(8.25)^7; f(8) = 2861345
D. f(8) = 1.1(8.25)^8; f(8) = 23606102
Answer:
f(8) = 8.25(1.1)^7 ; f(8) = 16.077 ⇒ answer B
Step-by-step explanation:
* Lets explain how to solve the problem
∵ The x-coordinate is the number of the obstacle
∵ The y-coordinate is the average time to complete the obstacle
∵ The order pairs of function are (1 , 8.25) , (2 , 9.075) , (3 , 9.9825) ,
(4 , 10.98075)
- From these order pairs
# The time to finish the 1st obstacle is 8.25 minutes
# The time to finish the 2nd obstacle is 9.075 minutes
# The time to finish the 3rd obstacle is 9.9825 minutes
# The time to finish the 4th obstacle is 10.98075 minutes
∵ 2nd ÷ 1st = 9.075/8.25 = 1.1
∵ 3rd ÷ 2nd = 9.9825/9.075 = 1.1
∵ 4th ÷ 3rd = 10.98075/9.9825 = 1.1
∴ There is a constant ratio 1.1 between each 2 consecutive terms
∴ The order pairs formed a geometric series
- Any term in the geometric series Un = a r^(n - 1) , where a is the 1st
term in the series , r is the constant ratio and n is the position of the
term in the series
∵ a = 8.25 ⇒ the time of the first obstacle
∵ r = 1.1
- Sheila wants to find the average time she will need for the 8th
obstacle
∴ n = 8
∵ The explicit formula is f(x) = a r^(n - 1)
∴ f(8) = 8.25 (1.1)^(8 - 1)
∴ f(8) = 8.25(1.1)^7
∴ f(8) = 16.076916 ≅ 16.077
* f(8) = 8.25(1.1)^7 ; f(8) = 16.077
Answer:
Option) BEE is the correct answer!
Step-by-step explanation:
find the distance between the points (5, -3) and (0, 2).
Answer:
Distance between points (5, -3) and (0, 2) is √50 or 7.07
Step-by-step explanation:
We need to find distance between two points (5,-3) and (0,2)
The distance formula used is:
[tex]d= \sqrt {\left( { x_2-x_1 } \right)^2 + \left( {y_2-y_1} \right)^2 }[/tex]
here
x₁= 5, y₁=-3, x₂=0 and y₂=2
Putting values in the formula:
[tex]d= \sqrt {\left( {x_2-x_1} \right)^2 + \left( {y_2-y_1} \right)^2 }\\d= \sqrt {\left( {0-5} \right)^2 + \left( {2-(-3)} \right)^2 }\\d= \sqrt {\left( {-5} \right)^2 + \left( {2+3} \right)^2 }\\d= \sqrt {25+25}\\d= \sqrt {50}\\d= 7.07[/tex]
So, distance between points (5, -3) and (0, 2) is √50 or 7.07
construct a difference table to predict the next term of the sequence -1,3,18,47,93,159,248
Answer:
362
Step-by-step explanation:
-1,3,18,47,93,159,248
First difference (just do term minus previous term):
4, 15, 29, 46, 66 ,89
The first differences are not common.
Second difference (doing term minus previous term)
11, 14, 17, 20, 23
Third difference:
3 ,3 ,3, 3
So it is a cubic because the third differences are the same.
Anyways we don't have to find the explicit form of this sequence. We just have to find the next term.
Let's go back through starting with second difference:
11 , 14, 17, 20, 23 , (25)
(25) would be next term here.
Let's go back to first difference:
4, 15, 29, 46, 66 ,89 , (89+25)
4, 15 ,29, 46, 66, 89 , (114)
Now let's go back to original sequence:
We want 114+248 to be the next term.
That equals 362.
410 in 8 Hours At A Unit Rate !
Answer:
12 miles per hour
Step-by-step explanation:
There are 9 students in a class. The teacher chooses 2 students to go to the
library. The order in which they are chosen does not matter. How many ways
are there to choose the students?
Answer: 72
Step-by-step explanation:
There are 9 students to choose from to go the library. After that person is chosen there are 8 students remaining.
First student and Second student
9 x 8 = 72
There are 36 ways for a teacher to choose 2 students out of 9 to go to the library, using combinations where the order of selection is not important.
The student is asking how many ways there are to choose 2 students out of 9 to go to the library, with the order of selection being irrelevant. This is a classic combinatorics problem that involves calculating combinations. Combinations are used in mathematics to count selections where order does not matter.
To find the number of combinations, denoted as C(n, k), where n is the total number of available options and k is the number of selections made, you can use the formula C(n, k) = n! / (k! * (n - k)!), where ! denotes a factorial. For this specific problem, the formula becomes C(9, 2) = 9! / (2! * (9 - 2)!), which simplifies to C(9, 2) = 9 * 8 / (2 * 1) = 36 ways to choose 2 students out of 9.
what expression is equivalent to (3x^2+4x-7)(x-3)
Answer:
[tex]\arge\boxed{B.\ (3x^2+4x-7)(x)+(3x^2+4x-7)(-3)}[/tex]
Step-by-step explanation:
[tex]\text{The distributive property:}\ a(b+c)=ab+ac.\\\\(3x^2+4x-7)(x-3)=(3x^2+4x-7)(x)+(3x^2+4x-7)(-3)[/tex]
The width of a soccer field should be 60% of its length. Write and simplify an expression for the perimeter of a soccer field with a length of x feet.
Answer:
here you go
Step-by-step explanation:
W = (0.6) L
P = 2 ( L + W )
P = 2 [ L + (0.6) L ]
P = 2 ( 1.6 L )
P = (3.2) L
P = (3.2) x
The perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to
[tex]3.2x[/tex] feet.
What is the perimeter?" Perimeter is defined as the total length around the given geometrical shape."
Formula used
Perimeter of the soccer field [tex]= 2 ( L + W)[/tex]
[tex]L=[/tex] length of the soccer field
[tex]W =[/tex] width of the soccer field
According to the question,
Given,
[tex]'x'[/tex] represents the length of the soccer field
As per the given condition,
Width = [tex]60\%[/tex] of length
[tex]= \frac{60}{100} \times x\\\\= 0.6x[/tex]
Substitute the value in the formula to get the perimeter,
Perimeter of the soccer field [tex]= 2 ( x+ 0.6x)[/tex]
[tex]= 2(1.6x)\\\\= (3.2x) feet[/tex]
Hence, the perimeter of the soccer field with the length of [tex]x[/tex] feet is equal to [tex]3.2x[/tex] feet.
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A simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be 28, with a standard deviation of 5. Which of the following values is within the 95% confidence interval (z-score = 1.96) for the population mean? Remember, the margin of error, ME, can be determined using the formula ME=z*s/square root n. The value of 26, because it’s not greater than 26.7 and less than 29.3. The value of 27, because it’s greater than 26.7 and less than 29.3. The value of 32, because it’s greater than 23 and less than 33. The value of 34, because it’s not greater than 23 and less than 33.
Answer:
The value of 27, because it’s greater than 26.7 and less than 29.3.
Step-by-step explanation:
You should find the confidence Interval at 95%
The formula to apply is;
C.I= x±z*δ/√n
where C.I is the confidence interval, x is the mean of the sample, z is the z* value from the standard normal distribution for 95% confidence interval, δ is the standard deviation and n is the sample size
Substitute values in the formula
[tex]z*=1.96\\\\[/tex]
Find δ/√n
[tex]=\frac{5}{\sqrt{60} } =0.64549722436\\\\\\[/tex]
Calculate z*δ/√n
[tex]=1.96*0.64549722436=1.2652\\\\\\[/tex]
C.I= 28±1.2652
Upper limit is = 28+1.2652=29.2625
Lower limit is =28-1.2652=26.7348
Solution
The value 27 is within 95% confidence interval because it is greater than 26.7 and less than 29.3
Answer:
B.The value of 27, because it’s greater than 26.7 and less than 29.3.Step-by-step explanation:
Which of the following data sets has the mean, median, and mode as the same number?
A. 10,10,12,12,13,13
B. 2,3,4,4,5,7
C. 4,7,11,11,16,17
D. 1,2,3,3,5,6
Answer:
C. 4, 7, 11, 11, 16, 17
Step-by-step explanation:
The mean is the average of the numbers'
The median is the middle number
The mode is the number that occurs most often.
Let's look at each data set I turn.
A. 10, 10, 12, 12, 13, 13
Mean = 11. 7; Median: = 12; Modes: 10, 12, 13
All three measures are different.
B. 2, 3, 4, 4, 5, 7
Mean = 4.2; median = 4; mode = 4
Median and mode are the same, but the mean is different.
C. 4, 7, 11, 11, 16, 17
Mean = 11; median = 11; mode = 11
All three measures are the same.
D. 1, 2, 3, 3, 5, 6
Mean = 3.3; median = 3; mode = 3
Median and mode are the same, but the mean is different.
A flight from Seattle to New York takes 5 1/4 hours. We have traveled 5/8 of the way. How many hours until we land in New York?
Answer:
1.97 hours to land in New York
Step-by-step explanation:
We know that the number of hours it takes to complete the flight is: 5 [tex]\frac{1}{4}[/tex] hours
This is the same as [tex]5 + \frac{1}{4} = 5.25\ hours[/tex]
If we have traveled [tex]\frac{5}{8}[/tex] of the way, then [tex]\frac{3}{8}[/tex] more of the way to get to New York is missing, therefore the number of hours remaining is:
[tex]\frac{3}{8}*5.25\ hours = 1.97\ hours[/tex]
1.97 hours to land in New York
The time left for the flight from Seattle to New York, after travelling 5/8 of the way, is approximately 2 hours.
Explanation:The flight from Seattle to New York takes 5 1/4 hours. If you've travelled 5/8 of the way, it means you've covered a significant portion of the total flight time. Here's how you would figure out how much time you have left:
First, convert the total flight time to a straight decimal for simplicity. 5 1/4 hours is equivalent to 5.25 hours.Next, multiply that total flight time by the fraction of the flight completed, which is 5/8. This gives you how many hours you've already flown. So, 5.25 * 5/8 = approximately 3.28 hours.Finally, to find out how much longer you have to fly, subtract the time already flown from the total flight time. So, 5.25 – 3.28 = approximately 1.97 hours, or about 2 hours left.Learn more about Flight Time Calculation here:
https://brainly.com/question/23345050
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7z-[(2z+y)-(-5y+3z)+9]-12z
Answer:
-4z-6y-9
Step-by-step explanation:
7z-[(2z+y)-(-5y+3z)+9]-12z
=7z-[2z+y+5y-3z+9]-12z
=7z-2z-y-5y+3z-9-12z
=7z-2z-12z+3z-y-5y-9
=-4z-6y-9
Which are the solutions of the quadratic equation?
x2=7X+4
-7-165 -7 + 165
-7.0
7- 165 7+ / 65
7,0
For this case we must find the roots of the following equation:
[tex]x ^ 2-7x-4 = 0[/tex]
We have to:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 1\\b = -7\\c = -4[/tex]
Substituting the values:
[tex]x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {7 \pm \sqrt {49 + 16}} {2}\\x = \frac {7\pm\sqrt {65}} {2}[/tex]
We have two roots:
[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]
Answer:
[tex]x_ {1} = \frac {7+ \sqrt {65}} {2} = 7.53\\x_ {2} = \frac {7- \sqrt {65}} {2} = - 0.53[/tex]
Answer:
(C)
Step-by-step explanation:
♥☺
which of the following correctly describes the end behavior of the polynomial function f(x)=-x^3+x^2-4x+2
Answer:
The left end goes up and the right end goes down.
Step-by-step explanation:
Lets solve the function first and then find out the end behavior of the polynomial:
The given function is f(x)=-x^3+x^2-4x+2
First step is: Identify the degree of the polynomial. For this we have to find out the variable with the largest exponent.
The variable with the largest exponent in the given function is -x³
The degree of the polynomial is the largest exponent on the variable.
3 is the degree of the polynomial.
Since the degree is Odd, the ends of the function will point in the opposite direction.
Now find out the leading coefficient of the polynomial which is -1.
Since the leading coefficient is negative the graph falls to the right.
To find the behavior we have to use the degree of the polynomial as well as the sign of leading coefficient.
If it is ODD and NEGATIVE then the the left end goes up and the right end goes down.
Therefore the end behavior of the given function will be described as "the the left end goes up and the right end goes down"....
What is the measure of arc ABC?
Answer: A
Step-by-step explanation:
360°-50°=310°
Answer:it’s actually 260
Step-by-step explanation:
I just did the test
which of the following is a trinomial with a constant term?
A nominal has three terms.
Only B and D have three terms.
A constant term would be a number without a variable.
All the terms in B have variables ( x , y are part of each term).
The last term in D is the number 12, with no variable associated with it.
The answer would be D.
Answer:
it's d y^5+13x+12. you feel me you gon get it right
The curved part of this figure is a semicircle. What is the best approximation for the area of this figure? 18+12.125π units² 36+24.25π units² 36+12.125π units² 18+24.25π units²
Answer:
18+12.125π units²
Step-by-step explanation:
The diameter of the semicircle can be found by the use Pythagoras theorem.
Δx²+Δy²=d²
Δx=3--1=4
Δy=3--6=9
d²=4²+9²
d=√(16+81)
Area=πr²/2
=π×(√(16+81)/2)²÷2
=[π×(97)/4]/2
=97π/8
=18+12.125π units²
97π/8 is equivalent to 18+12.125π units²
Answer:
18+12.125π units²
I tooked the test (●'◡'●)
Step-by-step explanation: