the middle value in a data set when the values are put in order
For example, the set {3,1,2} sorts to {1,2,3} where the median is 2.
Another example: The set {1,2,3,4} has 2 and 3 tied for the middle most position. The midpoint is (2+3)/2 = 5/2 = 2.5 which is the median.
What is 2 polynomials called?
Binomial is the referred to the polynomial algebraic expression that has two terms.
What is Binomial?An expression with two dissimilar terms joined by an addition or subtraction operator is called a binomial in algebra. Since there are two terms, for instance, 2xy + 7y is a binomial. According to the quantity of terms present, algebraic expressions can be divided into different types, such as monomial, binomial, trinomial, etc.
An expression in algebra with two terms is called a binomial. Alternatively stated, a binomial expression is an algebraic expression made up of two terms that are dissimilar and have constants and variables. Using mathematical operators like + (plus) and - (minus), these terms are joined. Depending on how many terms it contains, an algebraic expression is classified as a binomial, monomial, trinomial, quadrinomial, etc.
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which statement correctly compares the function shown on this graph with
the function y = 4x + 2?
A. The function shown on the graph has a smaller rate of change, but
a higher starting point.
O B. The function shown on the graph has a greater rate of change, but
a lower starting point.
C. The function shown on the graph has a greater rate of change and
a higher starting point.
D. The function shown on the graph has.a omaller rate of change and
a lower starting point.
B. The function shown on the graph has a smaller rate of change, but a higher starting point.
What is rate of change in linear graph?Rate of change = slope of a linear graph.
Given the linear function, [tex]y=4x+2[/tex] , the rate of change here is represented by the slope of the line, which is 4.
Let's find the rate change of the function represented on the graph using slope formula:
Rate of change = [tex]\frac{y2-y1}{x2-x1}[/tex]
Use coordinates of any two points on the line. Let's take,
[tex](0,4)= (x1,y1)\\(1,7)=(x2,y2)[/tex]
Rate of change = [tex]\frac{7-4}{1-0} = 3[/tex]
Rate of change of the linear function of the graph = 3.
Thus the function on the graph has a smaller rate of change, than the function, y = 4x + 2.
The starting value of a function is the y-intercept, that is, the value of y, when x = 0. It is the point at which the line intercepts the y-axis.
The starting value of the linear function, y = 4x + 2 is 2.
The starting value of the function on the graph is 4. At this point, x = 0.
Thus, the function on the graph has a higher starting point.
The statement that correctly compares the function shown on this graph with the function y= 4x+2 is:
B. The function shown on the graph has a smaller rate of change, but a higher starting point.
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Suppose Johnny applied for a job at companies A and B.
Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A, a 50%
chance of getting a job offer from company B, and a 30% chance of getting a job offer from both companies A and B.
What is the probability of Johnny not getting a job offer from either company?
The probability of Johnny not getting a job offer from either company is 0.8
Suppose Johnny applied for a job at companies A and B.
Through extensive research, Johnny determined he has a 60% chance of getting a job offer from company A,
A = 0.6
a 50% chance of getting a job offer from company B,
B = 0.5
and a 30% chance of getting a job offer from both companies A and B.
What is the probability of Johnny not getting a job offer from either company?
Suppose, probability of an event A occurring is P(A)
and that of is B IS P(B)
P(A) = 0.6
and
P(B)= 0.5
probability of either or P(AUB)=0.3
Now we need to find the probability of neither nor, which is
P(A∪B) = P(A) + P(B) - P(A∩B)
P(A∩B) = P(A) + P(B) -P(A∪B)
= 0.6 + 0.5 - 0.3
= 0.8
Now the events are mutually exclusive, so
Therefore, the probability of neither nor is 0.8
The probability of Johnny not getting a job offer from either company is 0.8
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Rewrite 16r²s² as a power of a product.
The solution is
[tex]16r^2s^2[/tex] as the product of power is written as [tex](4rs)^2[/tex]
How would you characterize a product's strength?The power of a product rule states that [tex](a^m)(a^n) = a^(m+n)[/tex], where "a" is the base, "m" is the exponent of the first term, and "n" is the exponent of the second term. This rule allows us to simplify expressions where multiple variables are being raised to a power and multiplied together by adding the exponents.
For example, [tex](a^2)(a^3) = a^(2+3) = a^5[/tex].
It is also important to remember that when we are using the power of a product rule, the bases must be the same. If we have different bases, we cannot use this rule.
For example, [tex](a^2)(b^3) = a^2 * b^3, not a^(2+3) = a^5[/tex].
Rewritten as power of product:
[tex]16r^2 s^2= 4*4*r*r*s*s\\16r^2s^2= 4^2*r^2*s^2\\16r^2s^2=(4rs)^2[/tex]
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help me i been stuck for like a good 20 min
[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]
notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.
A utility pole is 5 ft high. A 8 ft cable is stretched from the top of the pole to a stake in the ground. How far is the stake from the pole?
The distance between the stake from the pole is 6.25 ft.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that a utility pole is 5 ft high. An 8 ft cable is stretched from the top of the pole to a stake in the ground.
The distance will be calculated as,
B² = H² - P²
B = √(8² - 6²)
B = √ ( 64 - 36 )
B = √39
B = 6.25 ft
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Which expression can be used to represent the
volume of this prism?
6 × 11 units³
78°F
Sunny
O 48 x 3 units³
O 14 x 3 units³
O 8x9 units³
H
а
1
i
8 units
1
1
2
3
3 units
6 units
4
5
Volume of prism is given by V= base area × height cubic unit. The expression 48 × 3 unit³ can be used to represent the volume of the prism.
What is prism?Prism is a three-dimensional geometrical figure having identical two ends. A prism has flat faces, similar bases and equal cross sections. A prism is normally bounded by plane faces.
What is volume of prism?
Volume of prism is calculated by the product of base area and height of the prism. At first, we need to calculate the base area and then height is multiplied with it.
Prisms are different types such as triangular prism, rectangular prism, pentagonal prism and hexagonal prism so depending on the figure area for the base is different. As a result, different shaped prism has different formula for volume calculation.
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Why is the sine of an acute angle less than one?
The sine of an acute angle is less than one because it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio is always less than one.
To what does sin equate?
In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.
It's also the same reason why the cosine of an acute angle is always less than one because it is the ratio of the adjacent side of the angle to the hypotenuse.
It's important to note that this is only true for acute angles, angles smaller than 90 degrees.
For obtuse angles, greater than 90 degrees, the sine and cosine values are greater than one.
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Sarah has 3 bags of marbles. Each bag has 16 marbles. If 3/4 of the marbles are blue, what is the total number of blue marbles in the bags?
Answer: 12
Step-by-step explanation: 3/4 divid by 3
Find the derivative of the function.
F(x) =
x2 integral et7dt
x
The requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].
What is implicit differentiation?The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol
here,
Given expression,
[tex]F(x) = \int\limits^{x^2}_x {e^{t^7}} \, dx[/tex]
Following the Leibniz rule
[tex]F'(x) = \frac{d}{dx}[ \int\limits^{x^2}_x {e^{t^7}} \, dx]\\F'(x) = \int\limits^{x^2}_x \delta/\delta x (e^{t^7}) + (e^{(x^2)^7}) d/dx (x^2) - e^{x^7}d/dx [x] \\F'(x) = 0 + 2xe^{x^{14}} - e^{x^7}\\F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex]
Thus, the requried derivative of the given function is [tex]F'(x) = 2xe^{x^{14}} - e^{x^7}[/tex].
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9. Isosceles trapezoid ABCD has legs AB and CD, and base BC.
If AB = 4y - 6, BC = 2y - 3, and
CD = 3y - 4.
Find the value of y. (hint: draw it to help!)
Therefore , the solution of the given question of triangle comes out to be y=2.
Defining a triangleYou can link any three points in a plane to form triangles, which have three sides and three angles. They were among of the first geometric forms to be examined. Since triangles may be divided into any polygon, regardless of whether it has four, five, six, or n sides, they are very significant.
Here,
Since it is an isosceles trapezoid the length of the two legs (i.e. AB = 4y - 6 and CD = 3y - 4) are equal. In other words,
4y - 6 = 3y - 4.
Subtract 2y from each side:
4y - 3y - 6= -4
Now add 10 to each side
=> 4y - 3y - 6 + 4
=> y - 2 =0
=> y = 2
Therefore , the solution of the given question of triangle comes out to be y=2.
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Please Answer This For Me<33
Answer:
a) 4.2 - 2.8 = 1.4
b) 72.1 - 45.6 = 26.5
c) 82.2 - 41.3 - 29.2 = 11.7
d) 17.1 - 11.7 - 0.8 = 4.6
e) 29.2 - 12.5 - 0.9 = 15.8
f) 21 - 14 = 7
g) 71 - 37 - 18 = 16
h) 50 - 19 - 8 = 23
i) 92 - 57 - 16 = 19
j) 44 - 18 - 9 = 17
50% of 188 is equal to what number?
Answer:
Step-by-step explanation:
a.50%=[tex]\frac{1}{2}[/tex]
b.so 50% of 188 means 188·[tex]\frac{1}{2}[/tex]=94
answer is 94
Mason has 2 1/2 cups of peanut
butter. He is making peanut butter
sandwiches. If he uses 1/8cup of
peanut butter in each sandwich,
how many sandwiches can he
make?
Help
Answer:
Mason can make 20 sandwiches.
Step-by-step explanation:
2 1/2 ÷ 1/8 = 20SU is a midsegment of QRT
If QR=-5v+96 and SU = 19v-38 than what is the value of X
Answer:
v = 4
Step-by-step explanation:
⭐What is the midsegment of a triangle?
a segment that runs from the midpoints of two opposite sides⭐What are some properties of the midsegment?
the midsegment is 1/2 of the length of the baseThus, we have to make an equation using the properties of the midsegment to solve for v.
Working:
[tex]SU = \frac{1}{2}(QR)[/tex]
[tex]19v - 38 = \frac{1}{2}(-5v + 96)[/tex]
[tex]38v - 76 = -5v + 96[/tex] . . . . . multiply both sides by 2 to get rid of the fraction
[tex]43v = 172[/tex] . . . . . add 5v and 76 to both sides
∴ [tex]v = 4[/tex] . . . . . . . . . divide both sides by 43 to isolate v
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What does Scrooge see out of the window when Marely leaves?
(A Christmas Carol) (it was an English question)
Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.
What is the ghost?Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.
Here, we have,
Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.
Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.
Therefore, option B is the correct option.
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-97.54 es racional o irracional
Respuesta: Racional
Explicación:
El número es racional ya que podemos representarlo como una fracción de enteros.
Más específicamente, -97.54 = -9754/100
-----------------------------------------------------------------------------
Translation to English:
Answer: Rational
Explanation:
The number is rational since we can represent it as a fraction of integers.
More specifically, -97.54 = -9754/100
Where is the graph of inequality 2x 3y 6 lies?
The graph of the inequality 2x+3y>6 is a half-plane the neither contains origin nor the points of the the line 2x+3y=6.
A linear inequality is a mathematical statement involving a linear function and one of the symbols <, >, ≤, or ≥. It represents a range of values for the variables that satisfy the inequality. The solution to a linear inequality is the set of all points that make the inequality true. These points form a region in the coordinate plane, which is known as the solution set. The solution set can be represented graphically as a half-plane, a line, or a combination of lines and half-planes, depending on the inequality.
The graph of the inequality 2x+3y>6 is the set of all points (x,y) that satisfies the inequality 2x+3y>6. It can be represented by a line 2x+3y=6 and all the points on one side of the line. This side is determined by the inequality sign ( > in this case).The side is away from the origin and the line 2x+3y=6 is the boundary line, and all the points on one side of the line satisfy the inequality while all the points on the other side do not.
The line 2x+3y=6's origin and its points are not present on the half-plane that represents the inequality 2x+3y>6.
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What is the solution to the equation 9(x + 2) = 27?
A. x = 2.5
B. x = 0.5
C. x = −0.5
D. x = −3.5
Find the area of the right triangle below.
9m
4m
Area = 1/2*base*height = 1/2*9*4 = 18 sq.m
The length and breadth of the three rectangles are as given below:(a) 9 m and 6 m(b) 17 m and 3 m(c) 4 m and 14 mWhich one has the largest area and which one has the smallest?Solution:
We will be using the area of rectangle formula to calculate the areas of the three rectangles given.
(a) Length(l) = 9 m and Breadth(b) = 6 m
Area of rectangle = l × b
= 9 × 6
= 54 m2
(b) Length(l) = 17 m and Breadth(b) = 3 m
Area of rectangle = l × b
= 17 × 3
= 51 m2
(c) Length(l) = 4 m and Breadth(b) = 14 m
Area of rectangle = l × b
= 4 × 14
= 56 m2
Therefore, the area of the rectangle with the dimensions 4m and 14m having an area of 56 m2 that is (c) has the largest area whereas, the area of the rectangle with dimensions 17m and 3m having an area of 51 m2 that is (b) has the smallest area.
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What’s the formula to find principal please tell me please
Answer:
Step-by-step explanation:
(100xInterest)(RatexTime)
hope this helps
Step-by-step explanation:
The formula for calculating Principal amount would be P = 100I / (RT) where Interest is Interest Amount, R is Rate of Interest and T is Time Period.
Thirty people are waiting in line at the cinema. Alex counts 13 people in front of him. Gina counts 21 people between her and Dana. What is the least possible number of people between Dana and Alex
Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are:
20.
What is the number line called?In advanced mathematics, the number line can be called as a real line or real number line, formally defined as the set R of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one.
Why is number line important?A number line is useful because it acts as a visual math aid. It can support teachers and parents as they teach children how to count and write numbers. It's also a tool that can help build understanding behind adding, subtracting, multiplying, and dividing numbers.
Let's assume that Gina is standing on first number while Dana on the last. Hence the total number of people in the line are: n= 23.Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are: (n-2) = 20.
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find the ratio of 15 min and 1 hrs.
Quadrilateral TEAMTEAMT, E, A, M i rotated -180^\circ−180
∘
minu, 180, degree about the origin
The quadrilateral's image points will be,A(3, 3) → A'(-3, 3) R(5, 7) → R'(-7, 5) M(7, 5) → M'(-5, 7) Y(5, 1) → Y'(-1, 5).
If a point (x, y) is rotated 180 degrees anticlockwise with respect to the origin, the rotational rule is:
(x, y) → (-y, x) (-y, x)
Consequently, the image point's coordinates following rotation will be (-y, x).
Using this guideline,
The quadrilateral's image points will be,
A(3, 3) → A'(-3, 3)
R(5, 7) → R'(-7, 5)
M(7, 5) → M'(-5, 7)
Y(5, 1) → Y'(-1, 5)
By graphing the image points we can get the graph of the image quadrilateral A'R'M'Y'.
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The question is incomplete, complete question:
Quadrilateral ARMY is rotated 180 degrees about the origin. Draw the image of this rotation.
Help ASAP!!!!!!!!!!!!!!!!
The correct order of match is 1-a, 2-b, 3-d and 4-c.
What are conic sections?The term "conic" refers to a curve formed by the intersection of a right circular cone with a plane. In Euclidean geometry, it has distinctive features. The cone is split into two nappes, the upper nappe and the lower nappe, at its vertex.
A plane crosses the cone, and the resulting section is referred to as a conic section.
Given the equations,
the equation for parabola is given by
(y - b)² = 4p(x - a)
Vertex is (a,b)
equation 2 follows the same
x = -2(y - 4)² + 3
this is the equation for parabola.
Equation for ellipse is
(x − a)²/h² + (y − b)²/k² = 1
the equation x²/4 + (y - 8)²/144 = 1
(x/2)² + ((y - 8)/12)² = 1
the equation is same is equation for ellipse,
Equation for circle
(x - h)² + (y - k)² = r²
fourth equation
(x - 9)² + (y + 2)² = 7²
is same as equation of circle
Equation for hyperbola
(x − a)²/h² − (y − b)²/k² = 1
equation (x - 3)²/5 - (y + 4)²/25 = 1
is same as equation of hyperbola.
Hence the correct order is a, b, d, and c.
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On a coordinate plane, polygon S prime T prime U prime V prime has points (negative 2, 4), (negative 4, 1), (negative 2, negative 2), and (0, 1).
Given the dilation rule DO,1/3 (x, y) → (one-third x, one-third y)
and the image S'T'U'V', what are the coordinates of vertex V of the pre-image?
(0, 0)
(0, One-third)
(0, 1)
(0, 3)
The vertex of V' had a preimage of V(0, 3) as V' has a dilation of 3.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, On a coordinate plane, polygon S'T'U'V' has points (- 2, 4), (- 4, 1),
(- 2, - 2), and (0, 1) with a dilation rule DO,1/3 (x, y) to [(1/3)x, (1/3)y].
Therefore, The coordinates of the vertex V had a preimage of,
3(V'), which is 3(0, 1) = (0, 3).
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The KOT club has 5 pledges. They will send at least 2 and no more than 4 pledges to work at Goodwill on Helping-Out Day. In how many ways can this be done?
Answer:
The KOT club has 5 pledges and can send between 2 and 4 pledges to work at Goodwill on Helping-Out Day. This can be done in 10 different ways
Step-by-step explanation:
What is line segment Theorem?
Line segment theorem states that if a line segment is bisected by another line, then the two parts of the line segment are equal.
This theorem is also known as the Midpoint Theorem. The formula for the Line Segment Theorem is A/B = C/D, where A and C are the two halves of the line segment, and B and D are the distances from the midpoint to the two endpoints of the line segment.
For example, consider a line segment AB with endpoints at A(-3, 2) and B(3, 2). The midpoint of the line segment is at (0,2). To calculate the length of each half of the line segment, we would use the distance formula and plug in the coordinates of the two endpoints and the midpoint.
For half A, the distance is d(A, M) = sqrt[(-3 - 0)^2 + (2 -2)^2] = 3.
For half C, the distance is d(M, B) = sqrt[(3 - 0)^2 + (2 -2)^2] = 3.
Therefore, A/B = 3/3 = 1 and C/D = 3/3 = 1. This confirms that the two halves of the line segment are equal in length.
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ENTERING INTERVAL ANSWERS. PLEASE SHOW YOUR WORK!!
The intervals that are equivalent to each inequality are given as follows:
2 < x ≤ 5: (2,5].x > 7: (7, ∞).Which interval represents each inequlity?The interval notation of an inequality of lower bound a and upper bound b is given as follows:
(/[a,b]/).
The closing notation can be in either parenthesis or brackets, as follows:
(: open interval.[: closed interval.For the first interval, 2 < x ≤ 5, it is an open interval at the lower bound of 2 and closed at the upper bound of 5, hence the notation is given as follows:
(2,5].
For the second interval, x > 7, we have that it has only a lower bound of 7, which is open. Hence, the upper bound is of infinity, and an infinite bound is always open, hence the notation is given as follows:
(7, ∞).
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Lesson 1. 12
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth.
Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point.
Assume at x= O the buoy is at normal ocean depth.
Find the following:
Period =
Equation of the mideline:
Amplitude =
Maximum =
Minimum =
For the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
What is the sine function?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Asin(Bx)+C is the usual sine function formula.
A buoy bobs 6 meters up and down.
That is, the amplitude of the buoy shifts by 6 meters both vertically and horizontally.
A=6 Amplitude
The x-axis distance that constitutes one complete oscillation is known as the period.
We are aware that it takes a buoy 10 seconds to go from its greatest position to its lowest point (half oscillation).
20 seconds make up the complete oscillation period.
⇒ 20 (B) = 2π
B=2π /20
= π/ 10
Given that the buoy is 10 meters under the ocean's surface, C equals –10.
Using the formula's whole range of values:
⇒y = 6sin ( (π/ 10) x ) - 10
The midline is the initial point.
x=0 is the first point.
⇒y=6sin(0)-10
y= -10
The line is drawn from the origin at y = -10.
Either the highest or smallest value is at the second point.
Therefore, (5,-4) and (15, -16.)
Therefore, for the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
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Complete question:
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.