The sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Let us assume: 3 consecutive integers are x, x+1 , x+2.
on adding these three numbers we get,
x + x+1 + x+2 = 3x + 3
which can be further reduced to the form 3(x+1).
If you add any 3 consecutive numbers together it will always equal a multiple of 3, e.g.
1+2+3=6
2+3+4=9
3+4+5=12
4+5+6=15
5+6+7=18
Thus , the sum of 3 consecutive numbers is always of the form 3(x+1) which is always a multiple of 3.
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How do you solve the mean step by step?
The two steps for calculating the mean:
Add up all the values in the data set.
Divide this number by the number of values.
The mean of a dataset is the sum of all values divided by the total number of values. It’s the most commonly used measure of central tendency and is often referred to as the “average.”
There are two steps for calculating the mean [tex](\bar{x})[/tex]:
(1) Add up all the values in the data set.
Sum of all the observations of given data denoted by [tex]\sum x[/tex]
(2) Divide this number by the number of values.
The total number of values of given data denoted by 'n'
Sample mean:
[tex]$$\overline{x}= \frac{\sum x}{n} $$[/tex]
Example: Find the mean step by step?
42, 13, 31, 87, 24, 58, 76, 69
Solution:
Step 1: Find the sum of the values by adding them all up.
[tex]\sum x=[/tex] 42 + 13 + 31 + 87 + 24 + 58 + 76 + 69 = 400
Step 2: Divide the sum by the number of values
In the formula, n is the number of values in your data set. Our data set has 8 values.
[tex]$$\overline{x}= \frac{\sum x}{n} $$[/tex]
[tex]$$\overline{x}=\frac{400}{8}[/tex]
[tex]$$\overline{x}[/tex] = 50
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Answer: okay so you add all of the numbers in the data set and then divide by how many numbers there were in the set.
Step-by-step explanation:
Calculate the perimeter of the irregular shape please show ur work because i have too
Answer: 34cm
Step-by-step explanation:
4cm + 3cm = 7cm
9cm - 7cm = 2cm
The missing value is 2cm
Leading the perimeter to be 34cm
What are the possible rational zeros of F X X 4 2x 3 3x 2 4x 20?
The possible rational zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.
What is mean of rational zero ?
A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.
By Rational Zero Theorem,
If P(x) is a polynomial with integer coefficients and if is a zero of P(x) i.e.,(P( ) = 0),
then p is a factor of the constant term of P(x)
q is a factor of the leading coefficient of P(x)
Possible value of rational zero is p/q
Have given, f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex]
Here, constant term, p = +20
Leading coefficient, q = +1
The factors of the constant term +20 are ±1, ±2, ±4, ±5, ±10, ±20.
The factor of the leading coefficient is ±1.
Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 2x^{3} - 3x^{2} - 4x +20[/tex] are ±1, ±2, ±4, ±5, ±10, ±20.
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What must be added to 2x² 5x 6 to get X³ 3x² 3x 5?
To obtain xA³ + 3xA² + 3x + 5 we msut add xA³ + xA² - 2x - 1 to
2xA² + 5x + 6.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, A polynomial 2xA² + 5x + 6.
Now, We know we can do arithmetic operations on like terms.
So to obtain xA³ + 3xA² + 3x + 5 we must subract 2xA² + 5x + 6.
Therefore, ( xA³ + 3xA² + 3x + 5) - (2xA² + 5x + 6).
= xA³ + xA² - 2x - 1 should be added to obtain xA³ + 3xA² + 3x + 5.
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PLEASE HELP!!!!!!
This visual representation shows the sets of real numbers. Which statement is true regarding the number sets? Responses Integers and rational numbers have no numbers in common. Integers and rational numbers have no numbers in common. Some integers are also rational numbers, but not all integers are rational numbers. Some integers are also rational numbers, but not all integers are rational numbers. All rational numbers are also integers. All rational numbers are also integers. All integers are also rational numbers. All integers are also rational numbers.
All integers are also rational numbers.
How do you identify a rational number?Integers, fractions, decimals, and more are all included in the set of rational numbers. The term "rational numbers" refers to all numbers that may be written as ratios with a non-zero denominator.We attempt to express an integer as a ratio of two numbers in order to determine whether it is a rational number. Writing it as a fraction with one as the denominator is a simple approach to accomplish this. All integers are rational numbers because any integer may be expressed as the ratio of two other integers.Any number that cannot be stated as a fraction for any integers is considered to be irrational. The decimal expansions of irrational numbers are neither periodic nor do they come to an end.To learn more about rational numbers refer,
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Raven can walk 2 2/5 miles in 3/5 hour.
At this rate, how far can she walk in 1 hour?
The distance traveled by Raven in 1 hour at the given rate is 4 miles.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
Raven can walk 2 (2/5) miles in 3/5 hours.
so,
2 (2/5) = 0.6 hours.
12/5 = 0.6 hours.
2.4 = 0.6 hours.
then,
if 2.4 = 0.6 hour
for x = 1 hour
By cross multiplying:
x = 2.4/0.6 miles
= 4 miles
Hence, the distance traveled by Raven in 1 hour at the given rate is 4 miles.
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Probability and Statistics - Colored Points Six points are drawn from uniform distribution U10,1]. The first three points are marked green and the next three are marked red on the real line. What is the probability that all adjacent points differ in color? Pick one of the choices 1/20 1/10 1/6 1/5 Clear selection Probability and Statistics - Dice Consider an unbiased six-faced dice with integers 1 through 6 marked on the faces. Assume the dice is thrown repeatedly, until the sum of the numbers cast till that point is a multiple of 6. What is the expected number of throws? Pick one of the choices 03 4.5 Clear selection
The probability that all adjacent points differ in colour is [tex]\frac{1}{5}[/tex].
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given ,
We have first three colour Green that is g1 , g2 and g3
And We have next three colour red that is r1 , r2 and r3
The probability that all adjacent points differ in colour = 3! * [tex]^{4}C_{3}[/tex] 3! / 6!
=> [tex]\frac{ 3! * 4! *3!}{6!}[/tex]
=> [tex]\frac{1}{5}[/tex]
The probability that all adjacent points differ in colour is [tex]\frac{1}{5}[/tex].
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Ursula pours equal volumes of vinegar into five separate containers. The total volume of vinegar in the five containers is one liter. What is the volume of vinegar in each container? 0. 02 milliliters 0. 20 milliliters 20 milliliters 200 milliliters.
The volume of vinegar in each container is 200 milliliters.
Since the total volume of vinegar in the five containers is one liter, and a liter is equal to 1000 milliliters, the volume of vinegar in each container is 1000/5 = <<1000/5=200>>200 milliliters.
The amount of space a container encloses, or how much room is inside of it, is measured by its volume. The volume of a box is easily calculated using the following formula: Volume of a box with dimensions H, W, and L is equal to L×W×H. Many different units can be used, however because of the way this formula is stated, the volume would have length to the third power dimensions. For instance, if the container's measurements are given in meters, the capacity of the box will be given in meters cubed, or m³.
The volume of vinegar in each container is 200 milliliters.
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Since the total volume of vinegar in the five containers is one liter, and a liter is equal to 1000 milliliters, the volume of vinegar in each container is 1000/5 = <<1000/5=200>>200 milliliters.
A container's volume is a measure of how much space it contains or how much space is inside of it. The following formula makes calculating a box's volume simple: LWH is the volume of a box having the dimensions H, W, and L. Although many various units can be used, the volume would have length to the third power dimensions due to the way this formula is written. For instance, the capacity of the box will be specified in meters cubed, or m3, if the container's dimensions are given in meters.
The volume of vinegar in each container is 200 milliliters.
A soccer coach has $265 to buy packs of bottled water for her team this season. Each pack costs $8. If the coach buys as many packs as she can, how much money will she have left?
Answer: She can buy a total of 33 packets and have 25 cents leftover.
Step-by-step explanation:
Answer:
she will have $1 left
Step-by-step explanation:
265÷8=33.125 or 33 1/8
she will have $1 left
What is the slope of the line segment − 3 3?
The shift in the line's y coordinate relative to its x coordinate is known as the slope of a line. The slope of the given line graph is 3.
Calculating the slope of a lineThe slope of a line is defines as the change in the y coordinate of the line to the x-coordinate. Mathematically, the slope of a line is expressed according to the formula below:
Slope = y₂-y₁/x₂-x₁
Using the following coordinate from the given graph (0, 0) and (1, 3), we will substitute the coordinates into the formula to have:
Slope = 3-0/1-0
Simplify to have:
Slope = 1/3
Slope = 3
Hence the slope of the given line graph is 3.
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The number of cubes form a pattern.
a) Draw an expression for the number of cubes in figure n.
b) How many cubes are there in the 50th figure?
c) What number has the figure consisting of 156 cubes
Answer:
in the 50th cube I think it's 250, because your just adding 5 each time, and for the cube equal to 156 that is uh I don't really know, try the 50th one, because 5x50 is 155
Step-by-step explanation:
I am so sorry if I'm wrong.
What is the factor of 3x² 2x 1?
Therefore, the solution to the given problem of the equation whose factors are (3x - 1)(x + 1).
Examine the equation.
An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. This equation's solution reveals that the value of the variable x is 5.
According to the given question:
Given : 3x² + 2x - 1
Factorizing using splitting the middle term
= 3x² + 3x - x - 1
= 3x(x + 1) - 1(x + 1)
= (3x - 1)(x + 1)
Therefore , the solution to the given problem of the equation whose factors are (3x - 1)(x + 1) .
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What is the mode of 1234?
There is no mode in the given data.
To find: Mode of the given data.
Given data is 1, 2, 3, 4
Mode: The mode of data is the observation having the highest frequency in a set of data. There is a possibility that more than one observation has the same frequency, i.e. a data set could have more than one mode. In such a case, the set of data is said to be multimodal.
The data is already arranged in ascending order. Therefore, there is no need to arrange the data in increasing order.
Constructing the frequency for given data:
Number: 1 2 3 4 5
Frequency: 1 1 1 1 1
Since the frequency of all the numbers are same, therefore, there is no specific mode for the given set of data distribution.
Conclusively, if no numbers in the data distribution are repeated, then there is no mode for such observation.
Therefore, there is no mode for given data.
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Which statement best describes the current price for the good shown in this graph of supply and demand schedules? A. The current price should be raised to reflect lower supply. B. The current price reflects the point where supply and demand are balanced. C. The current price should be lowered to reflect higher supply. D. The current price should be lowered to reflect lower demand.
According to this graph of supply and demand schedules, the current cost of the good is:
The price should increase to reflect the reduced supply at this time.What is meant by demand schedule ?A demand schedule in economics is a table that displays the quantity demanded of an item or service at various price points. On a graph where the X-axis is quantity and the Y-axis is price, a demand schedule can be represented as a continuous demand curve.
A demand schedule, also known as a tabular representation or statement, displays the various quantities of goods that are wanted at various price points throughout a given time period. The precise quantity of goods and services that will be purchased at each price will be shown on a demand schedule.
The complete question is : Which statement best describes the current price for the good shown in this graph of supply and demand schedules? A. The current price should be raised to reflect lower supply. B. The current price reflects the point where supply and demand are balanced. C. The current price should be lowered to reflect higher supply. D. The current price should be lowered to reflect lower demand.
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5. The equation y = 1/3(x-6)² + 6 is shifted 3 units to the left and 7 units up.
What is the value of h in the new equation?
A.-6
B. -3
C. 13
D. 3
Answer:
D. 3
Step-by-step explanation:
Initially, the vertex is at [tex](6,6)[/tex]. After the transformation, the vertex moves to [tex](3,13)[/tex].
So, [tex]h=3[/tex].
if (x+a) is a factor of x^2+px+q and x^2+mx+n, then prove that a=(n-q) /(m-p)
Given polynomials are,
[tex]\rm{f(x)=x^2+px+q}[/tex]
[tex]\rm{g(x)=x^2+mx+n}[/tex]
According to Remainder Theorem, if (x + a) is a factor of f(x), then,
[tex]\longrightarrow\rm{0=f(-a)}[/tex]
[tex]\longrightarrow\rm{0=(-a)^2+p(-a)+q}[/tex]
[tex]\longrightarrow\rm{0=a^2-pa+q\quad\dots(1)}[/tex]
Similarly, if (x + a) is a factor of g(x), then,
[tex]\longrightarrow\rm{0=g(-a)}[/tex]
[tex]\longrightarrow\rm{0=(-a)^2+m(-a)+n}[/tex]
[tex]\longrightarrow\rm{0=a^2-ma+n\quad\dots(2)}[/tex]
Subtracting (2) from (1),
[tex]\longrightarrow\rm{0=(a^2-pa+q)-(a^2-ma+n)}[/tex]
[tex]\longrightarrow\rm{0=a^2-pa+q-a^2+ma-n}[/tex]
[tex]\longrightarrow\rm{0=(m-p)a+q-n}[/tex]
[tex]\longrightarrow\rm{0=(m-p)a-(n-q)}[/tex]
[tex]\longrightarrow\rm{(m-p)a=n-q}[/tex]
[tex]\longrightarrow\rm{\underline{\underline{a=\dfrac{n-q}{m-p}}}}[/tex]
Hence Proved!
3. Convert 78.125 to degrees, minutes, seconds.
The angle 78.125° is rewritten as 78 degrees 7 minutes and 30 seconds.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The angle is given below.
⇒ 78.125°
Convert the decimal part into minutes and seconds. Then we have
⇒ 78° + 0.125 x 60
⇒ 78°7.5'
⇒ 78°7' + 0.5 x 60
⇒ 78°7'30''
The angle 78.125° is rewritten as 78 degrees 7 minutes and 30 seconds.
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Is infinity positive or negative?
if the woman and a man with normal clotting function have children, what is the probability of their children exhibiting hemophilia a?
A man who has hemophilia and a woman who is a carrier has:
a 25% (one in four) chance of having a son with hemophiliaa 25% chance of having a son with normal blood clottinga 25% chance of having a daughter who is a carriera 25% chance of having a daughter who has hemophiliaA hemophilia carrier is what?
Both an X chromosome from the mother and an X chromosome from the father are passed down to a daughter. Let's say the gene for typical blood coagulation is present on her mother's X chromosome. Let's say her father's X chromosome carries the hemophilia gene.
Since the normal blood clotting gene from the mother is dominant, the daughter won't get hemophilia. The hemophilia gene's instructions cannot be transmitted because of this.
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If PR= 12x- 8, RQ = 9x+26, and PQ = 144, calculate the length of RQ
Answer:-21788
Step-by-step explanation:
Is AAS and ASA congruence are same?
No, AAS ( Angle , Angle , Side) congruence postulate is not same as ASA (Angle, Side, Angle) congruence postulate, because in AAS consists one equal side between both triangles either it PR = AC or PQ = AB . But ASA must include side equality in this case i.e BC = QR and both are not same.
Two triangles are said to be congruent if they have all three same angles as well as same sides. AAS and ASA are basic methods through which we can prove that two triangles are congruent. So, to check that wheather both methods are same we will take one example of two triangles. So, consider two triangles, ∆ABC and ∆PQR as seen above in figure, ∠ ABC = ∠ PQR = 40° and ∠ACB = ∠ PRQ = 80° and AC = QR
According to AAS rule, if two pairs of corresponding angles with opposite or non- including side is same and the equality in opposite sides are equal to each other then the triangles are congruent. We have ,
∠ PRQ = ∠ ACB , ∠ABC = ∠PQR
and either PR = AC or PQ = AB.
if the above three conditions are satisfied then ∆ABC congruent to ∆PQR.
According to ASA rule , if two angles of one triangle with one side contained between two angles are respectively equal to two angles of another triangle and one side contained between them , then triangles are congruent. We have, ∠ R =∠C , ∠B = ∠Q and BC = QR
if the above three conditions are satisfied then both triangles are congruent. As we see clearly both congruence postulates are not same.
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What is the value of the discriminant of the given equation 2x² 4x 3?
the value of the discriminant of the given equation is -20.
The discriminant of a quadratic equation is a value derived from the coefficients of the equation that can be used to determine the number and type of solutions of the equation. The discriminant of a quadratic equation in the form ax2 + bx + c is calculated by the formula b2 - 4ac. In this case, the equation is 2x2 + 4x + 3. Plugging the coefficients into the formula, we get (4)2 - 4(2)(3) = -20. Therefore, the value of the discriminant of the given equation is -20.
(4)2 - 4(2)(3) = 16 - 24 = -8
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What is the median of 7 3 5 8 6 10 9 12?
For a given collection of data, the median is 7.
What is median?The median is the value in the center of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. The median is the value in the center of a group of numbers. The median corresponds to the 50th percentile of the collection of numbers. In other terms, the median is the value in the center of a group of numbers where half of the values are less than the median and half are more than the median.
Here,
First we have to arrange the numbers in ascending order.
3,5,6,7,8,9,10,12
There are 8 terms.
8 is an even number
So the median term is 8÷2=4th term
4th term =7
The median for given set of observations is 7.
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9. Given the graph of f(x), what is the quadratic equation in root form.
| 1(x)
A. f(x) = 2(x + 32)² + 1
B. f(x) = 2(x - 3)(x + 5)
C. f(x) = 2(x - 1)² - 32
D. f(x) = 2(x + 3)(x - 5)
OA
(-3,0)
OB
(1, -32)
(5,0)
Answer:
[tex]f(x)=2(x+3)(x-5)[/tex]
Step-by-step explanation:
Using the roots, [tex]f(x)=a(x+3)(x-5)[/tex].
Using the point [tex](1,-32)[/tex] to solve for [tex]a[/tex],
[tex]-32=a(4)(-4) \\ \\ -32=-16a \\ \\ a=2 \\ \\ \\ \therefore f(x)=2(x+3)(x-5)[/tex]
What is the area of a 4cm circle?
the area of 4 cm circle is 12.568 cm² whose radius is 2 cm
What is circle?the round shaped figure having a fixed center and specific diameter is called circle.
how to measure area of circle?area of a circle having known radius is calculated by the formula
A =πr²
r is the radius of circle
in the above question 4cm circle refer the diameter of circle is 4cm
so, radius is r= 2 cm
Area = 3.142x2²
12.568 square cm
hence, area is 12.568 square centimeters.
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Answer:
i just want the points
Step-by-step explanation:
There is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons. 3 cups is equivalent to 48 tablespoons, is plotted in the graph. For which value y is (1,y) on the line you just drew?
Since there is a proportional relationship between a volume measured in cups and the same volume measured in tablespoons, the value of y in the ordered pair (1, y) is 16.
How to determine the volume measured in tablespoons?Mathematically, a proportional relationship or direct variation can be represented by the following equation:
y = kx
Where:
k is the constant of proportionality.y represents volume measured in tablespoons. x represents the volume measured in cups.In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality. Next, we would determine the constant of proportionality (k) based on the given parameters:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 48/3
Constant of proportionality (k) = 16.
Therefore, a linear equation that relates the volume measured in tablespoons (y) and volume measured in cups (x) is given by;
y = kx
y = 16x
When x = 1 cups, the value of y is given by;
y = 16(1)
y = 16 tablespoons.
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If you have dimes, quarters and 1-dollar bills, in how many ways can you make up $2? THIS IS URGENT PLS HELP
Answer:
9 ways
Step-by-step explanation:
2 × $1
1 × $1 + 4 × $0.25
1 × $1 + 2 × $0.25 + 5 × $0.10
1 × $1 + 10 × $0.10
8 × $0.25
6 × $0.25 + 5 × $0.10
4 × $0.25 + 10 × $0.10
2 × $0.25 + 15 × $0.10
20 × $0.10
I count 9 ways.
Word Problem The number of people who bought admission to the movies last Saturday was 215. Admission was $7.89. Estimate the amount of money that the movie brought in.
Answer:
Step-by-step explanation:
7.89 is about 8 so we can multiply 215*8 to get 1720 dollars
Answer:
$1696.35
Step-by-step explanation:
$7.89 × 215 = $1696.35
Brainliest, please!What is the set formula?
The formula of the set is generally written as follows.
The term set in math is defined as an organized collection of objects and can be represented in set-builder form or roster form.
Here we need to find the formula that can be used in set.
The general formula of the set can be written as follows:
=> n ( P ∪ Q ) = n(P) + n(Q) – n ( P ∩ Q)
where
n(P U Q) refers the number of elements present in one of the sets P or Q.
n(P ⋂ Q) refers the number of elements present in both the sets P & Q.
Where as If P ∩ Q = ∅, then the value is calculated as,
=> n ( P ∪ Q ) = n(P) + n(Q)
Here we have also want to know that sets P and Q are equal only if all the elements they contain intersect, and none of them have any unique elements which are not present in the other set.
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help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
From above graph
(A) The domain can be best described using
Interval notation
The domain is
-infinity , infinity
(a) The range cambe best described wing
Interval notation
The range is [4, infinity )