Percentage change expresses the ratio of the change in the amount of an initial quantity to the initial quantity as a percentage.
What is the mathematical formula for percentage change?Mathematically, the formula for percentage change, C, can be presented as follows;
[tex]C = \dfrac{x_{2} - x_{1} }{ x_{1} } \times 100[/tex]
Where:C = The percentage change
[tex]x_{1} [/tex] = The original value
[tex]x_{2} [/tex] =The new value
Graphically, percentage change can be presented as follows;
When the number of fruits that drops from a three each month, changes from 10 to 8, the percentage change is therefore;
[tex] C = \dfrac{10-8}{10} = 20\% [/tex]The percentage change is 20%
Initial number of fruits that drops monthly from the tree;
##########
The new number of fruits that drops from the tree on the specified month;
########
The difference in the number of fruits that drops from the tree is 2, which corresponds to the 20 % calculated for the percentage change.
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1. Fill in the missing Terms for the sequence
2. Find the number the sequence is going by
3. Write the explicit formula
The answer r = 7, and the missing terms are -2, -14, -98, -686, -4802. in the Geometric progression.
What is Geometric progression?
A geometric progression, sometimes termed a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. A geometric progression with the common ratio 3 is, for instance, the sequence 2, 6, 18, 54,... A geometric series having a common ratio of 1/2 is also 10, 5, 2.5, 1.25, etc.
By calculating the product of the values of a set of numbers, the Geometric Mean (GM) is the average value or mean that denotes the central tendency of the data. The average of the data set's numbers is defined by the mean. There are several distinct forms of means, including arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM).
Here 1st term a = -2
4th term given is ar³= -686
r³= -686/-2
r=∛343
a) r=7
2nd term will be -14
3rd term will be -98
5th term will be -4802
b) -2, -14, -98, -686, -4802.
Hence, r = 7, and the missing terms are -2, -14, -98, -686, -4802.
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if one cup of pancake mix will yield 15 pancakes, how many cups of pancake mix will be required to yield 60 pancakes? report your answer as a whole number without any decimal places.
Using the concepts of unitary method, we got that 4 cups of pancake mix will be required to yield 60 pancakes.
The unitary method is the method for solving the problem by the first value of a single unit and then finding the value by multiplying the single value.
We are given that one cup of pancake mix will yield 15 pancakes, and we are asked to yield 60 pancakes.
So,15 pancakes will be yielded by as many as pancake mix=1
therefore, 60 pancakes will be yielded by as many as pancake mix=(60/15)=4.
Hence, if one cup of pancake mix will yield 15 pancakes, then 4 cups of pancake mix will be required to yield 60 pancakes.
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The width of a rectangle is 7 meters than it’s length. If the area of the rectangle is 170 square meters, what is the measure of its length and width
Answer:
[tex]\frac{\sqrt{170} }{7}[/tex]
Step-by-step explanation:
Length = x
Width = 7x
Therefore 7x into x = 170, Rectangle area formula
7x^2=170
7x=root over 170
x = root over 170/ 7
Suppose we are given the following.
Line 1 passes through (-3, 8) and (0,4).
Line 2 passes through (4, 4) and (-4,-2).
Line 3 passes through (4, 1) and (8,4).
(a) Find the slope of each line.
Slope of Line 1-
Slope of Line 2-
Slope of Line 3-0
(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2: OParallel
Line 1 and Line 3:
OParallel
Line 2 and Line 3:
OParallel
Operpendicular ONeither
Operpendicular
ONeither
OPerpendicular
Neither
Slope of line 1 is -4/3, slope of line 2 is 3/4, slope of line 3 is 3/4, and Line 1 and Line 2 are perpendicular, Line 1 and Line 3 are also perpendicular, Line 2 and Line 3 are parallel.
What is slope of a line?
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate points and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates on a line in order to determine its slope.
Slope of a line can be calculated using the formula:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, m = slope and (x1, y1), (x2, y2) are two points on the line,
Calculating the slope of line 1 whose points are (-3, 8), (0, 4)
[tex]m = \frac{4 - 8}{0 - (-3)}[/tex]
m = -4/3
Calculating the slope of line 2 whose points are (4, 4), (-4, -2)
[tex]m = \frac{-2 - 4}{ -4 - 4}[/tex]
m = 3/4
Calculating the slope of line 2 whose points are (4, 1), (8, 4)
[tex]m = \frac{4 - 1}{ 8 - 4}[/tex]
m = 3/4
Now we know that if lines are parallel that their slope is equal and when lines are perpendicular the product of their slope is -1,
Therefore, Line 1 and Line 2 are perpendicular, Line 1 and Line 3 are also perpendicular, Line 2 and Line 3 are parallel.
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The tens digit of a two-digit number is five more than the units digit. The number itself is equal to the sum of its digits multiplied by 8. Find the number
Answer:
72
Step-by-step explanation:
- reason why it's 72
tens ones
(2+5)=7 2
A/Q:
7+2=99*8=724x+y=104, x, plus, y, equals, 10
Complete the missing value in the solution to the equation.
Answer:36,37,38,39 one of the those or between
Step-by-step explanation:
Henry reads 3/5 chapters in 5/6 hours. What is the unit rate in chapters per hour? Write your answer in simplest form.
Answer:
18/25 chapters / hour
Step-by-step explanation:
Use a graphing calculator to find A1, if it exists.
A =
-5 -4 -5
-4 -4 -3
-1 -1 -1
The [tex]A^{-1}[/tex] for the matrix is
[tex]A^{-1} = \left[\begin{array}{ccc}-1&-1&8\\1&0&-5\\0&1&-4\end{array}\right][/tex]
How to find inverse of a matrix ?
Only square matrices with an equal number of rows and columns, such as 2 *2, 3* 3, etc., allow us to find the inverse of the matrix. The adjoint of the provided matrix is divided by the determinant of the given matrix to produce the inverse matrix, to put it simply.
[tex]A^{-1} = \frac{1}{|A|} Adj A[/tex]
|A|=-5(4-3)+4(4-3)-5(4-4)
|A|=-5+4
|A|=-1
[tex]Adj A = \left[\begin{array}{ccc}1&1&-8\\-1&0&5\\0&-1&4\end{array}\right][/tex]
[tex]A^{-1} = \frac{1}{-1}\left[\begin{array}{ccc}1&1&-8\\-1&0&5\\0&-1&4\end{array}\right][/tex]
[tex]A^{-1} = \left[\begin{array}{ccc}-1&-1&8\\-1&0&-5\\0&1&-4\end{array}\right][/tex]
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Which statement is the correct interpretation of the inequality –5 > –6? (1 point)
a
On a number line, −5 is located to the left of 0 and –6 is located to the right of 0.
b
On a number line, −5 is located to the right of 0 and –6 is located to the left of 0.
c
On a number line, −5 is located to the left of –6.
d
On a number line, −5 is located to the right of –6.
The correct statement of the inequality representation is d On a number line, −5 is located to the right of –6.
What is a number line?A number line is a horizontal representation of parts with equal intervals
The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values
-5 > -6
this is read as -5 is greater than -6 therefore
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The area of a circle is 25pieft2. What is the circumference, in feet? Express your answer in terms of pie
The circumference of the circle in feet is 10π feet.
According to the question,
We have the following information:
Area of the circle = 25π square feet
We know that the following formula is used to find the area of circle:
π[tex]r^{2}[/tex] where r is the radius of the circle
π[tex]r^{2}[/tex] = 25π
Dividing by π on both the sides:
[tex]r^{2}[/tex] = 25
r = 5 feet ...(1)
We know that the following formula is used to find the circumference of circle:
2πr
Putting the value of r from equation 1:
2π*5
10π feet
Hence, the circumference of the circle in feet is 10π feet.
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explain why the exterior angle of a regular polygon could be 20* 30* or 40* but not 50*
Answer:a polygon cannot have 7.2 sides
Step-by-step explanation:
each exterior angle of a regular polygon with n sides is equal and these angles add up to 360∘ . a polygon cannot have 7.2 sides. since , the exterior angle of a regular polygon cannot be 50∘
22 Of the 20 students in Kendra's class, 5 have black hair, 8 have blonde
hair, 5 have brown hair, and 2 have red hair. Kendra used the spinner to
find the experimental probability that this week's class leader will have b
blonde hair. She spun the spinner 15 times and recorded her results.
Black
Red
Brown
Blonde
Color
Black
Blonde
Number of Times
2
9
Brownelding
3
Red
1
What is the experimental probability that this week's class leader will
have blonde hair?
experimental probability = 0.6
What is experimental probability ?
Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A number of real experiments are carried out in order to ascertain the likelihood of any event. Random experiments are studies that don't have a predetermined outcome. The results of such experiments are unpredictable. The likelihood of random experiments is calculated repeatedly. A trial is a repeating of an experiment that is performed a certain number of times. The experimental probability's mathematical formula is denoted by;
Probability of an Event P(E) = Number of Trials / Total Number of Occurrences of an Event
15 times were used in the experiment by Kendra.
According to the table, out of the 15 instances, we receive a blonde class leader 9 times.
Therefore, the experimental likelihood that the class leader for this week has blonde hair is = [tex]\frac{n(blonde)}{n(all trails)} =\frac{9}{15} =\frac{3}{5} = 0.6[/tex]
0.6 will be the experimental probability that this week's class leader will
have blonde hair
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Could I get help with this?
Answer: convergencnt
Step-by-step explanation:
by collecting the appropriate data, the students can determine the relationship between the acceleration of the cart and the net force exerted on the cart. which of the following graphs should the students produce to show the correct relationship?
Force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity.
Forces it to accelerate in the direction of the force , this is a vector quantity that is represented in newtons.
net force = total pulling force = weight of the hanging mass.
Force will remain constant.
acceleration = constant pulling force / total mass to be pulled.
acceleration also remain constant.
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The product of 4 different positive integers is 30 .what is the sun of the integers
Answer:
11
Step-by-step explanation:
1x2x3x5 = 30 Product means the answer in a mulitplication problem.
Sum is the answer to an addition problem
1+2+3+5 = 11
[tex]\sf 10+2x=4[/tex]
Answer:
10+2x=4first, by using inverse operations subtract 10 on both sides.
10-10+2x=4-104-10 is -6. whys the 6 negative? because the number takes the sign of the bigge number.
2x=-6Divide by 2 to isolate x
2x÷2=-6÷2In multiplication and division one negative sign stays and 2 negative signs cancel eachother but here theres only one negative sign so;
~~~~~~~~~~~~~~~~
X=-3which of the following cannot be determined using only the information in the database? responses the date when a certain movie was purchased the greatest number of times the date when a certain movie was purchased the greatest number of times the number of movies purchased by an individual subscriber for a particular month the number of movies purchased by an individual subscriber for a particular month the total number of cities in which a certain movie was purchased the total number of cities in which a certain movie was purchased the total number of movies purchased in a certain city during a particular month
Answer: The answer would be B, The number of movies purchased by an individual subscriber for a particular month.
Step-by-step explanation:
Looking at the problem and graph it can be determined there is a day and date purchased. But there isn't a time frame over the course of a few months.
Using only the information in the database, we can conclude that the answer will be B, The number of movies purchased by an individual subscriber for a particular month.
There is a day and date purchased, it can be seen by looking at the problem and graph. But there isn't a timeline that spans several months. A graph is a diagram or visual representation that organizes the presentation of facts or values. The points on a graph are typically used to depict the relationships between two or more things. A straightforward two-dimensional graph is created when a vertical and horizontal line join at the origin. The y axis is vertical and the x axis is horizontal. In simple line graphs, the x and y axes are divided into evenly spaced subdivisions and assigned integer values.
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please help! ASAP! 50 points too whoever helps
Answer: 2050
Step-by-step explanation:
Solve the equation.
3(-2x+1)-2(x+13)=7x-4(1-x)
x=-1
Step-by-step explanation:
3(-2x+1)-2(x+13)=7x-4(1-x)
-6x+3-2x-26=7x-4+4x
-8x+3=7x-4+4x+26
-8x+3=7x+4x+22
-8x+3=11x+22
-8x-11x=22-3
-19x=19
-19/19x = 19/-19
x = -1
3/4x - 3 = 5/6 Rewrite the equation below so that it does not have fractions.
Do not use decimals in your answer.
Answer:
18x - 72 = 20
Step-by-step explanation:
[tex] \rm \implies \dfrac{3}{4} x - 3 = \dfrac{5}{6} \\ \\ \rm \implies \dfrac{3}{4} x - 3 \times \frac{4}{4} = \dfrac{5}{6} \\ \\ \rm \implies\dfrac{3}{4} x - \frac{12}{4} = \dfrac{5}{6} \\ \\ \rm \implies \frac{3x - 12}{4} = \frac{5}{6} \\ \\ \rm \implies \frac{3x - 12}{ \cancel{4}} \times \cancel{4} = \frac{5}{6} \times 4 \\ \\ \rm \implies 3x - 12 = \frac{20}{6} \\ \\ \rm \implies (3x - 12) \times 6 = \frac{20}{ \cancel{6}} \times \cancel{6} \\ \\ \rm \implies 18x - 72 = 20 [/tex]
Which decimal is equivalent to \
{31}{9}
9
31
start fraction, 31, divided by, 9, end fraction?
What effect do you think the sample size have on the mean of the sampling distribution of the mean?.
The effect that sample size on the mean of the sampling distribution has is that it effects the variations .
In the question ,
If the sample size is increased ,
which means if the number of sample is increased then the errors in the sampling distribution becomes very less .
and if the sample size is decreased then it leads to the increase in the error of the distribution .
The formula for the relationship between variation and sample size is given by ,
σx = σ / sqrt (n)
we can see that the variation and sample size are inversely proportional .
Which means that increase in the sample size results in a reduction of variation.
Therefore , The effect that sample size on the mean of the sampling distribution has is that it effects the variations .
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Find the fourth degree polynomial that contains the origin and to which the line x+2y=14 is tangent at both x=4 and x=-2.
Answer: 60,30,180, and 37
Step-by-step explanation:
5[tex]\sqrt{8}[/tex]simplified
Answer:
[tex]10\sqrt{2}[/tex]
Step-by-step explanation:
To simplify a square root you have to find any perfect square numbers.
(ex. 4, 9, 16, 25 ...)
[tex]\sqrt{8} = \sqrt{2*4} = \sqrt{2} * \sqrt{4}[/tex]
Simplify:
[tex]\sqrt{4} = 2[/tex]
[tex]2 \times \sqrt{2}\\ = 2\sqrt{2}[/tex]
Don't forget to multiply the 5, so:
[tex]5 \times 2\sqrt{2}\\ = 10\sqrt{2}[/tex]
IF LINE TV IS PARALLEL TO LINE ZX AND LINE ZX IS PARALLEL TO LINE QS, THEN IS LINE TV PARALLEL TO LINE QS BY TRANSITIVE PROPERTY?
Yes line TV is also parallel to line QS according to transverse property
What is transverse property?According to the transitive property, all the quantities are equal to each other if two quantities are equal to the third quantity.
When the term equal is replace by parallel it suits the case at hand hence transitive property of parallel lines is introduced
When attempting to demonstrate that several parallel lines have congruent properties, the transitive property of parallel lines can be used to create a link between numerous equal quantities.
Therefore, it can be interpreted as: if line TV || line ZX and line ZX || line QS then line TV || line ZX
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A recipe book shows measurement conversions for ounces to cups. It shows that 4 ounces converts to 0.5 cup and 12 ounces converts to 1.5 cups. Write an equation that shows the proportional relationship between cups and ounces where c represents cups and n represents ounces. c = 0.125n c equals 4 over 0.5 times n n equals 0.5 over 4 times c n = 0.125c
The equation that represents the proportional relationship between cups and ounces is n = 0.125c
The 4 ounce = 0.5 cup
Here we have to use the unitary method
Unitary method is the method of finding the value of the single unit
One ounce = 0.5 / 4
= 0.125
Where c represents the cups and n represents the ounce
Then,
n = 0.125c
Similarly
1.5 cups = 12 ounce
1 cup = 12 / 1.5
= 8 ounce
Then,
c = 8n
Then the the correct equation is n = 0.125c
Hence, the equation that represents the proportional relationship between cups and ounces is n = 0.125c
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Answer:
n = 0.125
Step-by-step explanation:
do not listen to the other answer I don't fell like explaining but I got it correct.
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (6, −1), and Monique's desk is located at (−3, 1). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
square root of 98 feet
square root of 85 feet
square root of 6 feet
square root of 5 feet
The distance between two points of a line is given as:
Distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2 }[/tex]
The distance from Maria's desk to Monique's desk is √85.
Option B is the correct answer.
What is the distance between two points of a line?The distance between two points of a line is given as:
Distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2 }[/tex]
We have,
Maria's desk.
We will write the coordinates in the form of (x, y).
(6, -1) = [tex](x_1, y_1)[/tex]
Monique's desk.
We will write the coordinates in the form of (x, y).
(-3, 1) = [tex](x_2, y_2)[/tex]
The distance between Maria's desk and Monique's desk.
= [tex]\sqrt{(-3 - 6)^2 + (1+1)^2 }[/tex]
= √(81 + 4)
= √85
Thus,
The distance from Maria's desk to Monique's desk is √85.
Option B is the correct answer.
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A basketball has a volume of about 452.1 cubic inches. Fine the radius of the basketball in inches
The radius of the basket ball having volume 452.1 cubic inches is 4.76 inches.
What is the volume?
Volume is the 3 dimentional occupied space by any object. It is measured in SI units [tex]\textnormal{m}^3[/tex] and other derived units like [tex]\textnormal{in}^3[/tex].
All properties of a spherical shape is defined by its radius. The shape of a basketball is spherical hence, the formula of the volume is given by the followin expression:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Here, V is the volume of the basket ball and r is the radius of the basket ball.
Rearrange the above equation for [tex]r[/tex].
[tex]3V=4\pi r^3\\\frac{3V}{4\pi}= r^3[/tex]
[tex]r=[\frac{3V}{4\pi}]^{1/3}[/tex]
Substitute values.
[tex]V=[\frac{3(452.1 \ \textnormal{cubic inches})}{4\pi}]^{1/3}\\=4.76 \ \text{inches}[/tex]
Hence, the radius of the basket ball is 4.76 inches.
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Why is the following no solution?
|x| = -5
sketch a graph that shows the relationship between grams of honey and cups of flour needed for a bakery recipe. Show on the graph how much honey is needed for 17 cups of flour
Sketch a graph that shows the relationship between grams of honey and cups of flour needed for a bakery recipe. To know how much honey is needed for 17 cups of flour
Given data:
Let flour x grams plotted on x-axis
honey y grams plotted on y-axis
We have 2 points to find the slope of linear equation
[tex]m = \frac{y_{2}- y_{1} }{x_{2}- x_{1} } = \frac{35-14}{25-10} = \frac{21}{15} = \frac{7}{5} = 1.4[/tex]
[tex](x_{1}, y_{1}) = (10,14)\\ \\(x_{2}, y_{2}) = (25,35)[/tex]
Linear equation is
y = mx+c
[tex]y = \frac{7}{5}x+c = 1.4x+c[/tex]
Adding points (10,14) in above equation
[tex]y = \frac{7}{5}x+c \\\\14 = \frac{7}{5}*10+c\\ \\[/tex]
c = 0
So, the relation between x grams of flour requires y grams of honey is
[tex]y = \frac{7}{5}x[/tex]
or
y = 1.4x
When x = 17
[tex]y = \frac{7}{5}*17 = 23.8[/tex]
Hence the answer is, y = 23.8 g of honey is needed for 17 cups of flour.
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