The median of the list of numbers is 7
How to determine the median?The number is given as:
9.5, 4.4, 8.1, 2.9, 9.2, 3.2, 9.4, 7, 2.5
Rearrange the numbers in ascending order
2.5, 2.9, 3.2, 4.4, 7, 8.1, 9.2, 9.4, 9.5
The median is the middle number.
The middle number here is 7
Hence, the median of the list of numbers is 7
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Write the inequality represented on each graph. Use n for the variable.
Graphs 1 and 2's respective inequalities are n14 and n14.
What exactly is inequality?"Inequality" is the term used in mathematics to describe a connection between two expressions or values that is not equal to one another.
the first graph
line excluding number 14 is extending to the left.
The disparity is as;
n < 14.
Within Graph 2,
The number 14 is part of a line that is diverging to the right.
The disparity is as;
n≥14
As a result, graphs 1 and 2's respective inequalities are n14 and n14.
Graph 1 and Graph 2 each have n14 and n14 inequalities.
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In a bag of apples and oranges, the ratio of apples to oranges is 4:3.
The bag contains 70 apples and oranges, how many oranges are there?
Only possible answers
35
30
25
40
Answer:
30 Oranges
Step-by-step explanation:
The ratio of apples to oranges is 4:3. For every 4 apples there are 3 organges. We can write that as 4A/3O, where A and O are Apples and Oranges. This can be rewritten as percentages of each fruit. A bag of 7 would have 4 Apples (4/7) or 0.5715 [57.15%] and 3 Oranges (3/7) or 0.4285 [42.85%].
A bag of 70(A and O) can be determined to have:
Apples: 70*(0.5715) = 40 Apples, and
Oranges: 70*(0.4285) = 30 Oranges
Is triangle FHK similar to triangle GHJ? If so, which postulate or theorem proves these two triangles are similar?
The correct statement regarding the similarity of triangles GHJ and FHK is given as follows:
Triangle FHK is similar to triangle GHJ by the SAS Similarity Theorem.
What are similar triangles?Similar triangles are triangles that share these two features given as follows:
Congruent angle measures.Proportional side lengths.For this problem, the similar triangles are given as follows:
FHK and GHJ.
They are similar because:
They share a common angle, which is angle H.Side length HF is proportional to side length HG.Side length HK is proportional to side length HJ.As they have two proportional side lengths, along with the angle between them, the congruence theroem is the SAS theorem.
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I am atempting my math homework but I do not understand this question It says "Vera spent 0.04 of of the earnings on a new phone apps What percent of monthly earnings did she spend on phone apps" Can someone help?
The percent of monthly earnings that Vera spends on phone apps is 4%.
How to express the percentage?.The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
Since Vera spent 0.04 of of the earnings on a new phone apps, the percent of monthly earnings did she spend on phone apps will be:
= 0.04.
= 4/100
= 4%
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can somebody help me I been doing this all day please dont guess its for a test
decide if thee absolute value inequality is an "and" compound inequality, an "or" compound inequality or nether.
1. |5+m|<13
a. and b. or c. neither
2. 4|y+6|≥3
a. and b. or c. neither
3. |g - 3| = -2
a. g=5 or -5 b. g = 1 or -1 c. null set
Answer: its number 2
Step-by-step explanation:
The probability for event a is 0. 3, the probability for event b is 0. 6, and the probability of events a or b is 0. 8.
The events are not mutually exclusive because P(A or B) ≠ P(A) + P(B). The probability of either event happening is not equal to the sum of each event happening.
What are mutually exclusive events?Mutually exclusive events are events that cannot happen at the same time. For example, when you are tossing a coin, you cannot get head and tail at the same time. They are mutually exclusive, also called disjoint events, where P(A and B) = 0.
In mutually exclusive events, it also states that the probability of either event happening is the sum of probabilities of each event happening. It means that P(A or B) = P(A) + P(B).
Your question is incomplete and here is the complete question.
The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8. Why are the events not mutually exclusive?
From the information, we have:
P(A) = 0.3P(B) = 0.6P(A or B) = 0.8Let's check if the events are mutually exclusive!
P(A or B) = P(A) + P(B)
P(A or B) = 0.3 + 0.6
P(A or B) = 0.9
0.8 ≠ 0.9
P(A or B) ≠ P(A) + P(B)
The probability of A or B is not equal to the sum of the individual probabilities. It proves that A and B are not mutually exclusive.
Hence, A and B are not mutually exclusive because the probability of A or B is not equal to the sum of the individual probabilities.
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Can you PLSS help me answer these question?
AND PLS GIVE A EASY + DETAILED STEP BY STEP ON HOW U GOT THE ANSWER BC IM SLOW LOL
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. 1 /x^2 + x^4
The partial fraction decomposition of the function is[tex]\\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}[/tex]
In algebra, a rational fraction—that is, a fraction where the numerator and denominator are both polynomials—can be partially decomposed or expanded by adding a polynomial (potentially zero) and one or more fractions with a lower denominator to the original fraction.
In symbols, the partial fraction decomposition of a rational fraction of the [tex]{\textstyle {\frac {f(x)}{g(x)}},}[/tex]
[tex]{\displaystyle {\frac {f(x)}{g(x)}}=p(x)+\sum _{j}{\frac {f_{j}(x)}{g_{j}(x)}}}[/tex]
Where p(x) is a polynomial, [tex]g_{j}[/tex] for each j is a power of an irreducible polynomial (which cannot be factored into polynomials of positive degrees), and [tex]f_{j}[/tex] for each j is a polynomial with a smaller degree than this irreducible polynomial's degree.
The numerical values of the coefficients is [tex]\frac{1}{x^2+x^4}$[/tex].
Now,
[tex]$\begin{aligned} x^2+x^4 & x^2+x^4 \\ = & x^2\left(1+x^2\right)\end{aligned}$[/tex]
Therefore, the form of the partial fraction decomposition is
[tex]\begin{aligned}& \frac{1}{x^2\left(1+x^2\right)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1} \\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}[/tex]
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a light year is defined as 5.88 times 10^12 miles: the distance that light travels in 1 year. How far will light travel in 3 years?
The distance that light will travel in 3 years, given the speed it travels in one year is
How to find the speed travelled ?The notion of a Light Year allows us to quantity the distance that light travels in an entire year. This has allowed scientists to quantify with more ease, the distance to other galaxies and planets.
The distance that light travels in a year is 5. 88 x 10¹² miles.
In 3 years therefore, the distance would be:
= 3 x ( 5.88 x 10 ¹²)
= 17.64 x 10 ¹² miles
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x^2 = 361 Which represents the solution of the given equation?
Answer: X=19
Step-by-step explanation:
x^2=361
Square root both sides to get rid of the exponent above x.
[tex]\sqrt{x^2}[/tex]=[tex]\sqrt{361}[/tex]
x=19
What are the 7 types of functions?
The eight categories are power, quadratic, rational, exponential, logarithmic, sinusoidal, polynomial, and linear.
what is functions ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
The eight categories are power, quadratic, rational, exponential, logarithmic, sinusoidal, polynomial, and linear.
Functions can be roughly categorized into four sorts. Based on the element, the following relationships are possible: One to One Function, Many to One Function, Onto Function, One to One and Into Function. Based on the following domains: logarithmic functions, trigonometric functions, and algebraic functions.
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The function a(n)= 2n-5 represents the value of the nth term in a sequence. What is the sum of the 2nd and 3rd terms of the sequence?
The sum of the second and third terms of the arithmetic progression is equal to 0.
How to analyze arithmetic progressionsArithmetic progressions are sets whose terms are generated by expressions of the form:
y = a + r · (n - 1)
y = r · n + (a - r)
Where:
a - Value of the first term.r - Common raten - Index of the n-th term of the progression.
The sum of the second and third elements is:
n = 2
y = 2 · 2 - 5
y = - 1
n = 3
y = 2 · 3 - 5
y = 1
S = - 1 + 1
S = 0
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PLEASE HELP
is this equation an exponential decay of 40% or 30%
y=0.4(0.7)^t
Answer:
30%
Step-by-step explanation:
The level of decay is determined by the number raised to the power.
y = 0.4(0.7)^t
If you had 1^t, there would be no decay or growth since 1^t is always 1.
Instead, you have 0.7^t
As t increases, 07^t decreases. That is where the decay comes from.
Now look at 0.7
In the general decay equation, you have
y = a(1 - r)^t
r is the rate of decay.
Here we have 0.7
0.7 = 1 - 0.3
the rate of decay is 0.3 or 30%
Answer:
The equation y = 0.4(0.7)^t represents an exponential decay of 30%. The decay rate is determined by the value in the parentheses, which in this case is 0.7. To calculate the decay rate, you can subtract this value from 1, giving you 1 - 0.7 = 0.3, or 30%.
Step-by-step explanation:
Why do we calculate residuals?
The difference between the value predicted by the regression and the observed value for a given data point is known as the residual. The residual calculation offers a useful indicator of how well your model matches the given data set.
What is residual?The discrepancies between actual and expected data values are known as residuals in statistical or machine learning models.
They serve as a diagnostic tool for evaluating a model's quality. They are also called mistakes.
The table below's main column, Inflation, displays information on US inflation for each month of 2017. The Predicted column displays forecasts from a model that aims to forecast the pace of inflation.
The residuals are calculated as follows: Residual = Inflation - Predicted. They are displayed in the Residual column. In the instance of the data for January 2017, the model projected 1.8%, but the observed inflation was 0.5%, leaving a residual of -1.3%.
Hence, The residual calculation offers a useful indicator of how well your model matches the given data set.
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(Linear Relationships MC) An indoor soccer field can be rented for personal use. The total cost for renting the field can be found by using the equation y=225x + 200 The x-variable is the number of hours the field is being rented, the constant is the flat rate for renting the field, and the y-variable is the total cost, in dollars Which statement is true based on the given equation? The equation shows a linear relationship, but not a proportional relationship The equation shows a linear relationship and a proportional relationship The equation does not show a linear relationship or a proportional relationship The equation shows a proportional relationship but not a linear relationship
first statement is true, the equation shows a linear but not proportional.
what is linear equation?The equation which has two variables with first order term and only a constant available in the equation is termed as linear equation. Example of a linear equation, y =mx + b
Which statement is true for this question?
Given, an equation, y = 225x + 200
where x and y are two variables
x denotes the number of hours the field is being rented
y denotes the total cost
constant 200 implies the flat rate for renting the field.
If we compare this equation to the standard form of linear equation, y = mx + b, where m = slope and b is the y intercept.
we will find that the above two equation is similar and therefore the equation given in question is a linear relationship.
the coefficient 225 is the slope of equation and the constant 200 is the y intercept.
this given equation is not a proportional relationship.
The first statement is true.
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What is the slope of the line through (-9,6(−3,9)
Answer:
0.6 cause I got it correct.
In preparation of a company's annual dinner, 450 notebooks and 315 fridge stickers are to be
distributed equally into goodie bags without leftovers.
(a) Is it possible to prepare 21 goodie bags exactly? Explain your answer.
(b) What is the largest number of goodie bags that can be prepared?
(c) Using the answer from (b), how many notebooks and fridge stickers will there be in a goodie bag?
(a) To determine if it is possible to prepare 21 goodie bags exactly, we need to check if 450 notebooks and 315 fridge stickers can be divided equally into 21 goodie bags without any leftovers.
To do this, we can use the greatest common divisor (GCD) of 450 and 315, which is 15. If the GCD is not 1, it means that the two numbers cannot be divided exactly, so it is not possible to prepare exactly 21 goodie bags with 450 notebooks and 315 fridge stickers.
(b) To find the largest number of goodie bags that can be prepared, we can use the least common multiple (LCM) of 450 and 315. The LCM is 990, which means that 990 notebooks and 990 fridge stickers can be divided into the same number of goodie bags without any leftovers. Therefore, the largest number of goodie bags that can be prepared is 990/450 = 990/315 = 2.
(c) Using the answer from (b), we can calculate how many notebooks and fridge stickers will be in a goodie bag. If we divide 990 by 2, we get 495. Therefore, there will be 495 notebooks and 495 fridge stickers in each goodie bag.
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find x and mut pleaase
The formula for a circle's sector's area is /360o (r2), where r is the circle's radius and is the sector's angle.
Formula for a Sector's Circumference
The following is the formula for a circle's sector's perimeter:
Sector perimeter equals radius plus radius plus arc length.
Sector perimeter equals 2 radius plus arc length.
The relation is used to compute arc length:
Arc length is equal to l = (/360) 2r.
Therefore,
Sector perimeter: 2 Radius + ((/360) 2r)
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Assuming that r is the circle's radius and that is the sector's angle, the formula for the area of a circle's sector is /360o (r2).
What are sectors in a circle?A circular sector (also known as a circle sector or a disc sector; symbol: ) is the area of a disc (a closed region bordered by a circle) enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger as the major sector.
The radius of the circle, r, and the sector angle (in degrees) that the arcs at its centre subtend are also given. A = 1/2 r2 gives the area if the subtended angle is provided in radians.
The area, A, of just the segment may be calculated using the following formula if you know the circle's radius, r, and the sector's central angle,, in degrees.
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2+sqrt{4-p} = sqrt {2p-4}
Please show work.
The value of the given expressions is p = -1.281, though it is also possible for p = 0.781 to be the value.
what is equation ?Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, slope-intercept form, and point-slope form are the three primary formats for linear equations. In a mathematical expression known as an equation, the equals sign appears. Algebra is used in a variety of equations. When you don't know how much to compute in math, you use algebra to approximate the answer.
given
-4p^2=2p-4
p=(-1-sqrt(17))/4=-1.281
p=(-1+sqrt(17))/4=0.781
The value of the given expressions is p = -1.281, though it is also possible for p = 0.781 to be the value.
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I need to find the rise over run
Calculate the rise between the two points and divide it by the difference in the horizontal direction to arrive at the answer (run).
How do you find the rise over run?An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). Calculate the rise over the run ratio of a line going through the points (-7,3) and (4, 2). With this in mind, the rise over run ratio of the line joining the two points is -1/11. Decide on the coordinates of two spots along the line.
Find the location of these two points' respective y-coordinate differences (rise). The difference between these two places' x-coordinates should be known (run). In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates. Rise is the quantity you gain or lose when moving from one location to another. That would result in a modification of the y values on the graph.
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Darnell can buy a particular brand of fruit juice in a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in the juice in a 6-ounce bottle
Answer:
90 calories in a 6 ounce bottle
Step-by-step explanation:
6oz/x
10oz/150
150 divided by ten is 15
15 times 6 equals 90
Answer: 90 calories is in 6 ounce bottle which is 90
You swam 4 sets of 200 yards and your friend swam 5 sets of 150 yards. How many more yards did you swim?
You swam 50 yards more than your friend.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, you swam 4 sets of 200 yards and your friend swam 5 sets of 150 yards.
Total number of yards you swam 4×200
= 800 yards
Total number of yards your friend swam 5×150
= 750 yards
Number of yards more you swam =800-750
= 50 yards
Therefore, you swam 50 yards more than your friend.
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Translate the following arguments into symbolic form. Then determine whether each is valid or invalid by constructing a truth table for each.
If national elections deteriorate into TV popularity contests, then smooth-talking morons will get elected. Therefore, if national elections do not deteriorate into TV popularity contests, then smooth-talking morons will not get elected.
Symbolic Form:
P: National elections deteriorate into TV popularity contests
Q: Smooth-talking morons will get elected
The argument can be expressed as:
If P then Q
Therefore, if not P then not Q
This is a valid argument as it follows the logical form of Modus Ponens. We can verify this using a truth table:
P | Q | P → Q | ¬P | ¬P → ¬Q
T | T | T | F | T
T | F | F | F | T
F | T | T | T | T
F | F | T | T | T
The truth table shows that the argument is valid because the final column (¬P → ¬Q) is true for all four cases. This indicates that if the symbolic form of premise (P) is false, then the conclusion (Q) must also be false.
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Jack wants to buy a coat that costs $74.95. The sales tax rate in his city is 612%
. What is the total cost for the coat? Round to the nearest cent.
Answer:
The total amount that will be paid for the coat would be; $79.95 to the nearest cent.
Step-by-step explanation:
What is income tax?
Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
Given that Jack wants to buy a coat that costs $74.95. The sales tax rate in his city is 6 and 1/2 percent.
Thus, the total cost for the coat can be calculated as;
The amount that will be paid for the coat will be;
= Amount of shirt + Tax
= $74.95 + (6.5% × $74.95)
= $74.95 + (6.5/100 × $74.95)
= $74.95 + $4.80
= $79.95
The total amount that will be paid for the coat would be; $79.95 to the nearest cent.
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The total cost for the coat is $79.55
The total cost of the coat is the sum of the cost of the coat and the sales tax. To find the sales tax, Jack needs to multiply the cost of the coat by the sales tax rate as a decimal.
$74.95 x 0.0612 = $4.60452
To find the total cost, he would add this amount to the cost of the coat:
$74.95 + $4.60452 = $79.55452
Rounding to the nearest cent , the total cost of the coat is $79.55. It means Jack has to pay $79.55 including the sales tax, which is $4.60452 on the original price of $74.95 for the coat.
The total cost of the coat is $79.55.
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If y varies directly as the square of x and y = -54 when x = 9, then y = -1 1/3 when x = 6
Therefore , the solution of the given problem of equation comes out to be k1 = - 0.67 and k2 = -0.1.
Describe equation.A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A scientific statement that verifies the equality of two formalisms is known as an equation in algebra. For instance, the pieces ptdc + 6 and 12 are separated by an equal sign in the solution obd + 6 = 12. The relationship between the two phrases on either flank of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 4x – 4 = 0.
Here,
If y varies in this case simply also as square of x
k is the proportionality constant, and
y = kx² in mathematics.
Considering y = -54 and x = 9,
y = kx²
k = y/ x²
k = -54/ 9²
k = -54/81
k1 = - 0.67
Moreover, if y=-11/3 and x=6,
k = y/x²
k = -3.667/ (6)²
k = -3.667/36
k2 = -0.1
Therefore , the solution of the given problem of equation comes out to be k1 = - 0.67 and k2 = -0.1.
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unit 8 right triangles and trigonometry homework 7 law of cosines
The value of x will be cos^-1 549/900.
What is Law of Cosine ?
The relationship between a triangle's side lengths and the cosine of its angle is known as the law of cosines. Additionally known as the cosine rule.
We know that ,
a²= b²+c² - 2bc cosα, where α is the angle between b and c.
Here, b = 18 , c= 25, a = 20 and cos x
So, a²= b²+c² - 2bc cosα
(20)² = (18)² + (25)² - 2×18×25 cos x
400 = 324 + 625 - 900 cos x
900cos x = 549
cos x = 549/900
hence, x = cos^-1 549/900
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1. At Franklin High School, there are 480 male students, 320 female students, and 40
teachers. Find the following ratios and write them as a fraction in simplest form.
1A. Female students to male students
2. Teachers to male students
Which has exactly 12 angles?
A dodecagon or 12-gon is a twelve-sided polygon.
One of the polygonal shapes with 12 sides, 12 vertices, and 12 angles is the dodecagon. A dodecagon is a two-dimensional plane figure, just like other polygons. 12 equal sides and 12 equal angles make up a standard dodecagon polygon.
Dodecagons that are irregular have uneven sides and angles. Dodecagons can also be concave or convex polygons. The dodecagon's inner angles add up to 1800° in total.
The word dodecagon is derived from Greek words, ‘dodeka‘ which means ‘twelve’, and ‘gon‘ means ‘sides’.
Thus, A dodecagon or 12-gon is a twelve-sided polygon.
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Find the measure of angles 1 and 2.
Explain your reasoning as to how you determined the measurements of angles 1 and 2.
Answer:
135 degrees
Step-by-step explanation:
You use Alternate interior angles to get angle 2, then vertical angles to find angle 1
Red is alternate interior angles
Yellow is vertical angles
Step-by-step explanation:
when a line intersects 2 or more parallel lines, it must have the same intersection angles with each of the parallel lines. otherwise the lines are not parallel after all, because parallel lines imitate each other's properties and behaviors exactly except for the actual location.
so,
angle 1 = 135°
the intersection angles between 2 lines must be the same in each side of each line, they are just left-right mirrored.
so,
angle 2 = angle 1 = 135°
Segment JK has endpoints J(2,4) and K(6,2). You dilate the segment using a dilation centered at the origin with a scale factor of 1/2 and then reflect the image over the x-axis. Where is the final image of K?
The final image of K would be at (3,-1) after the given sequence of transformation Segment JK.
What is Dilation?Dilation is a process for creating similar figures by changing the size.
Segment JK has endpoints J(2,4) and K(6,2).
A dilation by a factor of 1/2 means that each coordinate value will be multiplied by 1/2.
The dilation of segment JK with a scale factor of 1/2 would shrink the segment by half, so the coordinates of K would be (3,1).
Reflecting over the x-axis would change the sign of the y-coordinate, so the final image of K would be at (3,-1).
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