No, the given relation is not a function. An association between items of two sets—the domain and the codomain—is known as a binary relation.
What is a function ?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A binary connection in mathematics links elements of one set, referred to as the domain, with elements of another set, referred to as the codomain. A new set of ordered pairs made up of elements from sets X and Y and x in X is known as a binary relation across these sets.
Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest documented treatment of the concept of function. Initially, functions represented the idealised relationship between two changing quantities.
Consider the given relation
{(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}
We need to check whether the given relation is function or not.
A relation is a function if there exist a unique value of y for each value of x.
In the given relation, for x=0.3 there exist more than one value of y.
y=0.6 at x=0.3
y=0.7 at x=0.3
For one input there exist more than one output. Therefore, the given relation is not a function.
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A restaurant uses four pounds of potatoes for a party of 12 people They are cooking potatoes for a party of 60 people what should I do
a new over-the-counter medicine to treat a sore throat is to be tested for effectiveness. the makers of the medicine take two random samples of 25 individuals showing symptoms of a sore throat. group 1 receives the new medicine and group 2 receives a placebo. after a few days on the medicine, each group is interviewed and asked how they would rate their comfort level 1-10 (1 being the most uncomfortable and 10 being no discomfort at all). the results are below. find the 95% confidence interval in the difference of the mean comfort level. is there sufficient evidence to conclude that the new medicine is effective? assume the data is normally distributed with unequal variances. (round answers to 4 decimal places) make sure you put the 0 in front of the decimal. average group 1
A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence.
In case the 95 % confidence interval would be given by
[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]
What is meant by confidence interval?A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence. It exists often denoted a % whereby a population means lies between an upper and lower interval".
The margin of error exists the range of values below and above the sample statistic in a confidence interval.
Normal distribution, exists a "probability distribution that exist symmetric about the mean, showing that data near the mean exists more frequent in occurrence than data far from the mean".
[tex]$\bar{X}_1=5.84$[/tex] represent the sample mean 1
[tex]$\bar{X}_2=3.96$[/tex] represent the sample mean 2
n 1 = 25 represent the sample 1 size
n 2 = 25 represent the sample 2 size
[tex]$s_1=2.211334$[/tex] sample standard deviation for sample 1
[tex]$s_2=2.35372$[/tex] sample standard deviation for sample 2
[tex]$\mu_1-\mu_2$[/tex] parameter of interest.
The confidence interval for the difference of means exists given by the following formula:
[tex]$\left(\bar{X}_1-\bar{X}_2\right) \pm t_{\alpha / 2} \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} \text \dots{ (1) }$$[/tex]
The point of estimate for [tex]$\mu_1-\mu_2$[/tex] exists just given by:
[tex]$\bar{X}_1-\bar{X}_2=5.84-3.96=1.88$$[/tex]
In order to estimate the critical value [tex]$t_{\alpha / 2}$[/tex] we require to estimate first the degrees of freedom, given by:
[tex]$d f=n_1+n_2-1=25+25-2=48$$[/tex]
Since the Confidence is 0.95 or 95 %, the value of [tex]$\alpha=0.05$[/tex]and α 2 = 0.025, and we can utilize excel, a calculator or a table to estimate the critical value. The excel command would be: " = -T.INV (0.025, 48) ". And we see that [tex]$t_{\alpha / 2}=2.01$[/tex]
In order to replace into formula (1), we get
[tex]$1.88-2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=0.582$[/tex]
[tex]$1.88+2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=3.178$[/tex]
In case the 95 % confidence interval would be given by
[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]
Because all the values for the confidence interval are higher than 0, we may infer that there are significant differences between the means of the two groups in this case, with the mean for group 1 (Medicine) being considerably higher than the mean for group 2 (Placebo) at 5% of significance.
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The Sticker Company shipped 5,693,123,456 stickers last month. This month the company shipped 6,966,632,877 stickers. About how many more stickers were shipped this month than last month? A.11,000,000,000B.10,000,000,000C.3,000,000,000D.1,000,000,000
SOLUTION
To get how many more stickers were shipped last month than this month, we simply subtract this month's shipment from last month's shipment.
This becomes
[tex]\begin{gathered} 6,966,632,877-5,693,123,456 \\ =1,273,509,421 \end{gathered}[/tex]Therefore, the we have 1,000,000,000 to the nearest billion.
Option D is the correct answer
Suppose a ray of sunlight bounces off a window at a point P, and that
line mis perpendicular to the window at point P. Angles of inflection
and reflection are created as shown.
Write an equation and then solve for x.
m
-
(3x - 10)°
(2x + 5)°
P
By applying the law of reflection to the ray of sunlight, the value of x is equal to 5.
What is the law of reflection?The law of reflection is a theorem which states that the magnitude of the angle of incidence is equal to the magnitude of the angle of reflection when a ray of light is reflected off a surface such as a plane mirror.
Mathematically, law of reflection can be represented or modelled by this mathematical expression:
sinθi = sinθr
Where:
sinθi represents the angle of incidence.sinθr represents the angle of reflection.By applying the law of reflection to the ray of sunlight (see attachment), we have the following equation:
(3x - 10)° = (2x + 5)°
3x + 2x = 10 + 5
5x = 15
x = 15/3
x = 5.
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I have the problem as a picture, can I show u?
corresponding (option D)
Explanation:Since the lines are parallel and a tranversal line cuts the two lines:
The angle 2 at the top of the first line correspods to angle 6 at the top of the second line.
Angle 2 and angle 6 are equal.
Hence. we say angle 2 and angle 6 are corresponding angles (option D)
about 4% of the population has a particular genetic mutation. 300 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 300.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
How to calculate the probability distribution's mean: Steps
change every percentage to a decimal probability.Create a probability distribution table in step two. Multiply each column's values. Combine the outcomes from step 3.A specific genetic mutation affects 4% of the population. 300 persons are chosen at random. Find the standard deviation for the proportion of the 300 groups who have the genetic mutation.
Standard deviation is calculated as follows: 0.04 * 0.93/300 * sqrt(p*(1-p)/n) (0.000124).
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Please help! Super confused!
Enter the inverse function of f(x) = -9x - 10.
Answer: [tex]f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
Step-by-step explanation:
[tex]f(x)=-9x-10 \implies x=-9f^{-1}(x)-10\\\\x+10=-9f^{-1}(x)\\\\f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]
if charlene brewster has times of 8.4, 8.6, 8.3, 8.5, 8.7, and 8.5 and a performance rating of 110%, what is the normal time for this operation? is she faster or slower than normal? [px]
Normal time taken for operation = 7.7
Charlene's work performance is faster than normal time.
Need to define Charlene's average time:
8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5)/6
Avg time taken= 8.5.
Performance rating = 110/100 = 1.1
normal time taken: 8.5/1.1
normal time taken= 7.7
hence, 8.5 [tex]\geq[/tex] 7.7
Charlene is faster than normal time.
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8. A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of
materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality
12n> 170 +3.50n represents the situation in which the artist makes a profit.
a. Will the artist make a profit if he sells 15 necklaces? Show how you know.
b. Solve the inequality and explain what the solution means in regards to the jewelry artist.
By solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
What is inequality?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. In mathematics, larger than symbol (>), less than symbol (<), less than or equal to a symbol (<), greater than or equal to a symbol (≥), less than or equal to a symbol (≤), and not equal to a symbol (≠).So, is the artist in profit if he sells 15 necklaces:
The cost to rent a booth is $170.The cost of making a necklace is $3.50.The selling price is $12.Inequality is 12n ≥ 170 +3.50n: (let n = 15)
12n ≤ 170 +3.50n12(15) ≤ 170 +3.50(15)180 ≤ 170 + 52.5180 < 222.5Therefore, by solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.
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The correct question is given below:
A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality 12n> 170 +3.50n represents the situation in which the artist makes a profit. Will the artist make a profit if he sells 15 necklaces? Show how you know.
The Winchester Opera House sold 4,600 tickets this year, but it has been experiencing a 10%drop in sales from one year to the next. If this trend continues, then how many tickets willthe opera house sell 8 years from now?
Exponential decay formula:
[tex]y=a(1-r)^t[/tex]y is the number of tickets sold at t years
a is the initial number of tickets sold
r is the rate of drop (in decimal form)
t is the time in years
[tex]y=4600(1-0.1)^t[/tex]8 years from now:
[tex]\begin{gathered} y=4600(1-0.1)^8 \\ \\ y=4600(0.9)^8 \\ \\ y=1980.149 \end{gathered}[/tex]Then, if the trend continues, 8 years from now the number of tickets sell will be approximately 1980-12/7 = 6y solve for y and simplify your answer as much as possible
Answer:
[tex]\displaystyle y = \frac{-2}{7}[/tex]
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
-12/7 = 6y
Divide:
[tex]\displaystyle \frac{\frac{-12}{7} }{6} =\frac{6y}{6}[/tex]
Simplify the right side:
[tex]\displaystyle \frac{\frac{-12}{7} }{6} =y[/tex]
"Keep, change, flip" on the left side:
[tex]\displaystyle \frac{-12}{7} *\frac{1}{6} = y[/tex]
Multiply:
[tex]\displaystyle \frac{-12*1}{7*6}= y[/tex]
[tex]\displaystyle \frac{-12}{42}= y[/tex]
Simplify and reflexive property:
[tex]\displaystyle y = \frac{-2}{7}[/tex]
Hello,Can you help me with question #56 in the photo?Thank you,
In order to calculate the total spending in the town each year, first, multiply by the 70% that is spent within the town,
[tex]\begin{gathered} \text{\$}4,000,000\times70\% \\ \text{\$}4,000,000\times0.70 \\ =\text{\$}2,800,000 \end{gathered}[/tex]Also, multiply by 70% of the amount people will spend after they receive it in town,
[tex]\begin{gathered} \text{ \$}2,800,000\times70\% \\ \text{ \$}2,800,000\times0.70 \\ =1,960,000 \end{gathered}[/tex]Answer:
The total spending in the town each year is $1,960,000
What is the slope of the line through the points (6,5) and (4, 10)?
m=
The slope of the line through the points (6,5) and (4, 10) exists -5/2.
What is meant by the slope of a line?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. where "m" represents a line's slope. So, the slope of a line is tan.
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Let the two points are (6, 5) and (4, 10)
(x1, y1) = (6, 5) and (x2, y2) = (4, 10)
The equation of slope of the line through the points (x1, y1) and (x2, y2) = y2 - y1 / x2 - x1
substitute the values in the above equation, and we get
= 10 - 5 / 4 - 6
= 5 / -2
Therefore, the slope of the line through the points (6,5) and (4, 10) exists -5/2.
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A public storage company charges new customers an initial fee of $35.00. Each month of storage costs $18.75. The company uses the formula T = 35.00 + 18.75m to calculate the total charges, where T is the total charges, and m is the number of months of storage. How many months of storage would cost a new customer $260.00?
Answer:
12 months
Explanation:
Given the function that models the total chacrge of a company as T = 35.00 + 18.75m where;
T is the total charges,
m is the number of months of storage
Given
T = $260.00
we are to find the value of m
Substitute
260 = 35 + 18.75m
18.75m = 260 - 35
18.75m = 225
m = 225/18.75
m = 12
Hence it will take 12 months to cost a new custimer $260.00
what do the factoring of special products have in common?
We know that specific products multiply specific kinds of binomials, so these binomials will be the product's factors.
Example:
2 × 3 = 6Factors of 6: 2 × 3What are special products?Simply put, special products are just special cases of multiplying together specific types of binomials. We offer three unique products: (a + b)(a + b) (a - b)(a - b)So, we know that special products are multiplying special types of binomials which means that these binomials will be the factors of the product.
For example:
2 × 3 = 6Factors of 6: 2 × 3Therefore, we know that specific products multiply specific kinds of binomials, so these binomials will be the product's factors.
Example:
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one student from the school will be selected at random. what is the probability that the student is in the age-group of 6 to 8 years given that the selected student responded joy?
Given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So, the likelihood that a pupil is between the ages of 6 and 8 can be calculated using the techniques below:
Step 1: 89 pupils out of a possible 200 answered with joy, as shown in the table.Step 2 - It is also stated that there were a total of 28 students in the age range of 6 to 8 years who answered positively.Step 3 - Accordingly, the likelihood that the pupil belongs to the 6 to 8-year-old age range is:P = 28/89
Therefore, given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
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The complete question is given below:
Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age group. One student from the school will be selected at random. What is the probability that the student is in the age group of 6 to 8 years given that the selected student responded with joy?
Mind doing this too?
The expression that represents the perimeter and area of the rectangle are 10x + 4 and 6x²- 24.
How to find the area and perimeter of a rectangle?The rectangle is a quadrilateral with opposite sides equal to each other.
Opposite sides of a rectangle is also parallel to each other.
Therefore,
perimeter of a rectangle = 2(l + w)
where
l = side lengthw = widthTherefore,
l = 3x + 6
w = 2x - 4
Hence,
perimeter of a rectangle = 2(3x + 6 + 2x - 4)
perimeter of a rectangle = 2(5x + 2)
perimeter of a rectangle = 10x + 4
Let's find the expression that represent the area of the rectangle.
Hence,
area of a rectangle = lw
area of a rectangle = (3x + 6)(2x - 4)
area of a rectangle = 6x² - 12x + 12x - 24
Therefore,
area of a rectangle = 6x²- 24
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Which of the following values make the inequality x≤16.3 truea 18.5b 8c 1/4d 32e -3f 16.3
SOLUTION
We want to find which of the following values make the inequality
x ≤ 16.3 to be true.
This inequality means that x is equal to 16.3 or less than 16.3. So the numbers that fall under this are numbers smaller than 16.3 and also 16.3.
The numbers that fall under here are 8, 1/4, -3 and 16.3
Hence the answer b, c, e and f
I Really Need Help..
PHOTO BELOW:
Answer: He is not correct because when simplifying an expression, you can only add like terms together.
Step-by-step explanation:
you are given the expression: x^2 + 4x - 2x
when simplifying an expression, you can only add/subtract like terms (terms that have the same variable which are raised to the same power).
in the expression, you can only subtract 4x - 2x because they have like terms/the same variable.
you cannot add x^2 to 4x because x^2 and x are NOT like terms/the same variable. (If 4x was 4x^2, then you would be able to add them together.
meaning the simplified expression should be: x^2 + 2x and not 3x^2
If point A, havingcoordinates (p, 3) andpoint B, with coordinates(6, p) lie on a line havinga slope of 2, what is thevalue of p?
Take into account that the slope of a line is given by the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are two points on the line.
In this case:
(x1,y1) = (p,3)
(x2,y2) = (6,p)
By replacing the previous values into the formula for m, we get:
[tex]m=\frac{p-3}{6-p}[/tex]Now, by making m = 2 and solving for p, we obtain:
[tex]\begin{gathered} \frac{p-3}{6-p}=2 \\ p-3=2(6-p) \\ p-3=12-2p \\ p+2p=12+3 \\ 3p=15 \\ p=\frac{15}{3}=5 \end{gathered}[/tex]Hence, the value of p is p = 5
Please help me on this question.
Math
Simplify each expression. show your solution
To simplify a phrase, create an equivalent expression without any terms that are identical.The expression will then be rewritten using the fewest terms feasible.
What is an equation to simplify?
A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.The fundamental guidelines and procedures to simplify any algebraic statement are as follows:By multiplying factors, remove any grouping symbols like brackets and parenthesis.If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.Add the constants together. Add numbers
2+1
= 3
2³ = 8
first one 8
2. x²× x°
= x ²+°
3.a6_a4
= a2
4. x×x×y×y
=x²y²
5 x²×x×y×y²
= x³y³
6.(mn)5
= m5N5
7 (abc)²
= a²b²c²
8.(p²q)³
p6q3
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-11x-y+3z=-21
(5x-y-5z=-5)
(3x+y+z=13)
Answer: [tex]y=15-5x, z=2x-2[/tex]
Step-by-step explanation:
Subtracting the first equation from the second equation yields [tex]16x-8z=16 \implies 2x-z=2 \implies z=2x-2[/tex].
Substituting this into the first equation,
[tex]-11x-y+3(2x-2)=-21\\\\-11x-y+6x-6=-21\\\\-5x-y-6=-21\\\\-5x-y=-15\\\\5x+y=15\\ \\ y=15-5x[/tex]
I used 999 sheets of toilet paper each day for 777 days. The roll had 969696 sheets when it was new. How many sheets of toilet paper have not been used? please get the answer right
The number of sheets of toilet paper that have not been used is 193473.
What is multiplication?Multiplication simply has to do with the product of numbers.
From the information, the roll had 969696 sheets when it was new and the person used 999 sheets of toilet paper each day for 777 days.
Therefore, the sheet left will be:
= Number in the new roll - Sheets used
= 969696 - (777 × 999)
= 969696 - 776223
= 193473
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determine the equation of line from the graph
Answer:
y = 2x
Step-by-step explanation:
The slope is 2. Find a point on the line, to go back to the line, go up two and one to the right. You will be back on the line. This pattern repeats over and over and again.
Recall that the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width.
Find the area of a rectangle that has a length of 3.5 centimeters and a width of 2.2 centimeters. The answer is 7.7
Using the formula for the area of a rectangle is, A = l×w where l represents the length of the rectangle and w represents its width, the area of a rectangle with the length of 3.5 centimeters and a width of 2.2 centimeters will be 7.7 cm^2.
What is the area of a rectangle?The area of the rectangle can be calculated using the formula,
(A = l×w )
and the l = the length of the rectangle
w = represents the width of the rectangle
Then to calculate the area of the rectangle, we can substitute the values that is been given as :
(A = l×w )
A = (2.2 * 3.5) = 7.7 cm^2
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Answer:
7.7
Step-by-step explanation:
The answer was already in the question... He must've edited it or somethin'
Ken wants to install a row of ceramic tiles on a wall that is 21 3/8 inches wide each tile is 4 1/2 inches wide how many whole dose he need
the width of the wall is 21 3/8 = 171/8
the width of a tile is 4 1/2 = 9/2
so the number of tiles is
(171/8) / (9/2) = 171x2 / (9 x8) = 4.75
so the no of tiles needed is 5.
Find the equivalent ratio to the ratio 9 to 27 by simplifying the ratio. 3 to 1 , 1 to 3, 1 to 27 ,9 to 3
Given data:
The given ratio is 9:27.
The given ratio can be written as,
[tex]\begin{gathered} 9\colon27=\frac{9}{27} \\ =\frac{1}{3} \\ =1\colon3 \end{gathered}[/tex]Thus, the given ratio can be written as 1:3 so, second option is correct.
When Madison left her house this morning, her cell phone was 80% charged and itthen started to lose 8% charge for each hour thereafter. Write an equation for B, interms of t, representing the charge remaining in Madison's battery, as a percentage, thours after Madison left her house.
Given:
Initially, the cell phone was 80% charged.
Then started to lose 8% charge for each hour thereafter.
To find:
The equation for B in terms t
Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week?
True or false?
The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true.
As given in the question,
If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them
a:b = c:d
a ÷b = c ÷d
ad = bc
let Sal earns $480 per week and he works 40hours per week
480÷40 = 12
Lidia earn $300 per week and she works 25 hours per week
300÷25 = 12
Cross product of their salaries is
480×25=1200
300×40=1200
The ratio of their salaries and their product are equal.
Hence, The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true
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