If the given point is p(x, y) and change the sign of its x coordinates and y coordinates, then the new location will be on third quadrant
The coordinates of the point p = (x, y)
In the graph, there are four quadrants.
In first quadrant the x axis value and y axis value will be positive. In second quadrant the value of x will be negative and y will be positive. In the third quadrant the value of and y will be negative. In fourth quadrant the value of x will be positive and y will be negative
Here at first both x and y are positive and it will be on first quadrant. The the sign of the x coordinates and y coordinates will change sign. So both of them will be negative.
Therefore, the location of will be on third quadrant
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two websites sell the same type of headphones. website a website b e47.68 16.95 cost of headphones cost of postage including the cost of postage which website is cheaper and by how much? e49.95 14.39
Website B is cheaper then website A.
What are headphones?
A user wears headphones, which are a pair of small loudspeaker drivers, on or near their head over their ears.
They function as electroacoustic transducers, converting an electrical signal into an associated sound.
People can listen to music and carry on conversations at any time and from any location thanks to headphones. It is impossible to overstate how simple it is to use headphones and how much mobility they provide.
There are two types of headphones, website A and website B.
First to find the cost for website A.
Cost of website A = Cost of headphone + cost of postage
= 47.68 + 16.96
Cost of website A = 64.63
Cost of website B = Cost of headphone + cost of postage
= 49.95 + 14.39
Cost of website B = 64.34
The cost of website B is less than the cost of website A.
Hence, website B is cheaper then website A.
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twenty high school students took an examination and received the following scores: 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73 determine what percent of the students scored within ( ) one standard deviation of the mean
70% of students had scores that were within (±) one standard deviation of the mean.
Explain the term standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.For the stated question-
Total number of students = 20
Scores received; 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73.
Mean = Sum of all/ Total number
Mean x = 79.7
standard deviation = 8.7
Thus, (±) one standard deviation SD of the mean becomes;
-1 SD; 79.7 - 8.7 ≈ 70.994
+1 SD; 79.7 + 8.7 ≈ 88.406
Thus, 71 to 88
Percentage = scores between 71 to 88/ total scores
Percentage = 14/20 x 100 %
Percentage = 70%
Thus, 70% of students had scores that were within (±) one standard deviation of the mean.
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the weight distribution of parcels sent in a certain manner is normal with mean value 12 lb and standard deviation 3.5 lb. the parcel service wishes to establish a weight value c beyond which there will be a surcharge. what value of c is such that 99% of all parcels are at least 1 lb under the surcharge weight (that is, only 1% are beyond c-1 lb)?
The value of c should be 20.2 so that 99% of all parcels are at least 1 lb under the surcharge weight (that is, only 1% are beyond c-1 lb).
What is surcharge?
Surcharges are extra fees or taxes, as the name implies. A 10% surcharge on a 30% tax rate effectively increases the total tax burden to 33%. A 10% surcharge is added to the tax obligation for people whose net taxable income exceeds Rs 1 crore. The surcharge is increased to 5% if the net income is greater than Rs 10 crore. If a company's net income surpasses Rs. 1 crore and Rs. 10 crore, they are both provided a margin of relief.
Solution Explained:
Given,
m = 12
d = 3.5
P(z<x) = 0.99 = ¢(Z)
Z = 2.33
Since Z = (x - m)/d
x = dZ + m
x = 3.5*2.33 + 12
x = 20.155 lb approximately
x = 20.2 lb
Therefore, the highest weight for 99% if the parcels is 20.2 lb.
That is, the surcharge weight = 20.2 + 1 = 21.2 lb
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In recent years, only 79% of the fruit sold at Fred's Fruit stand has been any good. Fred recently started buying fruit from new farmers and wants to know if there is a statistically significant increase in the percentage of good fruit. In a random sample of 475 pieces, 85 were bad.
The conclusion does not change if the significance level went from 7% to 5%.
According to the given situation, 79% of the fruits sold are good and whether there is an increase in the percentage of good fruit is to be tested. If there is no increase in percentage of good fruit, p = 0.79 and if there is an increase in percentage of good fruit, p > 0.79.
The test statistic is given by z = (X - µ)/(σ/√n)
In the given data, µ = 0.79 and σ = √(0.79(1-0.79) = 0.407
In a random sample n = 475 and 85 are bad.
Good fruits = 475 – 85 = 390
X = 390/475 = 0.8211
Hence,
z = (0.8211 – 0.79)/(0.407/√475) = 1.66
From the z-table, p value is 0.9515.
The p value of the test that no increase in percentage of good fruits = 1 – 0.9515 = 0.0485
If the p-value is less than 0.05 it is statistically significant. As 0.0486 is less than 0.05 and 0.07 there is sufficient evidence to conclude that there is a statistically significant increase in the percentage of good fruit. It is true for each significance level. Hence, the change in significance levels does not change the conclusion.
Note: The question is incomplete. The complete question probably is: In recent years, only 79% of the fruit sold at Fred's Fruit stand has been any good. Fred recently started buying fruit from new farmers and wants to know if there is a statistically significant increase in the percentage of good fruit. In a random sample of 475 pieces, 85 were bad. How would the conclusion change if the significance level went from 7% to 5%?
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if f(x)= 5x+7 then what is f(7)
A. 64
B. 42
C. 19
Answer:
f(7)= 42
Step-by-step explanation:
we fill in 7 where x is
f(7)=5(7)+7
f(7)=35+7
f(7)=42
Hopes this helps please mark brainliest
create a table of values and graph the following function rule. you must find at least 4 points in your table/graph. then, determine if the function is linear or non-linear, explaining your reasoning. show your work. y=2x^2-5.
then answer if the function is linear or nonlinear. explain?
please someone answer this ASAP I will give brainlist and 100 points!!!!! please.
The function y = 2x² - 5 is a nonlinear equation and the table of values is
x 0 1 2 3
y -5 -3 5 13
How to determine the category of the equation?From the question, we have the following equation that can be used in our computation:
y = 2x² - 5
As a general rule, a linear equation can take any of the following forms
Slope-intercept form: y = mx + xStandard form: Ax + Bx = CPoint slope form: y - Y = m(x - X)By comparing y = 2x² - 5 to the above forms, we can see that the equation does not take any of the forms represented above
This means that the function is not a linear function
i.e. The function is a nonlinear function
Also, we set x = 0, 1, 2 and 3
So, we have
y = 2(0)² - 5= -5
y = 2(1)² - 5= -3
y = 2(2)² - 5= 5
y = 2(3)² - 5 = 13
So, the table of values is
x 0 1 2 3
y -5 -3 5 13
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please help fast! ........................................................................
Answer: no i need this too :(
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $115 to spend on parking and admission. Parking is $15, and tickets cost $25 per person, including tax. Write and solve an inequality which can be used to determine xx, the number of people who can go to the amusement park
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $115 to spend on parking and admission. Parking is $15, and tickets cost $25 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.
115 ≥ 25p + 15
115 ≥ 25p + 15
subtract 15 from both sides:
115 - 15 ≥ 25p + 15 - 15
100 ≥ 25p
divide both sides by 25:
100/25 ≥ 25p/25
4 ≥ p
4 people
The number of people who can go to the amusement park is 4.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number lineby their size.
Given that, the money to be spend, is no more than $115 to spend on parking and admission.
Parking is $15, and tickets cost $25 per person, including tax.
we need to determine the maximum number of people that can go to the park,
115 ≥ 25p + 15
115 ≥ 25p + 15
subtract 15 from both sides:
115 - 15 ≥ 25p + 15 - 15
100 ≥ 25p
divide both sides by 25:
100/25 ≥ 25p/25
4 ≥ p
Hence, the number of people who can go to the amusement park is 4.
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Which of the following techniques might be most useful in helping a restaurant determine how to position itself in the marketplace?
a. factor analysis
b. multiple regression analysis
c. conjoint analysis
d. perceptual mapping
16. if alexa's car can typically travel 300 miles on a full tank of gasoline, and if her car's tank can hold 18 gallons, then at this rate how far should the car be able to travel on 12 gallons of gasoline?
The distance covered by the car with 12 gallons of gasoline is 200 miles.
Given,
Distance travelled by a car with full tank gasoline = 300 miles
The capacity of the car's tank = 18 gallons
We have to find the distance covered by the car with 12 gallons of gasoline;
Here,
x be the distance covered by the car with 12 gallons of gasoline
Then,
300/18 = x/12
x = (300 x 12) / 18
x = (300 x 2) / 3
x = 100 x 2
x = 200 miles
That is,
The car will cover 200 miles with 12 gallons of gasoline.
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the longer leg of a right triangle is three times as long as the shorter leg. the hypotenuse is $\sqrt 5.$ what is the area of this triangle?
The area of the triangle is 3/4 units.
What is area of the triangle?
The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.
Suppose
x is the shorter leg of the triangle.
As the longer leg of a right triangle is three times as long as the shorter leg.
⇒ 3x is the longer leg of the triangle.
The hypotenuse of the triangle is, √5.
By using Pythagorean theorem,
[tex]x^2 + (3x)^2 = (\sqrt{5} )^2\\x^2 + 9x^2 = 5\\10x^2 = 5\\x^2 = \frac{5}{10}\\ x^2 = \frac{1}{2} \\x = \frac{1}{\sqrt{2} }[/tex]
⇒ Shorter leg of the triangle is 1/√2.
⇒ Longer leg of the triangle is 3/√2.
Now to find the area of the triangle.
Area of triangle = [tex]\frac{1}{2}(\frac{1}{\sqrt{2} })(\frac{3}{\sqrt{2} } )[/tex]
[tex]A = \frac{3}{4}[/tex]
Hence, the area of the triangle is 3/4 units.
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via gelato is a popular neighborhood gelato shop. the company has provided the following cost formulas and actual results for the month of june: fixed element per month variable element per liter actual total for june revenue $ 13.00 $ 72,540 raw materials $ 4.75 $ 30,330 wages $ 5,700 $ 1.50 $ 14,560 utilities $ 1,730 $ 0.30 $ 3,800 rent $ 2,700 $ 2,700 insurance $ 1,450 $ 1,450 miscellaneous $ 660 0.45 $ 2,990 while gelato is sold by the cone or cup, the shop measures its activity in terms of the total number of liters of gelato sold. for example, wages should be $5,700 plus $1.50 per liter of gelato sold and the actual wages for june were $14,560. via gelato expected to sell 6,000 liters in june, but actually sold 6,200 liters.
Via Gelato total revenue for the month of June as the the details of expenses is equal to $7870.
As given in the question,
Total revenue is:
= (6200 × 13) - 72,540
=$ 8060
Details of all expenses are as follow:
Expense on raw material:
= (6200 × 4.75) -30,330
= -$880
Wages :
= (6200 ×1. 50) + 5,700 - 14,560
= $440
Utilities:
= (6200 × 0.30) +1730 - 3,800
= -$210
Rent:
= (2700-2700)
= 0
Insurance :
= (1450-1450)
= 0
Miscellaneous :
= (6200 × 0.45) + 660 -2,990
= $460
Total expense
=-$190
Net operating income :
=$ [8060-190]
=$7870
Therefore, Via Gelato's total revenue of the June month is equal to $7870.
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w + 2 + 2(w + 3)
HELP FASTTTT
Answer:
Step-by-step explanation:
=w + 2 + 2w + 6
= 3w + 8
3w = -8
w =-8/3
question content area top part 1 determine how many terms of the following convergent series must be summed to be sure that the remainder is less than in magnitude.
The number of terms that must be added together to achieve this series s is 5000.
Given that,
The remainder of the following convergent series must be less than 10 Superscript negative 5 in magnitude.
We have to calculate the number of terms that must be added together to achieve this.
Given
S= summation n=0 to infinity (-1)ⁿaₙ.
An upper bound for the error of the series Rₙ is aₙ₊₁ so
Rₙ=|s-sₙ|≤aₙ₊₁
In this case we have
1/2n+1≤1/10⁴
10⁴≤2n+1
(10⁴-1)/2≤n
(10⁴-1)/2 is approximately 5000.
Therefore, the number of terms that must be added together to achieve this series s is 5000.
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1. Marcus is training for a bike race and has biked 25 miles this week. He needs to bike at least
80 miles this week to complete his training. How many miles should Marcus bike on each of the 5
remaining days this week?
Answer: 11 miles each day for the remaining 5 days
Step-by-step explanation:
First, you subtract the miles already done (25) from the total (80) to get 55 (miles left to do) then next divide 55 by 5 (days left), and then your left with 11. Finally, check the work and see how 11x5=55 then 55+25=80.
That's how to get the answer :)
3(n - 6) = 27
please help
Answer:
n=15
Step-by-step explanation:
Ue the right triangle and the given information to olve the triangle. A = 3; b = 64\deg ; find b, c, and a
The value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.
Define the term trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.For the given question-
The length of the side are-
a = 3 units
Angle B = 64°.
Then,
Applying trigonometric properties-
Tan B = b/a
b = a tan B
b = 3 tan 64°
b = 12.47 units
Now,
Sin B = b/c
c = b sin B
c = 12.47 sin 64°
c = 11.21 units.
Thus, the value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.
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If x = 2, y = -5 and z = -7, then find the value of the following expression. (4x^3-10)/((〖3y〗^2+5)-(〖4x〗^3 (z^2-8))/((y^3+5)))
The value of the mentioned expression is -43.24.
To solve the expression, firstly rewriting the equation followed by keeping the values of x, y and z at their respective places.
Equation = (4x³ - 10)/(3y² + 5) - (4x³ (z² - 8))/(y³ + 5)
Now keeping the values of each variable in the equation
Equation = (4×2³ - 10)/(3×(-5)²) - (4×2³ ((-7)² - 8))/((-5)³ + 5)
Taking cube and square on Right Hand Side of the equation
Equation = (4×8 - 10/(3×15)) - (4×8 (49 - 8))/(25 + 5)
Solving the bracket first where we will perform multiplication on the Right Hand Side
Equation = (32 - 10/45) - ((32 × 41)/30)
Equation = 22/45 - 1312/30
Now performing division on Right Hand Side of the equation
Equation = 0.49 - 43.73
Performing subtraction on Right Hand Side of the equation
Equation = -43.24
Hence, the value is -43.24.
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Review the four points on the complex plane. On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point a is (1, 3), b is (negative 3, 1), c is (negative 1, negative 3), d is (3, negative 1). Which point represents the quotient of startfraction 3 minus i over i endfraction ? a b c d.
The complex numbers will be 3-i and I and the coordinates will be (-1,-3) or C point on the coordinate plane.
What is coordinate plane?Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.
Here,
A=(1,3)
B=(-3,1)
C=(-1,-3)
D=(3,-1)
=(3-i)/i
=-1-3i
The coordinates will be (-1,-3) that is C point on the coordinate plane and the complex numbers be 3-i and i.
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What is the answer to 2(3x - 10) + 3x
Answer: 9x - 20
Step-by-step explanation:
You can graph 2(3x - 10) + 3x.
Here is how I would do it:
First, Distribute
2(3x - 10) + 3x (Original)
6x - 20 + 3x (Distribute)
Second, Combine like terms
6x - 20 + 3x
9x - 20
Therefore, the solution to your problem is 9x - 20
unlike the coefficient of determination, the sample correlation coefficient in a simple linear regression . multiple choice can be greater than 1 measures the percentage of variation explained by the regression line indicates whether the slope of the regression line is positive or negative is a proportion
the regression line indicates whether the slope of the regression line is positive or negative is a proportion will be between 0 to 1
Regression is a statistical method that links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether variations in the dependent variable are related to variations in one or more of the explanatory variables.
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onstruct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint. 0.810.870.901.051.111.141.301.30 1.481.481.591.601.661.691.781.84
A sample observation results in a point estimate of 0.53 for the mean value of paint thickness.
The mean value theorem states that there is one point on a curve where the tangent is parallel to the secant running through the two points.
A low-viscosity paint sample with the following thickness is provided to us.
0.810.870.901.051.111.141.301.301.481.481.591.601.661.691.781.84
a) Point estimate of the mean value of coating thickness.
To estimate the mean coating thickness, we use the mean value of the sample.
mean= sum of all observations/total number of observations
mean=8.16/16
mean=0.53
Question:Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint. 0.810.870.901.051.111.141.301.30 1.481.481.591.601.661.691.781.84 Determine the z percentile associated with each sample observation. (Round your answers to two decimal places.)
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Please I need help on this I don’t get how to do it, show your explanation please and thank you!
Answer:
B/A = 1/2
Step-by-step explanation:
You want the scale factor between the two figures shown.
Scale factorThe scale factor is the ratio of the length in one figure to the corresponding length in the other figure. Often, we're interested in the scale factor B/A, which is what A dimensions need to be multiplied by in order to match the B dimensions.
ApplicationYou can pick any corresponding dimensions. Often, it is convenient to choose a short one, so you don't have to count so many grid squares.
We can choose the line from the center, where the lines cross, up and to the right to the upper right corner. In the A figure, that line goes 2 squares to the right and 2 squares up. In the B figure, that line goes 1 square right and 1 square up. Then the scale factor is ...
(B dimension)/(A dimension) = 1/2
We can choose to look at the lengths of that line (A: 2√2; B: √2), or the x-dimension (A: 2; B: 1) or the y-dimension (A: 2; B: 1). All the measurements are proportional, so we get the same ratio for any pair of corresponding measures.
The scale factor B/A is 1/2.
__
Additional comment
The horizontal magenta lines in the attached figure are another possibility for determining the scale factor. B/A = 2/4 = 1/2.
You need to be careful to understand what scale factor you want. Sometimes it is described as "A to B", which can be ambiguous.
Here, the ratio of an A dimension to a B dimension is A : B = 2 : 1. The same wording can be interpreted to mean "the scale factor that multiplies A to transform it to B." That is the scale factor we have shown.
What could be the right answer for this question? with explanation pls. :))
Answer:
x ≤ -5
Step-by-step explanation:
Treat this EXACTLY like you would an equation:
-3(x+4) ≥ x+8
-3x - 12 ≥ x + 8
-4x - 12 ≥ 8
-4x ≥ 20
Except here (when dividing BOTH sides by a negative):
-4x ≥ 20 ⇒ x ≤ -5
what is the statement of |×+1|+5=2
Step-by-step explanation:
|x+1|=2-5
|x+1|= -3
statement doesn't have solution
Let A (t) = 2 cot-3 cot1, 0 ≤t ≤ 2. 1. Factorize A(t). 2. Hence, olve the equation A(t) = 0 for 0 ≤t≤ 2. (4 mark)
Answers to both the subparts are as follows:
(A) In order to factor A(t), we obtain A(t) = -cost + 1.
(B) t = 1.57 after solving the equation A(t) = 0 for 0 ≤ t ≤ 2.
What are equations?Two expressions are combined by the equal sign to form a mathematical statement known as an equation.
For instance, a formula might be 3x - 5 = 16.
After solving this equation, we learn that the value of the variable x is 7.
(A) Factorize A(t):
A(t) = 2cost - 3cost + 1
After assembling the cost terms, we have:
A(t) = cost(2 - 3) + 1
A(t) = cost(- 1) + 1
A(t) = -cost + 1
In order to factor A(t), we obtain A(t) = -cost + 1.
(B) Solving equation A(t) = 0 for 0 ≤t≤ 2:
Since A(t) = -cost + 1
When we solve A(t) = 0 for 0 ≤ t ≤ 2, we get:
A(t) = 0
-cost + 1 = 0
-cost = -1
cost = 1
If we take the inverse cosine, we get:
t = cos⁻¹(1)
t = π/2
t = 3.142/2
t = 1.571
t ≅ 1.57
t = 1.57 after solving A(t) = 0 for 0 t 2
Therefore, answers to both the subparts are as follows:
(A) In order to factor A(t), we obtain A(t) = -cost + 1.
(B) t = 1.57 after solving the equation A(t) = 0 for 0 ≤ t ≤ 2.
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Complete question:
Let A (t) = 2 cost-3 cost+1, 0 ≤t ≤ 2
A. Factorize A(t).
B. Hence, solve the equation A(t) = 0 for 0 ≤t≤ 2.
A student reads at a constant rate in her chapter book, where the red fern grows. This can be described by the equation y=1/2x. Complete the chart below.
(Pls help)
The chart can be completed by substituting the value of x and y in the given equation in two variable y = 1/2 x
What are Linear Equations in Two Variables?
The linear equations in two variables are the equations in which each of the two variables are of the highest exponent order of 1 and have one, none, or infinitely many solutions. The standard form of a two-variable linear equation is ax + by + c = 0 where x and y are the two variables.
According to the given question:
(Check the attachment below for complete question)
The given function is y = x/2
Let x be the minutes taken by the student and y be the pages read by him.
The chart can be completed by substituting the value of x that is minutes taken in the given equation to find the value of y. (Check attachment below)
If the teacher recommended that student must be read 20 min each night then the page read by the student is y = 20/2 = 10 pages.
If he reads 18 pages then time taken by him is x = 2×18 = 36 min.
If there are 245 pages then the time taken by the student is
x= 2×245 = 490 min
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Please help i am so confused
The domain and the range of the functions are given by the images at the end of the answer.
How to obtain the domain and the range of the function?The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, on the graph, it will be given by the values of x of the graph, the values assumed by the horizontal axis of the graph.
The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, on the graph, it will be given by the values of y of the graph, the values assumed by the vertical axis of the graph.
The notations are given as follows:
Discrete functions -> composed by dots -> the domain and the range are given by the {}, as only the values are assumed, not intervals.Continuous functions -> continuous functions -> domain and range are given by intervals.More can be learned about the domain and range of functions at brainly.com/question/2264373
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Solve for x: x^2 + 6√3 x – 9 = 0
Step-by-step explanation:
use this equation : if , ax² + bx + c = 0 [tex] x \: = \frac{ - b \: \frac{ + }{ } \sqrt{ {b}^{2} - 4ac} \: }{2a} [/tex]so here, a = 1 b = 6√3 c = -9
let's use the formula .......
[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{36 \times 3 - 4(1)( - 9)} }{2(1)} [/tex]
[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{108 \: + 36} }{2} [/tex]
[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{144} }{2} [/tex]
[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} 12 }{2} [/tex]
[tex]x \: = \: \frac{ - 6 \sqrt{3} + 12 }{2} [/tex] OR .......[tex]x \: = \: \frac{ - 6 \sqrt{3} - 12 }{2} [/tex]
so , X = -3√3 +6 ............ or X = -3√3 -6 ............What is 4/250 as a decimal and percentage
Answer:
As a decimal:0.016
As a percentage:1.6%
Step-by-step explanation: