find domain and range?Type in the answer in interval notation. Example: [2,5)
Use U for union to combine intervals. Example: (-oo,2] U [4,oo)Enter DNE for an empty set. For the infinity symbol
, type oo (two lowercase o's)
Answers
The domain and range of the given function are Domain: (−∞,∞),{x|x∈R} and Range: [−2,∞),{y|y≥−2}.
A polynomial function of the form f(x) = ax² + bx + c is called a quadratic function. We already know that the x-intercepts of a quadratic function are given by the quadratic formula (or can be found by factoring). In this worksheet we learn that the graph of any quadratic function is a parabola.
From the given graph, the vertex is (0, -2).
So, the quadratic equation is f(x)=x²-2.
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (−∞,∞),{x|x∈R}
Range: [−2,∞),{y|y≥−2}
Therefore, the domain and range of the given function are Domain: (−∞,∞),{x|x∈R} and Range: [−2,∞),{y|y≥−2}.
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Related Questions
the line with a slope of 9/7 & containing a midpoint of the segment whose end points are (2, -3) & (-6, 5)
Answers
1. Find the midpoint of the segment using the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
2. Use the midpoint and the slope to find the equation of the line in point-slope form. The point-slope form is given by:
y - y1 = m(x - x1), where (x1, y1) is the midpoint and m is the slope.
Substituting the values:
y - 1 = (9/7)(x - (-2))
y - 1 = (9/7)(x + 2)
y - 1 = (9/7)x + (18/7)
3. Simplify the equation to obtain the slope-intercept form:
y = (9/7)x + (18/7) + 1
y = (9/7)x + (18/7) + (7/7)
y = (9/7)x + (25/7)
So, the equation of the line with a slope of 9/7 and containing the midpoint of the segment with endpoints (2, -3) and (-6, 5) is y = (9/7)x + (25/7).
Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:
y = (9/7)x + 25/7.
Step-by-step explanation:Step 1: Find the midpoint of the line segment.
The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:
Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)
Midpoint = (-4 / 2, 2 / 2)
Midpoint = (-2, 1)
So, the midpoint of the line segment is (-2, 1).
Step 2: Write the equation of the line using the slope-intercept form.
The slope-intercept form of a line is given by:
y = mx + b
where m is the slope and b is the y-intercept.
Given the slope as 9/7, we have:
y = (9/7)x + b
Step 3: Substitute the coordinates of the midpoint to find the value of b.
Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:
1 = (9/7)(-2) + b
1 = -18/7 + b
To find the value of b, we can solve this equation:
1 + 18/7 = b
25/7 = b
Step 4: Write the final equation of the line.
Using the value of b, the equation becomes:
y = (9/7)x + 25/7
Evaluate the function values. g(x)=3-2x² ; g (3), g(-4)
Answers
Answer:
Step-by-step explanation:
Which statement applies to the transformed function f(x)−4
?
Answers
The function is odd, and the graph would be shifted downward. option(2)
The statement "f(x) - 4" represents a transformation applied to the original function f(x). This transformation involves subtracting 4 from the values of the function f(x) for all x. In other words, it shifts the entire graph of f(x) downward by 4 units along the y-axis.
Specifically, each y-value of the original function f(x) is reduced by 4. For example, if the original function had a point (x, y), the transformed function f(x) - 4 would have the corresponding point (x, y - 4). This means that every point on the graph is shifted downward by 4 units.
This transformation affects the overall shape, position, and properties of the function. The new graph will have the same general shape as the original, but it will be translated downward. If there were any intercepts or turning points in the original function, they will also be shifted downward by 4 units.
The statement "f(x) - 4" represents a transformation applied to the original function f(x). This transformation involves subtracting 4 from the values of the function f(x) for all x. In other words, it shifts the entire graph of f(x) downward by 4 units along the y-axis.
Specifically, each y-value of the original function f(x) is reduced by 4. For example, if the original function had a point (x, y), the transformed function f(x) - 4 would have the corresponding point (x, y - 4). This means that every point on the graph is shifted downward by 4 units.
This transformation affects the overall shape, position, and properties of the function. The new graph will have the same general shape as the original, but it will be translated downward. If there were any intercepts or turning points in the original function, they will also be shifted downward by 4 units. Option(2)
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QUESTION FOUR
A. Use Excel to prepare an appropriate type of chart (bar, line, pie, scatter) to display
the U.S. energy consumption data. You may modify the default colors, fonts, etc., as
you judge appropriate to make your display effective. (15 pts)
B. What type of chart did you choose, and why did you choose this chart? (5 pts.)
pts.).
3. Explain why you chose each chart; be as thorough as you can on why the selected cha
the type of data (Part B- 5 pts)
4. Note: there may be more than one type of chart that is appropriate. You only need to c
however, if you like, you may also create a second chart for the same question (optiona
URGENT
Answers
The most appropriate chart to depict US energy consumption would be a pie chart since a pie chart helps to see the composition of different proportions representing total consumption.
How to explain the chartsChart A is not appropriate because a line graph is used to depict information to analyze changes over time or over a period. However, to show the energy consumption, the line graph is not an accurate depiction since the type of energy source is a categorical variable.
Chart B is also appropriate because it is a column graph and such type of graphs are used to represent categorical variables. The US energy consumption can be represented well through a column graph as it well depicts the highest consumption source and the lowest consumption source.
Yes more than one kind of display would therefore be acceptable as we can use to show the information through both a pie chart and a column graph.
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A restaurant manager just installed a new dishwasher. She claims that 18% of customers who
have received a drink this week complained that the cup looked dirty.
If this pattern holds, and 3 more customers receive drinks this week, what is the probability
that exactly 3 of the customers will complain that their cup looks dirty?
Write your answer as a decimal rounded to the nearest thousandth.
Answers
The probability that exactly 3 customers out of 3 will complain that their cup looks dirty is 0.006 to the nearest thousandth.
What is the probability?The probability that exactly 3 of the customers will complain that their cup looks dirty is determined as follows:
Using the binomial distribution formula, the probability is calculated as:
P(X = k) = [tex]^{n}C_k * (p^{k}) * (1-p)^{(n-k)}[/tex]
Where:
P(X = k) is the probability of getting exactly k successes.n is the total number of trials.k is the number of desired successes.p is the probability of success in a single trial.[tex]^{n}C_k[/tex] represents the combination of n things taken k at a time.Substituting the values:
P(X = 3) = ³C₃ * (0.18³) * ((1-0.18)³⁻³
P(X = 3) = 0.18³
P(X = 3) = 0.006
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QUESTION TWO
A. Use Excel to prepare an appropriate type of chart (bar, line, pie, scatter) to display
the U.S. petroleum import data. You may modify the default colors, fonts, etc., as you
judge appropriate to make your display effective. (15 pts)
B. What type of chart did you choose, and why did you choose this chart? (5 pts.)
USE DATA FOR QUESTION 2 to SOLVE ANSWER
URGENT
Answers
1) The chart for the above data is attached accordingly.
2) The type of chart chosen is a line chart. This is because it is able to display the undulations in each of the data given.
What is a line chart?A line chart is a graphical depiction of an asset's historical price activity in which a sequence of data points are connected by a continuous line.
This is the most basic sort of chart used in finance, and it generally merely shows the closing prices of a securities over time.
Line charts may be used for any timescale, however they are most commonly used for tracking day-to-day price fluctuations.
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I’LL GIVE BRAINLIEST, A HEART, AND 5 STARS TO WHOEVER ANSWERS FIRST
(Please answer ALL questions and show how you got the answer!)
Answers
Group B has a lower range of salsa students and Group A shows more variability in the ages of salsa students.
To determine which group has a lower range of salsa students, we need to calculate the range for each group.
The range is obtained by finding the difference between the maximum and minimum values.
Group A:
Minimum age: 5 years
Maximum age: 29 years
Range for Group A: 29 - 5 = 24 years
Group B:
Minimum age: 7 years
Maximum age: 21 years
Range for Group B: 21 - 7 = 14 years
Comparing the ranges, we find that Group B has a lower range of salsa students.
To determine which group shows more variability in the ages of salsa students, we can compare the ranges, as calculated above.
A larger range indicates greater variability.
From the previous calculations, we found that Group A has a range of 24 years, while Group B has a range of 14 years.
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HELPP BUISNESS MATH
Loan comparison
Answers
Loan 1 would require more money over the time of the loan.
Does more time mean that you pay back more money on a loan at a given interest rate?When you borrow money, the lender assesses interest as compensation for letting you use their resources. The principal, or the amount borrowed initially, and the length of time it takes to repay the loan are used to compute interest. Interest must accumulate over a longer length of time the longer the repayment duration.
The number of interest accrual periods rises as a result of extending the payback period, which raises the total amount of interest paid. The total interest paid over a longer term will be larger than over a shorter period even if the interest rate stays the same.
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Identify the Focus, directrix, and axis of symmetry of the
parabola modeled by 3x² - 6y = 0
thanks :)
Answers
From this parabola, we are able to identify that:
The focus lies at (h, k + p). In this case, the center is at (0, + 1/2) = (0, 1/2).The directrix could be an even line found at y = k - p. In this case, the directrix is y = - 1/2 = -1/2.The axis of symmetry is the vertical line passing through the center and directrix. In this case, the hub of symmetry is x = 0.How to identify the focus, directrix, and axis of the symmetry of the parabolaTo distinguish the focus, directrix, and axis of symmetry of the parabola modeled by the condition 3x² - 6y = 0, ready to revamp the condition in standard shape, which is (x - h)² = 4p(y - k).
Comparing this standard frame with the given condition, we have:
3x² - 6y =
Isolating the condition by 3, we get:
x² - 2y =
Presently, we are able to rework it within the standard frame by completing the square:
(x - 0)² = 2(y - 0)
(x - 0)² = 2y
Subsequently, the focus is (0, 1/2), the directrix is y = -1/2, and the axis of symmetry is x = for the parabola modeled by the condition 3x² - 6y = 0.
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Mrs may is planning for her son's graduation and decides to invest her bonus money for two years. She invests the money in an institution offering interest that is compounded annually at an interest rate of 5.8% for the first year and 6,5% for the second year.
An annual bonus is a 13th chequered which is equal to a monthly salary without deductions.
She only used one year's annual bonus.
Her annual income is R 336000 after she received an increase of 6.5%.
4.1 calculate her annual income before she received the increase.
4.2 Calculate how much money will be paid out to her after the two year period
Answers
Let's assume her annual income before the increase is X.
After receiving an increase of 6.5%, her new annual income becomes:
X + 6.5% of X = X + (0.065 * X) = 1.065 * X
Given that her new annual income is R 336,000, we can set up the equation:
1.065 * X = R 336,000
To find X, we divide both sides of the equation by 1.065:
X = R 336,000 / 1.065
X ≈ R 315,492.96
Therefore, Mrs. May's annual income before she received the increase was approximately R 315,492.96.
4.2 To calculate how much money will be paid out to her after the two-year period, we can calculate the compound interest for each year and add it to the initial investment.
The initial investment is the annual bonus she used, which is equal to her monthly salary without deductions. Since the problem does not provide the exact amount, we cannot calculate the exact payout. However, we can calculate the payout based on a general assumption.
Let's assume the annual bonus she used is X.
For the first year, the interest rate is 5.8%. Therefore, the investment after the first year is:
X + 5.8% of X = X + (0.058 * X) = 1.058 * X
For the second year, the interest rate is 6.5%. Therefore, the investment after the second year is:
1.058 * X + 6.5% of (1.058 * X) = 1.058 * X + (0.065 * 1.058 * X) = 1.058 * X + (0.06887 * X) = 1.12687 * X
The payout after the two-year period is the final investment, which is 1.12687 times the initial investment:
Payout = 1.12687 * X
Since the problem does not provide the exact value of X, we cannot calculate the exact payout amount. However, you can substitute the value of X (Mrs. May's annual bonus) into the equation to calculate the specific payout amount based on the given information.
I am struggling bad help please
Answers
Answer:
Step-by-step explanation:
What fraction is shown on the number line?
Answers
Answer:
3/4 there are 4 lines indicating the numbers and it is on the 3rd.
a 20-ft long ladder against the side of his house. The ladder reaches to a height of 16-ft up the side of the house. Which of the following will give the angle of elevation of the ladder?
Answers
The angle of elevation is 44.4°
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. The angle of elevation is calculated by using trigonometry ratio.
Example is a man that is looking at a mango on the mango tree by an angle. This angle is angle of elevation.
sinθ = opp/hyp
cosθ = adj/hyp
tanθ = opp/adj
The opposite to the angle of elevation is the height of the house and the hypotenuse is the length of the dollar.
sinθ = 14/20
sinθ = 0.7
θ = 44.4°
therefore the angle of elevation is 44.4°
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Please solve this with clear steps!!!!! 20 POINTS
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The width of the river using the similar triangle is 43.3 metres.
How to find the width of the river?The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.
Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Hence, let's find the width of the river.
Therefore,
18.6 / 34.2 = AB / 79.6
cross multiply
18.6 × 79.6 = 34.2 AB
34.2 AB = 1480.56
divide both sides of the equation by 34.2
AB = 1480.56 / 34.2
AB = 43.2912280702
AB = 43.3 metres
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Remove the largest possible common factor. Check your answer by multiplication.
Answers
The greatest common factor of 25x⁵ - 15x² - 20x is 5x.
How to find the greatest common factor of a polynomial?The greatest common factor (GCF) of a set of numbers is the largest factor \that all the numbers share.
In other words, the greatest common factor (GCF) of a set of whole numbers or polynomial is the largest positive integer that divides evenly into all numbers with zero .
Therefore, let's find the greatest common factor of 25x⁵ - 15x² - 20x.
Hence,
25x⁵ - 15x² - 20x = 5x(5x⁴ - 3x - 4x)
Therefore, the greatest common factor is 5x.
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Lucia has $10.00 less than her sister. Lucia has n-10 dollars.
Answers
Lucia's sister has n - 10 dollars.
To solve this problem
We can create an equation to depict the relationship between Lucia's and her sister's financial situations if Lucia has n–10 dollars and her sister has $10.00 more.
Assume that Lucia's sister has $x. We can write the equation using the information provided:
n - 10 = x
According to this formula, Lucia's wealth (n-10) is equivalent to her sister's wealth (x). We may find the quantity for Lucia's sister by rearranging the equation as follows:
x = n - 10
Therefore, Lucia's sister has n - 10 dollars.
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Point on a graph of function f(x)=2(×-4)^-1 and x=2
Answers
f(x) = 2/(x-4)
f(2) = 2/(2-4)
f(2) = -1
Therefore, the point on the graph of f(x) at x=2 is (2, -1).
(Y-2)^2/16-(x+1)^2/144+1
Answers
[tex]\textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y-2)^2}{16}-\cfrac{(x+1)^2}{144}=1\implies \cfrac{(y-2)^2}{4^2}-\cfrac{( ~~ x-(-1) ~~ )^2}{12^2}=1[/tex]
now, since the positive fraction is the one with the "y" in it, that means the traverse axis is running over the y-axis in short the hyperbola is opening up and down.
From the same equation above, we can see the center is at (-1 , 2) and the conjugate axis has a half which is "b" or namely b = 12, since that's half of the conjugate axis, then the conjugate axis must be 2b or 24.
What is the value of y in the equation 4 + y = −3? (1 point) a 7 b 1 c −1 d −7
Answers
Answer:
-7
Step-by-step explanation:
someone please tell me what is the equation of the blue line
Answers
Hope this helps!
Answer:
y = - 1/2 x + 2
Step-by-step explanation:
Main concepts:
1. Slope intercept form of Equation for a line
2. ordered pairs
3. Finding the y-intercept
4. Finding slope
5. Finding the equation for our line
1. Slope intercept form of Equation for a line
For any non-vertical line, the equation can be written in "slope-intercept" form: [tex]y=mx+b[/tex] where b is the y-coordinate of the y-intercept of the line, m is the "slope" of the line, and x & y are the (x,y) coordinates of any point you choose on the line.
2. ordered pairs
Any point on the coordinate system (whether on the line or not) is defined by an (x,y) coordinate pair. All points are measured starting from the origin (0,0).
The "x-coordinate" is the distance to the left or right of the origin, and the "y-coordinate" is the distance above or below the origin.
3. Finding the y-intercept
The y-intercept of a line is the place where the line crosses the "y-axis" (the vertical axis). Notice that the blue line crosses the y-axis at a height of 2, so the y-intercept is (0,2), and [tex]b=2[/tex]
4. Finding slope
The slope of any non-vertical line can be found from two known points [tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex] using the following formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Both to minimize error to to work with "nicer" numbers, try to choose points that are crossing through the intersection of grid lines (but any two points will work). Two points that are fairly easy to identify on this line are (0,2) and (4,0). (these two points are the y-intercept that we already identified, and the place where the blue line crosses the horizontal axis -- called the x-intercept).
Substituting into the formula:
[tex]m=\dfrac{(0)-(2)}{(4)-(0)}[/tex]
[tex]m=\dfrac{-2}{4}[/tex]
[tex]m=-\frac{1}{2}[/tex]
5. Finding the equation for our line
Knowing both the y-intercept and the slope, we can now substitute the values into the equation and get the equation for this line:
[tex]y=- \frac{1}{2}x+2[/tex]
How to Graph -2x^2+12x-17
Answers
The graph of equation is shown in figure.
We have to given that,
The equation is,
⇒ y = - 2x² + 12x - 17
Now, We have the given equation is a quadratic equation.
Hence, We can simplify as,
⇒ y = - 2x² + 12x - 17
⇒ y = - 2 (x² + 6x) - 17
⇒ y = - 2 (x² - 6x + 3² - 3²) - 17
⇒ y = - 2 (x - 3)² + 18 - 17
⇒ y = - 2 (x - 3)² + 1
Hence, This represent the equation of parabola with vertex (3, 1).
Thus, The graph of equation is shown in figure.
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Can someone please help awnser these.
Answers
The answers are 4. a) 15.7 cm, b) 26.25 m, 5. a) 128.74 cm, b) 40.82 mm, c) 45 cm and 6. 777.28 cm
Given are the circles and the circular items we need to find their circumference,
Circumference of a circle = 2π × radius = Diameter × π
4. a) Circumference = 5 × 3.14 = 15.7 cm
b) Circumference = 8.36 × 3.14 = 26.25 m
5. a) Circumference = 41 × 3.14 = 128.74 cm
b) Circumference = 13 × 3.14 = 40.82 mm
c) Circumference = 14.3 × 3.14 = 45 cm
6.
The perimeter of the cloth = circumference of the circular ends plus length in the middle,
= 76 × 2 × 3.14 + 150 × 2
= 477.28 + 300
= 777.28 cm
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solve please! x − 6y = –15
Answers
The equation x - 6y = -15 does not have a unique solution without additional information or constraints. It represents a line with infinitely many solutions (x, y) that satisfy the equation.
To solve the equation x - 6y = -15, we need to isolate one variable and solve for it. Let's solve for x in terms of y:
x = -15 + 6y
Now we have an expression for x in terms of y. This means that for any given value of y, we can substitute it into the equation to find the corresponding value of x.
Alternatively, if you have another equation involving x and y, we can substitute the expression for x into that equation to solve for y.
However, if we're only given the equation x - 6y = -15 without any additional information or constraints, we cannot find unique values for x and y. This equation represents a straight line in the coordinate plane, and there are infinitely many points (x, y) that satisfy this equation.
To illustrate this, let's plot the equation x - 6y = -15 on a graph:
We can rearrange the equation to the slope-intercept form y = (1/6)x + (15/6). From this form, we can see that the coefficient of x is the slope of the line, which is 1/6, and the y-intercept is (0, 15/6).
Using this information, we can plot the line and see that it extends infinitely in both directions.
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tebogo is a street vendor who buys blankets from a wholesaler for R60 per blanket.he is restricted to 50 blankets per month.his total costs include a monthly delivery fee of R120 and rent for selling space .calculate his total cost per month
Answers
Answer:
here is not much information
Step-by-step explanation:
To calculate Tebogo's total cost per month, we need to consider the cost of blankets, delivery fee, and rent for selling space.
Cost of blankets:
Tebogo buys blankets from the wholesaler at R60 per blanket. Since he is restricted to 50 blankets per month, the cost of blankets is calculated as follows:
Cost of blankets = R60 per blanket x 50 blankets = R3000
Monthly delivery fee:
Tebogo incurs a monthly delivery fee of R120.
Rent for selling space:
The rent for selling space is not provided in the given information. To calculate the total cost per month, we would need the specific amount for rent.
To determine the total cost per month, we can sum up the costs:
Total cost per month = Cost of blankets + Monthly delivery fee + Rent for selling space
However, since the rent for selling space is not provided, we cannot calculate the exact total cost per month without that information.
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(Please answer ALL questions and show how you got the answer!)
Answers
Group B has lower range.
Group A shows variability.
Mean is the best to make concussion about age of Salsa students.
Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.
This inference is supported by the observation that the majority of data points in Group B are concentrated around younger ages.
In contrast, Group A exhibits a more dispersed distribution of data points across a wider range of ages, including higher.
So, Group B has lower range.
and, Group A shows variability.
Lastly, Mean is the best to make concussion about age of Salsa students.
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Which of the following is true for congruent triangles ABC and DEF?
Any transformation will map one triangle onto the other
AB = EF
Only a reflection will map one onto the other
Answers
The transformation mapping triangle ABC into triangle DEF is given as follows:
A. reflection.
What are transformations on the graph of a function?Examples of transformations are given as follows:
A translation is defined as lateral or vertical movements.A reflection is either over one of the axis on the graph or over a line.A rotation is over a degree measure, either clockwise or counterclockwise.For a dilation, the coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.For this problem, the biggest change is in the orientation of the figure, hence the figure was a reflection.
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It represents the numerical value of a simple event of an experiment.
Answers
The significance of sample size in statistical experiments cannot be overstated. A larger Sample size enhances the reliability and generalizability of the results, reducing sampling errors and increasing statistical power.
Sample size is a critical aspect of statistical experiments that significantly impacts the reliability of the results. It represents the number of individuals, observations, or data points included in a study. Understanding the significance of sample size is essential for ensuring the validity and generalizability of statistical findings.
The size of the sample directly influences the precision and accuracy of the estimates or conclusions drawn from the data. A larger sample size generally leads to more reliable results by reducing sampling errors and increasing the representativeness of the population under study. With a larger sample, the estimates are likely to be closer to the true values, providing greater confidence in the findings.
When the sample size is small, the variability in the data may be magnified, making it challenging to draw accurate conclusions. Results obtained from a small sample may not adequately capture the diversity or complexity of the population, leading to biased or misleading findings. This is known as sampling error, where the sample does not fully reflect the characteristics of the larger population.
Moreover, the statistical power of an experiment is directly related to the sample size. Statistical power refers to the ability of a study to detect true effects or relationships between variables. A larger sample size increases the power of the analysis, allowing researchers to identify smaller, yet meaningful, differences or associations. In contrast, a small sample size may result in low statistical power, making it difficult to detect significant effects even if they exist.
It is important to note that sample size requirements can vary depending on the research design, objectives, and the anticipated effect size. Complex studies or analyses involving rare events or small effect sizes may require larger sample sizes to achieve sufficient power and precision.
In conclusion, the significance of sample size in statistical experiments cannot be overstated. A larger sample size enhances the reliability and generalizability of the results, reducing sampling errors and increasing statistical power. Researchers should carefully consider sample size calculations to ensure their studies yield robust and trustworthy conclusions.
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The figure below shows part of a circle, with central angle as marked. What part of
the full circle does the figure represent? Express your answer as a fraction in simple
terms.
150°
Answers
The part of the circle represented by an angle of 150º is given as follows:
5/12.
How to obtain the part of the circle?The part of the circle represented by an angle of 150º is obtained applying the proportions in the context of the problem.
The angle measure representing the entire circle is given as follows:
360º.
The central angle for the circle in this problem is given as follows:
150º.
Hence the part of the circle represented by an angle of 150º is given as follows:
150/360 = 15/36 = 5/12.
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What’s the square root of √125
Answers
Answer: [tex]5\sqrt 5[/tex]
Step-by-step explanation:
Sol [tex]\sqrt 125[/tex] = [tex]\sqrt{25.5}[/tex]
= [tex]\sqrt{25}[/tex] x [tex]\sqrt{5}[/tex]
[tex]5 \sqrt{5}[/tex]
For each equation, write the coordinates of the vertex of the graph that represents the equation.
1.3 = (x - 3)? + 5
2.y = (= + 7)? + 3
39= (¢ = 4)2
4.1=12-1
5.g= 2(2+ 1)2- 5
69=-2(+12-5
Answers
The coordinates of the vertex for each quadratic function are given as follows:
1. (3,5).
2. (-7,3).
3. (4,0).
4. (0,-1).
5. (-1,-5).
6. (-1,-5).
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.More can be learned about quadratic functions at https://brainly.com/question/1214333
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