Answers
Let y = f(x). Then we have:
y = 3/(7x + 1)
Multiplying both sides by 7x + 1, we get:
y(7x + 1) = 3
Expanding the left side, we get:
7xy + y = 3
Subtracting y from both sides, we get:
7xy = 3 - y
Dividing both sides by 7y, we get:
x = (3 - y)/(7y)
Therefore, the inverse of f(x) is:
f^-1(x) = (3 - x)/(7x)
Explanation: To find the inverse function, we set y = f(x) and solve for x. By isolating x on one side of the equation in terms of y, we obtain the inverse function.
B. Let g(x) = (3 - x)/(7x). We need to verify that (f(g(x))) = x for all values of x in the domain of f(x) and g(x).
We have:
f(g(x)) = f((3 - x)/(7x)) = 3/(7((3 - x)/(7x)) + 1) = 3/(3 - x + 7x)/(7x) = 3/(3 + 6x)/(7x) = (21x)/(3 + 6x) = 7x/(1 + 2x)
To show that (f(g(x))) = x, we need to show that:
7x/(1 + 2x) = x
Multiplying both sides by (1 + 2x), we get:
7x = x(1 + 2x)
Expanding the right side, we get:
7x = x + 2x^2
Subtracting 7x from both sides, we get:
0 = x + 2x^2 - 7x
Simplifying, we get:
2x^2 - 6x = 0
Dividing both sides by 2x, we get:
x - 3 = 0
Therefore, x = 3.
Since we have shown that (f(g(x))) = x for x = 3 (which is in the domain of both f(x) and g(x)), we can conclude that g(x) is the inverse of f(x).
C. We cannot answer part C of the question because no function is given. The table provided only shows a set of input-output pairs, but we need the function itself to perform any further analysis.
The domain and range of the inverse function f^-1(x) = (3 - x)/(7x) depend on the domain and range of the original function f(x) = 3/(7x + 1).
The domain of f(x) is all real numbers except -1/7 (since division by zero is undefined). Therefore, the range of f^-1(x) is all real numbers except 0, since division by zero is also undefined.
To find the domain of f^-1(x), we can consider the denominator of the expression for f^-1(x), which is 7x. Since division by zero is undefined, we need to exclude any value of x that makes the denominator equal to zero. Therefore, the domain of f^-1(x) is all real numbers except 0.
In summary:
Domain of f^-1(x): All real numbers except 0
Range of f^-1(x): All real numbers except 0
Related Questions
6. When was Harriet Tubman born?
Answers
Answer: 1945
Step-by-step explanation:
Answer:
Harriet Tubman was born in 1820.
Step-by-step explanation:
Showing how brave and resourceful she was in running such a dangerous operation. A black woman operating in slave territory could be highly noticeable. It is a testament to her courage, brains, and fortitude that she was successful. Also, kudos to the many white persons who manned the stations along the Underground Railroad who coordinated with her.
Her impact on America—demonstrating an individual with struggle can accomplish much and correct wrongful structures in our land.
Slope models the direction and steepness of a line, while the y intercept defines the starting point. Explain what following equation of a line represents y=-2/3x+6
Answers
The equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).
What is the Slope?The slope refers to the measure of the steepness of a line or a curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or the curve.
The equation of a line can be written as with the help of slope intercept form is given by:
y = mx + b
Where "b" is the y-intercept and "m" is the line's slope of the line.
In the equation y = (-2/3)x + 6, we can see that the slope 'm' is -2/3, which means that for every unit increase in x, the y-value decreases by 2/3 of a unit. This tells us that the line represented by this equation is decreasing (i.e., sloping downwards) from left to right.
The y-intercept 'b' is 6, which means that the line intersects the y-axis at the point (0, 6). This is the starting point of the line, where the value of y is 6 when x is 0.
Therefore, the equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).
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Let C be a unit circle centred at the origin, evaluate the complex integral of zdz/((z-a)^2) when; a<1 and a>1
Answers
The complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C is [tex]\frac{-4\pi i}{a}[/tex] if a < 1, and 0 if a > 1.
Evaluating the complex integralFrom the question, we are to evaluate the given complex integral when a <1 and a > 1
We can evaluate the complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C using the residue theorem. Since the function has a pole of order 2 at z = a, we need to compute the residue of the function at that point.
If a < 1, then the point a is inside the unit circle C. To compute the residue at z = a, we can expand the function in a Laurent series centered at z = a:
[tex]\frac{zdz}{(z-a)^2}= (\frac{1}{(z-a)})^2 d(z-a)[/tex]
= (1/(z-a))^2 dz - (2/(z-a))^1 da + ...
[tex](\frac{1}{(z-a)})^2dz -(\frac{2}{(z-a)})^1 da + ...[/tex] (Laurent series expansion)
The residue of the function at z = a is given by the coefficient of the [tex](z-a)^{-1}[/tex] term in this expansion, which is:
[tex]Res[z=z0] \frac{z dz}{(z-a)^2} = \frac{-2}{(a - 0)^1} = \frac{-2}{a}[/tex]
Therefore, by the residue theorem, the value of the integral is given by:
[tex]\oint \frac{c zdz}{(z-a)^2} = 2\pi i \times \frac{-2}{a} = \frac{-4\pi i}{a}[/tex]
If a > 1, then the point a is outside the unit circle C. Since the function is holomorphic on and inside the unit circle, it has no singularities inside C and the integral is zero:
[tex]\oint \frac{c zdz}{(z-a)^2} = 0[/tex]
Hence, the complex integral is [tex]\frac{-4\pi i}{a}[/tex] when a < 1, and 0 if a > 1.
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pls help im very stuck
Answers
Answer:
Step-by-step explanation:
zachary climed 9.5 m
erin climed 8.8m
to 2 dp
zachary-9.51
erin-8.76
the sum of the base and the height of a triangle is 22cm find the dimension for which the area is a maximum height and base
Answers
Answer: Let's call the base of the triangle "b" and the height of the triangle "h". We are given that the sum of the base and the height is 22 cm, so we can write:
b + h = 22
We want to find the dimensions for which the area of the triangle is a maximum. The formula for the area of a triangle is:
A = (1/2)bh
We can use the equation b + h = 22 to solve for h in terms of b:
h = 22 - b
We can substitute this expression for h into the formula for the area:
A = (1/2)b(22 - b)
Simplifying this expression, we get:
A = 11b - (1/2)b^2
To find the value of "b" that maximizes the area, we can take the derivative of this expression with respect to "b" and set it equal to zero:
dA/db = 11 - b = 0
Solving for "b", we get:
b = 11
Substituting this value of "b" back into the equation b + h = 22, we get:
h = 22 - b = 22 - 11 = 11
Therefore, the dimensions for which the area of the triangle is a maximum are:
base = 11 cm
height = 11 cm
And the maximum area is:
A = (1/2)bh = (1/2)(11 cm)(11 cm) = 60.5 square cm
Step-by-step explanation:
Division - Answer in gallons and quarts.
12.) 3 ) 10 gallons 11 quarts
1 gal. = 4 quarts
Answers
The answer to this question is 4 Gallons and 1 quart or we can say 17 quarts.
What is Gallon?The US Customary System defines a unit of liquid volume or capacity as 4 quarts (3.79 liters).
we have to find the value of 10 gallons and 11 quarts in gallons and quarters after dividing by 3.
As we know,
1 gallon = 4 quarts
10 gallons = [tex]10 * 4[/tex]=40 quarts
so 40 quarts + 11 quarts= 51quarts
It must be divided by 3 (According to the question we have to divide by 3 )
So, it becomes,
[tex]\frac{51}{3} =17[/tex]
Now we get 17 quarts.
And 17 quarts= 4 gallons and 1 quarts
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Help!!!!!!!
Convert this rational number to its decimal form and round to the nearest thousandth. 2/7
Answers
Answer: 2/7 as a decimal rounded to the nearest thousandth is 0.286.
Hugo averages 72 words per minute on a typing test with a standard deviation of 7 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(72,7). Suppose Hugo types 80 words per minute in a typing test on Wednesday. The z-score when x=80 is ________. This z-score tells you that x=80 is ________ standard deviations to the ________ (right/left) of the mean, ________. Correctly fill in the blanks in the statement above. Select the correct answer below:
Answers
Answer:
i don't know
Step-by-step explanation:
good luck bro
(alright I'm just here for the points so yeah bye)
I have tried x-1*2 and it didn't work. Please help
Answers
Answer:
(x - 1 ) × 3or3x - 3Step-by-step explanation:
I think a number
x
tke away 1x - 1
multiply the result by 3 (to do t his you have to put the brackets at x - 1)(x - 1 ) × 3
solve(x - 1 ) × 3 =
3x - 3
you didn’t multiply by 3
Which is equivalent to 3√2
? Select all that apply
Responses
tan 45°
tan 45°
cos 45°
cos 45°
sin 45°
sin 45°
sin 30°
sin 30°
sin 60°
sin 60°
cos 30°
cos 30°
tan 30°
Answers
Answer:
Sin 60°
Sin 60°
Cos 30°
Cos 30°
what is -7 in binary and also what is -5 in binary
Answers
Answer:
-7 in binary is -0b111.
-5 in binary is -0b101.
Step-by-step explanation:
Answer:
-111
-101
Step-by-step explanation:
Binary uses powers of 2.
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
7 = 4 + 2 + 1
7 = 1 × 2^2 + 1 × 2^1 + 1 × 2^0
7 in binary is 111
-7 in binary is -111
5 = 4 + 1
5 = 1 × 2^2 + 0 × 2^1 + 1 × 2^0
5 in binary is 101
-5 in binary is -101
Carlo is shown the results of two surveys about the preferred practice day of all players in a soccer league. The surveys are based on two different samples, and the results are very different. What information about the surveys might help Carlo decide which result is likely to be more accurate?
Please help, I really need to turn it in.
Answers
Carlo should consider the sample size, sampling method, response rate, and sampling frame when determining which survey result is likely to be more accurate. By investigating these factors, Carlo can make an informed decision as to which survey result is likely to be more accurate.
What is sample size?Sample size is the number of participants or observations in a given study or experiment. It is an important factor in determining the validity and accuracy of the results. Large sample sizes are typically needed for experiments that involve multiple variables and for research with a small population. Sample size also affects the power of a test, which is the probability of correctly rejecting the null hypothesis.
In order to determine which survey result is more accurate, Carlo should first consider the sample size of each survey. If the sample size of one survey is significantly larger than the other, it is likely to be more accurate. Additionally, Carlo should consider the sampling method used in each survey. If one survey used a random sampling method while the other was not, then the random sample is more likely to be more representative of the entire population of players in the soccer league. Carlo should also consider the response rate for each survey, as surveys with higher response rates tend to be more accurate. Finally, Carlo should investigate the sampling frame used in each survey. If one survey used a sampling frame that was more representative of the population than the other, then it is likely to be more accurate.
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A firm’s profit increased from 2020 to 2021 by 20%, but it decreased by 17% from
2021 to 2022. Which of the years 2020 and 2022 had the higher profit
Answers
Answer:
Step-by-step explanation:
Let the profit in 2020 be P.
The profit in 2021 would then be 1.20P (20% increase).
The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).
We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).
Therefore, the higher profit was in 2020.
The solution is, the higher profit was in 2020.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
Let the profit in 2020 be P.
The profit in 2021 would then be 1.20P (20% increase).
The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).
We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).
Therefore, the higher profit was in 2020.
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Select the correct answer. Given: p || q, and r || s. Linear pair theorem that is angle 1 is supplementary to angle 2 moves down to angle 2 equals angle 6. As for parallel lines cut by a transversal, corresponding angles are congruent. This moves down to blank box with question mark. Prove: ∠1 and ∠14 are supplementary angles. Two vertical parallel lines p and q runs through two horizontal parallel lines r and s to form 16 angles numbered from 1 to 16. What is the next step in the proof? Choose the most logical approach. A. Statement: ∠6 ≅ ∠14 Reason: For parallel lines cut by a transversal, corresponding angles are congruent. B. Statement: ∠6 ≅ ∠7 Reason: Vertical Angles Theorem C. Statement: ∠6 and ∠5 are supplementary. Reason: Linear Pair Theorem D. Statement: m∠6 + m∠8 = 180° Reason: angle addition
Answers
Since p || q and r || s, we know that angle 6 and angle 14 are corresponding angles. By the Corresponding Angles Theorem, we know that corresponding angles are congruent when parallel lines are cut by a transversal. Therefore, we can say that ∠6 ≅ ∠14.
To prove that ∠1 and ∠14 are supplementary angles, we can use the fact that ∠1 and ∠6 are a linear pair, which means that they are adjacent angles that form a straight line and are therefore supplementary. Since ∠6 ≅ ∠14, we can substitute ∠14 for ∠6 in the equation to get:
∠1 + ∠14 = 180°
Therefore, we have proved that ∠1 and ∠14 are supplementary angles.
7,707 ÷ 24
what is also the R
Answers
Answer:321.125 and i think the R that you are trying to say stands for remainder
Step-by-step explanation:
Postal order:
Value
N15
N20
N50
N100
Commission
50K
N1.20K
N3.10K
N5.50K
Money order:
Value
Up to N50
N50 to N100
N100 to N500
N500 to 1000
Commission
N7.50
N11.30
N14.70
N15.50
1.Use the poster order table to calculate the cost of buying a postal order of N365=
10. Use the poster order table to find the buying of a poster order of N15.=
Answers
The total cost of buying a postal order of N15 would be N15.50.
How to solveTo calculate the cost of buying a postal order of N365, we need to determine the commission associated with the value of N365 in the postal order table.
Since N365 is between N100 and N50, the commission for this amount would be N5.50.
Therefore, the total cost of buying a postal order of N365 would be N365 + N5.50 = N370.50.
To find the cost of buying a postal order of N15, we look at the postal order table and find that the commission associated with N15 is 50k.
Therefore, the total cost of buying a postal order of N15 would be N15 + 50k = N15.50.
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The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:
Constraint Television Radio Online
Audience per advertisement 140,000 18,000 30,000
Cost per advertisement $1,500 $200 $550
Maximum media usage 15 19 12
To ensure a balanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 15% of the total number of advertisements authorized.
(a) If the promotional budget is limited to $24,100, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”.
Advertisement Alternatives No of commercial
messages
Television
Radio
Online
What is the allocation of the budget among the three media?
Advertisement Alternatives Budget Allocation
Television $
Radio $
Online $
What is the total audience reached?
(b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.
Increase in audience coverage of approximately
Answers
The commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.
Linear programming: What is it?A mathematical method called linear programming is used to maximise a linear objective function under the restrictions of linear equality and inequality. Finding choice variable values that maximise or decrease the objective function while meeting the limitations is required.
Let us suppose the number of advertisement run on television = x.
Let us suppose the number of advertisement run on radio = y.
Let us suppose the number of advertisement run on online = z.
Then,
140,000x + 18,000y + 30,000z
The constraints on the ads run on are as follws:
1,500x + 200y + 550z <= 24,100 (budget constraint)
x <= 15 (television usage limit)
y <= 19 (radio usage limit)
z <= 12 (online usage limit)
y <= 0.45(x+y+z) (radio usage limit as a percentage of total usage)
x >= 0.15(x+y+z)
Using the linear programming model we have:
x = 15, y = 7 and z = 12.
Substitute the value of x, y, and z:
140,000(15) + 18,000(7) + 30,000(12) = 2,910,000
Hence, the commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.
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Bian wants to write the integers 1 to 9 in the nine boxes shown so that the integers in any three adjacent boxes add to a multiple of 3. In how many ways can she do this?
Answers
Answer: To satisfy the given condition, we need to place the numbers in the boxes in a way that the sum of any three adjacent boxes is divisible by 3.
We can divide the boxes into three groups as follows:
Group 1: Boxes {1, 4, 7}
Group 2: Boxes {2, 5, 8}
Group 3: Boxes {3, 6, 9}
For any three boxes in a group, the sum of their contents must be divisible by 3. We can place any multiple of 3 in the middle box of each group, and the other two boxes will have to be filled accordingly.
Step-by-step explanation:
For Group 1:
If we place 3 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 1.
If we place 6 in the middle box, then the boxes 1 and 7 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 5}, {1, 8}, {4, 5}, {4, 8}, {7, 5}, {7, 8}. This gives us another 6 possible ways to fill the boxes in Group 1.
For Group 2:
If we place 3 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 2}, {1, 5}, {4, 2}, {4, 5}, {7, 2}, {7, 5}. This gives us 6 possible ways to fill the boxes in Group 2.
If we place 6 in the middle box, then the boxes 2 and 8 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {1, 8}, {1, 5}, {4, 8}, {4, 5}, {7, 8}, {7, 5}. This gives us another 6 possible ways to fill the boxes in Group 2.
For Group 3:
If we place 3 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 9}, {2, 6}, {5, 9}, {5, 6}, {8, 9}, {8, 6}. This gives us 6 possible ways to fill the boxes in Group 3.
If we place 6 in the middle box, then the boxes 3 and 9 must be filled with numbers that add up to a multiple of 3. We can choose from the following pairs: {2, 6}, {2, 3}, {5, 6}, {5, 3}, {8, 6}, {8, 3}. This gives us another 6 possible ways to fill the boxes in Group 3.
Therefore, the total number of ways to fill the boxes is:
6 x 6 x 6 x 6 = 1296.
Thus Bian can write the integers 1 to 9 in these ways.
hope it helps...
Find the value of X using Trigonometry. Round your answer to the nearest tenth.
Answers
Answer:
x ≈ 10.4
Step-by-step explanation:
using the tangent ratio in the right triangle
tan41° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{x}[/tex] ( multiply both sides by x )
x × tan41° = 9 ( divide both sides by tan41° )
x = [tex]\frac{9}{tan41}[/tex] ≈ 10.4 ( to the nearest tenth )
Answer:
x=10.34
Step-by-step explanation:
tanФ=opposite ÷ adjacent
tan41°=9/x
0.87=9/x
x=9/0.87
=10.34
Find the equation of the ellipse, centre and directrices given that the end points of the major axis are (4,1) and (8,1) and the eccentricity is 1/3
Answers
The equation of the ellipse is (x - 6)² / 4 + (y - 1)² / (16/9) = 1, the center is (6,1), and the directrices are x = 0 and x = 12.
How to explain the equationThe center of the ellipse is the midpoint of the major axis. The midpoint of the line segment connecting (4,1) and (8,1) is ((4+8)/2, (1+1)/2) = (6,1). Therefore, the center of the ellipse is (6,1).
The distance between the center and one of the vertices (say, (8,1)) is the length of the semi-major axis, a. This distance is (8-6) = 2. Therefore, the semi-major axis is a = 2.
The eccentricity, e, is given as 1/3.
The distance between the center and one of the foci, c, is related to the semi-major axis and eccentricity by the equation c = ae. Plugging in the values we know, we get c = (1/3)(2) = 2/3.
We can write the equation of the ellipse in standard form:
(x - 6)² / 2² + (y - 1)^2 / b² = 1
where b is the semi-minor axis. We can solve for b using the relationship between the semi-major axis, semi-minor axis, and eccentricity:
So the equation of the ellipse is:
(x - 6)² / 4 + (y - 1)² / (16/9) = 1
The directrices are located a distance of a² / c = (2²) / (2/3) = 6 units away from the center along the major axis. These are the lines x = 6 - 6 = 0 and x = 6 + 6 = 12.
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Find the value of a that makes the ordered pair a solution of the equation. Y=3x+7; (-3, a)
Answers
When a is equal to -2, the ordered pair is an equational solution.
What Exactly Is a Linear Equation's Solution?The places where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation is the solution set of the system of linear equations.
Given:y=3x+7
Ordered pair (-3,a)
introducing x=-3 as a value in the equation
y=3(-3)+7
y=-9+7
y=-2
Hence,value of a is -2 that makes the ordered pair a solution of the equation.
y=3x+7 represents the equation of a straight line. So, it can satisfy infinite ordered pair.
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The graph of y= h (x) is shown. Draw the graph of y = - h (x) - 4
Answers
Answer:
See graph
Step-by-step explanation:
The transformation is as follows
The transformation of h(x) to -h(x) - 4 is a combination of two transformations
1. A reflection around the x -axis. Every point(x, y) in h(x) becomes (x', y') where x' = x and y' = -y so (x, y) → (x, -y)
2. A translation of each reflected point 4 units down; x value does not change but y values are shifted down so the new y is y'-4 = -y -4
The result of both transformations is:
every coordinate (x, y) in h(x) will be transformed to (x, -y -4)
Seeing as the graph consists of two straight lines meeting at the origin, all we need to do is take any 3 points in h(x), find the transformed coordinates and connect them with straight ilnes
h(x0 -h(X) - 4
(-2, 4) ⇒ (-2, -4-4) = (-2, -8)
(0, 0 ) ⇒ (0, -0 - 4) = (0, -4)
(4, 2) ⇒ (4, -2 -4) = (4, -6)
take these three points and plot
The number of meters a student swam this week are listed.
600, 750, 800, 850, 900, 1100
What is the appropriate measure of variability for the data shown, and what is its value?
The mean is the best measure of variability and equals about 833.
The median is the best measure of variability and equals 825.
The range is the best measure of variability and equals 500.
The IQR is the best measure of variability and equals 150.
Answers
Answer: The range is the best measure of variability for the given data set and its value is 500.
The range is the difference between the maximum and minimum values in a data set, and in this case, the maximum value is 1100 and the minimum value is 600, so the range is 1100-600=500. The range gives us an idea of how spread out the data is, but it can be affected by outliers. In this case, it seems like a reasonable measure of variability since there are no extreme values that would greatly affect the range.
Step-by-step explanation:
From the data of the number of meters swam by students , range is the best measure of variability and equals 500
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the data set be represented as A
Now , the value of A is
A = { 600, 750, 800, 850, 900, 1100 }
The appropriate measure of variability for the given data is the range. The range is the difference between the largest and smallest values in the data set.
And , range = 1100 - 600
R = 500
Hence , the range of the data set is R = 500
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5. When will the rock be 125 feet above the beach?
b. What is the maximum height reached by the rock and how many seconds did it take for the rock
to reach that height?
Answers
The height of the rock is described by the quadratic equation:
h = -16t² + 79t + 50.
a. The rock will be 125 feet above the beach for approximately 3.66 and 1.28 seconds.
b. The rock will reach its maximum height in about 2.5 seconds, reaching a height of around 147.5 feet.
A quadratic equation is what?An equation of the form f(x) = ax² + bx + c, where a 0 and a, b, and c are numbers, is a quadratic equation.
a. The following is how the rocket's height function is presented:
h(t) = -16·t² + 79·t + 50
The time at which the height is 125 feet is as follows:
h(t) = 125 feet
h(t) = 125 = -16·t² + 79·t + 50
-16·t² + 79·t + 50 - 125 = 125 - 125 = 0
-16·t² + 79·t - 75 = 0
The quadratic formula indicates:
t = (-79 ± √(79² - 4 × (-16) ×(-75)))/(2 × (-16)) = (79 ± √(1441))/32
t = (79 ± √(1441))/32
t = (79 + √(1441))/32 ≈ 3.66
t = (79 - √(1441))/32 ≈ 1.28
Therefore, the times at which the height of the rock is 125 feet above the beach are t ≈ 3.66 seconds, and t ≈ 1.28 seconds.
b.The formula for determining the input value at the maximum value of a quadratic function, which is: at the maximum height, x = -b/2a, can be used to determine the time at which the rock is at the maximum height.
Consequently, we obtain at the highest height;
t = -79/(2 (-16)) = 2.46875 is the time.
The rock climbs to its highest point in 2.46875 seconds, or 2.5 seconds.
Hence, h (2.46875) = -162.46875² + 792.46875 + 50 = 147.515625 147.5 is the maximum height.
The rock can rise up to a height of approximately 147.5 feet.
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Find the linear function with the following properties.
f(−3)=−12
f(−7)=4
Answers
Answer:
To find the linear function with the given properties, we need to determine the slope and y-intercept of the function.
We can use the slope-intercept form of a linear function, which is:
y = mx + b
where m is the slope and b is the y-intercept.
First, we can find the slope using the two given points:
slope = (y2 - y1) / (x2 - x1)
slope = (4 - (-12)) / (-7 - (-3))
slope = 16 / (-4)
slope = -4
Now that we have the slope, we can use one of the given points to find the y-intercept. Let's use the point (-3, -12):
y = mx + b
-12 = (-4)(-3) + b
-12 = 12 + b
b = -24
Therefore, the linear function that satisfies the given properties is:
f(x) = -4x - 24
f(x) = -4x - 24
Step by step Explanation:
To find the linear function f(x) with the given properties, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
Using the two given points, we can find the slope of the line:
m = (y2 - y1) / (x2 - x1)
m = (4 - (-12)) / (-7 - (-3))
m = 16 / (-4)
m = -4
Now we have the slope of the line, and we can use one of the given points to find the y-intercept:
f(x1) = y1
f(-3) = -12
So when x = -3, y = -12. We can use this point to find the y-intercept:
y - y1 = m(x - x1)
y - (-12) = -4(x - (-3))
y + 12 = -4(x + 3)
y = -4x - 24
Therefore, the linear function f(x) that satisfies the given properties is:
f(x) = -4x - 24
Ivanna runs 10 miles in 96 minutes. How many minutes does she take per mile?
Answers
Answer:
Ivanna takes 9.6 minutes per mile.
To find out, you can divide the total time by the total distance:
time per mile = total time ÷ total distance
time per mile = 96 minutes ÷ 10 miles
time per mile = 9.6 minutes/mile
Step-by-step explanation:
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What is the area of a rhombus whose sides are all 15 units and whose height is 6 units?
A) 90 units2
B) 88 units2
C) 76 units2
D) 63 units2
Answers
15*6 =90unit^2
Which statement describes how to solve
Square both sides once and then solve the resulting linear equation.
Square both sides once and then solve the resulting quadratic equation.
Square both sides twice and then solve the resulting linear equation.
Square both sides twice and then solve the resulting quadratic equation.
Answers
The statement "Square both sides twice and then solve the resulting linear equation." describes the correct process to solve √(3x+4)=√3x+4
How to solve √(3x+4)=√3x+4?Given equation:
[tex]\sqrt{3x} + 4= \sqrt[]3{x} + 4[/tex]
Square both sides :
[tex]3x+4=3x + 16+8\sqrt{3x}[/tex]
= [tex]8\sqrt{3x} =-12[/tex]
Square both sides again
[tex]64[/tex] × [tex]3x[/tex][tex]=144[/tex]
= x=3\4
What are linear equations?Linear equations are mathematical expressions that describe a straight line on a coordinate plane. They are used to model relationships between variables that have a constant rate of change or a constant slope.
Linear equations are fundamental and essential in many areas of mathematics, science, and engineering, and are used extensively in algebra, geometry, calculus, statistics, and physics.
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Complete question:
Which statement describes how to solve √(3x+4)=√3x+4?
Pleaseeeeeeeeeeeee help!
Answers
The symbolic quantified statement is given as:
For all real integers x and y, if x³ = y³, then x = y.
Using quantifiers, this can be written as:
∀x,y∈ℝ, (x³ = y³) → (x = y)
What is the explanation for the above?
The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.
The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.
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A clinic can vaccinate 270 children in 3 days. How many children could it vaccinate in 5 days?
Answers
Answer:
450
Step-by-step explanation:
270/3=90, 90*5=450