Answer: f(x) and g(x) are inverse functions
Step-by-step explanation:
\(Let f^{-1}(x) = y\\f^{-1}(x) = y = \frac{7x - 2}{4} \\4y = 7x - 2\\x = \frac{4y+2}{7}\\x = f^{-1}(y)=\frac{4y+2}{7}\\ So, f^{-1}(x) = \frac{4x+2}{7} = g(x)\)
f(x) and g(x) are inverse functions
what are the solutions to this system of equations 2x y 3 y 3 2 x 2 2
The solutions to the system of equations 2x + y = 3 and y - 3 = 2x - 2 are (1,5) and (-2,-1).
What formulae are used?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.
What is an equation example?The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.
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An article considered various issues associated with determining endotoxin concentration. The following data on concentration (EU/mg) in settled dust for one sample of urban homes and another of farm homes was kindly supplied by the authors of the article.
U: 6.0 5.0 11.0 33.0 4.0 5.0 89.0 18.0 35.0 17.0 23.0
F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0 9.2 3.0 2.0 0.3
(a) Determine the value of the sample standard deviation for each sample. [Hint: sum.gifxi = 246.0 for the urban sample and 128.4 for the farm sample, and sum.gifxi2 = 11,600 for the urban sample and 1617.94 for the farm sample.](Round your answers to two decimal places.)
urban-settlings=?
farm-settlings=?
Interpret these values.
Contrast variability in the two samples:
*The variability in endotoxin concentration is far less in urban homes than in farm homes.
*The variability in endotoxin concentration is far greater in urban homes than in farm homes.
*The variability in endotoxin concentration is similar in urban homes than in farm homes.
(b) Compute the fourth spread for each sample and compare. Do the fourth spreads convey the same message about variability that the standard deviations do? Explain.
*Yes, The fourth spreads do communicate the same message as the standard deviations did.
*No, The fourth spreads do not communicate the same message as the standard deviations did.
Answer:
The variability in endotoxin concentration is far greater in urban homes than in farm homes.
Yes, The fourth spreads do communicate the same message as the standard deviations did.
Step-by-step explanation:
Given the data:
U: 6.0 5.0 11.0 33.0 4.0 5.0 89.0 18.0 35.0 17.0 23.0
F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0 9.2 3.0 2.0 0.3
Farm sample:
Σx = 128.4
Σx² = 1617.94
n = 15
Sample mean, m = Σx / n ; 128.4 / 15 = 8.56
Standard deviation :
sqrt[(Σx²/n-1) - (m²)]
sqrt[(1617.94/14) - (8.56^2)]
sqrt(42.293542) = 6.50
Fourth spread = 3rd quartile - 1st quartile
3rd quartile = 3/4(n+1)th term
1st quartile = 1/4(n+1)th term
Using calculator :
Q3 = 11 ; Q1 = 4
Fourth spread = 11 - 4 = 7
Urban sample:
Σx = 246.0
Σx² = 11600
n = 11
Sample mean, m = Σx / n ; 246 / 11 = 22.36
Standard deviation :
sqrt[(Σx²/n-1) - (m²)]
sqrt[(11600/10) - (22.36²)]
sqrt(660.0304) = 25.69
Fourth spread = 3rd quartile (Q3) - 1st quartile(Q1)
3rd quartile = 3/4(n+1)th term
1st quartile = 1/4(n+1)th term
Q3 = 33 ; Q1 = 5
Fourth spread = 33 - 5 = 28
Standard deviation of farm sample = 6.50
Standard deviation of urban sample = 25.69
From the standard deviation values obtained, it could be observed that the urban sample has greater Variability than the farm sample, this is due to the higher standard deviation value of the urban sample and this shows that variation about the mean value is higher for urban sample.
Looking at the fourth spread value for both urban and farm samples ; the fourth spread value for urban is greater Than for farm sample.
Find amplitude,period,and frequency
The sinusoidal function have the following features:
Amplitude: 1
Period: 2π
Frequency: ω = 2π / 2π = 1
How to analyze a sinusoidal function
Herein we find an example of a sinusoidal function, whose definition is shown below:
f(x) = A · sin (2π · x / T + Φ) + x'
Where:
x' - MidpointA - AmplitudeT - PeriodΦ - PhaseThe frequency (ω) is equal to the following formula:
ω = 2π / T
If we know that the sinusoidal function f(x) = sin (x + π / 2) - 2, then the amplitude, the period and the frequency, that is, the features of the sinusoidal function, are, respectively:
Amplitude: 1
Period: 2π
Frequency: ω = 2π / 2π = 1
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What is the value of x in the equation below? 150 = 35 x
Answer:
x = 30/7 = 4 2/7
Step-by-step explanation:
150 = 35x
35x = 150
x = 150/35
x = 30/7
x = 4 2/7
Answer:
x = 30/7 =4 2/7 or 4.2
Step-by-step explanation:
tell me love brainiest.
Please I really need help I’ll mark brainlist
Answer:
So, cows heart best is faster than horse.
Step-by-step explanation:
Time and heartbeats are in direct proportion.
p = kx
Where p is the beats per minute and x represents time in minutes
Now, to find the value of k, substitute p = 152 and x = 4
152 = 4k
k = 152/4
k = 38
\(\sf \boxed{p = 38x}\)
Cow: y = 65x
So, cows heart best is faster than horse
For safety reasons, the angle a ladder makes with the ground should be no greater than 67°. Find the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high.
Using trigonometric function the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high is calculated as 25 feet.
What are trigonometric functions?
Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trigonometric functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given the angle a ladder makes with the ground should be no greater than 67°.
So the angle θ ≤ 67°.
Let us assume the angle to be equal to 67°
The height of the roof from the ground is 23 feet.
The ladder and wall form the right triangle where the ladder works as hypotenuse and the wall as perpendicular.
With the sine function, find the length of the ladder -
sin θ = perpendicular/hypotenuse
Let the length of ladder be x.
sin 67° = 23/x
x = 23/sin 67°
x = 23/0.920
x = 25 feet
Therefore, the length of the ladder is 25 feet.
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The graph of a line and an exponential can intersect twice, once or not at all. Describe the possible number of intersections for each of following pairs of graphs. Your solution to each part should include all possibilities and a quickly sketched example of each one. Part 2; (SHOW WORK)
c. A parabola and a circle
d. A parabola and the hyperbola y = 1/x
Answer:
c) parabola and circle: 0, 1, 2, 3, 4 times
d) parabola and hyperbola: 1, 2, 3 times
Step-by-step explanation:
c. A parabola can miss a circle, be tangent to it in 1 or 2 places, intersect it 2 places and be tangent at a 3rd, or intersect in 4 places.
__
d. A parabola must intersect a hyperbola in at least one place, but cannot intersect in more than 3 places. If the parabola is tangent to the hyperbola, the number of intersections will be 2.
If the parabola or the hyperbola are "off-axis", then the number of intersections may be 0 or 4 as well. Those cases seem to be excluded in this problem statement.
Different events have the following likelihoods. sort them from least to greatest with 1 (smallest probability to 5 (largest probability).
we have
60%=60/100=0.60
8 out 10 =8/10=0.80
0.37
20%=20/100=0.20
5/6=0.83
order from least to greatest
so20%, 0.37, 60%, 8 out 10, 5/6 what is the area of the rectangle
Plz help ASAP 20 points
please help me solving this question please i want all solve please help
List three examples of words/phrases that describe the mathematical operation of addition. (Example "Increased by") *
Answer:
Increased by, added, brought up (All I know of haha)
Step-by-step explanation:
Theres really no explanation to this other than learning your mathematical terms.
send answer really need it
Answer:
DO U KNOW HOW TO GET MORE POINTS?
Step-by-step explanation:
Answer:
3/18 foot³
Step-by-step explanation:
okay, so the formula for volume is height x base, which is real confusing, but lets go:
first, you have to figure out the base, which is the surface that's on the bottom:
1/2 x 1/2 = 1/4
so you then multiply that by how high the figure is:
1/4 x 3/4 = 3/16
So your answer is option D. 3/18 cubic foot
hope this helps:)
What is the overlap between the distribution for Plot A and the distribution for Plot B? A) 1 to 7 B) 1 to 5 C) 2 to 5 D) 3 to 5
Answer:
2 to 5 .......................
The overlap between the distribution for Plot A and the distribution for Plot B is 2 to 5. Option C is correct.
What is dot plot?
The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.
The overlap between the distribution for two dot plots means the overlaps of height which both the plots have same in graph. In the given plots,
The plot A has values from 1 to 5.The plot A has values from 2 to 7The common height in both plot is 2 to 5.Thus, the overlap between the distribution for Plot A and the distribution for Plot B is 2 to 5. Option C is correct.
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In each diagram, line f is parallel to line g, and line t intersects lines f and g
In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.
Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.
Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.
Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.
Alternate interior angles are congruent, as well as alternate exterior angles.
By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.
It is important to measure angles systematically and compare them to find congruent or equal measures.
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En un triatlón, Jenny nadó durante 1 hora, anduvo en bicicleta durante 1,75 horas y corrió durante 1 hora. Su velocidad promedio en bicicleta fue 2 veces su velocidad promedio para correr, y su velocidad promedio para correr fue 8 veces su velocidad promedio para nadar. La distancia total del triatlón fue de 55,5 kilómetros. Escribe una ecuación y resuélvela para encontrar la velocidad de nado promedio de Jenny en kilómetros por hora. Explique su ruta de solución y el razonamiento detrás de su trabajo.
Jenny's Average swimming speed is 1.5 km/h.
Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.
We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.
Thus, the distance she swam is S * 1 = S km.
Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.
Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.
Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.
She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.
The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.
Therefore, we can write the equation:
S + 8S + 28S = 55.5.
Simplifying the equation, we get:
37S = 55.5.
To solve for S, we divide both sides of the equation by 37:
S = 55.5 / 37 = 1.5.
Thus, Jenny's average swimming speed is 1.5 km/h.
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A ball is thrown downward from the top of a 150-foot building with an initial velocity of 23 feet per second. The height of the ball h after t seconds is given by the equation h= - 16t? - 23t+150. How long after the ball is thrown will it strike the ground?
Answer:
362 the answer
Step-by-step explanation:
follow nmn i hope its help
Please Help Solve This
Answer:
what kind of math is this?...
the volume of a rectangular prism is 10 cubic feet. what could the dimensions of the prism be
Answer: 2x5x1, 1x10x1 (in any order) and any 3 multiples that make 10
Step-by-step explanation:
Answer:
There are multiple possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet. Here are some possible solutions:
A rectangular prism with dimensions of 1 ft x 2 ft x 5 ft (length x width x height) would have a volume of 10 cubic feet, since 1 x 2 x 5 = 10.
A rectangular prism with dimensions of 2 ft x 1 ft x 5 ft (length x width x height) would also have a volume of 10 cubic feet, since 2 x 1 x 5 = 10.
A rectangular prism with dimensions of 0.5 ft x 1 ft x 20 ft (length x width x height) would also have a volume of 10 cubic feet, since 0.5 x 1 x 20 = 10.
A rectangular prism with dimensions of 5 ft x 1 ft x 2 ft (length x width x height) would have a volume of 10 cubic feet, since 5 x 1 x 2 = 10.
There are infinitely many other possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet.
What number goes into 12 20 and 16
Answer:
2
Step-by-step explanation:
I need help with finding the pair of angles
Answer:
Straight
Step-by-step explanation:
supplementary means sum of two angles
with 180
9.) If a dozen balloons cost 30 cents, how many balloons can you get for 1 dollar?
A. 40 balloons
C. 36 balloons
B. 44 balloons
D. 50 balloons
1 dozen = 12
1 dollar / 30 cents = 3 1/3
You can buy 3 1/3 dozen.
12 x 3 1/3 = 40
You can buy 40 balloons for a dollar.
Answer:
44
Step-by-step explanation:
30=12 Balloons
30 goes into 100 3 times
3 x 300 =90
now there are only ten cents left
3x10 = 30
12/3=4
40 + 4 = 44
Factoriseeeee COMPLETELY 12x²y² - 17xy- 40 (Show all steps) :D be quickkkk
12x²y² - 17xy - 40
xy (12xy - 17) - 40
As the x and y are shown in both variables but there is no other common factors. I didn't include the 40 as it didn't share any common factors with all of them.
Saeed wants to have his birthday at an amusement park with a few of his friends but he can't spend no more then $80. The amusement park charge6a flat admission fee of $35 for a private party and 6.50 per person for food and drinks
Write an inequality that represents the total cost of seeds birthday for n people given his budget
Answer:
T=35X6.50
Step-by-step explanation:
Question 1 of 10
Identify the terminal point for a 30' angle in a unit circle,
O A. (24)
O B. (1,7)
OC. (2,4)
OD. (1,4)
SIIRRAT
help
Which graph shows a function and it’s inverse?
HELP PLEASE
Answer:
C
Step-by-step explanation:
A function and its inverse are obtained by reflecting in the line y = x
Under a reflection in the line y = x
a point (x, y ) → (y, x )
In graph C
the red line has a point (0, 2 )
the blue line has a point (2, 0 )
Then graph C shows a function and its inverse
Your total monthly bill (T
) from the Electric and Gas Company depends on how much electricity and how much gas you use each month. For every kilowatt hour of electricity (k
) you use, you are charged $0.25
and for each therm (t
) of gas used you are charged $0.97
.
Which of the following equations represents the relationship between electricity and gas used and your bill?
The equation representing the relationship between Electricity and Gas used, and your Bill is:
T = 0.25 * k + 0.97 * t
Step-by-step explanation:
Make a plan:
We need to find the equation that represents the relationship between the total monthly bill (T), The Kilowatt Hours of Electricity used (k), and the Terms of Gas used (t).
T = 0.25 * k + 0.97 * t
Solve the problem:
1 - Write the Equation for the cost of Electricity:
0.25 * k
2 - Write the Equation for the Cost of Gas:
0.97 * t
3 - Combine the Equations to Represent the total Monthly Bill (T):
T = 0.25 * k + 0.97 * t
Draw the Conclusion:Hence, The equation representing the relationship between Electricity and Gas used, and your Bill is:
T = 0.25 * k + 0.97 * t
I hope that helps!
Expand and simplify (2x - 1)(x + 3)(x - 5)
Answer:
2x^3-5x^2-28x+15 -------------------------expanded
2x^3-5x^2-28x+15--------------------simplified
Step-by-step explanation:
\left(2x-1\right)\left(x+3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
simplyfied
\left(2x^2+5x-3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
=2x^3-5x^2-28x+15
Permudahkan ungk
8a + 3b - 2a - b
Answer:
answer:8a + 3b - 2a - b
=8a-2a+3b-b
=6a+2b or 2(3a+b) is your answer
Which of the following shows the inverse of {(0, 4), (5, -2), (-1, 8), (2, 5)}?
A:{(0, -4), (5, 2), (-1, -8), (2, -5)}
B:{(4, 0), (-2, 5), (8, -1), (5, 2)}
C:{(0, -4), (-5, 2), (1, -8), (-2, -5)}
D:{(0, 4), (-5, -2), (1, 8), (-2, 5)}
9514 1404 393
Answer:
B: {(4, 0), (-2, 5), (8, -1), (5, 2)}
Step-by-step explanation:
The inverse relation has the input and output swapped:
relation: (0, 4)
inverse relation: (4, 0)
You can identify the correct answer choice using just the first ordered pair. The inverse relation is ...
{(4, 0), (-2, 5), (8, -1), (5, 2)}
When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse?
when the scale factor is 1, we have:
(side length of side opposite ∠A) / (length of hypotenuse) = sin A
When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.
The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.
In mathematical terms, when the scale factor is 1, we have:
(side length of side opposite ∠A) / (length of hypotenuse) = sin A
It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.
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