Answer:
Step-by-step explanation:
1/2 < 3/5 < 2/3 < 5/7, 1/2 is the least while 5/7 is the greatest.
Solve the following systems of inequalities and select the correct graph: 2x − y > 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. What graph would I be using?
9514 1404 393
Answer:
see below
Step-by-step explanation:
The "solution" is the doubly-shaded area on the graph. Here, the dashed lines cross in a sort of X pattern, and the doubly-shaded area is the quadrant at the bottom (below both lines).
__
The "solution" involves graphing the boundary lines, and identifying the shaded area associated with each.
When equations are in standard form, there are a couple of different ways you can graph them. (I like to use a graphing calculator.) One way is to rewrite the equations to slope-intercept form:
y < 2x -4 . . . . . . slope of 2, y-intercept of -4, shading below the dashed line
y < -x -1 . . . . . . . slope of -1, y-intercept of -1, shading below the dashed line
__
Comment on multiple choice questions
You need to identify what makes each answer choice different from the others. It might be the slopes of the lines, the y-intercepts, the side that is shaded, the nature of the line (dashed, solid). You can usually eliminate the answer choices that don't make any sense, and concentrate on the subtleties of the remaining viable candidates.
The "solution" is the doubly-shaded area on the graph. Here, the dashed lines cross in a sort of X pattern, and the doubly-shaded area is the quadrant at the bottom (below both lines).
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The "solution" involves graphing the boundary lines and identifying the shaded area associated with each.
When equations are in standard form, there are a couple of different ways you can graph them. (I like to use a graphing calculator.) One way is to rewrite the equations to slope-intercept form:
y < 2x -4 . . . . . . slope of 2, y-intercept of -4, shading below the dashed line
y < -x -1 . . . . . . . slope of -1, y-intercept of -1, shading below the dashed line
Therefore "solution" is the doubly-shaded area on the graph. Here, the dashed lines cross in a sort of X pattern, and the doubly-shaded area is the quadrant at the bottom (below both lines).
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A normal population has a mean μ = 40 and standard deviation σ=9 What is the probability that a randomly chosen value will be greater than 57?
The probability that a randomly chosen value from this normal population will be greater than 57 is approximately 0.0297, or 2.97%.
To find the probability that a randomly chosen value will be greater than 57 from a normal population with a mean (μ) of 40 and a standard deviation (σ) of 9, you will need to follow these steps:
1. Calculate the z-score:
The z-score represents the number of standard deviations a value is away from the mean.
To calculate the z-score, use the formula:
z = (X - μ) / σ, where X is the value in question (57 in this case).
2. In this case, z = (57 - 40) / 9 = 17 / 9 ≈ 1.89.
3. Look up the z-score in a standard normal distribution table (or use a calculator or software) to find the probability of obtaining a z-score less than 1.89.
The table value for a z-score of 1.89 is approximately 0.9703.
4. Since we want the probability that the value is greater than 57, we need to find the probability of obtaining a z-score greater than 1.89.
To do this, subtract the table value from 1:
1 - 0.9703 = 0.0297.
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standard automobile license plates in a country display 3 numbers, followed by 2 letters, followed by 2 numbers. how many different standard plates are possible in this system? (assume repetitions of letters and numbers are allowed.) there are different standard plates possible in this system.
The system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.
Define the term permutation?The number of potential arrangements for a given set is assessed mathematical terms, but this procedure is referred to as permutation. The arrangement's order is essential when using permutations.For the stated data;
Standard car license plates in a nation typically have 3 digits, 2 letters, and 2 numbers.
There are total 9 digits (0 - 9).
There are total 26 letter (A - Z)
Repetitions of letters and numbers given allowed.
Thus, numbers and the letters ca be arranged as;
1st place = 9 ways.
2nd place = 9 ways.
3nd place = 9 ways.
4th place = 26 ways.
6th place = 26 ways.
7th place = 9 ways.
8th place = 9 ways.
Total ways = 9×9×9×26×26×9×9
Total ways = 39917124
Thus, the system of standard automotive license plates allows for a variety of standard plates is 39917124 ways.
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Use the graphing calculator to graph each function
and find the matching graph.
Cube Root
f(x) = x
DONE
Exponential
fx)= 2²
DONE
Logarithmic
f(x) = logx
Cute Root: C
Exponential: D
Logarithmic: A
A function assigns the value of each element of one set to the other specific element of another set. The options can be matched with the function as C, D, and A, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function of different functions is mentioned below.
f(x) =∛x → Option C → Red Linef(x) = 2ˣ → Option D → Green Linef(x) = log(x) → Option A → Blue LineHence, the options can be matched with the function as C, D, and A, respectively.
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Solve X for natural equation algebraically. Approximate your result to three decimal places.
\(\underset{same~base \qquad }{e^{4x}=e^{x^2+3}}\implies 4x=x^2+3\implies 0=x^2-4x+3 \\\\\\ 0=(x -3)(x - 1)\implies x= \begin{cases} 3\\ 1 \end{cases}\)
someone plz help me i'm so confused
(click on picture)
Answer:
the equation to finding slope is this:
y2-y1 / x2-x1
Where y2 is the y value of the second point, y1 is the y value of the first point, x2 is the value of the second x value, and x1 is the x value of the first point.
5-0 / -2-2
5/-4
-5/4 is the slope
Step-by-step explanation:
Answer:
\(m=\frac{-5}{4} \\\) which is the slope.
Step-by-step explanation:
Since we have two points on the line, we can easily calculate the slope.
Point 1 = (-2, 5)
Point 2 = (2, 0)
\(m=\frac{rise}{run}\\m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{0-5}{2-(-2)} \\m=\frac{-5}{4}\)
Count the number of atoms and elements in each substance. Then answer the questions below
O2
Fe2O3
NH3
H2SO4
-> Which substances are elements?
The substance that is element in the list is O₂
What is an element in chemistry?A substance that cannot be broken down chemically is referred to as an element. Although chemical processes cannot modify an element, nuclear reactions can create new elements.
The quantity of protons an element has defines it. An element's atoms all contain the same amount of protons, but its electron and neutron counts can vary. Ions are produced by altering the electron to proton ratio, and isotopes are produced by altering the neutron content.
Other substances can be broken down further chemically except O₂ and hence it is the only element in the list
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Just need to know the answer for this I’m stuck !
Answer:
6
Step-by-step explanation:
By intersecting chords theorem:
\(14(x - 3) = 12(x - 2) \\ \\ 14x - 42 = 12x - 24 \\ \\ 14x - 12x = 42 - 24 \\ \\ 2x = 18 \\ \\ x = \frac{18}{2} \\ \\ x = 9 \\ \\ LG = x - 3 \\ \\ LG = 9 - 3 \\ \\ LG = 6\)
Given z₁ = 4 cos(cos(π/4)+isin(π/4)) and z₂=2(cos(2π/3)+isin(2π/3)), i, find z₁z₂ ii, find z₁/z₂
z_1 and z_2 are complex number;
i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))
ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))
To calculate z₁z₂ and z₁/z₂, we need to perform the complex number operations on z₁ and z₂. Let's break down the calculations step by step:
i) To find z₁z₂, we multiply the magnitudes and add the angles:
z₁z₂ = 4cos(cos(π/4) + isin(π/4)) * 2cos(2π/3) + isin(2π/3))
= 8cos((cos(π/4) + 2π/3) + isin((π/4) + 2π/3))
= 8cos(7π/12) + isin(7π/12)
ii) To find z₁/z₂, we divide the magnitudes and subtract the angles:
z₁/z₂ = (4cos(cos(π/4) + isin(π/4))) / (2cos(2π/3) + isin(2π/3))
= (4cos((cos(π/4) - 2π/3) + isin((π/4) - 2π/3))) / 2
= 2cos(π/12) + isin(π/12)
i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))
ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))
Please note that the given calculations are based on the provided complex numbers and their angles.
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Find the solutions for F(x)=2x² + 4x + 2
X
f(x)
-3
-2
-1
0
1
2
3
4
Answer:
x= -1
Step-by-step explanation:
how many cards must be selected from a standard deck of 52 cards to guarantee that at least three cards of the same (matching) suit are chosen
Answer:
Step-by-step explanation:
17
The central angle of sector R is 38° and the central angle of sector Q is 39°. What is the probability that the spinner does not land on Q or R? P Q R S T U
Answer: 0.786
Step-by-step explanation:
Here i would assume that:
Sector R and Sector Q do not have any sections in common.
Then, the probability that the spinner does not land on Q or R, is equal to the probability where the spinner does not land in a specified section of:
38° + 39° = 77°.
Now, the total section off the spinner is 360°.
If we remove those 77°, we have a section of:
360° - 77° = 283°
So we have 283° where the spinner CAN land on.
Then the probability that the spinner does NOT land on R or Q is equal to the quotient between the section of the spinner that is not R or Q, and the total section of the spinner"
P = 283/360 = 0.786
So the probability is 0.786
solving multi step equations 3/4x + 3 - 2= -1/4 + 1/2x + 5
Answer:
The answer is X=15
League baseball team plays 122 games in a season. If the team won 14 more than three times as many games as they lost, how many wins and losses did the team have?
Given:
Total number of games in a season = 122
The team won 14 more than three times as many games as they lost.
To find:
The number of wins and losses.
Solution:
Let the number of losses be x.
Then, according to the question
Number of wins = 3x+14
We know that,
Win + losses = Total number of games
\((3x+14)+x=122\)
\(4x+14=122\)
Subtract 14 from both sides.
\(4x=122-14\)
\(4x=108\)
Divide both sides by 4.
\(x=27\)
Now,
Number of losses = 27
Number of wins \(=3\times 27+14\)
\(=81+14\)
\(=95\)
Therefore, the team won 95 games and they lost 27 games.
PLSS HELP ME ARGHHHHHH
Sarah wants to cover the rim of her circular pool with a foam covering. The foam covering is sold in boxes that will cover 40 feet. How many boxes of foam will Sarah need to cover the rim of the pool?
Answer:
this was m closet answer 39.3701 and it was using 12 small boxes.
Step-by-step explanation:
Complete the following statements. The functions f and g have. The y-intercept of f is the y-intercept of g. Over the interval [-6, -3], the average rate of change of f is the average rate of change of g.
The average rate of change of f is less than the average rate of change of g.
The symmetry axis for the functions f and g is either the same or different.The line that passes through the vertex's x value is known as an axis of symmetry. It is the line of symmetry, but for a quadratic equation, and it divides the equation in half.
By examining function f, we can determine the vertex's location by either the lowest point, or (-3, -10). This is so that the numbers before and after (-3, -10), which increase by the same amount, have the same interval as the x values. (For instance, the symmetric pairs x = -5 and x = -1 have y values of -2 and x = -4 and x = -2, respectively, have y values of -8.)
Consequently, x = -3 is the axis of symmetry for function F.because the vertex's x value is -3.The graph demonstrates that x = -3 is also the axis of symmetry for function g because an illustrative vertical line drawn through this value bisects the quadratic.As a result, the symmetry axis for the functions f and g is the same.
The relationship between f's and g's y-intercepts is (less than, equal to, greater than) Where an equation crosses the y axis is known as the y intercept. As x = 0 is the y axis, it always has a value of 0.Looking at function f, the y-intercept of the function is equal to 8 when x = 0.We can observe the y value of when the function g returns aOn the graph, the quadratic intercepts the y axis. It is y = -2.As a result, f's y-intercept is larger than g's y-intercept.The average rate of change of f is (equal to, less than, or greater than) the average rate of change of g across the range [-6, -3].The amount that the y value rises for each unit of x that passes is the rate of change.
For function f, we can see that the function declines by 18 between x = -6 and x = -3. The sum of the rate of change (the amount the y changed / difference between the x values of points) is therefore -18 / 3 = -6.For function g, we can see that the function grows between x = -6 and x = -3. In this instance y value, but we may calculate that it rises by around 9. 9 / 3 = 3.
The average rate of change of f is therefore lower than the average rate of change of g.
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X is an exponential random variable with a = 4. If Y= -2X+2, which of the following is closest to fy(0)? a. 0.12 b. 0.10 c. 0.08 d. 0.06 e. 0.04
The result is approximately 0.0366. Comparing this value with the given options, the closest answer is e. 0.04.
Given X is an exponential random variable with λ = 4. We want to find f_Y(0), where Y = -2X + 2.
First, let's find the inverse transformation of Y: X = (2 - Y)/2
Now, we'll find the Jacobian of the transformation:
dX/dY = -1/2
Next, we'll find the probability density function (PDF) of X: f_X(x) = λe^(-λx) = 4e^(-4x)
Now we can find the PDF of Y using the formula: f_Y(y) = f_X((2 - y)/2) * |dX/dY|
Substitute the values: f_Y(y) = 4e^(-4(2 - y)/2) * |-1/2|
Now we can find f_Y(0): f_Y(0) = 4e^(-4(2 - 0)/2) * |-1/2| f_Y(0) = 4e^(-4) * 1/2
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What are the solutions to the equation Sine (x + StartFraction 7 pi Over 2 EndFraction) = negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction over the interval [0, 2Pi]?
Given:
The equation is
\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}\)
To find:
The solutions of given equation over the interval \([0,2\pi]\).
Solution:
We have,
The equation is
\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}\)
\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\sin \dfrac{\pi }{3}\)
\(\sin\left(x+\dfrac{7\pi}{2}\right)=\sin (-\dfrac{\pi }{3})\)
If \(\sin x=\sin y\), then \(x=n\pi +(-1)^ny\).
Over the interval \([0,2\pi]\).
\(x+\dfrac{7\pi}{2}=4\pi-\dfrac{\pi }{3}\) and \(x+\dfrac{7\pi}{2}=5\pi+\dfrac{\pi }{3}\)
\(x=\dfrac{11\pi }{3}-\dfrac{7\pi}{2}\) and \(x=\dfrac{16\pi}{3}-\dfrac{7\pi}{2}\)
\(x=\dfrac{22\pi-21\pi }{6}\) and \(x=\dfrac{32\pi-21\pi }{6}\)
\(x=\dfrac{\pi}{6}\) and \(x=\dfrac{11\pi }{6}\)
Therefore, the two solutions are tex]x=\dfrac{\pi}{6}\) and \(x=\dfrac{11\pi }{6}\).
Answer:
C. π/6 & 11π/6
Step-by-step explanation:
If you graph the equation ( Sin (x+7π/2)=-√3/2) and look between 0 & 2π, you'll see that the lines intersect the x-axis at π/6 & 11π/6.
A rectangular prism has a length of 8 meters, a width of 6 meters, and a height of 3 meters.
Which equations could be used to determine the volume, V, of the prism?
Select each correct answer.
Responses
V = 8 × 9
V, = 8 × 9
V = 48 × 3
V, = 48 × 3
V = 8 × 6 × 3
V, = 8 × 6 × 3
V = 8 × 6 × 6
The correct answer will be V =8×6×3 & V= 48×3. The volume of a rectangular prism = Length x Width x Height.
Volume explain: What is it?Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. Although capacity can be measured in virtually any other unit, such as litres, gallons, pounds, etc., volume is determined in cubic units.
What do capacity and volume mean?Capacity. The total volume of space an object occupies in three dimensions is indicated by its volume. The term "capacity" describes something's ability to contain, absorb, or absorb by an object (such as a solid substance, gas, or liquid).
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Vance bought 2 packages of large beads and 1 package of medium beads. He bought 2 packages of large buttons and how many more beads than more buttons did vance buy
There are 472 more buttons bought by Vance than beads.
Define the term difference of number?One of the most crucial arithmetic operations, that is obtained by removing two integers, produces difference in mathematics.For the stated question table is made.
So,
Total number of beads bought by Vance = Number of beads(2 packages of large beads) + Number of beads(1 package of medium beads).
= (2 × 96) + (1 × 64)
= 2 × (90 + 6) + 64
= (2 × 90) + (2 × 6) + 64
= 180 + 12 + 64
= 256 beads
Now,
Total number of buttons bought by Vance = Total number of buttons (2 packages of large buttons) + Number of buttons (2 packages of medium buttons)
= (2 × 56) + (2 × 38)
= 2 × (50 + 6) + 2 × (30 + 8)
= (2 × 50) + (2 × 6) + (2 × 30) + (2 × 8)
= 100 + 12 + 600 + 16
= 728 buttons
Thus,
Difference for the number of buttons and beads
= 728 – 256
= 472 beads
So,
Therefore, there are 472 more buttons bought by Vance than beads.
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What type of correlation is the graph below?
a
no correlation
b
quadratic correlation
c
negative
d
positive
Consider a discrete random variable, X. Identify the correct statement for using the cumulative distribution function (cdf), F(x), to solve the probability below. P(X<12) F(13)1−F(12) F(13)−F(12) F(12)−F(11)1−F(13)F(12) None of the above. F(11) 10 0/6points Consider a discrete random variable, X. Identify the correct statement for using the cumulative distribution function (cdf), F ( (X ), to solve the probability below. P(X≤100) 1−F(100) F(99) ×O(100)−F(99) F(101) F(100) F(101)−F(100) 1−F(99) None of the above
The correct statement for using the cumulative distribution function (cdf), F(x), to solve the probability P(X<12) is: F(12) - F(11), We subtract the cdf value at x-1 from the cdf value at x.
The cumulative distribution function (cdf), denoted as F(x), gives the probability that a random variable X takes on a value less than or equal to x. In this case, we are interested in finding the probability that X is less than 12, which can be expressed as P(X<12).
To calculate this probability using the cdf, we need to find the difference between the cdf values at 12 and 11. The cdf value at 12, denoted as F(12), gives the probability that X is less than or equal to 12. Similarly, the cdf value at 11, denoted as F(11), gives the probability that X is less than or equal to 11.
Since we want to find the probability that X is strictly less than 12, we subtract the probability that X is less than or equal to 11 from the probability that X is less than or equal to 12. Mathematically, this can be written as F(12) - F(11).
Therefore, the correct statement for using the cdf to solve P(X<12) is F(12) - F(11).
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A rigid body exists in an n-dimensional space. How many coordinates are needed to specify the position and orientation of this body in this space
The number of coordinates needed to specify the position and orientation of a rigid body in an n-dimensional space is n.
A rigid body is an object that maintains its shape and size while in motion. In order to specify the position and orientation of a rigid body in an n-dimensional space, we need to know its coordinates in each of the n dimensions. The coordinates describe the location of the body in the space and the orientation of the body relative to the space's coordinate system. Thus, n coordinates are required to fully specify the position and orientation of a rigid body in an n-dimensional space.
However, it is important to note that if the rigid body is placed in a space that's non-Euclidean, other parameters could be necessary to fully describe the rigid body position and orientation.
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A cone-shaped container has a height of 240 in. And a radius of 150 in. The cone is filled with a liquid chemical. The chemical evaporates at a rate of 12,000 in³ per week. How many weeks will it take for all of the chemical to evaporate?.
Rounded to the nearest whole number, it will take approximately 1414 weeks for all of the chemical to evaporate from the cone.
To determine the number of weeks it will take for all of the chemical to evaporate, we need to calculate the volume of the cone and then divide it by the evaporation rate.
The volume of a cone can be calculated using the formula:
\(V = (1/3) * π * r^2 * h\)
where V represents the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius, and h is the height.
Plugging in the given values:
\(V = (1/3) * 3.14159 * (150^2) * 240\)
V ≈ 3.14159 * 22500 * 240
V ≈ 16964640 in³
Now, to find the number of weeks it will take for all of the chemical to evaporate, we divide the volume by the evaporation rate:
Number of weeks = Volume / Evaporation rate
Number of weeks = 16964640 in³ / 12000 in³ per week
Number of weeks ≈ 1413.72 weeks
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ERROR ANALYSIS Describe and correct the error in
graphing and comparing
y= x^2and y = 0.5x^2.
Answer:
I don't know the answer 1+1=2
Step-by-step explanation:
2=22+2
Find the domain of the graphed function.
Answer:
C
Step-by-step explanation:
the graph stops at x=0, and continues to the right
Answer:
C.
Step-by-step explanation:
Domain can be found by:
starting x-value < x < ending x-value (if thedot is opened)
or
starting x-value ≤ x ≤ ending x-value (if the dot is closed)
Our starting x-value is x = 0 by the graph.
For ending x-value, there is no ending x-value and thus:
0 ≤ x
x ≥ 0
5(8k + 9m) simplified expression
Answer:
40k+45m
Step-by-step explanation:
5(8k)=40k + 5(9m)= 45m
\(\frac{5^{7}x 125^3}{25^2 x 54}\)
244140625 x^{54} value of the Algebraic functions .
What is Algebraic functions?
A function that satisfies is said to be algebraic if it has integer coefficients and is a polynomial in the variables and. Algebraic functions include inverses of those that can be created using a small number of elementary operations as well as those that can be created using only those operations.Evaluate the exponent
= \(\frac{5^{7} . 125^{3} }{25^{2} } . x^{54}\)
Evaluate the exponent
= \(\frac{78125 . 125x^{3} }{25^{2} } . x^{54}\)
Multiply the numbers
= \(\frac{78125 . 1953125 }{25^{2} } . x^{54}\)
Evaluate the exponent
= \(\frac{152587890625}{25^{2} } . x^{54}\)
Cancel terms that are in both the numerator and denominator
= \(\frac{152587890625}{625} . x^{54}\)
= \(\frac{152587890625}{625} . x^{54}\)
= 244140625 x^{54}
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On the graph below, draw any line with a slope of *positive* 2 and draw any line with a slope of *negative* 2.
Refer to the image for the graph of the lines.
The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.
We need to draw any line with a slope m = 2, and
another line with a slope m = -2.
Disclaimer: Let us assume that the constant c = 0.
Then the equation to the line with a slope of "positive" 2 is given by
y = 2x
Then the equation to the line with a slope of "negative" 2 is given by
y = -2x
Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.
f: green line indicates a line with a slope of "positive" 2.
g: blue line indicates a line with a slope of "negative" 2.
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Using the following table of function values, calculate the average rate
of change from x = 4 to x = 12.
The average rate of change of the function is -4.75
How to find the average rate of changeAverage rate of change is calculated using the formula
= (y₀ - y₁) / (x₀ - x₁)
The average rate of change is also called the slope.
The slope by definition is the ratio change of the output values to the input values
the average rate of change for points x = 4 and x = 12
average rate of change = (44 - 9) / (4 - 12)
average rate of change = (35) / (-8)
average rate of change = -4.75
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