The function of g(x) is 3 ([tex]2^x[/tex]) + 3.
We have,
f(x) = 3 ([tex]2^x[/tex]) -3
Now, the function f(x) have shifted by -3 unit to move 6 unit up.
This means that we have the shifting of
= -3 + 6
= +3 unit
Also, g(x) crosses the y-axis at about 5 or 6 when x=0.
Then, the function of g(x) is
= 3 ([tex]2^x[/tex]) + 3
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3 A line passes through the point (-8, 9) and has a slope of 3/4
Write an equation in slope-intercept form for this line.
Answer:
y = 3/4x + 15
Step-by-step explanation:
Given;
A line passes through the point (-8, 9) and has a slope of 3/4
Question:
Write an equation in slope-intercept form for this line.
Solve:
Slope-intercept form ⇒ y=mx+b
Which-
m = Slopeb = y-intercepty and x = any point on the lineBased on the given;
m = 3/4b = ?y = 9x = -8Using slope intercept form to find y-intercept;
y=mx+b
9 = 3/4(-8) + b
9 = -6 + b
9+6 = -6+6 + b
b = 15
Therefore now we can write an equation.
y = 3/4x + 15
RevyBreeze
1. Out of 318 seventh and eighth grade CAVA students there were 48 students that chose Music as their elective
course and the rest chose World Language. There were a total of 124 eighth grade students and 108 of them
chose World Language as their elective.
Use this information to complete the two-way table completely.
Enter your answer by filling in the boxes to complete the table (5 pts)
Answer:
8th Grade
7th Grade
Totals
Music
48
World Language
108
Totals
124
318
The students in 8th class who choose music are 16 in number,
The students in 7th class who choose music are 32 in number
The total who choose world language is 270
The totals who are in 7th grade be 194
The number of students who choose world language in 7th class are 162
Let x be the students in 8th class who choose music
x+108=124
x=124-108
x=16 students
Now y be the students in 7th class who choose music
16+y=48
y=48-16
y=32
Let z be the total who choose world language
48+z=318
z=318-48
z=270
Now the totals who are in 7th grade be A
124+A=318
A=318-124
A=194
B be the number of students who choose world language in 7th class
Now 32+B=194
B=194-32
B=162
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Question 2: Perform the inverse Laplace transform of the following rational fractions using partial fraction expansion. List the procedures and verify the results with the MATLAB function "ilaplace". Attach the MATLAB codes and results. (1) F(s) = 5+1 ($2+28+2) (10 marks) (2) F(s) = s2+3+1 (s+2)(82+28+1) (10 marks)
(1) F(s) = 5+1 / (s^2 + 28s + 2)
To perform partial fraction expansion, we first need to factor the denominator:
s^2 + 28s + 2 = (s + 14 - sqrt(194))(s + 14 + sqrt(194))
We can then write:
F(s) = A / (s + 14 - sqrt(194)) + B / (s + 14 + sqrt(194))
where A and B are constants to be determined.
Multiplying both sides by the denominator and simplifying, we get:
5+1 = A(s + 14 + sqrt(194)) + B(s + 14 - sqrt(194))
Setting s = -14 - sqrt(194), we get:
5+1 = B(2sqrt(194))
Solving for B, we get:
B = (5+1) / (2sqrt(194))
Setting s = -14 + sqrt(194), we get:
5+1 = A(2sqrt(194))
Solving for A, we get:
A = (5+1) / (2sqrt(194))
Thus, the partial fraction expansion of F(s) is:
F(s) = [(5+1) / (2sqrt(194))] / (s + 14 + sqrt(194)) + [(5+1) / (2sqrt(194))] / (s + 14 - sqrt(194))
To find the inverse Laplace transform, we can use the table of Laplace transforms or MATLAB. Using MATLAB, we get:
ilaplace(F(s)) = (5+1) / (2sqrt(194)) * (exp(-14t) / sqrt(194)) * (cosh(sqrt(194)t) + sinh(sqrt(194)t))
(2) F(s) = s^2 + 3s + 1 / (s + 2)(s^2 + 8s + 1)
To perform partial fraction expansion, we first need to factor the denominator:
s^2 + 8s + 1 = (s + 4 - sqrt(15))(s + 4 + sqrt(15))
We can then write:
F(s) = A / (s + 2) + B / (s + 4 - sqrt(15)) + C / (s + 4 + sqrt(15))
where A, B, and C are constants to be determined.
Multiplying both sides by the denominator and simplifying, we get:
s^2 + 3s + 1 = A(s + 4 - sqrt(15))(s + 4 + sqrt(15)) + B(s + 2)(s + 4 + sqrt(15)) + C(s + 2)(s + 4 - sqrt(15))
Setting s = -4 + sqrt(15), we get:
-4 + sqrt(15) = A(-4 + sqrt(15) + 4 + sqrt(15))
Solving for A, we get:
A = (-4 + sqrt(15)) / (2sqrt(15))
Setting s = -4 - sqrt(15), we get:
-4 - sqrt(15) = A(-4 - sqrt(15) + 4 + sqrt(15))
Solving for A, we get:
A = (-4 - sqrt(15)) / (-2sqrt(15))
Setting s = -2, we get:
-1 = B(-2)(-2 + 4 + sqrt(15))
Solving for B, we get:
B = (-1) / (2sqrt(15) + 4)
Setting s =
Suppose it is known that the proportion of students at a local high school that take public transit to school is p = 0.15
The distribution of the sample is approximately normal with a mean of 0. 15 and a standard deviation of 0. 03852.
How to describe the distribution ?One can utilize the Central Limit Theorem (CLT) for proportions to detail the dispersion of the sample proportion. Explained by the CLT, if the size of the sample is sufficiently significant enough, then the distribution with respect to the sample proportion will be mostly indistinguishable from a typical distribution.
np ≥ 10
n(1-p) ≥ 10
Given that both conditions are fulfilled, we can essentially posit that the said sample proportion distribution is almost normal. In light of this knowledge, it would be pertinent to ascertain the mean (μ) and standard deviation (σ) of the sample proportion distribution.
Mean = p = 0.15
Standard deviation:
= √ ( ( 0.15 x ( 1 - 0. 15 ) ) / 86 )
= 0.03852
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Determine which function is represented by the graph.
(a) f ( x ) = 4 cos ( x + π )
(b) f ( x ) = 4 cos 4 x
(c) f ( x ) = 4 sin ( x − π )
(d) f ( x ) = − 4 cos ( x + π )
(e) f ( x ) = 1 − sin x /2
Answer:
The graph appears to be a cosine function that has been shifted π units to the left and vertically reflected.
Option (d) represents this transformation:
f(x) = -4 cos(x + π)
Therefore, the answer is (d).
Step-by-step explanation:
I NEED THIS NOW 40 POINTS!!!!!!
Question 1 Part C (4 points): Showing the steps of your work, factor the polynomial from part B completely.
18x^3 + 6x^2y - 9x^2 - 3xy
(I already know the answer: 3x(3x + y) (2x − 1) I just need the work on how to get to the answer)
The polynomial 18x^3 + 6x^2y - 9x^2 - 3xy when factored completely is (6x^2 - 3x)(3x + y)
Factoring the polynomial completely.From the question, we have the following parameters that can be used in our computation:
18x^3 + 6x^2y - 9x^2 - 3xy
Factoize the expression
So, we have
6x^2(3x + y) - 3x(3x + y)
Factor out 3x + y
So, we have
(6x^2 - 3x)(3x + y)
Hence, the solution is (6x^2 - 3x)(3x + y)
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Darcy is tiling a square area of her bathroom floor. For every 13 white tiles used, she wants to use 12 gray tiles.
The ratio to show the relationship is 13 : 12
Writing the ratio to show the relationshipFrom the question, we have the following parameters that can be used in our computation:
For every 13 white tiles used, she wants to use 12 gray tiles.
This means that
Ratio = White : Gray
Substitute the known values in the above equation, so, we have the following representation
Ratio = 13 : 12
Hence, the ratio of white tiles and the number of gray tiles is 13 : 12
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Complete question
Demetria is tiling a square area of her bathroom floor. For every 13 white tiles used, 'she wants to use 12 gray tiles.
Write a ratio to show the relationship between the number of white tiles and the number of gray tiles.
Molly has four t-shirts in her closet that she plans to wear over the next four days without wearing the same one twice. She has a blue, green, yellow, and black shirt. What are the chances that she will wear the black shirt the first day?
Write your answer as an exact fraction which is reduced as much as possible.
Answer:
Molly has four choices for which shirt to wear on the first day, and one of those choices is the black shirt. So the probability that she will wear the black shirt on the first day is 1/4. Therefore, the answer is 1/4.
Step-by-step explanation:
In how many way can a committee of three democrats And two republicans be formed from a group of ten democrats and ten republicans
The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.
We have,
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
Here, the differences between permutation and combination are described in detail.
The number of ways in which we can select a committee of 4 democrats from ten democrats is:
P = 10C 4 = 10! / (4)! (10 - 4)!
P = 210
The number of ways in which we can select a committee of 3 Republicans from 11 Republicans is:
P = 11C 3 = 11! / 3! (11 - 3)!
P = 165
The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is:
P = (210) (165) = 34650
The number of ways in which a committee of four Democrats and three Republicans be formed from a group of ten Democrats and eleven Republicans is 34650 ways.
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Can you help me with this question?
A Ferris wheel has a diameter of 14 meters determine the distance to the nearest meter that a rider travels after 2 complete laps.
Answer:
88
Step-by-step explanation:
The distance traveled by a rider on a Ferris wheel can be calculated by finding the circumference of the wheel and then multiplying it by the number of complete laps.
The formula for the circumference of a circle is:
C = πd
where C is the circumference, d is the diameter, and π is a constant approximately equal to 3.14.
In this case, the diameter of the Ferris wheel is 14 meters, so the radius (half the diameter) is 7 meters.
C = πd = π(14) = 43.9823 meters (rounded to 4 decimal places)
To find the distance traveled after 2 complete laps, we need to multiply the circumference by 2:
distance = 2C = 2(43.9823) = 87.9646 meters
Rounding to the nearest meter, the distance traveled by a rider after 2 complete laps is 88 meters.
How many times greater is the
value of the 4 in 2,849 than the
value of the 4 in 3,824?
Answer:
The value of the 4 in 2,849 is 4 x 100 = 400, while the value of the 4 in 3,824 is 4 x 10 = 40. Therefore, the value of the 4 in 2,849 is 400/40 = 10 times greater than the value of the 4 in 3,824.
Step-by-step explanation:
The 5-lb collar slides on the smooth rod, so that when it is at A it has a speed of 10 ft/s. A) if the spring to which it is at- tached has an unstretched length of 3 ft and a stiffness of k-= 10 lb/ etermine the normal force on the collar at this instant. B)Determine the acceleration of the collar at this instant.
The acceleration of the collar at point A is 5 ft/s^2.
A) To determine the normal force on the collar at point A, we need to consider the forces acting on the collar. The only force acting on the collar in the vertical direction is the weight of the collar (5 lb), which is balanced by the normal force exerted by the rod. Therefore, we can write:
N - 5 = 0
where N is the normal force. Solving for N, we get:
N = 5 lb
B) To determine the acceleration of the collar at point A, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force on the collar is given by the force exerted by the spring, which is equal to the spring constant times the displacement of the collar from its unstretched length. At point A, the displacement of the collar is:
x = L - y = 3 - 0 = 3 ft
where L is the length of the rod and y is the position of the collar on the rod. Therefore, the force exerted by the spring is:
F = kx = 10 lb/ft × 3 ft = 30 lb
The weight of the collar is:
W = mg = 5 lb
where g is the acceleration due to gravity. The net force on the collar is therefore:
Fnet = F - W = 30 - 5 = 25 lb
Using Newton's second law, we can write:
Fnet = ma
where a is the acceleration of the collar. Solving for a, we get:
a = Fnet / m = 25 lb / 5 lb = 5 ft/s^2
Therefore, the acceleration of the collar at point A is 5 ft/s^2.
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∠A and ∠B are vertical angles. If m ∠ A=(2x−2) ∘ and B=(3x−15) ∘ , then find the value of x
The value of x is 13°
What are Vertical Angles?When two lines intersect, four angles are formed. There are two pairs of nonadjacent angles. These pairs are called vertical angles.
In a coordinate plane, a line parallel to the Y-axis is called Vertical Line. It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate.
We have:
The angles are:
m ∠ A=(2x−2) ∘ and ∠ B=(3x−15) ∘
We have to find the value of x
Now, We know that :
m ∠A = m ∠B (Def. of Vertical Angles)
(2x−2) = (3x−15)
Combine the like terms:
2x - 3x = -15 + 2
-x = -13
x = 13
The value of x is 13°
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A man has 16 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.50, how many dimes and how many quarters does he have?
Let d = number of dimes, q = number of quarters.
Step one:
A man has 16 coins in his pocket, all of which are dimes and quarters.
Set up the first equation for the number of dimes and quarters. Help PLS
Answer: 10 dimes and 6 quarters, see below for the equations.
Step-by-step explanation:
We know how much a dime is worth and how much a quarter is worth, and they give us the total number of coins and the total number of change.
This equation shows the total number of coins:
d + q = 16
This equation shows the worth of these coins:
0.10d + 0.25q = 2.5
Now, we can graph these equations. See attached. The point of intersection, where the lines cross, is our solution. In the graph, d = x and q = y.
This point is (10, 6) meaning he has 10 dimes and 6 quarters in his pocket.
For a population growing at 3% a year, what is the yearly growth factor?
Verify
8. sin²a + cot²a sin²a = 1
Answer:
8sin²a + cot²a sin²a = 1 is true.
Step-by-step explanation:
A school is constructing a rectangular play area against an exterior wall of the school building. It uses 120 feet of fencing material to enclose three sides of the play area.
Write an equation to represent l, the length of the play area in feet, as a function of w, the width in feet.
An equation to represent A, the area in square feet, as a function of w, the width in feet is A = 120W -2W²
Here, we have,
According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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Find the area of the composite figure.
2 ft
F
4.5 ft
K
6.5 ft
1 ft
1 ft
Answer:
The area is 13 feet squared.
Step-by-step explanation:
To find the area, first separate the composite figure into two shapes: a rectangle and a triangle.
Find the area of each shape separately, and then add the areas together.
First, the rectangle:
length= 4.5 feet
width = 2 feet
[tex]2*4.5=9 ft^{2}[/tex]
The area of the rectangle is 9 feet squared.
Next, the triangle:
The base is 2 feet + 1 foot + 1 foot = 4 feet
The height is 6.5 feet - 4.5 feet = 2 feet
The formula to find the area of a triangle is [tex]\frac{h*b}{2}[/tex] (height times base over two)
[tex]\frac{2*4}{2}=4ft^{2}[/tex]
the area of the triangle is 4 feet squared.
Add the two areas together to find the total area of the composite figure:
[tex]9ft^{2} +4ft^{2}=13ft^{2}[/tex]
The area is 13 feet squared.
find the following arc measures
The measure of the angles are;
<KL = 23 degrees
m<LON is 23 degrees
m<OM = 113 degrees
m<KNL = 23 degrees
m<NL = 157 degrees
How to determine the measures of the arcTo determine the measures of the arc, we need to note the following;
Angles on a straight line is equal to 180 degreesAngle at right angle is equal to 90 degreesFrom the information shown in the diagram, we have;
<KL +<KM = 90 degrees
Now, substitute the values
<KL + 67 = 90
collect like terms
<KL = 23 degrees
m<LON and <KL are corresponding angles
Then, m<LON is 23 degrees
m<OM = m<LON + 90 degrees
Substitute the values
m<OM = 113 degrees
m<KNL = 23 degrees
m<NL = 90 + <LM
Substitute the values
m<NL = 157 degrees
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Five sevenths of the fifty six images used as backgrounds on julia iPad were photos from dance class that she took herself. How many photos are of julia dance class? **Make sure you provide Your final answer as a fraction with a denominator of 56
The number of photos from Julia dance class = 5/7 or 40/56 photos.
We shall use mathematical operations to calculate the photos that are of Julia dance class
How do we use mathematical operations to calculate the photos?Five sevenths of the images are photos from dance class, meaning that 5/7 x 56 = 40 photos from dance class.
We express the answer as a fraction with a denominator of 56 like this:
Number of photos / Total number of photos = 40/56
Number of photos from dance class / Total number of photos = 5/7
Therefore, the fraction of photos that are of Julia dance class (as a fraction with a denominator of 56) = 5/7 or 40/56.
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Vanilla rent increased by 5%. The increase was $82. What was the original amount of Pavati's rent?
expressions that are equivalent to x^6
The expressions for [tex]x^6[/tex] can be varied, one such basic expression is [tex](x^n)^m[/tex], where n and m are positive integers equal to 2 and 3.
A grouping of numbers, variables, and operations like addition, subtraction, multiplication, division, exponentiation and more is known as an expression. A single number or variable can be an expression it can also include a combination of terms or functions.
By simplifying the [tex]x^6[/tex] we can get the expression-
[tex]x^6=(x^2)^3 \\\\x^6=(x^3)^2\\\\x^6=x^2 * x^4 \\\\x^6=(x^2 + 1 - 1)^6\\\\x^6=(x^3 - x^2 + x - 1 + 1)^2[/tex]
all these expressions represent [tex]x^6[/tex].
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An urn contains 6 red and 8 black balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are black? Round your answer to three decimal places.
I need help to solve this...
Answer:
2.38888
Step-by-step explanation:
That's what is says hope this helps
Isosceles triangle LMN is graphed with vertices L(0, 1), M(3, 5), and N(6,1). What is the slope of side LN?
Negative StartFraction 4 over 3 EndFraction.
0
StartFraction 4 Over 3 EndFraction.
3
\
John paid $270 for a new mountain bicycle to sell in his shop. He wants to price it so that he can offer a 10% discount but still make 30% of the price he paid for. At what price should the bike be marked $?
John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.
If John wants to make a 30% profit on the price he paid for the bike, he needs to sell it for:
$270 + 30% of $270 = $270 + $81 = $351
To offer a 10% discount on the marked price, he needs to calculate the price that includes the discount. Let's call this price "x".
90% of the marked price "x" is the same as the price he wants to sell the bike for ($351):
0.9x = $351
x = $390
Therefore, John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.
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Here is question 3 of 6. Thank you for the help
Yes, data provide convincing evident that contest has increased participation.
We have,
H₀: p = 0.12
Hₐ: p > 0.12
So, z = (p' - p)/ (√pq/n)
z = 1/6 - 0.2/ √(0.12 x 0.88) /210
z= 2.08
The test is right tailed.
So, P value = P( z> 2.08) = 0.0188
and, P- value < α, Reject H₀
Yes, data provide convincing evident that contest has increased participation.
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128 3 мы - 5 20 14 ) 448 320 (20X14) 128 80 (5х16) 48 -48 (3 XI) vaku С
Beatrice is standing on a cliff 70 feet above the ocean. She sees a boat in the ocean that is 600 feet from the base of the cliff. What is the angle of depression at which Beatrice sees the boat?
The angle of depression at which Beatrice sees the boat is 83.35°.
How to find the angle of depression at which Beatrice sees the boat?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Check the attached image for the sketch of triangle ABC.
From the sketch, the angle of depression is represented with x:
tan x = 600/70 (tan = opposite/adjacent)
x = tan⁻¹(600/70)
x = 83.35°
Therefore, the angle of depression at which Beatrice sees the boat is 83.35°.
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Triangle ABC and triangle DEF are similar. What is the measure
of side DF?
B
E
9 cm
15 cm
D
с
? cm
25 cm
F
The measure of side DF is 15cm
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. For two traingles to be similar, the corresponding angles of the triangles must be equal.
And also, the ratio of corresponding sides of Similar triangles are equal
This means;
15 /25 = 9/DF
representing DF by x
15/25 = 9/x
15x = 25×9
15x = 225
divide both sides by 15
x = 225/15
x = 15cm
Therefore the measure of DF is 15cm
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