the graph of f(x)= 3 times 2x -3 is shown below. g(x) is a transformation of f(x).

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:

The angle of depression at which Beatrice sees the boat is 83.35°.

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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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.

The ratio to show the relationship is 13 : 12

From 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.

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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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:

(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 =

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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Answer:

8sin²a + cot²a sin²a = 1 is true.

Step-by-step explanation:

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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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.

Answer:

2.38888

Step-by-step explanation:

That's what is says hope this helps

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

To determine the measures of the arc, we need to note the following;

From 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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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.

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

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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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 value of x is 13°

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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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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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-

Based on the given;

Using 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

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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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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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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The distribution of the sample is approximately normal with a mean of 0. 15 and a standard deviation of 0. 03852.

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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The polynomial 18x^3 + 6x^2y - 9x^2 - 3xy when factored completely is (6x^2 - 3x)(3x + y)

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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The measure of side DF is 15cm

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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