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Need help part A, B and C

Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.

Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.

2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)

3. Create a graph of the polynomial function you selected from Question 2.

Part B
The second part of the new coaster is a parabola.

4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.

5. Create a graph of the polynomial function you created in Question 4.

Part C
6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.

Answer:

Step-by-step explanation:

3 things of triangle are given.

2 sides + 1 angle

so, possible triangles = 1 ans

The area of the rectangular field is 468cm².

Step-by-step explanation:

If, length is 18cm; width is unknown( let x represent width). Then,

Perimeter of a rectangle= Length + Width+ Length + Width

88= 18 + x + 18 + x

88= 36 + 2x

88-36 =2x

52= 2x

52/2=2x/2

26=x

•x=26cm

The width of the rectangle is 26cm.

Area of a rectangle= Length × Width

=18cm×26cm

= 468cm².

Answer:  [tex]\frac{\sqrt{7}}{7}[/tex]

========================================================

Explanation:

The reciprocal of x is 1/x where x is nonzero. Multiplying x with 1/x leads to 1. For example, the numbers 9 and 1/9 are multiplicative inverses of each other.

We'll stick 1 over the given square root expression. Then follow these steps to rationalize the denominator.

[tex]\frac{1}{\sqrt{7}}\\\\\\\frac{1*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\\\frac{\sqrt{7}}{(\sqrt{7})^2}\\\\\\\frac{\sqrt{7}}{7}\\\\[/tex]

In short, [tex]\frac{1}{\sqrt{7}}=\frac{\sqrt{7}}{7}[/tex]

The probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.9

Standard deviation = 0.2

Calculate the z-score at x = 0.92 using

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

z = (0.92 - 0.9)/0.02

Evaluate the numerator; subtract 0.9 from 0.92

z = 0.02/0.02

Divide 0.02 by 0.02. This gives

z = 1

The probability is then represented as:

P(x > 0.92) = P(z > 1)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.92) = 0.841

Hence, the probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

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The total value of the investment is $107,032.16.

The total interest earned is $53,032.16

The inheritance would last the tenure of the university.

The formula that can be used to determine the future value of the 18-year annuity is: annuity factor x amount deposited yearly

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$3000 x [(1.075^18 - 1) / 0.075] = $107,032.16

Amount deposited in the course of 18 years = (3000 x 18) = 54,000

Interest earned = 107,032.16 - 54,000 = $53,032.16

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The fraction computed shows that the total inches the infant grew over the three months is 3 3/4 inches.

First month = 2/4 inches

Second month = 1 inch

Third month = 7/4 inches.

The total inches the infant grew over the three months will be;

= 2/4 + 1 + 7/4

= 3 1/4 inches.

The difference in the infants from the second month to the third month will be:

= 7/4 - 1

= 3/4 inches.

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Answer:

(-oo, -8/3) U (-8/3, oo)

Step-by-step explanation:

Hope this helps.

The domain of the equation f(x) = 2/(3x + 1) is (-∝, -8/3) U (-8/3, ∝)

From the question, we have the following parameters that can be used in our computation:

f(x) = 2/(3x + 1)

The above equation is a rational function

The rule of a function is that

The domain is the set of all input numbers

For the domain, we set the denominator not equal to 0

So, we have

3x + 8 ≠ 0

Evaluate

x ≠ -8/3

When represented as interval notation, we have

Domain = (-∝, -8/3) U (-8/3, ∝)

Hence, the domain is (-∝, -8/3) U (-8/3, ∝)

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The sweatshirt size which the vendor should bring more of by virtue of that which is most likely to be sold is; Choice A; Extra-large.

If follows from the task content that the

ratio of extralarge shirts sold relative to the quantity he had to sell is

= 99/108

= 11/12,

This is a ratio which is larger than any other shirt.

Consequently, the vendor must bring more of the X-large shirts to avoid running out of them.

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All the angles required to complete each sentence are:

In this question we must take advantage of definitions and theorems of Euclidean geometry to complete the three sentences seen in the figure. Now we proceed to present each sentence completed in detail:

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The probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.

When a random variable X is normally distributed, with the mean as μ, and standard deviation as σ, then the probability P(X < x) is calculated using the Z-score table, as the probability P(Z < z), where z is calculated using the formula, z = (x - μ)/σ.

In the question, we are asked to find the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12.

We calculate as follows:

P(X < 105)

= P(Z < (105-90)/12)

= P(Z < 1.25)

Now we check the z-score table for the value of z as 1.25.

On the left column we choose the value 1.2.

On the top row, we choose the value .05.

The intersection of these, gives us the value,

P(Z < 1.25) = 0.8944.

Thus, the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.

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Answer:

A

Step-by-step explanation:

$30.00 ÷ 5 = $6.00

$6.00 × 3 = $18.00

Answer: 36

Step-by-step explanation:

As this is a two-digit number, it will have a digit in its 10's place and a digit in its 1's place. We can represent the 10's digit using x and the 1's digit using y.

Since the ones is twice the number of tens, this means that y is equal to 2*x. Let's put this into an equation.

[tex]y=2x[/tex]

If the 10's digit is x and the 1's digit is y, the original number would be [tex]10x + y[/tex], as x must be multiplied by 10 to get it to the 10's place. Similarly, the reversed number would be [tex]10y + x[/tex], as y must be multiplied by 10 to get it to the 10's place.

Twice the original number (10x+y) is equal to 9 more than (i.e. 9 plus) the reversed number. We can put this into an equation to help us answer the question.

[tex]2(10x+y)=9+10y+x\\20x+2y=9+10y+x\\19x+2y=9+10y\\19x=9+8y[/tex]

Now we have a system of two equations.

[tex]y=2x\\19x=9+8y[/tex]

We can solve this system by substituting y for 2x in the second equation. Then, we can isolate and get the value of x.

[tex]19x=9+8(2x)\\19x=9+16x\\3x=9\\x=3[/tex]

Now that we have the value of x, let's put it back into the first equation and solve for y.

[tex]y=2(3)\\y=6[/tex]

Remember that x is the 10's digit and y is the one's digit of our answer. Since x is 3 and y is 6, our answer is 36.

We can quickly check if our answer is right by making sure both conditions in the question are met.

6 (the one's digit) is twice the value of 3 (the ten's digit), making the first condition true. Twice of 36 is 72, which is 9 more than the reversed number, which is 63.

Answer:

y = 3/2x -15

Step-by-step explanation:

y = mx + b this is the slope intercept form.  We need the slope and the y intercept.  The slope (m) has been given (3/2), we just need the b (y-intercept).  We will use the point given to find b.  The point given is (8,-3).  8 is the x term and -3 is the y term.  We will plug them into y = 3/2x + b to solve for b.

y = mx + b

y = (3/2) x + b   The slope was given

-3 = (3/2)(8) + b  Plugged in the given x and y from the point (8, -3)

-3 = 12 + b  I can make 8 into a fraction by putting a 1 under it.

                   (3/2)(8/1).  I can cross cancel to make the number easier to

                    2 and 8 both share the factor 2 so I will divide both numbers

                   by 2 and I will now have (3/1)(4/1).  3x4 is 12 and 1x1 is 1, so

                   12/1 is  the same as 12.

-15 = b      Subtract both sides by 12.  -3-12 is -15

Now that I have the m and the b, I can write the equation in the slope intercept form.  y =  3/2 + (-15) or y = 3/2 -15    

Answer:

270 uits

Step-by-step explanation:

Answer:

113°

Step-by-step explanation:

Angles that form a linear pair are supplementary, and thus add to 180°.

The simplification of the equation above in words is = Twelve minus thirteen X.

In mathematics, coefficients are those numbers that multiplies a variable. For example in 13x, the coefficient is 13 which multiplies a variable known as X.

The equation given is,

10 - 13x + 2

Arrange the digits without a coefficient together.

That is ,

10+2 -13x

12 - 13x

Therefore the simplification of the given equation in words is Twelve minus thirteen X.

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The attached image shows the image of A"B"C" after the transformation

The transformation rule states:

A"B"C" = Ro90° (T(-4,3)(ABC))

This implies that one need to rotate the triangle in a 90⁰ clockwise direction, and then one need to translate the triangle.

Using the image shown, the coordinates of ABC are;

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The 90⁰ rule clockwise rotation  will be:

(x,y) -- (y,-x)

So, when translated, it will be:

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

Then the translation of the triangle using T(-4,3):

(x, y) -  (x - 4, y + 3)

So, there is:

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

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Answer:

-4

Step-by-step explanation:

in order to get from -6 to 24, you need to multiply x by -4 since -6* -4 is 24

The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)

Sequences are series of elements generated according to at least one condition, usually equations. geometric sequences are generated according to a exponential formulas, whose form and characteristics are described below:

f(n) = a · bⁿ ⁻ ¹    (1)

Where:

If we know that a = 4, b = 2 and n = 12, then the twelfth element of the geometric sequence from the statement is:

f(12) = 4 · 2¹² ⁻ ¹

f(12) = 4 · 2¹¹

f(12) = 4 · 2,048

f(12) = 4,096

The twelfth element of the geometric sequence is equal to 4,096. (Correct choice: D)

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The height of the ramp above the ground is 1.55 meters.

The difference between the height of the tree is 33.20 meters

The situation forms a right angle triangle.

Therefore, the height the ramp above the ground can be calculated as follows:

Using Pythagoras theorem,

sin 15  = opposite / hypotenuse

sin 15 = x / 6

cross multiply

x = 6 sin 15

x = 6 × 0.2588190451

x = 1.55291427062

x = 1.55

Therefore, the height of the ramp above the ground is 1.55 meters

tan 36  = opposite / adjacent

tan 36 = x / 60

x = 60 tan 36

x = 43.5925516803

x = 43.60 meters

tan 52 = y / 60

60 tan 52 = y

y = 76.7964979316

y = 76.79 meters

The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters

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Answer:

B. ABCD is a trapezoid because it has at least

one pair of parallel sides.  

Step-by-step explanation:

the two points A(-3,-1) and D(5,-1) have the same y-coordinates

Then

The line AD is parallel to the x-axis

On the other hand,

the two points B(1,5) and C(5,5) have the same y-coordinates

Then

The line BC is parallel to the x-axis.

We obtain :

• AD is parallel to the x-axis

• BC is parallel to the x-axis.

Therefore

AD // BC

Conclusion:

ABCD is a trapezoid because it has at least

one pair of parallel sides. 

Answer:

b

Step-by-step explanation:

plato

Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.

The break-even point is the value of x for which:

R(x) = C(x).

In this problem, the functions are:

Hence:

R(x) = C(x)

16x = 12x + 1424

4x = 1424

x = 1424/4

x = 356

The company will break-even when 356 widgets are sold.

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Answer:  True

Explanation:  Parallel lines are two lines that lie on the same plane and they never intersect.  

The following expressions set up as an equation to solve for the unknown numbers in the cases given below:

let

5x + 6 = 46

5x = 46 - 6

5x = 40

x = 40/5

x = 8

2/3x - 5 = 11

2/3x = 11 + 5

2/3x = 16

x = 16 ÷ 2/3

x = 16 × 3/2

x = 48/2

x = 24

1/3x + 4 = 45

1/3x = 45 - 4

1/3x = 41

x = 41 ÷ 1/3

x = 41 × 3/1

x = 123

3x - 12 = 18

3x = 18 + 12

3x = 30

x = 30/3

x = 10

40 - 2x = 16

-2x = 16 - 40

-2x = -24

x = -24/-2

x = 12

(x + 18) / 6 = 7

(x + 18) = 7 × 6

x + 18 = 42

x = 42 - 18

x = 24

2/3x - 8 = 6

2/3x = 6 + 8

2/3x = 14

x = 14 ÷ 2/3

x = 14 × 3/2

= 42/2

x = 21

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Answer:

11

Step-by-step explanation:

The focal length is 14, and thus the sum of the lengths of the blue and red segments is also 14.

a)

b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights

c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on

d) sample size [tex]n \approx 27[/tex].

Generally,
Here n = 17

T= 3.15

[tex]\sigma=0.40[/tex]

confidence level =c = 0.80

Here we will usethe  z critical value.

z critical value for (1+c) /2 = (1+0.80)/2

z critical value for (1+c) /2= 0.9

Zc = 1.28

Critical value = 1.28

a) Margin of error (E) :

[tex]E = Zc*\frac{\sigma}{\sqrt{n}}\\\\\E = 1.28*\frac{0.40}{\sqrt{17}}[/tex]

E =0.124

Margin of error = E =0.124

Lower limit = x-E

L= 3.15 - 0.124

L= 3.026

Lower limit =3.026

Upper limit = x + E

U= 3.15 + 0.124

U= 3.274

Upper limit =  3.274

The following is a confidence interval with a value of 80 percent for the mean weights of Allen's hummingbirds in the area under study: (3.02,3.28)

b) Conditions:[tex]\sigma[/tex] is understood to have a regular distribution of weights

c) Interpretation: 80 percent of the time, this range will include the actual average weight of Allen's hummingbirds, hence its reliability may be counted on.

d) When is already known, the following equation may be used to determine the appropriate number of samples, n:

[tex]n=(\frac{z_c*\sigma }{E})^2[/tex]

Margin of error = 0.13

Sample size (n):

[tex]n= (\frac{z_c*\sigma }{E})^2[/tex]

[tex]n=(\frac{ 1.28*0.36}{0.09})^2[/tex]

n = 26.21

[tex]n \approx 27[/tex]

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The proof that the diagram is a square is that; D: slopes are perpendicular where the sides meet

We know that a square is a quadrilateral that has 4 sides. Now, the 4 sides of a square are all equal and at right angles.

Since all sides of the square are equal, then it means that 2 consecutive sides must be perpendicular to each other. Thus, this means that the slope of 2 consecutive sides must be perpendicular to each other.

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