In this lesson, you sketched polynomial functions using factors and rewrote them in general form.
1 Use the factors to sketch each cubic function and label the zeros. Then rewrite the function
in general form.
F(x) = (x+3)(-x + 5)2 - 2x)

(1). The unit rate of per hour is 8 hours.

(2). He bikes 72 miles in 9 hours.

What do you mean by unit rate?

An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.

According to data in the given question,

We have :

Distance travelled in 3.5 hours = 28 miles

Now, firstly we need to find unit rate per hour,

Distance travelled in 1 hours = 28/3.5 miles

                                               = 8 miles

So, the unit rate of per hour is 8 hours.

Then, we will find the how far can he bike in 9 hours,

Distance travelled in 9 hours = 9*8 miles

                                                = 72 miles

Therefore, he bikes 72 miles in 9 hours.

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Taking into account the definition of a system of linear equations, Finally, the investor owns 80 and 120 shares of Stock A and B respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

A solution to a system is an assignment of values to the unknowns that makes each of the equations true. Solving a system means finding all the solutions of the system.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is:

A + B= 200

9.50A +27B= 4000

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "A" from the first equation you get:

A= 200 - B

Substituting the expression in the second equation:

9.50× (200 - B) +27B= 4000

Solving:

9.50×200 - 9.50B +27B= 4000

1900 - 9.50B +27B= 4000

- 9.50B +27B= 4000 - 1900

17.5B= 2100

B= 2100÷ 17.5

B= 120

Substituting this value in the expression A=200 - B you get:

A= 200 - 120

A= 80

Finally, the investor owns 80 shares of Stock A and 120 shares of Stock B.

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The solutions for the given conditions are;

1. True

2. True

3. False

4. False

5. False

6. True

7. True

1) For estimating a population parameter, a confidence interval is used.

TRUE → CI is used for estimating a population parameter. But, it can also be used to estimate the sample statistic.

2) The sample statistic is always captured by a confidence interval.

TRUE → CI is calculated using the sample statistic.

3) The population parameter is always captured by a confidence interval.

FALSE → There is a type 1 error possibility.

4) Z-critical values should always be used when creating confidence intervals.

FALSE → Z stat is used only in a normal distribution with sizes>30. Else, it is recommended to use a t distribution.

5) The center of the confidence interval is determined by the margin of error.

FALSE → ME determines the maximum deviation from the center at a given confidence level

6) In general, we would like to have a high level of confidence and a precise confidence interval.

TRUE → This is attainable when we increase the sample size.

7) A large sample size is required to create a proportion's confidence interval.

TRUE → Along with the large sample, we also need to have np and nq at least 10.

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The length of the guy wire will be equal to 27.78 feet.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that Janelys places a 5-foot tall pole to support the guy wire. After placing the pole, Janelys measures the distance from the stake to the pole to be 14 ft. She then measures the distance from the pole to the tower to be 24 ft.

The length of the wire will be calculated as,

L² = 24² + 14²

L² = 576 + 196

L² = 772

L = √772

L = 27.78 ft

Therefore, the length of the guy wire will be equal to 27.78 feet.

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Answer:

40ft

Step-by-step explanation:

The cost of each white led lights and colored led lights is $12 and $15 respectively.

Let

w + c = 27

3w + 2c = 66

From (1)

w = 27 - c

Substitute w = 27 - c into (2)

3w + 2c = 66

3(27 - c) + 2c = 66

81 - 3c + 2c = 66

- 3c + 2c = 66 - 81

- c = - 15

c = 15

Substitute c = 15

w + c = 27

w + 15 = 27

w = 27 - 15

w = 12

In conclusion, the task content can be solved using the concept of simultaneous equation.

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Answer:

Step-by-step explanation:

Location & Hours

Map

109 W 4th St

Ogallala, NE 69153

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7:00 AM - 3:00 PM

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7:00 AM - 3:00 PM

Thu

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Sun

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K B.

Fort Collins, CO

0223

6/18/2015

wonderful cinnamon rolls and sticky buns, so glad we stopped on our way thru town.

It's a small little place in  residential area, not far from a main road, definitely worth stopping by for a delicious treat!

Kaitlin J.

Cedar Grove, Panama City, FL

016

8/27/2020

2 photos

Erin is so friendly and truly a master of her trade! We ordered a cake shaped like a suitcase (complete with fondant flight attendant) as a surprise for our mom's retirement party. It turned out even better than we could have ever expected with the best hand-painted intricate details. She really went above and beyond, and the carrot cake was absolutely delicious!! We are all still so impressed. We just had such a great experience from start to finish--Erin is so friendly and easy to work with. She made our vision come to life and at an incredibly reasonable price. I can't recommend her bakery enough!

Answer: 5.5

Step-by-step explanation:

1/2 gallons of water rush down the slide each seconds.

For the given question-

Rate of running water = 1 half gallon every 3 seconds.

Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.

It means-

In every 3 seconds ----> 3/2 gallons water flows.

Thus for 1 sec, divide both side by 3.

1 seconds ----> 1/2 gallons water flows.

Therefore, 1/2 gallons of water rush down the slide each seconds.

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Answer:

Step-by-step explanation:

A B

We will see that the odd functions were f(x) = x5 - 3*x3 + 2*x and f(x) = 1/x since only those were true under the specified circumstances.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. The most basic definition is that a function is a collection of ordered pairs of items, which in our instance will be numbers, but they may also be anything else, and which have the feature that their initial members are all distinct from one another. The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.

Here,

A function is odd,

f(-x) = -f(x) for every value of x in its domain.

1) f(x) = x^3 - x^2

f(-x) = (-x)^3 - (-x)^2

= -x^3 - x^2

f(-x) ≠ -f(x)

This function is not odd.

2) f(x) = x^5 - 3*x^3 + 2*x

f(-x) = (-x)^5 - 3*(-x)^3 + 2*(-x)

= -x^5 + 3*x^3 - 2*x = -f(x)

This function is odd.

3) f(x) = 4x + 9

f(-x) = 4*(-x) + 9

= -4*x + 9

-f(x) = -( 4*x + 9)

= -4*x - 9

f(-x) ≠ -f(x)

This function is not odd.

Because only these were true under the specified circumstances, we will find that the odd functions are f(x) = x^5 - 3*x^3 + 2*x and f(x) = 1/x.

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The number of rides is the dependent variable, while the total cost is the independent variable.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables according to some law or rule.

The variable that the researcher modifies or manipulates in an experiment is known as the independent variable. The measured reaction is the dependent variable. The dependent variable is dependent on the change in the independent variable, to put it another way.

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The number of months required to complete the payments are 63 months.

We will make a equation, which represent total purchase amount in terms of number of months.

Let we consider number of months be t.

Total purchase amount = $17500, one time deposit = $1750

and monthly payment = $250

Then,

17500 = 1750 + 250t

250t = 17500-1750

250t = 15750

t = 15750/250

t = 63 months

Thus number of months required are 63.

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The triangles in the image given are classified as:

11. isosceles 12. scalene 13. equilateral

Therefore:

11. The triangle has two congruent sides, therefore, it is classified as isosceles.

12. The triangle has different side lengths, therefore it is scalene.

13. All the three sides of the triangle are congruent, therefore, it is an equilateral triangle.

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K-means clustering is a type of unsupervised learning which uses unlabeled data, or data without clearly defined categories or groupings.

Data is divided into k clusters using K-means clustering, with the goal of making the clusters closer together and the individual data points more dispersed.

K-means clustering is a sort of unsupervised learning which uses unlabeled data, or data without clearly defined categories or groupings.

Thus this algorithm's goal is to identify groups among the data, where K stands for the set of organizations.

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The complete question is-

Assume that you have a labeled dataset. Explain how you can use only K-means clustering to build a classification model for this dataset. What can go wrong?

Answer:

Below

Step-by-step explanation:

a = 1   b = 5    c  = 5

Using these values in the Quadratic Formula given results in zeroes of

x =    -5/2 ± sqrt (5) / 2

Since these two lines overlap, the variable's value is 25, and the angle's value is 38 degrees.

The empty set, a point, or another line can cross another line in Euclidean geometry. Examples of applications for identifying these circumstances and locating the intersection include computer graphics, motion planning, and collision detection. In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the crossing lines share a common point.

Here,

Both the angles are equal as they are intersecting lines and opposite angles are equal in this.

x+13=3x-37

3x-x=37+13

2x=50

x=25

x+13=25+13

angle=38

3x-37=3*25-37

angle=38

The value of variable is 25 and the value of angle in 38 degree as they are the intersecting lines.

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Answer:

39.9 yards

Step-by-step explanation:

Pythagorean theorem is a^2+b^2=c^2

Where a and b are the legs and c is the hypotheneus

We set this so it will be equal to a leg

a^2+b^2=c^2

     -b^2. -b^2

a^2=c^2-b^2

42^2-13^2=a^2

1764-169=a^2

1595=a^2

√        √

39.9=a

Hopes this helps please mark brainliest

ab⁶ is not a variable term found in the binomial expansion of [tex](a + b)^{8}[/tex]as this is because, the powers must sum up to 8

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

The Binomial Expansion of [tex](a+b)^8[/tex] is -

[tex](a + b)^8 = a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a3^b^5 + 28a^2b^6 + 8ab^7 + b^8.[/tex]

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Answer:

9

C

D

Step-by-step explanation:

Answer:

after 4 months dan and sydney will have paid the same amount

Step-by-step explanation:

Answer:

Step-by-step explanation:

dan and sydney are getting high speed internet access at the same time.dans provider charges $60 for installation and $42.95 each month. sydney's provider has free installation and charges 57.95 per month. after how many months will dan and sydney have paid the same amount?

let 'm' represent the number of months they have subscribed

dan's total:

42.95m + 60

sydney's total:

57.95m

we want to calculate 'm' when the two totals are equal:

42.95m + 60 = 57.95m

60 =15m

m = 60/15 = 4

after 4 months dan and sydney will have paid the same amount

The asymptotes of the graph of the function are given as follows:

The function has two types of asymptotes, which are given as follows:

The vertical asymptotes are the values of x for which the function is not defined, that is, empty spaces on the graph of the function, hence they are given as follows:

At x = 1, there is a closed circle, hence the function is defined and it is not a vertical asymptote.

The horizontal asymptote is the limit of the function as it goes to infinity, as long as this limit is different of infinity.

The limits are given as follows:

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Answer:

D

Step-by-step explanation:

Exam test completed. Your welcome

Answer:

Step-by-step explanation:

x is increasing by 2

y is decreasing by 4

Rise over run:

-4/2 --> -2

Answer: I believe the answer is -2

Answer:

  y = mx

Step-by-step explanation:

You want to know the slope-intercept formula for a line that represents a proportion.

A proportion is a linear function that includes the point (0, 0). The y-intercept is zero, so the slope-intercept equation is ...

  y = mx

Answer:

7 + 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a

([tex]\sqrt{2}[/tex] + 5)(1 + [tex]\sqrt{2}[/tex])

each term in the second factor is multiplied by each term in the first factor, that is

[tex]\sqrt{2}[/tex](1 + [tex]\sqrt{2}[/tex]) + 5(1 +[tex]\sqrt{2}[/tex]) ← distribute parenthesis

= [tex]\sqrt{2}[/tex] + 2 + 5 + 5[tex]\sqrt{2}[/tex] ← collect like terms

= 7 + 6[tex]\sqrt{2}[/tex]

At p = Θ(1/√n) the expected number of cliques in G will be going to be equal to 1.

The likelihood that a random event will occur is defined by probability. There are several real-life circumstances in which we must forecast the result of an occurrence. We might be certain or uncertain about the outcome of an event. In these circumstances, we state that there is a likelihood that this occurrence will occur or not. Generally speaking, probability has many useful uses in games, business (to make forecasts based on probability), and this emerging branch of artificial intelligence.

By simply dividing the favorable number of possibilities by the entire number of potential outcomes, the probability of an occurrence may be computed using the probability formula. Probability values range from 0 to 1, with a value of 1 being the most likely.

How to solve?

Fix any S-vertex subgroup that contains less than 5. Given that S includes (5, 2)=10 edges, the probability of S being a clique in G is p^10. Given that S has (n, 5) options, the predicted number of 5 cliques in G is (n, 5)p^10 due to linearity of expectation. The result of solving for (n, 5)p10 = 1 is^ p10 = (1/n^5).

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Answer:

a) 53+(8p+10)+(2p+17)=180

  p= 10

b) 53 degrees

   8p+10 = 90 degrees

  2p+17= 37 degrees

Step-by-step explanation:

sum of all angles of a triangle equal 180 degrees

so we can add all these angles together and set it equal to 180

53+(8p+10)+(2p+17)=180

53+10p+27=180

10p+80=180

    -80.    -80

10p=100

/10. /10

p=10

now we can fill in p to find the angles

we already know 53 degrees

8p+10

8(10)+10

80+10

90 degrees

2p+17

2(10)+17

20+17

37 degrees

hopes this helps please mark brainliest

Answer:

a)   53° + (8p + 10)° + (2p + 17)° = 180°

      p = 10

b)   53°, 90° and 37°

Step-by-step explanation:

Interior angles of a triangle sum to 180°.

Therefore, to find the value of p, equal the sum of the given angles to 180°, then solve for p.

⇒ 53° + (8p + 10)° + (2p + 17)° = 180°

⇒ 53 + 8p + 10 + 2p + 17 = 180

⇒ 8p + 2p + 53 + 10 + 17 = 180

⇒ 10p + 80 = 180

⇒ 10p + 80 - 80 = 180 - 80

⇒ 10p = 100

⇒ 10p ÷ 10 = 100 ÷ 10

⇒ p = 10

To find the measure of the angles, substitute the found value of p into the expression for each angle:

⇒ (8p + 10)° = (8(10) + 10)° = (80 + 10)° = 90°

⇒ (2p + 17)° = (2(10) + 17)° =  (20 + 17)° = 37°

Therefore, the measures of the three angles are:

The Frequency will be "266.14 Hz" and the number of loops are "60".

For the given question-

The formula for the linear velocity is given as;

Linear density; μ = mass/length

Put the values,

μ = 4.5 x 10⁻³/0.6

μ = 7.5 x 10⁻³ kg/m

The formula for the fundamental frequency is;

F = (1/2L)√(T/ μ)      

F = (1/2x0.6)√(765/ 7.5 x 10⁻³)      

F = 266.14 hz

The number of loops  is;

n = f'/f

n = 16000/266.14

n = 60

Thus, a person who can hear frequencies up to f = 16 kHz would be able to hear the highest harmonic with number n equal to 60.

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The complete question is-

A piano tuner stretches a steel piano wire with a tension of 765 N . The steel wire has a length of 0.600 m and a mass of 4.50g .

What is the frequency (f_1) of the string's fundamental mode of vibration?

What is the number n of the highest harmonic that could be heard by a person who is capable of hearing frequencies up to f = 16 kHzc?

The two boats will be 120 miles apart in five hours.

We need to find the time at which the boats will be 120 miles apart from each other.

It has been given that the total distance is 120 miles.

Now, let's take up the following assumptions in order to arrive at the time taken by two boats to cover the requisite distance:-

Let x= distance traveled by boat 1 at 10 miles per hour.

Let y= distance traveled by boat 2 at 14 miles per hour.

Thus, x+y=120(given)------(i) [That is, distance travelled by boat 1+ Distance travelled by boat 2= Total Distance]

Let t denote the time factor,

then, Boat 1 will travel x miles in T hours, and the Boat 2 will travel y miles in T hours.

We know, Distance= Rate * Time

Thus,  we can say, x= 10*T---------------(ii)

                               y=14*T-----------------(iii)

Adding equations ii and iii, we get

x+y=24T----------------(iv)

Now, subtracting equation (iv) from (i), we get

24T-120=0

24T= 120

thus, we get t=5

Hence, the time taken by two boats, to be 120 miles apart is five hours.

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