Using algebraic techniques, find the roots of:h(x)=x^3−2x^2+9x−18

Answer:

f(5)=21

Step-by-step explanation:

f(1) =5

f(2) =9

f(3)= 13

f(4)=17

there for f(5) =21 all added by four more

Alan would have to sell less than 540 boxes to earn less than $2050.

A transaction known as "selling" occurs when a product or service is traded for cash. The act of convincing a person or group to purchase something is sometimes referred to as persuasion. Your selling efforts should be concentrated on explaining the benefits to the customer if you're trying to sell a good or service. Selling's goal is to persuade customers to acquire something so they can use it. The course becomes further in-depth to explain the distinctions between traditional and consultant sales, two major schools in the field of sales. Transactional selling is one of the four forms of selling.

Selling solutions.

selling with consultation.

provocative sales tactics.

So, from the graph given it state that: Alan would have to sell less than 540 boxes to earn less than $2050.

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Answer: The actual selling price should be around $3472 and 22 cents.

Answer:

Step-by-step explanation:

elish as you know me lacey i will be glad to help you the correct awnser is 3472 dollars and 22 cents

Answer:

768

Step-by-step explanation:

2 gallons is 32 cups. Times 32 by the servings which is 24. 32 times 24 equals 768

Answer:

Given;

Total number of pencil=55

number of pencil lost=11

Then,

percentage of pencil lost=((Number of pencil lost/Total number of pencil)*100)

% of pencil lost= ((11/55)*100)

% of pencil lost=0.2*100

% of pencil lost=20%

Therefore,

The percentage of pencil lost is 20%

The instantaneous voltage across the capacitor is 4/53 * (-cos (106 t - 25)) (volts).

The instantaneous voltage across a capacitor is given by v(t) = 1/C * integral(i(t)dt) where C is the capacitance of the capacitor.

For the current i(t) = 4 sin (106 t - 25), the voltage across the capacitor can be found using the following definite integral:

v(t) = 1/C * integral(4 sin (106 t - 25)dt) from 0 to t

v(t) = 4/106C * (-cos (106 t - 25)) from 0 to t

So, the instantaneous voltage across a 2-F capacitor for this current will be:

v(t) = 4/53 * (-cos (106 t - 25)) (volts)

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Answer:

c = 3n + 5

Step-by-step explanation:

The equation c = 3n + 5 fits the data in the table. When n = -7, c = -7 * 3 + 5 = -16. When n = -6, c = -6 * 3 + 5 = -13. When n = 3, c = 3 * 3 + 5 = 14. When n = 5, c = 5 * 3 + 5 = 20. And when n = 9, c = 9 * 3 + 5 = 32. All the values of c in the table match the values predicted by the equation c = 3n + 5. Therefore, c = 3n + 5 is the correct equation for the data.

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

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The required equation is 2x + 2 = 6x and the value of 'x' is 1/2.

The total length covered by the outline or boundary of a rectangle is known as the perimeter of the rectangle. And the formula is given by

Where l = length and b = breadth  

Here we have

Rectangle-A and rectangle-B  

Dimensions of Rectangle-A are (x + 2) × x  

=> Perimeter of Recatngle-A = 2(x + 2 + x)

= 2(2x + 2)

Dimensions of Rectangle-B are 4x × 2x  

=> Perimeter of Rectangle-B = 2(4x + 2x)

= 2(6x)    

Given that both rectangles have the same perimeter

=> 2(2x + 2) = 2(6x)

=> 2x + 2 = 6x  [ Divide by 2 ]    

∴ The required equation is 2x + 2 = 6x

We can solve the above equation as follows

=> 2x + 2 = 6x

=> [ 2x + 2 - 2x] = 6x - 2x         [ Subtract -2x from both sides  ]

=> 4x = 2

=> x = 2/4

=> x = 1/2

Therefore,

The required equation is 2x + 2 = 6x and the value of 'x' is 1/2.

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Therefore , the solution of the given problem of expression comes out to be 2x² (2x² - 1 ) / (x⁴ + 1 - 2x²) .

Mathematical operations including addition, subtraction, multiplication, and division are required. They result in the following when combined: An equation, some information, and an arithmetic operator Values, parameters, and operations like adds, omissions, multiplications, and divisions make up a statement of fact. Different phrases and words can be contrasted and compared.

Here,

Given :

=> 2x² / x² -1

=> 2x² / x² -1  *  x² -1 /x² -1

=> 2x²(x²-1) / (x² -1)²

=> 2x⁴ - 2x² / (x⁴ + 1 - 2x²)

=>  2x² (2x² - 1 ) / (x⁴ + 1 - 2x²)

Therefore , the solution of the given problem of expression comes out to be 2x² (2x² - 1 ) / (x⁴ + 1 - 2x²) .

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The correct answer of this expression is (b) g>-6.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

a formula expression with the first part signifying a mathematical item and the second part signifying a statement about mathematical objects

given that;

-3 (g + 5) > 3

divide both side by -3, we get

⇒ g + 5 > 3/-3

⇒ g + 5 > -1

subtract both side by 5

⇒ g > -1 -5

⇒ g > -6

so the correct answer is g > -6

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Answer:

Step-by-step explanation:

The volume of a cube is the edge length cubed (S^3)

To find the edge length when the volume is known find the cubic root of the volume.

Edge = ∛1/27

Edge = 1/3 ft.

The area of rhombus KLMN is 287.3 in²

A rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.

Given that, a rhombus KLMN with diagonals KM and NL,

Since, the diagonals of a rhombus bisects each other at a right angle,

Let they bisect at O, so, KM = 2MO = 2KO = 2×11.4 = 22.8 in

Therefore, Δ KON is a right triangle,

Using Pythagoras theorem,

KN² = KO² + ON²

ON = √17²-11.4²

ON = 12.611 in

LN = 2×12.611

LN = 25.22 in

Area of a rhombus = 1/2 × diagonal 1 × diagonal 2

Area = 1/2 × 25.22 × 22.8

= 287.3 in²

Hence, the area of rhombus KLMN is 287.3 in²

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Answer:

Depreciation is the decrease in value of an asset over time. We know that the value of the equipment depreciates at a rate of 20% per year, and after 5 years the equipment is worth $98,304. We can use this information to set up an equation to find the original value of the equipment.

Let X be the original value of the equipment.

We know that:

X * (1 - 0.20)^5 = 98304

Where (1 - 0.20) is the depreciation rate, and the exponent 5 is the number of years.

We can solve for X by using the following steps:

X * (1 - 0.20)^5 = 98304

X * (0.8)^5 = 98304

X = 98304 / (0.8)^5

X = $143,680

So, the original value of the equipment was $143,680.

Step-by-step explanation:

If in the survey of a survey of a community, 55%. The percentage of the people who don't like to listen to the radio as well as watch the television​ is 15%.

The number of people who like to listen to the radio as well as watch the television = 35%.

So,

The number of people who like to listen to the radio but don't like to watch the television

=  55% - 35%

= 20%

The number of people who like to watch television but don't like to listen to the radio =  65% - 35% = 30%.

The percentage of people who don't like to listen to the radio as well as watch the television

= 100% - (35% + 20% + 30%)

= 100% - 85%

= 15%

Therefore  15% of the people in the community don't like to listen to the radio or watch the television.

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The tire will need to rotate 38.2 times to travel the whole length of the street.

We will first compute the tire's circumference in order to determine how many times it will need to revolve while traveling the distance of the roadway.

The formula for determining a circle's circumference may be used to get the tire's circumference because it is circular.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 3.5ft and π = 3.14

∴ C = 3.14 × 3.5

C = 10.99ft

Therefore, the circumference of the tire is 10.99ft

The tire will need to turn 38.2 times to travel the whole length of the street. We will now divide the street's length by the tire's circumference to determine how many times it tire will need to turn to go its whole length.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 420 ft ÷ 10.99 ft

Number of times the tire will have to turn = 38.2165 times

Number of times the tire will have to turn ≅ 38.2 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 38.2 times

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Using distributive property, each expressions are write in an appropriate form. The expression are shown below.

This characteristic states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend separately by the number and then combining the results collectively.

According to the property, the outcomes are the same whether the numbers in parenthesis are added before or after multiplication. In situations when the polynomial cannot be combined together before being multiplied, the distributive property is very helpful. Using this property the following expression are solved.

4(6 + 7) = 4.6 + 4.7

14.1 - (14 - 9) = 14 (1 - 9)

5 (z - 10) = 5.z - 5.10

8.6 + 8.2 = 8 (6 + 2)

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Answer:

w = 19

Step-by-step explanation:

w = 4 + 3p

w = 4 + (3 x 5) since p = 5

w = 4 + (15)

w = 19

Answer:

w = 19

If the equation is w = 4 + 3p, we can substitute the 'p' for five.

To solve for w, we need to first solve 3 times 5.

Now, just solve.

Therefore if p = 5, w = 19.

Answer:

see below

Step-by-step explanation:

road 1 100km/h x hrs

road 2 80km/hr y hrs

total 6hours

total 530 km

100x+80y=530

x+y=6

x=6-y

100(6-y) + 80y =530

600-100y+80y =530

20y=70

y=3.5

x =6-3.5 =2.5

Answer: x =2.5 y= 3.5

Step-by-step explanation:

The integral function is equal to, Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy = [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).

In calculus, an integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral include antiderivative and primitive.

Given that,

Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy

=  [tex]\int\limits^[/tex] y d([tex]e^{6y}[/tex])

= [ y ([tex]\frac{e^{6y} }{6}[/tex]) - [tex]\int\limits^[/tex] (1)  ([tex]\frac{e^{6y} }{6}[/tex]) ]

= [tex]\frac{ye^{-6y} }{6}[/tex] + [tex]\frac{e^{-6y} }{36}[/tex]  where, 0 and 1

= [ [tex]\frac{1}{6e^{2} }[/tex] + [tex]\frac{1}{36e^{2} }[/tex] ] - [1/36]

= [ 7/36[tex]e^{2}[/tex] ] - [1/36]

= [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

Therefore,

The integral function is equal to, Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy = [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

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Answer: D

Step-by-step explanation: y (Waffle cones) = 13 (Waffle cones sold during first hour) + x (Waffle cones sold during remaining hours.)

The Walmart is 2.8 miles away from her home. The result is obtained by using the speed formula in constant motion.

Speed is the change in position per unit of time. It can be expressed as

v = d/t

Where

A student walked to Walmart, bought a bike, and rode it home.

Determine the distance between the Walmart and her home!

Let's say

The distance traveled when student walked and the riding a bike is the same. It is the distance between the Walmart and her home.

d₁ = d₂ = d

So, we get t.

d₁ = d₂

v₁t₁ = v₂t₂

3.5t = 14(1 - t)

3.5t = 14 - 14t

3.4t + 14t = 14

17.5t = 14

t = 17.5/14

t = 0.8 hour

Substitute t in the walking speed formula!

d₁ = v₁t₁

d₁ = 3.5(0.8)

d₁ = 2.8 miles

d = d₁ = 2.8 miles

Hence, the distance between the Walmart and her home is 2.8 miles.

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30 hot dogs would contribute $60 to the GDP and 20 hamburgers would also contribute $60 to the GDP.

The calculation for the number of hamburgers that would contribute the same to the GDP as 30 hot dogs is as follows:

GDP (Hot Dogs) = 2 x 30 = 60

GDP (Hamburgers) = 3 x x = 60  

Therefore, the number of hamburgers needed to equal the GDP of 30 hot dogs is equal to 20:

GDP (Hamburgers) = 3 x 20 = 60

Therefore, the answer is C) 20.

To explain this in more detail, Gross Domestic Product (GDP) is a measure of the total value of all goods and services produced in a country during a specific period of time. It is calculated by multiplying the price of a good or service by the amount produced. In this case, the price of a hot dog is $2 and the price of a hamburger is $3. Therefore, 30 hot dogs would contribute $60 to the GDP and 20 hamburgers would also contribute $60 to the GDP.

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The rock that has a mass of 35.4 g has a density of: 5.06 g/ cm^3

It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

The density formula and the procedure we will use is:

d = m/v

Where:

Information about the problem:

Applying the density formula we get:

d = m /v

d = 35.4 g / 7.0 cm^3

d = 5.06 g/ cm^3

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Correctly written question:

If a rock has a mass of 35.4 g and a volume of 7.0 cm^3. What is the density of the rock in g/cm3

Logistic regression is a statistical method used for modeling the relationship between a dependent variable and one or more independent variables. Unlike multiple regression, which is used for continuous outcome variables, logistic regression is used for categorical outcome variables, such as yes/no or pass/fail. The key differences between logistic regression and multiple regression are as follows:

a) Logistic regression does not have "b" weights - Logistic regression models the relationship between the independent variables and the dependent variable by using the logit transformation. The logit transformation maps the continuous range of values of the dependent variable to a binary range of values, allowing the estimation of the probability of a specific event. Unlike multiple regression, which uses beta (b) coefficients to quantify the strength and direction of the relationship between the independent variables and the dependent variable, logistic regression models the relationship through the use of odds ratios.

b) Logistic regression is not immune to sources of bias - Like any statistical method, logistic regression is susceptible to sources of bias, such as omitted variable bias and measurement error. It is important to be aware of these potential sources of bias and to address them through appropriate data cleaning and variable selection procedures.

c) Logistic regression predicts a categorical outcome variable - As mentioned, logistic regression is specifically designed for categorical outcome variables, such as yes/no or pass/fail. The model predicts the probability of the dependent variable taking a specific value and uses a threshold value to convert the predicted probabilities into binary outcomes.

d) Logistic regression does not log-transform the predictor variables - Unlike some statistical methods, such as log-linear regression, logistic regression does not log-transform the predictor variables. This is because the logit transformation is already applied to the dependent variable in order to model its relationship with the independent variables.

In conclusion, logistic regression is a powerful tool for modeling the relationship between a dependent categorical variable and one or more independent variables. It is important to understand its key differences from multiple regression and to be aware of potential sources of bias in order to use this method effectively.

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Answer:

There are 31 quarters.  

There are 47 dimes.  

Step-by-step explanation:

let q = number of quarters

let d = number of dimes

d = 16 + q      

.10d + .25q = 12.45  Multiply through by 100

10d + 25q = 1245       Substitute 16 + q for d

10(16 + q) + 25q = 1245    Distribute the 10

160 + 10q + 25q = 1245  Combine like terms

160 + 35q = 1245  Subtract 160 from both sides

160 - 160 + 35q = 1245 - 160

35q = 1085  Divide both sides by 35

q = 31

There are 31 quarters.    

Substitute 31 for q

d = 16 + 31

d = 47

There are 47 dimes.

Check:

d = 16 + q

47 = 16 + 31

47 = 47  Checks

.10d + .25q = 12.45

.10(47) + .25(31) = 12.45

4.70 + 7.75 = 12.45

12.45 = 12.45  Checks.

Answer:

There are 31 quarters and 47 dimes.

Step-by-step explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

Values of the coins:

Given a coin bank contains $12.45 in quarters and dimes:

Given there are 16 more dimes than quarters:

Therefore, the system of equations that represents the problem is:

[tex]\begin{cases} 0.25q + 0.10d = 12.45\\d = q + 16\end{aligned}[/tex]

Substitute the second equation into the first equation to eliminate d:

[tex]0.25q+0.10(q+16)=12.45[/tex]

Solve the equation for q to find the number of quarters:

[tex]\begin{aligned}0.25q+0.10(q+16)&=12.45\\0.25q+0.10q+1.6&=12.45\\0.35q+1.6&=12.45\\0.35q&=10.85\\q&=31\end{aligned}[/tex]

Therefore, there are 31 quarters.

Substitute the found value of q into the second equation and solve for d:

[tex]\begin{aligned}d &= q + 16\\&= 31 + 16\\&= 47\end{aligned}[/tex]

Therefore, there are 47 dimes.

The probability of getting at least one question wrong on a 6 question multiple-choice test is 0.9874

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(get one question right) = 1/2

P (get all questions right) = (1/2)^6

P(get one question wrong) = 1 - P (get all questions right)

P(get one question wrong) = 1 - (1/2)^6

P(get one question wrong) = 0.9874

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The percentage decrease is 19.4%

In contrast to being expressed as a fraction, a percentage is a portion of a total expressed as a number between 0 and 100. The percentages are as follows: 100% of everything, 0% of nothing, 50% of something, and 0% of nothing. Divide the component by the total, then multiply the result by 100 to get the percentage.

(Original Cost - New Cost) / Original Cost x 100 equals the percentage decrease.

In this case, the original cost is $36 and the new cost is $29, so we plug these values into the formula:

Percentage decrease = ($36 - $29) / $36 x 100 = $7 / $36 x 100 = 0.1944 x 100 = 19.44%

We can round the answer to the nearest tenth of a percent:

19.44% rounded to the nearest tenth is 19.4%

So the percentage decrease is 19.4%

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As per the standard deviation the proportion of observations is in the interval between each pair of values is 190 and 310

The term in math known as standard deviation is defined as a measure of how dispersed the data is in relation to the mean.

Here we have know that the mean of a population is 250 and its standard deviation is 20.

Then the proportion of observations is in the interval between each pair of values is calculated as,

We have interval (190,310) and we can express this interval as:

=> (190,310) = (250−3⋅20, 250+3⋅20)

According to this interval , we have that k=3.

Based on the value of the constant the required percent of observations in interval(190,310) is at least 88.9%

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