a=460 rounded to the nearest 10 b=11.9 rounded to 1 dp find the minimum (to 2 dp) of a / b

The solution for the given inequality is −8<x<3 or 3<x<7.

The given inequality is (x+8)(x-3)²(x-7)³<0.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality can be solved as follows

Solve for x by simplifying both sides of the inequality, then isolating the variable.

Inequality Form: x+8<0

x<-8 (Subtract 8 on both the sides of the inequality)

(x-3)²<0

⇒ x-3<0

⇒ x<3 (Add 3 on both the sides of the inequality)

(x-7)³<0

⇒ x-7<0

⇒ x<7 (Add 7 on both the sides of the inequality)

Solution is −8<x<3 or 3<x<7

Therefore, the solution for the given inequality is −8<x<3 or 3<x<7.

To learn more about the inequality visit:

https://brainly.com/question/20383699.

#SPJ1

Answer:

Step-by-step explanation:

The difference between two consecutive even integers is 2.

Let the first of the three integers is x, then the following ones are:

x + 2 and x + 4.

The sum of the three is - 78. Express it as equation and solve for x:

The integers are - 28, - 26 and - 24

Let

A

be the event of selecting an American that believes that some people see the future in their dreams. From the problem,

P(A)=62.4%=0.624

Let

A' be the event of selecting an American who does not believe that some people see the future in their dreams

Remember that

P(A')=1-P(A)

substitute given value

P(A')=1-0.624=0.376=37.6%

Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 37.6%

Answer:

The ratio of the high-wire unicyclists to ball-balancing seals is;

Explanation:

Given that;

He has featured 32 high-wire unicyclists and 24 ball-balancing seals.

The ratio of the high-wire unicyclists to ball-balancing seals can be written as;

Reducing toits lowest form, we have;

divide both sides by 8;

Therefore, the ratio of the high-wire unicyclists to ball-balancing seals is;

The equation of the line 3y + x = 3 through pair of points (0,1) and (3,0), the equation of the line 6y = 2x +3 through pair of points (1/2,2/3) and (-3/2,5/3) and the equation of the line  y = 2x + 4 through pair of points (-3,-2) and (1,6)

The equation of the line through pair of points (0,1) and (3,0)

⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )

Here x₁ = 0 and y₁ = 1

x₂ = 3 and y₂ = 0

The equation of the line is obtained by substituting these values into the above equation;

⇒ y - 1 = [(0-1)/(3-0)](x -0)

⇒ y - 1 = (-1/3)x

⇒ 3y - 3 = x

⇒ 3y + x = 3

The equation of the line through pair of points (1/2,2/3) and (-3/2,5/3)

⇒ y - 2/3 = [(5/3 -2/3)/(-3/2-1/2)](x -1/2)

⇒ y - 2/3 = [(3/3)/(-4/2)](x -1/2)

⇒ y - 2/3 = (1/3)(x -1/2)

Multiply by 6 both sides of the equation,

⇒ 6y - 4 = 2(x -1/2)

⇒ 6y = 2x -1 + 4

⇒ 6y = 2x +3

The equation of the line through pair of points (-3,-2) and (1,6)

⇒ y - (-2) = [(6-(-2))/(1-(-3))](x -(-3))

⇒ y + 2= (8/4)(x + 3)

⇒ y = 2x + 6 -2

⇒ y = 2x + 4

Learn more about the Lines here:

brainly.com/question/14511992

#SPJ1

The complete statement is:

The slope

From the question, we have the following parameters

Point = (1, 3.20)

The point is a proportional relationship

So, the slope of the proportional relationship  is

Slope = y/x

Where

(x, y) = (1, 3.20)

Substitute the known values in the above equation

So, we have the following equation

Slope = 3.20/1

Evaluate

Slope = 3.20

The unit rate

Here, we have

Point = (1, 3.20)

Also, we have

The point is a proportional relationship

The unit rate is

Rate = y/x

Where

(x, y) = (1, 3.20)

Substitute the known values in the above equation

So, we have the following equation

Rate = 3.20/1

Evaluate

Rate = 3.20

Read more about proportional relationship at

https://brainly.com/question/12242745

#SPJ1

Answer:

5

Step-by-step explanation:

We know that - (-7) = +7, so

-2 - (-7) = -2 + 7 = 5

The equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.

According to the situation,

We have the following information:

The company charges $40 for set-up costs plus $12 per shirt.

So, the basic charge is added to every t-shirt.

Now, let's take the number of T-shirts on which the company prints designs on shirts to be x.

So, we have the charge for x number of t-shirts is:

$(40+12x)

Hence, the equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.

To know more about equation here

https://brainly.com/question/20687498

#SPJ1

We need to solve a system of two variables with two equations, using elimination method.

y=-2x+30 (1)

y=6x+41​ (2)

We are going to multiply first equation by 3, doing so the equation (1) can be written as:

3y = -6x + 90 (1)

Then, we are going to add the last equation to the second equation

3y = -6x + 90 (1)

+ y= 6x + 41​ (2)

-----------------------------

4y = 131

y = 131 / 4 Isolating y

y= 131/ 4

Then, we replace y= 131/4 in the first equation and solve for x

Since -11/8 is equal to -1.4 and x represents the number of years since 2000, then the year travel agents and the Internet were used equally was 1998.

Compute the given function

[tex]f(x)=- 3x^{2}-7x-3[/tex]

How the given function is computed?

Let us consider f (-3)

f(-3)= -3(9)- 7(-3) -3

     =-27+21-3

     = -9

Let us consider f (4)

f(4) = -3(16)-7(4)-3

    =-48-28-3

    = - 79

A) f(-3) * f (4)

= (-9) * (-79)

= 711

B) f(-3)  / f (4)

=  (-9) / (-79)

= 9/79 (or 0.11)

What are functions?

To learn more about functions, refer:

https://brainly.com/question/25638609

#SPJ13

The answer would be B.

The relationship is proportional. The constant of proportionality is 5.

The probability that you, Shirley, and Matthew are chosen is 0.0001

Probability:

Probability refers the measure of the likelihood of an event to occur.

The formula of Probability is

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Given,

Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat.

Here we need to find the probability that you, Shirley, and Matthew are chosen.

Here we have assuming that the selection process is fair;

We know that, the total number of employees is 28

Therefore, the probability of selecting each employee is,

=> 1/28

So, the probability of selecting yourself, Shirley, and Matthew is calculated as,

=> 1/28 x 1/27 x 1/26

=> 1/19656

=> 0.00005

When we round off it into four decimal place then we get,

=> 0.0001

Therefore, the probability that you, Shirley, and Matthew are chosen 0.0001.

To know more about Probability here.

https://brainly.com/question/11234923

#SPJ1

The fraction of fishes which are guppies in Marcus's aquarium is 2/3

Number of gold fishes in the aquarium = 1/9

Number of angelfish in the aquarium = 5/9

Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Let x be the total number of fishes in Marcus's aquarium:

Number of guppies = Total fishes - Number of gold fishes - Number of angelfishes

= x - 1/9 - 5/9

= x - 6/9

x = 6/9 or 2/3

Learn more about fractions:

https://brainly.com/question/10354322

#SPJ1

Question:

Solve

4n + 1 = 25

Solution:

Consider the following formula:

this is equivalent to:

this is equivalent to:

solving for n, we get

Then, we can conclude that the correct answer is:

Let's begin by listing out the given information:

Therefore, 90% of 20 is equal to 18

The table of values to represent the relationship between the number of days and the number of puzzles she has completed will be:

Days Puzzle completed

1. 4

2. 8

3. 12

4. 16

5. 20

From the information, Maddie is determind to finish some extra credit math homework by completeing 4 math puzzles each day.

Therefore, the first day, she will do 4 puzzles. The second day will be:

= 2 × 4 = 8 puzzles

Third day = 3 × 4 = 12 puzzles.

In this case, the method that was used is simply to multiply the number of days by 4 since he does 4 puzzles everyday.

It should be noted that this illustrates a proportional relationship

Learn more about tables on;

brainly.com/question/25630111

#SPJ1

According to the converse of corresponding angles theorem, the statement that allows Carmen to conclude that lines p and q are parallel is: ∠2 ≅ ∠6.

A transversal is a line that crosses two straight lines. For example, line t is a transversal that crosses the lines p and q in the given diagram above.

Parallel lines are lines that do not meet each other at any point and are of equal distant to each other.

When a transversal intersects two parallel lines, they form angle pairs. One of such angle pairs is, corresponding angles, which are always congruent to each other.

Thus, if corresponding angles are formed and are equal to each other, then the lines they lie on must be parallel lines based on the corresponding angles converse theorem.

Angles 2 and 6 are corresponding angles that are formed by the transversal that intersects lines q and p. If they are congruent angles, then the lines are parallel.

Therefore, Carmen can use the statement, ∠2 ≅ ∠6 to show that lines q and p are parallel.

Learn more about parallel lines on:

https://brainly.com/question/16742265

#SPJ1

The area of the triangle bounded by the x-axis, the y-axis, and the line y = −4x + 4 is 2 square units

given data

y = −4x + 4

Area of a triangle is equal to 1/2 * base * height

Assuming the y direction to be the height and the base is x direction

Point on the y direction is the y intercept since the line bounds the area

y intercept =  −4( 0 ) + 4

y intercept = 0 + 4

y intercept = 4

Point on the x direction is the x intercept since the line bounds the area

y = −4x + 4

4x = 4 - y

4x = 4 - 0

x = 1

Area of a triangle = 1/2 * 1 * 4

= 2 square units

Read more on area of triangle here: https://brainly.com/question/23945265

#SPJ1

After thoroughly calculation, we have come to find that, If equation x² = 25, where x ε z then x = √25 = 5, thus x is 5.

Equation, also known as a statement of equality between two expressions with variable- and/or number-based components. Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics.

From straightforward algebraic equations that only require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity. Numerous physics laws are expressed using them.

Simultaneously occurring equations, or system of equations Algebra requires the simultaneous solution of two or more equations (i.e., the solution must satisfy all the equations in the system). The quantity of equations must match the quantity of unknowns for a system to have a distinct solution.

Learn more about equations

https://brainly.com/question/12788590

#SPJ9

In order to calculate the percent of items that are collector's items, let's first find the amount of collector's items by subtracting the total number of items by the number of old used clothes:

Now, to find the percent from the total, let's divide this amount we calculated by the total number of items:

Therefore the percent of items that are collector's items is 66.9%.

The given expression is

To simplify it add the like terms

Then the simplest form is

-17x - 33

Problem

Steve scores in a card game is five points away from zero zinnias score is the opposite of an of Steve's score positive value what is the score ​

Solution

Let x the score for Steve and y the score for Denia.

We know that the score of Denia is the opposite of Steve

So then the scores needs to be:

Steve =-5

Denia =5

And with this we satisfy all the requirements

ANSWER:

$109.64

STEP-BY-STEP EXPLANATION:

The price after applying the tax would be the sum between the original value and the value equivalent to the established percentage, just like this:

The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

The standard form of a quadratic equation in vertex form is given as,

y = a(x-h)² + 8

Where (h,k) is the coordinate of the vertex and a is constant.

Given the vertex  (h,k) = (-1,8)

Substitute, vertex, and  (0,2)

2 = a(0 + 1)² + 8

a = -6

Therefore, the equation converts as,

y = -6(x+1)²+8

Hence "The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8".

For more about the quadratic equation,

https://brainly.com/question/17177510

#SPJ1

The mean of the data values is their average.

To obtain the average, find the sum of the data values and then divide the sum by total number of data.

In the given, we have 10 data values. Thus, the mean is as follows.

Therefore, the mean is 5.

No, the mean of a data set doesn't have to be one of the data values of the data set.

To know more about mean visit:

https://brainly.com/question/11163338

#SPJ13

Step 1:

Step 2:

There are 8 slices, hence the possible outcomes = 8

All the slices are color yellow. hence the required outcomes = 8

Step 3:

The probability that the dial stops on yellow slice = 1

Final answer

24x +8y ≥ 20

3x - 6y > 24

First, express both equations in slope-intercept form

y= mx+b

Where:

m= slope ( rise (y) / run (x))

b= y-intercept (where the line crosses the y axis)

Solve for y:

24x +8y ≥ 20

8y ≥ -24x +20

y ≥ (-24x +20 ) / 8

y ≥ -3x + 2.5

3x - 6y > 24

-6y > 24- 3x

y < (24 -3x) / -6

y < 1/2x -4

System:

y ≥ -3x + 2.5

y < 1/2x -4

Solution = the area where the 2 solutions overlap (blue+ red)

Answer:

the 8 pack

Step-by-step explanation:

So to start we should find how much an individual capsule in each is

Well start off by 5.99/8 which will give us 0.74875 per capsule and well round in to 0.75 each to put it in terms of money.

Now we will do 2.85/2 which then gives you 1.425 and well say that's about 1.43 per capsule