What is the relationship between the base and the height of an area formula?

The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.

a. The unemployment rate is 20%.

b. The labor-force participation rate is 60%.

According to the question,

Working age population- 100,000

Labour force - 60,000

Unemployed - 12000 instructions

a) The unemployment rate is the percentage of the labor force that is unemployed and it is calculated as follows:

Unemployment Rate = [tex]\frac{Number of unemployed People}{Labor force}[/tex] × 100

When an unemployed population is 12,000 and the labor force is 60,000,

the unemployment rate is  = [tex]\frac{12000}{60000}[/tex] × 100 = 20%

b) labor force participation rate is the percentage of working adult population that participates in labor either by actively looking for a job, or working. It is calculated as follows:

Labor Force Participation Rate = [tex]\frac{Labor force}{working age population}[/tex] × 100

When the labor force is 60,000 and the working-age population is 100,000

Labor Force Participation Rate = [tex]\frac{60000}{100000}[/tex] × 100 = 60%

So, a. The unemployment rate is 20%.

b. The labor-force participation rate is 60 %.

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Answer:

Neither

Step-by-step explanation:

It is not opposite to each other (perpendicular) or the same slope (parallel)

Answer:

5x + 8y = 24

Step-by-step explanation:

y = [tex]\frac{-5}{8}[/tex]x + 3  Add [tex]\frac{5}{8}[/tex]x  to both sides

[tex]\frac{5}{8}[/tex]x + y = [tex]\frac{-5}{8}[/tex]x + [tex]\frac{5}{8}[/tex]x + 3

[tex]\frac{5}{8}[/tex]x + y = 3  Multiply all the way through by 8 to clear the fraction

[tex](\frac{8}{1})[/tex][tex](\frac{5}{8})[/tex]x + (8)y= (8)(3)

5x + 8y = 24

The number of 5 digit numbers that can be formed is 3125

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

Digits = 0, 1, 2, 3, 4

These digits can be repeated

So, we have

n = 5 i.e. the count of digits in 0, 1, 2, 3, 4

The number of 5 digit numbers  is then calculated as

Count = n⁵

So, we have

Count = 5⁵

Evaluate

Count = 3125

Hence, the count is 3125

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Children who are 4 years old frequently count up to 1,0and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

In order to calculate the size of a set, or the number of items in a finite set, one must count. Calculating the amount or total number of items in a collection or group is what is meant when we say we are counting in arithmetic. To count, then, is to speak numbers in sequence while giving each item in a group a value based on a one-to-one correlation. Objects are counted using counting numbers.

Children who are eight years old frequently count up to 1,000 and have mastered skip counting. There are many chances to deepen their comprehension at home using basic math games.

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Answer:

$1.41

Step-by-step explanation:

0.20 * 5.8 ounces = $1.16

0.25 * 1.16 = $1.41

The mail  weighing 6.8 ounces cost 145 cents

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given here, the first ounce cost 25 cents and all subsequent ounces or parts of an ounce cost 20 cents each

therefore cost of the first ounce = 25

        and cost of 5.8 ounces = 20× 6

                                                = 120 cents

thus total cost is 120+25 =145 cents

Hence, the  total cost to mail a package is 145 cents

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Answer:

m = 3

Step-by-step explanation:

rise over run

Answer:

Hope it helps you ...........

The slope of the situation means: B. after the initial rental fee, the paddleboard costs an additional $12 every hour

If a situation is modeled as a linear relationship between two variables, the slope of the relationship is a measure of the strength and direction of the relationship between the two variables in that particular situation.

The slope is calculated as the change in the value of one variable (the "rise") over the change in the value of the other variable (the "run").

For example, consider a situation in which the number of hours that a student studies is related to their grades in a class. The slope of this relationship would indicate the strength and direction of the relationship between hours of study and grades in this particular situation.

A positive slope would indicate that as the number of hours of study increases, the grades also increase, while a negative slope would indicate that as the number of hours of study increases, the grades decrease.

To find the slope of the situation that is represented in the graph given, use two points on the line to calculate the slope.

Using (0, 10) and (2.5, 40)

Slope (m) = change in y / change in x = (40 - 10) / (2.5 - 0)

= 30/2.5

Slope (m) = 12

Therefore, this means that, B. after the initial rental fee, the paddleboard costs an additional $12 every hour.

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The distance the 12 centimeters minute hand moves in 20 minutes obtained by converting the angular motion to translational motion is about 25.133 centimeters

Angular motion is the circular motion of an object around a point or location.

The complete 360° rotation of the minute hand = 60 minutes

Therefore;

60 minutes is equivalent to 360°

1 minute is equivalent to 360°/60 = 6°

20 minutes is equivalent to 20 × 6° = 120°

The circular path motion following an angular rotation of angle theta = Radius × Theta

Where, theta is in radians

The radius of the minute hand = 12 centimeters

360° = 2•π radians

120° = 360°/3 = (2•π/3) radians

The distance moved by the the minute hand = 12 cm × (2•π/3) radians = 8•π cm

8•π cm ≈ 25.133 cm

The distance the minute hand moves in 20 minutes is about 25.133 cm

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The theorem that is a valid triangle congruence theorem is the: ASA

A triangle congruence theorem is a set of conditions that must be met by a set of triangles before both triangles can be said to be congruent to each other.

Some of the valid triangle congruence theorem are:

Therefore, from the option given, the only valid triangle congruence theorem is: ASA.

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Complete Question:

Which of the following is a valid triangle congruence theorem?

AAA

SSA

ASA

none of the above

The probability that the shipment will be rejected is 0.724.

Given :

Since we have given that

n = 125

p' = 8 % = 0.08

p = 10 % = 0.10

Test statistic value :

z = p' - p / [tex]\sqrt{p(1-p)/n}[/tex]

= 0.08 - 0.10 / [tex]\sqrt{0.10 * 0.90 / 125}[/tex]

= -0.75

p value at z = -0.75

p = 0.226

What is probability ?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Probability of shipment will be rejected = 1 - 0.226

= 0.724

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Answer:

k = -5

Step-by-step explanation:

The scalar product of vectors a and b is zero when the vectors are orthogonal (perpendicular):

[tex]\boxed{\begin{aligned}\vec a \cdot \vec b & = |a||b| \cos \theta\\& = |a||b| \cos 90^{\circ}\\& = 0 \end{aligned}}[/tex]

[tex]\textsf{Therefore, $\vec a$\; and \;$\vec b$\; are orthogonal when\; $\vec a\cdot \vec b=0$}[/tex]

Given:

Substitute the given vectors into the formula and solve for k:

[tex]\implies \langle 2, -2 \rangle \cdot \langle-5, k \rangle=0[/tex]

[tex]\implies (2)(-5) +(-2)(k)=0[/tex]

[tex]\implies -10-2k=0[/tex]

[tex]\implies 2k=-10[/tex]

[tex]\implies k=-5[/tex]

Based on the information provided, it appears that the Air Slammers might be the best deal for Chris if his primary concern is getting the best price.

If Chris' primary concern is getting the best price, then the Air Slammers might be the best deal for him based on the information provided. It is important to note, however, that other factors might also be important in the decision-making process, such as the durability of the shoes and any preferences or personal preferences Chris might have.

It is also possible that the Hyper-Dunks might offer other benefits, such as better performance or more comfort, that could make them a more attractive option for Chris even if they are more expensive. Ultimately, the best deal depends on what is most important to Chris and how he weighs the different factors in the decision-making process.

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The constraints for this situation are x>0, y>0, 340x + 670y < 5650 and x>1/3y

Let the number of bicycles = x

and the number of treadmills = y

Since the number of new bicycles must be more than 1/3 times of the new treadmills.

Inequality representing the statement will be,

x>1/3y

Each bicycle costs $340 and each treadmill costs $670.He must spend less than $5650,

Inequality will be,

340x + 670y < 5650

And the number of bicycles and treadmills should be greater than 0.

x > 0

y > 0

Therefore, constraints for this situation are, x>0, y>0, 340x + 670y < 5650 and x>1/3y

(Refer to the image attached for the complete question)

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Let the number of bicycles = x

and the number of treadmills = y

Inequality representing the statement will be,

x>1/3y

Each bicycle costs $340 and each treadmill costs $670.He must spend less than $5650,

Inequality will be,

340x + 670y < 5650

And the number of bicycles and treadmills should be greater than 0.

x > 0

y > 0

Therefore, constraints for this situation are, x>0, y>0, 340x + 670y < 5650 and x>1/3y

Answer:

  3x -y = -4

Step-by-step explanation:

You want the equation of the line parallel to 3x-y=5 through point (0, 4).

The equation for the parallel will differ only in the constant. To find the new constant, use the given point coordinates for x and y.

  3x -y = 3(0) -(4) = -4

The equation of the line is ...

  3x -y = -4

Answer:

θ = 15°

Step-by-step explanation:

The wheelchair ramp creates a right triangle figure. Look at the image I have attached to this response to see the figure.

⭐ What is the "angle of inclination"?

The angle of inclination is the base angle adjacent to the 90-degrees. The angle of inclination is often denoted as θ.

To solve for the angle of inclination, θ, we have to use the inverse of a trigonometric function.

⭐ What trigonometric function do we use?

Look at the side lengths you are given. Are they opposite of θ? Are they adjacent to θ? Are they the hypotenuse of the triangle? Whatever combination of 2 side lengths you have, see what trigonometric function uses those 2 side lengths.

We are given the side length opposite of θ and a side length that is the hypotenuse of the triangle. Therefore, we are going to use the sine function.

⭐ What is the sine function?

sin(θ) = opposite/hypotenuse

Now, we are going to create an equation of the wheelchair ramp using the sine function.

sin(θ) = 5.1/20

Next, find the inverse of the equation. Here is the inverse of the sine function:[tex]sin^{-1} (opposite/hypotenuse) =[/tex]

Let's substitute the opposite and hypotenuse into the inverse of the sine function and solve using a scientific calculator. Make sure to round to the nearest degree.

[tex]sin^{-1}(5.1/20) =[/tex]

∴ [tex]sin^{-1}(5.1/20)[/tex] ≈ 15°

On solving the provided question, we can say that - by prime factorization the factors of 5 are 5 and 1

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

The factors of 5 are -

5

and 1

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the value of |x-2| lies between 0 and 1 then λ also lies between 0 and 1. Then λ belongs to (0,1).

In the given question, if λ∈R and the domain of f(x) = [tex]\sqrt{\frac{log_{\lambda}|x-2|}{|x|}}[/tex] is [1,2)∪(2,3], then λ belong to

The given function is

f(x) = [tex]\sqrt{\frac{log_{\lambda}|x-2|}{|x|}}[/tex]

The function is belong in between [1,2)∪(2,3]. So

|x-2| ≠ 0  and  |x| > 0

x ≠ 2       and  x > 0

Since the value of x can not be equal to 2 and x value is always greater than 0. So

[tex]log_{\lambda}|x-2|\geqslant 0[/tex]

The value of |x-2| should be lies between 0 and 1 because x cannot be equal to 2 and greater than 1.

So 0< |x-2| < 1

If the value of |x-2| lies between 0 and 1 then λ also lies between 0 and 1.

Hence, 0 < λ < 1.

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Relation between base and height of parallelograms is a function  [tex]f(x)=\frac{48}{x}[/tex].

Relations called functions provide an output for each input. The characteristic that every input is associated to exactly one output defines a function as a relation between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

Based on the values listed in the table for the parallelograms' base length and height, you can see that the base length grows by one unit, giving you the numbers 1, 2, 3, and 4. When base length increases by one unit, height reduces by 1/x, as shown in the following example:

Height and base length have the following relation:

[tex]f(x)=\frac{48}{x}[/tex]

where x is the base length and f(x) is the height. 

[tex]f(1)=\frac{48}{1}= 48\\f(2)=\frac{48}{2}=24\\f(3)=\frac{48}{3}=16\\f(4)=\frac{48}{4}=12\\f(6)=\frac{48}{6}==6[/tex]

Relation between base and height of parallelograms is a function  [tex]f(x)=\frac{48}{x}[/tex].

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The total mileage on Joe's shoes after the 21 weeks is 2,457 miles.

The total mileage of Joe's shoes is the sum of all the distance travelled by Joe within the given time of period of 21 weeks.

The distance travelled by Joe in 1 week is calculated as follows;

distance travelled by Joe in 1 week = 1 mile/day  x  7 days = 7 miles

The distance travelled by Joe in 21 weeks is calculated as follows;

distance travelled in 21 weeks = ( 7 miles / week ) x ( 21 weeks )

distance travelled in 21 weeks = 147 miles

the number of additional mile added each week = 110 mile

for 21 weeks = 21 x 110 mile = 2,310 miles

The total mileage on Joe's shoes after the 21 weeks is calculated as follows;

total mileage = 2,310 miles  +  147 miles

total mileage = 2,457 miles

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There is major 3 types of expression. Numerical expression, algebraic expression and fractional expression.

This expression contains only two or more numbers along with symbols or operator. There is no variable present.

such as 226÷113+2×22-11

or (44÷88) ×100%

the above sign is percentage sign we can determine a percent value

or∛ (64)

the above sign represents a cubic root

we get the value 4

The expression having two or more fractional terms along with symbols are called fractional expression. There are numerator and denominator from which we need to determine a common denominator to obtain a result.

such as, 4/5+3/4

we have 2 different denominators 5 and 4. we need to find a common denominator by multiplying both. 5x4

                                                           20

In the next, common denominator is divided by each denominator and the result is multiplied with each numerator.

                 (4×4+3×5)/20

       hence, the result is 31/20

The expression contains both variables and numbers along with symbols are called algebraic expression. The algebraic expression having equal sign are termed as equation. Tha main purpose of using equation is to determine unknown value.

Algebraic expression are different types such as linear expression

2x+3-4y

2 and 4 are coefficient, 3 is constant

Polynomial expression as example 2x²-3y+4

Besides, we have other algebraic expression such as 3y+4 or x/4+y/3

and so on.

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In the figure, the angles m∠ 1 and m∠ 2 are corresponding angles

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).

In the question given, m∠ 1 and m∠ 2 are corresponding angles with each other.

This also implies that they are equal with one another using corresponding angle theorem.

Corresponding angle theorem states that : All corresponding angles are equal to one another.

Therefore, m∠ 1 and m∠ 5 are corresponding angles and are equal to one another.

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Answer: The second one.

There are countless possible solutions to some equations. In these equations, the equation is true regardless of the value given to the variable. If we try to solve an equation and receive a variable or a number equal to itself, there are infinitely many solutions to the equation.

Single-solution equations:

Some equations only have one precise solution. The variable in these equations can only take on one value in order for the equation to be true. When you solve an equation and the result is a variable equal to a number, you know that the equation only has one solution.

Example: For x, find the solution to the equation 6x-3=21.

6x \s= 24

To both sides, add 3.

x \s= 4

Subtract 6 from both sides.

For a single value of the variable, x=4, the equation is true. Consequently, there is only one solution to the equation 6x-3=21

Non-solvable equations:

There are certain equations with no answers. These equations don't have a value for the variable that would make them true. If you attempt to solve an equation and the result is false, the problem has no solutions.

Example: Solve the equation 4x+12=2x+12+2x.

4x+12

= 2x+12+2x

4x+12

= 4x+12 Combine like terms 2x and 2x.

12

= 12 Subtract 4x from both sides.

Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.

Equations that have infinitely many solutions:

The number of solutions to some equations is limitless. When a variable is used in these equations, any value makes the equation true. If you attempt to solve an equation and it yields a variable or value that is equal to itself, then the equation has an endless number of solutions.

Solve the equation 4x+12=2x+12+2x.

4x+12

= 2x+12+2x

4x+12

= 4x+12 Combine like terms 2x and 2x.

12

= 12 Subtract 4x from both sides

Since the equation 12=12 is always true, you can change the value of x to make it true. Therefore, 4x+12=2x+12+2x has an endless number of solutions.

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Answer:

  (c)  The range of the function is all real numbers less than or equal to 0

Step-by-step explanation:

You want the true statement describing the domain or range of f(x) = -√x.

The domain of the function is the set of values x for which the function is defined. The square root is only defined for non-negative arguments:

  x ≥ 0 . . . . . . not an answer choice

The range is of the function is the set of values f(x) that the function can produce. The square root function can produce any non-negative value, so the opposite of the square root function will produce any non-positive value:

  f(x) ≤ 0 . . . . . the range is real numbers less than or equal to zero

The equation for capital gain as a percent of the original purchase price will be equal to a = (y - x)/x × 100.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. A mathematical operation like reduction, addition, multiplication, or division is used to include terms in an expression.

As per the given information in the question,

Use the equation for capital gain,

Let the selling price be y and the purchase price is x dollars.

Capital gain = Selling price - Purchase

Substitute the values,

Capital gain = y - x

Now, let's find out the percent increase.

Let's assume that 'a' is the percent increase.

So, the equation will be,

(a)(x) = y - x

ax = y - x

Divide both sides by x.

(ax)/x = (y - x)/x

a = (y - x)/x

Multiply the equation by 100 to show in percentage form,

a = (y - x)/x × 100

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The way to write 'more than 3' is >3.

We have to find a way to write "more than 3" in a mathematical form.

The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. In mathematical writing, the greater-than sign is typically placed between two values being compared and signifies that the first number is greater than the second number.

Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.

We can use this mathematical symbol here, in order to denote "more than 3" mathematically.

> 3 denotes that a number is more than 3.

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Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.

We can use this mathematical symbol here, in order to denote "more than 3" mathematically.

> 3 denotes that a number is more than 3.

The equation of the line that passes through the given points in the slope-intercept form is y = (-5/2)x - 1

From the question, we are to determine the equation of the line that passes through the given points

We will pick two value pairs from the table

Picking (-4, 9) and (-2, 4)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Then,

(y - 9) / (x - (-4)) = (4 - 9) / (-2 - (-4))

Simplify

(y - 9)/(x + 4) = -5/(-2 + 4)

(y - 9)/(x + 4) = -5/2

Cross multiply

2(y - 9) = -5(x + 4)

2y - 18 = -5x - 20

2y = -5x -20 + 18

2y = -5x - 2

Divide through by 2

y = (-5/2)x - 1

Hence, the equation is y = (-5/2)x - 1

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