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This graph represents a continuous function. Also, the domain of this function is 0 ≤ x ≤ 6 and the range of this function is 20 ≤ y ≤ 200.

Mathematically, a range can be defined as the set of all real numbers that is associated with the elements of a domain. This ultimately implies that, a range simply refers to the set of all possible output numerical values which are shown on the y-coordinate (y-axis) of the graph of a function.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined and it connects with the range.

This ultimately implies that, a domain is the set of all possible input numerical values to a function. Additionally, the domain of the graph of a function comprises all the input numerical values which are shown on the x-coordinate (x-axis).

From the information provided, the total weight of the barbell and plates in pounds is represented by this function:

f(x) = 30x + 20.

When x = 6, we have:

f(6) = 30(6) + 20.

f(6) = 180 + 20

f(6) = 200 lb.

Therefore, the domain is equal to 0 ≤ x ≤ 6 while the range of this function is 20 ≤ y ≤ 200.

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The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.

acc to our question-

The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.

The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.

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The solutions are,

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

Given that;

Wade is traveling along a 0.8 km-radius circular ski trail. Wade moves 2.3 kilometers counterclockwise starting at the three o'clock position.

Radius (r) = 0.8km

Distance (s) = 2.3km

Here, we need to find three cases, they are;

Case(I): how many radians does wade sweep out;

The relation between radians and radius is given by,

s = rθ

2.3 = 0.8*θ

θ = 2.3/0.8

θ = 2.875

The radians wade sweep out is 2.875 radians.

Case (II): when wade stops skiing, how many km is wade to the right of the center of the ski trail;

Let, Ф = π - 2.875

      Ф = 0.266 radians

Then, x = r*cosФ

          x = 0.8*cos(0.266)

          x = 0.799

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

Case (III): when wade stops skiing, how many km is wade above the center of the ski trail;

Let, y = r*sinФ

      y = 0.8*sin(0.266)

      y = 0.003

When wade stops skiing, he is 0.003km above the center of the ski trail.

Therefore, the required solutions are;

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

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The solution of the linear equation 3.5g - 2.7g = -6 will be negative 7.5.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

If the maximum power of the equation is one. Then the equation will be a linear equation.

The linear equation is given below.

3.5g - 2.7g = -6

Simplify the equation, then we have

3.5g - 2.7g = -6

0.8g = -6

g = - 6 / 0.8

g = - 7.5

The solution of the linear equation 3.5g - 2.7g = -6 will be negative 7.5.

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Answer:

2 : 12 and 3 : 24 are the two equivalent ratios

Step-by-step explanation:

9x + 3y = 153

6x + 5y = 147

the first equation can be divided by 3 and then multiplied by 2. and from that we can subtract equation 2 :

9x + 3y = 153 | /3

3x + y = 51 | ×2

6x + 2y = 102

- 6x + 5y = 147

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

0 -3y = -45

3y = 45

y = 15

3x + y = 51

3x + 15 = 51

3x = 36

x = 12

1 bottle of water costs Rs 12.

1 bottle of juice costs Rs 15.

The amount of tax paid per tonne of sand is $14.835 as the sand costs $98.90 per tonne.

In mathematics, a percentage is a value or ratio expressed as a fraction of 100.

The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.

Given,

The cost of one Tonne of sand=$98.90

The tax on one Tonne=15%

The  amount of tax per Tonne of sand is,

=(15/100)×98.90

=$14.835

Hence, the amount of tax paid per tonne of sand is $14.835.

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3 is the amplitude, -4 is the minimum value, and 2 is the highest value.

acc to our question-

Hence,3 is the amplitude, -4 is the minimum value, and 2 is the highest value

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The distance between the anchor points of the two guy wires holding radio antenna is 181 feet (to the nearest foot)

The problem will be solved using SOH CAH TOA

let the distance between the 150 ft long guy wire and the radio antenna be x

let the distance between the 180 ft long guy wire and the radio antenna be y

cos 65° = x / 150

x = cos 65° * 150

x = 63.39 ft

The height of the antenna

sin 65° = height of antenna / 150

height of antenna = sin 65 * 150

height of antenna = 135.95

using Pythagoras theorem

(length of guy wire)² = (height of the antenna)² + (anchor distance)²

(anchor distance)² = 180² - 135.95²

anchor distance = √(180² - 135.95²)

anchor distance = 117.97

The anchor points distance apart

= 63.39 + 117.97

= 181 (to the nearest foot)

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Most researcher fix level of significance at 5% i.e. they conclude a significant relationship when nothing is going on in 5% of cases. Hence,

Option A is correct which is 1.5%

Given that,

The majority of social scientists are willing to claim that a link is statistically significant if the likelihood of observing the relationship in the sample when nothing is happening in the population is greater than a certain threshold.

To find:

Less than what percentage of the population truly experiences nothing at all (i.e., random chance)

The majority of researchers set the level of significance at 5%, which means they draw conclusions about a meaningful association even when nothing is happening in 5% of cases.

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Answer:

x=12°

Step-by-step explanation:

10x-20+6x+8=180°

16x=180+20-8

16x=192

x=12°

The vertex of the graph is (-2, 2), the axis of symmetry of parabola is -2 and the parabola opens downwards.

In the given question we have to find the vertex, axis of symmetry and whether the parabola opens upwards and downwards.

Firstly we find ing the vertex of the graph.

As we know that vertex is the highest and lowest point of the graph.

From the graph the highest point is (-2, 2).

So the vertex of the graph is (-2, 2).

As we know that the axis of symmetry always passes through the vertex of parabola. The x coordinate of the vertex of parabola is the axis of symmetry of parabola.

So the axis of symmetry of parabola is -2.

As we can see that the parabola opens downwards.

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Answer: The paintbrush will be your magic wand for weaving colors across the canvas. Artist paint brushes become beloved tools the more you use them! As you paint, you will become increasingly familiar with the way the brushes handle the paint and what they can accomplish for you. Pretty soon the paintbrush will become a part of you that you intuitively know how to maneuver.

If you're just starting out in acrylics, it can be a bit overwhelming standing in the paintbrush aisle at the art store, with a vast sea of artist paint brushes spread out before you. The wide selection even makes me dizzy sometimes!

Step-by-step explanation:

Answer:

-11.8

Step-by-step explanation:

68x0.8

11x3.8

11x3.8=41.8

68x0.8=54.4

54.4-41.8=12.6

Now minus add a minus to it and you get -12.6 FT

Answer:

See below

Step-by-step explanation:

Horizontal lines have ZERO slope

Vertical lines have 'undefined' slope

for this example  x = 1/2    includes the point and has undiefined slope

Given -

In a certain chemical, the ratio of zinc to copper is 4 to 13.

The chemical contains 546 grams of copper.

Prove  -

How many grams of zinc does it chemical contain.

Answer

suppose that scalar multiple of the  zinc and copper be y .

As given

In a certain chemical, the ratio of zinc to copper is 4 to 13.

The chemical contains 546 grams of copper.

Than equation is

13y = 546

13y = 546

y = 42

Zinc contain in the certain chemical = 4y

                                             = 4 42

                                             = 168 grams

Therefore 168 grams of zinc contain in a certain chemical .

Economic equilibrium is a condition or state in which economic forces are balanced. In effect, economic variables remain unchanged from their equilibrium values in the absence of external influences.

Economic equilibrium is also referred to as market equilibrium. Economic equilibrium is the combination of economic variables (usually price and quantity) toward which normal economic processes, such as supply and demand, drive the economy. The term economic equilibrium can also be applied to any number of variables such as interest rates or aggregate consumption spending. The point of equilibrium represents a theoretical state of rest where all economic transactions that “should” occur, given the initial state of all relevant economic variables, have taken place.

In a competitive market, demand for and supply of a good or service determine the equilibrium price.

MARKETS:

Equilibrium is achieved at the price at which quantities demanded and supplied are equal. We can represent a market in equilibrium in a graph by showing the combined price and quantity at which the supply and demand curves intersect.

For example, imagine that sellers of squirrel repellant are willing to sell 500 units of squirrel repellant at a price of $5 per can. If buyers are willing to buy 500units of squirrel repellent at that price, this market would be in equilibrium at the price of $5 and at the quantity of 500 cans.

Whenever markets experience imbalances—creating disequilibrium prices, surpluses, and shortages—market forces drive prices toward equilibrium.

A surplus exists when the price is above equilibrium, which encourages sellers to lower their prices to eliminate the surplus.

A shortage will exist at any price below equilibrium, which leads to the price of the good increasing.

For example, imagine the price of dragon repellent is currently $6 per can. People only want to buy 400 cans of dragon repellent, but the sellers are willing to sell 600 cans at that price. This creates a surplus because there are unsold units. Sellers will lower their prices to attract buyers for their unsold cans of dragon repellant.

Changes in the determinants of supply or demand result in a new equilibrium price and quantity. When there is a change in supply or demand, the old price will no longer be an equilibrium. Instead, there will be a shortage or surplus, and price will subsequently adjust until there is a new equilibrium.

For example, suppose there is a sudden invasion of aggressive unicorns. There will be more people who want to buy unicorn repellent at all possible prices, causing demand to increase. At the original price, there will be a shortage of unicorn repellant, signaling sellers to increase the price until the quantity supplied and quantity demanded are once again equal.

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By solving  a system of two simultaneous linear equations, it can be calculated that

Alicia will need 3 twigs and 6 flowers

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here, a system of two simultaneous linear equation needs to be solved

Let the number of twigs Alicia needed be x and the number of flowers Alicia needed be y

Alicia has to create an arrangement of twigs and flowers that has a total of 9 objects.

x + y = 9 ..... (1)

Alicia wants the arrangement to have twice as many flowers as twigs

2x = y .... (2)

Putting the value of x in (1)

x + 2x = 9

3x = 9

[tex]x = \frac{9}{3}[/tex]

x = 3

Putiing the value of x in (2),

y = 2 [tex]\times[/tex] 3

y = 6

Alicia will need 3 twigs and 6 flowers

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The new x-coordinate must be 2-2 = 0.

acc to our question-

Finding the distance between the known endpoint and the midpoint, then applying the same transformation to the midpoint, is the quickest technique to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, hence the new x-coordinate is 2-2 = 0.

Hence,The new x-coordinate must be  = 0.

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We can get heads for 200 times if we flipped the dime for 200 times.

What do you mean by Probability?

Probability is a mathematical measurement to measure the possibility of happening a particular incident or event mathematically.

Also, from the definition of probability, Probability is the ratio of the Number of Favorable event points to the number of total event points with respect to a particular event or incident.

[tex]Probability=\frac{Number of Favorable event Points}{Number of Total event Points}[/tex]

According to the given problem,

The probability of getting heads is 1.

Total number of flip of dime is 200

so, we can get heads from 200 flips [tex]=200*1=200 Times[/tex]

Hence, we get 200 heads from 200 flips of dime.

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Answer:

  2/5 = 0.4 = 40%

Step-by-step explanation:

You want the relative frequency of students who go to Cook Middle School and prefer Energy Flow.

The table tells us the number of students who go to Cook Middle School is 35, of which 20 prefer Energy Flow. The total number of students is 50.

The relative frequency of interest is ...

  (Cook & Energy Flow) / (All students)

  = 20/50 = 2/5 = 0.4 = 40%

The relative frequency of students who go to Cook and prefer Energy Flow is 2/5, or 40%.

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The missing terms for the congruent angles are;

Complementary angles

m∠1 + m∠3 = 90°

Transitive property of equality

Subtraction property of equality;

Congruent angles.

Congruent angles are defined as the angles that have equal measure. Therefore, all the angles that have equal measure are called congruent angles.

We are given that;

∠1 and ∠2 are complementary

∠1 and ∠3 are complementary

Now, we are told that m∠1 + m∠2 = 90°. Complementary angles are defined as the 2 angles that sum up to 90 degrees. Thus, ∠1 and ∠2 are complementary by definition.

Similarly, m∠1 + m∠3 = 90°

By the transitive property of equality, we can say that;

m∠1 + m∠2 = m∠1 + m∠3

By the subtraction property of equality;

m∠2 = m∠3

Thus;

∠2 = ∠3 by definition of congruent angles.

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Answer:  x = -2 through 1

Step-by-step explanation:

The domain are the x values that exist on the line. The line goes between -2 and 1. Therefore, that's the domain!

Step-by-step explanation:

if the solution has "nice" numbers, we can split the expression into 2 factors in the form

(x + a)(x + b) = x² + (a+b)x + ab

as this is equal to x² + 4x - 21.

ab = -21

so, one is positive and one is negative.

and 4 = a + b

we know the typical factors of 21 : 3×7

and then we see easily : 7-3 = 4

so,

we have

(x + 7)(x - 3) >= 0

this has 2 x-intercepts (x-values when y = 0) :

x = -7

x = 3

because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.

that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.

so, the solution are the intervals

x <= -7 and x >= 3

in these areas is the expression x² + 4x - 21 >= 0.

Answer: A. 9

Step-by-step explanation:

Answer:

The ratio of acid to water is 2 to 3 in the mixture of the two solutions

This can be thought of as a chemistry problem or a math problem, but both use practically the same process to find the final answer.

So, let's say 2 liters of 50% acid and 1 liter of 20% acid is mixed.
In total, there is 2*(50%) + 1*(20%) of acid, so there is 1 liter of pure acid in 2 liters of 50% acid, and 0.2 liters of pure acid in 1 liter of 20% acid. This in total is 1.2 liters of acid. The total volume is 2 + 1 liters, which is 3 liters. the percentage can be found by dividing the amount of pure acid by the total volume, so 1.2/3, which equals 0.4, or 40%. The ratio would be 40% to 100-40%, or 40% to 60%, or 2 to 3

Answer:

235

Step-by-step explanation:

When estimating the product of two decimals, first round the decimals to their nearest whole numbers.

Therefore,

So an estimate of the product of the two decimals is:

[tex]\implies 4.8 \times 47.1 \approx 5 \times 47[/tex]

Partition 47 into tens and units:

[tex]\implies 5 \times 47 = 5 \times (40 + 7)[/tex]

Apply the distributive property of multiplication over addition:

[tex]\begin{aligned}\implies 5 \times (40 + 7) &= (5 \times 40) + (5 \times 7)\\&=200+35\\&=235\end{aligned}[/tex]

Therefore:

[tex]\boxed{4.8 \times 47.1 \approx 235}[/tex]

The required value of x is x = [tex]\sqrt{79}[/tex]

Given : A right angled triangle

This right angles triangle is again divided in two parts

the first part has measures 3 , z and the other side can be calculated by using The Pythagoras Theorem

According to this theorem

3² + z² = y²

thus 9 + z² = y² ------------------equation 1

Also 7 + 3 = 10

thus 10²  = z² + x²-----------------equation 2

And 7² + y² = x² --------------- equation 3

from equation 1 we know

9 + z² + 49 = x²

58 + z² = x²

Thus on substituting this in equation 2 we get

100 = 58 + z² + z²

42 = 2z²

21 = z²

z = [tex]\sqrt{21}[/tex]

thus x² = 58 + 21 = 79

x = [tex]\sqrt{79}[/tex]

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The completed statement with regards to Chang and Carlotta's methods used for solving the word problem is presented as follows;

A word problem in mathematics and science is the verbal presentation of the information in a scenario required to mathematically solve a problem.

The steps to solve the problem is presented as follows;

The amount in the bank account = $50

Amount made per hour by mowing lawns = $8

The number of hours put into mowing lawns in order to have a total of $130 in the account can be found by using the equation;

The amount in the account increases based on the number of hours used for mowing lawns, therefore;

130 = 50 + 8 × h

8·h = 130 - 50 = 80

h = 80/8 = 10

Ten hours of lawn mowing is required to have a total of $130 in the bank.

Chang's method involve the use of expressing the situation mathematically, by use of variables.

Carlotta's method involves the use of verbal expressions to outline the relationship between the variables, simplifying them to arrive at the determining variable that indicates the number of hours require.

Therefore;

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