The solution of a system of linear inequalities is the intersection of the solutions to each inequality. Every point in the intersection region satisfies all inequalities in the system. Describe how you know which region, if any, represents the solution to a system of linear inequalities

The equation of the line is y = 0.4x - 793.65 and the minimum wage is $18.35

The equation of a line can be formed with the help of the slope of the line and a point on the line. Let us understand more about the slope of the line and the needed point on the line, to better understand the formation of the equation of a line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

a)

Taking two points from the table;

Using 1996 and 1997

The data are; (1996, 4.75), (1997, 5.15)

m = y₂ - y₁ / x₂ - x₁

m = 5.15 - 4.75 / 1997 - 1996

m = 0.4

The slope of the line is 0.4

Using the line equation;

y = mx + c

Taking one point, we can find y-intercept here

5.15 = 0.4(1997) + c

5.15 = 798.8 + c

c = 5.15 - 798.8

c = -793.65

The equation of the line is y = 0.4x - 793.65

b) The minimum wage in 2030

y = 0.4x - 793.65

y = 0.4(2030) - 793.65

y = 18.35

The minimum wage is $18.35

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Step-by-step explanation:meow

Answer:

100

Step-by-step explanation:

Use Pemdas or Order of Operations:

First in the brackets:

3+2=5
next in the brackets:

45 - 5 = 40

Now you get the equation:

3 x 20 + 40

First solve 20 x 3:

60; +40 = 100

Thus 100 is your total.

Answer:

the answer is

-3/2

I hope that helps

a)  The average score on the original exam is 76

b) The average score after 2 months = 67.41

c) The average score after 11 months = 56.574

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

For this case we know that the average scores for the class are given by the following model:

[tex]f(t) =76 - 18 log_{10} (t+1)[/tex] , 0≤ t ≤ 12

Where t is in months. The graph attached illustrate the function for this case

And for this case we can answer the questions like this:

Part a

We just need to replace t =0 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (0+1)[/tex] = 76

Part b

We just need to replace t =2 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (2+1)[/tex] = 67.41

Part c

We just need to replace t =11 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (11+1)[/tex] = 56.574

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Question:

Students in a mathematics class were given an exam and then tested monthly with an equivalent exam. The average scores for the class are given by the human memory model f(t) = 76 − 18 log10(t + 1), 0 ≤ t ≤ 12 where t is the time in months. Verify your answers in parts (a), (b), and (c) using a graphing utility.

(a) What was the average score on the original exam (t = 0)? f(0) =

(b) What was the average score after 2 months? (Round your answer to one decimal place.) f(2) =

(c) What was the average score after 11 months? (Round your answer to one decimal place.) f(11) =

The values that would be excluded from the domain of the function are those that create vertical asymptotes in the graph.

Vertical asymptotes can be found by setting the expression in the denominator equal to 0 (zero) and solving for x. The resulting values of x are the values that are excluded from the domain of the function.

Expression in the denominator = x^2 - 5x + 6

x^2 - 5x + 6 = 0

(Factor to solve)

(x - 3)(x - 2) = 0

x - 3 = 0 || x = 3

x - 2 = 0 || x = 2

The values that are excluded from the domain of the function are 3 and 2.

Hope this helps!

The lines with the equations 10x+5y =-5 and y=-2x+6 are parallel

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

10x+5y =-5 and y=-2x+6

Make y the subject in both equations

So, we have the following representation

y = -2x - 1 and y = -2x + 6

As a general rule of linear equations

Parallel lines have equal slope

A linear equation is represented as

y = mx + c

Where

slope = m

Using the above as a guide, we have the following:

The slope of y = -2x - 1 and y = -2x + 6 is -2

Hence, the lines are parallel

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Answer:

48°

Step-by-step explanation:

this is because no if you take any two points in along line AB and CB it will always be 48°.

The value of x for the given right-angle triangle using the trigonometric function will be 1.0.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

As per the given right angle triangle,

sin 16° = x/3.5

x = 1.0

Hence "Using the trigonometric function, the value of x for the given right-angle triangle will be 1.0.".

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True, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line.

As given in the question,

Given statement is: Parabola consist of set of all the points which are equidistant from fixed point and fixed line.

Therefore, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line is a true statement.

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The domain of the linear function that models the volume is:

D: 0 ≤x ≤640

The correct option is the fourth one, counting from the top.

Here we have the following linear function:

V(x) = 640 - x

V(x) represents the volume of water left in the bucket, while x represents the amount of water that has leaked from the bucket.

The domain will represent the possible values of x.

first, the smaller value of x.

It is x = 0, and it represents the moment before the leak started, when the bucket was completely full and had a volume of:

V(0)=  640 ounces.

The largest possible value of x is x = 640, which is the case where all the water in the bucket has come out.

Then the domain is:

D: 0  ≤x ≤640

Finally, the correct option is the last one.

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The length of the shadow of man is 0.8 m/s.

How to solve word problems?

Here are some actions to take:

1. Recognize the issue.

Recognize every term used to describe the issue, Recognize what you need to look for, Recognize the issue's context.

2. Convert the issue into an equation. Give the unknown a variable (or variables) to symbolise, Indicate exactly what the variable stands for.

3. Put the strategy into action and find a solution.

dx/dt  =1.2 m/s

4.5 / x+ y = 1.8 / y

1.8x + 1.8y = 4.5y

1.8x = 2.7y

2x = 3y

3 dy/dt = 2dx/ dt = dy/dt = 2/3

​ =0.8

Hence, The length of the shadow of man is 0.8 m/s

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Answer:

2 gallons

Step-by-step explanation:

1 1/4 = 1 + 1/4 = 4/4 + 1/4 = 5/4

Then:

5/4 gallons ⇒ 5/8 fence

x  gallons ⇒ 8/8 fence

x = (5/4)(8/8) / (5/8)

x = ((5*8)/(4*8)) / (5/8)

x = (5/4) / (5/8)

x = (5*8)/(4*5)

x = 40/20

x = 2

Answer:

Step-by-step explanation: Here's your answer 50√3 m.

Answer:

There are 6 large blue marbles, so there are 8 + 6 - 6 = 8 ways to choose a large blue marble or a large marble.

There are 10 blue marbles (6 large blue marbles and 4 small blue marbles), so there are 10 + 8 - 6 = 12 ways to choose a blue marble or a large marble.

Therefore, there are 8 + 12 = <<8+12=20>>20 ways to choose a blue marble or a large marble.

Step-by-step explanation:

Answer: 24 different ways.

Step-by-step explanation: Hope it helps, please pick brainliest!

Answer: 4

Step-by-step explanation:

10/14 = 5/7

As per the double integral, the flux of the vector is 2√11(6z + 1) + 176

What is double integral small definition?

In math, Double integrals are used to find the flux of a vector field through a given surface S and find the normal to the given surface and equations of the surface to find the limits of integration.

And it is calculate by the formula as Flux= ∫∫F⋅ndS

Here we have given that S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward.

And we need to find the the flux of the vector field F = 1i + 1j + 3k across the surface S.

As per the formula of flux of vector, it can be written as,

=>Flux =  ∫∫(1i + 1j + 3k) . 2 dS

When we integrate this one the we get,

=> Flux = 2√11(6z + 1) + 176

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The given statement is an example of "Principle of specificity or specific adaption to imposed demands (SAID Principle) ".

What is Principle of specificity ?

According to the specificity of training principle, each physical activity has a very unique physiological response. For instance, someone who jogs can anticipate that both their running performance and their level of aerobic fitness will be favorable.

if someone repeatedly lifts heavy weights, that person will produce higher levels of maximal strength.

This an example of  "Principle of specificity or specific adaption to imposed demands (SAID Principle) "

Tenet according to which the body will adjust to the unique demands imposed upon it.

Higher degrees of endurance can be attained by regularly lifting lesser weights for a large number of repetitions.

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Answer:2x^2+23

Step-by-step explanation:

7x^2+3-5x^2+20    (distribute (-5) to x^2 and (-4))

2x^2+3+20              (combine like terms)

2x^2+23

The supplied regular polygon's solitary outside angle measures 32.5 degrees.

additionally, we must determine the size of a single external angle.

As a result, the polygon that is presented has 11 sides.

What does the term "exterior angle" mean?

In a rectilinear figure, the angle between a side and its neighboring side stretched outward.

360 degrees is the sum of all outside angles.

By dividing 360 by the total number of sides, we must determine the size of a single outside angle.

As a result, the supplied regular polygon's solitary exterior angle has a measure of 32.5 degrees.

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Answer:

3 : 7

Step-by-step explanation:

Ratios are Proportinalised Numbers that we can use to compare number of units relative to the other value.

Eg. 3 : 15 = 1 : 5

Given Information from the Question:

15 Child Tickets : 35 Adult Tickets

Now we reduce them to simplest form.

(15 ÷ 5) : (35 ÷ 5) = 3 : 7.

Therefore the ratio of Child Tickets to Adult Tickets is 3 : 7.

There are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.

What is a combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we

Consider lining up all the blue marbles and placing one red marble in between them. Let that arrangement be fixed. The remaining red marbles will be 5 red marbles. Note that the arrangement will be:

x BR x BR x BR x BR x BR x BR x BR x B x

Note that this is the same even if our arrangement is

x B x RB x  RB x RB x RB x RB x RB x RB x

There is a total of 13 places to arrange 8 blue marbles among 12 red marbles.

8 marbles can be placed in ¹³C₈ ways

Total possible arrangements = ¹³C₈ = 1287

Hence, there are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.

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The empirical probability that George will get back on his feet the next time Angie knocks him down is 5/114.

Event probabilities are closely related to empirical probabilities, also called empirical probabilities.

Empirical probability is an estimate of the probability of a particular outcome occurring again, based on the number of instances of that outcome in the sample set.

In the given question.

Also includes George the Turtle, who flipped Angie the Tortoise 114 times.

Three times George got back on his feet with help. Empirical probabilities are exactly what we are looking for.

Based on our observations, we will now empirically calculate whether George will be able to stand again.

Therefore,

The Empirical probability = 5/114

So, the next time Angie knocks George down, the empirical probability that George will be able to get back up on his own will be his 5/114.

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The solution is

Angle 1 and Angle 5 = Corresponding Angles

Angle 1 and Angle 8 = Co-Interior Angles

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

What are Parallel Lines Cut by Transversal?

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

From the figure , we can see that

The angles 5 , 6 , 7 and 8 are all on the straight line t

The angles 1 , 2 , 3 and 4 are all on the straight line n

The line m is the transversal line

Now ,

From the theorem of angles on a parallel lines , we get

Alternate angles are equal

So , 2 = 8 and 3 = 5

Now ,

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

Corresponding angles are equal

So , 1 = 5 and 2 = 6

Now ,

Angle 1 and Angle 5 = Corresponding Angles

Co-Interior angles are supplementary

So , 1 + 8 = 180°

Now , Angle 1 and Angle 8 = Co-Interior Angles

Hence ,

Angle 1 and Angle 5 = Corresponding Angles

Angle 1 and Angle 8 = Co-Interior Angles

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

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The probability that A will have more heads than B is 1/2, when A and B are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

Given, a and b are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

we have to find the probability that a will have more heads than b.

Now, p1  = "probability that A obtains more heads than B.".

p2 = "probability that B obtains more heads than A.".

p3 = "probability that A obtains as many heads as B.".

Such that p1 + p2 + p3 = 1.

Since, both flips n coins, A wins with the same probability as B.

p1 = p2

Now, A flips and extra coin.

½ of the time it gives tails and doesn't contribute, but ½ of the time is gives heads meaning that A now wins if they before had equal number of heads.

p1+1/2(1 − p1 − p2)=1/2.

Hence, the probability that A will have more heads than B is 1/2, when A and B are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

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Answer:

2x² + 7x - 15.

Step-by-step explanation:

The product when x- 5 is multiplied by 2x + 3 is 2x² +7x - 15. To find the product, we need to use the distributive property. This states that for any two expressions, a and b, and a constant, c, we have the following:

c * (a + b) = c * a + c * b

We can use this property to expand the expression (x - 5)(2x + 3) as follows:

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

               = 2x^2 + 3x + (-10x) + (-15)

               = 2x^2 + 7x - 15

Therefore, the product of the expression (x - 5)(2x + 3) is 2x^2 + 7x - 15, which matches the answer choice 2x² + 7x - 15.

The mentioned data 100 kilometres in an hour is the speed of rate of object.

The 100 kilometres represents distance and an hour indicates the time. The complete data in the sentence is indicative of coverage of 100 kilometres in an hour by whatever the object is, which is not mentioned in the question.

However, writing distance with respect to time indicates the rate or speed. Widely applicable, it can anything. Few examples of its indication are rate of descending or ascending of plane, kite, lift or any other object. It can refer to the speed of person, car, train or other such objects or animals holding capacity to travel.

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The value of the odds of pulling a red marble is equivalent to 1/9 from an urn filled with marbles of various colors.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

By definition, the theoretical probability is equal to the ratio of the favorable event to the total number of events.

Given that:

The probability of pulling a red marble at random is 1/10

Probability of not pulling red marble is = 1-(1/10)= 9/10

The odds of pulling red marble is (1/10)/(9/10)

The probability of odds of pulling red marble is 1/9.

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Answer:

Step-by-step explanation:

This is not a valid proof, as it simply repeats the given statement without providing any justification or reasoning. To prove that AB CD, we need to use logical reasoning and the properties of lines and angles to show that the statement is true.

One way to prove this statement is to consider the angles of the quadrilateral ZBZD. Since ZBZD is a quadrilateral, it has four angles. We are given that ZB is parallel to AD and that BC is parallel to AD. This means that the angles formed by these lines must be equal.

Additionally, since ZBZD is a quadrilateral, the sum of its angles must be 360 degrees. Therefore, if the angles formed by ZB and AD are equal, and the angles formed by BC and AD are equal, then the angles formed by ZB and BC must also be equal.

Therefore, we can conclude that ZB and BC are parallel, which means that AB CD. This completes the proof.

Answer:

w + 18 = 22

Step-by-step explanation:

HC = 18 lb

HC + GD = 22 lb

GD + HC = 22

GD + 18 = 22

w + 18 = 22

The expression 0.5 (x + 3) written as a sum is 0.5x + 1.5

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

0.5 ( x +3)

Write the expression properly

So, we have the following representation

0.5 (x + 3)

Express the brackets as products

So, we have the following representation

0.5 (x + 3) = 0.5 * (x + 3)

Open the brackets using products i.e. distributive property

So, we have the following representation

0.5 (x + 3) = 0.5 * x + 0.5 * 3

Evaluate the products

So, we have the following representation

0.5 (x + 3) = 0.5x + 1.5

Hence, the expression as a sum is 0.5x + 1.5

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Answer:

1. 0.5x + 1.5

2. are not