Which graph shows the correct solution to the linear-quadratic system of inequalities below?
{y<0.5x^2+1
5x-2y>=-10}​

Answer:

  (b)  The data has a possible range of 19, which is a wide spread. This might mean that there is a large difference in the number of water-skiing trips taken by the students.

Step-by-step explanation:

You want the best description of the spread of data shown in the histogram.

The least data value that can be represented on the chart is 6. The greatest value the chart can represent is 25. This means the possible range of data values is ...

  range = max - min = 25 -6 = 19

This possible spread of 19 might mean there is a large difference in the number of trips taken by students, choice B.

__

Additional comment

The range must be at least 21 -10 = 11 trips, not an answer choice. The most common number appears to be in the range 16-20, so will likely not be 10. (This is referred to as the "mode range", as we cannot tell from the grouped data what the actual mode is.)

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The given statement "If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B" is true.

The standard deviation is a measure of a data set's dispersion. It tells us how far the data values are from the mean.

A larger standard deviation means that the data points are more spread out, i.e., they are farther from the mean.

Therefore, if data set A has a standard deviation that is greater than data set B, it means that the values in data set A are more spread apart.

Hence, the given statement is true.

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The option which is not personally liable for any losses or damages is Shareholders in a public corporation, the correct answer is A.

We are given that;

Four options of damages

Now,

Shareholders in a public corporation are not personally liable for any losses or damages caused by the corporation, because they have limited liability. This means that they can only lose the amount they invested in the corporation, and their personal assets are protected from creditors or lawsuits12.

Owner of a sole proprietorship, shareholders in a private corporation, and partners in a partnership are all personally liable for any losses or damages caused by their business activities, unless they have some form of liability insurance or protection12. This means that they can be sued for their personal assets if the business cannot pay its debts or obligations.

Therefore, by unitary method the answer will be Shareholders in a public corporation

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Step-by-step explanation:

Similar triangle ratio:

15  is to 10    as  AB is to 6

15/10 = AB / 6

6 * 15/10 =   AB  =  9   units

The missing statement about base angles of the isosceles trapezoid is ∠TPR ≅ ∠ TAR.

The base angles of isosceles trapezoids are congruent.

In an isosceles trapezoid, the base angles (the angles formed by one of the bases and a leg) are congruent.

Since the opposite angles in an isosceles trapezoid are congruent, the base angles must also be congruent.

In the given diagram, we will identify the base angles as follows;

∠TPR ≅ ∠ TAR

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The number of solutions of the system of equations in this problem is given as follows:

Infinitely many solutions.

The system of equations for this problem is defined as follows:

Writing the second equation in standard format like the second, we have that:

x/3 + y = -2.

Multiplying by 3:

x + 3y = -6.

The two equations are equal, meaning that the system has an infinite number of solutions, and the two equations are the same on the graph.

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A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.

In this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.

By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.

Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.

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Lee's TV costs $4.05 to operate for a month of 30 days.

To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.

First, let's find out how many watts Lee's TV consumes in a day:

250 watts/hour x 3 hours/day = 750 watts/day

To convert this to kilowatts, we divide by 1000:

750 watts/day ÷ 1000 = 0.75 kilowatts/day

Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:

0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours

Finally, we can calculate the cost of operating the TV for a month:

22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05

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The value of the expression is 13. 75

An algebraic expression is described as an expression that is known to consist of certain variables, terms, their coefficients, factors and also their constants.

Algebraic expressions are also known to be made up of some arithmetic operations such as;

From the information given, we have that;

14 minus 25%

This is represented as;

14 - 25%

Find the percent

14 - 25/100

Divide the values

14 - 0.25

13. 75

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The relation that is not a function is relation 3, and the other 3 are functions.

A relation is a function if each point on its domain is mapped into a single point in the range.

So if you see an input that is mapped into two different outputs, then it is not a function.

Then the relation 3 is not a function, because h is mapped to different things, meaning that we have the same input being mapped to different outpouts. While the other 3 relations are all functions.

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The amount of the interest, payment to principal, and new principal for the first payment is solved

Given data ,

Let the loan amount = $ 210,000

Let the interest rate r = 6.5 %

Let the monthly payment be = $ 1,362.06

Now , On calculating the monthly interest rate

Monthly interest rate = 0.065 / 12 = 0.00542 or 0.542%

Calculate the interest amount

Interest amount = 0.00542 x $210,000 = $1,138.20

Calculate the payment to principal

Payment to principal = $1,362.06 - $1,138.20 = $223.86

Calculate the new principal balance

New principal balance = $210,000 - $223.86 = $209,776.14

Hence , for the first payment, the amount of interest is $1,138.20, the payment to principal is $223.86, and the new principal balance is $209,776.14

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Answer:

only child

Step-by-step explanation:

Answer: If y varies inversely as x, then:

y = k/x

where k is a constant of proportionality. To find k, we can use the initial condition that y = 6 when x = 8:

6 = k/8

Solving for k, we get:

k = 48

Now we can use this value of k to find y when x = 2:

y = 48/2 = 24

Step-by-step explanation:

Answer:

Im pretty sure its the third one

Step-by-step explanation:

It all depends on the square root to find the nearest tenth and rounding it all up.

Check the picture below.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ triangle }{\cfrac{1}{2}(26)(17)}~~ + ~~\stackrel{ rectangle }{(26)(9)}}\implies 221+234\implies \text{\LARGE 455}[/tex]

Answer:

Step-by-step explanation:

You want the amounts in each of two accounts, one earning 8% interest, and the other, with an initial balance that is $450 greater, earning 12% interest. The total interest earned is $176.

Let x represent the initial balance in the 12% account. Then the initial balance in the 8% account is (x -450). The total interest earned is ...

  0.08(x -450) +0.12(x) = 176

  0.20x - 36 = 176 . . . . . simplify

  0.20x = 212 . . . . . . add 36

  x = 1060 . . . . . .  divide by 0.2

  x -450 = 610

The 8% account had $610 invested; the 12% account had $1060 invested.

The description of function transformations and an example is highlighted below

To describe the transformation of the functions, we need to identify the image and the preimage of the functions to be transformed

Take for instance the function is y = x² transformed to the function y = (x + 3)²

This means that the parent function is y = x²

When compared, we can see that

x in y = x² is x + 3 in y = (x + 3)²

This means that y = x² is shifted left by 3 units to form y = (x + 3)²

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Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15

The length of the shortest side is 0.28ft

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

Scale factor = dimension of new shape / dimension of old shape

Perimeter of new rectangle = 12 inches = 1 feet

perimeter of the old = 2(28+32)

= 100feet

scale factor = 1/100

therefore the dimension of the shortest length is

1/100 = x/28

100x = 28

x = 28/100

x = 0.28ft

The shortest length of scale drawing is 0.28feet.

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Answer:

Step-by-step explanation:

Yes, the student is correct. To write a percent as a fraction, we can write the number before the percent symbol as the numerator and 100 as the denominator. For example, 25% can be written as 25/100, which can be simplified to 1/4. This is because percent means "per hundred," so 25% means 25 per hundred, which can be expressed as a fraction with a denominator of 100.

The solution to the given system of equations is a = 6, b = 4.

The system of equations is given as follows:

a + b = 10  .....(i)

a - b = 2    .....(ii)

To solve this system of equations, we can use the method of elimination.

Adding the two equations, we get:

(a + b) + (a - b) = 10 + 2

2a = 12

a = 6

Substituting a = 6 into one of the equations, we get:

6 - b = 2

b = 4

Therefore, the solution to the system of equations is:

a = 6, b = 4.

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Answer:

Multiply row 1 by 1/7

The resulting matrix is
[tex]\begin{pmatrix}1&-\frac{4}{7}&\frac{8}{7}\\ -12&7&-13\end{pmatrix}[/tex]

Step-by-step explanation:

Original matrix is
[tex]\begin{pmatrix}7&-4&8\\ -12&7&-13\end{pmatrix}[/tex]

Multiplying any one row by a nonzero scalar is a valid matrix operation. This will not affect the final solution of the matrix

So all we have to do is to multiply row 1 by 1/7 and you get a 1 in row 1, column 1

[tex]R_1 \times \dfrac{1}{7} \longrightarrow \begin{pmatrix}1&-\frac{4}{7}&\frac{8}{7}\\ -12&7&-13\end{pmatrix}[/tex]

The graph of y = (x + 3)² is a transformation of the graph y = x². It is shifted left 3 units.

The equation of the function is given as

y = x²

The transformed function is

y = (x + 3)²

This means that the parent function is y = x²

When compared, we can see that

x in y = x² is x + 3 in y = (x + 3)²

This means that y = x² is shifted left by 3 units to form y = (x + 3)²

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The segments AB and CD on item 1 are classified as follows:

Perpendicular.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

The slope of segment AB is given as follows:

m = (3 - 13)/(0 - (-2))

m = -10/2

m = -5.

The slope of segment CB is given as follows:

m = (3 - 0)/(10 - (-5))

m = 3/15

m = 1/5.

The multiplication of these slopes is given as follows:

-5 x 1/5 = -1.

As the multiplication of the slopes is of -1, the segments are perpendicular.

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The solution to the system of equations, y = 2x -1 and y = x + 3 is: x = 4 and y = 7.

Given the system of equations as:

y = 2x - 1 ---> eqn. 1

y = x + 3 --> eqn. 2

Substitute y for (x + 3) into equation 1:

x + 3 = 2x - 1

Combine like terms:

x - 2x = -3 - 1

-x = -4

x = 4

Substitute x = 4 into equation 1:

y = 4 + 3

y = 7

The solution is: x = 4 and y = 7.

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The number that represents the phrase is -40.

Let's use algebra to solve the problem.

If we let "a number" be represented by the variable x, we can write the first part of the sentence as "Seventeen more than a number" which can be written as:

x + 17

The problem also says that this expression is equal to negative twenty-three.

We can write that as:

x + 17 = -23

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 17 from both sides:

x + 17 - 17 = -23 - 17

x = -40

Therefore, the number is -40.

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A point that represent a striking deviation in the box plot above include the following: C. P.

In Mathematics and Statistics, a box plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

In conclusion, we can logically deduce that point P represent a striking deviation in the box plot because it is an outlier (it is significantly far from all of the other data points).

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The area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.

Given that a circle has a diameter of 37 m, we will find the circumference of and the area of the circle,

Radius = diameter /2

Radius = 18.5 m

Circumference = π × diameter

= 3.14 × 37

= 116.18 m

Area = π × radius²

= 3.14 × 18.5²

= 1074.6 m²

Hence, the area and the circumference of the circle is 1074.6 m² and 116.18 m respectively.

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