Select all expressions are equivalent to - 1/2 ( 8 - 2+ 6/7x)

Integers are closed under addition by all the properties. Hence, the answer is True.

Integers are set of zero, positive, and negative numbers. The set of integers is represented by the symbol ‘Z’.

Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}

To check if the integers are closed under addition or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.

Let us consider each property one by one -

1. The closure property-

let's take two integers say 5 and 2.

now 5+2=7, but -2+5= -3 which is an integer.

Thus, integers are closed under addition by closure property.

2. The commutative property-

let's take two integers say 5 and 2.

now 5+2=7 and 2+5=-7

hence, we get 2+5 = 5+2.

Thus, integers are closed under addition by commutative property.

3. The associative property-

let's take three integers say 5, 3, and 2.

now (5+3)+2 = 10 and 5+(3+2)= 10

hence, we get (5+3)+2 = 5+(3+2).

Thus, integers are closed under addition by associative property.

4. The distributive property-

let's take three integers say -2, 6, and 5.

now, -2 × ( 6 + 5 ) =  -2 × 6 + (-2) × 5  = -12 - 10 = -22

        and -2 × ( 6 + 5 ) = -2 × 11 = -22

Hence, -22 = -22

Thus, integers are closed under addition by distributive property.

Hence, we can conclude that integers are closed under addition by all the properties.

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The complete question is-

Are Integers closed under addition. True or false?

Answer:

Leopard: 60 lb

Lion: 420 lb

Step-by-step explanation:

Let x = weight of leopard.

Weight of lion = 7x.

Sum of the weights = x + 7x = 8x

Total weight = 480 lb

8x = 480

x = 60

7x = 7 × 60 = 420

Answer:

Leopard: 60 lb

Lion: 420 lb

Answer: shown below

Step-by-step explanation:
x = 7y

x+y+ 480

7y+y = 480

8y = 480

y = 480/8 = 60 pounds for the leopard

x = 7(60) = 420 pounds for the lion

The answer is 7h and 12m

Step-by-step explanation:

To solve for time, divide the distance traveled by the rate. For example, if Sergio continues reading the total of 216 pages, then he had finish reading for 7 hours and 12 minutes!

The possible heights of the students in the surf club will be -  

73 inches ≥ h > 60 inches

Given is the University of Florida that has a surf club. It has 11 females and 12 males and [h] represents the height of a team member.

The given inequality is -

300 < 5.25h - 15 ≤ 368.25

So, we can write -

5.25h - 15 > 300

5.25h > 315

h > (315/5.25)

h > 60 inches

and

5.25h - 15 ≤ 368.25

5.25h ≤ 368.25 + 15

5.25h ≤ 383.25

h ≤ 73 inches

So, we can write the range as -

73 inches ≥ h > 60 inches.

Therefore, the height range of the students in the surf club will be between 73 inches ≥ h > 60 inches.

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The number of nickels and dimes Latanys have is 10 and 14.

An equation is a mathematical statement of two expressions connected by an equal sign.

We have,

Total coins = 24

$1 = 20 nickels

$1 = 10 dimes

Now,

Number of nickels = N

Number of dimes = D

Now,

N + D = 24 ____(1)

N = 24 - D _____(2)

0.05N + 0.1D = 1.90 ____(3)

Putting (2) in (3) we get,

0.05(24 - D) + 0.1D = 1.90

1.2 - 0.05D + 0.1D = 1.90

0.05D = 1.90 - 1.2

0.05D = 0.7

D = 0.7 / 0.05

D = 14

Now,

N = 24 - D

N = 24 - 14

N = 10

Thus,

The number of nickels is 10.

The number of dimes is 14.

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Answer:

233

Step-by-step explanation:

Number at the beginning: 137

Additional number per week: 2

Number of weeks: 48

Additional number: 2 × 48 = 96

Total number at end of 48 weeks: 137 + 96 = 233

Answer: 233

The correct answer is option D, which states tan∝ = 1/2

What is Trigonometry?

The field of mathematics concerned with the relationships between triangle sides and angles, as well as the pertinent functions of any angles is Trigonometry.

Solution:

we are given that tanθ = 1/2

this implies θ = 45°

We know that the sum of all interior angle of triangle is 180°

so, it can be calculated that the value of

angle ∝ = 45°

Therefore, tan∝ = 1/2

The correct answer is option D, which states tan∝ = 1/2

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The rectangular horse pasture's largest area, in square feet, can be enclosed in [tex]80000m^{2}[/tex]

Let the sides of the rectangle-shaped fence be a and b.

We have to use wire for the three sides of the fence.

[tex]a+b*2=800[/tex]

Area A is given by

[tex]A=a*b[/tex]

Also, we can write A as a function of b

[tex]A=A(b)\\=(800-2*b)b=800b-2b^{2}[/tex]

Taking the derivative of A

[tex]A'=800-4b\\A'=0\\b=200m[/tex]

Then the length of the other side

[tex]a=800-2*200\\=400m[/tex]

The largest area

[tex]A=400*200\\=80000m^{2}[/tex]

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Answer:

-g+12

Step-by-step explanation:

The yaw mark's radius is 11.2 feet, or one foot to the nearest tenth.

11.1634 miles per hour is considered the minimum speed.

Yaw marks are always curved. They are, initiated by a steering input. They're the remains of a tire that's still moving while also slapping sideways.

Using a chord and middle ordinate, you can calculate the radius using the following formula:

We must apply the algorithm to get the yaw mark's radius.

where the middle ordinate is m and the chord's length is c

With a 31 foot chord and a 3 foot middle ordinate, the tires leave a yaw mark.

so,

[tex]r^{2}=\frac{31^{2} }{8*3} + \frac{3}{2}[/tex]

[tex]r^{2} =[/tex] 40.041 + 1.5

[tex]r^{2}[/tex] = 41.041

We will now apply the following formula to get the minimum speed:

where 'f' is the drag factor and 'r' is the radius

0.2 is the drag factor, hence f=0.2

and r=41.541 feet

[tex]s= \sqrt{15*0.2*41.041}[/tex]

[tex]s=\sqrt{124.623}[/tex]

s= 11.1634 mph

11.1634 miles per hour was the lowest speed at which the brakes could be applied.

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The  ratio of the sides for triangle HIL is 1:1:√3.

A triangle is a three-sided polygon that consists of three edges and three vertices.

We need to find the ratio of HIL triangle.

In the triangle JKL, IL is perpendicular to the JH.

At I the angle is 90 degrees.

The length of JI is 11cm.

The angle of JKL is x degrees.

JK is 22 cm and the angle of ILJ is y degrees.

the ratio of the sides for triangle HIL is 1:1:√3.

Hence,  1:1:√3 is the  ratio of the sides for triangle HIL

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A quadrilateral has angles of 4x, 7x, 15x, and 10x.The smallest angle of the quadrilateral is 4x and the largest angle is 15x.

A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed into two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle. TA quadrilateral has angles that total 360 degrees. This information can be used to find the value of x.

360

= 4x + 7x + 15x + 10x

x = 360 / 36

x = 10

Therefore, the smallest angle is 40 degrees and the largest angle is 150 degrees.

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Answer:

x = -15

Step-by-step explanation:

[tex]\frac{x - 9}{3}[/tex] = -8  Multiply all the say through by 3

x - 9 = -24  Add 9 to each sides

x = -15

Answer: 60

6 x 10 is 60 and a negative times a negative is positive.

Answer: 60 hope this helps

A contingency is defined by miles as " a requirement of the activities belongs to one subunit which is affected by the activities of other subunits.

Step to Step Explanation:

Therefore, the contingency is defined by miles as " a requirement of the activities of one given subunit which is affected by the activities of other subunits.

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When both riders have stopped, the person that is further away from the parking lot is; The second rider.

Let the required distance be represented by x.

Using Pythagoras theorem, we have:

hypotenuse² =  opposite² + adjacent²

x = √(8² + 15²)

x = √289

x = 17 km

This means that the first biker is 17.0 km from the starting point.

Using the law of cosine which is given by the expression;

c² = a² + b² - 2ab cos C

x² = 8² + 15² - 2(8*15) cos (160)

x = 20.22 km

This means that the second biker is 20.22 km from the starting point.

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Center point of dilation is a fixed point in a plane about which all the points of the figure expanded or contract. And scale factor of a dilation is the ratio of new formed image to the old given image.

Explanation:

Therefore, the center of the dilation can be find using the translation and scale factor can be calculated using the ratio of the new to the old images.

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3 enlargement is the scale factor of the dilation.

What is dilation?

resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.

The options for this question are missing. Here are the missing options:

enlargement; 6

enlargement; 3

reduction; 3

reduction; 1/3

Hence, 3 enlargement is the scale factor of the dilation.

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The lines or angles with measure must be true for the lines and angles.

To predict the truthfulness of the statements, we must understand the concept of congruency. Any two entities will be congruent if they measure the same. In the question, the line AN will be congruent to line segment LB and line NC will be congruent to line BZ.

Similarly, the angle measurements should also be same to the angles to be congruent. In case of same angles, the Angle BMZ will be congruent to Angle CMZ and Angle ZBM will be congruent to Angle ZCM.

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Answer: D

Step-by-step explanation:

The Rule of translation of the point is (x, y) → (x+8, y - 12)

The translation is a transformation of a figure on the coordinate plane without changing its shape, or size.

The Coordinate rule for translation is (x, y) → (x ± h, y ± k)

where h and k are the units of horizontal and vertical shifting. Here if the movement is left then h will be negative. If movement is downwards then k will be negative.

Here we have

Point A(7, 3) is translated to A'(16, -9)

If we plot the given points in a graph the will as given below the graph

There we can observe that,

The x coordinate is moved left 8 units further and y is moved 12 units  downward

Therefore,

The Rule of translation of the point is (x, y) → (x+8, y - 12)

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The student that is correct is George as the ratio of pools open on weekends to the total number of pools is 6:16.

Ratio is the relationship between two or more numbers. It is the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.

In order to determine the ratio between the number of pools open on the weekend to the total number of pools express the numbers that represent each value as ratios.

This will be:

= number of pools open on weekends: total number of pools

= 6 : 16

George is correct.

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Answer:-59

Step-by-step explanation:

-2*36 + -2*-8

-72+16-3

-56-3

-59

The values of x that provide meaningful predictions for the output value y are given as follows:

c. Prediction values are meaningful only for X-values in (or close to the range of the original data.

Regression equations are built from a sample of a data-set, and are used to model the entire data.

Depending on the behavior of the data, the regression equation can be linear, quadratic, logistic, exponential, and so on...

These regression equations are not valid for all values of the input x, some conditions are given as follows:

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Answer:

A: The system of linear inequalities that fits the situation is:

15x + 13y >= 300

60x + 20y <= 1200

Where x is the number of dozen cookies and y is the number of dozen cupcakes.

B: The new inequalities that need to be added to the problem are:

x <= 12

y <= 40

C: The maximum amount of baked goods that she could make is:

x = 12

y = 40

D: The amount she will earn if she made the maximum amount of baked goods is:

15x + 13y = 15 * 12 + 13 * 40 = $660

E: The time it will take her to make the maximum amount of baked goods is:

60x + 20y = 60 * 12 + 20 * 40 = 960 minutes = 16 hours

F: The least amount of time she could work and still earn $300 is:

15x + 13y = 300

x + y = 20

Solving this system of equations, we get:

x = 8

y = 12

In this case, she would make 8 dozen cookies and 12 dozen cupcakes in a minimum of 8 hours.

Step-by-step explanation:

The dilation will change the size of the figure, so it can be getting bigger or smaller

The dilation is the process of changing the size of the figure, but the shape of the figure will be same. Therefore we can say that the dilation is one form of the transformation of the figure

The dilation can be increase the size or decrease the size

If you consider the case of dilation with scale factor, when the scale factor is greater than 1  the size will be bigger and if the scale factor is between 0 and 1 the size will be smaller than original size

Therefore, the dilation can be getting bigger or smaller

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While virtually all time series exhibit a random​ component, not all time series exhibit other components is a true statement.

It's accurate to say that while almost all time series show a random component, not all time series show additional components.

A time series is a collection of observations of discrete data points gathered over a period of time by repeated measurements. For instance, calculating the quantity of retail sales for each month of the year would be a time series. This is because sales income is consistently and precisely measured at regular times. Data collected once or irregularly are not time series data.

A time series observation can be divided into three categories: trend (long-term direction), seasonal (systematic, calendar-related motions), and irregular (unsystematic, short term fluctuations).

A time series is a group of data points that have been arranged chronologically in mathematics. Typically, a time series is a sequence that was captured at many equally spaced intervals in time. As a result, it is a collection of discrete-time data.

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The length of the perimeter is 44cm if the area of a rectangle is 105sq in and length of one of the side is 7 in.

A perimeter is a closed path that encompasses, surrounds, or delineates something, whether it be a two-dimensional shape or a one-dimensional length. The outermost border of an ellipse or circle is its circumference.

Knowing the perimeter is helpful in a variety of circumstances. Calculated perimeter refers to the length of fence required to entirely enclose a yard or garden.

Given,

Area of a rectangle=105cm²

And also given that,

Width w=7cm

Area= Length× Width

Length=Area/Width

Length-105/7

Length=15cm

Here, Now we have to calculate the perimeter of a rectangle

Perimeter=2(Width+ Length)

Perimeter=2(7cm+15cm)

Perimeter=44cm.

Hence, the length of the perimeter is 44cm.

Therefore, the length of the perimeter is 44cm if the area of a rectangle is 105sq in and length of one of the side is 7 in.

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