The set of integers forms a ring. Select the answer that is also valid. A. The set of integers is also a field because additive identity and additive inverse are defined, multiplication is associative, and multiplication distributes over addition. B. The set of integers is also a field because multiplication is commutative and the multiplicative identity is defined. C. The set of integers is not a field because there is no multiplicative inverse. D. The set of integers is not a field because it does not qualify as a group

Answer:

23.4

Step-by-step explanation:

Perimeter is the sum of length of all the sides.

The 2 sides on the left (the shorter ones) are equal.  Let x = short side:

3² + 4² = 25 = x²

x = √25 = 5

The 2 sides on the right (the longer ones) are equal.  Let y = long side:

3² + 6² = 45 = y²

y = √45 = 6.71

P = 2x + 2y = 2(5) + 2(6.71) = 23.4

The expression in the required form is log₂(8^x2^y)

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

xlog₂8 + ylog₂2

The law of logarithm states that

alog₂b = log₂b^a

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

xlog₂8 = log₂8^x

ylog₂2 = log₂2^y

Substitute the known values in the above equation, so, we have the following representation

log₂8^x + log₂2^y

Apply the product law

log₂(8^x2^y)

Hence, the expression is log₂(8^x2^y)

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The figurine would have a 30 square unit area.

We received 4 points (3, 2, -3, 2, and 3), respectively (3,-3). The area of the figure is to be determined by plotting these points on a coordinate plane.

We will obtain a rectangle after plotting the provided points, as illustrated in the attached file.

We can see that the width between the y-coordinates of point (3,2) and is 5 units (3,-3).

Width = 2 - (-3) = 2 + 3 = 5

As can be seen, there are 6 units between the x-coordinates of point (-3,2) and the length of the rectangle (3,2).

Length equals (3 - (-3)) + (3 + 3) = 6

We are aware that a rectangle's area equals its length times its breadth.

A = Length × Width

A = 6 × 5

A = 30

Therefore, the area of the figure would be 30 square units.

The complete question is:

Plot the following points and find the area of the figure. (3,2); (-3,2); (-3,-3); (3,-3)

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The shape of the base of a right circular cylinder is circle.

What is right circular cylinder?

The definition of a right circular cylinder is a cylinder with a closed circular surface, two parallel bases on either end, and elements that are perpendicular to the base. Right cylinder is another name for it. The distance between each point on the closed circular surface of a right circular cylinder and the cylinder's axis, which is a straight line, is constant. The two circular bases of the right circular cylinder are parallel to one another and have the same radius. It is a certain geometric shape that is widely utilised in everyday life.

The diagram of a right circular cylinder is attached below and it can be observed that the base is circular in shape.

Hence, the shape of the base of a right circular cylinder is circle.

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Yes, 4x² 3x 7 is a polynomial because it is an algebraic expression composed of constants, variables, and exponents, with the variables being multiplied together.

Step 1: 4x² 3x 7 can be expanded as 4x² + 3x - 7.

Step 2: 4x² + 3x - 7 can be further expanded into 4x2 + 3x - 7.

Step 3: Simplify the expression by combining like terms: 4x2 + 3x - 7 = 4x2 + 3x - 7.

Step 4: The final result is 4x2 + 3x - 7, which is a polynomial.

A polynomial is an algebraic expression composed of constants, variables, and exponents, with the variables being multiplied together. 4x² 3x 7 is an example of a polynomial. To expand this polynomial, we start by combining the like terms, 4x² and 3x, to get 4x2 + 3x. Then, we add the constant, -7, to get 4x2 + 3x - 7. This final expression is a polynomial because it has constants, variables, and exponents, and the variables are multiplied together. Therefore, 4x² 3x 7 is a polynomial.

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Hey there!

So, we are given the following to solve:

Solve for y.

[tex]-\frac{y}{3}+19=33[/tex]

_______________________________

1. Move 19 to the right side.

[tex]-\frac{y}{3}=14[/tex]

2. Multiply both sides by 3.

[tex]3(-\frac{y}{3})=14*3[/tex]

3. Simplify.

[tex]-y=42[/tex]

4. Divide both sides by -1.

[tex]\frac{-y}{-1}=\frac{42}{-1}[/tex]

5. Simplify.

[tex]y=-42[/tex]

__________________________________

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The smallest value of n needed so that the probability that the system functions is at least 0.90 is 12. Probability is a measure of the likelihood of an event occurring. In a mathematical sense, probability is a value between 0 and 1 that represents the chance of a particular event happening.

In a 3 out of n system, the probability that the system functions is given by the formula:

P(function) = [tex]1 - (1 - p)^3 * (1 - (1 - p)^(^n^ - ^3^))[/tex]

where p is the probability that each component functions (in this case, 0.9) and n is the total number of components.

To find the smallest value of n that satisfies the condition P(function) ≥ 0.9, we can rearrange the formula to:

n ≥ 3 + log(1 - 0.9) / log(1 - 0.9)

By solving this equation, we find that the smallest value of n that satisfies the condition is n ≥ 12.

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Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors.

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−1 (also known as negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0.

Now, According to the question:

Multiplying a number by −1 is equivalent to changing the sign of the number – that is, for any x we have (−1) ⋅ x = −x. This can be proved using the distributive law and the axiom that 1 is the multiplicative identity:

x + (−1) ⋅ x = 1 ⋅ x + (−1) ⋅ x = (1 + (−1)) ⋅ x = 0 ⋅ x = 0.

Here we have used the fact that any number x times 0 equals 0, which follows by cancellation from the equation

0 ⋅ x = (0 + 0) ⋅ x = 0 ⋅ x + 0 ⋅ x.

0, 1, −1, i, and −i in the complex or cartesian plane

In other words,

x + (−1) ⋅ x = 0,

so (−1) ⋅ x is the additive inverse of x, i.e. (−1) ⋅ x = −x.

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Answer:

[tex]y2 = -\dfrac{1}{3}x + 6[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that when multiplied will result in a value of -1

In other words, the slope of y2 = - 1/(slope of y1)

y1 = 3x - 6
Slope of y1 = 3

So slope of y2 = -1/3

Equation of y2 is of the form

[tex]y_2 = -\dfrac{1}{3}x_2 + b[/tex]

The line passes through (-3, 7)

To find b plug in y2 = 7, x2 = -3 into the above equation and solve for b

[tex]7 = -\dfrac{1}{3}(-3) + b[/tex]

=> 7 = 1 + b

b = 7-1 = 6

So the equation of line y2 is

[tex]y2 = -\dfrac{1}{3}x + 6[/tex]

Hint: If you look at the graph, line y2 crosses at b = 6

We need not have used equations to solve for b but we have to be careful. We can at least the graph value to see if our b value is close to it

The equivalent expression to the complex number (3 + 4i) + (3-5i) is option C: 6 - i.

What is complex number?

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively.

The complex number expression is -

(3 + 4i) + (3 - 5i)

= 3 + 4i + 3 - 5i

= 3 + 3 + 4i - 5i

= 6 - i

Therefore, the value for the expression is 6 - i.

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The smallest possible surface area of a single solid is 214

a) Each side of a cube with side length = 4 has an area of 16; the overall area is 6 x 16 = 96

A cube with sides of length 5 has an area of 25 on each side, making its overall area 6 x 25 or 150.

Both have a combined area of 96 + 150 = 246.

You will eliminate 16 if you glue one of the smaller cube's sides to one of the larger cube's sides.

246 - 16 - 16 = 214 is the result from each of the two cubes.

b) length  =  L

    width   =  W

    height  =  H

    L · W  =  6                   --->   W  =  6 / L

    W · H  =  15                 --->   W  =  15 / H

    L · H  =  40

Since  W  =  6 / L   and   W  =  15 / H

6 / L.  =  15 / H     --->     6H  =  15L     --->     H  =  15L / 6

Since  L · H  =  40     --->     L · ( 15L / 6 )  =  40     --->     15L2  =  240     --     L2  =  16     --->     L  =  4

Since  L  =  4     --->     L · W  =  6     --->     4 · W  =  6     --->     W  =  1.5

Since  L · H  =  40     --->     4 · H  =  40     --->     H  =  10

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Answer:

The other form of 15x^4y^3 − 45x^3y^4 is 15x^3y^3(x - 3y)

x=-1/10 is the value of x in the given expression 5(-3x+5x)+1

An expression is combination of variables, numbers and operators.

The given expression is 5(-3x+5x)+1

In the given expression x is the variable

Plus and minus are the operators.

-3x and 5x are the like terms because each term has same variable x.

5(-3x+5x)+1

5(2x)+1

10x+1

10x=-1

Divide both sides by 10

x=-1/10

Hence, x=-1/10 is the value of x in the given expression 5(-3x+5x)+1

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Answer: it should be 22

Step-by-step explanation:

If you put both of them into a TI-84 calculator and look at the equations, the y intercepts are 3 and -19 which are 22 units apart.

Answer:

22/-22

Step-by-step explanation:

First find the equation of graph

m = rise/run = 32-15/6-4 = 17/2 = 8.5

y = mx + b (feel free to use point slope form if you learned it, its much faster)

66 = 8.5(10) + b

66 = 85 + b

-19 = b

y = 8.5x - 19

Distance b/w y-int = -19 - 3 = -22 units or 22 units depending on where you're counting from

Michelle's position below the surface of water in meters is; 53 meter below water level

The absolute value is defined as the distance from zero. It is also called the non-negative quantity.

We are given;

Chris position in water = 40 meters below the surface of water

Michelle drove more than 13 meters below from Chris

We want to find Michelle's position below the surface of water.

Thus:

Michelle's position below the surface of water = Chris position in water + Extra dive then Chris

Michelle's position below the surface of water = 40 meters + 13 meters

Michelle's position below the surface of water = 53 meter below water level

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Answer: To solve for x, you can first simplify the right side of the equation by distributing the negative 4x:

-178 = -5x + (-16x - 52)

Next, combine like terms on the right side:

-178 = -21x - 52

Then add 52 to both sides:

-126 = -21x

Finally, divide both sides by -21 to solve for x:

x = 6

Step-by-step explanation:

The length of the hypotenuse is 10 cm.

Pythagoras' Theorem is the way in which you can find the missing length of a right-angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), the Opposite (which doesn't touch the hypotenuse), and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c²

However, it can also be written in the form of c²=a²+b²

In order to find the hypotenuse, you will have the length of two sides, for example, these could be 3 and 4.

As 'C' is always the hypotenuse, you have to work out the two other lengths, and you do this by squaring the numbers.

3²=9 and 4²=16.

As you're looking for C, you've got to add these together

9+16=25

As a²+b²=c², this means that the answer for C is the square root of 25.

√25= 5

Let the length of the hypotenuse be represented by l, the base be represented by b and the height be represented by h.

We are given that b = 6 cm and h = 8 cm.

Using Pythagoras' theorem,

l² = b² + h²

Substitute the values,

⇒ l² = 6² + 8²

⇒ l² = 36 + 64

⇒ l² = 100

∴ l = 10

Thus, the length of the hypotenuse is 10 cm.

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The system of equation A has been solved graphically and its solution is equal to the ordered pair (6, 13).

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y - 11x = -35            ........equation 1.

y = x² + 2x - 35       ........equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (6, 13).

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The 3 algebraic expressions are simple linear expression, linear expression and a product of two binomials.

Here are five examples of algebraic expressions:

1. 2x + 3: This is a simple linear expression that involves a variable (x) and two constants (2 and 3).

2. 4y - 7: Similar to the first example, this is also a linear expression, involving a variable (y) and two constants (4 and 7).

3. 3x^2 + 4x - 5: This is a quadratic expression, involving a variable (x) raised to the power of 2, a constant (3), a variable (x) and a constant (-5).

4. (x + 2)(x - 3): This is a product of two binomials, each one is a linear expression and the result of the product is a quadratic expression.

5. (3x + 4)/(x-2): This is a quotient of two expressions, the numerator is a linear expression and the denominator is a linear expression.

It's important to note that these are just a few examples and there are many different types of algebraic expressions, each with their own unique characteristics and properties. Algebraic expressions can become more complex as the student progresses, but the basic idea remains the same.

Therefore, The 3 algebraic expressions are simple linear expressions, linear expressions and a product of two binomials.

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The numbers that will be used in the numerator and denominator to calculate the probability that 2 selected students out of 10 are all boys

(6/10) and (5/9) respectively.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, In a class of 10, there are 4 girls and 6 boys.

The sample space N(S) = 10.

Number of boys N(B) = 6 and similarly N(G) = 4.

The probability that 2 selected students out of 10 are all boys will be,

P(B, B) = (6/10)×(5/9).

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Four two-digit numbers are constructed from numbers 1, 2, 3, ..., 8. The largest number of  primes that could possibly formed among those four numbers is 3 numbers.

A prime number is a whole number greater than 1 which only divisible by 1 and itself. Example of prime numbers are 2, 3, 5, 7, ...

We want to form 4 two-digit numbers from, 1, 2, 3, 4, 5, 6, 7, 8.

Recall that: other than 2, all even numbers are not prime since they are divisible by 2. Hence, from those numbers, we look at which odd two-digit numbers are prime.

We have four odd numbers in the list that can construct two-digit odd numbers: 1, 3, 5, 7.

However, two-digit numbers with 5 as its second digit is not prime since they are exactly divisible by 5.

Therefore, now we only have 3 numbers (1, 3, 7) that can construct two-digit odd numbers. Hence, the largest number of primes that could possibly formed is 3 numbers.

Example, the constructed four two-digit numbers are:

47, 53, 61, 28

47, 53, and 61 are prime, while 28 is not.

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Answer:

Step-by-step explanation:

The difference between the x coordinates is 6, (difference between -3 and 3). Half of 6 is 3. Add this to the lowest value (-3) to get to zero.

Repeating the exercise for the Y coordinates we get a difference of 0 (there's no difference between the values 5 & 5). So adding this difference (0) to the lowest value (5) we get 5 still.

So the midpoint is (0,5)

The amount of money Bilquis have more than Sophie when compounded continuously is given by the equation A = $ 42

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the compound interest amount of Bilquis be represented as B

Let the compound interest amount of Sophie be represented as S

The amount of money invested by Bilquis and Sophie is = $ 6,900

The rate of interest of Bilquis = 5 1/8 = 5.125 %

The rate of interest of Sophie = 4 3/4 = 4.75 %

The time period b = 18 months = 1.5 years

So , the amount after compound interest A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

The amount with Bilquis after 18 months B = Pe^rt ( compounded continuously )

The amount with Bilquis after 18 months B = 6900 ( 2.71828 )^(0.05125)(1.5 )

On simplifying the equation , we get

The amount with Bilquis after 18 months B = $ 7451.36

And ,

The amount with Sophie after 18 months S = Pe^rt ( compounded continuously )

The amount with Sophie after 18 months S = 6900( 2.71828 )^(0.0475)(1.5 )

On simplifying the equation , we get

The amount with Sophie after 18 months S = $ 7409.56

So , the difference in amount is A = amount with Bilquis after 18 months B - amount with Sophie after 18 months S

On simplifying the equation , we get

The difference in amount is A = 7451.36 - 7409.56

The difference in amount is A = $ 41.8

So , The difference in amount is A = $ 42

Hence , Bilquis had $ 42 more than Sophie

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'S' is the incenter, so Angle Bisectors type of segments are drawn.

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The cat is 17.5 millimeters away from the pupil.

Given is the image of Cat as shown in the figure.

It is given that both the triangles are similar. So, we can write -

10/7 = 25/x

{x} = 25 x 7/10

{x} = 17.5

Therefore, the cat is 17.5 millimeters away from the pupil.

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To calculate an expected value with absolute certainty is b. When your data points have various probabilities of occurring.

Expected cash flow is the sum of the cash flows times the likelihood that they will occur. Future financial inflows and outflows are calculated before accepting a project to help assess whether or not to take it on. The expected value is obtained by multiplying the supplied number by its likelihood. It is applied when estimating future projects.

Reasons why the other response is incorrect:

a. The present value of the data points, such as cash flows, is calculated and compared to cash outflows when they occur over different time periods.

c. It is impossible to accurately predict the value of an unknown future event.

d. When only one data point is available, it can be used for the desired outcome. If there are several possible outcomes or data points, probable outcomes can be estimated.

Note that the full question is:

When would you calculate an expected value?

a. When your data points occur on different dates

b. When your data points have various probabilities of occurring

c. When you need to know the exact outcome of a future, unknown event

d. When you only have one data point

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Answer:

Step-by-step explanation:

a