1
0
5
2 points
Determine whether 0.34567 is rational or irrational
irrational
rational
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The number line of x <-2 is added below

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

x < -2

For the inequality x < -2:

All real numbers that are less than -2 satisfy the inequality.

So, we can represent the solution set of the inequality using the interval (-∞, -2)

When represented on a number line, we have:

   -∞          -3        -2        -1        0        1        2        ∞

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

   .           <-          o         .         .         .         .        .

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The equation in slope-intercept form is  y = 5/7x + 3/7

It is important to note that the equation of a line is expressed with the formula;

y = mx + c

Such that the parameters are;

From the information given, we have that;

slope, m = 5/7

Now, let's substitute the points into the formula, we have;

9 = 5/7(12) + c

expand the bracket

9 - 60/7 = c

find the lowest common multiple

c = 63-60/7

c = 3/7

The equation of the line is ; y = 5/7x + 3/7

Hence, the equation is y = 5/7x + 3/7

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Franklin has 3 pennies and 15 nickels.

The number of pennies The first step is to form a system of equations that represent the question:

p + n = 18 equation 1

0.01p + 0.05n = 0.78 equation 2

Where:

The elimination method would be used to solve the system of equations.

Multiply equation 1 b y 0.01:

0.01p + 0.01n = 0.18 equation 3

Subtract equation 3 from equation 2:

0.04n = 0.60

n = 0.60 / 0.04

n = 15

Substitute for n in equation 1:

p + 15 = 18

p = 18 - 15

p = 3

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1st row

1. 2x + x + x, x = 0

Plug in 0 as x.

0 + 0 + 0 = 0

2. 2x + x + x, x = 1

Plug in 1 as x.

2 + 1 + 1 = 4

3. 2x + x + x, x = 2

Plug in 2 as x.

4 + 2 + 2 = 8

2nd row

1. 4x, x = 0

Plug in 0 as x.

4 * 0 = 0

2. 4x, x = 1

Plug in 1 as x.

4 * 1 = 4

3. 4x, x = 2

4 * 2 = 8

Notice how the answers are the same.

This is because 2x + x + x = 4x, meaning they are the same equation.

Answer:

Attached in file

Step-by-step explanation:

What does this mean by substitution?

The act of substituting in algebra / pre-algebra / etc is plugging in a number for 'x'

In this question, they are wanting you to plug in 0, 1, and 2 to two different equations (2x+x+x and 4x) to see if they are the same equations.

(I'm going to try and make a graph, as visual learning helps)

     | 2x+x+x       4x

x=0|      a             b

x=1 |       c             d

x=2|        e           f

Now I know that this is not perfect, but I inputted letters so that you know what I am solving for.

Solve for a:

Plug in x=0

2(0) + 0 + 0

2*0 = 0

0 + 0 + 0 = 0

So, a = 0 (What I am saying is the first blank is a, the blank next to it is b, etc)

Solve for b:

Plug in x=0

4(0) = 0

So, b = 0

Solve for c:

Plug in x=1

2(1) + 1 + 1

2 + 1 + 1

= 2  + 2

=4

b = 4

Solve for d:

Plug in x=1

4(1) = 4

d=4

Solve for e:

Plug in x=2

2(2) + 2 + 2

4 + 2 + 2

4 + 4

=8

e=8

Solve for f:

Plug in x=2

4(2)

f=8

There we go! I annotated this picture to have these values plugged into their respective spots!!

Hope this helped!!

A) All the first six terms in the pattern are,

⇒ 47, 39, 31, 23, 15, 7

Every number is 8 more than the next number.

B) The 30th term in this pattern is, - 185

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A pattern rule for a number pattern is represented by,

⇒ 55 - 8n, where n is the term number.

Now, All the first six terms in the pattern are,

Substitute n = 1;

⇒ 55 - 8n

⇒ 55 - 8 × 1

⇒ 55 - 8

⇒ 47

Substitute n = 2;

⇒ 55 - 8n

⇒ 55 - 8 × 2

⇒ 55 - 16

⇒ 39

Substitute n = 3;

⇒ 55 - 8n

⇒ 55 - 8 × 3

⇒ 55 - 24

⇒ 31

Substitute n = 4;

⇒ 55 - 8n

⇒ 55 - 8 × 4

⇒ 55 - 32

⇒ 23

Substitute n = 5;

⇒ 55 - 8n

⇒ 55 - 8 × 5

⇒ 55 - 40

⇒ 15

Substitute n = 6;

⇒ 55 - 8n

⇒ 55 - 8 × 6

⇒ 55 - 48

⇒ 7

B) The 30th term in this pattern is,

Substitute n = 30;

⇒ 55 - 8n

⇒ 55 - 8 × 30

⇒ 55 - 240

⇒ - 185

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Jen could send either a package of socks or the book.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

The table shows the items with weights which are already packed.

Total weight of the items already packed = 5.2 + 1.25 + 2.05 + 2.25

                                                                     = 10.75 pounds

But it is given that, package must weight less than 12 pounds.

Weight of the item that is being added must be less than weight = 12 - 10.75 = 1.25

Weight of sweatshirt is 1.25 pounds, so it can't be placed.

She could place either package of socks or book.

Hence Jen could any one of the following : a package of socks or book.

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She uses 27 ounces of solution A and 63 ounces of Solution B.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Solution A is 45% salt and Solution B is 95% salt.

Let x be the number of ounces of Solution A

and y be the number of ounces of Solution B

as, She wants to obtain 90 ounces of a mixture then

x + y = 90

y = 90 - x.........(1)

and, 0.45x + 0.95y = 0.80( 90)

0.45x + 0.95y = 72

Put the value of y from equation (1) we get

0.45x + 0.95( 90-x)= 72

0.45x + 85.5 - 0.95x = 72

0.5x = 13.5

x= 27 ounces

and, y= 90-27 = 63 ounces.

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The correct statement can identify by using a certain limit theorem.

The correct option is (c).

The sample size of J is 40.

The sample size of K is 100.

As per the central limit theorem, if the population with mean and standard deviation takes a large random sample from the population with replacement, then the distribution of the sample means will be approximately distributed.

Now from the definition of the central limit theorem, both J and K will the same means.

Write the expression for standard deviation.

[tex]s = \frac{\alpha }{\sqrt{n} }[/tex]

From the above expression, the standard deviation is inversely proportional to the sample size.

Thus, the correct statement is the expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

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The complete question is:

A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.

Which of the following must be true about J and K?

a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.

b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.

c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.

e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.

We may multiply the y-values by -1 to flip the graph of y = (x - 2)^3 + 5 vertically. This will display the graph along the x-axis. The inverted graph's equation is y = -((x - 2)^3 + 5).

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

To flip the graph of y = (x - 2)^3 + 5 vertically, we can multiply the y-values by -1. This will reflect the graph across the x-axis. The equation for the flipped graph is: y = -((x - 2)^3 + 5).

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The area of the composite figure is equal to 54 square inches and the perimeter is 35 inches.

The composite figure is made up of a trapezium and a rectangle, so we shall calculate for the areas of the two figures and then add the result to get the total area of the composite figure as follows:

area of the trapezium = [(9 + 12)/2] in × 4 in

area of the trapezium = (21/2) in × 4 in

area of the trapezium = 21 in × 2 in

area of the trapezium = 42 in²

area of the rectangle = 4 in × 3 in

area of the rectangle = 12 in²

total area of the composite figure = 42 in² + 12 in²

total area of the composite figure = 52 in²

perimeter of the composite figure = 12 + 4 + 5 + 3 + 4 + 7

perimeter of the composite figure = 35 in²

Therefore, the area of the composite figure is equal to 54 square inches and the perimeter is 35 inches.

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The area and the perimeter of the composite figure are 54 square inches and 35 inches, respectively.

In this problem we find the case of a composite figure, whose area and perimeter (p), in inches, should be found. Perimeter is the sum of all side lengths of the figure, while the area is the sum of areas of rectangles and triangles, whose formulas are listed below:

Rectangle

A = w · l

Triangle

A = 0.5 · w · l

Where:

First, determine the perimeter of the composite figure:

p = 12 in + 4 in + 5 in + 3 in + 4 in + 7 in

p = 35 in

Second, determine the area of the composite figure:

A = 0.5 · (4 in) · (3 in) + (9 in) · (4 in) + (4 in) · (3 in)

A = 6 in² + 36 in² + 12 in²

A = 54 in²

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Answer: I'm sorry this question cannot be answered because of the lack of information, please resubmit your question with a picture of the page.

Step-by-step explanation:

The quantity of jewelry that each sister will receive would be = 23+y/ 5

The total number of jewelry that was given out by Grandma Gertrude = 23 pieces

The total number of jewelry that was given out by Grandma Fien = y

The number of Carlson sisters = 5

Therefore, the quantity of jewelry that will be received by each of the sister would be represented by this expression = 23+y/ 5

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The complete question:

Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves. There are 5 Carlson sisters, How many pieces of jewelry did each sister receive?

The similar fractions to [tex]1\frac{1}{5}[/tex] are 12/10, 18/15, 24/20, 30/25, 36/30 etc

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, a fraction, [tex]1\frac{1}{5}[/tex]

Converting into improper fraction,

[tex]1\frac{1}{5}[/tex] = 6/5

So, similar fraction to 6/5 are,

12/10, 18/15, 24/20, 30/25, 36/30 etc

Hence, the similar fractions to [tex]1\frac{1}{5}[/tex] are 12/10, 18/15, 24/20, 30/25, 36/30 etc

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Answer: y = -x

Step-by-step explanation:

slope = (-5-3)/(5+3) = -1

using the point (-3,3)

y-3 = -(x+3)

y-3 = -x - 3

y = -x

Data collected about a population is not characteristic of both surveys and experiments. The correct answer would be an option (C).

The purpose of a survey is to understand populations as a whole by utilizing pertinent questions to collect data from a sample of people.

Data collected about a population is not a characteristic of both survey and experiment because, in an experiment, the researcher typically manipulates one or more variables and measures the effect on another variable, while in a survey, the researcher usually only measures variables and does not manipulate them. As a result, in a survey, the data is typically collected about a sample of the population, rather than the entire population.

Hence, the correct answer would be option (C).

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Answer:1/20

Step-by-step explanation:

trust

Answer:

1/20

Step-by-step explanation:

5 divided by 100 is =20

5divided by 5 is =1

=1/20

The degree of the polynomial that best describes the data is (c) cubic

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

See attachment

Find the first dfference D1 between the consecutive y-values

D1:   10     28.4     56.4    94

Calculate the second difference

D1:   18.4     28     37.6

Calculate the third difference

D3:   9.6     9.6

The third difference are equal

Hence, the degree is (c) cubic

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Answer:

4/3

Step-by-step explanation:

Answer:

$38.4

Step-by-step explanation:

In other words, a 20% discount for a item with original price of $48 is equal to $9.6 (Amount Saved).  - Note that to find the amount saved, just multiply it by the percentage and divide by 100.

$48 - $9.6 (amount saved) = $38.4

The GCF of the two expressions is (y + 5).

The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of each of the expressions. To find the GCF of two expressions, we need to factor out the common factors from each expression.

Given expressions: z(y + 5) - 3(y + 5)

We can start by factoring out (y + 5) from both terms:

z(y + 5) - 3(y + 5) = (y + 5)(z - 3)

So, the GCF of the two expressions is (y + 5).

The greatest common factor (GCF) is the largest positive integer that is a factor of two or more numbers. It is a useful concept in mathematics, especially in the study of numbers and their properties. The GCF helps us simplify expressions by cancelling out common factors and reducing the complexity of expressions. For example, the GCF of 12 and 18 is 6, meaning that 6 is the largest number that is a factor of both 12 and 18. To find the GCF, we can use prime factorization to identify the common factors and then multiply those factors to obtain the GCF.

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One efficient algorithm for finding the LCA in a tree is the Tarjan's off-line lowest common ancestor (LCA) algorithm. It uses DFS to preprocess the tree and build a table of ancestors for each node. The algorithm then uses this table to quickly find the LCA in constant time.

The running time of the algorithm is O(n) in both time and space, where n is the number of positions in the tree.

Here is a Java implementation of the Tarjan's off-line LCA algorithm:

class TreeNode {

 int val;

 List<TreeNode> children;

 public TreeNode(int val) {

   // constructor to initialize a node in the tree with a given value

   this.val = val;

   this.children = new ArrayList<>();

 }

}

public class LCA {

 private TreeNode root;

 private int[] depth;

 private int[] parent;

 private int[][] table;

 private int logN;

 public LCA(TreeNode root, int n) {

   // constructor to initialize the LCA class with a given root and number of nodes

   this.root = root;

   depth = new int[n];

   parent = new int[n];

   table = new int[n][20];

   logN = (int) (Math.log(n) / Math.log(2)) + 1;

   build();

 }

 private void build() {

   // preprocess the tree and build the ancestor table

   dfs(root, -1, 0);

   for (int i = 0; i < logN - 1; i++) {

     for (int j = 0; j < parent.length; j++) {

       table[j][i + 1] = table[table[j][i]][i];

     }

   }

 }

 private void dfs(TreeNode node, int p, int d) {

   // DFS to preprocess the tree

   parent[node.val] = p;

   depth[node.val] = d;

   for (TreeNode child : node.children) {

     dfs(child, node.val, d + 1);

   }

 }

 public int query(int p, int q) {

   // function to query the LCA of two nodes

   if (depth[p] < depth[q]) {

     int temp = p;

     p = q;

     q = temp;

   }

   int log = 1;

   while ((1 << log) <= depth[p]) {

     log++;

   }

   log--;

   for (int i = log; i >= 0; i--) {

     if (depth[p] - (1 << i) >= depth[q]) {

       p = table[p][i];

     }

   }

   if (p == q) {

     return p;

   }

   for (int i = log; i >= 0; i--) {

     if (table[p][i] != -1 && table[p][i] != table[q][i]) {

       p = table[p][i];

       q = table[q][i];

     }

   }

   return parent[p];

 }

}

And here is a test program:

public class Main {

 public static void main(String[] args) {

   TreeNode root = new TreeNode(0);

   TreeNode node1 = new TreeNode(1);

   TreeNode node2 = new TreeNode(2);

   Tree

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Π(x) is asymptotic to x/ln(x) as x approaches infinity.

The prime counting function (denoted as Π(x)) is the number of prime numbers less than or equal to x. The prime number theorem states that Π(x) is asymptotic to x/ln(x) as x approaches infinity. This can be conceptually seen in the graph of Π(x) and x/ln(x), which converges as x increases.

Formally, the prime number theorem states that:

lim x→∞ Π(x)/(x/ln(x)) = 1

This can be shown by the following calculation:

lim x→∞ Π(x)/(x/ln(x))

= lim x→∞ Π(x) ln(x)/x

= lim x→∞ 1/x Σ ln(p)/p

= lim x→∞ 1/x Σ 1/p

= lim x→∞ 1/x ln(x)

= 1

Therefore, Π(x) is asymptotic to x/ln(x) as x approaches infinity.

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The location of point A on the number line is -2.5, point B is -1.5, point C is -0.5, and point D is 1.5.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The number line can be divided into halves to find the halfway points between consecutive integers.

Point A is the halfway point between negative 3 and negative 2,

Point A = -2.5

Point B is the halfway point between negative 2 and negative 1,

Point B = -1.5

Point C is the halfway point between negative 1 and 0,

Point C = -0.5

Point D is the halfway point between 1 and 2.

Point D = 1.5

These halfway points can be used to approximate the location of -1.5 on the number line.

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The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C

From the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.

The amount of 150 dollars would then be added to the debt that has the second highest rate.

Hence the amount of debt that would be paid off first would be the first debt based on the stack method.

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The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.

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

RECT is a square (not drawn to scale).

RA = 13² - 3x - 3  

AC = x(x + 2)

The diagonals of the square will be RC and ET. And "A" is the intersection point. Then the equation is given as,

RA = AC

13² - 3x - 3 = x(x + 2)

169 - 3x - 3 = x² + 2x

x² + 5x - 166 = 0

x = [- 5 ± √(5² - 4 × 1 × (-166))] / (2 × 1)

x = 10.62, -15.62

Then the length of AC is given as,

AC = 10.62 (10.62 + 2)

AC = 134.13 units

The diagonals of the square are congruent. Then we have

ET = RC

ET = 2 AC

ET = 2 x 134.13

ET = 268.3 units

Then the length RT is given as,

RT = ET / √2

RT = 198.7 units

The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.

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The value of the deposit after 7 years is given as follows:

$30,746.85.

The situation is modeled with an increasing exponential function, which has the format presented as follows:

y = a(1 + r)^x.

In which:

Considering the deposit and the yearly increase, the parameters are given as follows:

a = 25000, r = 0.03.

Hence the function is given as follows:

y = 25000(1.03)^x.

The value after 7 years is given as follows:

y = 25000(1.03)^7

y = $30,746.85.

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The simplest form of the square root is 14x⁷√2x.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given the expression, [tex]\sqrt{(392x^{15} )}[/tex]

factors of 392 = 2*2*2*7*7

or factors of 392 = 2*14*14

and x¹⁵ = x¹⁴.x

substitute the values,

[tex]\sqrt{(2*14*14x^{14}x )}[/tex]

or √2x(√14²)(√x¹⁴)

= 14x⁷√2x

Hence option C is correct.

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The transformed vertices of the ΔABC will be A'(- 2, 0), B'(2, 3)

and C'(0, - 1).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The given triangle has vertices A(0, 4), B(6, - 4) and C(- 2, 0).

We know a rotation of 90° counterclockwise transforms (x, y) to (- y, x)

and a dilation factor of (1/2) would make it (- y/2, x/2).

Therefore, The vertices of the triangle A'B'C' will be,

A'(- 4/2, 0/2), B'(-(-4)/2, 6/2) and C'(0/2, - 2/2).

A'(- 2, 0), B'(2, 3) and C'(0, - 1).

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Answer:

the equation of the line that contains the points (1, 1) and (3, 9) is y = 4x + 3.

Step-by-step explanation:

To find the equation of the line that contains the points (1, 1) and (3, 9), we can use the slope-point form of the equation of a line, which is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are any other points on the line.

We can use the first point (1, 1) and the slope of the line to find the equation of the line:

m = (9 - 1) / (3 - 1) = 4

y - 1 = 4(x - 1)

y = 4x + 3

So, the equation of the line that contains the points (1, 1) and (3, 9) is y = 4x + 3.