A scientist is working with 3 meters of gold wire. How long is the wire in millimeters?

He will not be able to put an equal number of toy cars on 3 shelves.

He can put only 18 toy cars in equal number of toy cars of 6 on 3 shelves.

Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.

According to the question

Elliot has a collection of 20 toy cars.

Put an equal number of toy cars on 3 shelves.

= [tex]\frac{20}{3}[/tex]

= 6.6

Thus, He can put only 18 toy cars in equal number of toy cars of 6 on 3 shelves.

He will not be able to put an equal number of toy cars on 3 shelves.

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The probability that when a couple has two ​children, at least one of them is a boy is 0.75.

Based on the information given, the sample space will be (BB, BG, GB, GG)

where,

B = Boy

G = Girl

Therefore, based on the sample space given, at least a boy occurs in 3 places out of 4. This will be 3/4 = 0.75.

In conclusion, the correct option is 0.75.

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The probability of a couple having at least one boy when they have two children is 75%, as three out of four possible outcomes include at least one boy. These outcomes are two boys, a boy then a girl, and a girl then a boy.

The subject of the question is probability which is a branch of mathematics. In order to find the probability that when a couple has two children, at least one of them is a boy, we need to analyze possible outcomes. The couple could have two boys (BB), a boy and a girl (BG), a girl and a boy (GB), or two girls (GG). Hence, the total unique outcomes are 4 (BB, BG, GB, GG).

Considering at least one boy, the possible outcomes could be BB, BG, GB, which are 3 possibilities. Finally, the probability is given as the ratio of favorable outcomes to the total number of outcomes. So the probability of having at least one boy is 3/4 or 75%.

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We will use the slope formula and fill it in accordingly.

[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

Our x2 is 5 and x1 is -2; our y2 is -3 and y1 is 6

[tex] m=\frac{-3-6}{5-(-2)}=\frac{-9}{7} [/tex].

The slope of your line is -9/7

Answer

Find out the slope of the points  G(–2, 6) and H(5, –3).

To prove

The equation for finding the slope of two points be

[tex]m = \frac{y_{2} -y_{1}}{x_{2} - x_{1}}[/tex]

where m represented the slope .

As given

points G(–2, 6) and H(5, –3).

[tex]m = \frac{-3-6}{5+2}[/tex]

solving the above terms

[tex]m = \frac{-9}{7}[/tex]

Therefore the slope of  points G(–2, 6) and H(5, –3) is

[tex]m = \frac{-9}{7}[/tex]

The maximum number of students that will receive the paper and crayons are 30.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Given is Mrs. Evans who has 120 crayons and 30 pieces of paper to give to her students.

We have 120 crayons and 30 pieces of paper.

Then for 1 paper, we will have (120/30) which is equivalent to 4 crayons.

So, every student will get 1 paper and 4 crayons.

Assume that the maximum number of students that will receive the paper and crayons are [x]. Then, we can write -

x + 4x = 120 + 30

5x = 150

5x = 150

x = 30

Therefore, the maximum number of students that will receive the paper and crayons are 30.

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Answer:

605 words per 11 minutes!

Step-by-step explanation:

60 / 55 = 1.0909

11 x 60 = 660

660 / 1.0909 = 605 + (6x - [tex]\int\limits^a_c {b} \, dx[/tex]) / 10

605 + (6x - [tex]\int\limits^a_c {b} \, dx[/tex]) / 10 rounded = 605

Final answer:

To write a two-step inequality for a real-world problem, first identify the unknowns and known quantities related to the problem. Next, construct an inequality that represents the problem, and finally solve the inequality for the unknown variable. For example, budgeting for a party with a savings goal can be represented as an inequality.

Explanation:

To write a two-step inequality to solve a real-world problem, follow these steps:

Identify the unknowns: Understand what needs to be determined. This involves defining the variable(s) that will represent the unknown quantity(ies) in the problem.

Identify the known quantities: Make a list of the quantities that are given or can be inferred from the problem. These are the values you will use to construct your inequality.

Construct the inequality: Use the information from steps 1 and 2 to create an inequality that represents the problem. This often involves expressing the relationship between the known and unknown quantities using an inequality symbol (such as <, >, ≤, ≥).

Solve the inequality: Apply algebraic methods to solve for the unknown variable. This may involve isolating the variable on one side of the inequality.

For example, if you are planning a party and know you have a budget of $200 for decorations but want to save at least $50, you could set up the inequality x + 50 ≤ 200, where x represents the amount you can spend on decorations.

Answer: 4.25

Step-by-step explanation:

A line with a positive slope generally moves upward from left to right, representing an increase in y-values as x-values rise.

If a line has a positive slope, its general direction is upward from left to right. This means that as the x-values increase, the y-values also increase. The slope of a line in mathematics represents the rate at which y changes with respect to x. A positive slope indicates a direct relationship between the two variables involved; as one increases, so does the other. In the context of a graph, this manifests as a line that rises as it moves along the x-axis.

The nature of the slope determines the line's direction. A higher positive slope indicates a steeper ascent, while a smaller positive slope results in a less steep, flatter incline. The concept of slope is crucial in economics as well, as it measures the relationship between two variables, such as price and quantity supplied, where a positive slope illustrates that firms supply more as the price goes higher.

Answer:

0.7 (85 + h) = 74.90

Step-by-step explanation:

The centroid of the region bounded by [tex]\(y=x\), \(y=\frac{1}{x}\), \(y=0\),[/tex] and [tex]\(x=2\)[/tex] is at [tex]\((\frac{2}{3}, 0)\).[/tex]

To find the centroid of the region bounded by the curves[tex]\(y=x\), \(y=\frac{1}{x}\), \(y=0\), and \(x=2\),[/tex]we need to first find the area of the region and then compute the coordinates of the centroid using the following formulas:

The centroid of a region with area[tex]\(A\)[/tex]  is given by [tex]\((\bar{x}, \bar{y})\)[/tex]where

[tex]\[\bar{x} = \frac{1}{A} \int\int_R x \, dA\][/tex]

[tex]\[\bar{y} = \frac{1}{A} \int\int_R y \, dA\][/tex]

First, let's find the points of intersection for the curves:

1. [tex]\(y=x\) and \(y=1/x\):[/tex]

  [tex]\[ x = \frac{1}{x} \implies x^2 = 1 \implies x = 1 \][/tex]

  So, the intersection point is [tex]\((1,1)\).[/tex]

2. [tex]\(y=0\) and \(x=2\):[/tex]

  This intersection occurs at [tex]\((2,0)\).[/tex]

Now, we'll integrate to find the area and then the centroid:

1. Area:

[tex]\[ A = \int_{0}^{1} (x - \frac{1}{x}) \, dx + \int_{1}^{2} (\frac{1}{x}) \, dx \][/tex]

 [tex]\[ A = \left[\frac{x^2}{2} - \ln|x|\right]_{0}^{1} + \left[\ln|x|\right]_{1}^{2} \][/tex]

[tex]\[ A = \left(\frac{1}{2} - 0 - (0 - \infty)\right) + (\ln(2) - \ln(1)) \][/tex]

 [tex]\[ A = \frac{1}{2} + \ln(2) \][/tex]

2. Centroid[tex](\(\bar{x}\)):[/tex]

 [tex]\[ \bar{x} = \frac{1}{A} \left[\int_{0}^{1} x(x - \frac{1}{x}) \, dx + \int_{1}^{2} x(\frac{1}{x}) \, dx\right] \][/tex]

 [tex]\[ \bar{x} = \frac{1}{A} \left[\left[\frac{x^3}{3} - \frac{1}{2}\ln|x|\right]_{0}^{1} + \left[\ln|x|\right]_{1}^{2}\right] \][/tex]

 [tex]\[ \bar{x} = \frac{1}{A} \left(\frac{1}{3} - 0 - (0 - \infty) + (\ln(2) - \ln(1))\right) \][/tex]

 [tex]\[ \bar{x} = \frac{\frac{1}{3} + \ln(2)}{\frac{1}{2} + \ln(2)} \][/tex]

[tex]\[ \bar{x} = \frac{2}{3} \][/tex]

3. Centroid [tex](\(\bar{y}\)):[/tex]

[tex]\[ \bar{y} = \frac{1}{A} \left[\int_{0}^{1} (x - \frac{1}{x}) \cdot 0 \, dx + \int_{1}^{2} (\frac{1}{x}) \cdot 0 \, dx\right] \][/tex]

 [tex]\[ \bar{y} = 0 \][/tex]

Therefore, the centroid of the region is at the point [tex]\(\left(\frac{2}{3}, 0\right)\).[/tex]

Unfortunately, without the attachment or diagram, it is not possible to determine the measure of angle AEB.

The question asks for the measure of angle AEB. In order to find this angle, we need to refer to the given diagram or attachment. Unfortunately, there is no attachment provided with the question, so it is not possible to provide a specific answer to the question. Please provide the diagram or attachment so that I can accurately determine the measure of angle AEB.

A) X intercept is -12, this represent the number of weeks before her birthday she started saving money

B) Y intercept = 3, this is the amount of money she has in her piggy bank before her birthday

C) slope = change in Y over the change in X = 1/4, this means she is saving 25 cents per week

Congruent triangles have equal corresponding angles

The measure of <Q is 30 degrees

The given parameters are:

m∠R=80°, and m∠S=70°

△PQR≅△STU

Given that both triangles are congruent, then the measure of Q is calculated using:

Q = 180 - 80 - 70

Evaluate the difference

Q = 30

Hence, the measure of <Q is 30 degrees

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The equation which is equivalent to the given expression is 4x + y = 21.

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context. An expression is a combination of numbers, variables, or a combination of numbers and variables, and symbols and it is connected by the sign of equal.

We have,

Expression [tex]\frac{12x^4(x-3)(x+5)}{30x(x+3)(x+5)}[/tex]

So,

Now,

To get the equivalent expression,

Cancel the common factor (x + 5) of the given expression,

On solving,

We get,

[tex]\frac{12x^4(x-3)}{30x(x+3)}[/tex],

Now,

On solving further,

We get,

[tex]=\frac{2x^3(x-3)}{5(x+3)}[/tex]

So, We can not solve it further,

So, This is the expression that is equivalent to the given expression.

Hence, we can say that the equation which is equal to the given expression is [tex]\frac{2x^3(x-3)}{5(x+3)}[/tex].

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The expression "select".substring(4, 4) will return an empty string, as the start and end indices are the same and no characters are included in the specified range.

The substring method in many programming languages, including Java and JavaScript, is used to extract a portion of a string between two specified indices. In the expression "select".substring(4, 4), we are asking for the part of the string starting at index 4 and up to, but not including, index 4. Since the start and end indices are the same, the method will return an empty string.

It's important to note that string indices are zero-based, meaning that the first character of the string is at index 0. The string "select" has six characters, with indices ranging from 0 to 5. Therefore, calling substring with identical start and end indices will not include any characters in the resulting string.

The distance around the bases in yards is 30 yards.

In order to determine the distance between each base in yards the unit of conversion of feet to yards have to be first determined. 1 foot is equivalent to 0.333333 yards.

1 feet = 0.333333 yards

The second step is to multiply the distance between each base by the unit of conversion.

Distance between each base x unit of conversion

90 x 0.333333

= 30 yards

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