The point P(-4, -5) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, P′?

Final answer:

By calculating the volume of the gold pyramid using the given mass and density of gold, and then applying the volume of a pyramid formula, we find that the dimensions of the square base are approximately 14.75 cm by 14.75 cm.

Explanation:

To find the dimensions of the base of the pyramid made out of pure gold, we need to calculate the volume of the gold pyramid using the known mass and density of gold then use that volume to find the base area and, consequently, the dimensions of the base.

The density (d) of gold is given as 19.32 g/cm³, and the mass (m) of the pyramid is 298.7 kg. First, we convert the mass from kilograms to grams (since the density is in grams per cubic centimeter):

m = 298.7 kg * 1000 g/kg = 298700 g

Next, we use the formula for density d = m/V to find the volume (V) of the gold pyramid. Rearranging the formula to solve for V gives:

V = m/d

V = 298700 g / 19.32 g/cm³

V ≈ 15461.8 cm³

Since the base of the pyramid is a square and the pyramid is 2.13 meters tall, we can use the volume of a pyramid formula V = (1/3) * base area * height to find the base area. We first convert the height from meters to centimeters:

height = 2.13 m * 100 cm/m = 213 cm

Now applying the pyramid volume formula and solving for the base area, we have:

base area = 3V / height

base area = 3 * 15461.8 cm³ / 213 cm

base area ≈ 218.2 cm²

To find the dimensions of the square base, we take the square root of the base area:

side length = √(base area) ≈ √(218.2 cm²) ≈ 14.75 cm

Therefore, the dimensions of the base of the gold pyramid are approximately 14.75 cm by 14.75 cm.

Answer:

1.0625 gallons of water was used by her.

Step-by-step explanation:

Mrs McDonald used [tex]4\frac{1}{4}[/tex] gallons of water to water her flowers.

She used [tex]\frac{1}{4}[/tex] of the water on her flowers daisies.

We have to calculate the gallons of water used by her to water daisies.

Let Mrs McDonald used G gallons of water to water the flowers daisies.

Then one fourth of [tex]4\frac{1}{4}[/tex] = G

[tex]G=(\frac{1}{4}).(\frac{17}{4})[/tex]

[tex]G=\frac{17}{16}=1.0625 gallons[/tex]

Therefore 1.0625 gallons of water she used on the daisies.

Yes,

probability = favorable outcomes/ total outcomes

to calculate the probability for this to occur, we use nCr ( nCr = n!/r!)

there are total 10 digits

so probability of the number 0000 appear in a table of random digits=

(1*1*1*1)/(10C1 * 10C1 * 10C1 * 10C1)

= 1/10000

The correct answer is B. Clothing is to lace. The analogy asks to draw a comparison between an object and a characteristic of that object, so filigree is to jewelry as lace is to clothing.

The correct answer is B. Clothing is to lace. This analogy asks you to draw a comparison between an object and a characteristic or feature of that object. In the case of 'JEWELRY is to FILIGREE', filigree is a detailed, intricate design often found in jewelry. Similarly, in 'Clothing is to lace', lace is a material often found in clothing and contributes to the design or style of the clothing piece, much like filigree does for jewelry.

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Final answer:

The question appears centered around solving an equation or a system of equations to find values of variables in their simplest form. Strategies include simplification, elimination, substitution, or using matrices, depending on the equation's complexity.

Explanation:

The question seems to have a typo or confusion in presenting the equation properly. However, based on the context provided later in the information, solving equations and finding solutions in simplest form appears to be the central theme. When solving equations or systems of equations, the goal is to isolate the variable (for a single equation) or to find the variable values that satisfy all equations (for a system). This process often involves steps like simplifying equations, eliminating variables, and utilizing methods like substitution, elimination, or using matrices.

For simpler equations, like in the form of ax + b = c, you would solve for x by isolating it: x = (c - b) / a. When dealing with systems of equations, each equation provides a piece of the puzzle, and solving them together reveals all variable values that satisfy the system. The strategy often depends on the complexity and format of the equations involved.

The mentioned solutions, x = 3 and x = -7, imply that the problem revolves around finding specific values that satisfy a given equation or system. To confirm these solutions, one would substitute them back into the original equations to ensure they do not violate any of the given conditions. This step is crucial to validate the results of the solving process.

Statistics is a branch of mathematics dealing with data collection, analysis, interpretation, and presentation, consisting of two main types: descriptive and inferential. Statistical models use probability distributions to describe expected behaviors and variability within observations.

About Statistics

The field of statistics is an essential discipline within mathematics that entails the collection, analysis, interpretation, and presentation of data. In our daily lives, we encounter data in various forms, which can be meticulously examined and understood through statistical methods. Two main types of statistics exist: descriptive statistics and inferential statistics. Descriptive statistics summarize and describe the features of a specific data set, providing a way to visualize data through graphs, charts, and summary measures like the mean and standard deviation. On the other hand, inferential statistics allow us to make predictions or inferences about a population based on a sample of data.

Statistical models are used to describe phenomena, utilizing probability distributions to account for the expected behavior and variability of observations. When researchers collect data, they often use a random sample to represent the larger population. A statistic is a numerical characteristic derived from the sample that helps estimate the corresponding population parameter, which is a characteristic of the entire population.

Statistics and probability are intertwined; as we gather and inspect data, we use statistical tools to distinguish good data from bad and create accurate predictions. Properly understanding and applying statistics can lead to more informed decisions in science, business, policy-making, and virtually every other field where data is essential.

Answer:

72

Step-by-step explanation:

The value of F when G equals 10 is 20.

The given problem states that F varies inversely with G. In other words, as G increases, F decreases, and vice versa. The inverse variation can be represented by the equation F = k/G, where k is a constant.

We are given that when G = 5, F = 40. To find the value of F when G = 10, we can use the equation F = k/G and substitute the given values.

F = k/5, and when F = 40, we have 40 = k/5. Solving for k, we get k = 40 x 5 = 200.

Now, we can substitute k = 200 and G = 10 into the equation F = k/G. F = 200/10 = 20.

The distance between Shereen and Eric is approximately 8.0623 feet.

To find the distance between Shereen and Eric, we can use the information given in the question. Since Haley and Shereen are 4 feet apart, and Eric and Haley are 7 feet apart, we can calculate the distance between Shereen and Eric using the Pythagorean theorem. Let's label the distance between Shereen and Eric as 'x'. Based on the information, we have a right triangle with one leg of 4 feet and the other leg of 7 feet. Using the Pythagorean theorem, we can calculate the hypotenuse, which is the distance between Shereen and Eric: x^2 = 4^2 + 7^2. Solving for 'x', we find that the distance between Shereen and Eric is approximately 8.0623 feet.

The distance between Shereen and Eric is 3 feet.

To find the distance between Shereen and Eric, we can use the given information about the distances between the dancers. Let's assume the distance between Shereen and Eric is 'd' feet. Since Haley and Shereen are 4 feet apart and Eric and Haley are 7 feet apart, we can set up the following equations:

To solve these equations, we can use substitution. Rearrange the first equation to isolate Haley: Haley = Shereen + 4. Substitute this expression for Haley in the second equation: Shereen + 4 - Eric = 7. Simplify the equation:

Shereen - Eric = 3.

So, Shereen and Eric are 3 feet apart.

The smallest number of new spools that Ted will need for this job is 8 spools of cable.

Given that, Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable.

We need to find the smallest number of new spools that Ted will need for this job.

A cylindrical device on which film, magnetic tape, thread, or other flexible materials can be wound; a reel.

Now, 60 meters per apartment x 12 apartments =720 total meters for all 12 apartments.

720 meters / 100 meters per spool =7.2 spools

so, Ted will need at least 8 spools of cable.

Therefore, the smallest number of new spools that Ted will need for this job is 8 spools of cable.

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Given is a rectangular rug that she wants to put it in the space of her bedroom.

Given is the area of the rug = 6 square meters.

Also the height of the rug is given = 2.5 meters.

It says to find the base of the rug, let's assume base = B meters.

We know the formula for area of the rectangular shape is given as follows :-

Area = Base x Height

6 square meters = B meters x 2.5 meters

[tex] B = \frac{6}{2.5} =\frac{60}{25} = 2.4 \;meters [/tex]

Hence, the base of the rug = 2.4 meters.

Answer:

2.4 meters. is the answer

Step-by-step explanation:

A ratio table organizes equivalent ratios, aiding in systematic plotting of points to graphically represent the relationships between different quantities.

A ratio table is a useful tool in graphing equivalent ratios by providing a systematic and organized way to identify corresponding pairs of values. To use a ratio table for graphing equivalent ratios, follow these steps:

Identify the Original Ratio:

Start with the given ratio or pair of values. For example, if the original ratio is 2:3, write this pair in the first row of the ratio table.

Generate Equivalent Ratios:

Expand the ratio by multiplying or dividing both parts by the same factor. For instance, if you multiply both parts of the original ratio by 2, you get an equivalent ratio of 4:6. Record these equivalent ratios in subsequent rows of the table.

Create an Ordered Pair:

Pair each value from the ratio table to create ordered pairs. For the ratio 2:3, the pairs would be (1, 1.5), (2, 3), (3, 4.5), and so on.

Plot the Points:

Use the ordered pairs to plot points on a coordinate plane. Each point represents a pair of equivalent values.

Connect the Points:

Draw a line or curve that passes through all the plotted points. This line represents the graph of the equivalent ratios.

By systematically generating equivalent ratios and plotting the corresponding points, a ratio table facilitates the visualization of patterns and relationships, helping in the creation of a coherent graph.

A ratio table is used to graph equivalent ratios by listing pairs of numbers that maintain the same product and graphing those pairs as points on a coordinate graph. These points should line up to form a straight line, indicating equivalent ratios. Understanding the reciprocal of the numbers is key in constructing a clear and accurate graph.

How to Use a Ratio Table to Graph Equivalent Ratios

A ratio table is a tool that helps us understand the relationship between quantities. It is particularly useful for visualizing equivalent ratios and can be used to graph these ratios. When you use a ratio table, you list pairs of numbers that form equivalent ratios. By selecting values that multiply to a constant number, such as 10, you ensure that the ratios are equivalent.

For instance, if the ratio is 2:5, we know that any other pair of numbers that multiplies to 10 (like 4:2.5, 1:5, or 5:2) will be equivalent to this ratio. Once you have a set of equivalent ratios, you can graph them by plotting the pairs of numbers as points on a coordinate graph. The resulting points should form a straight line, which represents the constant relationship between the two quantities.

To effectively use a ratio table and subsequently graph equivalent ratios, it is important to understand the concept of the reciprocal and how it relates to the ratios. For example, the reciprocal of 8 is thought of as '1.25-like', which means it shares a fundamental relationship (125) despite the actual placement of the decimal point. This approach aids in easily identifying the patterns in the ratios and transferring them to a graph.

Bar graphs are also a vital tool in comparing quantities across different categories. By employing bar graphs, you can visually compare the relationships between different sets of data, such as population sizes or the number of students falling into different categories. Effective use of colors, legibility, and orderly display are essential features to ensure clarity in bar graphs.

The number of left-handed students in the class is 3.

The problem involves understanding and solving a simple algebraic equation. From the problem, we know that the number of right-handed students is nine times the number of left-handed students. We can use 'x' to represent the number of left-handed students, meaning 9x represents the number of right-handed students. The total number of students is given as 30.

So, we set up the equation: x + 9x = 30. Simplifying this gives 10x = 30. Solving for 'x', we find x = 3. So, there are 3 left-handed students in the class.

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