A video game store was getting rid of old games, selling them 5 for $102.05. If they sold 3 games, how much money would they have made?

The statements 'all squares are similar' and 'all equilateral triangles are similar' is true among the given statements.

Similar shapes refer to shapes with the same angles but sides of varying magnification. We can also say the ratio in dimensions of corresponding sides is in proportion.

In the case of isosceles triangles, the angles of each triangle can be unique and to say the sizes are in proportion to each other might not be true for every case. Thus, we can't say that all isosceles triangles are similar to each other.

In the case of rectangles, though the angles of each rectangle are equal and are 90°, to say the sizes are in proportion to each other might not be true for every case as the length and breadth may vary without any proper ratio. Thus, we can't say that all rectangles are similar to each other.

In the case of squares, the angles of each side of the square are equal and are 90°, and since all sides are equal to each other, the sides are also in proportion. Thus, we can say that all squares are similar to each other.

In the case of equilateral triangles, the angles of each side of an equilateral are equal and are 60°, and since all sides are equal to each other, the sides are also in proportion. Thus, we can say that all equilateral triangles are similar to each other.

In the case of right triangles, only one of the angles of each triangle is equal and is 90°, to say the sizes are in proportion to each other might not be true for every case as each side may vary without any proper ratio. Thus, we can't say that all right triangles are similar to each other.

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The solution to the expression 4+(−634) is -630

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

4+(−634)

Rewrite the expression properly

So, we have the following representation

4 + (−634)

Remove the bracket in the above expression

This gives

4 + (−634) = 4 - 634

Evaluate the difference

4 + (−634) = -630

Hence, the solution is -630

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A discrete random variable, x, represents the total number of motorbike accidents that occurred in California for a given year. Correct option is A.

A discrete random variable has gaps between each of its countable possible values. Since motorcycle accidents are discrete occurrences that can be counted, the total number of motorcycle accidents in this situation can only be a non-negative whole integer (0, 1, 2, 3,...).

On the other hand, continuous random variables can have an endless number of values inside a range or interval. They often reflect quantities like height, weight, or time, which can all fall within a certain range of values.

Motorcycle accidents have a variable x that can only take on whole numbers (e.g., 1.5 accidents), thus fractional or non-integer values for the number of accidents are meaningless. The random variable x is therefore regarded as discrete.

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Step-by-step explanation:

All you need to do is divide 1.20 by 5 (which is 0.24) then you can multiply that by 6 to get 1.44 or you can just add the 0.24 to 1.20

Answers:

Pt A- 0.24

Pt B- 1.44

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

If there is a low supply and a high demand, there is an increase in price and vice versa.

Last 2012, there was a virus which infected millions of chicken. It was known as Avian influenza or bird flu. It resulted to scarcity of eggs.

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

For example we can use water. If a product becomes scarce its price would increase due to supply in demand.

If drinkable water became scarce its price would be greatly increased to its need and being in extreme demand.

In short,  if there is a low supply and a high demand, there is an increase in price and vice versa.

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To find out the area of a rectangle, you multiply the length by the width.

18 x 25 = 250

Answer: 450 m²

Answer:

18 x 25 = 250

Answer: 450 m²

Step-by-step explanation:

Jev doesn't know you I am sorry...

Hypotheses are used to make predictions about data. They help identify what the data analyst wants to confirm or disprove.

Supervisor asks Junior Data Analyst to present her two hypotheses for a data analysis project.

We must explain the purpose of your hypothesis.

In other words, a type of statistical inference called

hypothesis testing uses data from a sample to infer population parameters or population probability distributions. First, an educated guess is made about the parameter or distribution.

Here, the hypothesis goal is to make inferences about the

data. Data analysts use them to decide what to prove or disprove.

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Answer:

yes

Step-by-step explanation:

For a relation to be a function each value of x in the domain must map to exactly one unique value of y in the range.

Since the relation is a straight line , then each value of x will only map to one unique value of y ( passes the vertical line test )

Answer:

119 g.

Step-by-step explanation:

11 cm has a mass of 187 g

So 1 cm has a mass of 187/11 g

7 cm ...............................  (187/11) * 7

= 17 * 7

=  119 g.

The normal price of the car on the basis that the sale price of the car was £7500 is £10,000.

The fact that the normal prices are reduced by 25% means that the actual price paid eventually is 75%, which is 100% minus discount of 25%, hence, the actual price of £7500 paid eventually represents 75% of normal price

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The schedule for the number of hours worked by employees at Waterloo Park is represented by the functions b(x), t(x), r(x), and s(x) for Bill, Ted, Rufus, and Socrates, respectively, on a given day x.

In the schedule, the function b(x) represents the number of hours worked by Bill on a given day x. Similarly, the function t(x) represents the number of hours worked by Ted, the function r(x) represents the number of hours worked by Rufus, and the function s(x) represents the number of hours worked by Socrates on the same given day x.

By using these functions, you can determine the specific number of hours each employee worked on any given day. For example, if you have a value for x, you can substitute it into the functions to find the corresponding number of hours worked by each employee.

It's important to note that the functions b(x), t(x), r(x), and s(x) are specific to Waterloo Park and the employees mentioned. The given schedule provides a way to track the hours worked by each employee on different days. By utilizing these functions, you can analyze and calculate the hours worked by each employee effectively.

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a. Using the information in the survey in PARADE magazine, the null hypothesis is H0: p = 0.15 while the alternative hypothesis is Ha: p < 0.15

b. From the test statistics result, the null hypothesis is rejected and we conclude that there is sufficient evidence that the proportion of parents who describe their children as overweight is less than that reported by American obesity association

c. The p-value is approximately 0.0006.

The null and alternative hypotheses are

H0: p ≥ 0.15 which means that the proportion of parents who describe their children as overweight is greater than or equal to 0.15 while Ha: p < 0.15  means the proportion of parents who describe their children as overweight is less than 0.15.

To test this hypothesis, use z-test for the proportion.

Significance level = 0.05

The test statistic is:

\(z = (x - np0) / \sqrt(np0(1-p0))\)

where

x is the number of parents who describe their children as overweight (x = 70),

n is the sample size (n = 700)

p0 is the hypothesized proportion under the null hypothesis (p0 = 0.15)

np0 = 105 is the expected number of parents who describe their children as overweight under the null hypothesis.

Plug in the values

\(z = (70 - 105) / \sqrt(105*0.85) = -3.25\)

The rejection region for a one-tailed test with a significance level of 0.05 is z < -1.645.

Since -3.25 is less than -1.645, we reject the null hypothesis and conclude that there is sufficient evidence that the proportion of parents who describe their children as overweight is less than that reported by American obesity association.

The p-value

Since this is a one-tailed test with a null hypothesis of p ≥ 0.15, the p-value is the area to the left of the observed test statistic in the standard normal distribution.

Using standard normal table, the p-value is approximately 0.0006.

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The question is incomplete, find the complete question below.

According to the survey in PARADE magazine, almost half of the parents say their children weight is fine. only 9% parents describe children as overweight. However, the American obesity association says that the number of over weight children and teen is at least 15%. suppose that you sample n = 700 parents and the number who describe their children as overweight is x = 70. (a) how would you test the hypothesis that the proportion of parents who describe their children as overweight is less than the actual reported by the American obesity association. State the null and alternative hypotheses.

H₀:p =0.15 versus Hₐ :p<0.15

H₀ :p=0.15 versus Hₐ:p>0.15

H₀:p=0.09 versus Hₐ:p<0.09

H₀:p=0.15 versus Hₐ:p<0.15

H₀:p=0.09 versus Hₐ:p>0.09

test statistic z= rejection region z> (b) What conclusion are you able to draw from these data at the α=0.05 level of significance? (c) What is the p-value associated with this test? (Round your answer to four decimal places.)

Answer:

Clay

Step-by-step explanation:

Clay soil has small, fine particles, which is why it retains the most amount of water. Sand, with its larger particles and low nutritional content, retains the least amount of water, although it is easily replenished with water. Silt and loam, with medium-size particles, retain a moderate amount of water.

The unit rate refers to the slope of the line which passes through the given points. So, we need to find the slope with the following formula

We are going to use points (4,5) and (8,10).

Therefore, the unit rate is 5/4.

An interpretation of this unit rate is: while the vertical coordinate varies 5 units, the horizontal coordinate varies 4 units.

The graph K must represent an investment that was compounded continuously because investments that are compounded continuously increase at a faster rate than investments that use either simple interest or are compounded monthly.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

\(A(t) = P_{0}e^{rt}\)

Where:

By critically observing the given graph, we can reasonably infer and logically deduce that the graph with line K represent an investment that was compounded continuously because the principal (initial amount of money) increases at a faster rate

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x = 2

y = -1

Step-by-step explanation:

x² + y = 3      --------------------(i)

x² = 3 - y

x² - y = 5 ---------------------(ii)

substitute x² = 3 - y in equation (ii)

x² - y = 5

3 - y -y = 5        {Add like terms}

3 - 2y = 5              {Subtract 3 from both sides}

3 - 2y -3 = 5 - 3

-2y = 2             {divide both sides by -2}

-2y/-2 = 2/-2

y = -1

Substitute the value of y in equation (i)

x² + y = 3

x² - 1= 3         {Add  1 to both sides}

x² - 1 + 1 = 3+ 1

x² = 4

x = √4

x = 2

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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The component form of the resultant vector is `(0, 0)`. The `x` and `y` components of this vector are both zero, indicating that the resultant vector is a zero vector.

The problem at hand asks us to calculate the component form of the vector obtained by summing up the vectors `ab` and `cd`. Let's begin by calculating these two vectors individually as follows: `ab

= b - a

= (2 - 1, 0 + 1)

= (1, 1)` and `cd

= d - c

= (-2 + 1, 2 - 3)

= (-1, -1)`.Next, we'll add these two vectors to obtain their resultant vector, as follows: `ab + cd

= (1, 1) + (-1, -1)

= (0, 0)`.The component form of the resultant vector is `(0, 0)`. The `x` and `y` components of this vector are both zero, indicating that the resultant vector is a zero vector.

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Step 1

Rearrange the equation

Step 2

Test all options by rearrangement

Option A

Option B

Option C

Option D

Hence, the equivalent options to the equation are options B and C

The particular solution to the given differential equation is

y_p(t) = sin(10t)

A particular solution to the differential equation using the Method of Undetermined Coefficients, we assume a particular solution of the form

y_p(t) = A sin(10t) + B cos(10t)

where A and B are undetermined coefficients that we need to determine.

Now, let's find the first and second derivatives of y_p(t):

y'_p(t) = 10A cos(10t) - 10B sin(10t) y''_p(t) = -100A sin(10t) - 100B cos(10t)

Substituting these derivatives into the original differential equation, we have:

(-100A sin(10t) - 100B cos(10t)) - (10A cos(10t) - 10B sin(10t)) + 100(A sin(10t) + B cos(10t)) = 10 sin(10t)

-100A sin(10t) - 100B cos(10t) - 10A cos(10t) + 10B sin(10t) + 100A sin(10t) + 100B cos(10t) = 10 sin(10t)

The terms with sin(10t) and cos(10t) cancel out, and we are left with

-10A cos(10t) + 10B sin(10t) = 10 sin(10t)

Comparing the coefficients of sin(10t) and cos(10t), we have

-10A = 0 (coefficient of cos(10t)) 10B = 10 (coefficient of sin(10t))

From the first equation, we find A = 0. From the second equation, we find B = 1.

Therefore, the particular solution to the given differential equation is

y_p(t) = sin(10t)

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Answer:

The answer is -7, or x = -7.

The required simplified solution of the given expression is 8√3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
=  2 √ 3 + 2 √ 27

Since √27 = 3√3
= 2√3 + 2× 3√3
= √3 [2 + 6]
= √3[8]
= 8√3

Thus, the required simplified solution of the given expression is 8√3.

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Answer:

C - LA = 2πrh

Step-by-step explanation:

Lateral surface area of right cylinder = 2 * π * radius * height

The resulting LCL for the three-sigma R-chart is approximately 8.08.

To determine the lower control limit (LCL) for a three-sigma R-chart, we need to calculate the control limits using the average range and the appropriate factors. In this case, the average range is given as 14.

The control limits for an R-chart can be calculated using the formula:

LCL = D3 * Average Range

For a three-sigma R-chart, the factor D3 is 0.577.

Substituting the values into the formula, we get:

LCL = 0.577 * 14

LCL ≈ 8.08

Therefore, the resulting LCL for the three-sigma R-chart is approximately 8.08.

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The graph is a disjoint collection of isolated vertices.

If all the entries in the ith row and ith column of the adjacency matrix of a graph are 0 for every positive integer i, we can conclude that the graph is a disjoint collection of isolated vertices.

In a graph, the adjacency matrix represents the connections between vertices. Each row and column in the adjacency matrix corresponds to a specific vertex in the graph.

A non-zero entry in the matrix indicates an edge between two vertices, while a zero entry indicates no edge.

If all the entries in the ith row and ith column are 0, it means that the vertex corresponding to that row/column is not connected to any other vertex in the graph.

In other words, each vertex is isolated and not connected to any other vertices.

Therefore, when all entries in every row and column of the adjacency matrix are 0, the graph consists of isolated vertices, and there are no edges connecting them.

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Given that e1 and e2 have a high spearman correlation, what we can say about the Pearson correlation of e1 and e2 is; The Pearson correlation must be high

A correlation coefficient is defined as the measurement of the extent to which two variables tend to change together.

Now, the Pearson correlation is the type that evaluates the linear relationship that exists between two continuous variables. A relationship is said to be linear as a result of a change in one variable being associated with a proportional change in the other variable.

Meanwhile, the spearman correlation is one that evaluates the monotonic relationship between two continuous or ordinal variables.

If the relationship described above tells us that one variable increases when the other increases, but then the amount is not consistent, then it means that the Pearson correlation coefficient is positive but less than +1. However, the Spearman coefficient still equals +1 in this case.

Thus, we conclude that as the spearman correlation is high, then the Pearson correlation is also high.

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