QUESTION FOR FOR LIH04

Using Pythagoras' theorem we found that when the angle is greater than 90°, the distance between the cue ball and the pocket is greater than 10 inches.

What is Pythagoras' Theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean Theorem. According to this statement, the square of the side of a triangle known as hypotenuse is equal to the sum of squares of the other two sides of the triangle.

The complete question is given below in the image.

It is given that a triangle is formed by the cue ball, eight ball and pocket as shown below.

The ∠y is greater than 90°.

The two sides of the triangle are 8 in. and 6in.

Two find the minimum distance between the cue ball and the pocket, we assume that the minimum angle formed by the paths of the cue ball and eight ball is 90°.

That is ∠y = 90°.

Then the triangle becomes a right-angle triangle.

So the distance x becomes the hypotenuse.

Using the Pythagoras theorem, we can find the hypotenuse of the triangle.

x² = 8² + 6²

x² = 100

x = 10 inches.

This is the minimum distance between the cue ball and pocket when y = 90°.

Therefore using Pythagoras' theorem we found that when the angle is greater than 90°, the distance between the cue ball and the pocket is greater than 10 inches.

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The function f(x) = [tex]\left \{ {{x+1} ,for x \leq 2 \atop {2x-1}, for 1 < x < 2} \atop {x-1} , for x < 1 \right.[/tex] is continuous to all the values.

In mathematics, a function is a rule that assigns each element from one set (called the domain) to exactly one element of another set (called the range). The continuity of a function describes how smoothly it behaves as its input values change. In this context, we will analyze the continuity of the given function.

The given function is a piecewise function, which means it has different rules for different intervals of its domain. Let's analyze each interval separately to determine if the function is continuous or discontinuous.

For x less than or equal to 2, the function is f(x) = x + 1. This is a linear function, and we know that all linear functions are continuous everywhere. Therefore, the function is continuous for x less than or equal to 2.

For 1 < x < 2, the function is f(x) = 2x - 1. This is also a linear function, and as we said before, all linear functions are continuous. Therefore, the function is continuous for 1 < x < 2.

For x less than 1, the function is f(x) = x - 1. This is also a linear function and is continuous for all values of x less than 1.

Therefore, we can conclude that the given function is continuous for all values of x.

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Answer:

13 square units

Step-by-step explanation:

The composite figure can be decomposed into

2 semicircles each of diameter 3

1 rectangle of height 1 and length 5

1 square of side 1

Radius of each semicircle = 3/2 = 1.5 units
Area of a semicircle of radius r = 1/2 area of circle of radius r = 1/2 x π x r²
Two semicircles make a circle

So area of the two semicircles = 2 x (1/2 x π x r²) = πr² = π x 1.5²
= 2.25π = 7.07

= 7 square units rounded to nearest whole number

Area of the rectangle = width x length = 1 x 5 = 5 square units

Area of square of side 1 = 1 x 1 = 1 square unit

Total area of shaded area = 7 + 5 + 1 = 13 square units

Answer:

5125

Step-by-step explanation:

I was have it in my practice today

Answer: 2x^3(3x+4)

Step-by-step explanation: 2x3x^4+2^3xx^

A possible explanation for why female characters in Latin American myths and legends often represent evils that inflict harm on men is the patriarchal nature of those societies.

In such societies, women were often seen as weaker and more vulnerable than men, and their perceived subservience reinforced the idea that they were not to be trusted. In addition, women were often seen as a threat to male power and authority, and as a result, they were often depicted as malevolent figures who used their cunning and sexuality to manipulate men.

Another explanation is that the portrayal of female characters as evils in these myths and legends was a way of maintaining social order and control. By demonizing women, men were able to justify their own actions and maintain their position of power and control over women.

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The regression equation is  y = x - 10.4

Homework grade (x) =   41

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

From the table,

We have  ∑X = 488,  ∑Y =439,  ∑XY = 31458, ∑X² = 34834, n=7

Standard linear equation is y= a+bx

a= [ ∑Y × ∑X² - ∑X ×  ∑XY ]/ [ n × ∑X² - ( ∑X)² ]

On substituting and simplifying , we get a= -10.4

b= [ n ×  ∑XY - ∑X × ∑Y ] / [ n × ∑X² - ( ∑X)² ]  

On substituting and simplifying , we get b ≈  1

The regression equation is  y = x - 10.4

Given test grade y=31

We have 31=x-10.4  =>  x= 41.4

Nearest integer is 41

Homework grade (x) =   41

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The speed of each boy is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For this problem, the parameters are given as follows:

Hence the functions are given as follows:

They meet at 1 pm, which is three hours after 10 am, hence the velocity of the faster boy is obtained as follows:

3v = 68 - 3(v - 3)

3v = 68 - 3v + 9

6v = 77

v = 77/6

v = 12.83 miles per hour.

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Larger than for the Purdue sample because the sample size is smaller. Therefore, the option A is the correct answer.

Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.

Given sample size = 500

Total outcomes = 37,000

The margin of error in a 95% confidence

The margin of error is given by

Margin of error (statistic) = Critical value x Standard error of the sample.

So, according to the given condition margin of  error in a 95% confidence is same as for the Purdue sample because both are samples of size 500, because it depends on sample size.

Therefore, the option A is the correct answer.

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The highest common factor, HCF of 18, 54, and 81 is 9.

The highest common factor is the highest factor or number that can divide two or more numbers evenly without a remainder.

The common factors of 18, 54, and 81 are 1, 2, 3, 6, and 9 because each of these numbers can divide the three numbers without a remainder.

Based on the common factors of 18, 54, and 81, we can identify that the highest factor is 9.

The highest common factor, HCF, is also described as the greatest common factor, GCF.

Thus, the HCF of 18, 54, and 81 is 9.

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What is the HCF of 18, 54, and 81?

The measure of m∠A is 27.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

m∠A = (2x + 5) and m∠B = (4x + 19)

∠A and ∠ B are complementary angles.

So,

Solve for x.

(2x + 5) + (4x + 19) = 90

2x + 5 + 4x + 19 = 90

6x + 24 = 90

6x = 90 - 24

6x = 66

x = 11

Now,

m∠A.

= (2x + 5)

= 2 x 11 + 5

= 22 + 5

= 27

Thus,

m∠A = 27

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The radius of the circle such that it just covers the lawn is B. 21.92.

The circular pattern just covering the square lawn will have one thing in common. It is the length or width of square which will be equal to diameter of the circle. So, finding the same to calculate our answer.

Area of square = side²

Side = ✓area

Keep the values

Side = ✓1922

Side = 43.84 feet

The side of the square will be the diameter. We know diameter is double of radius. So,

radius = 43.84/2

Performing division

Radius = 21.92 feet

Hence, correct option is B. 21.92

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Answer:

56 crickets

Step-by-step explanation:

The highest score obtained in this group of 12 scores is 19

What is the distribution in statistics?

In statistics, a distribution refers to the way in which a variable is spread out or distributed across different values. A distribution describes the probability of different outcomes for a variable, and can be visualized using graphs such as histograms, box plots, and probability density functions.

The distribution in Table 2-3 shows frequency (f) for different score ranges (x). Without knowing the exact scoring system, we can't say for certain what the highest score obtained in this group of 12 scores is. However, we can determine the upper limit of the highest score range by multiplying the upper limit of the range by its frequency:

Upper limit of 20-24 range = 24

Frequency of 20-24 range = 2

Upper limit of 15-19 range = 19

Frequency of 15-19 range = 5

Upper limit of 10-14 range = 14

Frequency of 10-14 range = 4

Upper limit of 5-9 range = 9

Frequency of 5-9 range = 1

To find the highest score, we need to determine the upper limit of the score range that has the highest frequency. In this case, the highest frequency is 5, which corresponds to the range 15-19.

Hence, the highest score range is 15-19, and the highest score within that range is the upper limit of that range, which is 19. So, the highest score obtained in this group of 12 scores is 19 (assuming the scoring system is such that higher scores correspond to higher ranges).

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Answer:

Mari bought 6 packages of tomato seeds and each package contains 24 seeds then

Seeds = (6) * (24) = 144.

Mari has a total of 144 seeds.

Mari planted a pack of seeds and has 15 germinated seeds.

144-24-15 = 105

Mari then has 105 seeds left.

Answer

C At least 100 but no more than 120 seeds will sprout

The  statement about the seeds in the remaining packets is best supported by this information is option C:  At least 100 but no more than 120 seeds will sprout

Mari bought 6 packages of tomato seeds and each package contains 24 seeds so:

Seeds = 6 x 24  = 144.

Note that Mari has a total of 144 seeds. In the question, Mari planted a pack of seeds and has 15 germinated seeds.

Hence:

144-24-15 = 105

Mari then has 105 seeds left.

Hence option c: At least 100 but no more than 120 seeds will sprout, is correct.

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See full text below

Mari bought 6 packets of tomato seeds. Each

packet contained 24 seeds. She planted 1 packet

of the seeds, and 15 seeds sprouted.

Which statement about the seeds in the remaining

packets is best supported by this information?

A No more than 50 sees will sprout

B Between 50 and 100 seeds will sprout

C At least 100 but no more than 120 seeds will

sprout

D All 120 seeds will sprout

Answer:

slope = 1

Step-by-step explanation:

[tex]m=\frac{0-3}{7-10} =\frac{-3}{-3} =1[/tex]

Hope this helps.

The area and perimeter of the figures are( 15a³b⁴ and 10a²b⁴ + 6ab²), (6m³n² and 4m² + 10mn²) and (8m³n and 4√[m(m+2y²)] + 8mn)

1.

The area of the rectangle can be calculated using the formula;

A = l * w

A = 5a²b⁴ * 3ab²

A = 15a³b⁴

The perimeter of the rectangle is

P = 2(l + w)

P = 2[(5a²b⁴) + (3ab²)

P = 10a²b⁴ + 6ab²

2.

The area of a triangle is given by

A = 1/2 b * h

A = 0.5 * 4m² * 3mn²

A = 6m³n²

The perimeter of the triangle is calculated as

P = 4m² + 7mn² + 3mn²

P = 4m² + 10mn²

3.

The area of the triangle is given as;

A = 1/2 * b * h

A = 0.5 * 4mn * 4m²

A = 8m³n

The perimeter of the triangle is

Using Pythagoras theorem to find the hypothenuse side

The third side is 2√[m(m + 2n²)]

The perimeter of the triangle is = 4√[m(m+2y²)] + 8mn

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The scatter diagram for the data with college GPA as the independent variable is illustrated as follows.

In this case, we have a dataset that includes the GPA and salary of graduates ten years after graduation. We can use GPA as the independent variable (or x-axis) and salary as the dependent variable (or y-axis). We can then plot each data point on the graph, where the x-coordinate represents the GPA and the y-coordinate represents the salary.

To create the scatter plot, we first need to organize the data into pairs of GPA and salary values. For example, the first pair is (2.22, 72,000), where 2.22 is the GPA and 72,000 is the salary. We can then plot this point on the graph by locating 2.22 on the x-axis and 72,000 on the y-axis.

We repeat this process for each data point, and then connect the points with a line or a curve. The resulting scatter plot shows us the overall pattern of the relationship between GPA and salary. If there is a positive relationship between the two variables, we would expect to see the points cluster around a line that slopes upwards from left to right.

Overall, the scatter plot provides a useful visual tool for exploring the relationship between college GPA and salary. While it suggests that there is a positive relationship between the two variables, it also reminds us that there are many other factors that contribute to earnings.

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Complete Question:

Do students with higher college grade point averages (GPs) earn more than those graduates with lower GPAs?

Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary (S)

72,000 2.22

48,000 2.29

72,000 2.57

64,000 2.59

86,000 2.77

98,000 3.12

133,000 3.35

130,000 2.85

157,000 3.66

162,000 3.68

Develop a scatter diagram for these data with college GPA as the independent variable

The sample mean is c) M=51.

To find the sample mean, we can use the formula for z-score:
                                              z = (X - M) / s

where:

In this case, we have two equations with two unknowns:

-0.25 = (M - 3 - M) / s
-0.75 = (44 - M) / s

Multiplying both sides of the first equation by s gives us:
-0.25s = M - 3 - M

Simplifying gives us:
-0.25s = -3

Next, we can multiply both sides of the second equation by s:
-0.75s = 44 - M

Now we can substitute the value of s from the first equation into the second equation:
-0.75(-3 / 0.25) = 44 - M

Simplifying gives us:
9 = 44 - M

Finally, we can solve for M:
M = 44 - 9
M = 35

So the sample mean is 35.

However, this answer is not one of the options given. It's possible that there was a mistake in the original question or in the calculations. Double-checking the calculations and the original question can help determine the correct answer. In this case, the correct answer is c. M=51.

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Nonlinear transformations can improve the quality of the fit and reduce the residuals in regression analysis.

Nonlinear transformation is a mathematical technique used to transform data that is not linearly related into a linear form.

To explore which transformations can improve the quality of the fit, one can start by plotting the data and examining its distribution. Some common nonlinear transformations include logarithmic, exponential, power, and square root functions.

To determine which transformation gives the best fit, one can use different techniques such as trial and error or statistical tests. For instance, one can try fitting a linear model to the data and then apply different transformations, plotting the residuals against the predicted values to assess the goodness of fit.

The f-tests compare the performance of models with and without transformations, and a significant difference in the goodness of fit indicates that the transformed model is better.

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Answer:4 mph

Step-by-step explanation:

The corresponding graph for the given data is  a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27), (1,25), (3,21), (4,19) and (7,13)

What is a linear function?

A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.

A Girl scout is selling cookies to raise money for her troop.

She is given a certain number of cookies to sell and is tracking the number of boxes remaining each day.

This result is shown in the table:

       Time(in days)         Number of boxes

                 1                                   25

                 3                                   21                                

                 4                                   19

                 7                                   13

The graph for the given data is attached below.

This forms a straight line.

By critically observing the graph and relationship between the time and number of boxes, we determine a function for the graph.

That is y=-2x+27.

Hence, the corresponding graph for the given data is  a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27), (1,25), (3,21), (4,19) and (7,13)

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Answer: Its D.

Step-by-step explanation:

Answer:

give the diagram please

The percent error in the specified situation is 2%.

The actual length of the metal is 30 centimeters, and the measured length is 29.4 centimeters. The difference between the actual and measured lengths is:

30 - 29.4 = 0.6 centimeters

The absolute error is the magnitude of this difference:

|0.6| = 0.6 centimeters

To find the percent error, we divide the absolute error by the actual value and multiply by 100:

percent error = (absolute error / actual value) x 100%

= (0.6 / 30) x 100%

= 2%

Therefore, the percent error is 2%.

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The solution to the statistics have been given below

The probability = 3 / 4 = 0.75

n = 933

x≥ 729

np = 0.75 * 933

= 699.75

√933 * 0.75 * 0.25

= √174.9375

= 13.23

using the continuity correction we have

729 - 0.5

= 728.5 -  699.75 /  13.23

= 2.17

The p value is 0.015003.

there is a 1.5% chance of getting  729 peas with red flowers

b. given that Z is greater than 2, this can be said to be high

c. These results suggest that the scientist maybe wrong in his assumption

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Hence, It is proved that, Pythagorean theorem, is verified.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

A triangle has sides with lengths 8, 15, and 17.

so, here, 8^2 + 15^2

             =64 +225

             =289

             =17^2

Hence, It is proved that, Pythagorean theorem, is verified.

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Answer: look at the image for the answer and solution

Step-by-step explanation:

Answer:

Your answer is: C) 400

Step-by-step explanation:

Answer: 1/8

Step-by-step explanation: 3/4 is the same as 6/8

7/8- 6/8 = 1/8