Solve the following simultaneous equations using an algebraic method.
4x - 7y = 15
5x - 2y = 12

The probability of having fifth tail occurring before the tenth head if a fair coin is flipped repeatedly is 0.377.

To solve this problem, we need to use the concept of negative binomial probability distribution.

The negative binomial probability distribution is a type of probability distribution that is used to describe the probability of k failures occurring before r successes in a sequence of independent and identical trials.

Let us consider the problem at hand.

We need to find the probability that the fifth tail occurs before the tenth head if a fair coin is flipped repeatedly.

Let X be the number of trials required to obtain the fifth tail. Then, X follows a negative binomial distribution with parameters r = 5 (number of successes we want) and p = 0.5 (the probability of obtaining a tail in a single flip).

The probability of obtaining the fifth tail on the kth trial is given by: P(X = k) = ᵏ-¹C₄(1 - p)ᵏ-ʳ *

where ᵏ-¹C₄ denotes the number of combinations of (k - 1) trials that yield 4 tails before the kth trial.

Since X should occur before the tenth head, k should be less than or equal to 9.

Therefore, we can calculate the required probability as follows:

P(X ≤ 9) = ∑P(X = k) for k = 5 to 9

= (⁴C₄*0.5⁵) + (⁵C₄*0.5⁶) + (⁶C₄*0.5⁷) + (⁷C₄*0.5⁸) + (⁸C₄*0.5⁹)

= (1*0.03125) + (5*0.015625) + (15*0.0078125) + (35*0.00390625) + (70*0.001953125)

= 0.376953125

Therefore, the probability that the fifth tail occurs before the tenth head if a fair coin is flipped repeatedly is 0.377.

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Answer:

(4 + 3) x 2

Step-by-step explanation:

In one day, Vesi would snowboard 4+3 hours, so in two days, we would multiply this by two and get the expression (4+3) * 2.

Answer:

Thursday morning temperature was -4 degrees Celsius.

Thursday afternoon temperature dropped by 3 degrees.

So Thursday afternoon's temperature was:- -4 - 3 = -7

On Friday, the temperature had risen by 5 degrees Celsius

So -7 + 5 = -2 degrees Celsius

Robyn has 4 important files saved on her computer.

To solve this problem, we can use a simple formula that relates the total space occupied by the files to the size of each file:

Total space occupied = Size of each file x Number of files

In this case, we know the total space occupied (84.6 megabytes) and the size of each file (21.15 megabytes), so we can rearrange the formula to solve for the number of files:

Number of files = Total space occupied ÷ Size of each file

Plugging in the values we know, we get:

Number of files = 84.6 megabytes ÷ 21.15 megabytes per file

Simplifying this expression gives us:

Number of files = 4

Therefore, Robyn has 4 important files saved on her computer.

It's important to note that this problem assumes that each file uses exactly 21.15 megabytes of memory. In reality, file sizes can vary depending on their content, so this may not always be the case. Additionally, it's worth noting that file size can be affected by various factors such as compression and encoding, so the actual size of a file on disk may differ from its theoretical size. Nonetheless, for the purposes of this problem, we can assume that each file uses exactly 21.15 megabytes of memory.

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The type of distribution which is utilized for the nominal data is option  b. Binomial distribution.

The appropriate distribution for nominal data is a binomial distribution.

The binomial distribution is used when the data consists of two possible outcomes.

The two outcomes such as success or failure, heads or tails, or pass or fail.

In nominal data, the categories do not have any inherent order.

And there is no numerical value associated with each category.

The binomial distribution gives the probability of obtaining a certain number of successes in a fixed number of independent trials.

The required probability of success is the same for each trial.

Therefore, option b.  binomial distribution is considered as more appropriate distribution for the nominal data.

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When the bottom of the 6-foot ladder is 2 feet from the wall, the bottom is moving along the ground at 1 foot per second.

To find the rate at which the bottom of the ladder moves along the ground, we can use the Pythagorean theorem and related rates. Let x be the distance from the bottom of the ladder to the wall, and y be the height of the ladder on the wall. The Pythagorean theorem is x² + y² = 36.

Differentiating both sides with respect to time (t) gives 2x(dx/dt) + 2y(dy/dt) = 0. We are given that dy/dt = -2 ft/s, and we need to find dx/dt when x = 2 feet.

To find y, we can use the Pythagorean theorem: 2² + y² = 36, so y² = 32, and y = 4√2. Plugging these values into the differentiated equation, we get 2(2)(dx/dt) + 2(4√2)(-2) = 0. Solving for dx/dt, we find that dx/dt = 1 ft/s.

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Answer:

it is 146  i no what work your doing i do i

Answer:

second that -x is the correct answer

Answer:

3. 75.4 and 4. 113.1

Step-by-step explanation:

Okay to find the volume of the cylinder the equation is πr⌃2h

3. so if H is 1.5 and r = 4 it would be π4⌃2(1.5) = 75.4 approx.

4. If h is 4 and r is 3 it would be π3⌃2(4) = 113.1 approx.

Answer:82.13

Step-by-step explanation: you break it down into different shapes then add it.

Semi circle-a=pie times radius squared. radius is 3 so 3 squared is 9 and you multiply that by pie which is 28.26 and half is 14.13.

rectangle=6times 6=36

rectangle=14 times 3=32

add that all up and you should get 82.13

Values of x for blanks 4 , 1 in inequality .

What in mathematics is an inequality number?

A relationship between two values in an algebraic statement that are not equal is shown by an inequality. One of the two variables on the two sides of the inequality can be represented by an inequality sign as greater than, greater than or equal to, less than, or equal to another value.

                              Despite the equals sign being substituted by an arrowhead, the formula 5x 4 > 2x + 3 resembles an equation. It serves as an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.

-3x/4 < 12/1

x < -16

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By consulting these tables, you can quickly access important data and information that can help you better understand the Earth and its various processes.

Sure, I'm happy to help! Without seeing the actual table, I'm not sure what information you are looking for specifically. However, I can tell you that Earth Science reference tables often contain important information about the Earth's systems, including geology, meteorology, oceanography, and astronomy.

For example, these tables might include information on rock types, mineral identification, weather patterns, ocean currents, and celestial objects like planets and stars. They may also provide key equations and constants for various scientific calculations.

In general, Earth Science reference tables are a valuable resource for students, researchers, and professionals in the field.

If you have a specific question about the table you're looking at, feel free to let me know and I'll do my best to provide a helpful answer!

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Each of the residual plots indicates the appropriateness of the linear model that was fit to the data. The appropriate answer for residuals plot (a) is: the fanned pattern indicates that the linear model is not appropriate.

The model's predicting power decreases as the values of the explanatory variable increase.

A residual is the difference between the actual y value and the predicted y value, which is determined by the regression equation or linear model. A scatterplot of residuals is often used to evaluate the appropriateness of a linear model in a regression analysis, as well as to check for other things like non-linear relationships or non-constant variance.

Residuals scatterplots assist in detecting various types of patterns or lack of patterns that may be present in data. Patterns in a residual plot indicate that the linear model does not fit the data well, whereas the lack of pattern in a residual plot indicates that the linear model is appropriate.In this problem, the residual plot (a) has a fanned pattern. This means that the linear model is not appropriate. Furthermore, the model's predicting power decreases as the values of the explanatory variable increase. This means that the model may overestimate or underestimate the response variable as the values of the explanatory variable rise.

Therefore, we can conclude that the fanned pattern on residual plot (a) indicates that the linear model is not appropriate.

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Answer:

3

Step-by-step explanation:

you want to flip your slope so the 3 goes over the 1 like this: 3/1

And then flip the sign so the negative turns to a positive

The test has average  80 true/false questions, 24 fill in the blank questions, and 28 multiple choice questions, with 7, 9 and 13 points respectively, totaling 1172 points.

The college entrance test consists of 112 questions in total, with different types of questions having different point values. There are 80 true/false questions, each worth 7 points, with a total of 560 points from these questions. There are also 24 fill in the blank questions, each worth 9 points, giving a total of 216 points from these questions. Finally, there are 28 multiple choice questions, each worth 13 points, for a total of 364 points from these questions. All together, the test has 1172 points available. The number of fill in the blank questions is 34 less than the number of true/false questions, meaning that there are more true/false questions than fill in the blank questions. The test is designed to assess a student's knowledge and comprehension of the subject they are taking the test for, and is made up of the three different types of questions to give a comprehensive assessment of their understanding.

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The value of x is 6m. Polygons can be regular or irregular, depending on whether all their sides and angles are congruent or not.

To find the value of x in the similar polygons shown in the figure, we can use the fact that corresponding sides of similar polygons are proportional. A polygon is a two-dimensional closed shape with three or more straight sides and angles. It is formed by connecting consecutive line segments, which are called sides, at their endpoints. The point where two sides of a figure meets is called a vertex. A polygon can have any number of sides, but it must have at least three. Polygons include triangles, quadrilaterals, pentagons, hexagons, and many more.

Since the polygons are similar so, the ratio of sides will be equal:

[tex]\frac{5}{10} = \frac{x}{12}[/tex]

x = 6 m.

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Therefore, the area of the pentagon is 928 square units.

Length is a measure of the size or extent of an object or a distance between two points. It refers to the longest dimension of an object or the distance between two points in space, typically measured in units such as inches, centimeters, meters, or miles. In mathematics, length is also used to describe the size of a line segment or a curve, which can be measured using various techniques such as Euclidean distance, arc length, or fractal dimension. Length is an important concept in many fields, including physics, engineering, geometry, and statistics.

Find the area.

Pentagon

apothem = 16 side = 23.2

Note: When necessary, enter your answer as a decimal If it is not a terminating decimal, round to the nearest hundredth

For the first question, we need more information to find the area of the triangle. Knowing the apothem and one side is not enough. We also need to know the number of sides of the triangle or the length of another side or the height.

For the second question, the formula to find the area of a regular pentagon is:

Area = (perimeter x apothem)/2

Since we are given the apothem and the side, we can find the perimeter of the pentagon as:

perimeter = 5 x side = 5 x 23.2 = 116

Substituting the values in the formula, we get:

Area = (116 x 16)/2 = 928

Therefore, the area of the pentagon is 928 square units.

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The percent increase in players from last year to this year = 20%

We know that the formula for the percentage change a quantity is :

(P) = [Final value - Initial value] / Initial value x 100

Here, a baseball team had 80 players show up for tryouts last year and this year 96 show up for tryouts.

initial number of players = 80

current number of players = 96

So, using above formula the percent increase in players is:

P = [(96 - 80) / (80)] x 100

P = (16 / 80) x 100

P = 0.20 x 100

P = 20%

Therefore, the percentage of increase in players =  20%.

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The measure of angle CED in a circle is  212°

The measurement of angles is done using basic geometric tools such as protractors and compasses. This tool helps to find precise measurements of angles. A protractor helps provide accurate measurements of angles, while compasses help construct angles. Angles are measured in three ways: degrees, radians, and revolutions.

In the given figure:

∠ EBD = 160°

and ∠ CBE = 52°

We have to tell the measure of arc CED.

Since  m( arc EBD) = 160° and m( arc CBE ) = 52°

From the figure:

m( arc CED ) = m( arc CBE ) + m( arc CBE)

= 160° + 52°

= 212°

Therefore, measure of angle CED = 212°.

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Using the probability multiplication we know that the defect probability of the final product will be 7.5%.

Simply put, the probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

The higher the likelihood, the more likely it is that the event will take place.

So, the probability formula is:

P(E) = Favourable events/Total events

So, in the given situation, the number of components integrated:

500

Defect probability of each component:

0.015%

Then, the defect probability of the final product:

= 500 * 0.015

= 7.5%

Therefore, using the probability multiplication we know that the defect probability of the final product will be 7.5%.

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The expression -(12 x - 6) + 18 is not equivalent to the other expressions.

Expression is a combination of words or symbols that communicate an idea, thought, opinion, or feeling. Expressions can be literal or figurative, and they often contain multiple layers of meaning. Expressions can be used to express emotions, opinions, beliefs, and values, and they are integral to communication and understanding.

This is because when all of the expressions are evaluated, the result of each expression is different. For example, when the expression -6(2 x - 4) is evaluated, the result is -24.

When the expression -4(3 x + 6) is evaluated, the result is -24. When the expression -3(4 x - 3) + 15 is evaluated, the result is -3. However, when the expression -(12 x - 6) + 18 is evaluated, the result is 12.

Therefore, the expression -(12 x - 6) + 18 is not equivalent to the other expressions.

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Complete questions as follows-
Which expression is not equivalent to the other expressions?
-6(2 x - 4)
-4(3 x + 6)
-(12 x - 6) + 18
-3(4 x - 3) + 15

Answer:

-39

Step-by-step explanation:

I cannot provide picture, but plug 10 in for x for both equations

-4(10)+1 = -39         -39 less than 3? yes

2/5(10)-3 = 1       1 is greater than or equal to 3? no

the value of y when f(10) is -39

since when you plug 10 in for x -39 is the result

Step-by-step explanation:

the general equation of a parabola is

y = a(x – h)² + k.

(h, k) is the vertex of the parabola.

comparing it to

y = 3(x + 4)² - 2

we see that (h, k) = (-4, -2).

the student made a sign mistake. it is "- h" in the squared factor. so, "+4" indicates "-4" as "h".

but the student simply used "+4".

Answer:

Similar: SAS

Step-by-step explanation:

The triangles are not congruent( they're not the equal) but the are similar because they form vertical angles that are congruent and their corresponding side lengths are in proportion

The area of the dilated triangle is 45 squared meters

Dilation is a geometric transformation that involves resizing a shape while maintaining its shape and proportions. The scale factor is the ratio of the size of the image to the size of the original shape.

In this problem, we are given a triangle with an area of 5 cm², and we are asked to find the area of the dilated triangle when it is scaled up by a factor of 3. To find the area of the dilated triangle, we need to use the formula for the area of a triangle, which is 1/2 * base * height.

When a triangle is dilated by a scale factor of k, both its base and height are multiplied by k. This means that the area of the dilated triangle is k^2 times the area of the original triangle. In this case, the scale factor is 3, so the area of the dilated triangle is 3^2 times the area of the original triangle.

Therefore, the area of the dilated triangle is 9 times the area of the original triangle, which is 9 * 5 cm² = 45 cm².

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The expected winnings for a ticket buyer is $0.8036.

The given details are:

Grand prize = $9000

Second prize = $1300

Cost of each ticket = $3

Total tickets sold = 11200

Expected winnings are calculated by finding the expected value. Expected value is calculated by multiplying each outcome by its probability and then adding the products.

The total amount collected from selling 11200 tickets will be:

Total amount collected = 11200 × $3 = $33,600

Probability of winning grand prize = 1/11200

Probability of winning second prize = 1/11200

Probability of losing = 1 - (1/11200 + 1/11200) = 1 - 2/11200 = 11200/11200 - 2/11200 = 11198/11200

Expected value = probability of winning grand prize × grand prize + probability of winning second prize × second prize + probability of losing × zero

Expected value = (1/11200) × $9000 + (1/11200) × $1300 + (11198/11200) × 0 = $0.8036

The expected winnings for a ticket buyer is $0.8036.

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Government benefit programs have been established for a range of assistance over time.

What is context of above answer?

The answer given was "Government benefit programs have been established for a range of assistance." This sentence is referring to various programs created by the government to provide support or aid to those in need.

These programs may include financial assistance, food assistance, housing assistance, medical assistance, and more. The sentence suggests that the government recognizes the importance of providing help to individuals and families who may be struggling and has taken steps to create programs to address these needs.

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Complete Question:

What types of assistance have government benefit programs been established for?

The equation of the line parallel to y = -3x + 7 and passing through the point (2, -1) is y = -3x + 5, written in slope-intercept form.

The given equation is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

The slope of the given equation is -3, which means any line parallel to it will have the same slope.

Using the point-slope form of a linear equation, we can write the equation of the line passing through the point (2, -1) and having a slope of -3:

y - y1 = m(x - x1) where (x1, y1) = (2, -1) and m = -3

y - (-1) = -3(x - 2)

y + 1 = -3x + 6

y = -3x + 5

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