Please write linear equation in standard form

2y=8

The experimental probability of each event is as follows:

The experimental probability of an event is the ratio of the number of outcomes that favored the event to the total number of outcomes in the experiment.

In the question, we are given that Jake tossed a paper cup 50 times and recorded the position how it landed, which is shown in the table:

Open-sided up: 1

Closed side up 5

On the side: 44.

We are asked to determine the experimental probability of each outcome.

The number of outcomes, when the landing is open-sided up is 1.

The number of outcomes, when the landing is closed-sided up is 5.

The number of outcomes, when the landing is on the side up is 44.

The total number of times the experiment took place is 50.

Thus, the experimental probability of each event is as follows:

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The factors of 32 are 2,2,2,2,2 and the multiples of 32 are 64, 96, 128, 160, 192, 224, 256, 288 and 320.

A multiple is a number that is divisible by another number any number of times, they are what we get after multiplying the number by an integer (not a fraction).

A factor is one of two or more numbers that divides a given number without remainder. 

Factors and multiples are important aspects of mathematical structure that support the understanding of a range of other ideas including multiplication and division, and later on, factorization.

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The given expression, 14⁻³ · 14¹², written as a single, positive exponent is 14⁹

From the question, we are to write the given expression using a single, positive exponent

From the given information,

The given expression is

14⁻³ · 14¹²

This means

14⁻³ × 14¹²

To solve this, let us revise some of the laws of indices

Thus,

The expression

14⁻³ × 14¹²

can be written as

14⁻³ ⁺ ¹²

14⁹

Hence, the expression written as a single exponent is 14⁹

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Answer:

58.50

Step-by-step explanation:

Hope it helps and I hope you have a wonderful rest of your day!!!! :)

Answer:

18 tablespoons

Step By Step:

The sequence of transformations that take quadrilateral ABCD to quadrilateral A'B'C'D' is given by:

Examples of transformations are given as follows, along with explanations on the changes caused by the transformations.

As a dilation changes the side lengths the figure, a dilated figure is not congruent to the original figure, hence a dilation does not happen for this problem.

The first change was in the inclination and orientation of the figure, hence it underwent a rotation. From the movement of the vertices, for example, A to the bottom to the top, B from right to left, the rotation was of 90º clockwise.

Then, the function had the base at the same position, however it moved left, hence the second transformation was a translation left.

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Answer:

120.

Step-by-step explanation:

That would be factorial 5, written 5!.

That  is 5*4*3*2*1

= 120.

Answer:

120

Step-by-step explanation:

We have 5 digits that can be used to create different 5 digit numbers. We are also not allowed to repeat any numbers. Let's say we have 5 boxes to put the 5 numbers in.

Box 1

Box 2

Box 3

Box 4

Box 5

In the first box, we have 5 different choices. Since we aren't allowed to repeat any digits, the second box only has 4 different choices. And so on...

Box 1 --> 5 choices

Box 2 --> 4 choices

Box 3 --> 3 choices

Box 4 --> 2 choices

Box 5 --> 1 choice

Therefore the amount of 5 digit numbers that can be created is:

\(5\times4\times3\times2\times1\) or 5 factorial (a factorial is all the product of all the positive integers equal to and less than the number), which is equivalent to:

120 5-digit numbers

The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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The train will take 3hour 7.5min to travel a distance of 250 km

Given that,

Distance of 250 km with a speed of 80 kmh

To find: Time taken by train to travel a distance of 250 km with a speed of 80 kmh

Distance = 250km

Speed of the train =80km/h

Speed is calculated as distance times speed. You need to be aware of the units for distance and time in order to calculate the units for speed. The units in this example will be metres per second (m/s), since the distance is measured in metres (m) and the time is measured in seconds (s).

Time = Distance /speed

=250km /80km/h

=25/8 h

= 3⅛h

= 3hour ⅛*60

= 3hour 7.5min.

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Answer:

3 hours 7.5 mim

Step-by-step explanation:

The train will take 3hour 7.5min to travel a distance of 250 km

Given that,

Distance of 250 km with a speed of 80 kmh

To find: Time taken by train to travel a distance of 250 km with a speed of 80 kmh

Distance = 250km

Speed of the train =80km/h

Speed is calculated as distance times speed. You need to be aware of the units for distance and time in order to calculate the units for speed. The units in this example will be metres per second (m/s), since the distance is measured in metres (m) and the time is measured in seconds (s).

Time = Distance /speed

=250km /80km/h

=25/8 h

= 3⅛h

= 3hour ⅛*60

= 3hour 7.5min.

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The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups to determine if there is a significant difference between the medians of the groups. The test statistic used in this test is denoted by the letter "H," which is calculated based on the ranks of the data.

True. The test statistic calculated in the Kruskal-Wallis test is denoted by the symbol H, not to be confused with the Shapiro-Wilk test statistic denoted by W. The Kruskal-Wallis test is a non-parametric test used to compare the median ranks of three or more independent groups. The test statistic H is calculated by comparing the between-group sum of squares to the total sum of squares. H follows a chi-squared distribution with degrees of freedom equal to the number of groups minus one. The p-value obtained from the chi-squared distribution is used to determine whether to reject or fail to reject the null hypothesis that there is no significant difference between the groups.

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Answer:

Step-by-step explanation:

1. 1 3/4

2. 3 3/8

Answer:

The answer to your question is Marissa = 6, Trevor = 16

Step-by-step explanation:

Data

total number of t-shirts = 26

Marissa has 6 fewer than trevor

Process

1.- Write equations to solve this problem

Marissa = m

Trevor = t

                     m + t = 26                Equation l

                      m = t - 6                  Equation ll

- Substitute equation ll in equation l

                  (t - 6) + t = 26

-Simplify

                   t - 6 + t = 26

                   2t = 26 + 6

                   2t = 32

                     t = 32/2

                     t = 16

- Find m

                   m = 16 - 6

                   m = 10

-Conclusion

Trevor has 16 t-shirts and Marissa has 10 t-shirts.

Answer:

$378

Step-by-step explanation:

If 42 t-shirts are sold, that means that the company earns 9 dollars 42 times.

9 x 42 = 378

have a nice day!

Use both!

You want to minimize P, so differentiate P with respect to x and set the derivative equal to 0 and solve for any critical points.

P = 8/x + 2x

dP/dx = -8/x² + 2 = 0

8/x² = 2

x² = 8/2 = 4

x = ± √4 = ± 2

You can then use the second derivative to determine the concavity of P, and its sign at a given critical point decides whether it is a minimum or a maximum.

We have

d²P/dx² = 16/x³

When x = -2, the second derivative is negative, which means there's a relative maximum here.

When x = 2, the second derivative is positive, which means there's a relative minimum here.

So, P has a relative maximum value of 8/(-2) + 2(-2) = -8 when x = -2.

Answer:

\(x=\pm\frac{1}{2}\)

Step-by-step explanation:

On a unit circle, \((x,y)=(\cos\theta,\sin\theta)\), so \(\sin\theta=\frac{\sqrt{3}}{2}\) in this case. If you look at the attached circle, the only time that the y-coordinate is \(\frac{\sqrt{3}}{2}\) is when \(x=-\frac{1}{2}\) and \(x=\frac{1}{2}\), which correspond to angles of \(\theta=\frac{2\pi}{3}\) and \(\theta=\frac{\pi}{3}\) respectively

Answer:

The critical value Za /2 that corresponds to 98% confidence level is (d) 2.33

Step-by-step explanation:

To obtain the critical value Za/2 that corresponds to a 98% confidence level, we need to determine the value that leaves 2% (0.02) in the tails of the distribution.

Since the confidence level is two-tailed, we need to divide the significance level by 2 to find the area in each tail. In this case, we have 2% divided by 2, resulting in 1% (0.01) in each tail.

Looking up the critical value in a standard normal distribution table or using statistical software, we obtain that the closest value to 0.01 in the table is approximately 2.33.

Therefore, the correct answer is D. 2.33.

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The work done by the force field F in moving an object from P(2, -2) to Q(5, 0) along any path is 67.

To find the work done by the force field in moving an object from point P(2, -2) to point Q(5, 0) along any path, we can use the line integral of the force field along the path.

The line integral of a vector field F along a curve C is given by:

∫ F · dr

where F is the vector field, dr is the differential displacement vector along the curve C, and the dot (·) represents the dot product.

Let's calculate the line integral step by step:

Parametrize the curve C from P(2, -2) to Q(5, 0):

We can choose a linear parametrization for simplicity. Let t vary from 0 to 1 as we move from P to Q:

x = 2 + 3t

y = -2 + 2t

Calculate the differential displacement vector dr:

dr = dx i + dy j

Since x = 2 + 3t and y = -2 + 2t, we can differentiate both equations with respect to t to find dx and dy:

dx = 3 dt

dy = 2 dt

Therefore, dr = (3 dt) i + (2 dt) j

Calculate F · dr:

\(F(x, y) = 7(y + 2)^6 i + 42x(y + 2)^5 j\)

Substituting x = 2 + 3t and y = -2 + 2t:

\(F(x, y) = 7(-2 + 2t + 2)^6 i + 42(2 + 3t)(-2 + 2t + 2)^5 j\\= 7(2t)^6 i + 42(2 + 3t)(2t)^5 j\\F. dr = [7(2t)^6 i + 42(2 + 3t)(2t)^5 j] . (3 dt i + 2 dt j)\\= 21t^6 dt + 84(2 + 3t)t^5 dt\)

Integrate F · dr along the curve C:

\(\int\ F . dr = \int\(21t^6 + 84(2 + 3t)t^5) dt\\= \int\ (21t^6 + 168t^5 + 252t^6) dt\\= \int\(273t^6 + 168t^5) dt\\= 273\int\ t^6 dt + 168∫ t^5 dt\\= 273 * (t^7 / 7) + 168 * (t^6 / 6) + C\)

Evaluating the integral from t = 0 to t = 1:

\(\int\ F . dr = 273 * (1^7 / 7) + 168 * (1^6 / 6) - (273 * (0^7 / 7) + 168 * (0^6 / 6))\\= 273/7 + 168/6\\= 39 + 28\\= 67\)

Therefore, the work done by the force field F in moving an object from P(2, -2) to Q(5, 0) along any path is 67.

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Answer:

2^(3/7)

Step-by-step explanation:

For these types of questions, what is inside the root is the numerator, and what is on top is the denominator.

3 is in the root, so it is the numerator

7 is outside the root, so it is the denominator

Therefore, The answer is 2^(3/7)

Answer:

12.5 sec

Step-by-step explanation:

distance = speed x time

distance / speed = time

100/8 = 12.5

12.5seconds

hope this helps

brainliest plz?

x

The answer to the question is True. This can be answered by the concept of Trigonometry.

First, let's recall the definitions of the asymptotic notations used in the question

f(n) = O(n²) means that there exists a positive constant c and a positive integer N such that f(n) <= c × n² for all n >= N.

g(n) = Theta(n²) means that there exist positive constants c1, c2, and a positive integer N such that c1 × n² <= g(n) <= c2 × n² for all n >= N.

Now, since f and g are non-decreasing positive functions, we can assume without loss of generality that N > 0 and c1 > 0. Then, for all n >= N, we have:

f(n) <= c × n² (by the definition of O notation)

c1 × n² <= g(n) <= c2 × n² (by the definition of Theta notation)

Multiplying the first inequality by c1, we get:

c1 × f(n) <= c × c1 × n²

Since c1 and n^2 are positive, we can divide both sides by n² to obtain:

c1 × (f(n) / n²) <= c × c1

Now, let's define a new function h(n) = f(n) / n². Since f(n) and n² are both non-decreasing positive functions, h(n) is also non-decreasing and positive. Moreover, for all n >= N, we have:

h(n) <= (c × c1) / c1 = c

Therefore, we have shown that there exists a positive constant c and a positive integer N such that h(n) <= c for all n >= N. This means that h(n) = O(1).

Using this result, we can conclude that:

f(n) = h(n) × n² = O(1) × n² = O(n²)

Therefore, we have:

f(n) = O(n²) and g(n) = Theta(n²) => f(n) = O(g(n))

Therefore, the answer to the question is True.

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The answer are (a)  the percent change in the population of the type of plant that is changing by a constant percent rate each year is -12.5% for the buttercups population. (b) the initial amount of money that Bree put in the savings account was $650.

A savings account is a type of bank account where individuals can deposit their money and earn interest on the balance. It is typically offered by banks and other financial institutions as a safe place to store money while earning a small amount of interest. Savings accounts are often used by individuals to save for short-term financial goals or to build an emergency fund.

(a)To determine the percent change in population for each type of plant, we can calculate the percent change from year to year using the following formula:

percent change = (new value - old value) / old value * 100

We can then look for the type of plant with a constant percent change each year.

Starting with the thistles population:

From year 1 to year 2, the percent change is: (317-271)/271*100 = 17%

From year 2 to year 3, the percent change is: (323-317)/317*100 = 1.89%

From year 3 to year 4, the percent change is: (348-323)/323*100 = 7.75%

Therefore, the thistles population is not changing by a constant percent rate each year.

Moving on to the buttercups population:

From year 1 to year 2, the percent change is: (448-512)/512*100 = -12.5%

From year 2 to year 3, the percent change is: (392-448)/448*100 = -12.5%

From year 3 to year 4, the percent change is: (343-392)/392*100 = -12.5%

Therefore, the buttercups population is changing by a constant percent rate of -12.5% each year.

Finally, looking at the blueberries population:

From year 1 to year 2, the percent change is: (309-326)/326*100 = -5.21%

From year 2 to year 3, the percent change is: (292-309)/309*100 = -5.50%

From year 3 to year 4, the percent change is: (299-292)/292*100 = 2.40%

Therefore, the blueberries population is not changing by a constant percent rate each year.

Thus, the percent change in the population of the type of plant that is changing by a constant percent rate each year is -12.5% for the buttercups population.

(b) To find the initial amount of money that Bree put in the savings account, we need to look for the value in the table that represents the amount of money after 0 years. From the table, we see that the amount of money in the savings account after 0 years is $650. Therefore, the initial amount of money that Bree put in the savings account was $650.

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The four distinct integers a, b, c, and d have the following properties:

1. When added in pairs, the sums obtained are 10, 18, 19, 20, 21, and 29.
2. The integers are distinct, meaning that no two integers are the same.

To find the four integers in increasing order, we can start by analyzing the given sums.

First, let's look at the smallest sum, which is 10. To obtain 10 by adding two distinct integers, we can have a + b = 10.

Next, let's consider the largest sum, which is 29. To obtain 29 by adding two distinct integers, we can have c + d = 29.

Now, let's consider the remaining sums: 18, 19, 20, and 21. Since these sums are all greater than 10 and less than 29, they cannot be obtained by adding the smallest and largest integers. This means that the remaining sums must be obtained by adding the middle two integers, b + c.

From this analysis, we can conclude the following:

1. a + b = 10
2. b + c = 18, 19, 20, or 21
3. c + d = 29

To find the four integers, we can start by finding the value of b. Since a + b = 10, we can subtract a from both sides to get b = 10 - a.

Next, we can substitute this expression for b into the equation b + c = 18, 19, 20, or 21. This will give us an equation involving c in terms of a.

Finally, we can substitute the expression for c into the equation c + d = 29 to find the value of d in terms of a.

By solving these equations, we can find the four distinct integers a, b, c, and d in increasing order.

Note: Since there are multiple possible values for b, c, and d depending on the specific sum obtained from b + c, there are multiple valid solutions to this problem.

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The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).

Let's simplify the given expression step by step using the given terms:
Expression:

\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)

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Answer:

r = - 2

Step-by-step explanation:

Use the slope formula to find m then equate to - 1

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (6, r) and (x₂, y₂ ) = (9, - 5)

m = \(\frac{-5-r}{9-6}\) = \(\frac{-5-r}{3}\)  = - 1 ( multiply both sides by 3 )

- 5 - r = - 3 ( add 5 to both sides )

- r = 2 ( multiply both sides by - 1 )

r = - 2

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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Answer:

$52.50

Step-by-step explanation:

1. You take 550 and divide by 5.

2. Then you would takw that number (105) and multiply by 2 (210)

3. Then you take 210 and divide by 4 which equals 52.5

4. The answer is 52.5 because she takes 1/4 of the 2/5 for vacation a month.

The most basic distinction between types of data is that some data are quantitative while other data are qualitative. Quantitative data consists of numerical information that can be measured or counted, allowing for statistical analysis and objective comparisons. This type of data can be further classified into two subcategories: continuous data and discrete data.

Continuous data represent measurements that can take on any value within a specified range, such as height, weight, temperature, or time. These measurements can be represented using fractions or decimals and are typically collected using precise instruments like rulers or thermometers.

Discrete data, on the other hand, consist of distinct, separate values that can be counted or categorized. Examples of discrete data include the number of students in a class, the number of cars in a parking lot, or the number of books sold in a month. Discrete data is often collected through surveys or counting processes.

In contrast, qualitative data are non-numerical and describe attributes, characteristics, or experiences. This type of data is typically obtained through observation, interviews, or open-ended survey questions. Examples of qualitative data include feelings, opinions, beliefs, or descriptions of events.

In summary, the primary distinction between types of data lies in their nature: quantitative data is numerical and allows for objective measurement, while qualitative data is descriptive and explores subjective aspects. Understanding the difference between these two types of data is essential for conducting accurate and meaningful research.

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Answer:

Always

Step-by-step explanation:

The equilateral triangles have all the angles and all the sides congruent. That is the definition of a regular polygon

Answer:

Equilateral Triangles are always regular polygons.

Step-by-step explanation:

This is because all of the interior angles are the same(60 degrees). Regular polygons have the same interior angles. For instance, a pentagons interior angle is 108 degrees.

Answer:

dx/dy = y/2x

Step-by-step explanation:

-4x × dx/dy = -2y..... that's all

There will be a population of 2,097,152 rabbits after 5 years.

A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, a quantity expands more quickly the greater it is. A prime example of exponential expansion is the rabbit population, which doubles in size every three months.

Given that, population of rabbits is doubling every 3 months.

That is,

5 years = 5 x 12 = 60 months

Number of doublings = 60 / 3 = 20

For every doubling, the population will be twice as large.

Thus,

P = 2 x 2²⁰ = 2 x 1,048,576 = 2,097,152 rabbits

Therefore, there will be approximately 2,097,152 rabbits after 5 years.

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The square root function involves the square root symbol √ which is  mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.

We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.

If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.

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