(6)/(a^(2))+(5a^(-2))/(3^(-3))

Eggs are generally sold in batches of 12 (or dozens). The image shows the 3 different ways that 12 eggs can be packaged into arrays. Note that the array 3 by 4 is taken to be equivalent to the array 4 by 3 and therefore is not included. If it was decided that eggs should be sold in batches of 24, then these 24 eggs could be packaged into a total of 4

different arrays.

The arrangement is checked by writing out the factors of 24

24 = 1, 2, 3, 4, 6, 8, 12, 24

grouping them in pairs

1 * 24

2 * 12

3 * 8

4 * 6

this gave a total of 4 arrays

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To solve for x in this equation, we must first perform the operations inside the parentheses. This gives us:

X = 40 * (25x^2 + 75x + 75x - 75)

Next, we can distribute the 40 and combine like terms to get:

X = 1000x^2 + 3000x - 3000

Now, we can set this expression equal to X and solve for x.

1000x^2 + 3000x - 3000 = X

We can use the quadratic formula to find the solutions for x:

x = (-3000 +/- sqrt(3000^2 - 4 * 1000 * (-3000))) / (2 * 1000)

This simplifies to:

x = (-3000 +/- sqrt(9000000 + 24000000)) / 2000

Finally, we can simplify further to get:

x = (-3000 +/- sqrt(33000000)) / 2000

Thus, the solutions for x are:

x = (-3000 + sqrt(33000000)) / 2000

x = (-3000 - sqrt(33000000)) / 2000

These are the possible values for x that satisfy the given equation.

The rate of the boat approaching the dock when 125 ft of rope is out is 101.6 ft/min

let x be the horizontal distance to the dock. And the rope is attached to the boat 10 feet below the pulley

Using Pythagorean theorem

x^2=R^2-10^2

where R is the rope length to the pulley.

Differentiates with respect to time t

2x dx/dt=2RdR/dt

Xdx/dt = RdR/dt ...... (1)

If the boat is approaching the dock when 125 ft of rope is out

This is R = 125ft

Using Pythagorean theorem again

X^2 = R^2 - 10^2

X^2 = 125^2 - 10^2

X^2 = 15525

X = 124.6 ft

The rate the boat approaching the dock = dx/dt

While the rope is pulled through the pulley at a rate of 20 ft/min = dR/dt

Solve for dx/dt when R is 125, x= 124.6, and dR/dt= 20ft/min

Substitute all in equation 1

124.6 dx/dt = 125 × 20

dx/dt = 2500/124.6

dx/dt = 101.6 ft/min

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The combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.

According to the question,

We have the following information:

A sandwich hop serve 4 ounce of meat and 3 ounce of cheese on each sandwich. After making sandwiches for an hour the hop owner has used 91 combined ounce of meat and cheese.

Combined ounces for 1 sandwich:

Ounces of meat + ounces of cheese

4+3

7 ounces

It is given that in an hour 91 ounces of combined cheese and meat are used.

Now, we have:

Number of sandwiches made in 1 hour = 91/7

Number of sandwiches = 13

Ounces of meat used in 13 sandwiches can be found using multiplication as follows:

13*4

Ounces of meat used in 13 sandwiches = 52 ounces

Ounces of cheese used in 13 sandwiches can found using multiplication as follows:

13*3

Ounces of cheese used in 13 sandwiches = 39 ounces

Hence, the combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.

complete question is

A andwich hop erve 4 ounce of meat and 3 ounce of cheee on each andwich. After making andwiche for an hour, the hop owner ha ued 91 combined ounce of meat and cheee. How many combined ounce of meat and cheee are ued on each (1) andwich?

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The length of BR is 40 cm.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

YN is parallel with BR.

Triangle HYN is congruent with Triangle HBR.

HN = 5 cm

NR = 15 cm

YN = 10 cm

Now,

HR = HN + NR

HR = 5 + 15 = 20 cm

YN/HN = BR/HR

10/5 = BR/20

2 = BR/20

BR = 20 x 2

BR = 40 cm

Thus,

The value of BR is 40 cm.

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Answer: The answer is B: 0.9

If a fraction's denominator is not a factor of 10 or 100, we can divide the number in the numerator by the number in the denominator to obtain a decimal.

Let us take an example. Say we have a fraction- 3/2

here numerator = 3 and denominator = 2

To convert this into a decimal, we need to divide 3 by 2

2 goes in 3 one time and remainder left is 1.

Then we put a decimal and divide 10 by 2 which gives us 5

Thus, on dividing 3 by 2, we get a quotient of 1.5

Hence the fraction 3/2 becomes 1.5 as a decimal.

Similarly, we can convert any fraction into decimal.

Thus, we can see that if a fraction's denominator is not a factor of 10 or 100, we can divide the number in the numerator by the number in the denominator to obtain a decimal.

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4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.

Given that,

A cyclist travels at a speed of 24 miles per hour on average.

We have to find what is the required riding time (in hours) if she wants to cycle 180 km.

We know that,

The velocity is a vector quantity (has magnitude and direction) that is calculated by dividing the distance by the amount of time needed to travel the distance in question.

So, the distance is 180 km, and the speed is 24 miles per hour.

To calculate the amount of time needed to travel the distance, we divide the distance by the speed.

The distance is first converted to miles as 1 mile is equal to 1.6098 kilometers,

180 kilometers are equal to 111.84681 Miles.

111.84681 miles traveled in 24 hours

111.84681/24

4.66 hours.

Therefore, 4.66 hours is the required riding time (in hours) if she wants to cycle 180 km when cyclist travels at a speed of 24 miles per hour on average.

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The equation of the blue line is: y = 3x - 1.

The equation of the red line is: y = 3x + 2.

To find the equation of a given line on a coordinate plane, find the slope along the line, m (rise / run), and also determine the value of the y-intercept (b), which is the point on the y-axis where the line intercepts it.

The equation of the red line:

Slope of the line (m) = rise / run = 3 units / 1 units

Slope (m) = 3

The red line intersects the y-axis at 2, this means the y-intercept of the line would be b = 2.

To write the equation of the red line, substitute m = 3 and b = 2 into y = mx + b:

y = 3x + 2

The equation of the blue line:

Slope of the line (m) = rise / run = 3 units / 1 units

Slope (m) = 3

The blue line intersects the y-axis at -1, this means the y-intercept of the line would be b = -1.

To write the equation of the blue line, substitute m = 3 and b = -1 into y = mx + b:

y = 3x - 1.

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Answer:

graph D

Step-by-step explanation:

x - 1 ≥ 0

x ≥ 1

if x ≥ 1

x - 1 < 4

x < 4 + 1

x < 5

1≤ x < 5

if x < 1

-x + 1 < 4

-x < 4 - 1

- x < 3

x > -3

-3 < x < 1

final solution

-3 < x < 5

Answer:

To find the prime factors of 28, we can start by dividing 28 by the smallest prime number, which is 2. 28 divided by 2 is 14, so 2 is a prime factor of 28. We can then divide 14 by the next smallest prime number, which is 2 again. 14 divided by 2 is 7, so 2 is also a prime factor of 28. We can repeat this process with the number 7, dividing it by the next smallest prime number, which is 3. 7 divided by 3 is 2 with a remainder of 1, so 3 is not a prime factor of 28. Since we have reached a number that is not divisible by any more prime numbers, we have found all of the prime factors of 28. In this case, the prime factors of 28 are 2 and 2.

To write 28 as a product of its prime factors, we simply need to multiply the prime factors together in the correct order. Since the prime factors of 28 are 2 and 2, and the factors are to be written in order from smallest to largest, we can write 28 as 2 x 2 = 4. This is the prime factorization of 28, and it shows that 28 can be expressed as a product of its prime factors.

The measure of angle c is 136/6 degrees

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

∠l = (6c 35)°

Exterior of l = 79

As a general rule, the sum of an angle and its exterior is 180 degrees

This means that

6c - 35 + 79 = 180

Evaluate the like terms

So, we have

6c = 136

Divide both sides by 6

c = 136/6

Hence, the measure is 136/6 degrees

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The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above. So, option e is correct.

What is meant by null hypothesis?

The null hypothesis, often known as H₀, is the assertion that there is no difference between two sets of data or variables under analysis, or that there is no relationship between them. Because there is no underlying causative relationship, the null hypothesis holds that any experimentally detected difference is merely the result of chance; therefore, the name "null."

We can create a z-test hypothesis by assuming that the amount of rain produced by thunderheads follows a distribution that is nearly normal:

300 acre feet is the null hypothesis for the average quantity of rain that thunderheads produce on their own without fertilizing the clouds.

Alternative Hypothesis: The amount of rain that thunderheads often produce by seeding the clouds is greater than 300 acre feet.

This test has a right tail.

So, The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above.

So, option e is correct.

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The equations log₂ (0.25) = -2, 5² = 25, log₂ 32 = 5 and 25⁻¹ = 0.04 are equivalent to the equations 2⁻² = 0.25, log₅ 25 = 2, 2⁵ = 32, log₂₅ 0.04 = -1 respectively.

Logarithms are another way, which is the opposite of writing exponents. A number raised to some power will give some other values in case of exponentiation process. This power is called the logarithmic value.

We can write it as,

logₐ x = n ⇔ aⁿ = x

We have the equations on the left equivalent to the equations on the right using the definition of logarithms as,

log₂ (0.25) = -2 ⇔ 2⁻² = 0.25

5² = 25 ⇔ log₅ 25 = 2

log₂ 32 = 5 ⇔ 2⁵ = 32

25⁻¹ = 0.04 ⇔ log₂₅ 0.04 = -1

Hence the equations on the lefts log₂ (0.25) = -2, 5² = 25, log₂ 32 = 5 and 25⁻¹ = 0.04 are equivalent to the equations on the rights 2⁻² = 0.25, log₅ 25 = 2, 2⁵ = 32, log₂₅ 0.04 = -1 respectively.

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Answer:

Step-by-step explanation: : 630°, 990°, -90°, -450°

Answer:

14 volleyballs  and 7 handballs

Step-by-step explanation:

sum the parts of the ratio , 2 + 1 = 3 parts , then

21 ÷ 3 = 7 ← value of 1 part of the ratio , so

volleyballs = 2 × 7 = 14

handballs = 1 × 7 = 7

Answer:

Hey

volleyball = 14

Handball = 7

Step-by-step explanation:

21 pieces = 2:1n

step 1

Add the ratios together

21 = 3n

Step 2

divide both sides by 3

n = 21/3 = 7

where n = number of balls

volley ball = n × 2 = 7 × 2 = 14

handballs = n × 1 = 7 × 1 = 7

total = 21

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The first and the second terms of the recursive sequence are given as follows:

a) u(1) = -25.

b) u(2) = -15623.

The definition of the recursive sequence is presented as follows:

u(n + 1) = u(n)³ + 2.

The initial term is needed to solve the sequence, hence it is given as follows:

u(0) = -3.

Thus the term with index 1 is given as follows:

u(1) = u(0)³ + 2.

u(1) = -3³ + 2

u(1) = -27 + 2

u(1) = -25.

Considering the term with index 1, the term with index 2 is obtained as follows:

u(2) = u(1)³ + 2

u(2) = (-25)³ + 2

u(2) = -15623.

And then the same rule is obtained if needed to obtain the 3th, 4th terms, and so on, considering the previous term and the definition.

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The time of highest water level is an inflection point of this functionand the time when the water first began to rise more slowly is a critical point of this function.

A critical point is a point on a graph at which the gradient of the graph (or the rate of change of the graph) is equal to zero. This means that the rate of change of the function at the critical point is neither increasing nor decreasing. An inflection point is a point on a graph at which the concavity of the graph changes. When the graph is concave up, the rate of change is increasing, and when the graph is concave down, the rate of change is decreasing.In the case of the rising and falling of a river during a flood, the time of highest water level is an inflection point because it marks the point at which the water level changes from rising to falling. The rate of change of the water level is increasing as it rises, and decreasing as it falls. At the time of highest water level, the rate of change is at a maximum and is equal to zero, making it an inflection point. The time when the water first began to rise more slowly is a critical point because it marks the highest point of the water level. The gradient of the graph at this point is equal to zero, making it a critical point.

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Answer:

1/1000000 One gram is one millionth of a ton

Step-by-step explanation:

1 ton is 1000 kg = 1 million grams

1 gram = 1/1000000 ton

Hope this helps

The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $21,000 and the standard deviation is $1000. Use the 68-95-99.7 Rule the percentage of buyers that paid between $20,000 and $21,000 is 68%

68 percent of the data falls within one standard deviation of the mean,

95 percent falls within two standard deviations, and

99.7 percent falls within three standard deviations.

In the problem, it was given that the mean is $21 000 and the standard deviation is $1 000

The deviation between $20,000 and $21,000

= $21,000 - $20,000

= $1,000

The standard deviation is $1000 hence buyers within $20,000 and $21,000 are within one standard deviation. according to the 68-95-99.7 Rule they are 68%

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The statement that best justifies the conclusion based on the given information is given as follows:

C) If a plane contains a line, it contains the points on the line.

We are given these two pieces of information:

When a line belongs to a plane, as is the case in this problem, with Line l belong to plane M, then all the points of the line will belong to the plane.

Hence, point x belongs to the plane M in this problem, as the plane M contains the line l for which point x belongs, and thus statement c is correct.

(basically, the transitive property can be applied to conclude that every point on a line belonging to a plane also belong to the plane).

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Although part of your question is missing, you might be referring to this full question: Right triangles MNP and QRS are congruent. What is the area of △MNP? (Picture as attached)

The area of △MNP is 60 m².

Since △MNP and △QRS are congruent, then SQ = MP, NM = RQ, and RS = NP.

The formula to find the area of a triangle is:

= 1/2 * base * height

As shown in the picture, height = 15, and base is unknown.

To find the base, we use Pythagoras 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.

So, MP = √ 17² – 15²

MP = 8m = the base

Hence, area of △MNP:

= 1/2 * 8 * 15

= 60 m²

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By applying the fraction concept, it can be calculated that Mrs. Stewart sold 300 cakes.

How does the concept of fractions apply in real life?

In real life, the concept of a fraction is often used when we want to talk about a part of a whole, a part of something, a part of a group of people, etc.

In this case, it is stated that Mrs. Stewart made several pies, some of which were sold and given to food banks, and some were left over.

If we know that 1/4 of the unsold pies were given to the food bank, then the unsold pies that were not given to the food bank = 1 - 1/4 = 3/4 part.

Additionally, we also know that the number of unsold pies that were not given to the food bank (leftover pies) was 150.

If x is the number of unsold cakes, then the two statements above can be written in mathematical notation:

3/4 x = 150

      x = 150 : 3/4

         = 150 x 4/3

         = 200 pies

If pies made are y, then pies not sold = pies made - pies sold

x = y - 3/5y

  = 2/5y

if we put the value of x into this equation it becomes:

200 = 2/5y

    y = 200 : 2/5

       = 200 x 5/2

       = 500 pies

Then the pies were sold = 3/5y

                                         = 3/5 x 500

                                         = 300 pies

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point coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

Given that,

We have to find what are the endpoint coordinates for the middle portion of the parallel to PQ segment of the PQR.

We know that,

First we write the co-ordinates of the triangle in the given graph.

P is (-3,3)

Q is (2,1)

R is (-4,-2)

The triangle's midpoint, which is parallel to section PQ, must be located. As a result, we would need to locate the midpoints of the segments PR and QR before joining the points to obtain the mid segment.

Midpoint Formula is

(x₁+x₂/2, y₁+y₂/2)

So,

The midpoint of the side PR is

(-3+(-4)/2, 3+(-2)/2)

(-3-4/2, 3-2/2)

(-7/2,1/2)

So, S point is (-3.5, 0.5)

The midpoint of the side QR is

(2+(-4)/2, 1+(-2)/2)

(2-4/2, 1-2/2)

(-2/2,-1/2)

So, T point is (-1, -0.5)

Therefore, The endpoint coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

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Answer:

if Kira drives at the same rate, she would drive 567 miles in 9 hours.

Step-by-step explanation:

To determine how many miles Kira would drive in 9 hours at the same rate, we need to first calculate her average speed in miles per hour. To do this, we divide the total number of miles she drove (441 miles) by the number of hours she drove (7 hours):

441 miles / 7 hours = 63 miles/hour

Once we know her average speed, we can use it to calculate the number of miles she would drive in 9 hours. To do this, we multiply her average speed (63 miles/hour) by the number of hours she would drive (9 hours):

63 miles/hour * 9 hours = <<63*9=567>>567 miles

A complete model that shows the system's whole data flow is a physical data model.

A thorough model that depicts the general flow of data through a system is a physical data model.

A physical data model is a thorough representation of the overall organizational data structure that is not dependent on a database management system or any other implementation factors.

A physical data model is a database-specific model that depicts relational data objects and their associations (such as tables, columns, primary keys, and foreign keys).

DDL statements can be produced from a physical data model and then delivered to a database server.

Examples of physical models include bridges, cell models, human organs, crash test dummies, landform models, building models, and chemical compound models.

Therefore, a complete model that shows the system's whole data flow is a physical data model.

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A data series contains the actual values that are plotted on the chart. So the option c is correct.

In the given question, we have to find the answer to fill in the blanks.

The given statement is:

"A ________ contains the actual values that are plotted on the chart."

As we know that;

A data series, such as a list of quarterly corporate profits, is a row or column of figures that are input in a worksheet and plotted in your chart. Even if you generated your chart in a different software, like Word, Office automatically associates charts with an Excel-based worksheet.

A data series contains the actual values that are plotted on the chart.

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The complete question is:

A ________ contains the actual values that are plotted on the chart.

(1) data source

(2) category values

(3) data series

(4) legend

No, it is not appropriate to estimate the probability using an approximately normal model because the population is not normal and the sample size is small.

The details given are,

Sample size = 9

mean = 43 sec

Standard deviation = 8.99

Therefore we conclude that is it not  appropriate to calculate the likelihood of the sample mean being less than 30 seconds using an approximately normal model.

Mean is also know as the average of a given data . We calculate the mean by the formula :   ∑xifi / ∑fi.

Normal Distribution is the probability density function ( pdf)  for a continuous random variable in a system .

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