There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).​

Answer:

28.57

Step-by-step explanation:

Answer:

16 miles

Step-by-step explanation:

Step-by-step explanation:

the second one is the answer

\( \frac{ {8}^{5} \times {10}^{15} }{ {10}^{9} \times {8}^{2} } = {8}^{5 - 2} \times {10}^{15 - 9} = {8}^{3} \times {10}^{6} \)

Answer: Last one

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2 is farther right on the number line because it is a positive number while -2 is negative.

To show that the given differential form is exact, we need to find a function f(x,y) such that its partial derivatives with respect to x and y are equal to the coefficients of dx and dy, respectively.

Let's consider the differential form:

M(x,y)dx + N(x,y)dy = (y^2-2xy)dx + (x^2-2xy)dy

Taking the partial derivative of M(x,y) with respect to y and the partial derivative of N(x,y) with respect to x, we have:

dM/dy = 2y - 2x = dN/dx

Since the partial derivatives are equal, the differential form is exact.

Now we need to find the potential function f(x,y) such that:

df/dx = M(x,y) and df/dy = N(x,y)

Integrating the first equation with respect to x, we obtain:

f(x,y) = y^2x - x^2y + g(y)

where g(y) is a constant of integration that depends only on y.

Now we differentiate f(x,y) with respect to y and compare it with N(x,y):

df/dy = 2xy - x^2 + g'(y) = x^2 - 2xy

Equating the coefficients of x^2 and xy, we get:

g'(y) = 0, and -2x = 0

Solving these equations, we obtain:

g(y) = C, and x = 0

where C is an arbitrary constant.

Substituting these results back into the expression for f(x,y), we get:

f(x,y) = y^2x - x^2y + C

Therefore, the potential function of the given differential form is f(x,y) = y^2x - x^2y, and we can evaluate the integral as follows:

∫ C dx + ∫ (-x^2 + y^2) dy

where C is a constant of integration.

Evaluating the first integral with respect to x, we get:

C x + g(y)

where g(y) is another constant of integration.

Evaluating the second integral with respect to y, we get:

C x + (1/3) y^3 - (1/3) x^3 + h(x)

where h(x) is another constant of integration.

Therefore, the general solution is:

C x + (1/3) y^3 - (1/3) x^3 + g(y) + h(x)

Since the initial point is (0,0), we have:

C (0) + (1/3) (0)^3 - (1/3) (0)^3 + g(0) + h(0) = 0

Simplifying, we get:

g(0) + h(0) = 0

Therefore, the value of the integral at the point (0,0) is:

∫ (y^2-2xy)dx + (x^2-2xy)dy = 0 + 0 + g(0) + h(0) = 0

Hence, the value of the integral at the point (0,0) is 0.

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There are 46 elements in total for 4 sets A, B, C, and D.

Consider 4 sets A, B, C, and D.

Each set has 15 elements.

The pair-wise intersection has 4 elements.

The three-way intersection has 3 elements.

There are 2 elements in the intersection of all sets.

So,

P(A) = P(B) = P(C) = P(D) = 15

P(A ∩ B) = P(A ∩ C) = P(A ∩ D) = P(B ∩ C) = P(B ∩ D) = P(C ∩ D) = 4

P(A ∩ B ∩ C) = P(A ∩ B ∩ D) = P(A ∩ C ∩ D) = P(B ∩ C ∩ D) = 3

P(A ∩ B ∩ C ∩ D) = 2

The total number of elements are:

P (A U B U C U D) = P(A) + P(B) + P(C) + P(D) - P(A ∩ B) - P(A ∩ C) - P(A ∩ D)- P(B ∩ C) - P(B ∩ D) - P(C ∩ D) + P(A ∩ B ∩ C) + P(A ∩ B ∩ D) + P(A ∩ C ∩ D) + P(B ∩ C ∩ D) - P(A ∩ B ∩ C ∩ D).

P (A U B U C U D) = 15 + 15 + 15 + 15 - 4 - 4 - 4 - 4 - 4 - 4 + 3 + 3 + 3 + 3 - 2

= 60 - 24 + 12 - 2

= 60 + 12 - 24 - 2

= 72 - 26

= 46

Therefore there are 46 elements.

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You can convert from scientific notation to simple notation using the fact that negative powers can be converted to division.

The correct option is given by

Option C. The greatest number is 8. 2 × 10-3. It is 2,000 times greater than the smallest number.

Suppose you have got \(a^{-b}\)

Then we have

\(a^{-b} = \dfrac{1}{a^b}\)

\(8.2 \times 10^{-3} = \dfrac{8.2}{10^3} = \dfrac{8.2}{1000} = 0.0082\\\\5.2 \times 10^{-6} = \dfrac{5.2}{10^6} = \dfrac{5.2}{1000000} = 0.0000052\\\\4.1 \times 10^{-6} = \dfrac{4.1}{10^6} = \dfrac{4.1}{1000000} = 0.0000041\)

Thus, we can see that

The greatest number among given numbers is \(8.2 \times 10^{-3}\)

The smallest number among the given numbers is \(4.1 \times 10^{-6}\)

Dividing greatest number by smallest to see how many times the greatest number is greater than the smallest number

\(\dfrac{8.2 \times 10^{-3}}{4.1 \times 10^{-6}} =\dfrac{8.2}{4.1} \times \dfrac{10^{-3}}{10^{-6}} = 2 \times 10^{-3 - (-6)} = 2 \times 10^3 = 2000\)

Remember that when base are same, and there is division, then power gets subtracted, that's why we got \(\dfrac{10^{-3}}{10^{-6}} = 10^{-3 - (-6)} = 10^3\)

Thus, we have the greatest number 2000 times bigger than the smallest number among the numbers given.

Thus, the correct option is

Option C. The greatest number is 8. 2 × \(10^{-3}\). It is 2,000 times greater than the smallest number.

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The answer is , an approx. value of m such that the equation cos(x) = mx has exactly two solutions is m = 1 and m = -0.3183

To find an approximate value of m such that the equation cos(x) = mx has exactly two solutions, we can use the fact that the graph of y = cos(x) intersects the line y = mx at exactly two points.

The graph of y = cos(x) is a periodic function with a maximum value of 1 and a minimum value of -1.

Since we want the line y = mx to intersect the graph of y = cos(x) at exactly two points, the slope m must satisfy the condition -1 ≤ m ≤ 1.

Furthermore, for the line y = mx to intersect the graph of y = cos(x) at exactly two points, the line must pass through the maximum and minimum points of the graph of y = cos(x).

These occur at x = 0 and x = π.

At x = 0, we have cos(0) = 1 and the equation cos(x) = mx becomes 1 = m(0), which simplifies to m = 1.

At x = π, we have cos(π) = -1 and the equation cos(x) = mx becomes -1 = m(π), which simplifies to m = -1/π.

Therefore, an approx. value of m such that the equation cos(x) = mx has exactly two solutions is m ≈ 1 and m ≈ -0.3183 (rounded to four decimal places).

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In degrees Celsius, the difference between Michigan's record low temperature and Colorado's record low temperature  to the nearest tenth if necessary is 5.50°C

The concept that wil be used here is temperature conversion. The degrees Celsius,  of Michigan's record low temperature can be calculated as

-51.7 °F we can convert to  °C,Using the equation below

F=1.8C+32

-51.7 ° = 1.8C+32

1.8C=-51.7 ° - 32

1.8C= -83.7

°C= -83.7/1.8

=-45.5°C

The degrees Celsius,  of Michigan's record low temperature can be calculated as -51. °C

The difference, in degrees Celsius, between colorado's record=( -45.5°C)  -(-51. °C) = 5.5°C

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Answer:

B

Step-by-step explanation:

We know that it costs 37 cents to mail a letter that weighs 1 oz or less. This would mean that for x ≤ 1, P(x) should equal 37. Already, we can eliminate A and D.

We also know that it costs an additional 26 cents for at most another ounce added to the original 1 ounce. This means that for 1 < x ≤ 2, P(x) = 26 + 37 = 63. This is shown by B.

Thus, the answer is B.

~ an aesthetics lover

Answer:

4x and -2y

Step-by-step explanation:

The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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Answer:

34.2508% decrease

Step-by-step explanation:

Percent decrease = 100 x (starting value-new value/starting value)

100 x ((3.27 - 2.15)/3.27)

Answer:

$1.12

Step-by-step explanation:

$3.27-$2.15=$1.12

$1.12 + $2.15= $3.27

Mean, median and mode are the measures of central tendency that are used to describe a statistical sample. These measures are commonly used in statistical analysis and are important in understanding the general characteristics of a data set.

Here is a brief explanation of each of these measures Mean: The mean is the arithmetic average of a set of data. It is calculated by summing up all the values in a data set and dividing by the number of values in the set. The mean is sensitive to outliers, meaning that if there are any extreme values in the data set, the mean will be affected.Median: The median is the middle value in a set of data. It is the value that divides the data set into two equal parts. If there is an even number of values in a data set, the median is the average of the two middle values.

The median is less sensitive to outliers than the mean, meaning that extreme values will not have as much of an effect on the median. Mode: The mode is the most common value in a set of data. It is the value that appears most frequently in the data set. The mode is not sensitive to outliers, meaning that extreme values will not affect the mode. The mode can be used to describe the typical value of a data set. In summary, the mean tells you about the average value of a data set, the median tells you about the middle value of a data set, and the mode tells you about the most common value in a data set. These measures of central tendency are useful for understanding the general characteristics of a data set.

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Given info:There is a favourite sport and number of people watching and participating in the colony is given.

Draw the double bar graph for the data ?

Explanation:

See the attachment

Number of people watching cricket = 1240

Number of people participating cricket =620

Number of people watching Basket ball =470

Number of people participating Baskets ball=320

Number of people watching Swimming =510

Number of people participating Swimming= 320

Number of people watching Hockey=430

Number of people participating Hockey =250

Number of people watching Athletics =250

Number of people participating Athletics =105

Scale:-

On X - axis taking favourite sport

On Y-axis taking Number of people in the colony

First bar represents Watching

Second bar represents Participating

On Y-axis 1 cm = 100 units

(i)

⇛The number of people who are watching and participating in their favourite sport.

(ii)

⇛Cricket is the most popular of all other sports .

⇛It has the most watching people and the more participants

(iii)

⇛Watching is more preferred than Participating according to the given data of the colony.

Bar graph:-

⟨Hope this helps.⟩

Answer:

Student 1

Step-by-step explanation:

Student one attempts to divide both sides by -2, however only divides one term by -2, instead of all the terms

The value of the one-gram quantity in ounces will be 0,35274 ounces.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the quantity of some materials is measured in 10 grams. The quantity of the material in ounces will be calculated as,

1 grams = 0.035274

10 grams = 10 x 0.035274

10 grams = 0.35274 ounces

Therefore, the value of the one-gram quantity in ounces will be 0,35274 ounces.

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Answer:

b

Step-by-step explanation:

BCCCCCC

Explanation:

The figure preserves its size in certain transformations and only its location is changed. Examples of this kind of transformation are: translations, rotations, and reflections. The size of the figure can change with other transformations, such as dilations.

A translation is a transition that slides through a plane or through space through a figure. Both points of a diagram travel the same distance and the same direction as a translation. A TRANSLATION IS A CHANGE IN LOCATION. A translation is usually specified by a direction and a distance.

A rotation is a move that transforms a figure around a point or a line (around). Rotation involves simply rotating a shape. The center of rotation is called the point at which a figure revolves. The rotation center may be on or outside of the shape. What seems like a rotation? Rotation Core A ROTATION Implies TO Transform A FIGURE.

A transformation that flips a figure over a line is a mirror. A REFLECTION IS FLIPPED OVER A LINE. Note, it's the same but it looks like a mirror image of itself when a shape is mirrored. Remember, the line that forms a shape is flipped precisely over the same distance that is considered a line from the reflection. Reflection line on both ends. It is possible to reflect on the outline or it may be outside the shape.

Without modifying the shape, dilation shifts the scale of the shape. When you go to the eye specialist, your pupils are dilated. Let's try it by shutting the lights off. Dilations are created as you enlarge a photograph or use a copy machine to minimize a map. To render a shape larger, Widen means. Reducing involves having a shape smaller.

The scale factor shows you how much you enlarge or decrease something.

Hope this helps :D (paraphrased; no plagiarism)

Hi! Could you please send a picture of the full problem? Thanks!

Answer :  I thinks it’s 3

Answer:

275 = 25 × 11

The greatest perfect square factor of 275 is 25.

The greatest perfect square that is a factor of 275 is 25.We were able to determine this by breaking down 275 into its prime factors and looking for pairs of factors that were the same.

We can break down 275 into its prime factors to help us determine the greatest perfect square that is a factor of 275.275 = 5 * 5 *11. Since a perfect square is the product of a number multiplied by itself, we need to look for pairs of prime factors that are the same. We can see that 5 is a repeated factor, which means that it is a perfect square. So, we can take out a pair of 5s and get:$$275 = 5 \times 5 \times 11 = 5^2 \times 11$$Therefore, the greatest perfect square that is a factor of 275 is 25.

we have found that the greatest perfect square that is a factor of 275 is 25. Since 5 was a repeated factor, we were able to take out a pair of 5s and get 5 squared, which is 25.

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The solution to the equation is -1.5 or -3/2.

We have the equation:

x² + 3-2x= 1+ x² +5

Combine Terms and subtract x² from both sides:

x² - x² + 3 -2x = 1 + 5 + x² - x²

3 -2x = 1 + 5

Add:

3 -2x = 6

Combine Terms and subtract 3 from both sides:

-2x + 3 -3 = 6 - 3

-2x = 3

Dividing by -2 we get:

x = 3/(-2)

x = -3/2

x = -1.5

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Step-by-step explanation:

Let ABC be an isosceles triangle with sides AC and BC of equal length.                

We need to prove that the medians AD and BE are of equal length.

Consider the triangles ADC and BEC.

They have two congruent sides that include congruent angles.

Indeed, AC = BC by the condition, because the triangle ABC is isosceles.

Since the lateral sides AC and BC are of equal length, their halves EC

and DC are of equal length too: EC = DC.

Finally, the angle ECD is the common angle.

Thus, the triangles ADC and BEC are congruent, in accordance to the

postulate P1 (SAS) (see the lesson Congruence tests for triangles of the

topic Triangles in the section Geometry in this site).

Hence, the medians AD and BE are of equal length as the corresponding sides

of these triangles.

The proof is completed.

a) 2.7% of mayflies live at least 26.8 hours.

b) 85% of the mayflies die after approximately 26.2 hours.

a) We can begin by standardizing the value of 26.8 hours:

\(z = \frac{26.8 - 23.7}{1.6} = 1.9375\)

Using a standard normal table or a calculator, we can find that the probability of a standard normal random variable being greater than 1.9375 is approximately 0.027, or 2.7%. Therefore, about 2.7% of mayflies live at least 26.8 hours.

b) We want to find the value of x such that 85% of the mayflies have a lifespan less than x. To do this, we need to find the z-score corresponding to the 85th percentile of the standard normal distribution:

\(z = \text{invNorm}(0.85) \approx 1.04\)

Then we can solve for x:

\(x = \mu + z\sigma = 23.7 + 1.04(1.6) \approx 26.2\)

Therefore, 85% of the mayflies die after approximately 26.2 hours.

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Answer:

The pizza restaurant put 1/10 of the sauce on each pizza.

Step-by-step explanation:

Take the 3/5, and on a calculator divide the 3 by the 5:

0.6

Then, take the 0.6 and divide it by the 6 pizzas:

0.1, converted into a fraction equals 1/10.

The pizza restaurant put 1/10 of the sauce on each pizza.

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Answer:

scale factor = 2

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, that is

scale factor = \(\frac{BC}{DE}\) = \(\frac{10}{5}\) = 2

Answer:

6741

Step-by-step explanation:

if its 10% smaller you would have to do the original precent, which is 100%, and subtract 10%, (90%) then divide 90 by 100 to get 0.9 and  multiply it by the total population, in this case 7,490, and you get your answer. i hope this helps :)