6.85 x 10^8 = 685,000,000

can any of you guys help out by showing work on how this is the answer

It is requred to test the exactness of the given ODE and then find its general solution. Then, if the given ODE is not exact, an integrating factor must be used to make it exact.

This given ODE is:(2xy - 2y²e^(3x))dx + (x² - 2ye^(2x))dy = 0.To verify the exactness of the given ODE, we determine whether or not ∂Q/∂x = ∂P/∂y, where P and Q are the coefficients of dx and dy respectively, as follows: P = 2xy - 2y²e^(3x) and Q = x² - 2ye^(2x).Then, we have ∂P/∂y = 2x - 4ye^(3x) and ∂Q/∂x = 2x - 4ye^(2x).Thus, since ∂Q/∂x = ∂P/∂y, the given ODE is exact.To solve the given ODE, we have to find a function F(x,y) that satisfies the equation Mdx + Ndy = 0, where M and N are the coefficients of dx and dy respectively. This is accomplished by integrating both P and Q with respect to their respective variables. We have:∫Pdx = ∫(2xy - 2y²e^(3x))dx = x²y - y²e^(3x) + g(y), where g(y) is a function of y. We differentiate both sides of this equation with respect to y, set it equal to Q, and then solve for g(y). We have:(d/dy)(x²y - y²e^(3x) + g(y)) = x² - 2ye^(2x)Thus, g'(y) = 0 and g(y) = C, where C is a constant.Substituting the value of g(y) in the equation above, we get:x²y - y²e^(3x) + C = 0, as the general solution.The given ODE is exact, so we can solve it by finding a function that satisfies the equation Mdx + Ndy = 0. After integrating both P and Q with respect to their respective variables, we find that the general solution of the given ODE is x²y - y²e^(3x) + C = 0.

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The number of miles in 4 weeks is 20 mules

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

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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Answer:

8.373

Step-by-step explanation:

Cone

Find the volume of the cone

V = 1/3 pi r^2 h

r = d/2

r = 4/2

r = 2 inches

h = 6 inches

pi = 3.14

V = 1/3 * 3.14 * 2^2 *  6

V = 25.12

Half sphere

V = 1/2 (4/3) pi r^3

r = 2 from above calculation

pi = 3.14

V = 2/3 * 3.14 * 2^3

V = 2/3 * 3.14 * 8

V = 16.74

Nothing spills out so I scoop must be a whole sphere. The sphere is 2 times what I calculated it to be or

V = (4/3) * 3.14 * 2^3

V = 33.49 cubic inches

The difference in volume is 33.49 - 25.12 = 8.373

The results also suggest that television advertising may be slightly more effective than newspaper advertising in generating revenue.

(a)The estimated regression equation with the amount of television advertising as the independent variable is as follows: ŷ = 20.2650 + 22.1250x1(b)The proportion of variation in the sample values of weekly gross revenue that the model in part

(a) explains is given by the coefficient of determination. It is equal to the square of the correlation coefficient, r, and is calculated as follows: r² = 0.5145Thus, the model explains 51.45% of the variation in the sample values of weekly gross revenue. When converted to a percentage, the answer is 51%. Therefore, the answer is 51%.

(c)The estimated regression equation with both television advertising and newspaper advertising as the independent variables is given by:ŷ = -0.2154 + 19.4649x1 + 30.2941x2We will test whether the regression parameter β0 is equal to zero at a 0.05 level of significance using the t-test. The null and alternative hypotheses are as follows:H0: β0 = 0 (the y-intercept is zero)Ha: β0 ≠ 0We use a t-test to calculate the p-value. t = -0.2286 and the p-value is 0.8292. Since the p-value is greater than 0.05, we fail to reject H0. Hence, we cannot conclude that the y-intercept is not equal to zero.

The next step is to test whether the regression parameter β1 is equal to zero at a 0.05 level of significance. The null and alternative hypotheses are as follows:H0: β1 = 0 (there is no relationship between the amount spent on television advertising and weekly gross revenue)Ha: β1 ≠ 0We will use a t-test to calculate the p-value. t = 2.5494 and the p-value is 0.0382.

Since the p-value is less than 0.05, we reject H0. Hence, we can conclude that there is a relationship between the amount spent on television advertising and weekly gross revenue. We will also test whether the regression parameter β2 is equal to zero at a 0.05 level of significance. The null and alternative hypotheses are as follows:H0: β2 = 0 (there is no relationship between the amount spent on newspaper advertising and weekly gross revenue)Ha: β2 ≠ 0

We will use a t-test to calculate the p-value. t = 3.2487 and the p-value is 0.0128. Since the p-value is less than 0.05, we reject H0. Hence, we can conclude that there is a relationship between the amount spent on newspaper advertising and weekly gross revenue.

(e)The next step should be to use the model with both independent variables to make predictions and test the model's accuracy.

(f)The managerial implications of these results are that management can feel confident that increased spending on both television and newspaper advertising coincides with increased weekly gross revenue. The results also suggest that television advertising may be slightly more effective than newspaper advertising in generating revenue.

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Answer:

-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2

Step-by-step explanation:

-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2-11x-7=-3x^2

Answer:

\(y=-\frac{1}{4}x\\\)

Step-by-step explanation:

The slope is calculated by "up ÷ across".

= -1 ÷ 4

= \(-\frac{1}{4}\)

The y-intercept is just 0 (because the line meets at the y axis at 0).

So, using \(y=mx+b\) (where m = slope and b = y-intercept),

\(y=-\frac{1}{4}x+0\)

but the '+0' is unnecessary so we just say \(y=-\frac{1}{4}x\)

Answer:

D

Step-by-step explanation:

Plug in 6 as x in the function

h(6) = 3(6) - 4

h(6) = 18 - 4

h(6) = 14

Answer:

The answer is 14 because 3 x 6 is 18 and 18 - 4 is 14

Step-by-step explanation:

To determine the values of b for which the series converges, we can use the p-series test. The p-series test states that a series of the form Σ 1/n^p converges if and only if p > 1.

We can express this answer using interval notation as (1, ∞).To determine the positive values of b for which the series converges, we'll analyze the series using the convergence test:Σ (1/(b * n))For this series, we can apply the Integral Test for convergence. The Integral Test states that if f(n) = 1/(b * n), where f is a positive, continuous, and decreasing function, then the series converges if the integral of f(x) from 1 to infinity converges.

Let's evaluate the integral:∫(1/(b * x)) dx from 1 to infinityWhen integrating, we get:(ln(|b * x|) / b) | from 1 to infinityTo make the integral converge, we need the upper bound (when x approaches infinity) to be finite. In other words, the natural logarithm must grow slower than b. This is true when b > 1.Therefore, the positive values of b for which the series converges are given by the interval (1, ∞).

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Answer:

A

Step-by-step explanation:

I am not sure but I think A

Answer:

a) 22583

b) 37345

Step-by-step explanation:

Divisibility by 11

Rule: A number passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.

For example, the number 14982 is divisible by 11. Sum the digits

1+9+2=12

4+8=12

Subtract them: 12-12=0. Since 0 is divisible by 11, then the number also is.

The number 745102 is not divisible by 11:

7+5+0=12

4+1+2=7

12-7=5. 5 is not divisible by 11.

a) 2_583. Let's call X to the unknown digit 2X583

2+5+3=10

X+8 should be 10 or 21, so 10-10=0 or 21-10=11 are divisible by 11, but X cannot be greater than 9, thus

X+8=10 => X=2. The number is 22583

b) 37X45

4+7=11

3+X+5 should be 11 or 21. Again, X must be less than 10, thus

3+X+5=11 => X=3. The number is 37345

Here is the two-column proof proving SMRN, given RMSN and MRSNSR:

Statement Reason

RM = SN (Given) |

RS = NR (Reflective property) |

MRS = NSR (Given) |

SM = RN (Transitive property) |

We are given that RM = SN. This means that the length of line segment RM is equal to the length of line segment SN.

The reflective property of congruence states that any object is congruent to itself. Therefore, RS = NR.

We are given that MRS = NSR. This means that the angles MRS and NSR are congruent.

The transitive property of congruence states that if two objects are congruent to a third object, then they are congruent to each other. Therefore, SM = RN.

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The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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To find the equilibrium point between the supply and demand functions, we need to set the supply function S(x) equal to the demand function D(x) and solve for x.

Given:

S(x) = 9x + 8

D(x) = 83 - 6x

Setting S(x) = D(x), we have:

9x + 8 = 83 - 6x

Combining like terms, we get:

15x = 75

Dividing both sides by 15, we find:

x = 5

So the equilibrium point is (xE, PE) = (5, PE).

To find the equilibrium price (PE), we can substitute the value of x = 5 into either the supply or demand function. Let's use the demand function D(x):

D(x) = 83 - 6x

D(5) = 83 - 6(5)

D(5) = 83 - 30

D(5) = 53

Therefore, the equilibrium point is (xE, PE) = (5, 53).

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Explanation

8 x 5 means 8 in 5 places

Answer: 40

The cost of 1 oz in dollars if 10 oz cost $0.95 is $0.095

Based on the given concept; we can solve by using ratio

Cost of 10 oz = $0.95

Cost of 1 oz = x

Equate the ratio of number of oz to cost in dollars

10 : 0.95 = 1 : x

10/0.95 = 1/x

cross product

10 × x = 0.95 × 1

10x = 0.95

divide both sides by 10

x = 0.95/10

x = $0.095

In conclusion, 1 oz cost $0.095

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Yes, the implications of leaving farm fields unused for the economy's PPF diagram can be seen in the output of agricultural products.

The PPF diagram shows the maximum output of two products that an economy can produce at a given time, and it is shaped like a curve. When farm fields are left unused, the amount of agricultural products that can be produced is decreased, resulting in a shift in the PPF curve inwards. This means that the economy has to sacrifice other goods to maintain the same level of production of agricultural products, leading to an opportunity cost. Thus, leaving farm fields unused has implications for the economy's PPF diagram, as it reduces the output of agricultural products, resulting in a shift in the PPF curve inwards.

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total no of marbles = 10

no of marbles which are not white = 8

8/10 = 4/5

hope it helps...!!!

a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

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The dimensiοns οf the deck are 15 ft x 45 ft.

A quadrilateral with fοur right angles is a rectangle (90-degree angles). It has twο pairs οf parallel sides that are each the same length, making it a twο-dimensiοnal geοmetric shape. A rectangle has equal and parallel οppοsite sides, and adjacent sides that are perpendicular tο οne anοther.

Let's represent the width οf the deck as "w". Then, accοrding tο the prοblem statement, the length οf the deck is 3 times the width, which we can represent as "3w".

The area οf a rectangle is given by the fοrmula A = length x width. In this case, the area οf the deck is given as \(675 ft^2\), sο we can write:

A = lw = 675

Substituting the expressiοns fοr length and width in terms οf w, we get:

(3w)w = 675

Simplifying this equatiοn, we get:

\(3w^{2} = 675\)

Dividing bοth sides by 3, we get:

\(w^{2} = 225\)

Taking the square rοοt οf bοth sides, we get:

w = 15

Sο the width οf the deck is 15 feet. The length is 3 times the width, οr 45 feet. Therefοre, the dimensiοns οf the deck are 15 ft x 45 ft.

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A true statement about a negatively skewed distribution is that the tail of the distribution extends towards the lower values and there are a few extreme low values that pull the mean towards the left side. Therefore, the statement that is most likely to be true about a negatively skewed distribution is option A, i.e., the mean is greater than the median.

This is because the median is not affected by extreme values in the distribution, whereas the mean is influenced by the presence of outliers, causing it to shift towards the direction of the outliers. Thus, in a negatively skewed distribution, the mean will be pulled towards the left side by the low extreme values, making it lower than the median, which is the middle value of the data. Therefore, it can be concluded that the mean and median are not equal in a negatively skewed distribution.

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The statement that is most likely to be true about a negatively skewed distribution is B. The median is greater than the mean. A negatively skewed distribution is a distribution in which the tail on the left side of the distribution is longer than the tail on the right side.

This means that there are more scores on the right side of the distribution and fewer scores on the left side. As a result, the mean is pulled to the left side of the distribution, making it smaller than the median, which is the middle score of the distribution.

In a negatively skewed distribution, there may be some extreme scores on the left side that are pulling the mean in that direction, but the majority of the scores are clustered around the median, making it the most representative measure of central tendency.

Therefore, it is most likely that the median is greater than the mean in a negatively skewed distribution.

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Hey there,

We have,

f(x) = x² + 11x + 30g(x) = x + 6

Now,

(f.g)(x) = f(g(x))

Substituting...

g(x) = x + 6f(g(x)) = f(x + 6)

Now,

f(x + 6)= (x + 6)² + 11(x + 6) + 30= x² + 12x + 36 + 11x + 66 + 30= x² + 23x + 132

So,The value is x² + 23x + 132

To represent the final price (Px) of the items purchased, we first apply the 30% holiday sale discount and then the 15% off coupon. Let's find the correct function:

1. Apply the 30% holiday sale: Price becomes 0.7x (as 100% - 30% = 70%)
2. Apply the 15% off coupon: Final price becomes 0.85 * 0.7x (as 100% - 15% = 85%)

Now, multiply 0.85 by 0.7, which equals 0.595.

Therefore, the function representing the final price is Px(x) = 0.595x.

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Answer:

A≈1256.64

Step-by-step explanation:

A=3.14r^2

r=radius=20

A≈1256.64

the actual perimeter of the living room  in the scale drawing  is 216 inches.

We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.

When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.

When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.

When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.

One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.

You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.

If the length and breadth of the living room in real life are 9/4 inches each, we can use the given scale of the drawing to find the corresponding dimensions of the living room in the drawing:

1/4 inch = 2 feet

So, 9/4 inches in real life is equal to:

(9/4) inches / (1/4 inch per 2 feet) = 18 feet

This means that each side of the living room in the drawing would be 18/2 = 9 inches long.

To find the actual perimeter of the living room, we need to convert the dimensions back to real-life measurements and add up the lengths of all four sides:

Length in real life = 9/4 inches x 2 x 12 inches/foot = 54 inches

Breadth in real life = 9/4 inches x 2 x 12 inches/foot = 54 inches

Perimeter in real life = 2 x (Length + Breadth)

Perimeter in real life = 2 x (54 inches + 54 inches)

Perimeter in real life = 2 x 108 inches

Perimeter in real life = 216 inches

Therefore, the actual perimeter of the living room is 216 inches.

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The figure that shows a reflection of pre-image ABC over the y-axis is the third figure.

From the complete information, the triangle ABC is reflected over the y axis.

The vertices of the triangle are A(1, 1), B(3, 4) and C(3, 1). The vertices of the images are A(1, 1) = A'(-1, 1). B(3, 4) = B(-3, 4) ans C(3, 1) = C'(-3, 1).

In conclusion, the figure that shows a reflection of pre-image ABC over the y-axis is the third figure.

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The expected value of the sum of the two extreme numbers is 1/2.

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

The optimal strategy for you would be to choose the number 0.5, as it maximizes the probability that your pair will have the highest sum, and minimizes the probability that your pair will have the lowest sum.

This is because if all players choose a number uniformly at random, the expected value of the lowest and highest numbers will be 0 and 1 respectively, and the expected value of the middle two numbers will be 0.5. Therefore, by choosing 0.5, you have the best chance of having the highest sum, which means you will have to pay the least amount of money.

Therefore, the expected value of the sum of the two extreme numbers is 1/2.

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The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.

To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.

Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.

The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).

Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:

yz + λ = 0

xz + 3λ = 0

x*y + 4λ = 0

x + 3y + 4z - 9 = 0

Solving these equations simultaneously, we get:

x = 1.5, y = 1, z = 2.25, and λ = -0.5625

Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.

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