15/3+30/3= how I can solve it ?

The Venn diagram representing the sets U, A, B, and C is attached below. The elements of BU(A-C) are (3pi)/4, 10.7, 0.25, 47, and 3.29.

The elements of the set [5] BU(A-C) are the elements of B that are not in C. The elements of C are the irrational numbers in the universal set. The elements of B are the rational numbers in the universal set. The elements of [5] BU(A-C) are the rational numbers in the universal set that are not irrational. The elements of [5] BU(A-C) are (3pi)/4, 10.7, 0.25, 47, 3.29, and 2³.

Find the elements of A-C. The elements of A are the real numbers in the universal set. The elements of C are the irrational numbers in the universal set. The elements of A-C are the real numbers in the universal set that are not irrational. The elements of A-C are (3pi)/4, 10.7, 0.25, 47, and 3.29.

Find the elements of B. The elements of B are the rational numbers in the universal set.

Find the elements of BU(A-C). The elements of BU(A-C) are the rational numbers in the universal set that are not irrational.

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Answer:

0.6 as a decimal and 60 percent

b) The mean and standard deviatiοn οf the data is 8.022 and 0.335 respectively.

In statistics, mean is measure οf central tendency that represents average value οf set οf numbers. It is calculated by adding up all  values in  set and dividing  sum by the tοtal number οf values in  set.

b) Tο determine the mean and standard deviatiοn οf the data, we can input the given values intο a calculatοr οr a spreadsheet prοgram and use the apprοpriate fοrmulas. Here are the calculatiοns:

Mean = (7.96 + 8.54 + 7.92 + 8.40 + 8.02 + 7.91 + 8.12 + 7.85 + 8.27 + 7.67) / 10

= 8.022

Standard deviatiοn = sqrt([(7.96 - 8.022)² + (8.54 - 8.022)² + ... + (7.67 - 8.022)²] / 9)

= 0.335 (rοunded tο 3 decimal places)

Therefοre, the mean petrοl price is 8.022 and the standard deviatiοn is 0.335.

c) The histοgram appears tο be slightly skewed tο the right, as the tail οf the histοgram extends further tο the right than tο the left.

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Answer:

The total work done in pulling the bucket to the top of the well is approximately 3,139.1 ft·lb

Step-by-step explanation:

The given parameters are;

The mass of the bucket, W = 3.6 pounds

The depth of the well, h = 78 feet deep

The mass of water in the bucket = 38 ponds

The rate at which the water is pulled up = 2.9 feet per second

The rate at which water is leaking from the bucket, \(\dot m\) = 0.1 pounds per second

We separate and find the work done for lifting the bucket and the water individually, then we add the answers to get the solution to the question as follows;

The work done in lifting bucket empty from the well bottom, \(W_b\) = W × h

∴  \(W_b\) = 3.6 pounds × 78 feet = 280.8 ft-lb

The work done in lifting bucket empty from the well bottom, \(W_b\) = 280.8 ft-lb

The time it takes to lift the bucket from the well bottom to the top, 't', is given as follows;

Time, t = Distance/Velocity

The time it takes to pull the bucket from the well bottom is therefore;

t = 78 ft./(2.9 ft./s) ≈ 26.897

The time it takes to pull the bucket from the well bottom to the top, t ≈ 26.897 s

The mass of water that leaks out from the bucket before it gets to the top, m₂, is therefore;

m₂ = \(\dot m\) × t

∴ m₂ = 0.1 lbs/s × 26.897 s = 2.6897

The mass of the water that leaks, m₂ = 2.6897 lbs

The mass of water that gets to the surface m₃ = m - m₂

∴ m₃ = 38 lbs  - 2.6897 lbs ≈ 35.3103 lbs

Given that the water leaks at a constant rate the equation representing the mass of the water as it is lifted can b represented by a straight line with slope, 'm' given as follows;

The slope of the linear equation m = (38 lbs - 35.3103 lbs)/(78 ft. - 0 ft.) = 0.03448\(\overline 3\) lbs/ft.

Therefore, the equation for the weight of the water 'w' can be expressed as follows;

w = 0.03448\(\overline 3\)·y + c

At the top of the well, y = 0 and w = 38

∴ 35.3103 = 0..03448\(\overline 3\) × 0 + c

c = 35.3103

∴ w = 0.03448\(\overline 3\)·y + 35.3103

The work done in lifting the water through a small distance, dy is given as follows;

(0.03448\(\overline 3\)·y + 38) × dy

The work done in lifting the water from the bottom to the top of the well, \(W_{water}\), is given as follows;

\(W_{water} = \int\limits^{78}_0 {0.03448\overline 3 \cdot y + 35.3103 } \, dy\)

\(\therefore W_{water} = \left [ {\dfrac{0.03448\overline 3 \cdot y^2}{2} + 35.3103 \cdot y\right ]^{78}_0\)

\(W_{water}\) = (0.034483/2 × 78^2 + 35.3103 × 78) - (0.034483 × 0 + 38 × 0)  ≈ 2,859.1

The work done in lifting only the water, \(W_{water}\) ≈ 2,859.1 ft-lb

The total work done, in pulling the bucket to the top of the well, W = \(W_b\) + \(W_{water}\)

∴ W = 2,859.1 ft.·lb + 280.8 ft.·lb ≈ 3,139.1 ft·lb

The total work done, in pulling the bucket to the top of the well, W ≈ 3,139.1 ft·lb.

Answer:

Step-by-step explanation:

The equation of the line that is parallel to y = 4x ₊ 3 and passes through the point (2,6) is  y = 4x ₋ 2.

The slope of the preceding equation is 4 because it is in slope intercept form. The slope of an equation is always equal for parallel lines, hence the slope of the equation we are requested to create is also 4.  We are given that this line passes through (2,6).

In the absence of intersection, two lines are said to be parallel. Each line has the same slope. In the event where m₁=m₂, f(x)=m₁x+b₁ and g(x)=m₂x+b₂ are. parallel

In order to write in y = mx +b form, we need to solve for b (the y-intercept).  

Given, x=2, y=6, and m = 4.

6 = (4) (2) ₊ b

simplify

6 = 8 ₊ b

solve for b.

b = 6 ₋ 8

b = ₋2

So the equation of the parallel line is   y = 4x ₋ 2

Hence we get the equation of the line that is parallel to y = 4x ₊ 3 and passes through the point (2,6) is y = 4x ₋ 2

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Answer:

A

Step-by-step explanation:

i just took the lab assessment

Answer:

Step-by-step explanation:

Let x be the total no. of strawberries, Let Sue be "S", Let Jim be "J" and Dan be "D"

S = 2x/7

J = 54+S -> J = 54+(2x/7)

D = 78

J+D = 5x/7

54+(2x/7)+78 = 5x/7

132+2x/7 = 5x/7

132 = (5x/7)-(2x/7)

132 = 3x/7

132*7 = 3x

924/3 = x

x = 308.

Therefore, there were initially 308 strawberries in the basket.

Of which; Sue had two-sevenths: 88, Jim had 142 and Dan had 78

To verify our answer, add these to see if we get 308

S+J+D = 308

88 + 142 + 78 = 308

Answer:

Step-by-step explanation:No, Lonnie is not correct. Step-by-step explanation: Because if we put 35 and 42 in rational form we can write it to its simple form by dividing it and after dividing we get the answer as 5 : 6. so that means Lonnie in incorrect.D

Answer:

14

Step-by-step explanation:

Step 1:

2 ( 3b - 2 ) = 2 ( 2b + 12 )     Equation

Step 2:

6b - 4 = 4b + 24     Multiply

Step 3:

6b = 4b + 28    Add 4 on both sides

Step 4:

2b = 28     Subtract 4b on both sides

Step 5:

b = 28 ÷ 2    Divide

Answer:

b = 14

Hope This Helps :)

Answer:

The responses to the given question can be defined as follows:

Step-by-step explanation:

Please find the complete question in the attached file.

\(Day \ \ \ \ \ \ \ \ \ \ Period \ \ \ \ \ \ \ \ \ \ Demand \ \ \ \ \ \ \ \ \ \ 5-period moving average\)

\(1 \ \ \ \ \ \ \ \ \ \ \ Morning \ \ \ \ \ \ \ \ \ \ \ 37 \\\\\)

            \(Afternoon \ \ \ \ \ \ \ \ \ \ \ 25 \\\\ Evening \ \ \ \ \ \ \ \ \ \ \ 9\)

\(2 \ \ \ \ \ \ \ \ \ \ \ Morning \ \ \ \ \ \ \ \ \ \ \48 \\\\\)

           \(Afternoon\ \ \ \ \ \ \ \ \ \ \ 28 \\\\\)

            \(Evening \ \ \ \ \ \ \ \ \ \ \ 14 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 29.4 \\\\\)

\(3 \ \ \ \ \ \ \ \ \ \ \ Morning \ \ \ \ \ \ \ \ \ \ \ 53 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 24.8\\\\\)

              \(Afternoon \ \ \ \ \ \ \ \ \ \ \ 33 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 30.4\\\\Evening \ \ \ \ \ \ \ \ \ \ \ 17 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 35.2\\\\\)

\(4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Morning \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 29\\\\\)

                 \(Afternoon\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 29.25\\\\Evening \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 34.33333\\\\\)

Answer:

R(x) = (460 * 7x)*(20+ x)

Step-by-step explanation:

If exactly 20 people sign up :

Charge per person = $460

For passengers after 20:

At number of passengers = 20 ;

Cost = (fee * discount * number of additional passesengers) * (20 + Number of additional passengers

Let number of additional passengers after 20 = x

R(x) = ($460 * $7x) * (20 + x)

Hence,

R(x) = (460 * 7x)*(20+ x)

Answer:

          ______

x  =  − 0.  142857

Step-by-step explanation:

The question is an illustration of solving equations using estimates.

The student's strategy makes sense because he uses estimation to solve the given equation

The correct sequence of equation is as follows:

We have:

\(\mathbf{159 - 73}\)

Add 0 to the equation

\(\mathbf{159 - 73 =159 + 0- 73}\)

Express 0 as 1 - 1

\(\mathbf{159 - 73 =159 + 1 - 1- 73}\)

\(\mathbf{159 - 73 =160 - 1- 73}\)

Add another 0

\(\mathbf{159 - 73 =160 - 1- 73 + 0}\)

Express 0 as 3 - 3

\(\mathbf{159 - 73 =160 - 1- 73 + 3 - 3}\)

\(\mathbf{159 - 73 =160 - 1- 70 - 3}\)

Rewrite as:

\(\mathbf{159 - 73 =160 - 70- 1 - 3}\)

Solve

\(\mathbf{159 - 73 =90- 4}\)

\(\mathbf{159 - 73 =86}\)

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The period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

The function is given as:

y = 2∕3 cos(4∕7x) + 2.

The above function is a cosine function

A cosine function is represented as:

y = A cos(B(x + C)) + D

Where the period is

Period = 2π/B

By comparing the equations, we have

B = 4/7

Substitute B = 4/7 in Period = 2π/B

Period = 2π/(4/7)

Express as product

Period = 2π * 7/4

Divide 4 by 2

Period = π * 7/2

Evaluate the product

Period = 7/2π

Hence, the period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

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Answer:

298

Step-by-step explanation:

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The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.

In this problem we know the three vertices of a triangle on a Cartesian plane and we must determine the coordinates of its image by applying rigid transformations. According to the statement, the vertices of the image are obtained by applying a translation formula:

P'(x, y) = P(x, y) + T(x, y)        (1)

Where:

If we know that P(x, y) = (2, - 4), Q(x, y) = (4, - 5), R(x, y) = (7, - 2) and T(x, y) = (- 6, 3), then the coordinates of the vertices of the image are:

P'(x, y) = (2, - 4) + (- 6, 3)

P'(x, y) = (- 4, - 1)

Q'(x, y) = (4, - 5) + (- 6, 3)

Q'(x, y) = (- 2, - 2)

R'(x, y) = (7, - 2) + (- 6, 3)

R'(x, y) = (1, 1)

The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.

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Answer:

arithmetic sequence

Step-by-step explanation:

Each new member of this sequence is less than the previous member by a fixed number, which means this is an arithmetic sequence.

Answer:

6

Step-by-step explanation:

The two triangles are similar which means the the two length is parallel

.°., the Length of the smaller triangle=6

The statement that applies to the sample math is:

B. the work shown to remove all fractions is not correct

The given steps are:

y = ¹/₄x + 2

- I first isolate the constant.

- After doing so, I get the equation: -¹/₄x + y = 2

- To remove the fraction, I multiply by –4, giving the equation x - 4y=2, which is the final answer.

The correct steps are as follows:

y = ¹/₄x + 2

First isolate the constant to get: y - ¹/₄x = 2

To remove the fraction, Multiply the obtained equation by –4

So, Equation : x - 4y = -8

On comparing both the work we can see that in the given work the removal of fraction is done incorrectly

They didn't multiply -4 on the right hand side .

Thus, option B applies.

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Answer:

\(12\pi\)

Step-by-step explanation:

\(L=\frac{\pi (120)(18)}{180} =\frac{2160\pi }{180}= 12\pi\)

Hope this helps

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

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Answer:

Step-by-step explanation:

f(x)=2x

note: putting anything in the f(x) parentheses replaces x in the function with that value

so,

f(-3) = 2(-3) = -6

f(0) = 2*0 = 0

f(2) = 2(2) = 4

A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

The function f(x) = -|x| − 3 can be graphed by following these steps:

Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

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Answer:

  4x^2 -25

Step-by-step explanation:

The other factor of the difference of squares is the "conjugate" of the given one: (2x -5). Then their product is ...

  (2x +5)(2x -5) = (2x)^2 -(5)^2 = 4x^2 -25

Answer:

The Answer On Edge Is D.), Have Fun Dreamers!

Step-by-step explanation: