Coach Peters has 12 gallons of water to fill buckets for field day. If
each bucket needs of a gallon to fill, how many buckets can he fill?

The value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345​ is 38.0

The equations are given as:

tan(x)=sin38°

cosec( x+10°)=1.345​

In tan(x)=sin38°, we have:

tan(x)=0.6157

Take the arc tan of both sides

x = 31.6

Also, we have:

cosec(x+10°)=1.345​

Take the inverse of both sides

sin(x+10°) = 0.7434

Take the arc sin of both sides

x+10 = 48.0

Subtract 10 from both sides

x = 38.0

Hence, the value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345​ is 38.0

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9514 1404 393

Answer:

  n cm = 3 cm

Step-by-step explanation:

The total surface area is the sum of the base areas and the lateral area. The base areas are the sum of the areas of the rectangle and triangle that define the shape of the base.

The rectangle has dimensions 5 cm by n cm. The triangle is 5-2 = 3 cm high and 4 cm at the base. Then the front face area is ...

  A = lw + 1/2bh

  A = (5 cm)(n cm) +1/2(4 cm)(3 cm) = (6 +5n) cm²

The lateral area is the product of the perimeter of the base and the depth of the prism.

  A = Ph

  A = (5 cm + n cm + 2 cm + 5 cm + 4 cm + n cm)(4 cm) = (64 +8n) cm²

The total surface area is the sum of the areas of the two bases and the lateral area:

  130 cm² = 2(6 +5n) cm² +(64 +8n) cm²

  130 = 76 +18n . . . . . . divide by cm², collect terms

  54 = 18n . . . . . . . . . subtract 76

  3 = n . . . . . . . . . . divide by 3

The value of n in centimeters is 3 cm.

The direction of the electric field can be determined by taking the negative gradient of the electric potential function. At the point (3.0 m, 2.0 m), the electric field is directed in the positive x-direction.

To find the electric field at a given point, we can take the negative gradient of the electric potential function. The electric potential function V(x, y) is given as V = 2.0x^2 - 3.0y^2 + 5xy.

Taking the partial derivatives with respect to x and y, we obtain:

dV/dx = 4.0x + 5y

dV/dy = -6.0y + 5x

At the point (3.0 m, 2.0 m), we substitute x = 3.0 and y = 2.0 into the partial derivatives:

dV/dx = 4.0(3.0) + 5(2.0) = 22.0

dV/dy = -6.0(2.0) + 5(3.0) = 1.0

The electric field E is given by E = -∇V, where ∇ is the gradient operator. Therefore, the electric field at (3.0 m, 2.0 m) is E = (-22.0 i + 1.0 j) N/C.

To find the magnitude of the electric field, we calculate:

|E| = sqrt((-22.0)^2 + (1.0)^2) ≈ 60.1 N/C.

The magnitude of the electric field is approximately 60.1 N/C, and its direction is in the positive x-direction.

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Answer:

264

Step-by-step explanation:

Divide 480 by 20. (24)

Multiply 24 by 11.  

Answer should be 264

* Hope that helped

\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)

➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]

➝ -4 × (-2) [2 × (-6) + 3 × (4) ]

➝ -4 × (-2) [2 × (-6) + 12 ]

➝ -4 × (-2) [(-12) + 12 ]

➝ -4 × (-2) [0]

➝ -4 × 0

➝ 0

Answer:

-4*-2

Step-by-step explanation:

the multiple of both side is 4*2*,26+*32*--=6 44

To classify the rings rq = r[x]/(q) up to isomorphism, we need to consider the cases where two such rings are isomorphic and when they're not.

1. If two quadratic polynomials q1 and q2 are irreducible and have different roots, then the rings rq1 and rq2 are not isomorphic. This is because the roots of q1 and q2 determine the elements in the rings, and if the roots are different, the rings will have different elements.

2. If two quadratic polynomials q1 and q2 are reducible and have the same roots, then the rings rq1 and rq2 are isomorphic. This is because the roots of q1 and q2 determine the elements in the rings, and if the roots are the same, the rings will have the same elements.

3. If two quadratic polynomials q1 and q2 are reducible but have different roots, then it depends on whether the roots are linearly dependent over the base field r. If the roots are linearly dependent, then the rings rq1 and rq2 are isomorphic. If the roots are linearly independent, then the rings rq1 and rq2 are not isomorphic.

In summary, the rings rq = r[x]/(q) are isomorphic if and only if the quadratic polynomials q have the same roots, up to linear dependence over the base field r.

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Answer| range: {15, 11, 7, -3, -7}

Step-by-step explanation:

Plug in the domain to find the range:

x = 4

2(-4) + y = 7

-8 + y = 7

y = 15

x = -2

2(-2) + y = 7

-4 + y = 7

y = 11

x = 0

2(0) + y = 7

0 + y = 7

y = 7

x = 5

2(5) + y = 7

10 + y = 7

y = -3

x = 7

2(7) + y = 7

14 + y = 7

y = -7

Answer:

10. 7 + 4a

11. 7a + 4

12. 12a - 4

13. 14(a - 4)

14. 2a + b

15. 2(a + b)

16. 1/3x - 5

17. 3x/8

18. ab / a+b

Step-by-step explanation:

Let x be the number.

Can't explain, I need to do homework.

Hope this helps :)

To find the absolute maximum and minimum values of the given function on the unit disc, we can use the method of Lagrange multipliers.

The function to optimize is: f(x, y) = x² + y² - x - y + 6.

The constraint equation is: g(x, y) = x² + y² - 1 = 0.

We need to use the Lagrange multiplier λ to solve this optimization problem.

Therefore, we need to solve the following system of equations:∇f(x, y) = λ ∇g(x, y)∂f/∂x = 2x - 1 + λ(2x) = 0 ∂f/∂y = 2y - 1 + λ(2y) = 0 ∂g/∂x = 2x = 0 ∂g/∂y = 2y = 0.

The last two equations show that (0, 0) is a critical point of the function f(x, y) on the boundary of the unit disc D.

We also need to consider the interior of D, where x² + y² < 1. In this case, we have the following equation from the first two equations above:2x - 1 + λ(2x) = 0 2y - 1 + λ(2y) = 0

Dividing these equations, we get:2x - 1 / 2y - 1 = 2x / 2y ⇒ 2x - 1 = x/y - y/x.

Now, we can substitute x/y for a new variable t and solve for x and y in terms of t:x = ty, so 2ty - 1 = t - 1/t ⇒ 2t²y - t + 1 = 0y = (t ± √(t² - 2)) / 2t.

The critical points of f(x, y) in the interior of D are: (t, (t ± √(t² - 2)) / 2t).

We need to find the values of t that correspond to the absolute maximum and minimum values of f(x, y) on D. Therefore, we need to evaluate the function f(x, y) at these critical points and at the boundary point (0, 0).f(0, 0) = 6f(±1, 0) = 6f(0, ±1) = 6f(t, (t + √(t² - 2)) / 2t)

= t² + (t² - 2)/4t² - t - (t + √(t² - 2)) / 2t + 6

= 5t²/4 - (1/2)√(t² - 2) + 6f(t, (t - √(t² - 2)) / 2t)

= t² + (t² - 2)/4t² - t - (t - √(t² - 2)) / 2t + 6

= 5t²/4 + (1/2)√(t² - 2) + 6.

To find the extreme values of these functions, we need to find the values of t that minimize and maximize them. To do this, we need to find the critical points of the functions and test them using the second derivative test.

For f(t, (t + √(t² - 2)) / 2t), we have:fₜ = 5t/2 + (1/2)(t² - 2)^(-1/2) = 0 f_tt = 5/2 - (1/2)t²(t² - 2)^(-3/2) > 0.

Therefore, the function f(t, (t + √(t² - 2)) / 2t) has a local minimum at t = 1/√2. Similarly, for f(t, (t - √(t² - 2)) / 2t),

we have:fₜ = 5t/2 - (1/2)(t² - 2)^(-1/2) = 0 f_tt = 5/2 + (1/2)t²(t² - 2)^(-3/2) > 0.

Therefore, the function f(t, (t - √(t² - 2)) / 2t) has a local minimum at t = -1/√2. We also need to check the function at the endpoints of the domain, where t = ±1.

Therefore,f(±1, 0) = 6f(0, ±1) = 6.

Finally, we need to compare these values to find the absolute maximum and minimum values of the function f(x, y) on the unit disc D. The minimum value is :f(-1/√2, (1 - √2)/√2) = 7 - √2 ≈ 5.58579.

The maximum value is:f(1/√2, (1 + √2)/√2) = 7 + √2 ≈ 8.41421

The absolute minimum value is 7 - √2, and the absolute maximum value is 7 + √2.

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Answer:48x14=672

139x12=1668

1668+672=2340

Step-by-step explanation:

You're finding the area of each stamp in length, so add the total area for each stamp together.

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Answer:

x = 4

Step-by-step explanation:

If 2 chords of a circle intersect , then the product of the parts of one chord is equal to the product of the parts of the other chord, that is

x(x + 6) = 5 × 8 = 10

x² + 6x = 40 ( subtract 40 from both sides )

x² + 6x - 40 = 0 ← in standard form

(x + 10)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 10 = 0 ⇒ x = - 10

x - 4 = 0 ⇒ x = 4

However, x > 0 , then x = 4

Answer:

60%

Step-by-step explanation:

The mean is 41.37
The Median is 36

The first step is to arrange the number orderly

31, 32,34,35,37,38,40,84

The mean is

= 31 + 32+34+35+38+37+40+84/8

= 331/8

= 41.37

The median

= 35+37/2

= 72/2

= 36

The mode
= N/A

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Step 1

Given;

Required; To find the side length.

Step 2

State the area(A) of an equilateral triangle.

Step 3

Find the side length

But, the side length cannot be negative, therefore, the side length of the equilateral triangle = 12 units

Answer:36

Step-by-step explanation:

60÷5×3=36

E(Y/n) = p. This result shows that Y/n is an unbiased estimator for p since its expected value is equal to the true value of the parameter p. As n gets large, the term 1/n approaches zero, and therefore, the variance V(Y/n) approaches zero as well.

a) To derive the expected value of Y/n, we can use the linearity of expectation. Since Y follows a binomial distribution with parameters n and p, we have:

E(Y/n) = E(Y) / n

The expected value of Y is given by:

E(Y) = np

Substituting this into the expression, we get:

E(Y/n) = np / n

Simplifying, we find:

E(Y/n) = p

This result shows that Y/n is an unbiased estimator for p since its expected value is equal to the true value of the parameter p.

b) To derive the variance of Y/n, we can use the properties of variance. Since Y follows a binomial distribution with parameters n and p, the variance of Y is given by:

V(Y) = np(1 - p)

Using the properties of variance, we have:

V(Y/n) = V(Y) / n²

Substituting the expression for V(Y), we get:

V(Y/n) = (np(1 - p)) / n²

Simplifying, we find:

V(Y/n) = (p(1 - p)) / n

As n gets large, the term 1/n approaches zero, and therefore, the variance V(Y/n) approaches zero as well. This means that as the sample size increases, the variability of the estimator Y/n decreases, indicating a more precise estimate of the true parameter p.

In conclusion, the expected value of Y/n is equal to the true value of the parameter p, making Y/n an unbiased estimator. Additionally, as the sample size increases, the variance of Y/n decreases, leading to a more precise estimate of the parameter p.

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Answer:

-4

Step-by-step explanation:

Move variables to one side and numbers on the other.

12 - 3x = -6x

+ 3x +3x

12 = -3x

/-3 /-3

-4 = x

Answer:

The equation is;

f(x) = -2·x² + 5·x - 1

Step-by-step explanation:

The general form of a quadratic equation  or function f(x) is, f(x) = y = a·x² + b·x + c

Given that the points representing the quadratic function are;

(-1, -8), (0, -1), (1, 2) which  are of the form (x, y)

When x = -1, f(x) = y = -8

Plugging in the above values into the general form of a quadratic function, we have;

-8 = a·(-1)² + b·(-1) + c = a - b + c

-8  = a - b + c.........................(1)

When x = 0, y = -1, we have;

-1 = a·(0)² + b·(0) + c = c

c = -1.......................................(2)

When x = 1, y = 2, which gives;

2 = a·(1)² + b·(1) + c = a + b + c

2 = a + b + c........................(3)

Adding equation (1) to equation (3), we have;

-8 + 2 = a - b + c + a + b + c

-8 + 2 = 2·a + 2·c

From equation (2) c = -1, we get;

-8 + 2 = -6 = 2·a + 2·c = 2·a + 2 × (-1)

-6 = 2·a - 2

-4 = 2·a

a = -2

From equation (3), we have

2 = a + b + c

Substituting the values of a, and c gives;

2 = -2 + b - 1

b = 2 + 2 + 1 = 5

b = 5

The equation is therefore;

f(x) = -2·x² + 5·x - 1.

Answer:

b

Step-by-step explanation:

Answer:

y= 3/4x+5

Step-by-step explanation:

Answer:

The equation would be y=3/4x+5

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Answer:

C: 0.000568 miles

Step-by-step explanation:

Essentially, the exponent on the 10 is how many places to move the decimal point, and negative versus positive dictates whether to move it right or left respectively.

Answer:

Step-by-step explanation:

The answer is A. 0.568

True: A Chorochromatic map is a type of cartographic map that represents features depending on how they are distributed across the surface in terms of quality.`

We have,

The art and science of cartography involves visually depicting a geographic location, typically on a flat surface like a map or chart. It could include superimposing a region's depiction with non-geographical distinctions like political, cultural, or other ones.

Making and utilizing maps is the theory and application of cartography. Cartography, which combines science, aesthetics, and method, is based on the idea that reality may be described in ways that effectively convey spatial information. The same basic components are included on most maps: the main body, the legend, the title, the scale and orientation indications, the inset map, and the source notes.

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complete question:

a cartographic map style that symbolizes features based on the qualitative surface distribution of a mapped feature is called a chorochromatic map.

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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Answer:

Step-by-step explanation:

Since each table can fit 10 people, we need to divide 214 by 10 to find out how much tables were used.

214/10=21 remainder 4.

The problem says that every table was full except for the last one. So, there can’t be 4 remainder people in a 10 person table. Therefore we should add another table which makes 22.

Answer: 22 tables were used.

Answer:

1.12 < mn

xy - x + y

2/3x - x²

xy + x/y - 10

(x + 2)³

2(4b - 2x)