If 60% of the students prefer waffles to pancakes. If there are 5 students in the class, how many students prefer waffles?

ED = 3.8(tan 40°) (option A)

ED = 3.8/tan 50° (option D)

opposite = side opposite the angle 40° = DE

hypotenuse = EF = 5

adjacent = DF = 3.8

Since we are looking for DE, we can apply the sine ratio (SOH) or the tangent ratio (TOA)

The options are in tan, so we would focus on this.

tan 40° = opposite/adjacent

tan 40° = ED/3.8

ED = 3.8(tan 40°) (option A)

Since we have 40 degree as angle F, it means the third angle is 50 degree. This because 90- 40 = 50°. The 50°is angle E.

Using the angle as 50°:

opposite becomes = 3.8 as this is the side facing 50°

adjacent = ED

tan 50° = opposite/ adjacent

tan 50°= 3.8/ED

ED = 3.8/tan 50° (option D)

The answer of the question is ,field along an arbitrary path gives

= - (p cosθ/4πεr) and,

the work done to move a charge Q from P  is θ = arccos(z/r).

Work done is defined as energy transferred to or from  object when force is applied to it, causing it to move certain distance in direction of the force.

(a) To integrate the electric field along an arbitrary path, we need to use the definition of potential difference, which is the negative of the line integral of the electric field:

V(F) = - ∫F Edl

where V(F) is the potential difference between the endpoints of the path, F is the path, E is the electric field, and dl is an infinitesimal element of the path.

the electric field in the spherical coordinates are  given by:

Edipole (r, 0) = (P/4πε) [(2cosθ/r^2) i + (sinθ/r^2) j]

where θ = 0 on the z axis.

F = r(θ) i + r(φ)sinθ j

where r(θ) and r(φ) are the functions of θ and φ that describe the path.

Then, we can express dl in terms of these functions:

dl = dr(θ) i + r(θ) dφ j

Substituting the expression into  line integral, we get:

Vdipole = - ∫F Edl = - ∫θ1θ2 ∫φ1φ2 Edr(θ) - Er(φ)sinθ dθ dφ

Integrating with the respect to φ , we get:

Vdipole = - ∫θ1θ2 [(P/4πε) (2cosθ/r^2) r(φ)]dθ

= - (P/4πε) [(r(φ)/r^2)|θ1θ2] ∫θ1θ2 2cosθ dθ

= - (P/2εr) [cosθ1 - cosθ2]

where r = r(θ1) = r(θ2) is the constant radius of the path.

Substituting θ1 = 0 and θ2 = θ, we get:

Vdipole = - (P/2εr) cosθ

= - (p cosθ/4πεr)

(b ) To find the work done to move a charge Q from P to Q, we need to use the formula for potential difference:

W = Q[V(Q) - V(P)]

where W is the work done, Q is the charge, and V(Q) and V(P) are the potentials at the endpoints of the path.

For a charge Q moved from P = √(x + y) to Q = - (ŷ+2), the potential difference is:

V(Q) - V(P) = - (p cosθ/4πεr(Q)) + (p cosθ/4πεr(P)))

where r(Q) and r(P) are the distances from the dipole to the endpoints of the path.

Substituting the given values for P and Q, we get:

r(P) = √(x^2 + y^2), r(Q) = √[(y+2)^2 + x^2]

θ = arccos(z/r).

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* The complete question is :

The electric field of a dipole situated at the origin and pointing in the z direction is given by

Edipole (r, 0) =P Απεργ

(2 cos 0 + + sin 00),

where p = [p] is the magnitude of the dipole moment and (r, 0) are the usual spherical coordinates.

(a) Integrate the field along an arbitrary path and show that V(F) = - [Ē - dī gives,

Vdipole (r, 0) =p cos 0 Απεργ

Note: You are requied to compute the indefinite integral and so no limits are required.

(b) Find the work done to move a charge Q from P = √(x + y) to Q = -(ŷ+2).

The height of the school is 9 meters.

What is proportion?

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4).

Angle of incidence = Angle of reflection

As we can see in the picture attached, both the angles (θ) are equal.

m∠ACB = m∠ECD = 90° - θ

m∠ABC = m∠ADC = 90°

Therefore, both the triangles ΔABC and ΔEDC will be similar.

And by the property of similar triangles, their corresponding sides will be proportional.

 AB/ED = CB/CD

1.35/ED = 2.15/13.95

     ED = 8.75 meters

     ED ≈ 9 m.

Hence, the height of the school is 9 meters.

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Answer:

C

Step-by-step explanation:

hope this helps :)

Answer:

I assume that this is a math question not a chemistry question...

In math I assume the answer is 1 liter....

total = 2 liters (1 liter water 1 liter ammonia )

If this is a chemistry question there is a difference between total

volume, and total weight, which would not result in the answer being 1 liter

Step-by-step explanation:

The difference between the length of arc BD and CE is 1.57 units

length of arc = ∅ / 360 × 2πr

where

Therefore,

BD = 45 / 360 × 2 × 3.14 × 6 = 1695.6 / 360 = 4.71 units

CE = 45 / 360 × 2 × 3.14 × 8 = 2260.8 / 360 = 6.28 units

Therefore, the difference between the length of arc BD and CE is as follows:

6.28 - 4.71 = 1.57 units

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Answer:

1.57 units

Step-by-step explanation:

Answer:5/4

Step-by-step explanation: i think this is the answer

Answer:

The area is 30 units squared, the perimeter is 17 units, and the answer to the question below is 9

Step-by-step explanation:

Answer:

The sum of interior angles of a triangle is 180°

In a right triangle, one of the three angles is 90°.  Therefore, the sum of the other two angles is 90°.

Let a = one unknown angle

Let b = the other unknown angle

As the sum of the angles is 90°:

⇒ a + b = 90°

As the difference between the two angles is 20°:

⇒ a - b = 20°

Rewriting the first equation to make a the subject:

⇒ a = 90° - b

Substituting this into the second equation and solving for b:

⇒ 90° - b - b = 20°

⇒ 90° -2b = 20°

⇒ 70° = 2b

⇒ b = 35°

Substituting found value for b into  a = 90° - b  and solving for a:

⇒ a = 90° - 35°

⇒ a = 55°

Therefore, the two unknown angles are 35° and 55°

The number of ants after 1 year=464 and the table will follow no-linear function as the equation will be a exponential equation for the growth of ants.

What is a exponential equation?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 6^2y - 7 = 121 etc are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay, etc.

Now,

The exponential equation that will be followed by given ant's growth will be

y=29(2)^t/3

where 29=initial population

t=Number of months

and It will represent a non-linear function as a exponential function is a no-linear function.

Population after 1 year

                                   y=29(2)^12/3

                                     =29*16

                                      =464

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My teacher:
- 5'3
- 5.25 ft
- 63 in
- 160 cm

The Interstate 90 freeway in the US is (D) 123.9 miles.

Therefore, the Interstate 90 freeway in the US is (D) 123.9 miles.

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Correct question:

i-90 is the longest freeway in the us, stretching from Seattle to Boston. how many miles is it?

a. 248.1

b. 302.1

c. 437.1

d. 123.9

Answer: In mathematics, the additive inverse of a number is the number that, when added to the original number, results in zero.

Step-by-step explanation: The additive inverse of 21.9 can be found by simply negating the value, which means changing the sign from positive to negative, or vice versa. Therefore, the additive inverse of 21.9 is -21.9, because 21.9 + (-21.9) = 0.

As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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using the fifth partial sum of the exponential series, the approximation for e^(-2.5) is approximately 1.649 (rounded to three decimal places).

To approximate the value of e^(-2.5) using the fifth partial sum of the exponential series, we can use the formula:

e^x = 1 + x + (x^2 / 2!) + (x^3 / 3!) + (x^4 / 4!) + ... + (x^n / n!)

In this case, we have x = -2.5. Let's calculate the fifth partial sum:

e^(-2.5) ≈ 1 + (-2.5) + (-2.5^2 / 2!) + (-2.5^3 / 3!) + (-2.5^4 / 4!)

Using a calculator or performing the calculations step by step:

e^(-2.5) ≈ 1 + (-2.5) + (6.25 / 2) + (-15.625 / 6) + (39.0625 / 24)

e^(-2.5) ≈ 1 - 2.5 + 3.125 - 2.60417 + 1.6276

e^(-2.5) ≈ 1.64893

Therefore, using the fifth partial sum of the exponential series, the approximation for e^(-2.5) is approximately 1.649 (rounded to three decimal places).

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The fractional equivalent of the repeating decimal 0.2 is 2/9

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

Repeating decimal = 0.2

Represent properly

So, we have

Repeating decimal = 0.2222

Express as fraction

So, we have

Fraction = 2/(10 - n)

In this case

n = 1

So, we have

Fraction = 2/(10 - 1)

Evaluate

Fraction = 2/9

Hence, the fractional equivalent is 2/9

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Answer:

True, True, False, True, False for part 1

Step-by-step explanation:

Make me brainliest

Answer:true,true,false,true part one

Step-by-step explanation:

Answer:

She left at 7:55

Step-by-step explanation:

She travels 150 miles at 50 miles an hour, it takes her 3 hours to get to stoke but she stopped for 20 minutes. Subtract 20 minutes from 11:15, and you get 10:55, then subtract 3 hours. You get 7:55. This means she left the house at 7:55.

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer:

Step-by-step explanation:

take angle A as reference angle

using cos rule

cos A=adjacent/hypotenuse

cos A=12/13

cos A=0.92

A=cos 23

A=23 degree

for ratio,

cos A=12/13

Cos( A ) = AC / AB [ Ratio ]

Cos( A ) = 12 / 13 [ Ratio ]

Cos( A ) = 0. 92307 [ Exact value ]

Answer:

(-90)

Step-by-step explanation:

45*-2 = (-90)

The difference in mail handled between 195 and 1965 is -5.4 x 10

The data on the pieces of mail handled by the United States Postal Service is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100

Difference in mail handled = mail handled in 1995 - mail handled in 1965

(1.8 x \(10^{11}\)) - (7.2 x \(10^{10}\))

(1.8 - 7.2)  x \(10^{11 - 10}\)

-5.4 x 10

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The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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Answer:

39...........

Step-by-step explanation:

plz mark me as brainest answer

Answer:

39

Step-by-step explanation:

the sequence increases by seven every time so 32+7 =39

Answer:

the answer is  13 months

Step-by-step explanation:

Answer:

I think itsb6 months

Step-by-step explanation:

The correct option is f(x) is greater than g(x).Because we get the new function by putting value of x. we get by performing f first and then performing g.

A linear function is a function that has either one or two variables without exponents.Linear functions has a graph in a straight line.The slope of linear function is always constant because the slope of a straight line is always constant.

The function f with g is (f∘g)(x)=f(g(x)) and is read f of g of x . It means that wherever there is an x in the function f , it is replaced with the function g(x).we can find f(x) and g(x) by adding value of x in the function.

Now we have

f(x)=3x+1

when x=3 we get

f(x)= 3(3) +1

f(x) = 10

Similarly from graph of g(x)

when x=3

g(x)=7

g(3)=7

f(3) > g(3)

Hence proved that f(x) is greater than g(x).

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The quadratic function f(x) = -3(x + 2)²  + 1is represented in the graph below

When graphing parabolas, we want to include certain special points in the graph. The y-intercept is the point where the graph intersects the y-axis. The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of the graph. Lastly, the line of symmetry (also called the axis of symmetry) is the vertical line through the vertex, about which the parabola is symmetric.

In the function given;

f(x) = -3(x + 2)² + 1

vertex of the function = (-2, 1)

Axis of symmetry =

This can be graphed using a graphing calculator;

Kindly find the attached image

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Answer:

Step-by-step explanation:

In a right triangle, the sides forming the right angle also determine the angle opposite one of the sides.

Tan(29) =26/x                Multiply both sides by x

x tan(29) = 26                 Divide by tan(29)

x = 26/tan(29)                Find tan(29)

x = 26/0.5543                Divide

x= 46.9