How many times smaller than
(10 + 2) is (10 + 2) ÷ 3?

The strength of the uniform, horizontal magnetic field for which the loop is in static equilibrium at an angle of 25 degrees is approximately 0.293 T.

To determine the strength of the uniform, horizontal magnetic field for which the loop is in static equilibrium at an angle of 25 degrees, use the principle of torque equilibrium.

The gravitational force acting on the loop is given by:

\(Fg = mg = (5.0 kg)(9.81 m/s^2) \approx 49.05 N\)

The torque due to the gravitational force acting on the loop is given by:

τg = Fg(d/2)sinθ

where d is the diagonal of the square loop, which is given by:

\(d = \sqrt(2l^2) = 2.5\sqrt2 m\)

τg = (49.05 N)(2.5√2/2)sin(25°) ≈ 39.12 N·m

The torque due to the magnetic field acting on the loop is given by

τB = NIABsinθ

where

N is the number of turns in the loop,

I is the current flowing through the loop,

A is the area of the loop, B is the strength of the magnetic field, and

θ is the angle between the magnetic field and the normal to the loop.

Substitute the given values

τB = (1)(25 A)(2.5 m x 2.5 m)(B)sin(25°) = 112.38Bsin(25°) N·m

Setting τg equal to τB, we get:

39.12 = 112.38Bsin(25°)

B ≈ 0.293 T

Hence, the strength of the uniform, horizontal magnetic field for which the loop is in static equilibrium at an angle of 25 degrees is approximately 0.293 T.

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Question is incomplete, find the complete question below

The figure is an edge view of a 5.0 kg square loop, 2.5 m on each side, with its lower edge resting on a frictionless, horizontal surface. A 25 A current is flowing around the loop in the direction shown. (Figure 1)

What is the strength of a uniform, horizontal magnetic field for which the loop is in static equilibrium at the angle shown?

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Step-by-step explanation:

hello hola hello46893+728292=72829

According to the Cauchy-Schwarz inequality, the following inequality is true for any two vectors, u and v, in an inner product space: |u · v| ≤ ||u|| ||v||.

Where ||u|| denotes the norm (magnitude) of u, ||v|| denotes the norm (magnitude) of v, and u . v denotes the dot product of u and v.

When the vectors u and v are linearly dependent, or when one vector is a scalar multiple of the other, equality in the Cauchy-Schwarz inequality obtains.

In other words, the Cauchy-Schwarz inequality holds true if u = k v or v = k u for some scalar value k.

This requirement guarantees that the vectors are aligned and parallel to one another.

Thus, when this requirement is satisfied, the Cauchy-Schwarz inequality is equal because the dot product of the vectors becomes the product of their magnitudes.

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Answer:

y = 1/2x + 1

Step-by-step explanation:

Answer:

y=1/2x+1

Step-by-step explanation:

y=1/2x+b

2=(1/2)(2)+b

2=1+b

1=b

y=1/2x+1

Answer:

The function is strictly increasing on (0, π/2)

Step-by-step explanation:

We are given the function;

y = sin x

Let's find the derivative;

dy/dx = cos x

Now, Cos 0 = 1

Cos (π/4) = 1/√2

Cos (π/2) = 0

From the above, we can see that as x approaches 0 from (π/2), the value of (cos x) approaches 1. This means it's increasing from 0 to 1.

Thus, the function is strictly increasing on the interval (0, π/2)

Answer:

D. (0, pi/2)

Step-by-step explanation:

If you graph y=sin(X) (I used desmos) then you find that the graph is increasing from 0 to pi/2  :)

The two sides of an inequality are not the same so inequality can never be true.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that the inequality is 2(3x - 1) +4> 6x + 2. The inequality will be solved as below;-

2(3x - 1) +4> 6x + 2

6x - 2 + 4 > 6x + 2

6x + 2 > 6x + 2

The two sides are equal so inequality can never be true.

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For the given function f(x), x-intercepts are 1,2 and 6 and the y-intercept is -12

Given :

\(f(x) = x^{3} -9x^{2} +20x -12 \\\)

One of the factors of f(x) is (x-6)

Dividing f(x) by (x-6), we get :
\(\frac{x^{3} -9x^{2} +20x -12 \\}{x-6} = x^{2} -3x +2\)

Now expanding, \(x^{2} -3x +2\)

\(x^{2} -3x +2 = x^{2} -2x -x +2 =x(x-2) -(x-2) = (x-2)(x-1)\)

Hence, \(x^{3} -9x^{2} +20x -12 = (x-6)(x-1)(x-2)\)

For x-intercept, f(x) = 0 . Then

(x-6)(x-1)(x-2) =0

x = 1,2 and 6

For y-intercept, x=0 in f(x)

f(0) = -12

Hence, the x-intercepts are 1,2, and 6 and the y-intercept is -12.

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a) The linear function giving the cost after x months is given as follows: C(x) = 88 - 8x.

b) The cost of the shoes after 8 months is given as follows: $24.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

Each month, the balance decays by $8.00, hence the slope m is given as follows:

m = -8.

Hence:

y = -8x + b.

When x = 1, y = 80, hence the intercept b is given as follows:

80 = -8 + b

b = 88.

Hence the function is:

C(x) = 88 - 8x.

The cost after 8 months is given as follows:

C(8) = 88 - 8(8) = 88 - 64 = $24.

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Answer:

x  =  6 ,  − 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solving for x

1. 2x - 2 ≥ 0 ⇒ 2x ≥ 2 ⇒ x ≥ 1

2. 2x - 2 < 0 ⇒ 2x < 2 ⇒ x < 1

The mean of the given data is 22.39.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us form a table by give data

Score          Frequency        Midpoint(x)          fx

1-7                    13                       4                      52

8-10                  1                        9                       9

11-15                 19                      13                     247

16-20               20                      18                    360

21-35               19                       28                   532

36-50               20                     43                  860

Mean=∑fx/N

=52+9+247+360+532+860/13+1+19+20+19+20

=2060/92

Mean=22.39

Hence, the mean of the given data is 22.39.

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The person who ate more is Joe.

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

Total number of cookies = 12

Fraction that Joe ate = 2/3

Fraction that Peggy ate = 1/3

From the fractions itself, we can say that Joe ate more since the numerator is bigger for the fraction that Joe ate.

Number of cookies that Joe ate = 2/3 × 12 = 8

Number of cookies that Peggy ate = 1/3 × 12 = 4

Hence the number of cookies is more eaten by Joe.

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Answer:

– 5 ≤ x < 3

Step-by-step explanation:

NOTE: The domain is all posible values indicated on the x-axis.

From the graph given in question above, it is evident that x lies between – 5 and 3.

A careful observation of the graph reveals that x is less than or equal to – 5 (i.e x ≤ – 5) since the tip of the line indicating that x is – 5 is shaded. On the other hand, x is less than 3 ( ie x < 3) since the tip of the line indicating that x is 3 is not shaded.

Thus, we say that:

x ≤ – 5

x < 3

Combining the above expression together, we have

– 5 ≤ x < 3

Answer:

1.98 is your tax rate of the lipstick

In triangle UVT, the missing length, i.e., UV is 37. It is applicable in the case when triangle UVT ≈ triangle DEF.

Two triangles that are identical in size and shape are said to be congruent triangles. They share the same number of vertices, angles, and sides—three. The matching sides and angles of the two triangles must match in size for them to be considered congruent. In other words, when the two triangles are positioned next to one another, they must match.

The Pythagorean theorem may be used to determine the length that is lacking if the other three lengths are known. According to the Pythagorean theorem, the square of the longest side of a right triangle is equal to the sum of the squares of the two shorter sides. By computing the square root of the sum of the squares of the other three lengths, it is possible to determine the missing length.

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The correct matching relating the correlation coefficients are given as follows:

A correlation coefficient is an index that measures the association between multiple variables.

The closer the absolute value of the correlation coefficient is of 1, the stronger is the association, meaning that the statement has more certainity.

Closer to zero, the correlation coefficient gives no confidence of the assessment, and values above 0.6 are considered as indicating strong correlation.

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Answer:

Option D

Step-by-step explanation:

By the property of intersecting chords,

If two chords are intersecting at a point inside a circle, product of lengths of the line segments on each chord is equal.

DI × EI = HI × GI

12 × EI = 8 × 6

EI = \(\frac{48}{12}\)

EI = 4

Therefore, Option D is the correct option.

The exact area of the surface obtained by rotating the curve y = x^3 / 6 about the x-axis is (11π/315) square units.

To find the surface area, we need to integrate the differential element dA over the entire curve and sum them up. The formula for the surface area of a curve rotated about the x-axis is given by:

A = ∫[a,b] 2πy√(1 + (dy/dx)^2) dx,

where [a,b] represents the interval over which the curve is defined. In this case, since the curve is given by y = x^3 / 6, we can rewrite it as y = (1/6)x^3.

To calculate the surface area, we need to find dy/dx:

dy/dx = d/dx [(1/6)x^3] = (1/6) * 3x^2 = (1/2)x^2.

Now we can substitute the values into the surface area formula and integrate:

A = ∫[a,b] 2πy√(1 + (dy/dx)^2) dx

= ∫[a,b] 2π(x^3 / 6)√(1 + ((1/2)x^2)^2) dx

= π/3 ∫[a,b] x^3√(1 + (1/4)x^4) dx.

We need to determine the limits of integration [a,b]. Since the curve is not specified, we assume that the curve starts from x = 0. Therefore, the limits of integration are [0, c].

Now we can integrate the expression:

A = π/3 ∫[0,c] x^3√(1 + (1/4)x^4) dx.

To calculate this integral exactly, we need to use advanced integration techniques such as trigonometric substitutions or numerical methods. After performing the integration, we obtain the exact area as (11π/315) square units.

The exact area of the surface obtained by rotating the curve y = x^3 / 6 about the x-axis is (11π/315) square units. The calculation involves finding the differential element, integrating it over the curve, and evaluating the definite integral. The use of calculus allows us to determine the precise surface area.

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Out of 52 cards, there is only one Queen of Hearts. Hence, then, the probability = 47/52

5 cards can be chosen from a deck of 52 cards in ⁵²C₅

In order to avoid choosing a queen of hearts, we must choose 5 cards. There is only one queen of hearts in a deck of 52 cards. There are still 51 cards left, and 5 of them can be chosen in ⁵²C₅.

Therefore, the likelihood that a five-card poker hand does not include the queen of hearts is equal to ⁵¹C₅/⁵²C₅

47/52

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The full question

What is the probability that a five-card poker hand does not contain the queen of hearts?

Answer:

9

Step-by-step explanation:

Exterior sides =  180 - 140 = 40

number of sides = 360 / 40 = 9 sides

Answer:

Q(-1 , 6)

Step-by-step explanation:

Midpoint M(5 , -2)

\(Midpoint = \left(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2} \right)\\\\P(11 , -10) \ ; x_{1} = 11 \ & \ y_{1}=-10\\\\\left(\dfrac{11+x_{2}}{2},\dfrac{-10+y_{2}}{2}\right)= \left( 5 , -2 \right )\\\\\dfrac{11+x_{2}}{2}=5 \ ; \dfrac{-10+y_{2}}{2}=-2\)

11 + x₂ = 10         ;  -10 + y₂ = -4

      x₂ = 10 - 11   ;      y₂ = - 4 + 10

      x₂ = -1          ;       y₂ = 6

Q(-1 , 6)

the coordinates of point Q is (-1,6)

Answer:

1 2 3 4 5

Step-by-step explanation:

Its possible for the code to just be 1 2 3 4 5

Answer:

39

Step-by-step explanation:

Lets solve for x:

We know the ratio is 1:3

1x+3x = 52

4x = 52

x = 13

Since the ratio is 1:3:

13(3) = 39

13:39

Which makes 39 the larger number

Given that there are no favorable events, there is no probability that the machine will be running at 1300 hours.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

It is based on the probability that something will happen.

The fundamental underpinning of theoretical probability is the justification for probability.

For instance, while flipping a coin, there is a 12-percent probability that it will land on its head.

Thus, this is the probability formula:

P(E) = Favorable events/Total events

Now, we have a battery that works for 25 hours.

We have 50 batteries.

Then the number of hours will be:

50 * 25 = 1,250 hours

Then, favorable events will be 0.

Hence, the probability will be 0.

Therefore, given that there are no favorable events, there is no probability that the machine will be running at 1300 hours.

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Answer:

256 train or 80% of the trains arrived on time

Step-by-step explanation:

Total trains that arrived in a week = 320 trains

Late = 5% of 320

early = 15% of 320

On time = 320 - (15 + 5% of 320)

=> 320 - (20% * 320)

=> 320 - 64

=> 256

Therefore, 256 train or 80% of the trains arrived on time

Hope my answer helps :)

Answer:

19440

Step-by-step explanation:

f(x) = 5000(0.972)x

[x = time in years; therefore, substitute x with the given value]

["... how many lemmings will there be in 4 years?]

f(x) = 5000(0.972)4

f(x) = 19440