Which of the following can you determine, when you use deduction and start
from a given set of rules and conditions?
A. What may be true
B. What must be true
C. None of these
D. What may be false
k

Only 3 & 5 from the set {1,2,3,4,5,6} are primitive root (mod7), therefore, sum of integers is 3 + 5 = 8.

A number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n in modular arithmetic. That is, g is a primitive root modulo n if for every integer a coprime to n, some integer k for which gk ≡ a (mod n).

The index or discrete logarithm of a to the base g modulo n is a value k like this. So, if and only if g is a generator of the multiplicative group of integers modulo n, g is a primitive root modulo n.

In Article 57 of his Disquisitiones Arithmeticae (1801), Gauss defined primitive roots and credited Euler with coining the term.

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As a result, the response to the query that the area provided With interiors of 32 and 44 square feet, respectively, the future complex will consist of a 60.1-foot circular.

Finding out how big a rectangle or rectangle is is the simplest (and most used) method. Divide the width by the altitude to find the area of a rectangle. Since all sides of a square are equal in length, determining the area of unit only requires knowledge of the size of one of its sides.

Here,

Here is the formula for area:

The area formula is length times width.

=> 8 × 4

= >32ft²

Following space will be on the trapezoid:

=>(14 + 18)/2 × 4

=> 44ft²

By multiplying the measurement by two, the perimeter will indeed be determined. Knowing this,

= 2(8 + 4) + (14 + 8 + 4 + 5.6 + 4.5)

= 24 + 36.1

= 60.1 ft

In light of this, the answer to the area-related question is

For the specified polygon, 60.1 square feet.

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The area of the semicircle is, 6.28 unit².

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

BC is the diameter of the semicircle.

And, The area of rectangle ABCD is 20 and the length of line AB is 5.

Now, We have;

The area of rectangle ABCD is 20 and the length of line AB is 5.

Let the width of rectangle = x

So, We can formulate;

⇒ 20 = x × 5

⇒ x = 4

Here, the width of rectangle is the diameter of the semicircle.

So, The radius of semicircle = 4 / 2

                                            = 2 units

We know that;

Area of semicircle = π r

Where, 'r' is radius of semicircle.

Hence, We get;

⇒ Area of semicircle = π r

⇒ Area of semicircle = 3.14 × 2

                                 = 6.28 unit²

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Time taken to travel from North Carolina to Florida driving an average speed of 70 mph is 7 hours.

Calculating average speed involves dividing the total distance traveled by the total time it took to cover that distance.

Given,

Time taken to travel = 9hours

average speed =55 mph

distance between North Carolina to Florida = speed x distance

distance= 55 x 9

distance= 495 miles

if driving at speed of 70 mph

time taken = distance/speed

time taken=495/70

time taken=7 hours

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Answer:

Here are a few of the factor pairs. The rest you can find in the pdf below.

Answer:

F and C

Step-by-step explanation:

CUZ AAS means angle angle side

Answer:

see explanation

Step-by-step explanation:

for the triangles to be congruent by the angle- side- angle (ASA postulate )

if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle ( included side is the side between the vertices of the two angles ) , then the triangles are congruent.

given

∠ B ≡ ∠ D and AB ≡ PD

then the included sides are AB and PD

the other 2 angles for congruency are ∠ A ≡ ∠ P

-----------------------------------------------------

By the AAS postulate

If two angles and a non included side of one triangle are congruent to the corresponding parts of the other triangle, then the triangles are congruent

for AAS then ∠ C ≡ ∠ F

Two statements are logically equivalent if they have the same truth value in all possible circumstances, meaning that they are either both true or both false in any given context.

For example, the statement "All dogs are mammals" is logically equivalent to the statement "All non-mammals are not dogs." Although the statements use different words and phrasing, they convey the same information and are both true.

Another example would be the statement "x>2" is logically equivalent to the statement "x>=3" because they both would have the same solutions.

Logical equivalence is important in logical reasoning, proof and in computer science where it is used to determine if two statements are logically equivalent which leads to simplify the boolean expressions.

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The probability best prediction for the number of times that Ellen will draw a blue marble is 200.

Number of blue marbles: 222

Number of red marbles: 333

Total number of marbles: 555

Probability of drawing a blue marble:

222/555

= 0.4

Number of times drawing a blue marble:

300300300 x 0.4

= 120,120,120

Rounded to nearest whole number:

120,120

Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is

222/555

= 0.4.

Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.

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Answer:

6

Step-by-step explanation:

x² + 8² = 10²

x² + 64 = 100

x² = 36

x = 6

[tex](69)(5.6\times 10^{5})\implies (69)(560000)\implies 3\underset{\leftarrow 7\to }{\underline{8640000}}\implies 3.864\times 10^{7}[/tex]

What is the image of ( 12 , − 4 ) after a dilation by a scale factor of 1/4 centered at the origin is (3, -1)

Transformation is the movement of a point in the coordinate plane. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease of a figure by a scale factor k. If the value of k > 1, then it is an enlargement but if k < 1, it is a reduction.

The point (12, -4) is dilated by a scale factor of 1/4 using the rule (x, y) ⇒ (x/4, y/4). The new point is (4, -1)

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Answer:

5 ( or ) - 5

Step-by-step explanation:

12/3 = 4

240/4 = 60

m² + 35 = 60

m² = 60 - 35

m² = 25

m = - 5 ( or ) 5

Because,

( - 5 )² = - 5 * - 5 = 25

5² = 5 * 5 = 25

The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

What is a peripheral coordinate?

A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.

To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:

[tex]r=\sqrt{(x^2 + y^2 + z^2)} = \sqrt{((-2)^2 + (2\sqrt3)^2 + 4^2)} = \sqrt{(4 + 12 + 16)} = \sqrt32 = 4\sqrt2[/tex]

θ = [tex]tan^{-1}(y/x) = tan^{-1}(2\sqrt3/(-2)) = tan^{-1}((-\sqrt3)/1) = -60^o[/tex]

φ = [tex]cos^{-1}(z/r) = cos^{-1}(4/4\sqrt2) = cos^{-1}(1/\sqrt2) = \degree 45 ^o[/tex]

So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

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The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

What is a peripheral coordinate?

A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.

To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:

[tex]r=\sqrt{x^2+y^2+z^2} = \sqrt{(-2)^2+(2\sqrt{3})^2+4^2}=4\sqrt{2}[/tex]

θ = [tex]tan^{-1}(y/x)=tan^{-1}(2\sqrt{3}/(-2))=60^o[/tex]

φ = [tex]cos^{-1}(z/r)=tan^{-1}(4/4\sqrt{4})=45^o[/tex]

So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

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A. The amplitude of the sinusoidal function 's' would increase.

B. The midline of the sinusoidal curve will upshift.

A function that repeats its values at regular intervals is said to be periodic. For instance, periodic functions include trigonometric functions, which repeat every 2 pi radian. In science, periodic functions are used to describe oscillations, waves, and other periodic events. Aperiodic refers to any nonperiodic function.

We know the moving mechanism of the pendulum can be graphed as a periodic function.

A. If the pendulum is pulled farther away from its resting point it will reach a greater height on both sides this would have an effect of an increase in the amplitude of the sinusoidal curve.

B. If the pendulum is pulled farther away from its resting point the midline of the sinusoidal curve would move up along the y direction as a result of an increase in magnitude.

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The cost of the four points will be $8296.8496

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

$ 128,000 is the amount financed (P).

t = 15 years

The interest rate equals 5.05%.

Amount after 15 years equals,

A = [tex]P(1+\frac{r}{100}[/tex]

=128,000[tex](1+\frac{5.05}{100} )^{15}[/tex]

=268009

Rose and Andrew has taken four points to lower their rate to 4.81% .

A =128,000 [tex](1+\frac{4.81}{100} )^{15}[/tex]

A = 259,713

Cost of four points = 268,009.890 - 259,713.040  = $8296.8496

Hence, the cost of the four points will be $8296.8496

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The required system of inequality will be

t + r ≤ 25

25t + 12r ≥ 200

What is system of equations?

A set or group of equations that are solved together is referred to as a system of equations. Both algebraic and graphic solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.

If 't' represents the number of hours Joanne tutors and 'r' represents the number of hours she works as a receptionist.

Then the total hours she can work = t + r

Since she can work up to 25 hours.

Thus  t + r ≤ 25

If she earns $25 per hour by tuition and $ 12 per hour by working as a receptionist .

Then her total earning = $25t + 12r

Since she must earn $200.

Then 25t + 12r ≥ 200

Hence, the required system of inequality will be

t + r ≤ 25

25t + 12r ≥ 200

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Answer:

x = 60 , y = 85

Step-by-step explanation:

assuming the figure is a trapezoid

• each lower base angle is supplementary to the upper base angle on the same side.

x + 2x = 180

3x = 180 ( divide both sides by 3 )

x = 60

and

y + y + 10 = 180

2y + 10 = 180 ( subtract 10 from both sides )

2y = 170 ( divide both sides by 2 )

y = 85

The correct comparison of solutions for the expression is x < 2

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

2(5-x) > 6 and 22 > 2(9+x)

Rewrite the expression properly

So, we have the following representation

2(5 - x) > 6 and 22 > 2(9 + x)

Divide both sides of the expressions by 2

So, we have the following representation

5 - x > 2 and 11 > 9 + x

Subtract both sides of the expression by the constant term

This gives

-x > -3 and 2 > x

Rewrite as

x < 3 and 2 > x

So, we have

x < 3 and x < 2

When combined, we have

x < 2

Hence, the solution is x < 2

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The correct option for the given linear equation is option (B).

What is a linear equation?

An equation is said to be linear if the maximum power of the variable is always 1. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

The given equation is y =20x + 35

       y = total amount of money

       x = number of months the customer has been renting the storage unit

A) If x = 355

        y = 20 * 355 + 35 = $7135

    This is not the correct option.

B) If x = 16

      y = 20*16 + 35 = $355

     This is the correct option.

C) if x = 320

      y = 20 * 320 + 35 = $6435

      This is not the correct option.

D) If x = 16

       y = 20*16 + 35 = $355

      This is not the correct option.

Therefore the correct option for the given linear equation is option (B).

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The modulus increases by a factor of 10 and the argument increases by 5π/3.

Modulus of the complex number:

The modulus of a complex number is the square root of the sum of the squares of the complex number's real and imaginary parts. If z is complex, the absolute value of complex z is given by √{[Re(z)]2 + [Im(z)] and denoted by |z|. exclusive. The absolute value of a complex number z = a + ib is the distance between the origin (0, 0) of the complex plane and the point (a, b). The modulus of a complex number is a distance, so its value is always non-negative.

The absolute value of a complex number z = x + iy denoted by |z| is given by the formula |z|. Given = √(x2 + y2), where x is the real part of the complex number z and y is the imaginary part. The modulus of a complex number z can also be computed using the conjugate of z. Since

z. z = (x+ iy)(x −iy)

=x²+y² , we have

    z. z = |z|²

⇒ |zI =√z. z.

Then,

The modulus of the z will be =|z|= √p²+q²

We have,

z = 5 – 5i √3

So,

Now rewrite this given equation in the form of z = r(Cosθ + iSinθ),

For this first calculate the modulus,

|Z| = √((5√3)² + 5²)

|Z| = √(25×3 + 25)

|Z| = √(100) = 10

And,

Argument, θ = tan⁻¹ (b/a)

θ = tan⁻¹ (5√3/5)

θ = tan⁻¹ (√3)

θ = 71

Therefore, the modulus increases by a factor of 10, and the argument increase by 5π/3.

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Answer:

The modulus increases by a factor of ✔ 10.

The argument increases by ✔ 5π over 3

Step-by-step explanation:

correct on edge 2023

Permutations for each word can be calculated by considering the number of unique letters in it and taking factorial of it.

a) Inverary: There are 8 letters in the name "Inverary" (I, N, V, E, R, A, R, Y), so there are 8! (8 factorial) permutations of all the letters in the name. This equals 40320 permutations.

b) Beamsville: There are 9 letters in the name "Beamsville" (B, E, A, M, S, V, I, L, E), so there are 9! (9 factorial) permutations of all the letters in the name. This equals 362880 permutations.

c) Mattawa: There are 7 letters in the name "Mattawa" (M, A, T, T, A, W, A), so there are 7! (7 factorial) permutations of all the letters in the name. This equals 5040 permutations.

d) Penetanguishene: There are 14 letters in the name "Penetanguishene" (P, E, N, E, T, A, N, G, U, I, S, H, E, N), so there are 14! (14 factorial) permutations of all the letters in the name. This equals 87178291200 permutations.

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No, three 4 5 triangles are not always right triangles.

A right triangle is a triangle in which one of the angles is a right angle (90°). Therefore, in order to be a right triangle, the following criteria must be met: a^2 + b^2 = c^2, where c is the longest side and a, b are the other two sides. In a 3 4 5 triangle, the longest side is 5, so a^2 + b^2 = c^2 becomes 3^2 + 4^2 = 5^2. Using simple algebra, this equation becomes 9 + 16 = 25, which is true. Therefore, a 3 4 5 triangle is a right triangle. However, if one of the sides is different, for example a 3 4 6 triangle, the equation becomes 9 + 16 = 36, which is not true. Therefore, a 3 4 6 triangle is not a right triangle. To summarize,3 4 5 triangles are right triangles, but three 4 6 triangles are not.

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Answer:

Y=54x−2y=54x−1

I hope this helps you!

Answer:

--------------------------------------------------

Permutation of 5 mountain photographs:

Since all are next to each other, the mountain photographs count as one item along with the other 3 + 4 = 7 photographs and therefore the permutation for this is:

Total arrangements is:

Answer:

4

Step-by-step explanation:

This question basically asks you to substitute the value of x to find the value of function g(x).

Given x = -2,

g(-2) = -4(-2) - 4 = 8 - 4 = 4

Answer:

4

Step-by-step explanation:

g(x) = -4x - 4

Let x = -2

g(-2) = -4(-2) - 4

          = 8 -4

           =4

[tex]8\frac{1}{4}d =\frac{2}{11}[/tex]

a) Simplify both sides of the equation.

[tex]\frac{33}{4}d=\frac{2}{11}[/tex]

b) Multiply both sides by 4/33.

[tex](\frac{4}{33} ) \times (\frac{4}{33}d)=(\frac{4}{33}) \times (\frac{2}{11} )\\[/tex]

d = [tex]\frac{8}{363}[/tex]

[tex]8\frac{1}{4} \div d=\frac{2}{11}[/tex]

= [tex]\frac{33}{4d} =\frac{2}{11}[/tex]

a) Cross Multiply.

[tex](33)\times(11)=2\times 4d[/tex]

[tex](363) =8d[/tex]

b) Flip.

[tex]8d=(363)[/tex]

c) Divide both sides by 8

[tex]\frac{8d}{8} = \frac{363}{8}[/tex]

[tex]d=\frac{363}{8}[/tex]

Answer:

10^14

Step-by-step explanation:

The expression (10^2)^7 uses an exponent rule known as power raised to a power.

The rule states that when you multiply a base and its exponent to a power, you multiply the inner exponent and the outer exponent:

[tex](a^m)^n\\a^m^n[/tex]

Thus, we have

[tex](10^2)^7\\10^2^*^7\\10^1^4[/tex]

The wheel will travel 131.8cm in 3 rotations.

The radius of the wheel, r = 7cm

Number of rotations, n= 3

distance covered in 1 rotation= circumference of circle=2πr

distance covered in 3 rotation= 2πr x 3

where π=3.14(fixed)

=2 x 3.14 x 7 x 3

Distance=131.88cm

Therefore, the distance covered in 3 rotations is 131.88cm

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Answer:

132cm

Step-by-step explanation:

use formula 22/7 *diameter which is 7*2 getting the answer as 44.For three rotations multiply the answer by three

Answer: To find the ratio of the dimensions of the actual room to that of the scale model, we can divide the dimensions of the actual room by the dimensions of the scale model.

The dimensions of the actual room are 15m by 9m by 12m, and the dimensions of the scale model are 5m by 3m by 4m.

Therefore, the ratio of the dimensions of the actual room to that of the scale model is:

length: 15m / 5m = 3 : 1

width: 9m / 3m = 3 : 1

height: 12m / 4m = 3 : 1

So, the ratio of the dimensions of the actual room to that of the scale model is 3:1 for all dimensions (length, width, and height)

The ratio of the dimensions of the scale model to that of the actual object is 1:16

so to find the length and width of the actual object, you can use this relation

length = scale model length * 16 = 2.416 = 38.4m

width = scale model width * 16 = 1.816 = 28.8m

So the length and width of the actual object are 38.4m and 28.8m respectively.

Step-by-step explanation: