Is Queen Beyoncé correct or incorrect? If she's incorrect, what did she do wrong?

The reason why the terms a and m have to be relatively prime integers is that it is the only way to make sure that ax≡1 (mod m) is solvable for x within the integers modulo m.

Theorem:"If a and m are relatively prime integers and m > 1, then an inverse of a modulo m exists. Furthermore, this inverse is unique modulo m. (That is, there is a unique positive integer a less than m that is an inverse of a modulo m and every other inverse of a modulo m is congruent to a modulo m.)"If a and m are relatively prime integers and m > 1, then an inverse of a modulo m exists. Furthermore, this inverse is unique modulo m. (That is, there is a unique positive integer a less than m that is an inverse of a modulo m and every other inverse of a modulo m is congruent to a modulo m.)The inverse of a modulo m is another integer, x, such that ax≡1 (mod m).

This theorem has an interesting explanation: if a and m are not co-prime, then there is no guarantee that ax≡1 (mod m) has a solution in Zm. The reason for this is that if a and m have a common factor, then m “absorbs” some of the factors of a. When this happens, we lose information about the congruence class of a, and so it becomes harder (if not impossible) to undo the multiplication by .This is the reason why the terms a and m have to be relatively prime integers.

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(a)Hence, the total savings is 249.95 - (149.97 + 7.50 + 12.60) = $79.88. (b)Therefore, Yasmin is offering a 31.95% discount on the kitchen sink to her customers.

a) Let us find the amount of the reduction; this can be obtained by multiplying the original price by the percent reduction, i.e., 249.95 x 0.4 = 99.98.

Thus, the new price is obtained by subtracting the reduction from the original price, i.e., 249.95 - 99.98 = 149.97. Therefore, the GST on the new price is 149.97 x 0.05 = 7.50.

The selling price (including GST but excluding PST) is therefore 149.97 + 7.50 = 157.47.

Finally, the PST is calculated by multiplying the selling price by 0.08, i.e., 157.47 x 0.08 = 12.60.

Hence, the total savings is 249.95 - (149.97 + 7.50 + 12.60) = $79.88.

b) The percentage of savings can be calculated using the formula: 100 x (amount saved) / (original price) %.

In this problem, the percentage of savings can be obtained as: 100 x 79.88 / 249.95 % = 31.95 % (approx).

Therefore, Yasmin is offering a 31.95% discount on the kitchen sink to her customers.

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Answer:

C. 50

Step-by-step explanation:

Answer:

A. 28.1 cm^2

Step-by-step explanation:

a = bh

a = (7.6)(3.7)

a = 28.12 cm^2

a = 28.1 cm^2

The distance from M to N is 248 kilometers. Let's break down the information provided. The man traveled from M to N at an average speed of 72 km/h and spent 2 hours on the journey. This means the distance from M to N is calculated by multiplying the speed (72 km/h) by the time (2 hours), resulting in 144 kilometers.

On the return journey, the man's boss traveled at an average speed of 40 km/h. We know that the distance covered by the boss was 2 kilometers longer than that of the man (chiropractor) at 1:55 p.m.

To find the distance covered by the boss, we subtract 2 kilometers from the distance traveled by the man, which is 144 kilometers - 2 kilometers = 142 kilometers.

Therefore, the total distance from M to N is the sum of the distance traveled by the man and the distance traveled by the boss: 144 kilometers + 142 kilometers = 286 kilometers.

However, the states that the distance from M to N is 1:55 p.m., which implies that this is the midpoint of the total journey. Since the man spent 2 hours on the first leg of the journey, we subtract this time from the total journey time of 5 hours, giving us 5 hours - 2 hours = 3 hours for the return journey.

Since the boss traveled at an average speed of 40 km/h for 3 hours, the distance covered on the return journey is 40 km/h × 3 hours = 120 kilometers.

Therefore, the distance from M to N is given by the total distance minus the distance covered on the return journey: 286 kilometers - 120 kilometers = 166 kilometers.

So, the final answer is that the distance from M to N is 248 kilometers.

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Answer:

Hey there!

4t(5t)=20t^2

4t(-4)=-16t

5(5t)=20t

5(-4)=-20

Hope this helps  :)

Step-by-step explanation:

This is just a matter of multiplication. 4t x 5t = \(20t^{2}\), so that will be in your first box. 4t x -4 = -16t, so that'll be in your second box. 5 x 5t = 25t, so that will be in your bottom-first box, and 5 x -4 = -20, so that will be in your last one.

Answer:

-4

Step-by-step explanation:

when the signs are different the result is negative

(+ )*( - )= ( -)

Answer:

160

Step-by-step explanation:

4 × 10 × 4 = 160

(Random words to hit the character limit please ignore)

The dimensions that will minimize the cost is

h= 2.82876 and r = 1.06078

Given That, C₁ = $10 and C₂= $10 and C₃ = $15

lets multiply the top and bottom, we get,

C₁ × C₂ = $10 ×$ 20 = $ 30

The total cost is,

C = (2πr²) C₁ + (2πrh)C₂

Here,  r is base radius and h is the side length.

The volume is given by and the volume to 20 m³

∴ V = πrh² ⇒ πr²h = 20

So, h = 20/πr²

Now, the problem can be  stated as

minimum h, r C(h, r) restricted to V(h, r) = V₀

Using language multiplier it reads,

L(h ,r,λ) = C(h, r) + λ [ V(h ,r) - V₀]

Solving for h, r, λ, we get,

h = ∛(2 C₁/C₂)² V₀ /π , r = ∛ (C₂/C₁) (v₀/2π)

λ = -2 ∛2πC₁C₂² /V₀

or, h= 2.82876 , r= 1.06078 with associated cost C= 424.214

We know that is a minimum because,

(C₀ V) = 2 ( C₁πr³ + C₂V₀) /r

d²/dr² (C₀V) (r) = 4 (C₁πr³+ C₂V₀)/ r³

and for the found solution has the value

d²/dr² (C₀V) (r) = 240 π > 0

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Answer:

the second picture answer is F.56

Step-by-step explanation:

if you add 16 + 40=56

Answer:

y = 2x + 3

Step-by-step explanation:

y = 2x + b

-1 = 2(-2) + b

-1 = -4 + b

-1 = -4+3

final equation: y = 2x + 3

Answer:

3

Step-by-step explanation:

add them all to get 18 then divide by 6 which is a total number of numbers there

Answer:

3

Step-by-step explanation:

Yes, the given equation is extrenous. Because, the value of the original equation is x = 3.5

An extraneous solution is a solution that does not satisfy the original equation.

In this case, the original equation is 2x-7=1, At x =3.5, plugging the value into the equation, the value obtained is - 3

Plugging in x=3.5, we get 2(3.5)-7=4-7=-3, which is not equal to 1. Therefore, x=3.5 is an extraneous solution.

Therefore, the given equation in the question is extrenous.

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Answer:

parallel

Step-by-step explanation:

Parallel lines have equal slopes.

Calculate the slopes m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (2, 3)

m = \(\frac{3-2}{2+1}\) = \(\frac{1}{3}\)

Repeat with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (3, 1)

m = \(\frac{1-0}{3-0}\) = \(\frac{1}{3}\)

Since slopes are equal then parallel

Comparison or relational operations, such as <, >, =, allow for comparing numbers. They determine if a number is less than, greater than, equal to, or not equal to another number, enabling decision-making and comparisons within arithmetic and programming operations.

When comparing numbers, you can use various relational operators to determine the relationship between them. Here are the commonly used comparison operators:

Less than (<): This operator compares two numbers and returns true if the first number is smaller than the second number. For example, 5 < 10 is true.

Greater than (>): This operator compares two numbers and returns true if the first number is larger than the second number. For example, 10 > 5 is true.

Less than or equal to (<=): This operator compares two numbers and returns true if the first number is smaller than or equal to the second number. For example, 5 <= 5 is true.

Greater than or equal to (>=): This operator compares two numbers and returns true if the first number is larger than or equal to the second number. For example, 10 >= 10 is true.

Equal to (==): This operator compares two numbers and returns true if they are equal. For example, 5 == 5 is true.

Not equal to (!=): This operator compares two numbers and returns true if they are not equal. For example, 5 != 10 is true.

These comparison operators allow you to compare numbers and make decisions based on their relationships within arithmetic or programming operations.

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Answer:

a

Step-by-step explanation:

a because they both have a right angle which is 90 degrees

and beacuse 90 - 42 = 48 degrees which means both triangles have a 48 degrees

The coordinates of vertex N are the ones in option B

(2a, 0).

On the image we can see an equilateral triangle.

This means that if we draw a vertical line that passes through the top vertex (the one located at (a, c)) that line divides evenly the triangle.

Now, first, notice that point N is on the horizontal axis, then it's y-value must be zero, then we can write:

N(x, 0)

Now, because of the first statement, if x = a reaches the midpoint of the triangle, then the last vertex is at x = 2a

Then the coordinates are:

N(2a, 0)

The correct option is B.

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Due to construction, approximately 5 minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit.

Given that,

length of highway is 8 miles

Reduced length is 55 miles

Hours taken is 35 miles per hour.

Let t₁ is time taken is 55 mph

t₁ = 8/55

Let t₂ is time taken is 35 mph

t₂ = 8/35

Difference in time = 8/35 - 8/55

= 8 × 20 / (35 * 55) hour

= 160 × 60 / (35 × 55) mins

= 4.7

= 5 minutes (approximately)

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The unit vector along A + 2B is (D) 0.9113ax - 0.1302ay + 0.3906az.

To find the unit vector along A + 2B, we need to calculate the vector A + 2B first and then normalize it to obtain its unit vector.

A + 2B = (10ax - 4ay + 6az) + 2(2ax + ay)

= 10ax - 4ay + 6az + 4ax + 2ay

= 14ax - 2ay + 6az

To normalize the vector A + 2B, we divide it by its magnitude:

Magnitude of A + 2B = √((14)^2 + (-2)^2 + 6^2)

= √(196 + 4 + 36)

= √236

= 15.362

Now, we divide each component of A + 2B by its magnitude:

(ax, ay, az) = (14/15.362, -2/15.362, 6/15.362)

Simplifying the components, we get:

(ax, ay, az) ≈ (0.9113, -0.1302, 0.3906)

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Answer:

Dude same

Step-by-step explanation:

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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Answer:

⇒   Let marked price be Rs.x.

⇒  Discount = 20% of marked price.

⇒  Discount=  

100

20

​  

×x=  

100

20x

​

⇒  Selling price = Marked price - Discount.

⇒  192=x−  

100

20x

⇒  192=  

100

80x

⇒  x=  

80

19200

=Rs.240

Answer:

S.p = 992

discount = 20%

marked price = S. p + discount

= 992 + 20/100*992

= 992 + 198.4

= 1190.4

(a) The problem deals with the difference of means, specifically, μ1 - μ2.

(b) To find a 95% confidence interval for μ1 - μ2, we can use the following formula:

CI = (x1 - x2) ± Z * sqrt((σ1²/n1) + (σ2²/n2))

Where x1 and x2 are the sample means, σ1 and σ2 are the population standard deviations, n1 and n2 are the sample sizes, and Z is the Z-score corresponding to a 95% confidence level (1.96).

CI = (14.9 - 9.9) ± 1.96 * sqrt((3.5²/35) + (2.7²/38))
CI = 5 ± 1.96 * sqrt(0.35 + 0.191)
CI = 5 ± 1.96 * 0.739
CI = 5 ± 1.45

The 95% confidence interval is (3.5, 6.5).

(c) The confidence interval contains only positive numbers (3.5 to 6.5). Therefore, at the 95% level of confidence, we can say that the profit as a percentage of stockholder equity is higher for retail stocks than for utility stocks. The correct answer is:

Because the interval contains only positive numbers, we can say that the profit as a percentage of stockholder equity is higher for retail stocks.

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Let S be and show is a sphere of radius R centered at the arigin. We will compare the flux that it does not depends on R. Parametic equation of sphare Y(4,0)= Rsind caso + Rsind sine j + R Cord F

and 014≤ 640 ≤ 2TT outward normal is

(r = 18) = √x² + y²+z2)

= F = ૪ 3

flux = [[Finds

. Rsing dodo = 83

(from put value of n

13 sind do do 23

2 TT, TT sing do do

R 11 R [["e. / sind dado (r= 171 = radius of ephare)

Π 2T ए [e" [" sind do do= ["- Casp" "do 0

[-(-1-1) do 2TT = 2x (2-0) 2 = do flux

flux = [[F·ñ-ds S = 4π

The flux is 411 and it depends on radius 'R'

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Answer:

i don't know this one!

Step-by-step explanation:

sorry!

Answer:

x = 10

Step-by-step explanation:

The secant- secant angle 3x is half the difference of the intercepted arcs, that is

3x = \(\frac{1}{2}\) (4x + 50 - 30 )

3x = \(\frac{1}{2}\) (4x + 20) = 2x + 10 ( subtract 2x from both sides )

x = 10

If the selling price is $90 and the rate of sales tax is 3%, then the total price is $92.7

The selling price = $90

The rate of sales tax = 3%

The amount of sale tax = The selling price × The rate of sales tax

Substitute the values in the equation

The amount of sale tax = 90 × (3/100)

= 90 × 0.03

= $2.7

The total price = The selling price + The amount of sale tax

Substitute the values in the equation

The selling price  = 90 + 2.7

= $92.7

Hence, if the selling price is $90 and the rate of sales tax is 3%, then the total price is $92.7

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