prove the product of two numbers is equal to the product of their gcd and lcm

The graph of g(x) is steeper than the graph of f(x). Then the correct option is A.

Functions are found all across mathematics and are required for the creation of complex relationships.

The graphs of f(x) = x and g(x) = f(5x).

Then the g(x) can be written as

g(x) = 5x

Then the slope of g(x) is more than the slope of f(x).

The graph of g(x) is steeper than the graph of f(x).

Then the correct option is A.

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Answer:Example: find the area of a sector. As established, the only two measurements needed to calculate the area of a sector are its angle and radius. For example, if the angle is 45° and the radius 10 inches, the area is (45 / 360) x 3.14159 x 10 2 = 0.125 x 3.14159 x 100 = 39.27 square inches.

Step-by-step explanation:

Answer:

70 cm²

Step-by-step explanation:

       length of arc = 14 cm

                          r = 10 cm

Here, radius r of an circle and length of the arc (perimeter of the sector) is given. We can find the area of sector by the below mention formula,

\(\boxed{\bf Area \ of \ sector = \dfrac{r}{2}*length \ of \ arc}\)

                          \(\sf = \dfrac{10}{2}*14\\\\= 10 * 7\\\\= 70 \ cm^2\)

Answer:

48

Step-by-step explanation:

if 3;12

12;X

so 3x=12 X 12

so x =48

Grant should pay approximately $211.96 today for the annual membership, considering an interest rate of 10% and the option to pay in 12 monthly installments of $55 each.

To determine how much Grant should pay today for the annual membership, we need to calculate the present value of the 12 monthly payments of $55 each, considering an interest rate of 10%.

The present value (PV) can be calculated using the formula:

PV = C * (1 - (1 + r)^(-n)) / r

Where:

C = the monthly payment amount ($55)

r = the monthly interest rate (10% / 12 = 0.00833)

n = the number of payments (12)

Plugging in the values into the formula, we can calculate the present value:

PV = 55 * (1 - (1 + 0.00833)^(-12)) / 0.00833

PV ≈ 55 * (1 - 0.6806) / 0.00833

PV ≈ 55 * 0.3194 / 0.00833

PV ≈ 211.96

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The equation of a quadratic function P with rational coefficients that has a zero of (3 + i) is p(x) = x² - 6x + 10.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The complex number value is given as (3 + i)

Since, x = (3 + i) is a complex zero of p(x), then -

It is known that , the complex zeros occur in pair.

So, x=(3 - i) is also a complex zero of the quadratic function of p(x).

So, {x − (3 + i)} and {x − (3 - i)} are the factors of p(x).

Substitute the values to form a quadratic function -

p(x) = {x − (3 + i)}{x − (3 - i)}

Open the brackets and evaluate -

p(x) = (x - 3 + i)(x - 3 - i)

Use the arithmetic operation of multiplication -

p(x) = x(x - 3 - i) - 3(x - 3 - i) + i(x - 3 - i)

p(x) = x² - 3x - ix - 3x + 9 + 3i + ix - 3i - i²

Collect all the like terms -

p(x) = x² - 3x - 3x - ix + ix + 9 + 3i - 3i - i²

p(x) = x² - 6x + 9 - i²

Substitute the value of  i² = -1 into the equation -

p(x) = x² - 6x + 9 - (-1)

p(x) = x² - 6x + 9 + 1

p(x) = x² - 6x + 10

Therefore, the quadratic function is x² - 6x + 10.

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Answer:

month 4

Step-by-step explanation:

I took the test

Answer:

Its month 4 on edge.

Step-by-step explanation:

The median exceeds the mean by more. The histogram is skewed to the right, which shows that lower values are dragging down the mean.

The median of the histogram on the right is higher than the mean. This is evident from the histogram's form, which is tilted to the right. This shows that the lower values tend to drag the mean down. The median is greater than the mean. The right-handed skewness of the histogram indicates that the mean is being pulled down by lesser values and However, because it is the centre number and is only impacted by the higher and lower values equally, the median is unaffected by the lower values. Because of this, the mean in this histogram is less than the median.

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The slope of a line parallel to the line x + 5y = 9 is; Choice B: -1/5

The slope of parallel lines from line geometry are equal.

The given parallel line equation is; x + 5y = 9:

Hence, it follows that the two lines have equal slopes.

By rewriting the equation to take the slope-intercept form of straight lines, it follows that;

On this note, the slope of the parallel lines is; -1/5

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When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:

P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.

In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for

d.P = 0.433d + 14.7

Substitute P = 159 and solve for

d.159 = 0.433d + 14.7

Subtract 14.7 from both sides.

144.3 = 0.433d

Divide both sides by 0.433 to isolate d.

d ≈ 333.06

Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

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k=6

have an amazing day bye!

Answer:

Hello! k = 6

Step-by-step explanation:

40 + 90 = 130 so our last angle must be 50 sense this will add up to 180 so k = 6 because 7 x 6 = 42 and 42 + 8 = 50 so answer 6

Answer:

x is less than or equal to 0

Step-by-step explanation:

- you need to multiply both sides of the inequality by 5/2

- then you reduce the numbers with the greatest common factor 5

- then you reduce the numbers with the greatest common factor 2

- any expression multiplied by 0 equals 0

- so you get x is less than or equal to 0

^^^ hope this helps! :)

Answer:

The apprentice

Step-by-step explanation:

They both make 5 burgers a minute because, 25/5=5, and 35/7=5

Answer:The apprentice is right.

Step-by-step explanation:

Shown in picture below

Hope this helps :)

Answer:

explanation:

√348 =

18.6547581062

Answer:

B) y = -2/3x -2

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (-3,0) (0, -2); we see the y decrease by 2 and the x increase by 3, so the slope is

m = -2/3 = -2/3

The Y-intercept is located at (0, -2)

So, our answer is B) y = -2/3x -2

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

The Radical Form (√x)  ,the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

The equation √x - 2 + 4 = x for x, we can follow these steps:

1. Begin by isolating the radical term (√x) on one side of the equation. Move the constant term (-2) and the linear term (+4) to the other side of the equation:

  √x = x - 4 + 2

2. Simplify the expression on the right side of the equation:

  √x = x - 2

3. Square both sides of the equation to eliminate the square root:

  (√x)^2 = (x - 2)^2

4. Simplify the equation further:

  x = (x - 2)^2

5. Expand the right side of the equation using the square of a binomial:

  x = (x - 2)(x - 2)

  x = x^2 - 2x - 2x + 4

  x = x^2 - 4x + 4

6. Move all terms to one side of the equation to set it equal to zero:

  x^2 - 4x + 4 - x = 0

  x^2 - 5x + 4 = 0

7. Factor the quadratic equation:

  (x - 1)(x - 4) = 0

8. Apply the zero product property and set each factor equal to zero:

  x - 1 = 0   or   x - 4 = 0

9. Solve for x in each equation:

  x = 1   or   x = 4

Therefore, the solutions to the equation √x - 2 + 4 = x are x = 1 and x = 4.

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To prove the opposite, we need to show that if G is not a pseudorandom generator (PRG), then Construction 3.17 cannot be EAV-secure.

Assume that G is not a PRG, which means it fails to expand the seed sufficiently. Let's suppose that G is computationally indistinguishable from a truly random function on its domain, but it does not meet the requirements of a PRG.

Now, consider the private-key encryption scheme Π described in Construction 3.17 using G as the pseudorandom generator. If G is not a PRG, it means that its output is not sufficiently pseudorandom and can potentially be distinguished from a random string.

Given this scenario, an adversary A could exploit the distinguishability of G's output and devise an attack to break the security of the encryption scheme Π. The adversary could potentially gain information about the plaintext by analyzing the ciphertext and the output of G.

Therefore, if G is not a PRG, it implies that Construction 3.17 cannot provide EAV-security, as it would be vulnerable to attacks by distinguishing the output of G from random strings. This contradicts Theorem 3.18, which states that if G is a PRG, then Construction 3.17 achieves indistinguishable encryptions.

Hence, by proving the opposite, we conclude that if G is not a PRG, then Construction 3.17 cannot be EAV-secure.

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Answer:

(6,0) and (0,-12) straight line graph

Step-by-step explanation:

The distance between the centers of the two wheels is approximately 11.86 feet.

The length of the conveyor belt is equal to the circumference of the circle formed by each wheel plus the distance between the centers of the two wheels.

Let's call the distance between the centers of the two wheels "d". The circumference of each wheel can be calculated using the formula

C = πd

Since each wheel has a diameter of 1 foot, its radius is 0.5 feet. Therefore, the circumference of each wheel is:

C = πd = π(0.5) = 1.57 feet (approx.)

The length of the conveyor belt is given as 15 feet. So we can write

2C + d = 15

Substituting the value of C, we get

2(1.57) + d = 15

3.14 + d = 15

d = 11.86 feet

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Answer:

This is gebber gabber but yes

Step-by-step explanation:

Answer:

3.9

Step-by-step explanation:

\(8^{2} -7^{2} =15\)

\(\sqrt{15} =3.9\)

Answer:

2x+3y=-6

Step-by-step explanation:

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Based on the equation y = 0.13x + 46, the correct statement is:

The equation indicates that for every additional unit (mile) in the independent variable (flight distance), the dependent variable (ticket price) increases by the coefficient 0.13, which represents 13 cents.

Therefore, the equation suggests a linear relationship between flight distance and ticket price, with a constant increase of 13 cents per mile.

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There are 1820 different groups of applicants for 4 management trainee positions, 126 different groups of trainees consisting entirely of women, and a 0.0692 probability that the trainee class will consist entirely of women.

The number of different groups of applicants that can be selected for the four management trainee positions can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of applicants (16 in this case) and r is the number of positions to be filled (4 in this case).

So the number of different groups of applicants that can be selected is:

16C4 = 1820

Therefore, there are 1820 different groups of applicants that can be selected for the four management trainee positions.

The number of different groups of trainees that would consist entirely of women can be calculated using the combination formula again, but this time we are selecting all 4 positions from the 9 female applicants:

9C4 = 126

Therefore, there are 126 different groups of trainees that would consist entirely of women.

Assuming that all groups of four are equally likely to be selected, the probability that the trainee class will consist entirely of women can be calculated by dividing the number of different groups of trainees that consist entirely of women (126) by the total number of different groups of applicants (1820):

Probability = 126 / 1820 = 0.0692

So the probability that the trainee class will consist entirely of women is 0.0692 (rounded to four decimal places).

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Answer:

Step-by-step explanation:

look at picture

Answer:

distance = 5 units

Step-by-step explanation:

we can calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (3, 4 )

d = \(\sqrt{(3-0)^2+(4-0)^2}\)

  = \(\sqrt{3^2+4^2}\)

  = \(\sqrt{9+16}\)

   = \(\sqrt{25}\)

   = 5

Formula to find the distance between two points is given by -

\( \small \underline{ \boxed{ \sf{ \pmb{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}}}\\\)

As per question, points are -

On substituting the values :-

\(\: \: \: \: \: \longrightarrow \sf {Distance(XQ) = \sqrt{ (0-4)^2 + (0-3)^2 }}\\\)

\(\: \: \: \: \:\longrightarrow \sf {Distance (XQ)= \sqrt{ (-4)^2 + (-3)^2 }}\\\)

\(\: \: \: \: \:\longrightarrow \sf {Distance(XQ) = \sqrt{ 16+9}}\\\)

\(\: \: \: \: \:\longrightarrow \sf {Distance (XQ)= \sqrt{ 25} }\\\)

\(\: \: \: \: \:\longrightarrow \sf {Distance(XQ) = 5}\\\)

\( \: \: \: \: \:\longrightarrow \boxed{ \tt{ \pmb{ \red{Distance(XQ) = 5 }}}}\\\)

\( \\ \therefore \underline{ \cal{ \pmb{The \:distance \: of \: the\: two \:points \: is \: \frak{\purple{ 5.} }}}}\\\)