There are 42 female performers in a dance retail. The ratio of men to woman is 3:7. How many men are in the dance recital

Answer: It's A, 1/6 is less than 1/5

Also could you mark my answer as brainliest? It helps and doesnt hurt

Answer:

Step-by-step explanation:

... g=10m/s??

Answer:

The diameter of Pluto is 2200

Step-by-step explanation:

Let u = the diameter of Uranus

Let e = the diameter of Earth

Let m = the diameter of Mars

Let p = the diameter of Pluto

u = 52000

e + m + p = 52000 - 30000

e + m + p = 22000

e = 2m

m = 3p or p = m/3

substitute 2m for e and m/3 for p in the bold equation above and solve for m

2m + m + m/3 = 22000  Multiply all the way through by 3 to clear the fraction.

6m + 3m + m = 66000  Combine like terms

10m = 66000  Divide both sides by 10

m = 6600

P = m/3

p = 6600/3 = 2200

The graph that represents the rational function f(2x) is given by:

Graph C.

The transformation to a function that generates an horizontal compression or stretch is in the domain of the function, as follows:

f(ax).

Then whether the transformation is a compression or a stretch depends on the absolute value of a, as follows:

In this problem, the transformation is defined as follows:

g(x) = f(2x).

Meaning that it is an horizontal compression by a factor of 1/2.

The vertical asymptote has the coordinate given as follows:

x = 2.

After the compression, the coordinate is given as follows:

x = 2 x 1/2

x = 1.

Which means that Graph C is the correct graph for the rational function after the transformation.

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The correct statement regarding the dilation is given as follows:

The new triangle is similar to the original triangle but not congruent.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The definitions for similar and congruent triangles are given as follows:

For the dilation, due to the multiplication of the side lengths by the scale factor, the side lengths are modified, meaning that the original triangle and the dilated triangle are not congruent.

The angle measures, conversely, remain constant, meaning that the original triangle and the dilated triangle are similar.

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The image of the triangle after the dilation with a scale factor of 2 is graphed on the image shown at the end of the answer.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Hence, to graph the image of triangle ABC on this problem, we have to:

The coordinates of the vertices of the original triangle are given as follows:

(0,0), (-4,-2), (-4,4).

The scale factor for the dilation is is given as follows:

k = 2.

Then the coordinates of the vertices of the image of the triangle after the dilation are given as follows:

(0,0), (-8,-4), (-8,8).

The triangle with these three vertices is graphed on the image presented at the end of the answer.

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Answer:

[tex]y=\frac{1}{2}x+1[/tex]

Step-by-step explanation:

The points [tex](-2,0)[/tex] and [tex](0,1)[/tex] lie on the line.

The slope of the line is [tex]m=\frac{1-0}{0-(-2)}=\frac{1}{2}[/tex].

Since the [tex]y[/tex]-intercept is [tex](0,1)[/tex], the equation is [tex]y=\frac{1}{2}x+1[/tex].

120 numbers greater than 4000 can be formed with the digits 2 3 4 5 and 6 when no digit is repeated.

In order to find out how many numbers greater than 4000 can be formed with the digits 2, 3, 4, 5 and 6 without repeating any digit, we can use permutation. The formula for permutation is n!/(n-r)! Where n is the total number of digits and r is the number of digits in the number.

In this case, n=5 and r=4.

Therefore, the formula is 5 x/(5-4)! which is 5x/(1x) = 5! = 5x4x3x2x1 = 120.

This means that there are 120 numbers greater than 4000 that can be formed with these five digits without repeating any digit.

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Answer:

If cos(E) = sin(F), then we know that m∠E + m∠F = 90 degrees (since E and F are acute angles).

We are given that m∠E = (8x - 12) degrees, and we want to find m∠F.

We can substitute the given value of m∠E into the equation m∠E + m∠F = 90 degrees, and solve for m∠F:

(8x - 12) + m∠F = 90

m∠F = 78 - 8x

So the measure of angle F is 78 - 8x degrees.

We are also given that m∠F = (6x - 10) degrees. So we can substitute this value into the equation we just found:

m∠F = (6x - 10) = 78 - 8x

We can now solve this equation for x:

6x - 10 = 78 - 8x

14x = 88

x = 6

So we know that x = 6.

Now we can substitute this value back into the equation m∠F = (6x - 10) to find the measure of angle F:

m∠F = (6x - 10) = (6 * 6) - 10 = 24 degrees

So the measure of angle F is 24 degrees.

The possible value of x is 17 and the degree measure of each angle is m∠P = 57°, m∠Q = 110°, and m∠R = 17°.

What are the degree measures of the three angles in triangle?

The angle sum of a triangle will always be equal to 180°. The angle sum of a quadrilateral is equal to 360°, and a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral, its angle measures should be half as well. Half of 360° is 180°.

We have given,

The triangle PQR,

m∠P=(4x - 9), m∠Q=(6x+2), and m∠R=x. (a) Write an equation to find x.

a)

In a triangle, the sum of the degree measures of the three angles must be 180 degrees.

So for the triangle with angles P, Q, and R, we can use this rule to write the following equation:

m∠P + m∠Q + m∠R = 180

(4x - 9) + (6x + 2) + x = 180

11x - 7 = 180

11x = 187

x = 17

This equation shows that x = 17 is the only possible value of x that satisfies the triangle inequality rule for the given triangle.

b) To find the degree measure of each angle:

m∠P = 4x - 9 = 4(17) - 9 = 57°

m∠Q = 6x + 2 = 6(17) + 2 = 110°

m∠R = x = 17°

Hence, the possible value of x is 17 and the degree measure of each angle is m∠P = 57°, m∠Q = 110°, and m∠R = 17°.

.

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The three examples of exponential decay are radioactive decay, carbon-14 dating, and medical imaging.

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. The most common type of radioactive decay is alpha decay, in which the nucleus emits an alpha particle (a helium nucleus) and transforms into an atom with a mass number that is four less than the original atom.

Carbon-14 dating is a method for determining the age of objects that contain organic material by measuring the radioactive decay of carbon-14. Carbon-14 is a radioactive isotope of carbon that is present in all living things in a constant amount.

When an organism dies, the carbon-14 begins to decay and is not replaced. The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the carbon-14 will have decayed.

Medical imaging, such as X-rays and CT scans, use ionizing radiation, which can damage living tissue. The amount of damage is a function of the radiation dose and the sensitivity of the tissue. The damage is typically repaired by the body, but at high doses, the damage can be permanent and result in cell

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Let M be the amount of money Melissa has, J be the amount of money Josh has, and P be the amount of money Pablo has. We can set up the following equation:

M + J + P = $66

P = 3J

J = M + $9

Substituting the second equation into the third equation, we get:

J = M + $9

3J = 3(M + $9)

3M + 3*$9 = 3J

3M + 3*$9 = 3(M + $9)

3M + 3*$9 = 3M + $27

$27 - $27 = 3M - 3M

0 = 0

Since 0 = 0, the equation holds true for any values of M, J, and P as long as they add up to $66. Therefore, there is not enough information to determine how much money Melissa, Josh, and Pablo have in their wallets.

The double integral of 4x + xydA over the region [0, 4] × [0, 1] is equal to 8.5. This can be computed by integrating x + xy with respect to x from 0 to 4 and then integrating with respect to y from 0 to 1.

The double integral of 4x + xydA over the region [0, 4] × [0, 1] is equal to 8.5. This can be computed by:

1. Integrate 4x with respect to x from 0 to 4:

∫04x dx = [x2/2]04

= (42/2) - (02/2)

= 16/2

2. Integrate xy with respect to x from 0 to 4:

∫04xydx = [x2/2]41

= (41/2) - (01/2)

= 1/2

3. Add the two integrals together to get the final answer:

16/2 + 1/2

= 8 + 1/2

= 8.5

The double integral of 4x + xydA over the region [0, 4] × [0, 1] is equal to 8.5. This can be computed by first integrating 4x with respect to x from 0 to 4, which gives 16/2, and then integrating xy with respect to x from 0 to 4, which gives 1/2. Adding these two integrals together yields 8 + 1/2, or 8.5.

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To do dilatation a triangle by a scale factor of k, we have to multiply the x and y-value of each triangle point by k.

A coordinate plane is a system that graphs and describes the position of points and lines. It consists of horizontal (x) and vertical (y) axes.

We can perform dilatation for a point or line in a coordinate plane system based on specific criteria.

Dilation is a form of image transformation that produces a new image, which is larger, or smaller, based on a certain scale factor. The new image is the same in shape, but different in size.

The rule of dilatation:

[tex]D_{k}[/tex](x,y) = (kx, ky)

where [tex]D_{k}[/tex] is the point of the new image and k is the scale factor.

When we want to dilate a triangle ABC, the result can be found by multiplying its original points with the scale factor.

For example:

Triangle ABC (-2,2), (-2,3), (1,2) is dilated by a scale factor of 2. The new triangle A'B'C' will be A’(-4,4), B’ (-4,6), and C’ (2,4).

Thus, to dilate a triangle by a scale factor of k, we have to multiply the x and y-value of each triangle point by k.

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The correct order of given information is 3, 2, 1 and 4.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Given that, the given graph represents the amount of water in a pool over a period of 5 hours.

Here, the order of given information is

Therefore, the correct order of given information is 3, 2, 1 and 4.

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We are unable to perform any additional iterations because y′(1)=0, hence the Newton's technique fails with the provided initial assumption.

An equation is a mathematical formula that joins two statements and uses the equal symbol (=) to indicate equivalence. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign divides the variables 3x + 5 and 14. The relationship between the two sentences on either side of a letter is explained by a mathematical formula. There is frequently only one variable, which also serves as the symbol. for instance, 2x - 4 = 2.

given

by newton's method

y = x3 − 2x − 2, x1 = 0

y′(1)=6−12+6

y′(1)=0

We are unable to perform any additional iterations because y′(1)=0, hence the Newton's technique fails with the provided initial assumption.

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The exponential function in the form y=ab^xy=ab^x is   [tex]y=14^{(2)}^{x}[/tex]

An exponential function is defined as a mathematical function of the following form:

f(x) = a^x. where x is a variable, and a is a constant and is also called the base of the function.

where a> 0 and a≠ 1.

first, we have to find a and b values, to find a and b values we have to substitute the points into the given equation.

y=ab^xy=ab^x we can rewrite it as y=ab^x

using (0, 14 ), then the equation becomes:

14=ab^0 [b^0 =1 ], then

14 = a × 1

⇒ a = 14

y = 14b^x

Now, use the second point: (6, 896 )

896 = 14 b^6 ( divide both sides by 14 )

64 = b^6 ( take the sixth root of both sides )

[tex]b=\sqrt[6]{64}[/tex]

b=2

substitute a and b values in the equation, and we get:

Hence, y = 14^(2)^x is the exponential function.

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Answer:

11 2 point and 6 3 point baskets

Step-by-step explanation:

Let x be the number of 2-point baskets the basketball player made, and let y be the number of 3-point baskets. We know that the player made a total of 17 shots, so x + y = 17. We also know that the player scored 40 points, and each 2-point basket is worth 2 points and each 3-point basket is worth 3 points, so 2x + 3y = 40.

We can solve this system of equations using substitution. From the first equation, x = 17 - y. Substituting this expression for x into the second equation, we get 2(17 - y) + 3y = 40. Expanding the left side, we get 34 - 2y + 3y = 40. Simplifying, we get y = 6.

Substituting this value for y back into the first equation, we get x = 17 - 6 = 11. Therefore, the basketball player made 11 2-point baskets and 6 3-point baskets.

The corresponding angle of angle 8 is angle 4.

When parallel lines are cross by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, linear angles, same interior angles, alternate exterior angles, vertically opposite angles.

In the diagram, j and k are parallel line cut by the transversal t. Let's find the corresponding angle of 8.

Corresponding angles are the angles which are formed in matching corners with the transversal when two parallel lines are intersected by any other line. corresponding angles are congruent.

Therefore,

∠4 is corresponding to ∠8.

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Nolen was 145.8 feet far away from the door.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms.

Given, In Washington, DC, Nolen was standing close to the Washington Monument. There was a sizable line to enter. He decided to have some fun and see how far he was from the entrance because he was bored. The monument is described as being 550 feet tall in the tourism brochure. He pulled out his phone and used the software to measure the monument's top at a 75° angle. He had 5.7 feet of eye height.

The accompanying image will assist us in better comprehending this situation.

Let's make the triangle from the eyes of the Nolen.

We will get the height of the triangle = 544.3feet

and the angle is 75

Thus, the Base of the triangle = height / tan∅

the Base of the triangle = 544.3 / tan 75

the Base of the triangle = 145.844 feet

Therefore, The distance between Nolen and the door of the monument is 145.8 feet.

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Answer:

Step-by-step explanation:

1+1=2 hope this helps

The sine value of the function will be 7 times square root of 74 over 74.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Firstly, we need to get for the value for r. This will be

r² = (−5)² + 7²

r² = 74

r = square root of 74

After, formulate the equation of a sine. This will be:

sin x = 7/r

sin x = 7/✓74

sin x = (7×✓74)/74

Therefore, the sine value of the function will be sin x = (7×✓74)/74.

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"Your question is incomplete, probably the complete question/missing part is:"

Engineers are analyzing the performance of windshield wiper blades. At the end of one swipe, the tip of a blade is at (−5, 7) when represented graphically. What is the sine value of this function?

Negative 7 square root 74 divided by 74 7 times square root of 74 over 74 square root 74 negative 5 times square root of 74 over 74

Answer:

a)(1.5,-4) true , (-4,-4) false / b) (0,-5) and (2,-4) are false and the other 2 is true / c) shade under the line d) they are not included because they are if you take any point on the line ot won't be less that 15

Step-by-step explanation:

in a) you substitute the x and the y to the equation and check if they are equal to 15 , b) you do the same thing but this time you check if its under 15 c) its less than so its below the line , d) already answered

If Washington Auto Repair originally paid its mechanics $40 per hour. Now that there is a new owner, mechanics make $30.90 per hour. The percent of decrease in pay is: 22.75%.

Using this formula to find or determine the percent decrease

Percent decrease = Original Value – New Value/Original value

Let plug in the formula

Percent decrease  = $40 per hour - $30.90 per hour / $40 per hour

Percent decrease = $9.10 /  $40 per hour × 100

Percent decrease = 22.75%

Therefore the percent decrease is 22.75%.

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The radius of convergence, r, of the series [infinity] 6(−1)nnxn n = 1 is 1.

The radius of convergence is the distance from the point of convergence to the origin. It tells us the distance at which a series converges or diverges. In this series, the point of convergence is at x = -1, so the radius of convergence, r, is the distance between -1 and the origin, which is 1. This means that the series converges for any x such that |x+1|<1, or in other words, for any x such that -2<x<0.

Outside of this range, the series will diverge and will not converge. This can be determined by looking at the terms of the series. For |x+1|>1, the terms of the series will become larger and larger, resulting in divergence. For |x+1|<1, the terms of the series will become smaller and smaller, resulting in convergence.

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The probability that the series will end only after 7 games are played is 1.77

Here we have given that teams A and B play until one team has won 4 games.

And here we also know that the probability of winning for Team A is 2/3,

Then the probability of winning Team B is calculated as,

=> 1 - 2/3

=> 1/3

Then the probability that the series will end only after 7 games are played is calculated as,

=> P(X = 3) + P(X = 4)

When we apply the values on it, then we get

=> 4C3(2/3)(1/3) + 4C4(2/3)(1/3)

When we simplify this one then we get,

=> 1.77

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By the property of regular hexagon , the total number of equilateral triangles are need to form a regular hexagon is six .

What is a Regular Hexagon ?

A regular hexagon is defined as a closed figure that is made up of six equal sides .

The Properties Of Regular Hexagon are :

(i) Regular Polygon has 6 equal sides and 6 equal angles.

(ii) The Sum of interior angles is equal to 720°.

(iii) Each Interior angle is of 120° and exterior angle is of 60°.

(iv) Regular Hexagon made up of six equilateral triangles.

(v) There are 9 diagonals that can be drawn inside a regular hexagon.

Therefore , 6 equilateral triangles are need to form regular hexagon .

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In the last two games, a basketball player has scored 94 points altogether.

The mathematical average of two or more numbers is known as the mean. It can be calculated using either the geometric or arithmetic mean methods.

Given, After 8 matches a basketball player has a mean of 27 points. After ten matches his mean was 31 points.

mean =  sum of total observation / no. of observations

let the sum of total points scored in 8 matches be x

x/8 = 27

x = 216

after three more matches, his mean was 31.

new mean = x + (points in last three games)/(8+2)

31 = (x + (points in last three games))/10

x + (points in last three games)=  310

we know that x = 216

216  + (points in last three games) = 310

points in the last three games = 310 - 216

Points in the last two games = 94

therefore, a basketball player scores a total of 94 points in the last two games.

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Yay! This one isn't that bad.  

Think of it like this:

123 = 123

1 = 1, 2 = 2, and 3 = 3.  

For angles, ABC = ABC, A = A, B = B, and C = C.

If you know that example SOQ = WHO, then S = W, O = H, and Q = O.  Nothing else though, unless there's a diagram and you are given information stating otherwise.

Hope that helps! xx And please make sure that you are not posting any questions about exams or tests.  That could endanger your grade.  I've seen quite a few exam questions on here, and teachers check these things.  And even if they don't, be honest! :) Honesty Policy.  

Answer:

hypotenuse = 4

Step-by-step explanation:

   Given triangle is a right-angled triangle. To find the unknown side, use Pythagorean theorem.

      hypotneuse² = leg₁² + leg₂²

                             [tex]\sf = (2\sqrt{3})^2 + 2^2\\\\= 2^2*(\sqrt{3})^2 + 4\\\\= 4*3 + 4\\\\= 12 + 4\\\\=16[/tex]

         [tex]\sf hypotenuse = \sqrt{16}\\[/tex]

                           [tex]\sf = \sqrt{4*4}\\\\ = 4[/tex]

The cost for each pot of ivy is obtained as $4.

A system of linear equations can be defined as a number of equations needed to solve the equations. For n number of variables n number of equations are required.

Suppose the cost of each host and ivy be x and y respectively.

Then, the system of equations for money spent by Mark and Shannon can be written as,

4x + 4y = 44                 (1)

2x + 5y = 34                 (2)

Multiply equation (2) by 2 then subtract from (1) to get,

4x + 4y - 2(2x + 5y) = 44 - 2 × 34

⇒ -6y = -24

⇒ y = 4

Hence, the cost of each pot of ivy is given as $4.

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