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The recent percentage of people that go out dancing at least one night a month, considering an initial percentage of 78% in 2010 and a recent increase of 2%, is 80%.

The percentage of people who went out dancing at least once a month in 2010 was 78%. If the number has recently increased by 2%, we need to add these two percentages together to find the recent percentage. In mathematics, when an increase is given in percentage, it's added to the original.

So, let's do the calculation:

78% (percentage in 2010) + 2% (recent increase) = 80% (recent percentage).

So, the recent percentage of people who go out dancing at least once a month is 80%.

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Answer:

1/16

Step-by-step explanation:

You need to know the following property

[tex]a^{(-b)} = \frac{1}{a^b}[/tex]

That means

[tex]4^{-2} = \frac{1}{4^2} = \frac{1}{4*4} = \boxed{\frac{1}{16}}[/tex]

The answer is:

The function intercepts de x-axis at "x" equal to 1.631.

To find the x-intercept of the function, we need to make f(x) or "y" equal to 0, and then, isolate "x".

So, isolating we have:

[tex]f(x)=3^{(x-1)} -2\\\\0=3^{(x-1)} -2\\\\3^{(x-1)}=2\\\\Log_{3}(3^{(x-1)})=Log_{3}(2)\\\\x-1=0.631\\\\x=0.631+1=1.631[/tex]

Hence, we have that the function intercepts de x-axis at "x" equal to 1.631.

Have a nice day!

Note: I have attached a picture for better understanding.

[tex]-\dfrac{5}{7}\cdot\dfrac{1}{5}=-\dfrac{1}{7}[/tex]

Answer:

2 is the bigger number

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Think about it this way your looking at a number line and at this point your looking at number -5 and then do bunny hops from -5 to 2 and however many hops you took is the difference between

Answer:

see explanation

Step-by-step explanation:

Note that 9x² and 49y² are perfect squares.

9x² = (3x)² → 3x is the first term

49y² = (7y)² → 7y is the second term

Hence

(3x + 7y)² = 9x² + 42xy + 49y²

Answer:

sqrt.(a) * absolutevalue(b)

Step-by-step explanation:

You do abs value when you have an even exponent with an odd exponent result from b^2 to b^1.

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Answer: Hello there!

Well, the square root is the inverse function of the square potential.

This is if you have [tex](\sqrt{x} )^{2}  = x[/tex] and [tex]\sqrt{x^{2} }  = +-x[/tex]

A interesting part of the square root is that (-4)*(-4) = 16, and 4*4 = 16, so the solutions for [tex]\sqrt{16}[/tex] are -4 and 4. For this is that you see a +- symbol in the second equation.

Now, if you have the number [tex](a*b)^{2}[/tex]

Now, we put this inside a square root: [tex]\sqrt{(a*b)^{2} } = +-a*b[/tex]

So the solutions for the square root of (a*b)^2 are a*b and - a*b.

in total: thirty-six (36) markers.

Answer:

P(6, 12 )

Step-by-step explanation:

Using the Section formula, then

[tex]x_{P}[/tex] = [tex]\frac{7(7)+1(-1)}{1+7}[/tex] = [tex]\frac{49-1}{8}[/tex] = [tex]\frac{48}{8}[/tex] = 6

[tex]y_{P}[/tex] = [tex]\frac{7(14)+1(-2)}{1+7}[/tex] = [tex]\frac{98-2}{8}[/tex] = [tex]\frac{96}{8}[/tex] = 12

Hence P(6, 12 )

Answer:

Third option: 2x^3-11x^2+16x-3

Step-by-step explanation:

The product to be found is:

[tex](x-3)(2x^2-5x+1)[/tex]

Distributive property will be used for the product:

[tex]x(2x^2-5x+1)-3(2x^2-5x+1)\\[/tex]

Multiplication will give us:

[tex]=2x^3-5x^2+x-6x^2+15x-3\\Combining\ alike\ terms\\=2x^3-5x^2-6x^2+x+15x-3\\=2x^3-11x^2+16x-3[/tex]

The product is: 2x^3-11x^2+16x-3

Hence, third option is the correct answer ..

Answer:

The product is 2x³ - 11x² + 16x - 3 ⇒ 3rd answer

Step-by-step explanation:

* Lets explain how to find the product of binomial by trinomial

- If (ax² ± bx ± c) and (dx ± e) are trinomial and binomial, where

 a , b , c , d , e  are constant, their product is:

# Multiply (ax²) by (dx) ⇒ 1st term in the trinomial and 1st term in the  

 binomial

# Multiply (ax²) by (e) ⇒ 1st term in the trinomial and 2nd term in

the binomial

# Multiply (bx) by (dx) ⇒ 2nd term the trinomial and 1st term in  

the binomial

# Multiply (bx) by (e) ⇒ 2nd term in the trinomial and 2nd term in    the binomial

# Multiply (c) by (dx) ⇒ 3rd term in the trinomial and 1st term in  

 the binomial

# Multiply (c) by (e) ⇒ 3rd term the trinomial and 2nd term in  

the binomial

# (ax² ± bx ± c)(dx ± e) = adx³ ± aex² ± bdx² ± bex ± cdx ± ce

- Add the terms aex² and bdx² because they are like terms

- Add the terms bex and cdx because they are like terms

* Now lets solve the problem

∵ The binomial is (x - 3) and the trinomial is (2x² - 5x + 1)

∴ (x)(2x²) = 2x³

∵ (x)(-5x) = -5x²

∵ (x)(1) = x

∵ (-3)(2x²) = -6x²

∵ (-3)(-5x) = 15x

∵ (-3)(1) = -3

∴ (x - 3)(2x² - 5x + 1) = 2x³ + -5x² + x + -6x² + 15x + -3

- Add the like terms

∵ -5x² and -6x² are like term

∴ Their sum is -11x²

∵ x and 15 x are like terms

∴ Their sum = 16x

∴ (x - 3)(2x² - 5x + 1) = 2x³ - 11x² + 16x - 3

* The product is 2x³ - 11x² + 16x - 3

Answer:

[tex]\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]

Step-by-step explanation:

we know that

Te volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=(r/2)\ units[/tex]

substitute

[tex]V=\frac{1}{3}\pi (r/2)^{2}h[/tex]

[tex]V=\frac{1}{12}\pi r^{2}h[/tex]

Te volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we know that

To find the volume of the space remaining in the cylinder after the cone is placed inside it, subtract the volume of the cone from the volume of cylinder

so

[tex]\pi r^{2}h-\frac{1}{12}\pi r^{2}h=\frac{11}{12}\pi r^{2}h\ units^{3}[/tex]

Answer:

Step-by-step explanation:

Begin with process of elimination: As seen on the graph, there is a discontinuity at x=3. this means that x>=3. so  we can eliminate B and C

Now you can see that at x = 3, two things happen. When moving to the left, x<3. when moving tot he right x>=3 so because of this you can eliminate D. The answer is A

Check the picture below.

Answer:

B

Step-by-step explanation:

We basically want to find the volume of this cylinder.

The volume of a cylinder is given by the formula  [tex]V=\pi r^2 h[/tex]

where r is the radius and h is the height.

We plug the info given and find the volume:

[tex]V=\pi r^2 h\\V=\pi (0.28)^2 (0.83)\\V=0.20[/tex]

Correct answer B

Answer:

y=

−1

2

x+3

Step-by-step explanation:

is solved for y

Answer:

The new volume is 8 times smaller than the original volume

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x ----> the volume of the reduced sphere

y ----> the volume of the original sphere

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=1/2[/tex] ----> scale factor

substitute

[tex](1/2)^{3}=\frac{x}{y}[/tex]

[tex](1/8)=\frac{x}{y}[/tex]

[tex]x=\frac{y}{8}[/tex]

therefore

The new volume is 8 times smaller than the original volume

Verify

The volume of the original sphere is

[tex]r=18/2=9\ cm[/tex] ---> the radius is half the diameter

[tex]V=\frac{4}{3}\pi (9)^{3}=972\pi \ cm^{3}[/tex]

the volume of the reduced sphere is

[tex]r=9/2=4.5\ cm[/tex] ---> the radius is half the diameter

[tex]V=\frac{4}{3}\pi (4.5)^{3}=121.5\pi \ cm^{3}[/tex]

Divide the volumes

[tex]972\pi \ cm^{3}/121.5\pi \ cm^{3}=8[/tex]

Answer:

=  1872x^2 - 1960q^2 - 1386xq

Step-by-step explanation:

First you should distribute.

(24x * 56q), (24x * 78x), (-35q * 56q), (-35q * 78x)

=1344xq + 1872x^2 - 1960q^2 - 2730xq

Now you combine like terms.

=  1872x^2 - 1960q^2 - 1386xq

**NOTE that (^2) means "squared"

Since there are no more like terms that is your final answer. I hope this helps love! :)

Answer:

Step-by-step explanation:

You would simplify 5/2, making it 2 and 1/2.  this would go in between 2 and 3 on a graph.

Step-by-step explanation:

5/2 = 2.5

see attached to find where 2.5 is located on the number line.

Answer:ZTSU

Step-by-step explanation:

Another way to name ∠UST is ∠TSU.

Option B is correct.

We have,

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

The angle mentioned in the figure is at the point S.

This angle is the smaller angle formed at the point S.

An angle can be represented in two ways, from left to right or from right to left.

Suppose, an angle is ∠ABC.

We can represent this as ∠CBA.

So, the angle represented is ∠TSU.

Hence the angle is ∠TSU.

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Answer:

x1=-11 x2=-1 y=11

Step-by-step explanation:

you can see the explanation in the pics

Answer:

Inconsistent equations describes a system of equations that has no solution.

Step-by-step explanation:

Inconsistent equations have no solutions and contain no further classes.

Inconsistent equations are defined as two or more equations that can never be solved, based on using one set of values for the variables.

Answer:

3

Step-by-step explanation:

[ 3.6 ] represents the greatest integer function [ x ]

If x is an integer use that integer

If x is not an integer use the next smaller integer

[ 3.6 ] is not an integer, hence

[ 3.6 ] = 3

Answer:3

Step-by-step explanation: edge 2021

Answer:

Step 1  1200/ ?

Step-by-step explanation:

There is a mistake in the very first step

He is writing par over whole

100% is the original amount of tickets x

150% is the 1200 tickets

150       1200

-----  =  ------------

100          ?

Answer:

a

Step-by-step explanation:

Answer:

278 probly

Step-by-step explanation:

i just subracted 981 and 703

[tex]1\cdot4\cdot3\cdot2+2\cdot4\cdot3\cdot2=24+48=72[/tex]

Answer:

72

Step-by-step explanation:

There are five possible digits to choose from: 3, 4, 5, 6, and 7.

The number must be greater than 5000, so there are 3 possibilities for the first digit: 5, 6, or 7.

There's no repetition, so the second digit is one of 4 remaining possible digits.

That leaves 3 possible digits for the third digit.  And 2 possible digits for the fourth digit.

So the number of possible four-digit numbers that can be formed is:

3 × 4 × 3 × 2 = 72

Answer:

Option B

The solution in the attached figure

Step-by-step explanation:

we have

Inequality A

[tex]y > -\frac{1}{3}x+1[/tex]

we know that

The solution of the inequality A is the shaded area above the dashed line

The equation of the dashed line is [tex]y=-\frac{1}{3}x+1[/tex]

The slope of the dashed line is negative [tex]m=-\frac{1}{3}[/tex]

Inequality B

[tex]y > 2x-1[/tex]

we know that

The solution of the inequality B is the shaded area above the dashed line

The equation of the dashed line is [tex]y=2x-1[/tex]

The slope of the dashed line is positive [tex]m=2[/tex]

therefore

The solution in the attached figure

The correct graph is:

                Graph B

First inequality is given by:

             [tex]y>\dfrac{-1}{3}x+1[/tex]

The inequality is a straight line that passes through (0,1) and (3,0) and also the line is dotted since the inequality is strict.

The shaded region is away from the origin since the inequality does not pass the zero point test.

Second inequality is given by:

            [tex]y>2x-1[/tex]

The graph of this inequality is a dotted line (since the inequality is strict) and passes through (0,-1) and (1/2,0) and the shaded region is towards the origin

( since the line passes the zero point test )

Graph B represents the system of inequality.

Answer:

83,962

Step-by-step explanation:

You must subtract the miles gained while on the road trip from the miles the car had after the road trip.

86,445-2,483=83,962

Experience and education are examples of advanced qualifications that is used to determine a high wage paid to an employee.

"Experience is the skill or knowledge that a person can get by learning or doing some professional work or from life."

"Education is an activity which helps an individual to achieve a particular aim of life."

"Advanced qualifications is an activity which helps an individual to increase in the level of education and their learning skills for achieving something better in life."

"Wage is the income which an individual earn with respect to the work he performed"

Hence, option d is correct.

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Answer:

[tex]g(x)=-2x[/tex]

Step-by-step explanation:

A point reflected across the y-axis maintains its y-coordinate, but its x-coordinate switches signs. So, a positive x-coordinate becomes negative, and a negative x-coordinate becomes positive.

Let's take a few points from the original function, f(x). Remember, if we know the function, we can find the y-coordinate for any x-coordiante by simply plugging it into the function's equation.

Generally, [tex]f(x)=2x[/tex]

So:

[tex]f(0)=2(0)=0\\f(1)=2(1)=2\\f(2)=2(2)=4[/tex]

Leading us to have the plot points (0,0), (1,2) and (2,4).

To reflect this across the y-axis for the g(x) equation, we just need to turn the x-coordinates negative, resulting in a set of (0,0), (-1,2), and (-2,4).

Since we know this is a linear function (because there are no exponents in the equation), we can calculate the slope of this new set of points by using just 2 of them. The slope will give us our equation, because since (0,0) is a point on our line, we know that the y-intercept is zero.

[tex]slope=\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})} \\slope=\frac{(4-2)}{((-2)-(-1))} \\slope=\frac{2}{-1}\\slope=-2\\\\g(x)=-2(x)[/tex]