There are 9 students performing in the talent show, 7 of whom will perform a dance.
If 6 students are randomly chosen to perform during the first section of the show, what is the
probability that all of them will perform a dance?

Write your answer as a decimal rounded to four decimal places.

The directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]

The parabola equation is given as:

[tex]\frac 14(y + 3) = (x -2)^2[/tex]

A parabola is represented as:

[tex]4p(y - k) =(x -h)^2[/tex]

By comparing both equations, we have:

4p = 1/4 ==> p = 1/16

-k= 3 ==> k = -3

The directrix is represented as:

y = k - p

So, we have:

[tex]y = -3 - \frac 1{16}[/tex]

Take the LCM

[tex]y = \frac {-16 * 3- 1}{16}[/tex]

Evaluate

[tex]y = \frac {-49}{16}[/tex]

Hence, the directrix of the parabola is [tex]y = \frac {-49}{16}[/tex]

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Step-by-step explanation:

a lot of typos in the problem description.

I assume the price of the mix is 1:1 related to the prices of the individual types of coffee.

so, from what I understood we can define

x = pounds of the first type of coffee.

y = pounds of the second type of coffee.

x + y = 21 pounds

1.4x + 2.95y = 2.6(x + y) = 2.6×21 = $54.60

in the second equation we have to bring the given "$2.60 per pound" to the total price, which is $2.60 times the total amount of pounds (which is 21).

from the first equation we get

x = 21 - y

and that we use in the second equation

1.4×(21 - y) + 2.95y = 54.6

29.4 - 1.4y + 2.95y = 54.6

1.55y = 25.2

y = 25.2 / 1.55 = 16.25806452... ≈ 16.26 pounds

x = 21 - y = 4.741935484... ≈ 4.74 pounds

so, he should mix 4.74 pounds of the first (cheaper) type and 16.26 pounds of the second (expensive) type.

Hello, the answer should be [tex]m=\frac{6}{5}= 1,2[/tex].

First, let's edit the given function as [tex]y[/tex] parameter leave alone.

[tex]15x+18y=270\\\\18y=270-15x\\\\y=\frac{270-15x}{18}\\ \\y=\frac{270}{18}-\frac{15x}{18}[/tex]

If the given equation looks like;

[tex]y=f(x)\\\\y=ax+b[/tex]

then, the slope of the equation is the coefficient of [tex]x[/tex] parameter ([tex]a[/tex])

The slope(m);

[tex]m=\frac{-15}{18}=\frac{-5}{6}[/tex]

The product of the slopes of two perpendicular lines must be [tex]-1[/tex]. By that way, the slope of a line perpendicular to the given line is below:

[tex]m_{expected}=\frac{-1}{m_{given}} \\\\m_{expected}=\frac{-1}{\frac{-5}{6} }=\frac{6}{5}[/tex]

Good luck. If you have any questions, then feel free to ask in comments!

Answer:

x = 15

Step-by-step explanation:

the sum of the exterior angles of a polygon = 360°

sum the 5 exterior angles and equate to 360

5x + 3 + 4x + 8 + 5x + 5 + 6x - 1 + 3x = 360 , that is

23x + 15 = 360 ( subtract 15 from both sides )

23x = 345 ( divide both sides by 23 )

x = 15

The graph of the function looks like V. And the vertex of the function will be at (-3, 0).

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = |x + 3|

Then the graph of the function looks like V. And the vertex of the function will be at (-3, 0).

The graph of the function is given below.

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The probability that a customer likes cake and pie is 0.16.

Probability is used to determine the odd that a random event would happen. The odds that the event happens usually lie between 0 and 1.

The probability that a customer likes cake and pie = total number of customers who like cake and pie / total number of customers

4/25 = 0.16

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The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex] and for line 2x + 3y = 6 will be,[tex]\rm y = \frac{-2}{3}x+2[/tex]

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

a) 2x + 3y = -6

The line in which the standard form is found as;

Ax + By + C = 0

The typical form of a slope intercept is

y = mx+c

where m denotes the slope and b the line's y-intercept.

[tex]3y= -6-2x\\\\ y=\frac{-6-2x}{3}\\\\ y= -\frac{2}{3}x -2[/tex]

To obtain the slope standard form, we rewrite. The obtained equation is in the form of the slope-intercept.

b) 2x + 3y = 6

The line in which the standard form is found as;

Ax + By + C = 0

The typical form of a slope intercept is

y = mx+c

where m denotes the slope and b the line's y-intercept.

[tex]\rm 3y= 6-2x \\\\ y= \frac{6-2x}{3} \\\\ y = \frac{-2}{3}x+2[/tex]

Hence, The equation of the graphed line 2x + 3y = -6 written in standard form is,[tex]\rm y= -\frac{2}{3}x -2[/tex]

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What is the equation of the graphed line written in standard form?

2x + 3y = -6, 2x + 3y = 6

Summary:

a. The equation of the graphed line 2x + 3y = -6 written in standard form is y= -2/3 x -2.

b. The equation of the graphed line 2x + 3y = 6 written in standard form is y= -2/3 x +2.

An equation is formed of two equal expressions. The vertex of the equation y=-2(x-4)²+3 will lie at (4,3).

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

If we plot the graph of y=-2(x-4)²+3, then the vertex of the graph will lie at (4,3).

Hence, the vertex of the equation y=-2(x-4)²+3 will lie at (4,3).

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A conditional statement to demonstrate the situation presented would be: If a person can vote -> Then they are over 18 years old. An alternative to this would be: If a person is 18 years or older -> Then they can vote in the United States elections.

A conditional statement is a type of structure to express the relationship between two dependent variables. Its structure is as follows:

According to the above, two conditional statements about voting in the United States would be:

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Answer:

140

Step-by-step explanation:

here,

You have 1050

now

$1050(45×6)

=140 items

The sample that is most representative of the population is: sample 3.

A representative sample of a population can be defined as a subset of that particular population that reflects almost or same characteristics of the main population such as the shape, center, and spread.

From the three dot plots given, the one that has almost same pattern and characteristics is sample 3 considering it has almost similar spread and shape.

Thus, the most representative sample is: sample 3.

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Answer:

I. Evaluate the largest angle when x = 15

Explanation:

First, solve for x:

x + 8x + x + 30 = 180

10x = 180 - 30

10x = 150

x = 15

Here in the question, his friend wants to find the largest angle in triangle.

So, input x = 15 in the largest angle.

Which is, 8x = 8(15) = 120° <--- largest angle in the triangle.

Answer:

hi look here https://www.louisianabelieves.com/docs/default-source/assessment/grade-6-answer-key.pdf?sfvrsn=293b981f_2

Step-by-step explanation:

Using the linear equation, Miguel must work for 160 hours to receive $10,000 in total pay

Miguel works as a technician in a company. If his hourly rate and flat pay are $50 and $2000, how many hours must Miguel worked to receive $10,000 in total pay?

Let the number of hours be x and the total pay be y.

The equation that represents the total pay is represented as:

y = Rate * x + Base pay

From the question, we have:

Base pay = 2000

rate = 50.

So, we have:

10000 = 50 * x + 2000

Subtract 2000 from both sides

8000 = 50x

Divide both sides by 50

x = 160

Hence, Miguel must work for 160 hours

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This proof was correctly started by both eric and maggie.

The next step in the proof is to set the right side of the equations equal.

This would be done by the transitive property of equality.

This refers to the use of inference to make an argument to show the logical conclusion to a set of assumptions.

Based on the given diagram that shows Triangle XYZ and the mathematical proof that both Eric and Maggie are trying to prove, they both give the correct proof and the next step was to make the right side of the equations equal.

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Answer:

1: both

2: set the right side

3: transitive property

Step-by-step explanation:

got it right on plato :)

Answer:

2(7x-1)

Step-by-step explanation:

14 & 2 gcf 2 factor and wal lah!

The slope and intercept of the line 3x - 2y - 7 = 0 are -1.5 and -3.5 respectively

The equation of the line is given as:

3x- 2y - 7 = 0

Add 7 to both sides

3x - 2y = 7

Subtract 3x from both sides

-2y = -3x + 7

Divide both sides by -2

y = -1.5x -3.5

A linear equation is represented as:

y = mx  + c

Where m represents slope and c represents the intercept

By comparison;

m = -1.5 and c = -3.5

Hence, the slope and intercept of the line 3x - 2y - 7 = 0 are -1.5 and -3.5 respectively

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Answer:

x

=

−

b

±

√

b

2

−

4

a

c

2

a

, we get that

x

=

−

2

,

0.6

Explanation:

Rearrange the equation so that it becomes:

5

x

2

+

7

x

−

6

=

0

The quadratic formula is:

x

=

−

b

±

√

b

2

−

4

a

c

2

a

In our equation above,

a

=

5

b

=

7

c

=

−

6

Plugging these values into the quadratic equation gives:

x

=

−

7

±

√

7

2

−

4

(

5

)

(

−

6

)

2

(

5

)

x

=

−

7

±

√

49

+

120

10

x

=

−

7

±

√

169

10

x

=

−

7

±

13

10

x

=

−

2

,

0.6

The only key feature that these functions have in common is that they have the same y-intercept. So the correct option is D.

Here we have the functions:

[tex]f(x) = -x^2 + 2x + 1\\\\g(x) = 2^x[/tex]

f(x) is quadratic, and g(x) is exponential.

Notice that the exponential function has a positive base, so it is increasing. For the quadratic equation we can see a negative leading coefficient, so it opens downwards.  So first and second options are false.

Also, g(x) never intersects the x-axis, so third option is false.

Finally, the y-intercepts of the given functions are:

[tex]f(0) = -0^2 + 2*0 + 1 = 1\\\\g(0) = 2^0 = 1[/tex]

So the y-intercepts are equal, meaning that the correct option is D.

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Answer:

Both f(x) and g(x) have the same y-intercept of (0, 1).

Step-by-step explanation:

I got it right on the test.

The fact that Dean Field places random numbers in the general ledger system to make it balance and leaves the office to catch his flight is wrong.

It should be noted that a ledger simply means a record of the balance of each of the accounts of a business.

In this case, when he realizes the company’s trial balance is a mess and it does not balance, he should have waited and ensured that he re calculated it and made it balance.

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Answer:

x = 24

Step-by-step explanation:

x - (3 · 4) = 12

x - 12   =     12

  + 12      + 12

x = 24

Answer:

COA opposite/ adjacent

16/12

A

Answer:

2, 4, 6, 8

Step-by-step explanation:

even numbers are numbers that can be equally split in half.

Example:

Answer:

y+12=1+s = (-5,8)(3,0)

y-17=12-9r = (2,3)(8,9)

y-15=-12+4x = (-2,3)(7,-6)

y+5=x-3x = (-2,5)(3,-5)

Answer:

2.66666666667

Step-by-step explanation:

(1/8)^-1/3 means 1/8 to the -1/3 power, which equals 2.66666666667. So the answer is 2.66666666667.

Answer:

0.00016098

Step-by-step explanation:

First multiply 9.8 by 10^-3 which equals 0.0098

Then add 0.0098 to 1.6 which equals 1.6098

Then multiply 1.6098 by 10^-4 which equals 0.00016098

Therefore, 0.00016098 is your answer

The solutions to the trigonometric inequality in the interval is given by:

[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex], or [tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]

It is given by:

[tex]\sin^{2}{x} > \cos{x}[/tex]

We have the following identity:

[tex]\sin^2{x} = 2\sin{x}\cos{x}[/tex]

Hence:

[tex]2\sin{x}\cos{x} > \cos{x}[/tex]

[tex]2\sin{x} > 1[/tex]

[tex]\sin{x} > \frac{1}{2}[/tex]

Between the first and second quadrant, the solution is:

[tex]\frac{\pi}{6} \leq x \leq \frac{5\pi}{6}[/tex]

Between the third and fourth quadrants, the solution is:

[tex]\frac{7\pi}{6} \leq x \leq \frac{11\pi}{6}[/tex]

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Answer:

-1/2 or - 0.5

Step-by-step explanation:

[tex]cos (\frac{2\pi }{3}) = cos 120^{o} = -\frac{1}{2}[/tex]