In a group of 36 pupils, 6 play the flute only.
6 play the piano only.
13 play neither instrument.
A student is selected at random.
What is the probability the student plays both instruments?

Help please

Answer:

I will assume that the term "x+2/2" is meant to be "(x + 2)/2)."  Otherwise the equation would read (x/3) = x + 1

Step-by-step explanation:

(x/3) = (x + 2)/2

x = 3*(x+2)/2   [Multiply both sides by 3]

x = (3x + 6)/2

x = (3/2)x + 6/2

x - (3/2)x = 3

-0.5x = 3

x = -6

====================

Check:

Does (x/3) = (x + 2)/2 for x = -6?

(-6/3) = (-6 + 2)/2

-2 = -4/2

-2 = -2  YES

Answer:

12

Step-by-step explanation:

36 divided by 3 =12 for 1 teacher

Answer:

[tex]m \times H=\left[\begin{array}{c c c}\boxed{-9} & \boxed{36} & \boxed{-\dfrac{9}{2}}\end{array}\right][/tex]

Step-by-step explanation:

Calculate the value of m

Given:

[tex]3\left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]=\dfrac{2}{3}m \times \left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right][/tex]

Therefore:

[tex]\implies 3=\dfrac{2}{3}m[/tex]

[tex]\implies m=3 \times \dfrac{3}{2}[/tex]

[tex]\implies m=\dfrac{9}{2}[/tex]

Calculate the value of H

Given:

[tex]\left(H+ \left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]\right)+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]=\left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]+\left(\left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]\right)[/tex]

Therefore:

[tex]\implies H= \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]

Calculating m × H

[tex]\implies m \times H=\dfrac{9}{2} \times \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]

[tex]\implies m \times H=\left[\begin{array}{c c c}\dfrac{9}{2}(-2) & \dfrac{9}{2}(8) & \dfrac{9}{2}(-1)\end{array}\right][/tex]

[tex]\implies m \times H=\left[\begin{array}{c c c}-9 & 36 & -\dfrac{9}{2}\end{array}\right][/tex]

60 forks 60÷3=$20

60 spoons 60÷4=$15

$20+$15=$35 total spent for forks and spoons

From the given mappings, we have

[tex]f(1) = 5, f(4) = 1, f(2) = 7[/tex]

and

[tex]g(3) = 1, g(5) = 4, g(-6) = 2[/tex]

Then the composition of [tex]f[/tex] with [tex]g[/tex], or [tex]f\circ g[/tex], is

[tex]\boxed{f\circ g = \{(3,5), (5,1), (-6, 7)\}}[/tex]

since

[tex]g(3) = 1 \implies (f\circ g)(3) = f(g(3)) = f(1) = 5[/tex]

[tex]g(5) = 4 \implies (f\circ g)(5) = f(4) = 1[/tex]

[tex]g(-6) = 2 \implies (f\circ g)(-6) = f(2) = 7[/tex]

Answer:

3x² +6

Step-by-step explanation:

(f-g)(x) = f(x) -g(x) = (4x²+1) -(x²-5) . . . . . substitute the function definitions

... = 4x² +1 -x² +5 . . . . . . . . . . . eliminate parentheses

... = (4-1)x² +(1+5) . . . . . . . . . . . collect like terms

... = 3x² +6

[tex](3^{2} )[/tex]^-2=(9)^-2=1/9^2=1/81

hope it helps!

[tex]9-10x=2x+1-8x\\\\9-10x=-6x+1\\\\9=4x+1\\\\8=4x\\ \\ x=\boxed{2}[/tex]

The value of the x in the equation 9 - 10x = 2x + 1 - 8x is 2. The correct answer is A) x = 2.

An equation is a combination of numbers, variables, functions, and often symbols arranged in a peculiar order. The equation comprises two or more expressions distinguished by the equality sign(=). The equations are solved to estimate the values of variables.

The given equation is

9 - 10x = 2x + 1 - 8x

-10x - 2x + 8x = 1 - 9

-4x = -8

4x = 8

x = [tex]\frac{8}{4}[/tex]

x = 2.

Thus, the correct option is A) x = 2.

Learn more about Equation here:

https://brainly.com/question/28953876

#SPJ7

Step-by-step explanation:

if I understand the question, write an equation for n in terms of i for number of Id cards an d for number driver license.

n = 15i + 20d

The value of n for a total minutes processing id card applications and driver's license applications would be 35 minutes.

Used the concept of addition that states,

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that,

For her job, Natasha spent a total of n minutes processing id card applications and driver's license applications.

And, it takes Natasha 15 minutes to process an id card application and 20 minutes to process a driver's license application.

Now by the given condition, we get;

n = 15 minutes + 20 minutes

n = 35 minutes

Therefore, the value n is 35 minutes.

To learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ4

Answer:

-104

Step-by-step explanation:

1) Substitute 50 into n.

-2(50) - 4

-100 - 4

-104

Answer:D

Step-by-step explanation:

this expression gives the original price reduce by 15%. The second term adds the tax to the price after the sale has been applied

Answer:

C

Step-by-step explanation:

Answer C is correct.  The absolute value of 10 is 10 and that of -10 is 10.  Same result.

La operación que representa 147.3 = 441 es dada por una multiplicación, por eso opción c es correcta.

El resultado del producto entre 147 y 3 es de 441, por lo que se hace una operación de multiplicación.

Así, hay que la opción c es correcta.

Puede-se aprender más a cerca de multiplicaciones en https://brainly.com/question/24615636

#SPJ1

Answer:

$110

Step-by-step explanation:

$30-$8=$22 each week

$22×5weeks=$110

Δ DGC is right angled triangle because Line E G is perpendicular-to CC', Option D is the correct answer.

Triangle is a polygon with three sides , angles and vertices.

It is given that the there are two Triangles , ABC and A'B'C' as an image of the ABC

* Line segment AA' has a midpoint at point F

*D is the mid point of the line joining BB' .*

The figure is attached with the answer.

the line of reflection of the object is always perpendicular to the object and the image.

it is also given that CGF is a right angle.

Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) ,  Line E G is perpendicular-to CC'.

Option D is the correct answer.

Please Refer to the image for correct coordinates.

To know more about Triangle

https://brainly.com/question/2773823

#SPJ1

The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The given linear equation in the problem is;

y = 2x+5

Compare the equation with the standard equation;

[tex]\rm y = mx+ c[/tex]

where,

m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;

m = 2

The product of the slope of the two-line perpendicular to each will be -1.

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is;

y = -2x+c.

m₁=2

m₂=-2

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is y = -2x+5.

Hence, option B is correct.

To learn more about the slope, refer to the link;

https://brainly.com/question/3605446

#SPJ1

Answer:

u = 10 ft

Step-by-step explanation:

cuboid volume = w × h × l

width * hight * length

560 = 7 × 8 × u

u = 10 ft

Answer:

u = 10 ft

Step-by-step explanation:

Volume of a rectangular prism = lwh

where:

Given:

Substitute the given values into the formula and solve for h:

⇒ 560 = 8 × 7 × u

⇒ 560 = 56u

⇒ 56u ÷ 56 = 560 ÷ 56

⇒ u = 10 ft

Therefore, the height of the prism is 10 ft.

The solution to the quadratic equation 3x² + 8x - 10 by using the quadratic formula is x = 0.927 or -3.594

Quadratic equations are algebraic expressions that are represented in the power of the second degree. They usually take the form ax² + bx + c

From the given information, we are to solve the quadratic equation:

Using the quadratic formula:

[tex]\mathbf{=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

where:

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{(8)^2 - 4(3 \times (-10))}}{2(3)}}[/tex]

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64 -4 (-30)}}{6}}[/tex]

[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64+120}}{6}}[/tex]

x = 0.927 or -3.594

Learn more about solving quadratic equations here:

https://brainly.com/question/8649555

#SPJ1

Answer:

700 kWh which is more than 200 so

0.10(x - 200) + 30

0.10( 700 -200)+ 30

0.10( 500) + 30

50 + 30

80

$80

Step-by-step explanation:

get the lcm of the numerals and the denominators then simplify

hope it is correct

Answer:

1/6

Step-by-step explanation:

As usual in trigonometry, there are so many relationships between the trigonometric functions, there is bound to be more than one method to arrive at the answer.

Knowing values for the sine and cosine function for certain angles on the unit circle proves to be quite helpful.  In general, I recommend 0°, 30°, 45°, 60°, and 90° at a minimum.

Recall the following 6 things:

Knowing these 6 things (4 things from the unit circle, a way to write the tangent function in terms of sine and cosine, and the definition of a squared trig function), we can simplify the given expression down to a single number:

The definition of the tangent squared function is that the output of the tangent function is squared...

[tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1-(\tan(30^o))^2}{1+(\tan(60^o))^2}[/tex]

Using fact 5, and turning the tangent function into sines and cosines...

[tex]=\dfrac{1-\left(\frac{\sin(30^o)}{\cos(30^o)}\right)^2}{1+\left(\frac{\sin(60^o)}{\cos(60^o)}\right)^2}[/tex]

Using facts 1-4, and substituting known values for sines and cosines...

[tex]=\dfrac{1-\left(\frac{(\frac{1}{2})}{(\frac{\sqrt{3}}{2})}\right)^2}{1+\left(\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}\right)^2}[/tex]

Division is multiplication by the reciprocal...

[tex]=\dfrac{1-\left(\frac{1}{2}*\frac{2}{\sqrt{3}}\right)^2}{1+\left(\frac{\sqrt{3}}{2}*\frac{2}{1}\right)^2}[/tex]

Reducing/simplifying common factors of 2...

[tex]=\dfrac{1-\left(\frac{1}{\sqrt{3}}\right)^2}{1+(\sqrt{3})^2}[/tex]

Squaring a square root...

[tex]=\dfrac{1-\left(\frac{1}{3}\right)}{1+(3)}[/tex]

Finding a common denominator...

[tex]=\dfrac{\frac{3}{3}-\frac{1}{3}}{4}[/tex]

Definition of subtracting fractions...

[tex]=\dfrac{\frac{3-1}{3}}{4}[/tex]

Arithmetic...

[tex]=\dfrac{\frac{2}{3}}{4}[/tex]

Division is multiplication by a reciprocal...

[tex]=\dfrac{2}{3}*\dfrac{1}{4}[/tex]

Simplification and reducing the fraction...

[tex]=\dfrac{1}{6}[/tex]

So, [tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1}{6}[/tex]

Answer:

[tex]3[/tex] and perpendicular

Step-by-step explanation:

It's important to remember that equations of lines are always set up in the format of [tex]y=mx+c[/tex].

[tex]y[/tex] is the [tex]y[/tex] value, [tex]m[/tex] is the gradient/slope, [tex]x[/tex] is the [tex]x[/tex] value and [tex]c[/tex] is the y-intercept.

Therefore, we must always rearrange our line equations so that [tex]y[/tex] is the subject.

In the first question, we are given the equation [tex]2x+6y=12[/tex].

We rearrange to make [tex]y[/tex] the subject:

[tex]6y = 12-2x[/tex]

Then, we divide both sides by 6 to have the [tex]y[/tex] isolated:

[tex]\frac{6}{6} y = \frac{12}{6} - \frac{2}{6}x\\\\ y = 2 - \frac{1}{3}x[/tex]

To find a perpendicular slope, we use the negative reciprocal of the original slope. The negative part of that means we negate the value (it becomes inverse) and the reciprocal part means that we flip the fraction.

So here, the slope is [tex]-\frac{1}{3}[/tex].

So, the negative reciprocal of that would be [tex]3[/tex] because we inverse the sign (the negative becomes positive) and the fraction is flipped to create [tex]\frac{3}{1}=3[/tex].

So, the perpendicular slope is [tex]3[/tex].

In the second question, we have two equations. They both need to be rearranged to isolate the [tex]y[/tex].

[tex]4x-y=5\\4x = 5 + y\\y = 4x - 5\\\\4y = -x-12\\y = -\frac{1}{4}x - 3[/tex]

Look at the slopes of the two equations. If you look carefully, you will see that they are inverse of each other (one is positive and one is negative) and if you imagine [tex]4 = \frac{4}{1}[/tex], the fraction is flipped.

This means that the values are negative reciprocals of each other, meaning the lines are perpendicular.

The path straight to the end of the hike is 6 km farther than past the scenic lookout.

The map is not given, but the question can still be answered

From the question, the positions are given as::

Maria = (4, -4)

Scenic = (2, 3)

End = (-5, 5)

The distance between Maria and the end point is calculated using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]Route\ 1 = \sqrt{(4 + 5)^2 + (-4 -5)^2}[/tex]

[tex]Route\ 1 = 13[/tex]

The distance between Maria and the scenic lookout is calculated using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]Route\ 2 = \sqrt{(4 - 2)^2 + (-4 -3)^2}[/tex]

[tex]Route\ 2 = 7[/tex]

The distance between both routes is:

Distance = 13 - 7

Evaluate

Distance = 6

Hence, the path straight to the end of the hike is 6 km farther than past the scenic lookout.

Read more about distance at:

https://brainly.com/question/7243416

#SPJ1

Answer:

3x^2+ 13x + 12

Step-by-step explanation:

Multiply the length and width:
(3x+4) * (x+3)
FOIL method:
3x^2 + 9x + 4x + 12
Combine like terms
3x^2+ 13x + 12

Answer:

Anne will walk for 2 hours.

Step-by-step explanation:

Distance formula = velocity × time

Total distance is 18.5 km

Anne travels by train = 10 km

and by bus = 1.5 km

let the distance covered by anne by walking be x

10 + 1.5 + x = 18.5

x = 18.5 - 10 - 1.5

x = 7km

Rate of walking is 3.5 km per hour

the time she will take while walking = 7 ÷ 3.5 = 2 hours.

Learn more about distance formula here - https://brainly.com/question/7245260

#SPJ10

The domain is (-∞,∞) and the range is [-2,∞)

From the graph, we can see that the x values extend at both sides of the graph.

This means that the domain is the set of real values i.e. (-∞,∞)

However, the minimum y value is -2 and it increases from their

This means that the range is [-2,∞)

Hence, the domain is (-∞,∞) and the range is [-2,∞)

Read more about domain and range at:

https://brainly.com/question/10197594

#SPJ1

The best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have given a three-dimensional figure.

As we can see the arrow is pointing at the plane.

A triangular prism is reflected over the given plane and creates a mirror image of a triangular prism.

A plane is a plane of symmetry.

Thus, the best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ1

Adam can see the horizon at a distance of [tex]\sqrt{6}mi.[/tex]

Given that the height of Pam's eye level above sea level is [tex]324ft[/tex] and the height of adam's eye level above sea level is [tex]400ft[/tex].

The formula used to find the distance they see in miles is [tex]d=\sqrt{\frac{3h}{2}}[/tex].

Let the height of Pam's is [tex]h[/tex] and the height of adam's is [tex]h'[/tex].

The distance of Pam from the horizon can be given as [tex]d=\sqrt{\frac{3h}{2}}[/tex].

Substitute these values,

[tex]\begin{aligned}d&=\sqrt{3\times \frac{324}{2}}\\ d&=\sqrt{486}\\ d&=\sqrt{81\times 6}\\ d&=9\sqrt{6}\end[/tex]

And the distance of adam from the horizon can be given as [tex]d=\sqrt{\frac{3h'}{2}}[/tex].

Substitute these values,

[tex]d'=\sqrt{3\times \frac{400}{2}}\\ d'=\sqrt{600}\\ d'=\sqrt{100\times 6}\\ d'&=10\sqrt{6}[/tex]

The net distance of adam from the horizon is

[tex]\begin{aligned}d_{\text{net distance}}&=d'-d\\ &=10\sqrt{6}-9\sqrt{6}\\&=\sqrt{6}\end[/tex]

Hence, the adam can see the horizon at a distance of [tex]\sqrt{6}mi[/tex].

Learn more about horizon and distance here brainly.com/question/10016098

#SPJ4

Answer:

B

Step-by-step explanation:

it said sooo