In a group of 33 pupils, 9 play the flute only.
8 play the piano only.
11 play neither instrument.
A student is selected at random.
What is the probability the student plays both instruments?

Answer:

[tex](2,4)[/tex]

Step-by-step explanation:

Hope it is helpful...

Answer:

S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }

Step-by-step explanation:

Remember that the distance between two points (a, b) and (c, d) is given by:

[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]

So, here we have that the distance between the point (x, y) and the origin, (0, 0) must have a magnitude of 5 units, then we want to solve:

[tex]5 = \sqrt{(x - 0)^2 + (y - 0)^2} \\5 = \sqrt{x^2 + y^2}[/tex]

If we square both sides, we get

[tex]5^2 = (\sqrt{x^2 + y^2} )^2\\25 = x^2 + y^2[/tex]

Now we want to find all the points (x, y) that meet this condition, suc that:

x ∈ Z

y ∈ Z

So both x and y must be integers.

So here we can just play with different values of x and y.

For example, if we define:

x = 0 we get:

25 = 0^2 + y^2

25 = y^2

√25 = y

Then we can have y = 5 or  y = -5

from this we got two points:

(0, 5) and (0, - 5)

if x = 1 we have:

25 = 1^2 + y^2

25 - 1 = y^2

24 = y^2

There is no integer such that its square is equal to 24, so we can stop here.

if x = 2 or - 2, we have:

25 = 2^2 + y^2

25 = 4 + y^2

25 -4 = 21 = y^2

Again, there is no integer such that its square is equal to 21, so we can stop here.

if x = +3 or -3, we have:

25 = 3^2 + y^2

25 = 9 + y^2

25 - 9 = 16 = y^2

√16 = y

then we can have y = 4 or y = -4

from this we got four points:

(3, 4)

(-3, 4)

(3, -4)

(-3, -4)

And for symmetry, if x = 4 or -4 we have the points:

(-4, 3)

(4, 3)

(-4, -3)

(4, -3)

finally, again for symmetry, if we take x = 5 or x = -5 we have the points:

(5,0)

(-5, 0)

Concluding, the set of all possible values (x, y) is:

S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }

Answer:

42 in binary number is 101010.

Answer:245

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

18x = 12(x+2)

18x = 12x+24

18x-12x = 24

6x = 24

x = 4

Step-by-step explanation:

[tex] \frac{ \frac{4x}{5 + x} }{ \frac{6x}{x + 2} } [/tex]

[tex] \ \frac{2(x + 2)}{3(5 + x)} [/tex]

[tex] \frac{2x + 4}{3x + 15} [/tex]

Answer:

2x+4 over 3x+15

Step-by-step explanation:

First divide 4x over 5+x by 6x over x+2 when multiplying 4x over 5+x by the reciprocal of 6x over x+2

Step 2: cancel out 2x in both numerator and denominator

Last step:use distributive property to multiply 2 by x+2 and 3 by x+5

Answer:

(1,5,7,-3,2)etc are the range of the relation.

Answer:

15/8

Step-by-step explanation:

Applying

tanθ = Opposite(O)/Adjacent(A)

tanθ = O/A............ Equation 1

From the diagram,

To get the opposite(O), we apply pythagoras theorem

a² = b²+c²

Where c = opposite

17² = 8²+c²

289 = 64+c²

c² = 289-64

c² = 225

c = √225

c = 15

Substitute into equation 1

Therefore,

tanθ = 15/8

Hence the exact value of tanθ is 15/8

Answer:

Given  : isosceles right triangle  hypotenuse = 8 cm  

To find : leg of  isosceles right triangle

Solution

isosceles right triangle

Hence Perpendicular = base  

Both legs are of Equal length

Applying Pythagoras theorem

Perpendicular² + base² = Hypotenuse²

Hypotenuse = 8 cm given

=> Perpendicular² + base² = 8²

Perpendicular = base   = x

=> x² + x² = 64

=> 2x² = 64

=> x² = 32

=> x  = 4√2

legs of  isosceles right triangle whose hypotenuse is  8 cm  

are 4√2  cm

Step-by-step explanation:

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

42.1

Step-by-step explanation:

15.2% = 0.152

277 * 0.152 = 42.104

42.1 megabytes have been downloaded.

Hope this is helpful.

Answer:

42.1

Step-by-step explanation:

thanks for the pts

✌️❤️✌️

Answer:

During a canoeing trip, it takes Raymond 4 hours to paddle 12 miles upstream. It takes him 3 hours to make the return trip paddling downstream. Find the speed of the canoe in still water

Step-by-step explanation:

sorry i dont know

Answer:

[tex]y=1[/tex]

Step-by-step explanation:

Given:

[tex]6=2(y+2)[/tex]

Distribute the parenthesis

[tex]6=2y+4[/tex]

Subtract both sides by 4

[tex]2=2y[/tex]

Divide both sides by 2 to get [tex]y[/tex] alone

[tex]1=y[/tex]

Hope this is helpful

Answer:

D

Step-by-step explanation:

We are given:

[tex]\displaystyle \sqrt{\sqrt[3]{2}}[/tex]

Recall the property:

[tex]\displaystyle \sqrt[b]{x}=x^{1/b}[/tex]

Hence:

[tex]\displaystyle \sqrt{\sqrt[3]{2}}=\sqrt{2^{1/3}}[/tex]

Using the same property:

[tex]\sqrt{2^{1/3}}=(2^{1/3})^{1/2}[/tex]

Recall the property:

[tex](x^a)^b=x^{ab}[/tex]

Hence, multiply:

[tex](2^{1/3})^{1/2}=2^{1/6}[/tex]

Therefore:

[tex]\displaystyle \sqrt{\sqrt[3]{2}}=2^{1/6}[/tex]

Our answer is D.

Answer:

The answer is [tex]2^{\frac{1}{6} }[/tex].

Step-by-step explanation:

To find which answer is equal to [tex]\sqrt{} \sqrt[3]{2}[/tex], start by simplifying [tex]\sqrt{} \sqrt[3]{2}[/tex]. The radical will simplify to [tex]\sqrt[6]{2}[/tex].

An easy way to determine which answer is correct, convert each of the numbers to decimal form.

For [tex]\sqrt[6]{2}[/tex], it will look like 1.122 in decimal form.

For [tex]2^{\frac{2}{3} }[/tex], it will look like 1.587 in decimal form.

For [tex]2^{\frac{3}{2} }[/tex], it will look like 2.828 in decimal form.

For [tex]2^{\frac{1}{3} }[/tex], it will look like 1.260 in decimal form.

For [tex]2^{\frac{1}{6} }[/tex], it will look like 1.122 in decimal form.

Then, by seeing which two decimal forms are the same, it causes the answer to be [tex]2^{\frac{1}{6} }[/tex].

Answer:

[tex]{ \tt{slope = \frac{7 - 1}{0 - ( - 2)} = 3 }} \\ \\ { \tt{y = mx + c}} \\ { \boxed{ \bf{y = 3x + 7}}}[/tex]

Answer:

x = + 5/4 or x = - 5/4

Step-by-step explanation:

[tex]4 x^2 = 6\frac{1}{4}\\\\4 x^2 = \frac{25}{4}\\\\x^2 =\frac{25}{16}\\\\x = \pm \frac{5}{4}[/tex]

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

Explanation:

Every point on the line y = 7 has a y coordinate of 7. Two such points are (0,7) and (1,7). The x coordinate can be anything you want. This line is completely horizontal and parallel to the x axis.

We can think of y = 7 as y = 0x+7. It's of the form y = mx+b with m = 0 as the slope and b = 7 as the y intercept.

Answer:

0

Step-by-step explanation:

tan2°- cot 88° = tan 2° - tan (90-88)°

= tan 2°-tan 2° = 0

Answer:

Step-by-step explanation:

➡️tan 2° - cot 88°

➡️tan 2° - tan (90° - 88°)

➡️tan 2° - tan 2°

➡️ 0 ✅

Answer:

36 9/16 inches

Step-by-step explanation:

Given that the piece is 45 1/2 inch long and 8 7/8 is cut from it, the remaining length should be the difference between the original length and the length cut from it

= 45 1/2 - 8 7/8

simplify

= 44 - 8  (8 + 4 - 7)/8

= 36 5/8

Given that 1/16 inch is wasted in the process, the remaining length would be

= 36 5/8 - 1/16

= 36 10 - 1/16

= 36 9/16 inches

Answer:

YES

Step-by-step explanation:

Find each length using the distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

✔️Distance between A(-4, 2) and B(1, 4):

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

Let,

[tex] A(-4, 2) = (x_1, y_1) [/tex]

[tex] B(1, 4) = (x_2, y_2) [/tex]

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

[tex] AB = \sqrt{(5)^2 + (2)^2} [/tex]

[tex] AB = \sqrt{25 + 4} [/tex]

[tex] AB = \sqrt{29} [/tex]

✔️Distance between C(2, -1) and D(4, 4):

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

Let,

[tex] C(2, -1) = (x_1, y_1) [/tex]

[tex] D(4, 4) = (x_2, y_2) [/tex]

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

[tex] CD = \sqrt{(2)^2 + (5)^2} [/tex]

[tex] CD = \sqrt{4 + 25} [/tex]

[tex] CD = \sqrt{29} [/tex]

AB = CD = √29

Therefore, they both have the same length.

Answer:

what are the choices?? if you don't mind me asking

Answer: 1: 8.973770492

2: 205.2727273

3: 198.0222222

4: 1894.6

5: 438

Answer:

1: 8.973770492

2: 205.2727273

3: 198.0222222

4: 1894.6

5: 438

Step-by-step explanation: Just use a caculator

Answer:

d is the answer ✌sin ०=3000/3050

Answer:

Average rate of change = 0.6

Step-by-step explanation:

Average rate of change of a function between x = a and x = b is given by,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

From the graph attached,

f(-5) = 0

f(0) = 3

Average rate of change of the graph between x = -5 and x = 0,

Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]

                                        = [tex]\frac{3}{5}[/tex]

                                        = 0.6

Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.

√9 is rational and √3 irrational number

53,38

Step-by-step explanation:

x = √15² + 8²

x = √225 + 64

x = √289

x = 17

circle's circumference = π × d

3,14 × 17 = 53,38