The following are the ages (years) of 5 people in a room:
23, 20, 15, 12, 17
A person enters the room.
The mean age of the 6 people is now 19.
What is the age of the person who entered the room?​

Answer:

1/64

Step-by-step explanation:

Simplify the following:

1/(4^(11/3)×4^(-2/3))

Hint: | Simplify radicals.

1/4^(2/3) = 1/(4^2)^(1/3) = 1/(2^4)^(1/3) = (1/2^(1/3))/2:

1/(4^(11/3)×(1/2^(1/3))/2)

Hint: | Multiply numerator and denominator of 1/(2 2^(1/3)) by 2^(2/3).

Rationalize the denominator. 1/(2 2^(1/3)) = 1/(2 2^(1/3))×(2^(2/3))/(2^(2/3)) = (2^(2/3))/(2×2):

1/(4^(11/3)×(2^(2/3))/(2×2))

Hint: | Multiply 2 and 2 together.

2×2 = 4:

1/(4^(11/3)×(2^(2/3))/4)

Hint: | Separate the exponent of 4^(-11/3) into integer and fractional parts.

4^(-11/3) = 4^(1/3 - 12/3) = 4^(-12/3)×4^(1/3):

(4^(-12/3) 4^(1/3))/((2^(2/3))/4)

Hint: | Divide 12 by 3.

12/3 = (3 (-4))/3 = 4:

(4^(-4) 4^(1/3))/((2^(2/3))/4)

Hint: | Compute 4^4 by repeated squaring.

4^4 = (4^2)^2:

(4^(1/3))/((2^(2/3))/4) 1/(4^2)^2

Hint: | Evaluate 4^2.

4^2 = 16:

(4^(1/3))/(16^2×(2^(2/3))/4)

Hint: | Evaluate 16^2.

| 1 | 6

× | 1 | 6

| 9 | 6

1 | 6 | 0

2 | 5 | 6:

(4^(1/3))/(256×(2^(2/3))/4)

Hint: | Simplify radicals.

4^(1/3) = (2^2)^(1/3):

1/(256×(2^(2/3))/4) 2^(2/3)

Hint: | Write (2^(2/3))/(256×(2^(2/3))/4) as a single fraction.

Multiply the numerator by the reciprocal of the denominator, (2^(2/3))/(256×(2^(2/3))/4) = (2^(2/3))/256×4/2^(2/3):

(2^(2/3)×4)/(256×2^(2/3))

Hint: | Cancel common terms in the numerator and denominator of (2^(2/3)×4)/(256×2^(2/3)).

(2^(2/3)×4)/(256×2^(2/3)) = (2^(2/3))/(2^(2/3))×4/256 = 4/256:

4/256

Hint: | Reduce 4/256 to lowest terms. Start by finding the GCD of 4 and 256.

The gcd of 4 and 256 is 4, so 4/256 = (4×1)/(4×64) = 4/4×1/64 = 1/64:

Answer: 1/64

Answer:

y=5/2x+9

Step-by-step explanation:

y-y1=m(x-x1)

y-4=5/2(x-(-2))

y-4=5/2(x+2)

y=5/2x+10/2+4

y=5/2x+5+4

y=5/2x+9

Answer:

1) tan π/4 = 1

2) cos π/4 = 0.7071

3) cot π/4 = 1

4) sin π/4 = 0.7071

5) sec π/4 = 1.4142

6) cosec π/4 = 1.4142

Step-by-step explanation:

Angle π is in radians

But converting to degree, it is;

π = 180˚

Thus; π/4 = 180/4 = 45°

Thus;

1) from calculator; tan π/4 = tan 45° = 1

2) from calculator, cos π/4 = cos 45° = 0.7071

3) cot is equivalent to 1/tan

Thus; cot π/4 = 1/(tan π/4) = 1/tan 45 = 1/1 = 1

4) from calculator, sin π/4 = sin 45° = 0.7071

5) sec in trigonometry is equivalent to 1/cos.

Thus;

sec π/4 = 1/cos π/4 = 1/cos 45° = 1/0.7071 = 1.4142

6) cosec in trigonometry is equivalent to 1/sin

Thus;

cosec π/4 = 1/sin π/4 = 1/sin 45° = 1/0.7071 = 1.4142

Answer:

Add all of them together. 1/5 + 2/4 + 4/3 + 3/2 = 53/15 miles

Step-by-step explanation:

1/5 + 2(1/4) + 4(1/3) + 3(1/2)

Answer:

Step-by-step explanation:

Rational numbers are numbers that can be expressed as a fraction or ratio of two integers. Rational numbers are denoted  Q

.

Since  −3  can be written as  −3/1

, it could be argued that  −3  is also a real number.

Answer:

yes

Step-by-step explanation:

Any rational number can be expressed in the form

[tex]\frac{a}{b}[/tex] ← a and b are integers , then

- 3 = [tex]\frac{-3}{1}[/tex] ← in rational form

Thus - 3 is a rational number

Answer:

if BD the bisector of angle ABC,

then Angle ABD = 1/2 * angle ABC

= 1/2 * 48

= 24

Answer:

24 °

Step-by-step explanation:

m< ABD = m< CBD + m< DBA

= 28 ÷ 2 = 24 °

Answer:

answer

Step-by-step explanation:

=convert 3.8 into mixed number

=3 4/5

=1 3/10+3 4/5

=5.1 in mixed fraction

=5 1/10

if i got it wrong i am seriously sorry!

Required picture attached below :

Answer:

2 1/4 inches

Step-by-step explanation:

From the line plot Given ;

The frequency or number of 3/4 inch button is 3

Therefore, lining up all the 3/4 inch button in the plot, we have :

3/4 + 3/4 + 3/4

(3 + 3 + 3) /4

9 /4

2 1/4 inch

Answer:11808

Step-by-step: so start by putting the 328 on top of 36 then after multiple 6 by 8 2 and 3 then bring down the answers then do a 0 then multiply 3 by 8 2 and 3 and you get 11808

Answer:

the slope of the line is -2

Answer:

a = 2/5 or 0.4 (a is the slope value)

Step-by-step explanation:

y-int=-2

x-int=5

| x-int | / | y-int | = slope

|-2| / |5| = 2/5

Answer: yep

Step-by-step explanation:

Answer:

217+25.5w

ye thats it

Answer:

c = 5/Cos 35

Step-by-step explanation:

We are given the following

m<ACB = 90degrees

m<ABC = 35degrees

The side opposite to m<ABC is AC

BA = hypotenuse

CB = adjacent = 5inches

Required

Equation to solve BA which is c

Using the Pythagoras theorem;

Cos theta = Adjacent/Hypotenuse

Cos m<ABC = CB/BA

Cos m<ABC = 5/c

c = 5/cosm<ABC

c = 5/Cos 35

Hence the equation that can be used to solve for c is c = 5/Cos 35

Answer:

10

Step-by-step explanation:

because it shows where the line is

Answer:

SA = 480 cm²

Step-by-step explanation:

Surface area of the composite figure given in the picture = (Surface Area of the triangular prism on the top - area of the rectangular base) + (Surface area of the rectangular prism - Area of the rectangular base)

Surface area of the triangular prism = Area of the triangular bases + (perimeter of the base × Height)

= [tex]2(\frac{1}{2}\times 3\times 8)[/tex] + [(5 + 5 + 8)×12]

= 24 + 216

= 240 cm²

Area of the rectangular surface of the prism = 8 × 12 = 96 cm²

Surface area of the rectangular prism = 2(lb + bh + hl)

Here, l = Length, b = width and h = Height of the rectangular prism

                                                  = 2(8 × 12 + 12 × 6 + 6 ×8)

                                                  = 432 cm²

Surface area of the composite figure = (240 - 96) + (432 - 96)

                                                                = 144 + 336

                                                                = 480 cm²

Answer:

60

Step-by-step explanation:

Use the Pythagorean Theorem to find the height. 13 squared minus 5 squared=144

Square rt= 12

Now use the formula (base times height) divided by 2  

(10 x 12)/2

120/2

60

Answer:

Area would be 110

Answer:

(r + 20)t = r

Step-by-step explanation:

Distance is constant in the scenario above, distance from home to wedding and wedding back home is the same.

From wedding back home. :

Recall : Distance = speed * time

Distance = r * 1 hour

From home to wedding :

Speed = 20 mph more ; r + 20

Time = t

Distance = (r + 20)* t = (r +20)t

Since the distance are the same, we can equate both :

(r + 20)t = r * 1

= (r + 20)t = r

Answer:x=3

Step-by-step explanation:

the 3 angles of a triangle equal 180

you add 105 and 46, which equals 151

you subtract 151 from 180 to see what the missing angle is (29)

you would make 6x+11 equal to 29

-subtract 11 from 29= 18

6x/6, 18/6

the answer is 3

hope this helps! :)

Answer:

Radius = 16cm

Diameter = 32cm

Step-by-step explanation:

The Radius of a circle is half the diameter of the circle. The radius is how far the outside of the circle is from the middle of the circle. To find the Diameter add the radius twice, for example 16+16. Don’t forget your UNIT it is in Centimeters in this case.

The radius is 16

Diamiter is 32

Answer:

Im pretty sure its 11 because if you look at 145 mark its at between 10 and 12, Hopefully that helps!

Step-by-step explanation:

Answer:

60 cm^3

Step-by-step explanation:

Answer:

i dont see an image

Step-by-step explanation:

Answer:

504in3 (cubed)

Step-by-step explanation:

Answer:

Two 1/6 pieces

Step-by-step explanation:

Two 1/6 pieces equals 1/3 of the apple

12 3/5 x 30 = 378

Can I get brainliest?

Answer:

378 is the answers it's not hard

Answer:

-10

Step-by-step explanation:

4a-2b=10

-1(4a-2b)=-1*10

-4a+2b= - 10

2b - 4a = - 10