How many ways can 6 people be chosen and arranged in straight line if there are 8 people to choose from? a. 48.b. 720.c. 20, 160.d. 40, 320.

Answer:

The prime factors are: 2 x 3 x 3 x 5 x 7

or also written as { 2, 3, 3, 5, 7 }

Written in exponential form: 2 x 3 × 3 x 5 ×1  x 7×1

Answer:

If x^n  = y, then y is a power of x

Step-by-step explanation:

Take two numbers, x & y

To check whether, y is a a power of x

By hit & trial method, calculate x^n (approximately considered to near y). Try for many such no.s

If at any value x^n = y, then y is a power of x

Ex : Let x = 5, y = 625

By hit & trial, n = 3 or 4,

5^3 = 125 , 5^4 = 625

So, 625 is a power of x

Answer:

Step-by-step explanation:

2t + 1.5s = 11

3t + 4s = 23.50

6t  + 4.5s = 33

-6t - 8s =   -47

-3.5s = -14

s = $4 a pound for sunflower seeds

Answer:

no

Step-by-step explanation:

b to d is 4 jumps away and c and e is 10 jumps

edit i meant 8 and d i messed up the calculations but the answer is correct

BD is 8 units long

CE is 10 units long

BD and CE are NOT congruent.

Answer:

0.16

Step-by-step explanation:

Simply divide  4 by 25

4/25=0.16

Hope this helps : )

Answer:

-47

Step-by-step explanation:

Answer:

-47

Step-by-step explanation:

The opposite of a number is just the number on the opposite side of zero on the number line.

For example, the opposite of 5 is -5.

Answer:

-3>x

Step-by-step explanation:

Rearrange the equation

1. Move - 5 onto the other side with - 32.

2. - 32 + 5 > 9x now because 5 was moved to the other side so the sign has changed.

3. - 27>9x, move 9 to the other side

4. - 27/9>X DIVIDE 27 by 9

5. - 3>X

Answer:

-4 ≥ x or 3>x

Step-by-step explanation:

Answer:

34+24.5h

Step-by-step explanation:

Answer:

see attechment: - vertex  (-1, 8)

Step-by-step explanation:

focus | (-1, 63/8) = (-1, 7.875)

vertex | (-1, 8)

semi-axis length | 1/8 = 0.125

focal parameter | 1/4 = 0.25

eccentricity | 1

directrix | f = 65/8

Answer:

2 is the answer to the question I think

Answer:

2/3

Step-by-step explanation:

Using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 0-4)/(-5-1)

   = -4/-6

   = 2/3

Answer:

y = -2/3x

Step-by-step explanation:

y2-y1 over x2-x1

0-4 over -5-1

Answer:

Step-by-step explanation:

You just need to find the corresponding coordinates on the graph by using one of the coordinates and the graph.

4) Find f(0.8)

Find the point 0.8 on the x-axis and check the point the vertical line from that point crosses the graph. See what that point is on the y-axis.

This is point 1

The answer is 1, the point has coordinates (0.8, 1)

5) Find x when f(x) = 3

Find the point of the graph against 3 on the y- axis

And check what is corresponding point on x-axis, this is point 4

So the answer is 4, the point has coordinates of (4,3)

Answer:?

Step-by-step explanation:

Answer:

U need to copy and paste more of the question

Step-by-step explanation:

Start copy at the top go all the way to the bottem of the question and paste into brainly.

use ctrl c for copy and crtl v for paste

Answer:

Then 9/20 got them right

Step-by-step explanation:

20/20-11/20=9/20

there isn't enough context so that's the best i can do

Answer: 16.5%

Step-by-step explanation:

given data:

estimated circumfrence of the earth = 250,000 stadia.

Actual value = 46,620km

expected Value = 40,030.3km

solution:

percentage error = actual value – expected value/ expected value * 100

= 46,620 – 40,030.3 / 40,030.3 * 100

= 6589.7 / 40,030.3 * 100

= 0.16462 * 100

= 16.5%

percentage error is 16.5%

Answer:

the hypothesis is 5or 13

Step-by-step explanation:

let the hypotenuse be y so the first side will be y-1 and the other side will be y-8 repectively and using the pythagoras theorem you solved for the hypotenenuse

Answer:

1,280

Step-by-step explanation:

Answer:

∠MON = 99

Step-by-step explanation:

∠LON = 180°

∠MON + ∠LOM = 180 -------equation

where:

∠MON = 8x - 13

∠LOM = 7x - 17

plugin values into the equation

8x - 13 + 7x - 17 = 180

8x + 7x - 13 - 17 = 180

15x - 30 = 180

15x = 180 + 30

x = 210 / 15

x = 14

plugin values to ∠MON = 8x - 13

∠MON = 8x - 13

∠MON = 8(14) - 13

∠MON = 99

Answer:

Angle MON = 99

Step-by-step explanation:

...........

..................

Answer:

The opposite of 25 degrese is -25 degrese.

Step-by-step explanation:

The opposite 25 degrees will be 205 degrees.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

For the opposite angle, add 180° to the given angle.

The opposite 25 degrees will be

⇒ 25° + 180°

⇒ 205°

The diagram is given below.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ2

The answer is 1728

First you must set up the equation

[tex](\frac{4*6}{2})^3[/tex]

Then, you must multiply the numerator

[tex](\frac{24}{2} )^3[/tex]

Next, divide

[tex](12)^3[/tex]

Finally, simplify exponents

[tex](12^3) =12*12*12[/tex]

12*12*12=1728

Answer:

3

Step-by-step explanation:

4 ×6 :2 ^3 =

24 :8 =

3

Answer: 3√2

Step-by-step explanation:

i had a quiz with this question and it said this was the correct answer

Answer:

-3x-x^2

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A number that can be written as a ratio of two integers, of which denominator is non-zero, is called a rational number.

Therefore 2/3 is a rational number.

Answer:

Graph b

Step-by-step explanation:

ED2020

Answer:

1/4  * 12

Step-by-step explanation:

It takes 1/4 hour to fill 1/12

It has to do this 12 times to be full

so 1/4 hour times 12

Answer:

An oil company fills  of a tank in  hour with gasoline. At this rate, which expression can be used to determine how long it will take for the tank to fill completely? (1 point)

Question 10 options:

1)  

⋅  

2)  

⋅ 4

3)  

⋅ 12

4)  

12 ⋅ 4

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

Please note that I'll replace all � with +

1. |10|

This implies the absolute value of 10 and it always returns the positive value;

Hence;

[tex]|10| = 10[/tex]

2. |-4|

Using the same law applied in (1)

[tex]|-4| = 4[/tex]

3.  5/8 - 3/8 = ?

Take LCM

[tex]= \frac{5 - 3}{8}[/tex]

Subtract the numerator

[tex]= \frac{2}{8}[/tex]

Divide the numerator and denominator by 2

[tex]= \frac{1}{4}[/tex]

Hence:

[tex]\frac{5}{8} - \frac{3}{8} = \frac{1}{4}[/tex]

4. 7/8 - 5/6

Take LCM

[tex]= \frac{21 - 20}{24}[/tex]

[tex]= \frac{1}{24}[/tex]

Hence;

[tex]\frac{7}{8} - \frac{5}{6} = \frac{1}{24}[/tex]

5. 6 * (-7/2)

[tex]= 6 * \frac{-7}{2}[/tex]

Multiply the numerator

[tex]= \frac{-42}{2}[/tex]

[tex]= -21[/tex]

Hence:

[tex]6 * \frac{-7}{2} = -21[/tex]

5. 6/5 /(-12/25)

[tex]= \frac{6}{5} / \frac{-12}{25}[/tex]

Change the divide to multiplication

[tex]= \frac{6}{5} * \frac{-25}{12}[/tex]

Divide 6 and 12 by 6

[tex]= \frac{1}{5} * \frac{-25}{2}[/tex]

Divide 5 and 25 by 5

[tex]= \frac{1}{1} * \frac{-5}{2}[/tex]

[tex]= \frac{-5}{2}[/tex]

Hence;

[tex]\frac{6}{5} / \frac{-12}{25} = \frac{-5}{2}[/tex]

6.  3 + 4^2  * 2

[tex]= 3 + 4^2 * 2[/tex]

Solve the exponent

[tex]= 3 + 16 * 2[/tex]

Apply B.O.D.M.A.S

[tex]= 3 + 32[/tex]

[tex]= 35[/tex]

[tex]3 + 4^2 * 2 = 35[/tex]

7.  2/3 + 5/6

[tex]= \frac{2}{3} + \frac{5}{6}[/tex]

Apply LCM

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

[tex]= \frac{9}{6}[/tex]

Divide the numerator and denominator by 3

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

Convert to mixed fraction

[tex]= 1\frac{1}{2}[/tex]

Hence;

[tex]\frac{2}{3} + \frac{5}{6} = 1\frac{1}{2}[/tex]

8.  16 - 12/(-4)

[tex]= 16 - \frac{12}{-4}[/tex]

Solve the fraction

[tex]= 16 - (-3)[/tex]

Open the bracket

[tex]= 16 + 3[/tex]

[tex]= 19[/tex]

Hence;

[tex]16 - \frac{12}{-4} = 19[/tex]

9.   -9(3w + x + 2)

[tex]= -9(3w + x + 2)[/tex]

Open brackets: Distributive property

[tex]= -9*3w -9* x -9 * 2[/tex]

[tex]= -27w -9 x -18[/tex]

Hence;

[tex]-9(3w + x + 2) = -27w -9 x -18[/tex]

10.  -2(w + 2) + 5w

[tex]= -2(w + 2) + 5w[/tex]

Open bracket: using distributive property

[tex]= -2*w -2 * 2 + 5w[/tex]

[tex]= -2w -4 + 5w[/tex]

Collect Like Terms

[tex]= 5w-2w -4[/tex]

[tex]= 3w -4[/tex]

Hence;

[tex]-2(w + 2) + 5w = 3w- 4[/tex]

11.   16x^2 + 8 + 10x + 2x^2 + 14x

[tex]= 16x^2 + 8 + 10x + 2x^2 + 14x[/tex]

Collect Like Terms

[tex]= 16x^2 + 2x^2 + 10x + 14x+ 8[/tex]

[tex]= 18x^2 + 24x + 8[/tex]

Expand the expression

[tex]= 18x^2 + 12x + 12x + 8[/tex]

Factorize:

[tex]= 6x(3x + 2) + 4(3x +2)[/tex]

[tex]= (6x + 4)(3x +2)[/tex]

Hence;

[tex]16x^2 + 8 + 10x + 2x^2 + 14x = (6x + 4)(3x +2)[/tex]

12. b = -5 and y = 6

[tex]b + 9y =?[/tex]

Substitute -5 for b and 6 for y

[tex]= -5 + 9 * 6[/tex]

[tex]= -5 + 54[/tex]

[tex]= 49[/tex]

Hence;

[tex]b + 9y = 49[/tex]

13.    y = -3

[tex]y^2 + 5y + 4 =?[/tex]

Substitute -3 for y

[tex]= (-3)^2 + 5(-3) + 4[/tex]

Open all brackets

[tex]= 9 -15 + 4[/tex]

[tex]= -2[/tex]

Hence;

[tex]y^2 + 5y + 4 = -2[/tex]

14.  

[tex](-4)^3[/tex]

Open bracket:

[tex]= -4 * -4 * -4[/tex]

[tex]= -64[/tex]

Hence;

[tex](-4)^3 = -64[/tex]

[tex](-7)^2[/tex]

Open bracket:

[tex]= -7 * -7[/tex]

[tex]= 49[/tex]

Hence;

[tex](-7)^2 = 49[/tex]

15.  Express as fractions:

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

Evaluate the denominator

[tex]= \frac{3}{125}[/tex]

Hence:

[tex]\frac{3}{5^3} = \frac{3}{125}[/tex]

[tex](\frac{-1}{3})^2[/tex]

Evaluate the exponent

[tex]= (\frac{-1}{3})*(\frac{-1}{3})[/tex]

[tex]=\frac{1}{9}[/tex]

Hence:

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

16. Evaluate

[tex](-7)^0 =[/tex]

Evaluate the exponent

[tex](-7)^0 = 1[/tex]

[tex]2 * (1/3)^0[/tex]

Evaluate the exponent

[tex]= 2 * 1[/tex]

[tex]= 2[/tex]

Hence;

[tex]2 * (1/3)^0 = 2[/tex]

17. Evaluate

[tex]3v^2(-5v^4)[/tex]

Open bracket

[tex]= 3 * v^2*-5* v^4[/tex]

Reorder

[tex]= 3 *-5* v^4 * v^2[/tex]

[tex]= -15* v^4 * v^2[/tex]

Apply law of indices

[tex]= -15* v^{4 +2}[/tex]

[tex]= -15* v^6[/tex]

[tex]= -15v^6[/tex]

Hence:

[tex]3v^2(-5v^4) = -15v^6[/tex]

18.

[tex]2y^2w^4*6y*2w^8[/tex]

Rewrite as

[tex]2 *y^2 * w^4*6 * y*2 * w^8[/tex]

Reorder the terms

[tex]=2*6 * w^4 * w^8*y^2 * y*2[/tex]

[tex]=12 * w^4 * w^8*y^2 * y*2[/tex]

Apply law of indices

[tex]=12 * w^{4+8} *y^{2+2}[/tex]

[tex]=12 * w^{12} *y^4[/tex]

[tex]=12 w^{12} y^4[/tex]

Hence:

[tex]2y^2w^4*6y*2w^8 =12 w^{12} y^4[/tex]

19.

[tex](\frac{4p^3}{3p^7})^{-2}[/tex]

Apply law of indices

[tex]= (\frac{4p^{3-7}}{3})^{-2}[/tex]

[tex]= (\frac{4p^{-4}}{3})^{-2}[/tex]

Apply law of indices

[tex]= (\frac{4}{3p^4})^{-2}[/tex]

Apply law of indices

[tex]= (\frac{3p^4}{4})^{2}[/tex]

[tex]= (\frac{3p^4}{4}) * (\frac{3p^4}{4})[/tex]

Evaluate

[tex]= \frac{9p^8}{16}[/tex]

Hence;

[tex](\frac{4p^3}{3p^7})^{-2} = \frac{9p^8}{16}[/tex]

20.

[tex]\frac{x^{-2}}{x^{-3}}[/tex]

Apply law of indices

[tex]= x^{-2 - (-3)}[/tex]

[tex]= x^{-2 +3}[/tex]

[tex]= x^1[/tex]

[tex]= x[/tex]

Hence:

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

Answer: So 5 + x = 8 beacase x is 3

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

The value is  [tex]y  =  5sin3x[/tex]

Step-by-step explanation:

From the question we are told that  

   [tex]y =  c_1\ cos3x + c_2 \  sin 3x[/tex]

given that y(0) =  0

We have that  

     [tex]c_1\ cos3(0) + c_2 \  sin 3(0)  =  0[/tex]

=>   [tex]c_1 =  0[/tex]

This means that

           [tex]y  =  c_2 \  sin 3x[/tex]

We also given that

          [tex]y[\frac{\pi}{6} ] =  5[/tex]

So  

         [tex]c_2  sin (3 *  \frac{\pi}{6} )  =  5[/tex]

=>    [tex]c_2  =  5[/tex]

Hence  

     [tex]y  =  5sin3x[/tex]

Answer:

Interval scale

Step-by-step explanation:

In statistics, there are 4 types of measurement scales namely;

Nominal scales, interval scales, Ordinal scales and Ratio scales.

Now, in this question Cassidy is trying to research the impacts of eating breakfast on college students who have classes prior to 9 am.

This has to do with order as it deals with people who have breakfast before 9 a.m. It also deals with the exact differences in the various answers on the scale of 1 - 10 for each student student in the research for the 20 questions.

This is exactly what the interval measurement scale is all about interval scale deals with order and exact differences in values.

Thus, the scale used is an interval scale.

Answer:

1. x = 3

2. The 5th term = Log₂768.

Step-by-step explanation:

From the question given above, the following data were obtained:

Log₂x, Log₂(x + 9, Log₂(x + 45)

x =?

5th term (T₅) =.?

1. Determination of the value of x.

We shall determine the value of x as follow:

First term = Log₂x

2nd term = Log₂(x + 9)

3rd term = Log₂(x + 45)

Common difference = 2nd term – first term = 3rd term – 2nd term

Log₂(x + 9) – Log₂x = Log₂(x + 45) – Log₂(x + 9)

Recall

Log M – Log N = Log (M/N)

Therefore,

Log₂(x + 9) – Log₂x = Log₂(x + 9)/x

Log₂(x + 45) – Log₂(x + 9) = Log₂(x + 45) /(x + 9)

Thus:

Log₂(x + 9) – Log₂x = Log₂(x + 45) – Log₂(x + 9)

Log₂(x + 9)/x = Log₂(x + 45)/(x + 9)

Cancel Log₂ from both side

(x + 9)/x = (x + 45)/(x + 9)

Cross multiply

(x + 9)(x + 9) = x(x + 45)

x² + 9x + 9x + 81 = x² + 45x

x² + 18x + 81 = x² + 45x

Rearrange

x² – x² + 81 = 45x – 18x

81 = 27x

Divide both side by 27

x = 81/27

x = 3

Therefore, the value of x is 3.

2. Determination of the 5th term.

We'll begin by calculating the common difference (d)

x = 3

First term = Log₂x

First term = Log₂3

2nd term = Log₂(x + 9)

2nd term = Log₂(3 + 9)

2nd term = Log₂12

Common difference (d) = 2nd term – first term

Common difference (d) = Log₂12 – Log₂3

= Log₂(12/3)

Common difference (d) = Log₂4

Finally, we shall determine the 5th term as follow:

First term (a) = Log₂3

Common difference (d) = Log₂4

5th term (T₅) =.?

T₅ = a + 4d

T₅ = Log₂3 + 4Log₂4

Recall:

nLogM = LogMⁿ

Therefore,

4Log₂4 = Log₂4⁴ = Log₂256

T₅ = Log₂3 + 4Log₂4

T₅ = Log₂3 + Log₂256

Recall:

Log M + Log N = Log (M×N)

Thus,

T₅ = Log₂3 + Log₂256

T₅ = Log₂(3 × 256)

T₅ = Log₂768

Therefore, the 5th term is Log₂768

Answer:

the answer is 13, because you need to divide 91 by 7.

Answer:

6/2 (1+2) = 9

Step-by-step explanation:

6/2 (1+2)

Order of operations PEMDAS

Parentheses first 6/2(3)

Multiplication and division go left to right

3(3)=9

Answer:6÷2(1+2)×3

Step-by-step explanation: