You can identify sample spaces for compound events using organized lists, tables, and tree diagrams. Which of the three methods do you find easiest to use? Which method is the most helpful? Why? Use the Internet or another resource to find the definition of the Fundamental Counting Principle. What does this principle state? How can the principle be used to help you identify a sample space for a compound event? What are the limitations of using the Fundamental Counting Principle when determining the probability of an outcome? Support your answers with an example.

Answer: d=2 and e= -3

Step-by-step explanation:

(8d-4e=28)*3 => 24d-12e=84

(6d+3e=3)*4 => 24d+12e=12

24d+24d-12e+12e=84+12

=> 48d=96

=> d=2

d=2 => 8*2-4e=28

=> e= -3

Answer:

x = 2 and x = 3

Step-by-step explanation:

Formulas used :

[tex]log_5 \ 5 = 1[/tex]

[tex]log_5 \ x + log_5 \ y = log_5 \ (xy)[/tex]

[tex]log_5 \ x = log_5 \ y => x = y[/tex]

Steps :

[tex]2 \ log_5 \ x = 1 + log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ 5+ log_5 (x - \frac{6}{5} )\\\\2 \ log_5 \ x = log_5 \ ( 5(x - \frac{6}{5} ))\\\\x^2 = 5(x - \frac{6}{5})\\\\x^2 = 5x - 6\\\\x^2 - 5x + 6 = 0\\\\x^2 - 2x - 3x + 6 = 0\\\\x(x - 2 ) - 3 (x - 2) = 0\\\\(x - 3)(x-2) = 0\\\\x = 3 , x = 2[/tex]

Answer:

468.75 Cubic meters

Step-by-step explanation:

15 x 12.5 x 2.5 = volume

187.5 x 2.5 = volume

468.75 = volume

Answer:

its 393.75 cubic meters

Step-by-step explanation:

I hope this helps

Answer:

option 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (- 4, 7) and r = 18 ÷ 2 = 9 , then

(x - (- 4) )² + (y - 7)² = 9² , that is

(x + 4)² + (y - 7)² = 81

Answer: 10.3 s

Step-by-step explanation:

Given

The height of the arrow is given by [tex]h=-16t^2+v_ot+h_o[/tex]

At  [tex]t=0, h=19\ ft[/tex]and [tex]v_o=163\ ft/s[/tex]

When arrow hits ground, h becomes 0 i.e.

[tex]\Rightarrow 0=-16t^2+163t+19\\\Rightarrow 16t^2-163t-19=0\\\\\Rightarrow t=\dfrac{163\pm \sqrt{(-163)^2+4(16)(19)}}{2(16)}\\\\\Rightarrow t=-0.115,10.30\ s[/tex]

Neglecting the negative value of t

So, the arrow hits the ground after 10.30 s

Answer:

x = 50 degree

Step-by-step explanation:

x + 10 + x + x + 20 = 180 degree (being linear pair)

3x + 30 = 180

3x = 180 - 30

x = 150/3

x = 50 degree

Answer:

A.

Step-by-step explanation:

we are going from a large shape to a smaller shape. the proof is that the side lengths go down from 7m to 0.5m. so, it is a reduction.

and the scaling factor s ? what do we need to multiply the original side lengths with to get the new ones ?

7 × s = 0.5 = 1/2

s = (1/2)/7 = (1/2)/(7/1) = (1×1)/(2×7) = 1/14

=> answer A is correct

The dilation from the figure on the left to the figure on the right is a reduction.  

Reduction scale factor 1/14.

The correct option is A.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

We have given that two figures.

The dilation from the figure on the left to the figure on the right is a reduction.

And the scale factor is,

= actual / scale

= 1/(7 / 0.5)

= 1/14

Therefore, the scale factor is 1/14.

To learn more about the scale factor;

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Answer:

7.22

Step-by-step explanation:

solved in the diagram

Answer:

x=2

HPT 3x+5y=6 (1) và 2x+y=4 (2)

Nhân phương trình (2) với 5 để hệ số y của 2 phương trình bằng nhau. Ta có:

(2)⇔ 10x+5y=20(3)

Trừ (3) cho (1), có: 7x+0y=14⇒x=2

Answer:

3x+5y=6.....eqn 1

2x+y=4.......eqn 2

y=4-2x.....eqn 3

Step-by-step explanation:

substitute eqn 3 into eqn 1

3x+5(4-2x)=6

3x+20-10x=6

-7x = -14

x=2

Answer:

y = (-1/2)x + 21/2

Step-by-step explanation:

Given equation:

y - 2x + 7

Coordinates = (5,8)

Find:

Perpendicular equation

Computation:

y = mx + c

y - 2x + 7

y = 2x - 7

So,

m = 2

The negative reciprocal of 2 is -1/2

So,

For,

Coordinates = (5,8)

y = mx + c

8 = (-1/2)(5) + c

8 = -5/2 + c

c = 8 + 5/2

c = 21 /2

So,

y = mx + c

y = (-1/2)x + 21/2

Answer:

369

Step-by-step explanation:

g(f(x)) simply means to put the whole expression of function f(x) into the place of "x" in g(x).

and to find the functional value for a specific x we just need to calculate functional value for f(x) and use that result as input for g(x).

f(6) = 8×6 + 5 = 48 + 5 = 53

and now

g(53) = 7×53 - 2 = 371 - 2 = 369

to check we do the general functional substitution :

g(f(x)) = 7×(8x+5) - 2 = 56x + 35 - 2 = 56x + 33

g(f(6)) = 56×6 + 33 = 336 + 33 = 369

correct

Answer:

$882.75

Step-by-step explanation:

In order to calculate tax, you need to multiply the percentage by the purchase costs. First, start by finding the decimal value of the percentage.

7 ÷ 100 = 0.07 — Percentage converted to a decimal.

[tex]825 \times 0.07 = 57.75[/tex]

— The tax. Now, in order to find the whole price, the tax and retail price must be added together.

[tex]825 + 57.75 = 882.75[/tex]

As per linear equation, the amount I have to pay in total is $645.

The simplified value of the given expression is (8 - 17x).

"A linear equation is an equation in which the highest power of the variable is always 1."

1. Given, the cost of television is $825.

The sales tax rate is 7%.

Therefore, total price of the television is

= $[tex][825 + (\frac{825(7)}{100})][/tex]

= $[tex](825+57.75)[/tex]

= $[tex]882.75[/tex]

2. The given expression is:

[tex]-4(3x - 2)- 5x\\= -12x + 8-5x\\= 8-17x[/tex]

Learn more about a linear equation here:

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Answer:

81

Step-by-step explanation:

90+25= 115

115 - 34 = 81

Answer:

480,700

Step-by-step explanation:

C(25,7)

25!/(7!*(25-7)!)

15511210043330985984000000/(6402373705728000*5040)

480700

Answer:

y= 3, x= 5

Step-by-step explanation:

4x+y=23

-x-y=-8

3x/3=15/3

x=5

for y

x+y=8

5+y=8

y=8-5

y=3

x=5

y=3

Answer:

si sumas 9+4×5 te da la respuesta

Answer:

Time required to hit the ground is 7.9 s.

Step-by-step explanation:

The height of the rocket is given by

[tex]y =- 16 x^2 + 119 x + 57[/tex]

For the time to hit the ground, put y = 0

[tex]-16x^2+119x+57=0\\\\16 x^2 - 119 x - 57 = 0 \\\\x = \frac{119\pm\sqrt{14161+3648}}{32}\\\\x = \frac{119\pm133.45}{32}\\\\t = - 0.45 s, 7.9 s[/tex]

Time cannot be negative, so time to hit the ground is 7.9 s.

Answer:

5

Step-by-step explanation:

Since it says the fraction, just divide 4000 by 800. So,

[tex]\frac{4000}{800}\\=>5[/tex]

That's it for the explanation. Hope it helped.

Answer:

$93.22

Step-by-step explanation:

bill = $79

tip = 18%

tip amount = tip % of bill

=18/100 * $79

=$1422/100

=$14.22

total cost = $79 + $14.22

=$93.22

Answer:

93.22

Step-by-step explanation:

Find the amount of the tip

79*18%

79 * .18

14.22

Add this to the amount of the bill

79+14.22

93.22

Answer:

6.875 degrees

Step-by-step explanation:

[tex]Total=7\times8=56\\56-1=55\\mean for 8 days=\frac{55}{8} =6.875 degrees[/tex]

Answer:

x = 260

Step-by-step explanation:

Add the two angles together.  They will sum to 180

x/2+ 50 = 180

Subtract 50 from each side

x/2+50-50 = 180-50

x/2 = 130

Multiply by 2

x/2*2 = 130*2

x = 260

Answer:

260°

Step-by-step explanation:

x / 2 + 50° = 180°

Subtract 50° from each side

x/2 + 50° - 50° = 180° - 50°

x / 2 = 130°

Multiply each side by 2

2 × x/2 = 130° × 2

x = 260°

Answer:

90 or -270

Step-by-step explanation:

Answer:

Un=n(n+1)/2

U=2013(2013+1)/2

U=2.027.091

Answer:

3

Step-by-step explanation:

Pythagorean rule

[tex]hyp = opp + adj \\ therefore. \\ opp = hyp - adj \\ and \\ adj = hyp - opp[/tex]

opp=13-10

opp=3

Answer: 1/6

Step-by-step explanation:

This is a question that has to do with the addition of a fraction. Since we are given the information that of the teacups in Bonnie's Tea Shop, 1/12 are blue and another 1/12 are orange.

Then, the fraction of the teacups that are either blue or orange will be calculated as:

= 1/12 + 1/12

= 2/12

= 1/6

Therefore, the fraction of the teacups that are either blue or orange is 1/6.

Step-by-step explanation:

first number=x

second number=x+2

third number=x+4

(x+2)(x+4)=3x+26

x(x+4)+2(x+4)=3x+26

x²+4x+2x+8=3x+26

x²+6x+8=3x+26

x²+6x-3x=26-8

x²+3x=18

x²+3x-18=0

you can use that to find the numbers

Answer:

6, 8 and 10

Step-by-step explanation:

Let the 3 consecutive odd numbers be x, x+2, x+4

product of the second and the third integer

(x+2)(x+4)

twenty-six more than three times the first integer is expressed as;

3x + 26

Equate

(x+2)(x+4) = 3x + 26

x²+4x+2x+8 = 3x + 26

x²+6x +8= 3x+26

x²+3x +8-26 = 0

x²+3x-18 = 0

Factorize

x²-6x+3x-18 = 0

x(x-6)+3(x-6) = 0

x+3 = 0 and x-6 = 0

x = -3 and 6

The first 3 number is are 6, 8 and 10

Answer:

y = 150

Step-by-step explanation:

y varies inversely as x²

yx² = k

----------------

y = 6 when x = 30

6(30²) = k

6(900) = 5400

--------------------------

what is y when x = 6

y(6²) = 5400

y(36) = 5400

y = 5400/36

y = 150

Answer:

     y= 150

Step-by-step explanation:

[tex]y\ \alpha \ \frac{1}{x^2}\\\\y = k \times \frac{1}{x^2}\\\\[/tex]

Given y = 6, and x = 30. Find k.

[tex]6 = k \times \frac{1}{30^2}\\\\6 \times 900 = k\\\\5400 = k[/tex]

Given  x = 6 and k = 180. Find y

[tex]y = 5400\times \frac{1}{6^2}\\\\[/tex]

 [tex]=5400 \times \frac{1}{36}\\\\=150[/tex]

Answer:

Sam is incorrect

Step-by-step explanation:

We can calculate the lengths of the diagonals using Pythagoras' identity.

The diagonals divide the rectangle and square into 2 right triangles.

Consider Δ SRQ from the rectangle

SQ² = SR² + RQ² = 12² + 6² = 144 + 36 = 180 ( take square root of both sides )

SQ = [tex]\sqrt{180}[/tex] ≈ 13.4 in ( to 1 dec. place )

Consider Δ ONM from the square

OM² = ON² + NM² = 6² + 6² = 36 + 36 = 72 ( take square root of both sides )

OM = [tex]\sqrt{72}[/tex] ≈ 8.5 in ( to 1 dec. place )

Now 2 × OM = 2 × 8.5 = 17 ≠ 13.4

Then diagonal OM is not twice the length of diagonal SQ