A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s. How many possible sequences of rolls could there have been? (For example, $3,2,3,1,3,2$ is one possible sequence.)

Answer: 5 by 12

Step-by-step explanation:

Let's call the dimensions of the rectangle w and w+7

The area is 60, so we can do 60=w(w+7)

60=w^2+7w

w^2+7w-60=0          factor the quadratic equation

(w-5)(w+12)=0

w-5=0, w=5

w+12=0, w=-12

Since the length of a rectangle cannot be negative, w=5

the dimensions of the rectangle are 5 and 12

Answer:

the awnser is d 1000 pediatricians

Answer: g(x) = (1/2)3^-x  reflection over y axis yields (-x,y)

Answer:

x < [tex]\frac{15-3a}{a-4}[/tex]; a > 4

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

Step-by-step explanation:

ax+3a < 4x + 15

ax - 4x < 15 - 3a

x( a -4) < 15 - 3a

x < [tex]\frac{15-3a}{a-4}[/tex]

ax + 3a < 5x + 15 -x

ax + 3a < 4x + 15

a( x + 3) < 4x + 15

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

Answer:

x <  (15 - 3a) / (a - 4). ( only true if a > 4)

a < (x + 15)/x

Step-by-step explanation:

a(x + 3) < 5x + 15 - x

ax + 3a < 5x + 15 - x

ax  - 5x + x < 15 - 3a

ax - 4x < 15 - 3a

x(a - 4) < 15 - 3a

Dividing both sides by (a - 4):

x <  (15 - 3a) / (a - 4)

a < (x + 15)/x

Answer:

(6x^2)(x^4 +x^2 + 1)

Step-by-step explanation:

6x^6 + 6x^4 + 6x^2

split it up into parts

6x^6 = (6x^2) * x^4

6x^4 = (6x^2) * x^2

6x^2 = (6x^2) * 1

so you can take out 6x^2 to get

(6x^2)(x^4 +x^2 + 1)

Answer:

increasing spread epidemics your outlook

hopefully this answer can help you to answer the next question.

Answer:

Hi!

Step-by-step explanation:

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

Let's distribute the -5 within its parentheses.

A negative multiplied by a negative number has a positive result.

Let's distribute the 3 within its parentheses.

-5x+15+12-3x+2x

Combine like terms...

-5x-3x+2x=-6x

15+12=27

-6x+27

Both numbers are divisible by 3...

3(-2x+9)

or -3...

-3(2x-9)

Answer:

Hello

y=(x+1)/12 +1

Step-by-step explanation:

[tex]\text{As the directrice is horizontal:}\\\\\\y=-2 ==> k=-2\\\\Focus=(a,b)=(-1,4)\\\\\boxed{y=\dfrac{x-a}{2(b-k)} +\dfrac{b+k}{2} }\\\\\\y=\dfrac{x+1}{2(4+2)} +\dfrac{4-2}{2} }\\\\\boxed{y=\dfrac{x+1}{12} +1}\\[/tex]

Step-by-step explanation:

Two angles are supplementary one angle is 4 degrees less than three times the other find the measures of the angles

x + y = 180

x = 3y - 4

3y - 4 + y = 180

4y = 184

y = 46

x = 134

Answer:

30°，150°

Step-by-step explanation:

Answer:

246.62007 cm. HTH!

Step-by-step explanation:

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving forA

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=8·9+5·9+10·9+1

2·﹣84+2·(8·5)2+2·(8·10)2﹣54+2·(5·10)2﹣104≈246.62007

Answer:

the total ratio is 1+1.5=2.5

to get the number of 5p coins you get (1/2.5)*75=30

To get the number of 10p you get

(1.5/2.5)*75=45

so he has 30 5p coins and 45 10p coins so the total value Is given by

(5*30)+(10*45)=600

Answer:

Q1. Volume of the prism

= 75(20)(14) cm3

=21000 cm3

Volume of the cylinder

= π(75^2)(120)cm3

=2120575cm3 (cor. to nearest int.)

The cylindrical bale has a greater volume.

Q3a. Volume of the pyramid

=(1/3)(40)(64)(64)m3

=54613 m3 (cor. to nearest int.)

Q3b. Volume of air per person

=(1/3)(40)(64)(64)(1/5000) m3

=10.9 m3 (cor to 3 sig fig)

Step-by-step explanation:

Bob's salary : $35000 per year plus 10% after one year

100% = 35000

1% = 100%/100 = 35000/100 = $350

10% = 10×1% = 10×350 = $3500

so in total, his salary will be $35000+$3500 = $38500 after one year.

Sam's salary : $3842.42 per month plus 5% after one year.

100% = $3842.42 per month. but to make it comparable to Bob's salary, we need to calculate the annual salary.

so, 100% 12×3842.42 = $46109.04

1% = 100%/100 = 46109.04/100 = $461.09

5% = 5×1% = 5×461.09 = $2305.45

so, in total, his salary will be $46109.04+$2305.45 = $

Answer:

B

Step-by-step explanation:

[tex] \frac{{3}^{5} }{ {3}^{3} } = {3}^{5 - 3} = {3}^{2} = 9 [/tex]

Answer: About 6.321 cm

Step-by-step explanation:

[tex]tan(x)=\frac{opposite}{adjacent}[/tex]

[tex]tan(36)=\frac{x}{8.7} \\\\x=8.7*tan(36)=6.3209...[/tex]

Answer: X = 1/4 or X = -1

Step-by-step explanation:

4x2+3x−1=0

(4x−1)(x+1)=0

4x−1=0 or x+1=0

4x=1 or x=-1

Now divide 4 from both sides

like this 4x/4=1/4

now cancel out two 4's so the answer will be x=1/4

Answer:

47.746, answer choice C

Step-by-step explanation:

47.746

Answer:

1. John still has 3 Apples

2. John now has 845679,63 Apples (I'm not sure if you've written the number of the multiplying fairy right...).

3. If the * is multiplying:

John now has 25937228,2 Apples.

Step-by-step explanation:

Just use the calculator.

Answer:

hhghhhhhhhhh

Step-by-step explanation:

yyyyjuiynrjdjf

HI THERE

the answer is -6

#YoghurtCup

Answer:

5 marbles

Step-by-step explanation:

Assume the first is color 1

and then the second is color 1

Now the third is color 2

The fourth is color 2

Now the 5th marble of either color will make 3 of one color

Answer:

Step-by-step explanation:

I can't give you either B or D, but I can calculate the answer.

2^5

=====

(2^5)(3^5)  

The 2^5s cancel out.

1

===

3^5

Another answer could be 3^-5

or

0.004115

Answer:

A number line going from negative 1 to positive 7. Points are at positive 1 and positive 7.

Step-by-step explanation:

We have the equation:

|8 - 2*p| = 6

Remember that the equation:

|f(x)| = A

with A > 0

means that:

f(x) = A

or

f(x) = -A

Then for our case, we can rewrite:

|8 - 2*p| = 6

as:

(8 - 2*p) = 6

or

(8 - 2*p) = -6

Now we can solve these two equations to find the two possible values of p.

From the first one, we get:

8 - 2*p = 6

8 - 6 = 2*p

2 = 2*p

2/2 = p = 1

so one solution is  p = 1

Now from the other equation, we can get the other solution:

(8 -2*p) = -6

8 - 2*p = -6

8 + 6 = 2*p

14 = 2*p

14/2 = p = 7

So the two solutions are p = 1 and p = 7

Then the correct option is:

"A number line going from negative 1 to positive 7. Points are at positive 1 and positive 7."

Answer:

The first reflection makes the points (1,1), (-1,1) and (1,4) and the second reflection changes THOSE to (-7,1) (-5,1) and (-7,4).  Just connect the dots to make the triangle.

Let me know if anything did not make sense.  

Step-by-step explanation:

Reflect just means how far away is each point to the line of reflection?  then ake a new point the sae distance, but in the opposite direction.  You always want to use a line that makes a right angle to the line of reflection too, so since x=2 and x=-3 are verticallines you are going to use horizontal lines to measure where A, B and C are.

So the three points are A:(3,1), B:(5,1) and C:(3,4)

Now use a horizontal line to measure how far A, B and C are from x=2.

A is 1 spance to the right of x=2, so A' (what A turns into) is 1 space to the left.  so (3,1) becomes (1,1)  The y value does not change since you are only using the horizontal direction for reflection.  B changes fro (5,1) to (-1,1) and finally C changes from (3,4) to (1,4)

Now the second reflection is the exact same process, but witht he new points reflected across x = -3.  So the new points are (-7,1) (-5,1) and (-7,4).

Answer:

ab+bc+ac=47

Step-by-step explanation:

(a+b+c)=12

Square both sides

a^2+b^2+c^2+2(ab+bc+ac)=144

2(ab+bc+ac)=94

ab+bc+ac=47

Answer:

ab + bc + ca = 47

Step-by-step explanation:

Using the algebraic identity

(a + b + c) = a² + b² + c² + 2(ab + bc + ca) , then

12² = 50 + 2(ab + bc + ca)

144 = 50 + 2(ab + bc + ca) ← subtract 50 from both sides

94 = 2(ab + bc + ca) ← divide both sides by 2

47 = ab + bc + ca