Larry rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 8.

Answer:

13

Step-by-step explanation:

7 cm +1 cm +2cm +2cm :12cm

Answer:

Step-by-step explanation:

The first term is a, common difference is d.

The 6th term:

The 12th term:

Solve the system by elimination:

Find a:

Answer:

6th term = 30

12th term = 54

First term

Common difference

We know that

[tex] \sf \: a_{n} = a + (n - 1)d[/tex]

For 6th term

[tex] \sf \: 30 = a + (6 - 1)d[/tex]

[tex] \sf \: 30 = a + 5d[/tex]

For 12th term

[tex]\sf \: a_{n} = a + (n - 1)d[/tex]

[tex] \sf \: 54 = a + (12 - 1)d[/tex]

[tex] \sf \: 54 = a + 11d[/tex]

On subtracting both

[tex] \sf \: 54 - 30 = a + 11d - (a + 5d)[/tex]

[tex] \sf \: 54 - 30 = a + 11d - a - 5d[/tex]

[tex] \sf \: 24 = 6d[/tex]

[tex] \sf \: \dfrac{24}{6} = d[/tex]

[tex] \sf \: 4 = d[/tex]

Now

Using 2

[tex] \sf \: 54 = a + 11d[/tex]

[tex] \sf \: 54 = a + 11(4)[/tex]

[tex] \sf \: 54 = a + 44[/tex]

[tex] \sf \: 54 - 44 = a[/tex]

[tex] \sf \: 10 = a[/tex]

Answer:

Step-by-step explanation:

(x+3)² -5 =0 , use the formula (a+b) ² = a²+b²+2ab

x²+9 +6x -5 =0 , combine like terms

x²+6x +4 =0, use the quadratic formula x = (-b±√b²-4ac)/2a

x= (-6 ±√6²-4*1*4)/2*1

x= (-6 ± √36-16) /2

x= (-6±√20)/2

x=(-6 +2√5)/2 and x=( -6-2√5) /2, factor 2 in the numerator and simplify

x= -3 +√5 and x= -3 -√5

Step-by-step explanation:

A1= 3.5×9=31.5

A2=2×2=4

A3=(1/2) × 5×2=5

A4= (1/2)×2×2=2

At=A1+A2+A3+A4

At= 31.5+4+5+2

At=42.5

Answer:

25/81 is already in the simplest form. It can be written as 0.308642 in decimal form (rounded to 6 decimal places).

Answer:

144 cm²

Step-by-step explanation:

This figure is formed by rectangles and triangles, so we need to find the surface area of they and add all to have the surface area of the figure:

area of the rectangles:

4×3 = 12, and there are two of these rectangles

6×3 = 18, and there are just one of that

4×6 = 24, and there are two of these

5×3 = 15, and there are two of these

Now the area of a triangle:

6×4/2 = 12, and there are two of these

12×2 + 18 + 24×2 + 15×2 + 12×2 = 144 cm²

Answer:

All Real Number greater than 0 or

(0, positive infinity)

Step-by-step explanation:

The range is all possible y values of a function. We can tell a range by looking at the lowest y vaule then going to the highest possible y value.

Look at the graph. There is a open circle at y=0. So this means we are not going to include 0 in our function. The graph approaches f(x) to positive Infinity so our highest y value is Infinity.

So we know that the function y values cannot be zero and it must be positive. So our range is

All Real Number greater than 0. Or

(0, positive infinity)

Answer:

No. The results speak to a possible difference between the proportions of people over 55 and under 25 who dream in black and white, but the results cannot be used to verify the cause of such a difference.  

Hence the correct option is option A.

Step-by-step explanation:

[tex]hope \: its \: helful[/tex]

if cos7x - cos8x/1 + 2cos5x = cos(ax) - cos(bx), where a, b are positive integers, then a²+b²= 100.

The given equation is:

cos7x - cos8x/1 + 2cos5x = cos(ax) - cos(bx)

The LHS can be expanded as follows:

cos7x - cos8x/1 + 2cos5x = (2*cos4x*sin3x)/(2*cos2x) = sin3x

The RHS can be expanded as follows:

cos(ax) - cos(bx) = -2sin((a + b)/2)*sin((a - b)/2)

For the given equation to be true, the following must be true:

sin3x = -2sin((a + b)/2)*sin((a - b)/2)

3x = 180(a + b)/2

3x = 180(a - b)/2

Solving for a and b, we get a=6 and b=3.

Therefore, a² + b² = 6² + 3²=100.

To learn more about positive integers, here

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ll,,Step-by-step explanation:

Answer:

Distributive property

Step-by-step explanation:

The rule being shown here is the distributive property, because the first binomial is taken apart and separately multiplied with the other binomial.

Answer:

h=2.142

Step-by-step explanation:

Area of triangle(a)=1/2 b* h

Area of scalene traingle(a)=√s(s-a)(s-b)(s-c)

Semi perimeter(s)=(a+b+c)/2=(6+10+14)/2=15 yd

√s(s-a)(s-b)(s-c)=√15(15-6)(15-10)(15-14)=√15*9*5*1=√225=15 yd

Area of triangle(a)=1/2 b* h

15*2=14*h

30/14=h

h=2.142

You dont have any of those options so it might a mistake.

9514 1404 393

Answer:

  3x -2y +11 = 0

Step-by-step explanation:

The equation of the line perpendicular to ax+by=c through point (h, k) can be written as ...

  b(x -h) -a(y -k) = 0

Simplifying this will put it in general form.

__

You have a=2, b=3, (h, k) = (-1, 4), so your equation is ...

  3(x +1) -2(y -4) = 0 . . . . fill in the values

  3x -2y +11 = 0 . . . . . . . simplify

Answer:

Step-by-step explanation:

Height of the triangle = apothem = 9 inches

Base = 6 inches

[tex]Area \ of \ triangle = \frac{1}{2}bh\\\\=\frac{1}{2}*6*9\\\\= 3*9\\\\= 27 \ in^{2}[/tex]

Area of regular polygon = Area of 5 triangle.

                                        = 5 * 27

                                        = 135 square inches

Answer:

B. 6 miles per practice

Step-by-step explanation:

12 miles over the course of 2 track practices divided by 2  

12/2 = 6

6 miles per one track practice

Answer:

7

Step-by-step explanation:

We know that a^b^c = a^(b*c)

7 ^ 1/5 ^ 5

7^ (1/5*5)

7^1

7

Answer:

6m

Step-by-step explanation:

The ratio of the length and the breadth of rectangle=2:1

Let length be 2x, then breadth = x

Now,

Length(l)=12 m

or,2x=12m

or,x=6m

x=breadth=6m

Answer:

The minimum value of f(x) is -21 and it occurs at x = 1

Step-by-step explanation:

f(x) =3x^2-6x-18

Factor out the greatest common factor out of the first two terms

f(x) =3(x^2-2x)-18

Complete the square

-2x/2 =-1  (-1)^2 = 1

Add 1  (But remember the 3 out front so we are really adding 3  so we need to subtract 3 to remain balanced)

f(x) = 3(x^2 -2x+1) -3 -18

f(x) = 3(x-1)^2 -21

This is vertex form

f(x) = a(x-h)^2 +k  where (h,k) is the vertex and a is a constant

The vertex is (1,-21)  

Since a > 0 this opens upward and the vertex is a minimum

The minimum value of f(x) is -21 and it occurs at x = 1

Answer:

Domain is the whole R and the range is R+. The domain is continuous

Answer:

V=w*h*l

Step-by-step explanation:

w=width

h=height

l=length

volume = w*h*l

volume = w*h*l

volume = w*h*l

Answer:

3.25 minutes

Step-by-step explanation:

3.25 minutes per green light x 24 = 78

the yellow light is a given, hence 6 cars pass through

78 + 6 = 84 cars

Answer:

y = 5x

In the coordinate (3, 3), the first number is the x value and the second number is the y value.

So, does 3 = 5(3).

The answer is no, so this coordinate does not make the equation true.

Let me know if this helps!

Answer: No, the given point does not make the equation true.

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

Explanation:

There are three different ways to approach this.

One way is to plug x = 3 into the equation to find that

y = 5x

y = 5*3

y = 15

But that doesn't match up with y = 3 from the point (3,3). So we see that (3,3) is not a solution to y = 5x.

------

Or another method we could do is plug x = 3 and y = 3 to find a contradiction

y = 5x

3 = 5*3

3 = 15

The contradiction being that 3 on the left side doesn't match with 15 on the right side. The false equation at the end means y = 5x is false for (x,y) = (3,3), and therefore this point is not a solution to y = 5x.

------

The third method involves graphing the line y = 5x. You can see that (3,3) is not on the line, which visually confirms the results of the previous two sections. So for a point to be a solution, it must be on the line.

Answer:

x^2 - 9

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

x^2 - 4

Step-by-step explanation:

x+3        x-3

------ * -----------

x+2       x-2

Notice that the numerator is the difference of squares and the denominator is the difference of squares

(a+b)(a-b) = a^2 - b^2

(x^2 - 3^2)

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

x^2 - 2^2

x^2 - 9

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

x^2 - 4

Answer:

A...

the parts of theis problem are "special factors" or conjugates

(a+b) (a-b) = a^2 - b^2

you have two of those (x+3)(x-3) = x^2-9

and (x+2)(x-2) = x^2 -4

Step-by-step explanation:

The two consecutive years in which there is the largest increase in the median income is option B i.e. 1997-1998.

Given that

So after analysis, we can conclude that The two consecutive years in which there is the largest increase in the median income is option B i.e. 1997-1998.

Learn more about the bar graph here: brainly.com/question/14894834

Answer:

15

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

The factors of 45 are: 1, 3, 5, 9, 15, 45

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Then the greatest common factor is 15.

Answer:

C

Step-by-step explanation:

As n → ∞

[tex]\frac{85}{n}[/tex] , [tex]\frac{75}{2n}[/tex] , [tex]\frac{15}{2n^2}[/tex] → 0

Then

15 - 35 - 0 + 55 + 0 + 0

= - 20 + 55

= 35 → C

Twice means muliply by 2

The difference of a number and 7 means subtract a number/variable and 7

Is equal to 9 means =9

2(X - 7) = 9

Answer:

y = -1/11

Step-by-step explanation:

-10y= y+ 1

-11y = 1

y = -1/11

[tex]\\ \sf\longmapsto -10y=y+1[/tex]

[tex]\\ \sf\longmapsto -10y-y=1[/tex]

[tex]\\ \sf\longmapsto -11y=1[/tex]

[tex]\\ \sf\longmapsto y=\dfrac{1}{-11}[/tex]