What is the value of the expression below when x=4 and y=3?
The question is 5x to the 3rd power plus 4y to the 3rd power

Answer:

15/169

Step-by-step explanation:

There are 52 cards in a standard deck.  Of those 52 cards, 12 are face cards and 20 are even numbered.  To find the probabily in this situation, we multiply 12/52 by 20/52.  This gives us 240/2704.  This can be reduced to 15/169.

Let

[tex]S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n[/tex]

where we assume |r| < 1. Multiplying on both sides by r gives

[tex]r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}[/tex]

and subtracting this from [tex]S_n[/tex] gives

[tex](1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}[/tex]

As n → ∞, the exponential term will converge to 0, and the partial sums [tex]S_n[/tex] will converge to

[tex]\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}[/tex]

Now, we're given

[tex]a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a[/tex]

[tex]a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}[/tex]

We must have |r| < 1 since both sums converge, so

[tex]\dfrac{15}a = \dfrac1{1-r}[/tex]

[tex]\dfrac{150}{a^2} = \dfrac1{1-r^2}[/tex]

Solving for r by substitution, we have

[tex]\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)[/tex]

[tex]\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}[/tex]

Recalling the difference of squares identity, we have

[tex]\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}[/tex]

We've already confirmed r ≠ 1, so we can simplify this to

[tex]\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15[/tex]

It follows that

[tex]\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12[/tex]

and so the sum we want is

[tex]ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}[/tex]

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

Answer:

The missing value is 6a

Step-by-step explanation:

Given:

[tex]\displaystyle \large{A(-3a,b)}\\\displaystyle \large{B(3a,b)}[/tex]

Find:

Missing Value

Distance Formula:

[tex]\displaystyle \large{\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

Determine:

[tex]\displaystyle \large{(x_2,y_2)=(3a,b)}\\\displaystyle \large{(x_1,y_1)=(-3a,b)}[/tex]

Input given information above in the formula:

[tex]\displaystyle \large{AB=\sqrt{(3a-(-3a))^2+(b-b)^2}}\\\displaystyle \large{AB=\sqrt{(3a+3a)^2+(0)^2}}\\\displaystyle \large{AB=\sqrt{(6a)^2}}\\\displaystyle \large{AB=6a}[/tex]

The length is 6a but since we want to find the value in the square root then the answer is still 6a

Answer:

y = - ½(x - 2)² + 3

Step-by-step explanation:

Answer:

p = 2

q = -1

k = -1

Step-by-step explanation:

Cosine functions always start above or below 0. So, the one that starts at (0, 1) is f(x) = (p)cosx + q. Sine functions always start at 0. So, the one that starts at (0, 0) is g(x) = (k)sinx.

Using the help image attached, we know that:

p and k = amplitude (top to midline)

q = vertical shift (movement of midline)

For f(x) = (p)cosx + q:

p = 2

q = -1

For g(x) = (k)sinx:

k = -1

Hope this helps!

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The required equation is :

[tex]\qquad \sf  \dashrightarrow \:y =a \cos(bx) + k[/tex]

Now, let's find the required values :

period (p) = 6

[distance between any successive Crest or trough]

a = - 4 (flipped)

b = 2π/p = 2π/6 = π/3

k = -2

Distance of starting position from origin = k

Now, plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2[/tex]

There is not crest given so use distance between troughs

Period (T):-

Frequency:-

[tex]\\ \rm\dashrightarrow \dfrac{1}{T}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{1}{6}[/tex]

[tex]\\ \rm\dashrightarrow 0.17Hz[/tex]

Answer: c

Step-by-step explanation: The cube represents the earth, the octahedron represents the air, the tetrahedron represents the fire, the icosahedron represents the water, and the dodecahedron represents the universe

The name of the platonic solid shown is hexahedron.

Tetrahedron - A tetrahedron, also referred to as a triangle pyramid, is a polyhedron with four triangular faces, six straight edges, and four vertex corners in geometry.

Hexahedron - Any polyhedron with six faces is called a hexahedron.

Octahedron - An octahedron is a polyhedron with eight faces in geometry.

Dodecahedron - In geometry, a dodecahedron or duo decahedron is any polyhedron with twelve flat faces.

The figure given in the question has clearly six flat faces and hence according to the definitions it is a hexahedron.

Learn more about shapes on:

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The complete question is attached.

Step-by-step explanation:

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

Distribute. Multiply 3 by 2x so the product keeps the variable, multiply 3 by 5 and keep the subtraction symbol. Multiply 4 by x so it would be 4x, multiply 4 by 3

(6x-5=4x+12) Answer

Answer:

The probability is 1/9

Step-by-step explanation:

1 - 8/9 = 1/9

Answer:

  no solution

Step-by-step explanation:

A graphing calculator shows the left-side expression is never equal to the right-side expression for any real-number value of A.

The equation is not an identity, and has no solution.

__

Additional comment

By subtracting the right-side expression from the left-side expression, we get an equation of the form f(A)=0. Any solutions will be x-intercepts of the graph. The graph for this equation never comes close to crossing the x-axis.

From the dots the parabola’s are the same size just transitioned to different locations.

blue = y = x^2 + 3

Green = y = (x-4)^2

Orange = y = x^2 - 3

Purple = y = (x+4)^2

Answer:

12ft trim

Step-by-step explanation:

assuming that she wants to use the same size on each side (3ft) of the window, we know that the window is a square

and a square has 4 sides

3 + 3 + 3 + 3 = 12ft

She needs 12 ft trim

Answer:

The battery seems to be charging at a rate of 1 percentage point per minute. So the battery should be fully charged at 10:11 AM.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given relations allow us to write three equations in the three unknown values. We can let x, y, z represent the three numbers, in order.

__

  x +y +z = 10 . . . . . . . the sum of the three numbers is 10

  2x +4y +5z = 33 . . . . . designated sum is 33

  6x -y = 28 . . . . . . . . 6 times the first is 28 more than the second

__

There are many ways to solve a system of equations like this. Perhaps one of the easiest is to enter the equations as an augmented matrix in your calculator, and let it do the work. (Some calculators will solve the equations directly.)

The three numbers are 5, 2, and 3.

_____

Additional comment

The third equation lets you write an expression for y in terms of x:

  y = 6x -28

Substituting this into the first two equations, we get ...

  x +(6x -28) +z = 10   ⇒   7x +z = 38

  2x +4(6x -28) +5z = 33   ⇒   26x +5z = 145

Subtracting the second from 5 times the first of these equations gives ...

  5(7x +z) -(26x +5z) = 5(38) -(145)

  9x = 45 . . . . . the y-variable is eliminated

  x = 5

Use equations from above to find z and y.

  z = 38 -7x = 3

  y = 6(5) -28 = 2

Answer:x=70

Step-by-step explanation:

STEP

1

:

           40

Simplify   ——

           x

Equation at the end of step

1

:

 4    40

 — -  ——  = 0

 7    x

STEP

2

:

           4

Simplify   —

           7

Equation at the end of step

2

:

 4    40

 — -  ——  = 0

 7    x

STEP

3

:

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       7

     The right denominator is :       x

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

7 1 0 1

Product of all

Prime Factors  7 1 7

                 Number of times each Algebraic Factor

           appears in the factorization of:

   Algebraic    

   Factor      Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

x  0 1 1

     Least Common Multiple:

     7x

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = x

  Right_M = L.C.M / R_Deno = 7

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      4 • x

  ——————————————————  =   —————

        L.C.M              7x  

  R. Mult. • R. Num.      40 • 7

  ——————————————————  =   ——————

        L.C.M               7x  

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4 • x - (40 • 7)     4x - 280

————————————————  =  ————————

       7x               7x  

STEP

4

:

Pulling out like terms :

4.1     Pull out like factors :

  4x - 280  =   4 • (x - 70)

Equation at the end of step

4

:

 4 • (x - 70)

 ————————————  = 0

      7x    

STEP

5

:

When a fraction equals zero :

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 4•(x-70)

 ———————— • 7x = 0 • 7x

    7x  

Now, on the left hand side, the  7x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  4  •  (x-70)  = 0

Equations which are never true:

5.2      Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.3      Solve  :    x-70 = 0

Add  70  to both sides of the equation :

                     x = 70

One solution was found :

x = 70

Answer:

1030 [tex]yd^{2}[/tex]

Step-by-step explanation:

split it into 2 different rectangular prisms

first one is 27 yd by 8 yd by 9 yd

second is 10yd by 8 yd by 12 yd

Answer:

1494 [yd²].

Step-by-step explanation:

1) the required area can be calculated as (see the attached picture):
A=A1+A2+A3+A4+A5+A6+2*A7;

2) finally,

A=9*8+17*8+8*12+10*8+(12+9)*8+27*8+2*(27*9+12*10);

A=1494 [yd²].

Note, the suggested solution is not the shortest one.

Using the permutation formula, it is found that there are 840 ways to place the letters.

The order in which the letters are placed is important, as PAST is a different arrangement that PTAS, for example, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 4 letters are taken from a set of 7, hence:

[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]

There are 840 ways to place the letters.

More can be learned about the permutation formula at https://brainly.com/question/25925367

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Answer:35

Step-by-step explanation:

Answer:

97.31 [tex]m^2[/tex]

Step-by-step explanation:

The area of the octagon is:

[tex]\frac{8 * 5.3 * 2.65\sqrt{3} }{2}[/tex] ~97.31 m^2

Answer:

-27.3 is the ans without decimal its -27-1/3

Answer:

-49 and 1/3

Step-by-step explanation:

− (-4 x -6) − (10 + 15) − 1/3

− (24) − (25) − 1/3

− 24 − 25 − 1/3

−49 − 1/3

-49 and 1/3

By solving a system of equations we will find the dimensions of the rectangle, and with these, we will see that the area is equal to 82.31 m^2

For a rectangle of length L and width W, the perimeter is:

P = 2*L + 2*W

In this case, we know that the perimeter is equal to 38m, then:

38m = 2*L + 2*W

We also know that if we subtract 3 meters from the length and 2 meters from the breadth, the length will e 2 times the breadth.

This is written as:

(L - 3m) = 2*(W - 2m)

Then we have a system of equations:

38m = 2*L + 2*W

(L - 3m) = 2*(W - 2m)

To solve this, we isolate one of the variables in one of the equations, I will isolate L on the second equation:

L = 2*(W - 2m) + 3m

Replacing that on the other equation we get:

38m = 2*(2*(W - 2m) + 3m) + 2*W

Now we can solve this for W.

38m = 4*(W - 2m) + 6m + 2*W

38m = 4*W - 2m + 2*W

38m + 2m = 6*W

40m = 6*W

40m/6 = W = 6.67m

Then the length is:

L =  2*(  6.67m - 2m) + 3m = 12.34 m

So the area of the rectangle is:

A = L*W = 12.34m*6.67m = 82.31 m^2

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

Answer:

The first 1 is the answer (a)

Step-by-step explanation:

The Formula for the volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex]

   Volume = [tex]\frac{4}{3} \pi (2)^3 = \frac{4*8}{3} \pi =33.510[/tex]

The volume is 33.51 cubic feet

Hope that helps!

133, 117, 152, 127, 168, 146, 174.

range.

first arrange the numbers in order, which gives you:

= 117, 127, 133, 146, 152, 168, 174

then subtract the lowest number from the highest, which gives you:

174 - 117

= 57

range= 57.

Answer:

$24.07

Step-by-step explanation:

57×44=2508 hrs

60376÷2508=$24.07 per hr

Answer:

$4.60

Step-by-step explanation:

Answer:

Step-by-step explanation:

front side: 6x3 = 18

back : 6x3 = 18

right:6x2 = 12

left:6x2 = 12

top: 3x2 =6

bottom: 3x2 =6

18 + 18 + 12 + 12 + 6 + 6

= 72

       Upon asking I got the rest of the information needed to answer this question.

-> Which one becomes a repeating decimal?

Your answer is D. 1/9.

       1/9 = 0.111111111111111111111111111111111 ... or 0.1 repeating. It can be written with a line over the 1 asyou can see in the attached.

       This means that D is the answer to your question.

The different recital programs that are possible is 80,730 ways

Permutation has to do with arrangement while combination has to do with the selection.

According to the question, a pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces, this shows that he can select the 5 pieces in any form.

The number of ways this can be done is given as:
[tex]27C_5=\frac{27!}{(27-5)!5!}\\ 27C_5=80,730[/tex]

Hence the different recital programs that are possible is 80,730 ways

Learn more on combination here: https://brainly.com/question/11732255