An ‘in shuffle’ is a perfect shuffle on a standard deck of 52 playing cards that splits the deck in half, then interleaves cards starting with the top half.

Required:
a. What is the position of the first card after the 7th shuffle?
b. How many times must one perform the shuffle so that the top card becomes the bottom card?
c. When do the first and last cards in the deck touch?

Answer:

see below (I hope this helps!)

Step-by-step explanation:

9) We know that the perimeters of the square and triangle are equal so to find x, we can write:

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

4x - 20 = 2x + 12

2x = 32

x = 16

10) To find the perimeter, we can substitute x = 16 into 4(x - 5) which would be 4(16 - 5) = 4 * 11 = 44.

Answer:

  2.67 liters

Step-by-step explanation:

Let "a" represent the number of liters of pure acid needed to make the desired solution. Then the amount of acid in the mix is ...

  (100%)x +(10%)(12 -x) = (30%)(12)

  (90%)x = 12(20%) . . . . . subtract (10%)(12)

  x = 12(2/9) . . . . . divide by 90%

  x = 2 2/3 . . . liters

You'll need 2.67 liters of the pure acid.

Answer:

=6 units squared

Step-by-step explanation:

area=1/2h(a+b)

        =1/2×2(4+2)

        =6

Answer:

[tex]\boxed{\sf C. \ 10}[/tex]

Step-by-step explanation:

[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]

[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]

[tex]NH \times HT = MH \times HY[/tex]

[tex](x+20) \times 8=12 \times 20[/tex]

[tex]\sf Expand \ brackets \ and \ multiply.[/tex]

[tex]8x+160=240[/tex]

[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]

[tex]8x+160-160=240-160[/tex]

[tex]8x=80[/tex]

[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]

[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]

[tex]x=10[/tex]

The value of x is 10.

We have a circle and inside it two chords MY and NT intersect at point H.

We have to find the value of x in the figure.

According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then

AO x OB = CO x OD

Applying the chord intersecting theorem to the figure in the question, we get -

MH x HY = NH x HT

12 x 20 = (x+20) x 8

240 = 8x + 160

8x = 80

x = 10

Hence the value of x is 10.

To solve more questions on Circles and chords, visit the link below -

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Answer:

7+sqrt(37)

Step-by-step explanation:

7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)

Answer: 139/7

Step-by-step explanation:

Answer:

139/7

Step-by-step explanation:

182/10 = 18.2 < 18 7/11

219/12 = 18 + 3/12 = 18 1/4  < 18 7/11

139/7 = 19 + 4/7 > 18 7/11

179/10 = 17.9 < 18 7/11

Answer:

[tex]\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }[/tex]

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

[tex]\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}[/tex]

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

[tex]f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240[/tex]

We identify the coefficients for the like terms, it comes

a = -2 and 16a = -32 (which is equivalent). So, we can write in [tex]\mathbb{R}[/tex].

[tex]\\f(x)=(x^2+16)(x^2-2x-15)[/tex]

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

[tex]f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}[/tex]

And we can write in [tex]\mathbb{C}[/tex]

[tex]f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

D

Step-by-step explanation:

Let's first find the mean and median of each class.

Class 1:

The mean is simply all the numbers added up and then divided by the number of elements. There are 9 students in Class 1. Thus, we add all the ages up and then divide by 9. Thus:

[tex]\text{Class 1 Mean }= \frac{14+15+15+16+16+16+17+17+18}{9} \\=144/9=16[/tex]

The median is simply the middle number when the data sets are placed in order. The median of Class 1 is 16, the number in the middle.

Class 2:

Again, Class 2 has 9 students. Add up all the ages and then divide:

[tex]\text{Class 2 Mean }= \frac{13+14+15+16+16+17+18+18+19}{9}\\ =146/9\approx16.2222[/tex]

The median is the middle number of the data set. The median of Class 2 is 16.

Therefore, the mean of Class 2 is larger than the mean of Class 1. The medians of the two classes are equivalent.

Of the answer choices given, only D is correct.

Answer:

The mean of class II is larger and the median is the same

Step-by-step explanation:

Class I

14,15,15,16,16,16,17,17,18

The mean is

(14+15+15+16+16+16+17+17+18)/9

144/9 = 16

The median is the middle number

14,15,15,16,    16,    16,17,17,18

median = 16

Class II

13,14,15,16,16,17,18,18,19

The mean is

(13+14+15+16+16+17+18+18+19)/9

146/9 = 16.2repeating

The median is the middle number

13,14,15,16    ,16,       17,18,18,19

median = 16

Answer:

6/50

Step-by-step explanation:

There are 50 tiles

6 purple

18 pink

26 orange

P( purple) = purple/ total

                = 6/50

Answer:

≈ 3.6

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)

d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]

   = [tex]\sqrt{(-2)^2+3^2}[/tex]

   = [tex]\sqrt{4+9}[/tex]

    = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )

Answer:

3.6

Step-by-step explanation:

Look above bru

Answer:

The probability is 0.31084

Step-by-step explanation:

We can calculate this probability using the z-score route.

Mathematically;

z = (x-mean)/SD/√n

Where the mean = 16, SD = 3 and n = 36

For 15.8, we have;

z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4

For 16.2, we have

z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4

So the probability we want to calculate is;

P(-0.4<z<0.4)

We can get this using the standard normal distribution table;

So we have;

P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)

= 0.31084

Answer:

The sum is represented by the polynomial:

[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]

Step-by-step explanation:

Recall that polynomials are added by combining like terms. The only like terms in this addition are: 5 x and 8 x  which added render: 13 x. therefore, the addition of these polynomials renders;

[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]

Answer:

Step-by-step explanation:

Given the following logarithmic expressions [tex]log_ax = 3, log_ay = 7, log_az = -2[/tex], we are to find the value of [tex]log_a(\frac{x^3y}{z^4} )[/tex]

[tex]from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}[/tex]Substituting x = a³, y = a⁷ and z = a⁻² into the log function [tex]log_a(\frac{x^3y}{z^4} )[/tex] we will have;

[tex]= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24[/tex]

Hence, the value of the logarithm expression is 24

Answer:

wat do u want me to do

Step-by-step explanation:

Answer:

I noticed that to babysit my cousin was the chore that doled out the most, and I wonder why pet my dog is even a chore. Do they not love their pets?

Answer:

See below.

Step-by-step explanation:

1 gal = 4 qt

With a full gallon oil tank, you can fill 4 1-qt bottles.

The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.

Also, is the full tank really only 1 gallon, or is there a number missing there too?

Answer:

9

Step-by-step explanation:

9 x 9 = 81

Answer:

x = ±9

Step-by-step explanation:

x^2 = 81

Take the square root of each side

sqrt(x^2 ) = ±sqrt(81)

x = ±9

Answer:

∠A and ∠G is the pair of vertical angles.

Step-by-step explanation:

From the figure attached,

Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.

Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."

Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.

From the given options,

∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.

Answer:

a

Step-by-step explanation:

Answer:

100°

Step-by-step explanation:

We know that angles EFD and AEF are the same as they are alternate interior angles.

We also can note that BEF and AEF are supplementary, meaning their angle lengths will add up to 180°.

So we can create an equation:

(2x + 60) + (3x + 20) = 180

Combine like terms:

5x + 80 = 180

Subtract 80 from both sides

5x = 100

Divide both sides by 5

x = 20.

Now we can use this to find the measure of BEF.

[tex]2\cdot20 + 60[/tex]

[tex]40 + 60 = 100[/tex]

Hope this helped!

Answer:

BEF = 100

Step-by-step explanation:

The angles are same side interior angles and same side interior angles add to 180 degrees

2x+60 + 3x+20 = 180

Combine like terms

5x+80 = 180

Subtract 80

5x = 100

Divide by 5

5x/5 = 100/5

x = 20

We want BEF

BEF = 2x+60

      = 2x+60

      = 2*20 +60

     = 40+60

     = 100

Answer:

slope = 2

Step-by-step explanation:

will make it so simple and short

slope = rise / run

slope = 6 / 3

slope = 2

Answer:

B

Step-by-step explanation:

The formula for slope is (y2-y1)/(x2-x1)

In this case it is (1+5)/(3-0)

6/3

2

Answer:

9/3 = 3x/3

3 = x

The spring stretches 9 inches with 3 kilograms of weight attached to it

Step-by-step explanation:

Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:

y = 3x

9 = 3x.

Divide both sides of the equation by 3

Answer:The spring stretches 9 inches with 3 kilograms of weight attached to it.

Step-by-step explanation:

Substitute y = 9 into the equation y = 3x, or locate the answer on the graph:

y = 3x

9 = 3x.

Divide both sides of the equation by 3:

The spring stretches 9 inches with 3 kilograms of weight attached to it.

Answer: Check out the diagram below for the filled in boxes

14 goes in the first box (inside A, but outside B)

7 goes in the overlapping circle regions

5 goes in the third box (inside B, outside A)

3 goes in the box outside of the circles

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

Explanation:

[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.

n(A) = 21 means there are 21 items in A

n(B) = 12 means there are 12 items in B

We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]

It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.

--------

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]

So there are 7 items in both regions.

This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.

Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.

Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.

The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.

Again the diagram is posted below with the filled in values.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

The filled Venn diagram is given below.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

n(A) = 21

This is the total of all the items included in Circle A.

n(B) = 12

This is the total of all the items included in Circle A.

n(A') = 8

The items that are not in circle A.

n(A U B ) = 26

The items that are in both circle A and circle B.

Now,

n (A U B) = n(A) + n(B) - n(A ∩ B)

26 = 21 + 12 - n(A ∩ B)

n(A ∩ B) = 33 - 26

n(A ∩ B) = 7

Thus,
The filled Venn diagram is given below.

Learn more about the Venn diagram here:

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Answer: The length is 4 centimeters and the width is 6 centimeters.

Step-by-step explanation:

If the length of the  rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 .   And we know that to find the area of a rectangle we multiply the length by the width  and they've already given the area  so we will represent the width by w since it is unknown.

Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.

w(2w-8) = 24

2[tex]w^{2}[/tex] - 8w = 24     subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.

2[tex]w^{2}[/tex] - 8w -24 = 0      divide each term by 2.

[tex]w^{2}[/tex] - 4w - 12 = 0          Five two numbers that multiply to get -12 and to -4

[tex]w^{2}[/tex] +2w - 6w - 12 = 0    Group the left hand side and factor.

w(w+2) -6( w + 2) = 0   factor out w+2

(w+2)(w-6) = 0         Set them both equal zero.

w + 2 =0      or w - 6 = 0  

    -2  -2                + 6   +6

w= -2       or   w=6  

Since we are dealing with distance -2 can't represent a distance so the wide has to 6.  

Now it says that the length is 8 less that twice the width.

So  2(6) - 8 = 12 -8 = 4  So the length in this care is 4.

Check.

6 * 4 = 24

24 = 24

Answer:

The numbers:

-43    and     58

Step-by-step explanation:

a + b = 15

a = b - 101

then:

(b-101) + b = 15

2b = 15+101

2b = 116

b = 116/2

b = 58

a = b - 101

a = 58 - 101

a = -43

Check:

a + b = 15

-43 + 58 = 15

Answer:

f(1/3) = 6

Step-by-step explanation:

f(x) =-3x+7

Let x = 1/3

f(1/3) =-3*1/3+7

        = -1 +7

       = 6

Answer:

f(1/3) = 6

Step-by-step explanation:

The function is:

● f(x) = -3x+7

Replace x by 1/3 to khow the value of f(1/3)

● f(1/3) = -3×(1/3) +7 = -1 +7 = 6

Answer: [tex]4x^2-21x-2[/tex] .

Step-by-step explanation:

Given: The difference of two trinomials is [tex]x^2 -10x + 2[/tex]. If one of the trinomials is [tex]3x^2 - 11x - 4[/tex].

Then, the other trinomial will be ([tex]3x^2 - 11x - 4[/tex] ) + ([tex]x^2 -10x + 2[/tex])

[tex]=3x^2-11x-4+x^2-10x+2\\\\=3x^2+x^2-11x-10x-4+2\\\\=4x^2-21x-2[/tex]

Hence, the other trinomial could be : [tex]4x^2-21x-2[/tex] .

This is equivalent to x^2+8x+13

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

Explanation:

The vertex of f is at (0,0). The vertex of g is at (-4, -3). The vertex has moved 4 units to the left and 3 units down.

To shift to the left, we replace x with x+4. So we have f(x) = x^2 turn into f(x+4) = (x+4)^2 so far.

Then we subtract off 3 to move everything 3 units down. We have

g(x) = (x+4)^2-3

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

Optionally we can expand things out like so

g(x) = (x+4)^2-3

g(x) = (x+4)(x+4)-3

g(x) = x(x+4)+4(x+4)-3

g(x) = x^2+4x+4x+16-3

g(x) = x^2+8x+13

Showing that (x+4)^2-3 is equivalent to x^2+8x+13

Answer:

1/2

Step-by-step explanation:

The probailty of an event A is:

● P(A) = ( outcomes that give A) / (total number of possible outcomes)

Let A be the event in wich we get an even number.

● The sample space is {2,4,6}

So there are 3 possible outcomes that give A .

The six-sided dice has 6 outcomes

● { 1,2,3,4,5,6}

■■■■■■■■■■■■■■■■■■■■■■■■■■

● P(A) = 3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

i took the test

Answer:

The test statistic is [tex]t = 2.79[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is [tex]\mu = 59.3[/tex]

    The sample size is  [tex]n = 79[/tex]

    The  sample mean is  [tex]\= x = 62.4[/tex]

    The  standard deviation is  [tex]\sigma = 9.86[/tex]

Generally the test statistics is mathematically represented as

            [tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]

substituting values

          [tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]

          [tex]t = 2.79[/tex]