in class, we proved that the number of ways of tiling a $1 \times n$ rectangle with $1 \times 1$ and $1 \times 2$ tiles is $f {n 1}.$ (a) use a tiling argument to give a combinatorial proof that \[f 1 f 2 f 3 \dots f n

The value of x of the given equation is 2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The given equation is

4(4 – 12x) – 2(x – 12) + 5x = –50

We have to find the value of x.

According to given question we have

4(4 – 12x) – 2(x – 12) + 5x = –50

Rearrange terms we get,

4(– 12x+4) – 2(x – 12) + 5x = –50

Distribute we get,

-48x+16-2x+24+5x=-50

Compare the like terms we get,

-45x=-50-40

-45x=-90

x=2

Therefore, the value of x of the given equation is 2.

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The probability of getting a 7-card poker hand that contains at least two 3-of-a-kind is 0.0013

For given question,

We need to find the probability of getting a 7-card poker hand that contains at least two 3-of-a-kind.

Total number of cards = 52

If a 7-card poker hand contains at least two 3-of-a-kind,

3-of-a-kind means the three cards of the same rank.

The expression for the probability is,

[tex]P=\frac{ ^7C_3}{ ^{52}C_4} +\frac{ ^7C_2}{ ^{52}C_5} +\frac{ ^7C_1}{ ^{52}C_6}\\\\P=0.0013[/tex]

So, the required probability is 0.0013

Therefore, the probability of getting a 7-card poker hand that contains at least two 3-of-a-kind is 0.0013

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Answer: C

Step-by-step explanation: Substitute four and zero in each of the choices and see if the sum becomes negative six and two, respectively. If it does, then the equation represents the line.

Third equation substitution:

x = 4

y = -2(4) + 2

y = -8 + 2

y = -6

x = 0

y = -2(0) + 2

y= 0 + 2

y = 2

Therefore, the answer is C.

Note: I skipped to the third equation because the other equations are false.

Answer:

B

Step-by-step explanation:

Graph is positive and y intercept is on negative 2.

10² = 100

28.007 × 100 / 2800.7

third option = 2,800.7

Answer: The answer is within the picture!

Step-by-step explanation:

The vertex of the parabola of the quadratic function that is increasing in the interval (-∞, 2), and decreasing in the interval (2, ∞), is the highest point on the parabola.

The given description of the quadratic function is presented as follows;

The interval the function is increasing = (-∞, 2)

The interval the function is decreasing = (2, ∞)

The graph of the function is therefore increasing from -∞ up to the point just before 2.

The graph of the function is decreasing from the point just after 2 to infinity.

The point 2 is therefore the highest point of the graph and also, the vertex of the quadratic function.

Therefore;

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Answer:

1

Step-by-step explanation:

If a person has 2 apples and gives someone 1 which is 2-1=1

Answer:

35ab = 48

Step-by-step explanation:

given

5a = 6 ( divide both sides by 5 )

a = [tex]\frac{6}{5}[/tex]

and

7b = 8 ( divide both sides by 7 )

b = [tex]\frac{8}{7}[/tex]

substitute these values for a and b into the expression and simplify

35ab

= 35 × [tex]\frac{6}{5}[/tex] × [tex]\frac{8}{7}[/tex] ( divide 35 and 5 by 5 )

= 7 × 6 × [tex]\frac{8}{7}[/tex]

= 42 × [tex]\frac{8}{7}[/tex] ( divide 42 and 7 by 7 )

= 6 × 8

= 48

There are some differences in the process of constructing a inscribed square and a hexagon inside a circle.

When constructing a square, we start with a circle. Then draw its diameter through the center of the circle. Now putting compass on end points of this diameter, measuring more than half the length of diameter on the compass, draw 4 arcs above and below the diameter. So we get a perpendicular bisector of the diameter. In total, we get 4 points on the circle. Joining the adjacent points, we get the inscribed square.

When constructing the regular hexagon, start drawing a circle. Put the compass on a point on the circle and measure the radius on it. Now draw an arc on the circle. Putting compass on this new point on the circle draw another arc. Continuing like this, we get a total of  6 arcs giving 6 points on the circle. Join the adjacent points to get an inscribed regular hexagon.

So the differences in constructing the square and the regular hexagon are:

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Answer:

Given,points (0,3)and(10,8)

Step-by-step explanation:

slope(m)=

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

=

[tex] \frac{8 - 3}{10 - 0} [/tex]

=

[tex] \frac{5}{10} [/tex]

=

[tex] \frac{1}{2} [/tex]

The slope is 1/2.

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The maximum number of meals the family can eat at the restaurant is 11

Amount saved by Dana for her upcoming vacation = 450

Average cost when Dana cooks lunch or dinner  = 10

Average cost when the family goes to a restaurant for lunch or dinner = 40

Maximum number of meals the family can have at the restaurant  = Amount saved by Dana/Average cost of a meal when the family goes to a restaurant

=450/40

= 11.25 or 11

So, the maximum number of meals the family can eat at the restaurant is 11 with a budget of 450.

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x1 = 4 x2 = -4

substitute the values into the given equations!!

(4 + (-4)) / 2 = (0 / 2) = 0

y1 = -5 y2 = 5

(-5 + 5) / 2 = (0 / 2) = 0

midpoint = (0, 0)

bold values - box answers :D

Answer:

x=2

Step-by-step explanation:

You would use substitution. In which x =-5y +2 and x = 6y+2. -5y + 2 = 6y + 2. So would solve for y value then plug it into the equation to solve x.

1) The standard deviation of the temperature readings in degrees Celsius is 1.66° C.

2) The mean and standard deviation of Ferguson tip distribution is 1.1 and 0.3 respectively.

1) Let, X be the temperature in Fahrenheit and Y be the temperature in Celsius.

Mean = 77° F

[tex]77^\circ \ F=\frac{5\times77}{9}-\frac{160}{9}[/tex]

[tex]= 25^{\circ}C[/tex]

Variance in Fahrenheit is [tex]3^2=9[/tex]

[tex]Var(aX+b)=a^2VarX[/tex]

Here, [tex]a=\frac{5}{9}[/tex] and [tex]b=-\frac{160}{9}[/tex]

[tex]Var(Y)=\frac{25}{81}\times9[/tex]

[tex]=2.77[/tex]

Standard deviation [tex]= \sqrt{Var(X)[/tex]

[tex]= \sqrt{2.77}[/tex]

[tex]= 1.66^{\circ}[/tex]

2) Let, X be the cost of them meal and Y be the tip he gives.

[tex]Y=2+0.1X[/tex]

[tex]E[X]=9, Var[X] = 9[/tex]

Therefore,

[tex]E[Y]=E[2+0.1X][/tex]

[tex]=0.1E[X]+2[/tex]

[tex]=0.1\times9+2[/tex]

[tex]=1.1[/tex]

[tex]Var[Y] = 0.12Var[X] = 0.01\times9=0.09[/tex]

Standard deviation of [tex]Y = \sqrt{Var[Y]}[/tex]

[tex]= \sqrt{0.09}[/tex]

[tex]= 0.3[/tex]

Therefore,

1) The standard deviation of the temperature readings in degrees Celsius is 1.66° C.

2) The mean and standard deviation of Ferguson tip distribution is 1.1 and 0.3 respectively.

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"Your question is incomplete, probably the complete question/missing part is:"

Coach Ferguson uses a thermometer to measure the temperature (in degrees Fahrenheit) at 20 different locations in the school swimming pool. An analysis of the data yields a mean of 77 degrees Fahrenheit and a standard deviation of 3 degrees Fahrenheit. Recall that [tex]C^{\circ}=\frac{5^{\circ}F}{9} -\frac{160}{9}[/tex]. What is the mean temperature reading in degrees Celsius? What is the standard deviation of the temperature readings in degrees Celsius? When Sam goes to a restaurant, he always tips the server $2 plus 10% of the cost of the meal. If Sam's distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of his tip distribution?

Answer:

the answer is 27

Step-by-step explanation:

The solution to a compound inequality to show the possible lengths of the third side is 18 ≤ x ≤ 33.

Two or more inequalities are connected together with or or and to form a compound inequality (also known as a combined inequality).

A value must only make one aspect of an inequality true in order to be the solution to an or inequality. An inequality's solution must make both portions true in order to be effective.

According to the given values;

given parameters are

Range = 45 to 60 inches

Sides = 9, 18 and x

The sum of the three sides is

sum=9 + 18 + x

Evaluate

Sum = 27 + x

Recall that

Range = 47 to 60 inches

So, we have

45 ≤ 27 + x ≤  60

Subtract through by 27

So, we have

18 ≤ x ≤ 33

Hence, the solution to a compound inequality to show the possible lengths of the third side is 18 ≤ x ≤ 33.

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Answer:

Dear Friend

To prove the given equation

Answer:

29%

Step-by-step explanation:

There are 100 boxes. 29 of them are shaded in, so we can divide that by 100.

29/100=0.29

0.29 is equal to 29%

The standard form of  (3.5 x 10^6) ÷ (5 x 10^-3) is 7*10^8

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

Given:

(3.5 x 10^6) ÷ (5 x 10^-3)

On further solving

3.5 * 10^(6 -(-3)) / 5

3.5* 10^9 /5

0.7 * 10^9

7*10^8

Hence, the standard form is 7*10^8.

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Answer: her mom is 35 and she is 14.

Answer:

D. 12X + 64

Step-by-step explanation:

4(4x+5)+4(11-x)

4(4x+5)+4(11−x)

4(4x + 5) + 4(11 - x)

1 Expand by distributing terms.

16x+20+4(11-x)

16x+20+4(11−x)

2 Expand by distributing terms.

16x+20+44-4x

16x+20+44−4x

3 Collect like terms.

(16x-4x)+(20+44)

(16x−4x)+(20+44)

4 Simplify.

12x+64

12x+64

Answer:

D. 12x + 64

Step-by-step explanation:

expand the brackets by multiplying:

= 16x + 20 + 44 - 4x

= 12x + 64

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So, the least number of cards they could have altogether is any value of integer Z, that is ranging from (0→∞). If starting from n=1, then X=8 and Y=9.

What is an integer?

Let Joe has x no. of cards,

then,

Millie has (3/4)x cards.

In that case, Let millie has a total y no. of cards,

then, Joe has (2/3) y cards.

This means that,

(3X)/4 = (2Y)/3

The alternate form shall be:

X = (8 Y)/9

(3 X)/4 - (2 Y)/3 = 0

Real solution:

Y=(9X)/8

Integer Solution shall be:

X=8n, Y=9n, n∈Z, where Z is the set of integers.

So, the least number of cards they could have altogether is any value of integer Z, that is ranging from (0→∞). If starting from n=1, then X=8 and Y=9.

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Answer:

0.00375 meters per second,

Step-by-step explanation:

0.00375 meters per second, we know this is the answer because, 4.25*60=255 and 255/11.2=0.00375

Answer:

9 and 15

Step-by-step explanation:

ans should be 9 and 15

i dun really understand what this qns wants u to find really bad qns to test

Answer:

1,1,2

Step-by-step explanation:

The solution to the given system of equations are:{ x = 1, y = 1, z = 2} which is the corrrect answer would be option (A).

The equation is defined as a mathematical statement with at least two terms that contain variables or values that are equal.

We have been given the system of equations as:

2x − y − z = −1

3x + y − z = 2

x + y − 5z = −8

Isolate the term of x in the equation 2x − y − z = −1, and we get

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

Substitute the value of x = (- 1 + y +z)/2 in the above both equations,

3(- 1 + y +z)/2 + y − z = 2

(- 1 + y +z)/2 + y − 5z = −8

Simplify the equation to you get,

(5y + z - 3) / 2 = 2

(3y - 9z - 1) / 2 = -8

Isolate the term of y : (5y + z - 3) / 2 = 2 ⇒ y = (-z +7 )/5

Substitute the value of y = (-z +7 )/5 in the equation (3y - 9z - 1) / 2 = -8

(3(-z +7 )/5 - 9z - 1) / 2 = -8

Simplify the equation to you get,

8(-3z + 1)/d = -8

Isolate the term of z : 8(-3z + 1)/d = -8 ⇒ z = 2

Substitute the value of z = 2 in the equation y = (-z + 7) / 5 to simplify to get

⇒ y = 1

Substitute the values of y = 1 and z = 2 in the equation x = (-1 + y + z) / 2 to simplify to get

⇒ x = 1

The solution to the given system of equations are:

{ x = 1, y = 1, z = 2}

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Answer:

4

Step-by-step explanation:

It look like your are missing a bracket.

Do the inner most parentheses first.

24 -(16 -(7))x2

24 - 9 x 2

24 -18

4

Answer:

1st box: 2000

2nd box: 1

3rd box: 22.99

4th box: 0.11

5th box: 23

Step-by-step explanation:

It's simply splitting up the 2000 and 1, and then diving them by 87 each.
After that you can divide them and round to the nearest 10th, and add them to get 23.