how many rectangles of different sizes can be formed from 36 identical rectangles

Slope can be found between two points using the formula [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

If we substitute in your points (which is x and which is y does not matter as long as it is consistent), we will get

[tex]\frac{(4-1)}{(2-0)}[/tex].

Simplifying this further, your slope will be

[tex]\frac{3}{2}[/tex].

hope this helps!

The trigonometric function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

In this problem we need to find a sinusoidal expression that models the curve seen in the picture. The most typical sinusoidal model is described below:

f(x) = a · sin (b · x + c) + d    (1)

Where:

Now we proceed to find the value of each variable:

Amplitude

a = - 2 - (-6.5)

a = 4.5

Angular frequency

b = 2π / T, where T is the period.

0.25 · T = 4 - 3

T = 4

b = 2π / 4

b = π / 2

Midpoint

d = - 6.5

Angular phase

- 2 = 4.5 · sin (π · 4/2 + c) - 6.5

4.5 = 4.5 · sin (π · 4/2 + c)

1 = sin (2π + c)

π = 2π + c

c = - π

The trigonometric function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

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The valid prediction for the mean of the population possible using these samples is C. Yes, the variation of the sample means is small

It should be noted that a sample mean is an average of a set of data . Also, the sample mean can be used to calculate the standard deviation, central tendency, and the variance of a data set.

The sample mean can be applied to a variety of uses, including calculating population averages.

Here, the sample variance is a measure of the degree to which the numbers in a list are spread out. Here, the numbers given are close to each other.

If the numbers in a list are all close to the expected values, the variance will be small and if they are far away, the variance will be large.

Therefore, the correct option is C.

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Answer:

C: Yes, the variation of the sample means is small.

Step-by-step explanation:

Correct answer on edge

The radius of the sector is 10.27 miles

The area of a sector can be represented as follows;

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅= 25 degrees

area of the sector  = 23 miles²

area of a sector = ∅ / 360 × πr²

23 = 25 / 360 × πr²

cross multiply

23 × 360  = 25πr²

8280 = 25πr²

divide both sides by 25

πr² =  8280 / 25

πr² =  331.2

r² =  331.2 / 3.14

r² = 105.477707006

r = √105.477707006

r = 10.2702336877 miles

Therefore, the radius of the sector is 10.27 miles

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[tex]\mathbf{u} =\langle -6, -10 \rangle \\ \\ \mathbf{v}=\langle 7,8 \rangle \\ \\ \mathbf{u} \cdot \mathbf{v}=(-6)(7)+(-10)(8)=-122 \\ \\ \therefore -3(\mathbf{u} \cdot \mathbf{v})=-3(-122)=\boxed{366}[/tex]

The value of -3(u•v) is 366 when vector u= -6i - 10j and vector v=-6i - 10j is given.

The dot product of two vectors is the sum of the products of their corresponding components.

Here, u= -6i - 10j, from the figure as u goes 6 coordinate left to the y axis and and 10 coordinates below the x axis.

v= 7i + 8j, from the figure as v corrdinates right to the y axis and 8 coordinats upwards to the x axis.

Therefore u.v= (-6i - 10j).(7i + 8j)

                      = -42 - 80

                      = -122

So, -3(u.v)= (-3)×(-122)

                =366

Hence, the value of -3(u•v) is 366

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Answer: C

Step-by-step explanation:

The red graph is the result of reflecting the graph of y=f(x) across the x-axis and then translating 1 unit to the right.

Answer: Choice D

Reason:

Add up the arc measures, then divide by 2

x = (32 + 54)/2

x = 86/2

x= 43 degrees

The probability that the outcome is red then yellow is 0.036.

Given that in a jar there are 8 red marbles, 1 yellow marble and 6 green marbles.

We are required to find the probability of obtaining a red then yelow marble if two marbles are drawn and replacement is used.

Probability is the calculation of finding the chance of happening a event among all the events possible. It lies between 0 and 1.

Probability=Number of items/ Total items.

Number of red marbles=8

Number of yellow marble=1

Number of green marbles=6

Total marbles=15

Probability of obtaining red marble=8/15

Probability of obtaining yellow marble=1/15 (Because replacing is there so the number of total marbles do not decrease)

Required probability=8/15*1/15

=8/225

=0.035555

After rounding off we will get 0.036.

Hence the probability that the outcome is red then yellow is 0.036.

Question is incomplete. The following line should be included in question:

A jar contains 8 red marbles , a yellow marble and 6 green marbles.

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The maximum height is; 180 ft and the Total time in the air is 12 seconds

We are given the equation that represents the height of the rocket as;

d = 60t - 5t²

Taking the derivative of the formula gives us;

d' = 60 - 10t.  

-10t represents the acceleration.  The 60 represents the initial velocity.

Set 60 - 10t = 0 and solve for t to get;

t = 60/10 = 6seconds.  

That's when the maximum height occurs. Plug that value of t into the original quadratic equation to get the maximum height.

d(6) = 60t - 5t²

d(6) = 60(6) - 5(6²)

d(6) = 180

So,  maximum height is about 180 ft.  

Thus, total time in air = 2 * 6 = 12 seconds

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Answer:

Step-by-step explanation:

the expected profit should be 2 dollars a drink

Answer:

  y = -5/3x   or   5x +3y = 0

Step-by-step explanation:

To write the equation of a line through the origin, we need only find its slope. It is parallel to the line through the given points, so will have the same slope.

The slope of a line through points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

  m = (5 -0)/(-6 -(-3)) = 5/(-3) = -5/3

The line trough the origin has a y-intercept of zero, so its equation will be ...

  y = mx

For the slope we found, the desired equation is ...

  y = -5/3x

If we multiply by 3 and add 5x, we have ...

  3y = -5x

  5x +3y = 0 . . . . . . standard form equation of the line

Answer:

x - 4 = 2y

Step-by-step explanation:

"four less than a number x" therefore; x - 4

"is twice another number y" therefore; 2y

The composition of transformation that maps ABCD to EHGF is "(x, y) → (x', -y') → (x' + 6, y' + 3)".

The basic transformation rules are:

The given quadrilateral ABCD has vertices,

A(-5, 2), B(-3, 4), C(-2, 4), and D(-1, 2)

The transformed quadrilateral EHGF has vertices,

E(1, 1), H(3, -1), G(4, -1), and F(5, 1)

In the map ABCD to EHGF, the transformations that took place are:

1) Reflection over x-axis

2) Translation by (x + a, y + b)

Step 1: Reflection over x-axis; (x, y) → (x, -y)

A(-5, 2) → A'(-5, (-2)) = A'(-5, -2)

B(-3, 4) → B'(-3, (-4)) = B'(-3, -4)

C(-2, 4) → C'(-2, (-4)) = C'(-2, -4)

D(-1, 2) → D'(-1, (-2)) = D'(-1, -2)

So, the reflected quadrilateral is A'B'C'D'

Step 2: Translation by (x, y) → (x + a, y + b);

The reflected quadrilateral A'B'C'D' is now translated by

A'B'C'D' → EHGF

So, (for A'(-5, -2) and E(1, 1))

x + a = 1

⇒ -5 + a = 1

⇒ a = 1 + 5

∴ a = 6

and

y + b = 1

⇒ -2 + b = 1

⇒ b = 1 + 2

∴ b = 3

Thus, the translation is (x + 6, y + 3).

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Answer:

-9

Step-by-step explanation:

To find the y intercept, substitute 0 in for x.

So, the equation looks like this:

[tex]y=6(0-\frac{1}{2} )(0+3)[/tex]

Now, just solve for y and you will get y = -9

The y-intercept of the graph of the equation is y = -9 which is the correct answer that would be an option (A).

The general equation of a line is y = mx + c

where m is the slope of the line and c is the intercept.

A linear equation is defined as an equation in which the highest power of the variable is always one.

Given equation as:

y = 6 (x - 1/2)(x+3)

To determine the y-intercept of the graph of the equation

Substitute the value x = 0 in the equation,

y = 6 (0 - 1/2)(0+3)

Apply the arithmetic operation and solve for y

y = -9

Hence, the y-intercept of the graph of the equation is y = -9.

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Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

Data analysis can be regarded as the  process of collecting as well as modeling, and analyzing data so as to be able to extract insights that support decision-making.

Some Types of Data Analysis are:

It should be noted that Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

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Answer:

-1/3

Step-by-step explanation:

1:make y the subject.

2:slope of line is the coefficient of x

The true statement relating to a property of the function y =sin x is that the maximum and minimum values of the function are 1 and -1 respectively. Option B

The following are the properties of the sin trigonometric ratio of the function;

From the above listed deductions, we can see that the true statement about the function y = sin x is that the range which is always known as the maximum and minimum values of the function are 1 and - 1 respectively.

Thus, the true statement relating to a property of the function y =sin x is that the maximum and minimum values of the function are 1 and -1 respectively. Option B

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Answer:

These ratios are not equivalent as Marcia is 2 per friend while Jen is 3 per friend

Step-by-step explanation:

Marcia made 10 bracelets for 5 friends where each friend will be getting 2 bracelets with a 1:2 ratio

Jen made 12 bracelets for 4 friends where each friend will be getting 3 bracelets with a 1:3 ratio

Answer:

C. 35.1

Step-by-step explanation:

First get the length of AC by using the Pythagorean Theorem, that ends up being about 11.18. Then you need to get the radius of the circle so you divide 11.18 by 2 and get 5.59. Then plug 5.59 for r into 2(pi)(r). 2(pi)(5.59) = 5.123

Answer:

Answer B is correct

Step-by-step explanation:

First, let us find the diameter (AC) of the circle using the Phythogerem theorem.

AC² = AB² + BC²

AC² = 2² + 11²

AC² = 4 + 121

AC² = 125

AC = √ 125

AC = 5√5

And now let us find the circumference of the circle.

C = π × d

C = π × 5√5

C = 5√5π in

Answers

The ratio x:y:z is 10:5:3  

Ali got 20,000

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

Explanation:

Let

Those amounts add to 36,000

x+y+z = 36,000

We're told that x = 2y, so let's replace x with 2y in the equation above to get these steps

x+y+z = 36,000

2y+y+z = 36,000

3y+z = 36,000

We're also told that 3y = 5z, so we can replace that previously mentioned 3y with 5z to end up with one variable, in which we can solve for like shown below.

3y+z = 36,000

5z+z = 36,000

6z = 36,000

z = (36,000)/6

z = 6,000

This tells us that Chris got 6,000

Use this to find y

3y = 5z

3y = 5*6,000

3y = 30,000

y = (30,000)/3

y = 10,000

Ben received 10,000

Lastly, determine x.

x = 2y

x = 2*10,000

x = 20,000 which is the amount Ali got.

The ratio x:y:z turns into 20,000:10,000:6,000 which fully simplifies to 10:5:3 after dividing all three parts by the GCF 2000. It might be tempting to try to reduce the 10:5 portion into 2:1, but we cannot divide by 5 since it's not a factor of that 3 at the end.

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

Check:

Ali + Ben + Chris = 20,000 + 10,000 + 6,000 = 36,000

which helps confirm the answer.

Answer:

63:70

Step-by-step explanation:

The ratio of apartments to bathrooms in the building is 9:10.

Given that, a building has 63 apartments and 70 bathrooms.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The ratio of apartments to bathrooms is 63:70

= 9:10

Therefore, the ratio of apartments to bathrooms in the building is 9:10.

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The value of 'a' closest to hundredths is 41.41

A triangle could also be  a polygon with three sides and three angles. The three sides for a triangle DEF shown above, written symbolically as △DEF, are line segments DE, EF, and DF

If three sides of a triangle are adequate to three sides of another triangle, then the triangles are congruent. (2) If three angles of a triangle are respectively  adequate to three angles of another triangle, then the 2 triangles are congruent.

Since this is often a right triangle, we'll  use trig functions:

cos theta = adjacent / hypotenuse;

cos a=FD/DE;

cos a=45/60.

Taking the inverse of each side:

cos-1(cos a) =cos-1(3/4);

a=41.40962211.

After Rounding to the closest hundredth:

The value of a is 41.41.

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Answer:

89.19

Step-by-step explanation:

           8 9  .  1     9

         79,56 . 00, 00

8    |  64

      |  1556

169 |  1521

      |      3500

1781 |      1781

              1719

17829|        6200

Answer:

23

Step-by-step explanation:

The question gives the first equation:

0.05N + 0.10D = 2.20

It can be rewritten as:

0.05$ times the number of nickels plus 0.10$ times the number of dimes is equivalent to $2.20.

Notice that 0.05$ or 5 cents is equivalent to one nickel and 0.10$ or 10 cents is equivalent to one dime.

The question asks for N+D. We know that N stands for the number of nickels Daniel has and D stands for the number of dimes Daniel has. We also know that Daniel only has dimes and nickels in his pocket. Therefore N+D most be equivalent to the total number of coins, which is given in the question to be equal to 23 coins.

Therefore...

N+D = 23

Number of ants = 6

Number of flies = 12

Number of buck = 1

Number of fawn = 1

Number of doe = 1

Number of squirrels = 3

Number of rabbit = 6

What is the number system?

A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

A system for representing numbers is called a number system. It also defines a set of numbers to represent a quantity and is referred to as the system of numeration.

Given,

Total number of animals Cory saw = 27

Number of insects = [tex]27 \times \frac{2}{3}[/tex]

                               [tex]= 18[/tex]

Remaining number of animals = [tex]27-18[/tex]

                                                   = [tex]9[/tex]

From the insects-

Number of ants = [tex]18 \times \frac{1}{3}[/tex]

                          [tex]=6[/tex]

Number of flies = [tex]18-6[/tex]

                          = [tex]12[/tex]

Number of buck  = 1

Number of fawn = 1

Number of doe = 1

Let the number of squirrels be [tex]x[/tex]

Then, the number of rabbits = [tex]2x[/tex]

Remaining animals = [tex]2x+x[/tex]

⇒ [tex]9=3x[/tex]

⇒ [tex]x= 3[/tex]

Therefore,

Number of squirrels = 3

Number of rabbits = [tex]2x[/tex]

                               = 6

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Answer:

Option A - 32 cm³

Step-by-step explanation:

Volume of a pyramid is given by the formula :

V = [tex]\frac{lwh}{3}[/tex]

Substituting values given gives us :

V = (4)(4)(6)/3

V = (16)(6)/3

V = 96/3

V = 32

Units will be cm³ as this is volume

Hope this helped and have a good day

Answer:

A. 32 cm³

Step-by-step explanation:

V = (1/3)(area of base)(height)

The base is a square of side 4 cm.

area of base = side × side

V = (1/3)(4 cm × 4 cm)(6 cm)

V = 32 cm³

Answer:

Step-by-step explanation:

The first three terms of the arithmetic sequence for the number of words written are 10010, 9760, 9510. These have a common difference of 9760-10010 = -250. The first term and common difference can be used to make the explicit equation for the words written on the n-th day.

The explicit formula for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...

  [tex]a_n=a_1+d(n-1)[/tex]

For first term a₁ = 10010 and common difference d = -250, the explicit rule is ...

  [tex]a_n=10010-250(n-1)[/tex]

On day 14, n=14, and the number of words written is ...

  [tex]a_{14}=10010-250(14-1)\\\\a_{14}=10010-250(13)=10010-3250\\\\a_{14}=6760[/tex]

The writer would write 6760 words on the 14th day.