Phoebe took a survey of her classmates' favorite sport. The results are in the table below:

What is the relative frequency of survey members who prefer football?

Based on the diagram, there are 8 triangles in total

A triangle is a polygon with three sides and three angles.

Therefore, there are 8 triangles in the diagram.

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Answer:

Step-by-step explanation:

The picture is below of how to separate this into 2 different regions, which you have to because it's not continuous over the whole function. It "breaks" at x = 2. So the way to separate this is to take the integral from x = 0 to x = 2 and then add it to the integral for x = 2 to x = 3. In order to integrate each one of those "parts" of that absolute value function we have to determine the equation for each line that makes up that part.

For the integral from [0, 2], the equation of the line is -3x + 6;

For the integral from [2, 3], the equation of the line is 3x - 6.

We integrate then:

[tex]\int\limits^2_0 {-3x+6} \, dx+\int\limits^3_2 {3x-6} \, dx[/tex]    and

[tex]-\frac{3x^2}{2}+6x\left \} {{2} \atop {0}} \right. +\frac{3x^2}{2}-6x\left \} {{3} \atop {2}} \right.[/tex]  sorry for the odd representation; that's as good as it gets here!

Using the First Fundamental Theorem of Calculus, we get:

(6 - 0) + (-4.5 - (-6)) = 6 + 1.5 = 7.5

The value of the integral   [tex]\int\limits^3_0 {|3x-6|} \, dx[/tex]  is -9/2.

The given integral is [tex]\int\limits^3_0 {|3x-6|} \, dx[/tex]

We have to find the value of this integral.

We know that ∫xⁿ dx= xⁿ⁺¹/n+1

So,  [tex]\int\limits^3_0 {|3x-6|} \, dx[/tex] = 3x²/2 -6x (from 0 to 3)

Apply the limits.

=3(3)²/2-6(3)

=27/2-18

=27-36/2

=-9/2.

Hence, the value of the integral   [tex]\int\limits^3_0 {|3x-6|} \, dx[/tex]  is -9/2.

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Answer:

I think 60 - 1200 but i am not conform

The angle of depression from the top of the lighthouse to the ship is 0.04998 radians.

Given that, the top of a lighthouse was 60 m above sea level. A ship located 1200 m from the shore could spot the lighthouse.

We need to find the angle of depression from the top of the lighthouse to the ship.

The angle is formed by the line of sight and the horizontal plane for an object below the horizontal.

Now, sin b=60/1200

⇒sin b=1/20

⇒sin b=0.05

⇒b=0.04998 radians

Now, b=x=0.04998 radians

Therefore, the angle of depression from the top of the lighthouse to the ship is 0.04998 radians.

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Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Step-by-step explanation:

The first piece wise function is from interval (-3,-1). The line during this interval isnt constant so this means that f(x) must be a linear equation along interval -3 to -1. The line has a slope of 1. And if we keep continuing, our y intercept will be 3. So we can say that

[tex]f(x) = x + 3 \ : if \: - 3 \leqslant x < - 1[/tex]

Foe the 2nd, the interval is between -1 and 1.

The line is constant so f(x) is going to be equal to one y value. The y value is passed through is 5 so we can say that

[tex]f(x) = 5 \: if \: - 1 \leqslant x \leqslant 1[/tex]

Answer:

Step-by-step explanation

- 7(6x-1)+x=36

- 11-2(8+3p)=7²

-  1/4(5b+11)=19

- 2/7(4m-18)=12

Answer:

If... 6.4 inches : 16 dollars

Then... 32 inches = 80 dollars.  

And, 1 inch of track = 80/32 dollars.

80/32 = 2.5.

So, the answer is: 1 inch of track costs 2.5 dollars.

The  constant of proportionality is $2,50.

The equation used to represent direct proportionality is: y = kx

Where:

y = dependent variable

x = independent variable

k = constant of proportionality

Here, the dependent variable is the cost of the track. The independent variable is the length of the tracks.

$16 = 6.4k

k = 16 / 6.4 = $2.5

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Answer:

70.7 deg, 19.3 deg

Step-by-step explanation:

The sum of the measures of complementary angles is 90 deg.

One angle measures x.

The other angles measures 51.4 deg less than x, or x - 51.4.

The sum of their measures equals 90.

x + x - 51.4 = 90

2x - 51.4 = 90

2x = 141.4

x = 70.7

x - 51.4 = 70.7 - 51.4 = 19.3

Answer: 70.7 deg, 19.3 deg

Answer:

Step-by-step explanation:

Bonsoir,

63°

The value of external angle x intercepted by two tangents is 63°

We have,

From the given figure,

External  angle = x

From the definition of external angle intercepted by two tangents.

External angle = 1/2 x difference of the intercepted arc length

Now,

Difference of the arc length.

= 243 - (360 - 243)

= 243 - 117

= 126

Now,

Substituting the values.

External angle = 1/2 x difference of the intercepted arc length

= 1/2 x 126

= 63

Thus,

The value of external angle x is 63°

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Answer:

The answer above is completely correct, but it may help the student to see how to reach it:

We seek a square root of

3

−

2

√

2

. This must have the form

a

+

b

√

2

.

(

a

+

b

√

2

)

2

=

a

2

+

2

a

b

√

2

+

2

b

2

So

a

2

+

2

b

2

=

3

and

2

a

b

=

−

2

⇒

a

b

=

−

1

These are two simultaneous equations for

a

and

b

.

Rearrange the second:

b

=

−

1

a

Substitute into the first:

a

2

+

2

a

2

=

3

a

4

+

2

=

3

a

2

a

4

−

3

a

2

+

2

=

0

Note that this is a quadratic in

a

2

:

(

a

2

)

2

−

3

(

a

2

)

+

2

=

0

Factorise:

(

a

2

−

2

)

(

a

2

−

1

)

=

0

This gives us two possible solutions for

a

2

:

2

and

1

, and so the four solutions for

a

:

±

√

2

and

±

1

.

We are looking for integer solutions for

a

, and so

±

1

are possible solutions. But the other two are possible too - they can simply be folded in to the

√

2

term. This wouldn't have been possible if we'd had the root of some other number in the solution for

a

, but this solution is a special case.

Now use the second equation to deduce the four equivalent solutions for

b

:

b

=

−

1

a

b

=

¯¯¯¯¯

+

1

√

2

=

¯¯¯¯¯

+

1

2

√

2

and

¯¯¯¯

+

1

.

So we have the four solution pairs

(

a

,

b

)

:

(

√

2

,

−

1

2

√

2

)

(

−

√

2

,

1

2

√

2

)

(

1

,

−

1

)

(

−

1

,

1

)

This is a bit suspicious - we expect only two solutions, positive and negative square roots, so we wonder if some of these are identical to each other: When we substitute them in to our desired expression

a

+

b

√

2

, we get:

√

2

−

1

2

√

2

√

2

=

−

1

+

√

2

−

√

2

+

1

2

√

2

√

2

=

1

−

√

2

1

−

√

2

−

1

+

√

2

So the two solutions with

√

2

are identical to the two simpler solutions, so we can get rid of them. We now have two solutions, positive and negative square roots:

1

−

√

2

−

1

+

√

2

When we take the written square root of a quantity, it is implied that the desired root is the positive root, the "principal value" of the square root function. So we take the single solution that comes from

a

=

+

1

:

1

−

√

2

Double check: Make sure that this produces the desired answer:

(

1

−

√

2

)

2

=

1

−

2

√

2

+

2

=

3

−

2

√

2

I think this will help you

Answer:

A is the answer to your question

Step-by-step explanation:

To do this, just distribute the 3 to each of the coefficient and see if it would result in the same coefficients in the original expression.

The method is Dr. Perry most likely to use is Participatory action research.

Participatory action research is a type of research characterized by :

Additionally, in this type of research, the community involved is treated as researchers and their contributions are taken into account in the result of the same.

According to the above, the type of research suitable for Dr Perry's study is participatory action research, since it includes all the factors that Dr Perry takes into account for her research such as quantitavie/qualitative method and active participation from the community involved.

On the other hand, case study, naturalistic observation, and focus group are not the correct options because they use other methods in which the studied community does not actively participate.

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Note:

This question is incomplete because the options are missing. Here are the options.

A. Case study

B. Naturalistic observation

C. Participatory action research

D. Focus group

Answer:

see explanation

Step-by-step explanation:

The volume cannot be 15 cm³ because it is not a perfect cube.

V = x³

let x = 4 then x³ = 4³ = 64 ← a perfect cube

There is not an integer when cubed gives 15

( yx + 4x - 5 )( y + 1 )

.....................................

Answer:

(7-d)(7+d)

Step-by-step explanation:

49 - d^2

Rewriting

7^2 - d^2

We know that a^2 - b^2 = (a-b)(a+b)

(7-d)(7+d)

The answer you are looking for is -(d+7)(d-7).

Answer:

In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.[1][2] The order of the magic square is the number of integers along one side (n), and the constant sum is called the magic constant. If the array includes just the positive integers {\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}, the magic square is said to be normal. Some authors take magic square to mean normal magic square.[3]

The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3

Magic squares that include repeated entries do not fall under this definition and are referred to as trivial. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant we have semimagic squares (sometimes called orthomagic squares).

The mathematical study of magic squares typically deals with its construction, classification, and enumeration. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares. There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. Magic squares are generally classified according to their order n as: odd if n is odd, evenly even (also referred to as "doubly even") if n is a multiple of 4, oddly even (also known as "singly even") if n is any other even number. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect magic squares, and so on. More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares. Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge. The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century.

Magic squares have a long history, dating back to at least 190 BCE in China. At various times they have acquired occult or mythical significance, and have appeared as symbols in works of art. In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations.

The sum area of shaded region​ is [tex]\frac{1}{3}[/tex].

The formula to find the sum of infinite geometric progression is

[tex]S_{n}=\frac{a_{1}(1-q^{n}) }{1-q} \ \ q \ne 1[/tex]

Given

S = [tex]\frac{1}{4} +\frac{1}{16} +\frac{1}{64} +.........[/tex]

Using geometric progression

S = [tex]\lim_{h \to \infty} [\frac{1}{4} +(\frac{1}{4} )^{2} +(\frac{1}{4} )^{3} +.........+(\frac{1}{4} )^{n}][/tex]

Using summation formula for geometric progression

[tex]S_{n}=\frac{a_{1}(1-q^{n}) }{1-q} \ \ q \ne 1[/tex]

= [tex]\lim_{h \to \infty} \frac{\frac{1}{4} (1-(\frac{1}{4} )^{n} }{1-\frac{1}{4} }[/tex]

= [tex]\lim_{h \to \infty} \frac{\frac{1}{4} (1-\frac{1}{4^{n} }) }{\frac{3}{4} }[/tex]

= [tex]\lim_{h\to \infty} \frac{1}{3}(1-\frac{1}{4^{n} } )[/tex]

[tex]\lim_{h\to \infty} \frac{1}{4^{n} }[/tex] = 0

S  = [tex]\frac{1}{3}(1-0) = \frac{1}{3}[/tex]

The sum area of shaded region​ is [tex]\frac{1}{3}[/tex].

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Answer:

C

Step-by-step explanation:

Simple Random Sample

A sample in which each individual in the population has an equal chance to be selected is a simple random sampling ( SRS )

The most accurate type of probability sampling is random sampling. Each person in a population has an equal probability of getting selected for the sample thanks to this method of sampling.

This kind of sampling is perfect for highly controlled investigations where it is unacceptable to have human bias in the selection of the sample.

Each sampling unit in a population has an equal probability of being included in the sample when using simple random sampling (SRS). As a result, each potential sample has an equal probability of being chosen.

Given data ,

Let the sampling be represented as A

Now , in the sampling , each individual in the population has an equal chance to be selected

So , Each sampling unit in a population has an equal probability of being included in the sample when using simple random sampling (SRS).

And , each potential sample has an equal probability of being chosen

Hence , the sampling is a simple random sampling ( SRS )

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Answer:

x=10

Step-by-step explanation:

hope it helps

After finding the equation of the line, it is found that:

Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear  equation.

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

Equation of a line:

The equation of a line is given by:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

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

Finding the slope:

Given two points (x,y), the slope is given by change in y divided by change in x.

Thus:

[tex]y = 3x + b[/tex]

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

To find the y-intercept, we replace one of the points into the equation. I will replace (3,6). Thus:

[tex]6 = 3(3) + b[/tex]

[tex]b = 6 - 9 = -3[/tex]

Thus, the equation of the line is:

[tex]y = 3x - 3[/tex]

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

Is (4,8) a solution of the same linear  equation?

We have to replace x by 4 and y by 8, and see if it results in an identity. So

[tex]8 = 3(4) - 3[/tex]

[tex]8 = 12 - 3[/tex]

[tex]8 \neq 9[/tex]

Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear  equation.

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Answer:

VOLUME OF RIGHT CIRCULAR CONE=≈74.93136cm^3

VOLUME OF SPHERE: ≈523.6cm^3

Answer:

see explanation

Step-by-step explanation:

He wants to buy at least 4 snacks , that is can be more than 4 , so

x + y ≥ 4

He only has $20 , thus total cost must be less than or equal to $20 , so

3x + 2y ≤ 20

Answer:

C

Step-by-step explanation:

As y is zero, y/x will be zero

Answer:

15

Step-by-step explanation:

Sum of 'n' terms formula is given by:-    

s=n/2(2a+(n-1)d)  

s=13/2[2xa+(13-1)5]    

s=13/2(2xa+12x5)    

s=13/2(2a+60)    

585=13/2(2a+60)    

585 x (2/13) = 2a + 60

90 = 2a + 60  

90-60 = 2a

30 = 2a

a = 15

I hope you see what I did there. if you still confused, comment and I'll help

Answer:

"A" seems to be incorrect....

Step-by-step explanation:

"A" seems to be incorrect....

[tex]\frac{\left(\sin \left(60^{\circ \:}\right)\cdot \:300\right)}{\sin \left(90^{\circ \:}\right)}=150\sqrt{3}\quad \begin{pmatrix}\mathrm{Decimal:}&259.80762\dots \end{pmatrix}[/tex]

Answer:

1.) C. - 1/125

2.) B. - -3x-4

3.) A. - 3^-12

4.) C. - 7^8

5.) D. - 8^5

6.) A.  - 9x8x4

7.) B. - 2x5/7x5 or A It's Almost the Same But I couldn't find the exact difference so Sorry.

Answer:

[tex] 3\sqrt{5} [/tex]

Step-by-step explanation:

Find the largest factor of 45 that is a perfect square.

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

The largest perfect square is 9.

Now breakup 45 into a product which has 9 as a factor.

45 = 9 * 5

[tex] \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} [/tex]

Answer:

I don't understand the question?