Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=−0. 595, α=0. 05, n=17

By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.

In this question we have hints from two trigonometric functions necessary to find the exact value of the cosine function. In accordance with trigonometry, cosecant function is positive and tangent function is negative in the third quadrant of Cartesian plane and therefore the cosine function must be a negative number. Therefore, we can derive the value of the latter function by trigonometric formulas:

cos θ = - √[1 - (1 / csc θ)²]

If we know that csc θ = 2, then the exact of the cosine function is:

cos θ = -√[1 - (1 / 2)²]

cos θ = -√(3 / 4)

cos θ = -√3 / 2

By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.

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The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]

Therefore  [tex](k o h)(x) = \frac{1}{5 + x}[/tex]

Given that the functions h is defined by h(x)=5+x

and k is defined by k (x) = [tex]\frac{1}{x}[/tex]

To find the composition of k and h that is: (k o h) (x)

Therefore

k (h(x)) = k (5+x)

k (h(x)) = [tex]\frac{1}{5+ x}[/tex]

The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]

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The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes

The volume of the composite cylinder is expressed as shown below;

V = πr²h

where

r is the radius

h is the height

According to the given diagram;

V = Vl - Vs

V = π(10)²*15 -  π(5)²*15

V = 1500π - 375π

V = 1125π cubic inches

If the value of π is 3.14, hence;

V = 1125(3.14) cubic inches

V = 3532.5 cubic inches

The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively

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The true statement is that no number in base 10 can be written in multiple ways in base 4

The base of the numbers are given as:

Base 10 and base 4

Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers

There is only one equivalent of each number in each base.

This means that (for instance)

357 in base 10 is 11211 in base 4

The above number does not have any other representation in base 4 and it can not be written in another way.

This is the same for other numbers in base 10

Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4

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The area of the trapezoidal tarp in the hotel is 47.3 square inches.

How do determine the area of the trapezoid?

From the complete question, the parallel sides are 10ft and 12ft.

Evaluate,

The height (h) is computed using the cosine function shown below:

This gives

Make h the subject:

Evaluate:

So, we get:

Evaluate:

Therefore, the area of the trapezoidal tarp in the hotel is 47.3 square inches.

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The complete question is given below:
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?

to find the height. first find that d is 60,45, or 120. this means the height of the trapezoid is approximately 2.5,4.3, or 3.5 feet. so the area of the tarp is approximately 47.3,30.0 or 38.5 square feet.

The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and

r(1, 1, 0) is x + y + z = 2  .

According to the question

Let the points

p(0, 1, 1) = (x1,y1,z1)

q(1, 0, 1)= (x2,y2,z2)

r(1, 1, 0)= (x3,y3,z3)

now,

The equation of the plane through the points

i.e

The formula of equation of a plane passing through three non collinear points

[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0[/tex]

by substituting the values in the formula of equation of a plane

[tex]\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0[/tex]

[tex]\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0[/tex]  

x(1) - (y-1)(-1) + (z-1)(1) = 0

x + y - 1 + z - 1 = 0

x + y + z = 2

Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2  .

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Answer:

○ [tex]x = -7[/tex]

Step-by-step explanation:

Given the equation:

[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex],

to solve for [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] its subject.

[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex]

⇒ [tex]10x + 100 - 4 = 11 - 10x -55[/tex]      [expand brackets]

⇒ [tex]10x + 96 = -44 - 10x[/tex]

⇒ [tex]10x + 10x + 96 = -44[/tex]                   [add [tex]10x[/tex] to both sides]

⇒ [tex]20x + 96 = -44[/tex]

⇒ [tex]20x = -44 - 96[/tex]                             [subtract 96 from both sides]

⇒ [tex]20x = -140[/tex]

⇒ [tex]x = \frac{-140}{20}[/tex]                                        [divide both sides by 20]

⇒ [tex]x = \bf-7[/tex]

Answer:

B) x = -7

Step-by-step explanation:

Given equation: [tex]10(x+10)-4=11-5(2x+11)[/tex]

Step 1: Distribute [tex]10[/tex] and [tex]-5[/tex] through the parentheses.

[tex]\implies 10(x)+10(10)-4=11-5(2x)-5(11)[/tex]

[tex]\implies 10x+100-4=11-10x-55[/tex]

Step 2: Simplify (combine like terms).

[tex]\implies 10x+100-4=11-10x-55[/tex]

[tex]\implies 10x+96=-44-10x[/tex]

Step 3: Add [tex]10x[/tex] to both sides.

[tex]\implies 10x+10x+96=-44-10x+10x[/tex]

[tex]\implies 20x+96=-44[/tex]

Step 4: Subtract [tex]96[/tex] from both sides.

[tex]\implies 20x+96-96=-44-96[/tex]

[tex]\implies 20x=-140[/tex]

Step 5: Divide both sides by [tex]20[/tex] to isolate [tex]x[/tex].

[tex]\implies \dfrac{20x}{20}=\dfrac{-140}{20}[/tex]

[tex]\implies \boxed{x=-7}[/tex]

Answer:

slope

(0, 6) and (-9, 0)

0 - 6 / -9 - 0 = -6/-9 = 2/3

y intercept is when the line intercepts the y axis and x = 0

The slope of the line shown in the graph is 2/3 and the y-intercept of the line is 6

Answer:

slope is 2/3

y intercept is 6

Step-by-step explanation:

We can find the slope of the line by using two point

(-9,0) and (0,6)

The slope formula is

m = ( y2-y1)/(x2-x1)

   = ( 6 - 0) /( 0 - -9)

   = (6-0)/(0+9)

  = 6/9

  = 2/3

The y intercept is where it crosses the y axis ( the value where x is 0)

The y intercept is 6

Answer:

1.5×2.5/2=1.875.

Step-by-step explanation:

We all know that area of triangle is base into hight upon 2.

Answer:

the graph is a linear function  

root (2,0) vertical intercept (0,2)

Step-by-step explanation:

The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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Equation that represents the total time t (in minutes) Ken spent running is = 10 + m/6.30.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed x Time

Total time t (in minutes) =Initial Time + distance/speed

Given :-

Thus,

t = 10 + m/6.30.

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Answer:

12 square in

Step-by-step explanation:

In the diagram, the diameter is 4 in. Radius is half the length of diameter, so the radius of the yellow circle is 2 in. Using the given formula, A = pi*r*r, we can calculate the approximate area of the circle.

A = pi*r*r = 3*2*2 = 12 square in

Answer:

12 in^2

Step-by-step explanation:

Since the formula to find the area of a circle is already up, we can use that to solve the question.

In the image, we can see that the diameter of the circle is 4inches. Since two radii equal one diameter, one radius is 2 inches.

--> The reason why we found the radius is because the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.

Now, we can just replace r with 2.

--> A = 4[tex]\pi[/tex]

Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.

--> A = 4 x 3

--> A = 12

We can conclude that the area of the circle is 12 in^2.

Answer:

  21.0 m²

Step-by-step explanation:

The formula for the area of a triangle from two sides and the included angle is ...

  A = 1/2ab·sin(C)

Using this formula, we find the area to be ...

  A = 1/2(14 m)(8 m)sin(22°) = 21.0 m²

The area of triangle ABC is about 21.0 square meters.

Answer:

11x9=99 16x9=144=243 144+99

The cost of the carpet required for the given rectangular floor is $1584.

A rectangle is a quadrilateral with equal pairs of sides.

Given that:

The shape of the floor is a rectangle.

The length of the floor is 16 feet.

The width of the floor is 11 feet.

So,

The area of the floor = length × breadth

                                   = 16 × 11

                                   = 176 sq feet

The area of the floor is 176 sq feet.

The cost of the carpet for a 1 sq foot floor = $9

The cost of the carpet for a 176 sq feet floor = $9 × 176

                                                                          = $1584

Thus, the cost of the carpet for a 176 sq feet floor is $1584.

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The polar coordinate of given cartesian coordinate (-6, -1) is

(6.08, 0.0523π)

In this question,

We have been given the cartesian coordinate (-6, -1)

We need to convert given cartesian coordinate to polar coordinates.

We know that the polar coordinates is of the form (r, θ)

where, r is the magnitude with r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]

and θ is the angle associated with the coordinates which is given by           θ =  [tex]tan^{-1}(\frac{y}{x} )[/tex]

The magnitude of the given polar coordinate is,

⇒ r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]

⇒  r = [tex]\sqrt{(-6)^{2}+ (-1)^{2} }[/tex]

⇒ r = [tex]\sqrt{36+ 1}[/tex]

⇒ r = [tex]\sqrt{37}[/tex]

⇒ r = 6.08

And the angle associated with the coordinate is,

⇒ θ =  [tex]tan^{-1}(\frac{-1}{-6} )[/tex]

⇒ θ =  [tex]tan^{-1}(0.167 )[/tex]

⇒ θ = 9.48°

⇒ θ = 0.0523π

So, the polar coordinate is (6.08, 0.0523π)

Therefore, the polar coordinate of given cartesian coordinate (-6, -1) is

(6.08, 0.0523π)

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The limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex]  using L'Hospital rule is 0.

According to the given question.

We have to find the limit of ln(x)/x when x approaches to infinity.

If we let x = ∞, we get an indeterminate form [tex]\frac{\infty}{\infty}[/tex] ie. [tex]\frac{ln(x)}{x} = \frac{\infty}{\infty}[/tex].

And, we know that whenever we get indeterminate form ∞/∞ we apply L'Hospital rule.

Therefore, defferentiating numerator ln(x) and x with respect to x.

[tex]\implies \frac{d(ln(x))}{dx} = \frac{1}{x}[/tex] and [tex]\frac{d(x)}{dx} =1[/tex]

So,

[tex]\lim_{x\to \infty}\frac{\frac{1}{x} }{1}[/tex]

[tex]= \lim_{x \to \infty} \frac{1}{x}[/tex]

As, x tends to ∞, 1/x tends to 0. Because ∞ is very large number and 1 divided by a very large number always approaches to 0 and it is very close to zero.

Therefore,

[tex]\lim_{x \to \infty} \frac{1}{x} = 0[/tex]

Hence, the limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] is 0.

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Hey there!

⇒ Use the vertex as the middle letter, and the point from each side (<ABC or <CBA)

⇒ Use the vertex only (<B)

⇒ Use a number (<1)

⇒ Acute angle: less than 90°

⇒ Right angle: exactly 90°

⇒ Obtuse angle: between 90° and 180°

⇒ Straight angle: exactly 180°

Thank you,

Eddie

See the attachment for a visual!

Answer:

g(2) = 16; g(-2) = 4; g(a) = 3a + 10; 3(a+2) = 3a + 16

Step-by-step explanation:

We want to substitute the value in the parentheses on the left-hand side for the value of x on the right-hand side

Thus, g(2) = 3(2) + 10 = 6 + 10 = 16

g(-2) = 3(-2) + 10 = -6 + 10 = 4

g(a) = 3(a) + 10 = 3a + 10

g(a + 2) = 3(a + 2) + 10 = 3a + 6 + 10 = 3a + 16

Answer:

100%, 20%, 60%

Step-by-step explanation:

250/250 = 100/100 = 100%

50/250 = 1/5 = 20/100 = 20%

150/250 = 3/5 = 60/100 = 60%

Option C is correct (y + z = 6) ⋅ −3

What is a linear equation in math?

As per the statement -

A student is trying to solve the system of two equations given below:

Equation P:   y + z = 6              ....[1]

Equation Q:  3y + 4z = 1           ....[2]

Multiply the equation [1] by -3 to both sides we have;

-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)

Add equation [2] and [3] to eliminate the y-term;

z = -17

Therefore, the  possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3

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The complete question is -

A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?

(y + z = 6) ⋅ 4

(3y + 4z = 1) ⋅ 4

(y + z = 6) ⋅ −3

(3y + 4z = 1) ⋅ 3

Answer:

5/6

Step-by-step explanation:

slope = 4-(-1)/8-2 = 5/6

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept.

we need to transform x + 2y = 6, so that we end up with y being all alone on one side, and the rest on the other side.

x + 2y = 6

2y = -x + 6

y = -x/2 + 6

The area of the square A2 is 20 squared units

The complete question requires that we calculate the area of square A2

The side length of each square is 6 units.

So, the side length (L) of A2 is

L^2 = (2)^2 + (6 - 2)^2

This gives

L^2 = 20

The above represents the area of the square A2

Hence, the area of the square A2 is 20 squared units

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Answer:

Step-by-step explanation:

assuming you are looking for the area of ​​the triangles, there is no specific question, they are right-angled triangles congruent with the catheti of 2 and 4 units.

Triangle area = 1/2 base x height.

so 1/2 2 * 4 = 4 units^2

Answer:

23.  216

24.  56

25.  52

26.  -7

27.  5

Step-by-step explanation:

Work out the differences between the terms until the differences are the same:

[tex]1 \underset{+7}{\longrightarrow} 8 \underset{+19}{\longrightarrow} 27 \underset{+37}{\longrightarrow} 64 \underset{+61}{\longrightarrow} 125[/tex]

    [tex]7 \underset{+12}{\longrightarrow} 19 \underset{+18}{\longrightarrow} 37 \underset{+24}{\longrightarrow} 61[/tex]

        [tex]12 \underset{+6}{\longrightarrow} 18 \underset{+6}{\longrightarrow} 24[/tex]

As the third differences are the same, the sequence is cubic and will contain an n³ term.  The coefficient of n³ is always a sixth of the third difference.  Therefore, the coefficient of n³ = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n³ and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} n&1 & 2 & 3&4&5 \\\cline{1-6} n^3 & 1 & 8 & 27 & 64 & 125 \\\cline{1-6} \sf sequence & 1 & 8 & 27 & 64 & 125 \\\cline{1-6}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^3[/tex]

So the next term in the sequence is:

[tex]\implies a_6=6^3=216[/tex]

Work out the differences between the terms until the differences are the same:

[tex]2 \underset{+4}{\longrightarrow} 6 \underset{+6}{\longrightarrow} 12 \underset{+8}{\longrightarrow} 20 \underset{+10}{\longrightarrow} 30 \underset{+12}{\longrightarrow} 42[/tex]

     [tex]4 \underset{+2}{\longrightarrow} 6 \underset{+2}{\longrightarrow} 8 \underset{+2}{\longrightarrow} 10 \underset{+2}{\longrightarrow} 12[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.  The coefficient of n² is always half of the second difference.  Therefore, the coefficient of n² = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +1 & +2 & +3 & +4 & +5 & +6 \\\cline{1-7} \sf sequence & 2 & 6 & 12 & 20 & 30 & 42 \\\cline{1-7}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^2+n[/tex]

So the next term in the sequence is:

[tex]\implies a_7=7^2+7=56[/tex]

Work out the differences between the terms until the differences are the same:

[tex]4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19 \underset{+9}{\longrightarrow} 28 \underset{+11}{\longrightarrow} 39[/tex]

     [tex]3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7 \underset{+2}{\longrightarrow} 9 \underset{+2}{\longrightarrow} 11[/tex]

As the second differences are the same, the sequence is quadratic and will contain an n² term.  The coefficient of n² is always half of the second difference.  Therefore, the coefficient of n² = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +3 & +3 & +3 & +3 & +3 & +3 \\\cline{1-7} \sf sequence & 4&7&12&19&28&39 \\\cline{1-7}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^2+3[/tex]

So the next term in the sequence is:

[tex]\implies a_7=7^2+3=52[/tex]

Given numbers:

-1, 2, -3, 4, -5, 6

As the list of numbers does not increase or decrease, we cannot apply the same method as the previous questions.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} \sf list & -1 & 2 & -3 & 4 & -5 & 6 \\\cline{1-7}\end{array}[/tex]

From comparing the position of the term to its number in the list, we can see that the nth term is the same as n, but the odd numbers are negative and the even numbers are positive.

Therefore, the rule is:

[tex]\implies a_n=n \quad \textsf{where }n \textsf{ is an even natural number}[/tex]

[tex]\implies a_n=-n \quad \textsf{where }n \textsf{ is an odd natural number}[/tex]

So the next term in the sequence is:

[tex]\implies a_7=-7[/tex]

(since 7 is an odd natural number)

Given numbers:

5, 3, 5, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 3, 5, 5, 5, 5

The pattern of these numbers appears to be an ascending number of 5s with a 3 in between:

Therefore, the next number of 5s will be five.  This means the next number in the list will be 5, since there are only four 5s after the last 3.

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Answer:

20

Step-by-step explanation:

x^2+18x-160

If you put this into your calculator or desmos, you will get a parabola. You want to know the value of x when y=600. You can look at the table for the graph or scan to where y = 600. The value of x is 20 at that point.

To check you can plug 20 in for x. When you do that, y = 600.

The approximately probability that a person will go to the Saturday morning game and buy nachos is 18%.

The approximately probability of a person going to a Saturday morning game and buying nachos:

Probabaility= [tex]\frac{150}{846} *100[/tex]

                   =17.7%

Approximately=18%.

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Part (a)

We'll use the distance formula.

[tex](x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956\\\\[/tex]

The diameter is exactly [tex]\sqrt{106}[/tex] units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.

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

Part (b)

We divide the diameter in half to get the radius.

Therefore, the radius is exactly [tex]\frac{\sqrt{106}}{2}[/tex] units long which is approximately 5.1478 units.

Step-by-step explanation:

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

The given height of this trapezoid is given to be 4.5m

We have to solve for this by making use of the height of a trapezoid. The height is given as

A = (1/2) h (b1 + b2)

The variables here are

h = height

b1 = lenght at base 1

b2 = length at base 2

If the trapezoid that we have is a isosceles triangle, then base 1 is going to be the same length as that of the first base

b1 = 4 ft is the area. Given that the height has to be at least 4.5feet, then this would ensure that the trapezoid would be able to hold the shed.

Hence the height would begiven as 4.5 ft

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Answer: 4.5

Step-by-step explanation: