Match each correlation coefficient to its corresponding description.

The distance between point [tex](8, \sqrt{17})[/tex] and the center (0,0) is of 9 units, which is less than the radius, hence the correct option is:

Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is of 9 units.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this problem, we have a circle with center at (0,0) and radius 10. Hence, every point that is less than 10 units of distance from point (0,0) will be on the circle.

The distance of [tex](8, \sqrt{17})[/tex] is:

[tex]D = \sqrt{(8 - 0)^2+(\sqrt{17} - 0)^2}[/tex]

[tex]D = \sqrt{81}[/tex]

D = 9 units.

9 < 10, hence the correct option is:

Yes, the distance from the origin to the point [tex](8, \sqrt{17})[/tex] is of 9 units.

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Answer:

3rd answer is correct

Step-by-step explanation:

Take the common factor out.

[tex]a {b}^{2} + 6ab + 7a ^{3} - 14a \\ a[ {b}^{2} + 6b + 7 {a}^{2} - 14] \\ \blue{ a[b(b + 6) + 7( {a}^{2} - 2)]}[/tex]

The correct option is: a(b² + 7a² + 6b - 14), which matches the factorized form of the given expression.

The expression ab² + 6ab + 7a³ - 14a can be factored as follows:

ab² + 6ab + 7a³ - 14a

a(b² + 6b + 7a² - 14)

a(b² + 7a² + 6b - 14)

The expression b(b + 6) + 7(a² - 2) does not appear to be directly related to the given expression.

The expression a[(b + 7)(b + 6)(a² - 2)] is not equivalent to the given expression either.

The correct option is: a(b² + 7a² + 6b - 14), which matches the factorized form of the given expression.

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Answer:

Step-by-step explanation:

Because of the word "or", this is a disjunction, or a union of all the solutions to the inequality as they present on a number line.

For the first inequality:

4(x + 1) > -4 we distribute through the parenthesis to get

4x + 4 > -4 and subtract 4 from both sides to get

4x > -8 and then divide both sides by 4 to get

x > -2.  That will be graphed on a number line with an open hole over the -2 and the arrow will go to the right where the numbers are bigger than -2. This arrow continues into positive infinity.

For the other inequality:

2x - 4 ≤ -10 we add 4 to both sides to get

2x ≤ -6 and then divide by 2 to get

x ≤ -3. That is a closed hole over -3 and the arrow goes to negative infinity (to the left). Since one arrow goes off to the right forever, and the other arrow goes off to the left forever, and the arrows do not intersect at any point, the interval notation answer is

(-∞, -3] or (-2, ∞).  The parenthesis mean that the number following it is not included (you can't include infinity, either negative or positive, because it's not actually a number) and the brackets mean that the number following it IS included. The hole is closed over the -3 so -3 is included in the solution, where the hole over the -2 is open and is not included.

Answer:

x=1, y=4;

x=2, y=13

Step-by-step explanation:

See attachment for the graph of the reflection of f(x) across the y-axis

The function is given as:

f(x) = 1.5(0.5)^x

The rule of reflection across the y-axis is

(x, y) = (-x, y)

So, we have the following equation

f'(x) = 1.5(0.5)^-x

Rewrite the function as

g(x) = 1.5(0.5)^-x

So, we plot the graph of the function g(x)

See attachment for the graph of the reflection of f(x)

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step 1 :

g(x) = 1.5

step 2 :

g(0): 1.5

step 3 :

plot at (0,1.5)

step 4 :

g(1) = 3

g(-1) = .75

step 5 :

plot (1,3) & (-1,0.75)

step 6:

y=0

Answer:

  a = 144

  b = 67

Step-by-step explanation:

Where a transversal meets parallel lines, consecutive interior angles are supplementary.

  a° +36° = 180° . . . . . . consecutive angles are supplementary

  a = 144 . . . . . . . . . . divide by ° and subtract 36

  b° +113° = 180° . . . . . . consecutive angles are supplementary

  b = 67 . . . . . . . . . . divide by ° and subtract 113

keeping in mind that the points are A(-8 , 6) and C(2 , 5), so

[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-8}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{2}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{2}{5}\textit{ of the way from A to C} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{2}-\stackrel{x_1}{(-8)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AC}}}{\left( 10 ~~,~~ -1 \right)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left( \stackrel{x_1}{-8}~~+~~\frac{2}{5}(10)~~,~~\stackrel{y_1}{6}~~+~~\frac{2}{5}(-1) \right)\implies \left(-8+4~~,~~6-\frac{2}{5} \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill B\left(-4~~,~~5\frac{3}{5} \right)~\hfill[/tex]

The angles and side lengths for both triangles are;

3) A = 36°; B = 54°; C = 90°; a = 7; b = 9.63; c = 4.11

4) A = 64°; B = 26°; C = 90°; a = 1.798; b = 0.88; c = 2

3) From the diagram, we are already given;

B = 54°

C = 90°

a = 7

We know that sum of angles in a triangle is 180° and so;

A = 180 - (90 + 54)

A = 36°

By trigonometric ratios;

b/7 = tan 54

b = 7 * tan 54

b = 7 * 1.376

b = 9.63

7/c = cos 54

c = 7 * cos 54

c = 4.11

4) From the diagram, we are already given;

B = 26°

C = 90°

c = 2

We know that sum of angles in a triangle is 180° and so;

A = 180 - (90 + 26)

A = 64°

By trigonometric ratios;

b/2 = sin 26

b = 2 * sin 26

b = 2 * 0.4384

b = 0.88

a/2 = cos 26

a = 2 * cos 26

a = 1.798

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Answer:

10 degrees

Step-by-step explanation:

8x = 2x + 60

6x = 60

x = 10

Answer:

A

Step-by-step explanation:

Find the ratio of pounds to dollars, [tex]\frac{3}{2}[/tex] or 1.5.

Next test each option by multiply the pounds by that ratio.

A: 28*1.5=42

B: 23*1.5=34.5

C: 11*1.5=16.5

D: 10*1.5=15

You can see A is the incorrect answer as 28 pounds would be 42 dollars, not 44.

The volume of the shelter is 1108.25 cu. ft.

A cuboid is a three-dimensional figure with 6 faces, all the faces are rectangular in shape.

The volume is the space occupied by it in a three-dimensional figure.

The volume of a cuboid whose length is l,

The width is w, and

Height is h.

V = length * Width * Height

V = lwh

The length of the shed is 16.25 ft.

The width of the shed is 11 ft.

The height of the shed is 6 1/5 ft

The height of the shed is 31/5 = 6.2ft.

The volume of the shed is given by

V = 16.25 * 11 * 6.2

V = 1108.25 cu.ft

Therefore, the shed has a volume of 1108.25 cu.ft.

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To fill in the values we have the following

a. log6⁰, log 2 . 1, log 8/3

b. log 1 .4 , 1 , log 4. 6

c. log 9/2, log 3. 5 , log 5⁷

To do this, you have to decide on that particular number that you want to find the logarithm on. Next you have to find the base of that number.

The logarithm of the number is the power that it would have to be raised for us to obtain a different number. You have to note that the logarithm of the number is the exponent that a base would have to be raised up to in order to get a particular number.

Log6⁰ for instance would give us the solution of 1 as the answer. While telling us that we have that the exponent is 0 while the base is 6.

One good property of logarithm is that log m/n = log m - log n also when we have log mn, it is the same as log m * log n

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Triangles DEF and JKL can be proven to be congruent triangles based on:

C. ASA

E. AAS

F. LA

The ASA congruence theorem states that if two triangles that are have two pairs of corresponding congruent angles and a pair of corresponding included congruent sides, then both triangles are congruent to each other.

The LA congruence theorem states that two right triangles are congruent if they have a pair of congruent legs and a pair of congruent angles that are corresponding to each other.

The AAS congruence theorem states that two triangles with two pairs of congruent angles and a pair of congruent non-included sides are congruent.

From the image given, triangles DEF and JKL can be proven to be congruent triangles using the LA, AAS, and ASA congruence theorems.

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Answer:

[tex] {216 \: in}^{3} [/tex]

Step-by-step explanation:

Split the chimney into 2 rectangular prisms. One is the short one, and the other is the tall one.

The dimensions of the short prism are 4 x 3 x 2. The volume of that prism is found by multiplying those numbers together, which is 24.

The dimensions of the tall prism are 4 x 4 x 12. The volume of that prism is 192.

Adding those 2 volumes together, you will get the volume of the composite figure. 192 + 24 = 216

Volume is always in cubic units

Answer: B

Step-by-step explanation: what I did was I drew a square and folded it if both sides matched i knew that that was a line of symmetry

In this case this "of" means we will multiply the two fractions "4/5 × 3/4" exists 3/5.

That operation exists utilized to 'simplify' a fraction (reduce it to lower terms).

When there exists no number that goes into both the top and bottom numbers, then the fraction is in simplest form (lowest terms).

We are looking for 4/5 of 3/4. In this case this "of" means we will multiply the two fractions. To multiply fractions, we multiply

top × top and bottom × bottom

4/5 × 3/4 exists 4 × 3 on top and 5 × 4 on the bottom.

= (4 × 3)/(5 × 4)

= 12 / 20

= 3 / 5

Therefore, the correct answer is 3/5.

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The number of rectangles of different sizes can be formed from 36 identical rectangles is 5

From the question, we have proofs of;

Total number of identical squares = 36

Now, let the measurement of the side of each square be 1 unit

We have that the formula for area of a square is;

Area of a square = Side × Side square units

We have the area of the square to be;

Area of each square = 1×1 = 1 square units

This is so because the rectangles are identical both in length and width

Let's find the area of the identical squares

Area of total 36 identical squares

=  36×1 square units

=  36 square units

So Area of the rectangle = length × breadth square units

if the rectangles are formed from 36 identical squares then their areas are the same

Total area of required rectangles = 36 square units

It can be written as;

36 = length × breadth

(1,36) , (2,18),(3,12),(4,9),(6,6) are the different rectangles formed from 36 identical squares

Total rectangles = 5

Thus, the number of rectangles of different sizes can be formed from 36 identical rectangles is 5

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To find the area, we take into account that your data is:

To calculate the area of the circle, we use the following formula:

Area: π * r²

We substitute the data in the formula, and we begin to solve.

taking the square root

Multiply the two numbers

Therefore, the area of the circle is 113.04 cm². The correct alternative is option "A".

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In the question, it is given that a circle has a radius of 6 cm , we have to find the Area.

To Find the area of the circle , we must know this formula:

[tex] \quad\quad\quad \longrightarrow\underline{\boxed{\color{violet}{A=\pi*r^2}}}[/tex]

Now, we will substitute the values in the formula:

[tex]\rightarrow\sf{A=\pi*r^2} \: \: \: \: \: \: \: ( \red{\pi = 3.14})[/tex]

[tex]\rightarrow\sf{A = 3.14 * 6^2}[/tex]

[tex]\rightarrow\sf{A = 3.14 * 36}[/tex]

[tex]\rightarrow\sf{A = 113.0}[/tex]

The area of circle is 113.0 approx .

[tex] \color{blueviolet}{ \mathfrak{llNotYourll}}[/tex]

Answer:

40

Step-by-step explanation:

11+29=40

Answer:

B)0 to 21 electoral votes

Step-by-step explanation:

edge 2023

Answer:

Q₃ = 185

Step-by-step explanation:

the first step is to find the median of the data set

the median is the middle value of the data arranged in ascending order

112 , 130 , 132 , 140 , 149 , 151 , 163 , 172 , 185 , 190 , 200

                                            ↑ middle value

median = 151

the upper quartile Q₃ is the middle value of the data to the right of the median

163 , 172 , 185 , 190 , 200

                   ↑ middle value

upper quartile Q₃ = 185

Answer:

Perimeter is 4a - 10

Area is a^2 - 5a

Step-by-step explanation:

Two sides of the rectangle are "a" and two sides of the rectangle are "a-5"  add all four sides and you get a+a+a-5+a-5  Combine the like terms and you get 4a - 10.

The area is when you multiple the two sides together

A = lw

A - a(a-5) = a^2 - 5a

Answer + Step-by-step explanation:

(a)

Check the attached image.

(b)

Range of sample means : 7.5 - 5.75 = 1.25

(c)

The closer the range of the sample means is to 0 ,

the more confident they can be in their estimate . [tex]\huge \checkmark[/tex]

The farther the range of the sample means is from 0 ,

the more confident they can be in their estimate . 

The mean of the sample means will tend to be a better estimate

than a single sample mean . [tex]\huge \checkmark[/tex]

A single sample mean will tend to be a better estimate

than the mean of the sample means .

Answer: A

Step-by-step explanation:

Let f(y)=x.

[tex]x=\frac{y+2}{7}\\\\7x=y+2\\\\y=7x-2\\\\f^{-1}(x)=7x-2[/tex]

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

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.

We know that,

A dummy variable is a binary variable that takes a value of 0 or 1.

In regression analysis, a dummy variable is one that takes only the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.

The number of dummy variables we must create is equal to k - 1, where k is the number of different values that the categorical variable can take on.

It is an artificial variable created to represent an attribute with two or more distinct categories/levels.

These are being used in order to sort out data into mutually exclusive groups.

It is used typically in time series analysis, response modelling, bio-medical studies, economic forecasting and credit scoring.

Therefore, a variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.

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The mean in minutes of the length of time given= 9.1

The formula used for the determination of mean when a frequency table is given is

= total/n

Where total = frequency×midpoint

n = 42

To calculate the total, the mid point of each length of time is determined as follows;

1+4/2 = 2.5 × 4 = 10

4+7/2= 5.5 × 8 = 44

7+10/2 = 8.5 × 14= 119

10+13/2 = 11.5× 9 = 103.5

13+16/2= 14.5×5 = 72.5

16+19/2= 17.5× 2= 35

Total= 10+44+119+103.5+72.5+35 = 384

Therefore mean = 384/42= 9.1

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