What is the correlation coefficient for the data shown in
the table?
О о
0 1
04
05

The triangles are congruent by SAS congruence theorem

From the figure, we have the following congruent sides

Also, both triangles share a common vertex at B

This means that:

<B = <B

Two sides and one angle are congruent in the triangles

Hence, the triangles are congruent by SAS congruence theorem

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Answer:

x < 7

Step-by-step explanation:

The domain encompasses all the "x" values (or inputs) of a function.

The arrow on the left line symbolizes that the function continues into the negative region for infinity. As such, this eliminates option C.

Closed dots are points whose "x" values are included in the function. Open-dots are on points whose "x" values are not included in the function. Although the open-dot on the left line at x = -1 generally means it is not included in the function, the closed dot on the right line overrides this. Therefore, x = -1 is in the domain. The value x = 7 is not within the domain of the function due to the open-dot. This eliminates option B and option D.

With this said, the domain of the function is x < 7.

The probability of first rolling a 1, then a 5, will be [tex]\frac{1}{36}[/tex].

To find the probability of getting a 1 the first time and a 5 the second time:

Probability of getting 1 in 1st time = [tex]\frac{1}{6}[/tex]

Probability of getting 5 in 2nd time = [tex]\frac{1}{6}[/tex]

The probability of first rolling a 1, then a 5, will be = [tex]\frac{1}{6}[/tex] × [tex]\frac{1}{6}[/tex]

[tex]= \frac{1}{36}[/tex]

Therefore, the probability of first rolling a 1, then a 5, will be [tex]\frac{1}{36}[/tex].

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The height of the cylinder is 4 x units.

The area of the cylinder’s base is One-fourthπx2 square units .

What is the volume of cylinder?

We know the volume of a cylinder is given by the formula  π r2 h, where r is the radius of the cylinder and h is the height.

Formula for volume of the cylinder

V = r² π h

Volume of the cylinder= πx³

Diameter=x

Radius (r)=diameter/2

       r  =  x/2

     V = r² π h

   πx³=(x/2)² πh

πx³= (x²/4)πh

Divide both sides by π

x³ =(x²/4)h

Make h the subject of the formula

  h = x³ ÷ x²/4

     =x³ ×4 / x²

     =4x³ / x²

     =4 * x * x * x / x * x

  h=4x

Area of the base:

B = r² π

r=x/2

B=(x/2)² * π

 =(x²/4)π

=πx²/4

=1/4(πx²)

Therefore, The area of the cylinder’s base is One-fourthπx2 square units.

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The complete question is -

A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.

The rational numbers are -5/250, [tex]\sqrt{400}[/tex] ,and irrational numbers are 5.012121212......., [tex]\sqrt[3]{30}[/tex] , 0.01562138411........,[tex]\sqrt{1000}[/tex]

Given six numbers:5.012121212..,[tex]\sqrt{1000}[/tex],[tex]\sqrt[3]{30}[/tex], -5/250,  0.01562138411.....,[tex]\sqrt{400}[/tex].

We have to identify which numbers are rational and which are irrational numbers.

Rational numbers are those numbers which can be written in p/q form where q cannot be equal to zero because if q is zeo then the value of p/q will be infinity.

Irrational numbers are those numbers which cannot be written in p/q form.

First number :5.0121212121....

In the above numbers 12 is repeating next to the decimals. So it is a irrational numbers.

Second number:[tex]\sqrt{1000}[/tex]

If we solve the above number we will find it 31.6227766017 . It is cannot be expressed in p/q form, so it is irrational number.

Third number:[tex]\sqrt[3]{30}[/tex]

The abov number is irrational number as we cannot express it in p/q form.

Fourth number:-5/250

The value of above number is -0.02.It can be in the form of -2/100. so it is rational number.

Fifth number:0.01562138411........

Because the digits are repeating after decimals so it is irrational number.

Sixth number:[tex]\sqrt{400}[/tex]

The value of above number is 20, so it is rational number.

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Question is incomplete as it should include figure.

The ordered pairs of Nicole and Ian's sequence pattern are:(5,1),(17,3),(53,5),(161,10),(485,20).

Given that Nicole uses the  rule multiply by 3 then add 2 starting with it and Ian uses the rule add 1/2 then multiply by 2 starting from 0,

We ar rquired to find the ordered pairs of Nicole's and Ian's rules.

We are told that Nicole's pattern is multiply by 3 then add 2 starting with 1.

Thus Nicole's pattern is :5,17,53,161,485.

Ian's pattern is add 1/2 then multiply by 2 and starting with 0.Thus the  numbers are :1,3,5,10,20.

If we combine the numbers of both the person'rule then we will get the ordered pairs which can be written as under:

The ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).

Hence the ordered pairs are (5,1),(17,3),(53,5),(161,10),(485,20).

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Answer:

The slope is -2

Step-by-step explanation:

To find the slope, we can use the slope formula

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

    = (-1 -3)/(-1 - -3)

   = ( -1-3)/(-1+3)

   = -4/2

   = -2

The slope is -2

The cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.

If the peak of the rectangular pyramid is directly above the center of the base, it creates a perpendicular to the base, indicating the height of the pyramid. This type of rectangular pyramid is known as the right rectangular pyramid.

A rectangle is a quadrilateral, that is a closed figure with 4 line segments, with all four interior angles at 90°.

When we slice a right rectangular pyramid vertically down at the red line by a plane, not passing through the vertex, of the pyramid will be a dilated image of its base.

A dilated image is an enlarged or diminished image of the preimage, similar with all angles.

Thus, the cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.

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For complete question, refer to the attachment.

Answer:trapozoid

Step-by-step explanation:

(a) The city with a larger median room temperature is city B.

(b) The city having the highest noon temperature is city B.

(c) The city having the noon temperatures with a higher interquartile range is city A.

(d) The city having more noon temperatures that 81°F is city B.

In the given question, the noon temperatures for two cities, A and B, recorded over a month are shown via the box-and-whisker plots.

We are asked to use it and answer the questions:

(a) The median of data is represented by the line in the box of the box-and-whisker plot. Thus,

The median noon temperature for city A is 73°F.

The median noon temperature for city B is 76°F.

Thus, the city with a larger median room temperature is city B.

(b) The highest temperature is seen as the end point of the whiskers. Thus,

The highest temperature for city A is 85°F.

The highest temperature for city B is 92°F.

Thus, the city having the highest noon temperature is city B.

(c) The interquartile range is the difference between the end line of the box and its start line. Thus,

The interquartile range for city A is (81 - 64)°F or 17°F.

The interquartile range for city B is (81 - 68)°F or 13°F.

Thus, the city having the noon temperatures with a higher interquartile range is city A.

(d) From the given box-and-whisker plots, we can see that after 81°F, city B has a long whisker, showing more outliers.

Thus, the city having more noon temperatures that 81°F is city B.

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Both ran equal and both covered equal distance.

As cruz ran 1 lap out of 4 to cover one mile.

and erica ran 3 lap out of 12 to cover one mile:

3/12 = 1/4

So Cruz = Erica = 1/4.

Hence Both ran equal.

Fraction:

Fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

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Answer:

7x = 14

x + 4y = 2

Step-by-step explanation:

3x − 2y = 6

x + 4y = 2

6x - 4y = 12

x + 4y = 2

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

7x = 14 Replace the first equation with this one.

Answer:

x-intercept = 8

Step-by-step explanation:

Hello!

An x-intercept is when the y-value is 0, or when the graph intersects the x-axis.

We can replace p(x) with 0 and solve for x.

The x-intercept is 8.

The probability of rolling an even number with six sided equally weighted die is 0.5.

Given a six sided equally weighted die.

We are required to find the probability of rolling an even number.

Probability is the calculation of  likeliness of happening an event among all the events possible. It lies between 0 and 1. It can be calculated  through simple values and with the formula of combination also. The formula of calculating probability is as under:

Probability= number of items/ total number of items.

Total sides in die=6

Total numbers=1,2,3,4,5,6, therefore 6.

Even numbers=2,4,6. Therefore 3.

Probability = even numbers/total numbers.

=3/6

=1/2

=0.5

Hence the probabilty of receiving an even number from a six sided equally weighted die is 0.5.

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Equation of the line which is passing through the points [tex](-1,7)[/tex] and perpendicular to the line [tex]$y=-\frac{1}{8}x-1$[/tex]

is [tex]y=8x+15[/tex]

How to find the equation which passing through one point [tex](-1,7)[/tex]and perpendicular to the equation [tex]$y=-\frac{1}{8}x-1$[/tex] ?

We know that the equation of line in form of slope and point is

[tex]y-y_{1} =m(x-x_{1} )[/tex]

So first equation of line which is passing through point [tex](-1,7)[/tex] is

[tex]y-7=m_{1} (x-(-1))\\y-7=m_{1}(x+1)[/tex].....(a)

Line [tex]$y=-\frac{1}{8}x-1$[/tex] perpendicular to the line (a)

And we know when two lines are perpendicular then

[tex]m_{1} m_{2} =-1[/tex]

So [tex]m_{1} =-1/m_{2}[/tex]

and we know [tex]m_{2} =-1/8[/tex]

So

[tex]m_{1} =-1/\frac{-1}{8} \\=-1*8/-1\\=8[/tex]

The equation of the line is

[tex]y-7=8(x+1)\\y-7=8x+8\\y=8x+8+7\\y=8x+15[/tex]

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Answer: The figure changed size.

Step-by-step explanation:  Dilations change the sizes of shapes.  They can either make them bigger or make them smaller.

Answer:

100.5 inches

Step-by-step explanation:

If each course has 3/8 inch of concrete below it  (including the bottom one)

  8 in * 12   + 3/8 in * 12 = 100 1/2 inches

The general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41

The given parameters are

Center = (0, 0)

Point = (4, 5)

Rewrite the given parameters are

(a, b)= (0, 0)

(x, y) = (4, 5)

The general form of the equation for the given circle is represented as:

(x - a)^2 + (y - b)^2 = r^2

Substitute the known values in the above equation to calculate the radius r

(4 - 0)^2 + (5 - 0)^2 = r^2

Evaluate the difference

4^2 + 5^2 = r^2

Evaluate the exponent

16 + 25 = r^2

Evaluate the sum

41= r^2

Rewrite as

r^2 = 41

Substitute r^2 = 41 in (x - a)^2 + (y - b)^2 = r^2

(x - a)^2 + (y - b)^2 = 41

Substitute (a, b)= (0, 0) in (x - a)^2 + (y - b)^2 = 41

(x - 0)^2 + (y - 0)^2 = 41

Evaluate the difference

x^2 + y^2 = 41

Hence, the general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41

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The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;

It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.

The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.

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The quantity of deciliters of apple juice a medium bottle contain is 10 deciliters

4s + 3l = 64

3s + 2l + 2m = 64

6s + 4m = 64

If

m = 10

s = 4

l = 16

Check:

3s + 2l + 2m = 64

3(4) + 2(16) + 2(10)

= 12 + 32 + 20

= 64

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Answer:

Graph number 2

Step-by-step explanation:

See attached image.

Given that price was $520 after a 30% increase,  the original price was $400.

Given that;

To determine the original price, we say;

x × ( 100% + 30% ) = $520

x × ( 130% ) = $520

x × (130/100) = $520

130x / 100 = $520

130x = $52000

x = $52000 / 130

x = $400

Given that price was $520 after a 30% increase,  the original price was $400.

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Using translation concepts, the correct values are given as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Researching this problem on the internet, we have that:

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answer:

+16

steps:

number without the x should be 9

number without the x should be 9c to be 9 needs +16

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divide the number next to the x by 2

-6 divided by 2 is -3

find the square

-3 squared is 9

number without the x should be 9

x²-6x=7

make the equation = 0

x²-6x-7=0

a is the number next x²

b is the number next to x

c is the number without the x

c has to be 9

c is -7

c to be 9 needs +16

x²-6x+9 =0

x²-6x+(-3)² =0

(x-3)²

Answer:

9

Step-by-step explanation:

Completing the square  is a method used to solve the quadratic equation.

        Coefficient of x is '6'. 6 ÷ 2 = 3

       3² = 9

            x² - 6x + 9 = 7 + 9

Answer: To make into a perfect square, 9 must be added.

Answer:

of course 0

Step-by-step explanation:

because it doesn't have any value in its first equation

Answer:

B.

Step-by-step explanation:

Vertex with (2,4) means that the equation will have:

y=a(x-2)^2 + 4

Open downwards means that the a will be negative:

so: y = -a (x-2)^2 + 4

Stretched by a factor of 3 means that the a=3

So if we combine all of these, we will get the equation:

y = -3 (x-2)^2 + 4

The extreme value of y = (x - h)² - c is the vertex of the equation.

The extreme values of a function are either the maximum or minimum values of the function.

The equation of a parabola in vertex form with vertex (h', k) is given by

y = a(x - h')² + k and its extreme values are

Since y = (x - h)² - c is the equation of a parabola in vertex form, comparing with y = a(x - h')² + k,

So, the cooordinates of the vertex of y = (x - h)² - c is (h, -c).

Now, since a = 1 > 0, (h, -c) is a minimum point.

So, the extreme value of y = (x - h)² - c is the vertex of the equation.

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Answer:

The lowest value is at (1, -8). H and C are equal to 1 and 8 in the equation y = (x - 1)2 - 8. Therefore, the minimum's x-coordinate corresponds to the equation's h-value, and its y-value is the opposite of the c-value.

Step-by-step explanation:

i re wrote it

The values which completes the table regarding summer camp is option b which is a=15,b=7, c=5, d=10, e=12.

Given that there are 32 campers, 22 of them can swim, 20 play softball and 5 do not play softball or swim.

We have to find the values of a,b,c,d,e so that we can complete the table.

Table is a combination of rows and columns. In our case the third row and third column shows the total.

from the table we can write that 22+d=32-----------1

so d=32-22

=10

d=10

c+5=d-----------2

c=10-5=5

c=5

a+c=20------------------3

a+5=20

a=20-5

a=15

a+b=22--------------3

15+b=22

b=7

20+e=32----------4

e=32-22

e=10.

Hence the values which completes the table is a=15,b=7, c=5, d=10,  e=12.

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Question is incomplete as it should include figure showing table of values.

The volume of the cylinder is approximately, 1,539.4 cubic meters.

Volume of a cylinder = πr²h

Given the following:

Diameter of cylinder = 14 m

Radius (r) = 14/2 = 7 m

Height of cylinder = 10 m

Volume of cylinder = πr²h = π(7²)(10)

Volume of cylinder ≈ 1,539.4 cubic meters.

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