9. Emily measured the depth of water in a bathtub at two-minute intervals after the tap was turned off and the
stopper released. The table shows her data.
a) Make a scatter plot for the data.
b) Describe the correlation of the scatter plot.
c) What will the approximate depth be at 15 seconds?

The vector <5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.

Vectors are described by two features: (i) magnitude, (ii) direction. The magnitude is the quantity associated with a vector and determine by Pythagorean theorem, and the direction indicates the "distribution" of the magnitude along the ortogonal axes of the vector. Unit vectors are vectors of magnitude 1 and we can determine it by using the following definition:

[tex]\vec u[/tex] = <x, y> / ||<x, y>||

Where ||<x, y>|| = √(x² + y²)

Please notice that [tex]\vec u[/tex] represents the unit vector.

If we know that <x, y> = <5, - 7>, then the unit vector is:

Magnitude

||<x, y>|| = √[5² + (- 7)²]

||<x, y>|| = √74

Unit vector

[tex]\vec u[/tex] = <5, - 7> / √74

[tex]\vec u[/tex] = <5 / √74, - 7 / √74>

[tex]\vec u[/tex] = <5√74 / 74, - 7√74 / 74>

<5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.

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Answer:

  y = 9x -78

Step-by-step explanation:

You want the equation y + 6 = 9(x − 8) written in slope-intercept form.

Solve for y and simplify.

  y +6 = 9x -72 . . . . . . . . eliminate parentheses

  y = 9x -78 . . . . . . . . . subtract 6

__

Additional comment

The given equation is written in point-slope form. It has a slope of 9 and goes through the point (8, -6).

Slope-intercept form is ...

  y = mx +b

where m is the slope and b is the y-intercept.

The difference is 4[tex]x^{2}[/tex] - 14x - 4

Given,

In the question:

To find the difference:

The difference of [tex]2x^2-9x+8[/tex] subtract from [tex]6x^2 -5x-12[/tex] .

Now, According to the question:

Based on the given condition:

Formulate:

[tex]6x^2 -5x-12[/tex] -  [tex]2x^2-9x+8[/tex]

Simplify and expand:

[tex]6x^2 -5x-12[/tex]  - [tex]2x^2-9x+8[/tex]

Reorder and gather like terms:

[tex](6x^2-2x^2)[/tex] + (-5x - 9x) + (-12 + 8)

Collect coefficient of like terms

(6 - 2)[tex]x^{2}[/tex] + (-5 -9)x + (-12 + 8)

Calculate the sum or difference:

4[tex]x^{2}[/tex] - 14x - 4

Hence, The difference is 4[tex]x^{2}[/tex] - 14x - 4 .

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Answer:

#0.85

Step by step:

13.60/16 = #0.85

pls give me brainliest

pls:(

The rectangle with the sides 4 and 3 is the required rectangle.

The correct option is third shape.

Area is the amount of area occupied by an object's flat (2-D) surface or shape.

The area of the triangle,

= 1/2 x base x height

= 1/2 x 6 x 4

= 12 square millimeters.

And rectangle has the same area as the triangle.

The rectangle with the sides 4 and 3 is the required.

Therefore, the rectangle with the sides 4 and 3 is the required rectangle.

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Answer: 10

Step-by-step explanation: The least common denominator is 10 because both integers 2 and 10 have a LCM OF 10. Your welcome. :’j

Answer: 10

Step-by-step explanation: The least common denominator is 10, cuz it is the lowest common multiple of 10 and 2, 2 × 5 =10, 10× 1 = 10. they r both common multiples.

The rectangular coordinates are

a. (1,0,0) ⇒ (x,y,z) = (0,0,1)

b. (18,1/3,1/4) ⇒ (x,y,z) = (11.022,11.022,9)

Let us take ( x, y, z ) as cartesian or rectangular coordinates and ( r, Θ, ∅ ) are the spherical coordinates, then

x   =   r.sinΘ.cos∅      →   1

y   =   r.sinΘ.sin∅       →   2

z   =   r.cosΘ               →   3

According to the given problem,

a.)   ( 1, 0, 0 )  =   ( r, Θ, ∅ )

Substitute the values r = 1, Θ = 0 and ∅ = 0 in 1, 2, 3.

1 ⇒ x   =   r.sinΘ.cos∅          

           =   1.sin0.cos0

           =   1.0.1

      x   =   0

2 ⇒ y   =   r.sinΘ.sin∅

            =   1.sin0.sin0

            =   1.0.0

      y   =   0

3 ⇒ z   =   r.cosΘ

            =   1.cos0

            =   1.1

       z   =   1

∴   ( x, y, z )   =   ( 0, 0, 1 )

b.)   ( 18, π/3, π/4 )   =   ( r, Θ, ∅ )

Substitute the values r = 18, Θ = π/3 and ∅ = π/4 in 1, 2, 3.

1 ⇒ x   =   r.sinΘ.cos∅

           =   18.sinπ/3.cosπ/4

           =   18.√3/2.1/√2

      x   =   11.022

2 ⇒ y  =   r.sinΘ.sin∅

           =   18.sinπ/3.sinπ/4

           =   18.√3/2.1/√2

       y  =   11.022

3 ⇒ z   =   r.cosΘ

            =   18.cosπ/3

            =   18.1/2

       z   =   9

∴   ( x, y, z )   =   ( 11.022, 11.022, 9 )

Therefore the rectangular coordinates for the spherical coordinates of

a. ( 1, 0, 0 )   is   ( 0, 0, 1 )

b. ( 18, 1/3, 1/4 )   is   ( 11.022, 11.022, 9 )

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The amount earned as commission in 2011 is $44928

From the question, we have the following parameters that can be used in our computation:

Commission percentage = 12%

Average sales per week = $7200

The amount earned as commission in the 2011 is then calculated as

Amount = Commission percentage x Average sales per week x Number of weeks

Substitute the known values in the above equation

So, we have

Amount = 12% x 7200 x 52

Evaluate

Amount = 44928

Hence, the commission amount is $44928

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Answer:

Step-by-step explanation:

an equation that takes two or more steps to solve is called a multi-step equation. let's take a multi-step equation that will satisfy the given condition:

4x - 8 = 22 + x

4x -x = 22 + 8      

3x = 30

x = 10          

Answer:

B

Step-by-step explanation:

Alright, to start off... we need to find a range of value that sqr 74 is between.

To do that, we can check by just trying some random numbers.

Let's try 8 -- 8^2 is 64. Let's try 9 -- 9^2 is 81. So the sqr 64 is 8 and sqr 81 is 9.

sqr 74 is between sqr 64 and sqr 81, so the statement is true. However, the multiple-choice has decimal numbers, meaning that they want us to be more specific.

First, we can cross out 9.5, because we don't want to expand our range, we want to keep it as accurate as possible.

That leaves us 8.5

To find if 8.5 fits the criteria, meaning that it can't be larger than sqr 74, we can use two methods.

The first method is preferred, you simply need to multiply them. I hope you know how to do that by hand. We get 72.25

The second method is less preferred but works. We need to approximate the value by finding the mean of 64 and 81, because 8.5 is the mean of 8 and 9. The approximate value should be very close to the true value. By doing (81+64)/2, we get 72.5

Now, double-check: is the 74 between 72.25 and 81? Yes, it is!
Hence, that gives us the answer that sqr74 is between 8.5 (sqr 72.25) and 9 (sqr 81)

By evaluating a linear equation, we will see that after two seconds there are 93 gallons of fuel.

We know that the tank initially has 103 galons of fuel, and we know that it releases 5 gallons per second at a constant rate.

So, after x seconds, the amount of fuel inside the container is:

F(x) = 103 - x*5

so we have a linear equation.

The amount of fuel in the tank after 2 seconds is given by:

F(2)=  103 - 2*5 = 103 - 10 = 93

After 2 seconds there are 93 gallons of fuel.

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Answer:

  1 1/2

Step-by-step explanation:

You want the other number when one of the two numbers that have a product of 7 is 4 2/3.

Let x represent the unknown factor. Then we have ...

  (4 2/3)x = 7

  (14/3)x = 7 . . . . . . write as improper fraction

  x = (3/14)(7) . . . . . multiply by the inverse of the coefficient of x

  x = 3/2 = 1 1/2

The other number is 1 1/2.

From the given relative frequency table , answer of the following questions are as follow:

a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.

b.  Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.

c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.

As given in the question,

From the given relative frequency table , answer of the following questions are as follow:

Total percentage of students completing the exam review = 65%

a. Completed the exam review with the condition that they have passed the exam = 55%

b. Completed the exam review with the condition that they have failed the exam = 10%

c. Yes, there is association between the two completing the exam review and passing the exam is only 55% and those who have completing the exam review but failed are 10%.

Therefore, from the given relative frequency table , answer of the following questions are as follow:

a. Percentage of students those who have completed the exam review with the condition that they have passed the exam is given by 55%.

b.  Percentage of students those who have completed the exam review with the condition that they have failed the exam is given by 10%.

c. Yes, there is association between the two completing the exam review and passing the exam is only 55%.

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Answer:

x = 139°

Step-by-step explanation:

The sum of the internal angles of a triangles is 180°

a + 59 + 80 = 180

a = 180 - 139

a = 41°

a and x are supplementary angles. Supplementary angles sum 180°.

Then:

a + x = 180

41 + x = 180

x = 180 - 41

x = 139°

Answer:

[tex]f( x) = x2 - 7 x[/tex]

The equation of the parallel line is 4x + 5y - 12 = 0

The equation is given as

4x + 5y + 2 = 0

The x-intercept is also given as

x-intercept = 3

We have

4x + 5y + 2 = 0

Make y the subject

5y = -4x - 2

Divide through by 5

y = -4x/5 - 2/5

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = -4/5

This means that the slope of 4x + 5y + 2 = 0 is =4/5

The slopes of parallel lines are equal

This means that the slope of the other line is -4/5

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = -4/5

(x₁, y₁) = (3, 0) i.e. the x-intercept

So, we have

y = -4/5(x - 3) + 0

Multiply through by 5

5y = -4(x - 3)

Open the brackets and evaluate

5y = -4x + 12

This gives

4x + 5y - 12 = 0

Hence, the parallel line has an equation of 4x + 5y - 12 = 0

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The height of woman who has a shoulder width of 18.5 inches is 74 inches.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Height of woman = 64 inches

Shoulder width = 16 inches

So, ratio = Height :  shoulder width = 64:16

let the height of a woman who has a shoulder width of 18.5 inches be x.

So, x:18.5.

Now,

64 / 16 =  x/ 18.5

4= x/18.5

x= 74

Hence, the height of woman who has a shoulder width of 18.5 inches is 74 inches.

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The unit rate of three dollars for 2 1/2 hours of work is 1.2.

The rate is a ratio of change in one quantity with respect to other. The unit rate is a rate such that the denominator of the rate must be one. An item's unit rate is its rate for one of them. How many units of the first type of quantity are needed to make up one unit of the second type is expressed using a unit rate (or unit ratio).

Now, finding the unit rate for three dollars for 2 1/2 hours of work,

Unit rate [tex]=\frac{3}{2.5}[/tex]

= 1.2

Therefore, the unit rate of three dollars for 2 1/2 hours of work is 1.2.

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Answer:

[tex]y=\frac{1}{2}x-5[/tex]

B: smaller rate of change but night y intercept

Step-by-step explanation:

y intercept is -5 because when x is zero y is -5

Now to find slope

-1-(-3)/8-4

-1+3/4

2/4

1/2

Now we can put it in an equation

y=1/2x-5

2nd question

-6-4/0-2

-10/-2

5

-6 is greater then -10 so the y intercept is bigger

So B is correct

Answer: i'm writeing this so you can mark the other person brainliest

Step-by-step explanation:

Answer:

ok

Step-by-step explanation:

The equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18]). So option(1) is correct.

Equivalent expressions are expressions that work the same way despite their appearance. When we plug in the same value(s) for the variable, two algebraic expressions have the same value (s).

Equivalent means that different terms and expressions with similar values are considered equal in mathematical form.

The given expression is

[(1.3^3)/(1.2^4)]^-6

Apply the indices power law to the above expression.

[(1.2^4)/(1.3^3)]^6

The exponents are then expanded using the power law of indices.

(1.2^[4x6])/(1.3^[3x6])

(1.2^[24])/(1.3^[18])

Hence, the equivalent expression of [(1.3^3)/(1.2^4)]^-6 is (1.2^[24])/(1.3^[18])

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slope = m = (4 - 0) / (1 - 0) = 4

y = mx + b

y = 4x + b

substitute (0, 0) to find b

b = 0

y = 4x

The percentage of games which Jay won is 44 percent.

This is referred to as a number or ratio expressed as a fraction of 100 and is usually denoted as %.

Percentage is calculated by : parts/whole × 100.

In this scenario we can deduce that the part is 154 while the whole is 350. Therefore: 154/350 × 100 = 44 percent.

Hence the most appropriate choice is 44 percent.

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Answer:

[tex] \sf \: \frac{7}{12} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{1}{4} + \frac{1}{3} [/tex]

[tex] \sf \rightarrow \: \frac{(1) \times 3}{(4) \times 3} + \frac{(1) \times 4}{(3) \times 4} [/tex]

[tex] \sf \rightarrow \: \frac{3}{12} + \frac{4}{12} [/tex]

[tex] \sf \rightarrow \: \frac{(3 + 4)}{12} [/tex]

[tex] \sf \rightarrow \: \frac{7}{12} [/tex]

Hence, the answer is 7/12.

Step-by-step explanation:

are you sure there is no other given info? do you have to solve in terms of m and D?

By the zero vector property x=y.

Suppose for full generality that V is any vector space and x,y,z is any vector in V. Suppose, x+z = y+z. Show that x=y. Since z is in v, there exists a vector z in v, such that

= z + (-z) = 0, because x+y=y+z

Thus x+z=y+z

= (x+z)+(-z) = (y+z)+(-z) and thus

= x+(z+(-z)) = y + (z+(-z)) because addition is associative in vector

= x+0 = y+0 because additive inverse exists in a vector

= and thus x=y by the properties of zero vector

Also according to the question, it is now proved that x+z=y+z implies x=y and v has the cancellation property.

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The sequence of transformations that we should apply is the one that appears on the top left option:

Reflection across the y-axis followed by a rotation of 90° counterclockwise.

We can see that the blue figure is on the third quadrant, and the "spiral" part is pointing upwards.

First, we would want to apply a rotation of 90° clockwise, this will move the blue figure to the second quadrant, and now the "spiral" part will point thowards the right.

Now you can see that the red figure is a reflection along the y-axis of the blue figure, so we need to apply that transformation.

Concluding, the sequence of transformations is:

Notice that this is equivalent to:

Then the correct option is the one in the top left corner.

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Using the completing-the-square method, find the vertex of the function f(x)=-2x^2+12x+5 and indicate whether it is a minimum or a maximum and at what point.

Given function is: [tex]f(x) = -2x^{2}+12x+5[/tex]

[tex]f(x) = a(x-h)^{2} +k[/tex] , where (h,k) is the vertex

Apply completing the square method to find vertex

[tex]f(x) = -2x^{2}+12x+5\\\\f(x) = -2(x^{2}-6x)+5[/tex]

Lets take half of coefficient of x is -6

divide by 2 that is -3

square it [tex](-3)^{2}[/tex] that is 9

Add and subtract 9

[tex]f(x) = -2(x^{2}-6x+9-9)+5[/tex]

Take out -9 and multiply by -2

[tex]f(x) = -2(x^{2}-6x+9)+18+5\\\\f(x) = -2(x^{2}-6x+9)+23[/tex]

Now factor the parenthesis part

[tex]f(x) = -2(x-3)^{2} +23[/tex]

The value of h=3  and k=23

So vertex is (3,23)

The value of 'a' is -2, it means the parabola is upside down. so vertex is maximum

Hence the answer is the vertex is maximum at (3,23)

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Answer: 5:1

Step-by-step explanation: 10:2 can be simplified by dividing both by 2, making it 5:1