Mathematics High School

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?

Answers

Answer 1

Considering the data in the table, it is found that:

a) The scatter plot is given by the image at the end of the answer.

b) The correlation of the scatter plot is negative, as when the input increases the output decreases.

c) The estimate for the depth at 15 seconds is of 50.37 cm.

How to built the scatter plot?

The scatter plot is built inserting all the points in the table, which are in the following format:

(Time, Depth).

Hence the points are given as follows:

(2, 47), (4, 41), (6, 38), (8, 37), (10, 32), (12, 24), (14, 20), (16, 19).

From both the table and the scatter plot given by the image at the end of the answer, as the input increases, the output decreases, hence the scatter plot has a negative correlation.

To make a prediction for a given input, the line of best fit has to be constructed using these points.

Inserting these points into a linear regression calculator, the line of best fit is:

y = -2.07x + 50.89.

At a time of 15 seconds = 0.25 minutes, the depth will be of:

y = -2.07 x 0.25 + 50.89 = 50.37 cm.

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Related Questions

Two number have a product of 7. One of the number i 4 2/3, what i the other number?

Answers

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.

Solution

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.

Statement Let V be any vector space and let x, y, z be in V. Prove that if x + z = y + z, then x = y. Proof Suppose for full generality that V is any vector space and x, y, z are any vectors 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+(-2) = 0 because implies Thus, x +z = y + z (x + 2) + (-2) = (y + 2) + (-2) and thus x+(2+(-2)) = y + (z + (-2)) because X+0 = y + 0 because and thus X = y by properties of the zero vector. Therefore, x +z = y + z implies x = y, and V has the cancellation property

Answers

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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Help me with this problem 16 point s

Answers

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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A woman who is 64 inches tall has a shoulder width of 16 inches.
Write an equation relating the height h to the width w. Find the height
of a woman who has a shoulder width of 18.5 inches. I know we have to multiply 18.5x4 but why?

Answers

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

What is Proportion?

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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Rewrite the following equation in slope-intercept form.
y + 6 = 9(x − 8)
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y = 9x -78

Step-by-step explanation:

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

Solution

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.

Find the unit vector in the direction of < 5, −7 >

Answers

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

How to determine the unit vector in the direction of a given vector

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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A container releases fuel at a rate of 5 gallons per second. If y represents the amount of fuel remaining in the container and x represents the number of seconds that have passed since the fuel started dispensing, then x and y satisfy a linear relationship. If the tank begins with 103 gallons, how many gallons will remain after 2 seconds?

Answers

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

How many gallons will remain after two seconds?

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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There are 10 squares and 2 circles. What is the simplest ratio of circles to squares?

Answers

Answer: 5:1

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

least common
Denominator of 7/2 &
3/10

Answers

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.

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.

Answers

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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i will mark brainliest pls help it was due last week

Answers

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

-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:

Which is an equation of the line that passes through the points (0, 0) and (1,
4)?
y = x + 1
y = 4x + 1
y = x
y = 4x

Answers

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

y = mx + b

y = 4x + b

substitute (0, 0) to find b

b = 0

y = 4x

Of 350 solitaire games that Jay played, he won 154 times. What percent of the games did Jay win?

Please help

Answers

The percentage of games which Jay won is 44 percent.

What is Percentage?

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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Solve
n=5(m^2+D)
(It's a literal equation)

Answers

Step-by-step explanation:

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

Add the fractions. **Remember to have a common denominator.**
1/4 + 1/3

Answers

first, you make it into a equivalent fraction by finding a common denominator for both of the fractions, now the problem is 3/12+ 4/12. Now add them together and get 7/12 as ur answer

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.

is a stockbroker. earns 12% commission each week. Last week, sold 7200$ worth of stocks. How much did make last week in commission? If averages that same amount each week, how much did make in commission in 2011?

Answers

The amount earned as commission in 2011 is $44928

How to determine the amount earned as commission?

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

Answers

Answer:

Step-by-step explanation:

Which transformation can be applied to the blue figure to create the red figure?

Answers

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.

Which sequence of transformations map the blue figure into the red one?

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:

rotation of 90° clockwise.reflection across the y-axis.

Notice that this is equivalent to:

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

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

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What’s the unit rate for three dollars for 2 1/2 hours of work

Answers

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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Without using a calculator, choose the statement that best describes the value of

Answers

Answer:

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)

f(x)=-x^2-7x please answer

Answers

Answer:

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

Create an equivalent expression for (1.3 3/1.2 4)-6

1.2²4/1.3 18

1.2²/ 1.3 3
1.3 18/ 1.2 24
1.3 3 / 1.2²

Answers

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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Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
4
6

Answers

20, you multiply 4x6 which equals 24 and round it to 20

HELP WHATS IS A multi step equation that has a variable on both side that equals 10

Answers

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

The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam
Passed exam Did not pass exam Row Totals
Completed exam review
55%
10%
65%
Did not complete exam review
20%
15%
35%
Column Totals
75%
25%
100%
Part A: What is the percentage of students who completed the exam review, given that they passed the exam? Round to the nearest percentage. (2 points)
Part B: What is the percentage of students who completed the exam review, given that they failed the exam? Round to the nearest percentage (2 points)
Part C: Is there an association between completing the exam review and passing the exam? Justify your answer. (2 points)

Answers

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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Find the value of X
(Triangle Congruence)

Answers

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°

Sharon spent #13.60 on baseball Cards. She bought 16 packs How much did each pack cost?

Answers

Answer:

#0.85

Step by step:

13.60/16 = #0.85

pls give me brainliest

pls:(

(Please help quick!)

Which rectangle has the same area as the triangle
shown?

Answers

Bottom left. The triangle’s area is 12. The bottom left is the only one that’s equal to 12.

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

The correct option is third shape.

What is area?

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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Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (1,0,0) (x, y, z) =( (b) (18, 1/3, 1/4) (X, Y, z)

Answers

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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Find an
for a line parallel to
4x + 5y + 2 = 0, with an
an x-intercept of 3

Answers

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

How to determine the line equation?

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

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?

Answers

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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?