The Data

Decorative glass pebbles are often used in vases for their appearance, and to have their weight stabilize the vase. The table below gives the total weight of a vase full of uniform glass pebbles.


TABLE OF DATA ATTACHED BELOW*


The Analysis

1- Using the table of data above, determine if this relationship is linear or not. Explain how you know.


2-Write an equation that best represents this relationship:
Explain how you reach your answer and show your work below.


3- Graph the data on the grid to the right, label both axes, and label it Line 1.

4-
a) What is the meaning of the initial value in this scenario?

b) What is the meaning of the slope in this scenario?


5- How would the graph AND equation change if a Styrofoam cup is used to collect the data, instead of a glass vase? Explain your reasoning.


6- Based on your equation in question #2, how much will 112 pebbles weigh with the vase?


7- If the total weight is 504 g, how many pebbles are in the vase?


8- Your friend Wilma shares her analysis of similar data about pebbles and a vase, but her equation is W = 10p + 80.


a) Graph it on the same grid as question #3. Label it Line 2.


b)What are the coordinates of the point of intersection?


c)What does it mean in this scenario?


9- Write a SIMPLIFIED algebraic expression to represent the area of the following trapezoid. Show all your work.
(Hint: area of a trapezoid = [tex]\frac{h(a+b)}{2}[/tex])

TRAPEZOID ATTACHED BELOW*

10- Tanya is 12 years older than Leah. Three years ago, Tanya was five times as old as Leah. What is the age of Tanya and Leah now?

I NEED IT TODAY PLESE!

The quotient in lowest term exists 2/3.

An improper fraction exists as a fraction whose numerator exists equivalent to, larger than, or of equivalent or higher degree than the denominator.

Given the quotient: [tex]$4\frac{2}{3} \div 7[/tex]

Write [tex]$\frac{2}{3}[/tex] in improper fraction

[tex]$4\frac{2}{3}= \frac{14}{3}[/tex]

Dividing throughout by 7 on both sides of the equation, we get

[tex]$4\frac{2}{3} \div 7 = \frac{14}{3}\div 7[/tex]

Change the division sign to multiplication by taking the reciprocal of 7

[tex]$\frac{14}{3}\div 7 = \frac{14}{3} \times \frac{1}{7}[/tex]

Simplifying the above equation, we get

[tex]$\frac{14}{3}\div 7 = \frac{2}{3}[/tex]

Therefore, the quotient in lowest term exists 2/3.

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The box and whisker plot is plotted with minimum value 24, maximum value 58, first quartile 29, third quartile 52 and median 40.

Given that, the ages of 15 music teachers in a school district are 24, 26, 27, 29, 29, 32, 37, 40, 40, 41, 45, 52, 56, 56, 58.

A box and whisker plot also called a box plot displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.

Minimum value = 24

Maximum value = 58

First quartile = 29

Third quartile = 52

Median = 40

Therefore, the box and whisker plot is plotted with minimum value 24, maximum value 58, first quartile 29, third quartile 52 and median 40.

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Answer:

A

Step-by-step explanation:

f(-3) = 2^-3

to get rid of a negative in an exponent, move the whole thing to the denominator.

1/(2^3)

2^3 = 2×2×2

1/(2×2×2)

1/8

A polynomial function exists a function that contains only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

The variety of function kinds can model circumstances in the real world. Properties or key components of functions create more or less suitable models, relating to the circumstances.

Linear: These relationships maintain constant rates of change. The distance traveled by a car moving at a constant speed over time exists linear.

Exponential: Connections that show a percent change exist exponential. The growth of a financial investment accumulating interest over time exists exponential.

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Answer:

130 degrees

Step-by-step explanation:

We know (x-10)+(2x+10) is 180 degrees.

So first we need to find x. (x-10)+(2x+10)=3x

3x=180

x=60

Angle TRV is 2x+10.

If we input 60 in the place of x, it is 2(60)+10=120+10=130.

The answer is 130 degrees.

Answer:

2

Step-by-step explanation:

slope : ( The amount y increases , when x is increased by 1 )

slope : { y2 - y1 / x2 - x1 }

slope : y2 = 2

           y1 = -4

           x2 = 5

           x1 = 2

You must minus the values in the formula to find the slope line that passes through the points:

slope : { y2 - y1 / x2 - x1 }

slope : (2) - (-4) / (5) - (2)

=> 2 + 3 / 3

=> 6/3

=> 2

Text explanation:

Difference between both y-coordinates. = 6

Difference between both x-coordinates. = 3

Divide the difference between y and x. =

y/x =2

Which means the slope of the line that passes through the points (2,-4) and (5,2) is 2.

Hope this helps! Sorry it took so long! ⸜(｡˃ ᵕ ˂ )⸝ xx

The slope of the line that passes through the points (2, -4) and (5, 2) is 2.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the line that passes through the points (2, -4) and (5, 2) can be calculated as shown below,

Slope = (y₂-y₁)/(x₂-x₁) =  [2 - (-4)] / (5 - 2)= 6/3 = 2

Hence, the slope of the line that passes through the points (2, -4) and (5, 2) is 2.

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Step-by-step explanation:

using gp formula

tn=ar^n-1

which our a which is the first term is = -3

our r which is t2/t1=-6

t8=(-3)(-6)^8-1

=(-3)(-6)^7

=(-3)(-279936)

=839808

The bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar

Feel great energy bars = Total cost / number of bars

= $18 / 12

= $1.5 per bar

Super power brand = Total cost / number of bars

= $21.75 / 15

= $1.45 per bar

Therefore, the bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar

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Answer: (a−c)(b−c)>0

Step-by-step explanation:

ab>1 and ac<01. a>0 if c<0 and also b>02. a<0 if c>0 and also b<0

how i did it:

At the vert first, write the inequality as an equation.

Solve the provided equation for one or more values.

Now, display all the values obtained in the number line.

Use open circles to show the excluded values on the number line.

Find the interim.

At the moment, take any random value from the interval and substitute it in the inequality equation to check whether the values reassure the inequality equation.

Intervals that reassure the inequality equation are the solutions of the given inequality equation.

The option that is true with regard to the following functions is Option B. "The domain g(x) and h(x) include all real number while the domain of i(x) and h(x) are restricted"

Note that this function is indicative of a straight-line. See the attached graph for function 1. Note that it doesn't have any end points. That is, it is Asymptote.

This represents an exponential graph. Just like the function above it doesn't have any end point. It however has an asymptote:

y = 0

This is indicative of logarithm graph. It doesn't have any end but has an asymptote x == 0

Notice that in the mid point there is an end point given as (0, -14). Thus, it is correct to state that the function in Option B is the only one that exhibits end behavior and as such is restricted.

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Answer: A. 33

Step-by-step explanation:

Answer:

15740000 million dollars in profit in year 4

Step-by-step explanation:

Now since you didn't provide the table, im going to have to assume the years are going to be the X while the Y is going to be profit.

Using the equation you provided y=-0.34x^2+4.43x +3.46, we can simply put 4 as our x value (since x represents years) and we would get 15.74. Now you have to remember to convert it into millions to show the profit so 15.74 times 1,000,000 would be 15740000 million dollars

the radius of the new circle =5cm

5cm is your answer love

Answer: No solution

Distribute the parenthesis

3x-15=2x-10+x

Combine like terms

3x-15=3x-10

This answer has no solution for x.

The numbers are 14.42 and 3.6055.

It is the whole which is to be divided into different equal parts. For example, if 10 divided by 2 is 5, then 10 is the dividend here, which is divided into two equal parts whereas 2 is the divisor, the quotient is 5 and the remainder is 0.

We can write the system of equations

x*y=52   .......(1)

[tex]\frac{x}{y}[/tex]=4         ........(2)

We can use substitution to solve

From equation (2) we get,

x = 4y     .......(3)

now substitute in equation (1)

4y*y = 52

[tex]4y^{2} = 52[/tex]

[tex]y^{2} = \frac{52}{4}[/tex]

[tex]y = \sqrt{13}[/tex]

y = 3.605

We can solve for x = ?

from equation (3)

x = 4y

x = 4*3.605

x =   14.42  

Hence, The numbers are 14.42 and 3.6055.

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Answer:

0

Step-by-step explanation:

In cartesian graphs, the slope or a gradient of a fully horizontal line will always be 0.

Step-by-step explanation:

I assume the measuring cylinder measures the cm³ of its normally liquid content.

because for anything else we would need more information about the dimensions of the cylinder.

and so, originally the cylinder shows 40 cm³.

after dropping the stone in, how many cm³ of water is the cylinder then showing ?

let's first mention some facts we are going to use :

water weighs 1 kg (1000 g) per liter.

and 1 liter fits exactly into a cube of

10 cm × 10 cm × 10 cm = 1000 cm³

so, 1 cm³ water weighs exactly 1 g and has therefore a density of 1 g / cm³.

the stone has a density of 8.6 g / cm³, is therefore heavier than water and sinks (and replaces water correspondingly).

how many cm³ does the stone have (and replaces water) ?

well, it has 129 g, and 8.6 g of the stone fill a cm³.

so, it has

129 / 8.6 = 15 cm³

therefore, as these 15 cm³ of stone replace 15 cm³ of water, this is the same as putting 40 + 15 = 55 cm³ of water into the measuring cylinder.

and the cylinder reads now 55 cm³.

FYI : but there is still only 40 cm³ of water in there.

this is actually used to calculate the density of objects (by first weighing and then dropping them into the water to see how much water they replace).

Answer: 55 cm³.

Step-by-step explanation:

[tex]\displaystyle\\m_{stone}=129\ g\ \ \ \ \ \rho_{stone}=8,6\ \frac{g}{cm^3} \ \ \ \ \ V_{water}=40\ cm^3\ \ \ \ \ V=?.\\ \boxed {\rho=\frac{m}{V} }\\V=\frac{m}{\rho} \\V=V_{water}+V_{stone}\\V_{stone}=\frac{m_{stone}}{\rho_{stone}} \\V_{stone}=\frac{129}{8,6}\\V_{stone }=15\ cm^3.\\V=40+15\\V=55\ cm^3.[/tex]

Answer:

99cm

Step-by-step explanation:

A meter is equal to 100cm

The rope is a metre (m) long but a centimetre (cm) less.

100cm - 1cm = 99cm

Answer: (2,9)

Step-by-step explanation:

The point lies in the region that is shaded by both inequalities.

The value of u in the special triangle is 2√3

The complete question is added as an attachment

From the attached figure, the value of u can be calculated using the following sine trigonometry ratio

sin(x) = Opposite/Hypotenuse

Where

x = 30

Opposite = u

Hypotenuse = 4√3

Substitute the known values in the above equation

sin(30) = u/4√3

Multiply both sides of the equation by 4√3

u = 4√3 * sin(30)

Evaluate the trigonometry expression sin(30)

u = 4√3 * 1/2

Evaluate the product

u = 2√3

Hence, the value of u in the special triangle is 2√3

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Answer:

60m3

Step-by-step explanation:

my son got the right anser

Answer:

60m^3

Step-by-step explanation:

The formula for volume of a rectangular prism is height*width*depth

We can see two distinct shapes here

First, we find the volume for the bigger shape

We can see the measurements that pertain to it...

Width is 6m, depth is 3m, and height is also 3m

Multiply those three, you get 54m^3

Now the smaller shape...

1m in width, 2m in height, and 3m in depth

Multiply those, get 6m^3

Add the two shapes together, 54+6=60m^3

Answer:

See below

Step-by-step explanation:

Out of 25 games, they won 14

Fraction won = won / total = 14 / 25

Percent won = won /total * 100 % = 14/25 * 100 = .56 * 100 % = 56 %

To find the number of games lost

25-14 = 11

Fraction won = won / total = 11 / 25

Percent won = won /total * 100 % = 11/25 * 100 = .44 * 100 % = 44 %

To check your work, the percent total should be 100

56+44 = 100

The average median and mode price is $18. Option C is correct.

Given that certain item is available at 7 stores, three stores sell them for $20, two stores sell them for $15, one store sells them for $13, and one sells them for $16.

The mean is the average of the given numbers and is calculated by dividing the sum of the given numbers by the total number of numbers.

Firstly, we will find the median of the given items by arranging the given numbers in ascending order, we get

13,15,15,16,20,20,20

To find the median use the formula (n+1)/2, where n is the number of values in your dataset.

(7+1)/2=8/2=4

In the ascending order numbers 4th term is 16.

So, median is 16

Mode is the highest repeating term in the set or numbers.

So, here mode is 20

Now, we will calculate the average of median and mode, we get

Average=(median +mode)/2

Average=(16+20)/2

Average=18

Hence, the average (arithmetic mean) of the median price and the mode price where certain item is available at 7 stores, three stores sell it for $20, two stores sell it for $15, one store sells it for $13, and one sells it for $16 is $18.

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Answer:

23. 216
24. 56

25. 52

for 26, 27 i'll try to calculate the answer, sorry

Answer:

step 3

Step-by-step explanation:

he should have subtracted 9 to the outside.

whatever you do to the inside you must do to the opposite to the outside

so your final form must be -7(x-3)^2 + 8

Answer:

Option 4

Step-by-step explanation:

By the Pythagorean identity, and the fact we are in the first quadrant,

[tex]\cos \theta=\frac{4}{5}[/tex]

Using the double angle formula for cosine,

[tex]\cos 2\theta=2\cos^{2} \theta-1=2\left(\frac{4}{5} \right)^2 -1=\frac{7}{25}[/tex]

Integrate both sides.

[tex]\displaystyle \int \frac{ds}{dt} \, dt = \int 36t (9t^2 - 7)^3 \, dt[/tex]

On the right side, substitute [tex]u=9t^2-7[/tex] and [tex]du=18t\,dt[/tex], so that

[tex]\displaystyle \int 36t (9t^2 - 7)^3 \, dt = 2 \int u^3 \, du = \frac12 u^4 + C = \frac12 (9t^2 - 7)^4 + C[/tex]

Use the initial value to solve for [tex]C[/tex].

[tex]s(1) = 1 \implies 1 = \dfrac12 (9 - 7)^4 + C \implies 1 = 8 + C \implies C=-7[/tex]

Then the particular solution is

[tex]s(t) = \boxed{\dfrac12 (9t^2 - 7)^4 - 7}[/tex]