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 distance from the center to where the foci is located is 8 units

The formula associated with the focus of an ellipse is given as;

c² = a² − b²

where;

Let's use the Pythagorean theorem

Hypotenuse square = opposite square + adjacent square

Substitute the values into the formula

c² = 10² - 6²

Find the square

c² = 100 - 36

c² = 64

Find the square root

c = √64

c = 8

Thus, the distance from the center to where the foci is located is 8 units

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The answer is A = m².

We know the general formula for finding the area of a square is :

Area = side²

Now, we are given the side is equal to m.

Hence, the expression which can be used to find the area is :

A = m²

The simplified form of the expression is given as 83x/56 -(97/105)

Alphabets are usually represented as unknown variables in a equation or expression.

Given the following expression shown below

6/7 x -2/3 + 3/5 + 5/8 x -6/7

Collect the like terms to have;

6/7 x+ 5/8 x  -2/3 + 3/5 -6/7

Simplify

48x+35x/56 - (70-63 + 90)/105

The final expression will be given as;

83x/56 -(97/105)

Hence the simplified form of the expression is given as 83x/56 -(97/105)

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The power output is  = 5W

Correct option is B.

Power is the quantity of energy that is transferred or transformed in a certain length of time. The unit of power is the watt, which in the International System of Units is equivalent to one joule per second.. Power may also be referred to as activity in earlier writings. The scalar property of power

Power is characterized as the rate at which a thing performs labor.

P = W/T ..... (1)

Work is calculated as the product of force applied to an item and the distance that object has traveled.

W = F.s

When we plug this value into the equation above, we get:

P = (F. s)/t

where,

power = P =?W

F = 10N Force Exercised

s = Displacement = 400cm = 4m  (1 meter = 100 centimeters).

t = Time required = 8s

Using the values in the equation above, we obtain

P = (10 x 4)/8

P = 5W

Hence, the correct option is Option b.

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I understand that the question you are looking for is :

Den pushes a desk 400 cm across the floor. He exerts a force of 10 N for 8 s to move the desk.

What is his power output? (Power: P = W/t)

a. 1.25 W

b. 5 W

c. 40 W

d.500 W

The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).

Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic equation by solving this system of linear equations:

(x₁, y₁) = (- 3.5, 0)

12.25 · a - 3.5 · b + c = 0       (1)

(x₂, y₂) = (11.5, 0)

132.25 · a + 11.5 · b + c = 0       (2)

(x₃, y₃) = (8.5, - 54)

72.25 · a + 8.5 · b + c = - 54     (3)

The solution of the system is a = 3.6, b = - 54, c = 144.9. Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:

y ≥ 3.6 · (x² - 15 · x + 40.25)

y ≥ 3.6 · (x - 11.5) · (x + 3.5)

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Answer:

Step-by-step explanation:

The answer is Economists

Answer: economists

Step-by-step explanation: got it right

Answer: 2

Step-by-step explanation:

remember y=mx^2+c

where m = gradient = slope

∴ expand and simplify y-5=2(x+3)

y-5=2x+6

y=2x+11

m=2  ∴ slope: 2

Answer:

4.378 MPH

Step-by-step explanation:

          Distance in Miles

MPH= -------------------------

           Time in Hours

19.7/4.5 = 4.378 MPH

Answer:$6

Step-by-step explanation:

If only 3 got the children's price, that means there were 4 adult tickets.
4*11=44

62-44=18

18/3=6

$6 per child ticket

x > 1 is the required solution of the given inequality - 3x + 7 < 4. This can be obtained by solving the inequality the same way as we solve an algebraic equation.

The inequality can be solved as the same way as we solve an algebraic equation.

Here in the question the inequality to be solved is given:

- 3x + 7 < 4

By subtracting 7 from both sides of the inequality we get,

⇒ - 3x + 7 - 7 < 4 - 7

⇒ - 3x < - 3

To make the side of the inequality with variable x positive we multiply the whole equation with - 1, then we have to reverse the sign of inequality since we have to multiply the whole inequality with a negative term,

we get,

⇒ 3 x > 3

Now finally by dividing the whole inequality by 3 we get,

⇒ x > 1

The number line representation can be done by marking values from 1 to numbers greater than 1.

Hence x > 1 is the required solution of the given inequality - 3x + 7 < 4.

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Answer:

50 ^^

Step-by-step explanation:

So first an easy way to solve this problem is by removing the zeros then you'll have 35 and
7x1=7

7x2=14

7x3=21

7x4=28

7x5=35

So 7x5 dont forget to add your zeros to 35 and 5 and boom your answer is 50

need more explaining tell me ^^

The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

Given four measurements:

We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.

A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as [tex]e^{-x}[/tex].

We know that exponent shows continuous growth or continuous decay.

Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.

Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

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Add 8 to both sides.

Add 7 and 8 to get 15.

Divide both sides by 3.

Divide 15 by 3 to get 5.

Subtract 9 from both sides.

Subtract 9 from −15 to get −24.

Divide both sides by 8.

Divide −24 entre 8 para obtener −3.

Swap the sides so that all the terms of the variables are on the left side.

Add 13 to both sides.

Add 8 and 13 to get 21.

Divide both sides by 3.

Divide 21 by 3 to get 7.

Subtract 22 from both sides.

Subtract 22 from 4 to get −18.

Divide both sides by 6.

Divide −18 entre 6 para obtener −3.

Swap the sides so that all the terms of the variables are on the left side.

Subtract 51 from both sides.

Subtract 51 from 84 to get 33.

Divide both sides by 11.

Divide 33 by 11 to get 3.

Solution 1 :-

>> 3k - 8 = 7

>> 3k = 7 + 8

>> 3k = 15

>> k = 15 / 3

>> k = 5

Solution 2 :-

>> 8b + 9 = -15

>> 8b = -15 - 9

>> 8b = -24

>> b = -24 / 8

>> b = -3

Solution 3 :-

>> 8 = 3x - 13

>> 3x = 13 + 8

>> 3x = 21

>> x = 21 / 3

>> x = 7

Solution 4 :-

>> 6p + 22 = 4

>> 6p = 4 - 22

>> 6p = -18

>> p = -18 / 6

>> p = -3

Solution 5 :-

>> 84 = 51 + 11c

>> 11c = 84 - 51

>> 11c = 33

>> c = 33 / 11

>> c = 3

A semicircle is a part of a circle, and it is referred to as half of a given circle. Thud the area of the semi-circle window is 982 [tex]in^{2}[/tex].

A circle is a shape that is bounded by a curved path which is referred to as the circumference. Some parts of a circle are radius, diameter, sector, arc, semi-circle, circumference, etc.

A semicircle is a part of a circle, and it is referred to as half of a given circle.

such that:

Area of a circle = [tex]\pi[/tex] [tex]r^{2}[/tex]

and

area of a semicircle = [tex]\frac{\pi r^{2} }{2}[/tex]

where: r is the radius of the circle, and [tex]\pi[/tex] is a constant with a value of [tex]\frac{22}{7}[/tex].

Thus from the given question, it can be inferred that;

r = [tex]\frac{50}{2}[/tex]

 = 25

r = 25 in

Thus, the area of the semi-circle can be determined as;

area of the semi-circle = [tex]\frac{1}{2}[/tex] * [tex]\frac{22}{7}[/tex] * [tex]25^{2}[/tex]

                                      = 982.1429

area of the semi-circle = 982.14 [tex]in^{2}[/tex]

The area of the semi-circle window is approximately 982 [tex]in^{2}[/tex].

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Answer:

C

Step-by-step explanation:

4 is a perfect square.  2 x 2.  You can pull the 2 out and everything else would be left under the square root symbol.

The question requires that we have to state the hypothesis:

null hypothesis;H0: u1 < u2, the alternate hypothesis;H1: u1 > u2. The one tail test is what is to be used.

H0: u1 < u2

H1: u1 > u2

The one tail test statistic is what is to be used here

[tex]\sqrt{\frac{30.8}{17} +\frac{6.1}{15} }[/tex]

= 1.49

The df = 17 + 15 - 2

= 30

test statistic = 18.9 - 17.4 / 1.49

= 1.007

We have the critical value on excel as T.INV(0.9,30)

=  1.310

E. At 0.1, we can conclude that  t-value (1.007) does not lies in the rejection area. We fail to reject the null hypothesis. Hence we conclude that the mean vacation with the unlimited plan is greater.

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Answer:

x=10.5

Step-by-step explanation:

if the two triangles were ratios it would be like

19.3:7.2 to x:3.9

so 75.27 = 7.2x

whcih is 10.45 which is approximately 10.5

Answer:

49,2

Step-by-step explanation:

i dont practice math in english so the variables might be a little different!! The little L with the squiggly is supposed to represent length

The length of the painting is 77 cm if the area of the painting is 4081 sq cm and the width is 53 cm.

The area of a rectangle is the product of the length and width of the same rectangle.

Given that:

The area of the painting, A = 4081 cm².

The width of the painting, b = 53 cm.

To find the length of the painting, use the following formula to obtain the area of the rectangle:

Area = length × breadth

Let the length of the painting is l, then

A = l × b

4081 = l × 53

l = [tex]\frac{4081}{53}[/tex]

l = 77

Thus, the length of the painting is 77 cm.

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Answer:

B.) f⁻¹(x) = (1/9)x - 7/9

Step-by-step explanation:

Remember, f(x) is another way of writing "y". The inverse can be found by swapping the positions if the "x" and "y" variables and then solving to isolate the "y" variable.

f(x) = 9x + 7                            <----- Original function

y = 9x + 7                               <----- Substitute f(x) for "y"

x = 9y + 7                               <----- Swap variable positions

x - 7 = 9y                                <----- Subtract 7 from both sides

(x - 7) / 9 = y                           <----- Divide both sides by 9

(1/9)x - 7/9 = y                      <----- Divide each term individually by 9

The inverse function is represented by the symbol f⁻¹(x).

The domain is the water balloon's height increasing will be (0, 2), staying the same will be (2, 4), decreasing the fastest will be (6, 10), and the height of the water balloon at 16 seconds the will be 0.

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds.

Part A:

As seen from the graphic, increase from 0 to 2 sec.

The domain is (0, 2), where the height of the water balloon increases.

Part B:

The water balloon stays the same from 2 to 4 sec.

The field means that the height of the water balloon remains the same (2, 4).

Part C:

Height decreasing fasted at 4 to 6 sec.

Because the slope is steepest downward from 4 to 6 sec as comfort to 6 to 10 sec.

The domain is where the height of the water balloon decreases rapidly (6, 10).

Part D:

The balloon's height will be almost near the ground as resistance will play its role.

But it will almost touch the ground.

The height of the water balloon will be 0 in 16 seconds.

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Answer:

$4.58

Step-by-step explanation:

Lets convert 10 feet to meters.

1 ft = 0.305m

10ft = 0.305 * 10

10ft = 3.05m

Now we will work out the cost of the fabric.

Given 1m = $1.50

3.05m = 3.05 * $1.50 = $4.58 (nearest cent)

The area of the given semicircle is 56.574 sq. units. Half of the area of the circle is the area of the semicircle.

The area of the semicircle is

A = [tex]\frac{1}{2}[/tex] πr² sq. units

Where r - radius

A semicircle is nothing but half part of the circle. So, its area is also half of the circle's area.

It is given that,

The radius of the semicircle is

r = 6

So, its area in terms of π is

A = [tex]\frac{1}{2}[/tex] πr²

   =  [tex]\frac{1}{2}[/tex] × π × 6²

   = 18π sq. units

On substituting π = 3.143, we get

A = 18 × 3.143 = 56.574 sq. units

Thus, the area of the given semicircle in terms of π is 18π or in terms of π =3.143 is 56.574 sq. units.

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By substitution, the value of x and y are 1 and 1 respectively.

3 / 8 x + 1 /3  y = 17 / 24

x + 7y = 8

x = 8 - 7y

Let's substitute the value of x in equation(ii)

3 / 8(8 - 7y) + 1 / 3 y = 17 / 24

3 - 21 / 8 y + 1 / 3 y = 17 / 24

1 / 3 y - 21 / 8 y = 17 / 24 - 3

8y - 63y/24 =  17 - 72/ 24

-55y / 24 = -55 / 24

cross multiply

-1320y = -1320

divide both sides by -1320

y = -1320 / -1320

y = 1

Hence,

x + 7(1) = 8

x = 8 - 7

x = 1

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Answer:

E. >

Because 65 is greater than 56.

dis i know functiin of fx is ♾

Answer:

4th option

Step-by-step explanation:

the end behaviour is what happens when x gets larger and positive (right- hand end )or larger and negative ( left- hand end )

f(x) = [tex]\frac{1}{2}[/tex] x² ← is of even degree (2) and has a positive leading coefficient , then

• even degree and positive leading coefficient

f(x) → +∞ as x → + ∞ and

f(x) → + ∞ as x → - ∞

1885.5 m^3 of water will fill the container.

To find how many cubic feet of water will it contain:

Given -

The pool comprises a 12-foot-radius cylinder with a height of 4.5 feet.

The volume of the water in this section of the cylinder will be equal to the volume of the cylinder formed.

Therefore, 1885.5 m^3 of water will fill the container.

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The complete question is given below:

Lauren has an above-ground pool. To keep the pool's skimmer working well, the water level must be 4 inches from the top of the pool. When the pool is filled to this recommended level, approximately how many cubic feet of water will it contain? Use π = 3.14

A cylinder with a radius of 12 feet and a height of 4.5 feet.

volume of pyramid = 1/3(5.2)h cm3

Prism is a three dimensional figure. A prism is a 3-dimensional shape with two identical shapes (bases) facing each other.

we know that,

The volume of the pyramid is equal to

volume = (1/3) × base area × height

we have height = h cm

area of base = 5.2 cm^2

substitute in the formula

                       v = 1/3 × 5.2 × h

                        volume = 1.73h cm^3

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Answer:

p - 4

Step-by-step explanation:

Prime number is a number that only has 2 factors, 1 and the number itself. Therefore, multiplying p by 2 or 7 means giving the number more than 2 factors, which would make the number no longer prime. Squaring the prime number itself does the same.

Let p = 7.

2p = 2*7 = 14                  14 = 1*2*7*14

7p = 7*7 = 49                 49 = 1*7*49

p - 4 = 7 - 4 = 3              3 = 1*3

p^2 = 7^2 = 49               49 = 1*7*49

Answer:

9

Step-by-step explanation:

listing the factors

27 : 1, 3, 9, 27

36 : 1, 2, 3, 4, 9, 12, 18, 36

the common factors are 1, 3, 9

the highest common factor is 9

Hi :)

The highest common factor is also known as the HCF

Let's find the HCF of [tex]\boldsymbol{27}[/tex] and [tex]\boldsymbol{36}[/tex].

[tex]\boldsymbol{Factors\:of\:27: 1, 3, 9, 27}[/tex]

[tex]\boldsymbol{Factors\:of\:36:1,2,3,4,6,9,12,18,36}[/tex]

HCF : [tex]\boldsymbol{9}[/tex]

[tex]\tt{Learn\:More;Work\;Harder}[/tex]

:)

The value of x in the system of equation is 6

The system of equations is given as:

y = 1/2 * 2^x

y = 5x + 2

Substitute y = 1/2 * 2^x in y = 5x + 2

1/2 * 2^x = 5x + 2

Multiply through by 2

2^x = 10x + 4

Next, we use the trial by error.

Set x = 6

This gives

2^6 = 10 * 6 + 4

Evaluate the product and the exponent

64 = 60 + 4

Evaluate the sum

64 = 64

Hence, the value of x in the system of equation is 6

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