50 POINTS!


Riley’s mother, Ms. Cooper, owns Cooper’s Storage and Shipping Company. Ms. Cooper took Riley with her to work for the day to show Riley the different jobs the company does.
1. Riley noticed an aquarium in his mother’s office. The aquarium has the dimensions 16 in. by 8.5 in. by 10.5 in. The formula for volume is: V = l x w x h  
(a) Riley noticed that the aquarium was three-fourths full of water. How many more cubic inches of water would be required to fill the tank? Show your work.

(b) Another aquarium in the building has dimensions that are each triple the dimensions of the aquarium in Riley’s mother’s office. Riley thought that the volume would also triple. Is Riley correct? How many times greater is the volume of the larger aquarium than the volume of the smaller one? Show your work and explain your reasoning.

(c) Riley also thought that the surface area would triple. Is Riley correct? How many times greater is the surface area of the larger aquarium than the surface area of the smaller one? Show your work and explain your reasoning.

Here is one more

Riley finds out that Cooper’s Storage and Shipping Company is working with a local business to package some office supplies. Some of the supplies are packed inside a cube-shaped box with side lengths of 4 1/2
in.
These boxes are then packed into a shipping box with dimensions of 18 in. 9 in. 4 1/2 in. 

(a) How many boxes of office supplies can be packed into the larger box for shipping? Show your work.

(b) Sometimes the shipping boxes are protected with an outer covering because of weather. Draw a net of the shipping box. Use the net to find the surface area of the shipping box to help decide how much outer covering will be needed to protect one box. Show your work. Answer

Answer:

22 fish

Step-by-step explanation:

cella has 12 fish. micheal has ten more 12+10=22. combind 22+12=34

Answer:

22 fish

Step-by-step explanation:

Answer: 14 gallons

Step-by-step explanation:

Let's call the total gallons of gas Abdul's tank can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{1}{5}x+7=\frac{7}{10}x[/tex]

Therefore, when you solve for x, you obtain the following result:

[tex]\frac{1}{5}x+7=\frac{7}{10}x\\\\\frac{1}{5}x-\frac{7}{10}x=-7\\\\-\frac{1}{2}x=-7\\\\-x=(-7)(2)\\x=14[/tex]

Answer:

  9.4 ft

Step-by-step explanation:

The formula for the circumference of a circle is ...

  C = πd . . . . . where d represents the diameter

Putting your numbers into this equation gives ...

  C = 3.14·(3 ft) = 9.42 ft

Rounding as required gives the length of fence as 9.4 ft.

To find the length of fencing needed for a circular flower bed, use the formula C = π * d, where C is the circumference and d is the diameter of the circle.

To find the length of fencing needed to go around a circular flower bed, we need to calculate the circumference of the circle. The circumference can be found using the formula C = π * d, where π is approximately 3.14 and d is the diameter of the circle. In this case, the diameter of the flower bed is 3 feet, so the circumference is 3.14 * 3 = 9.42 feet.

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Answer:

The acute angles of the rhombus are 80°; the obtuse angles are 100°.

Step-by-step explanation:

Since each diagonal bisects the angle of the rhombus, the given conditions are the same as saying the angles of the rhombus are in the ratio 4:5. Adjacent angles add to 180°, and the sum of the ratio units is 4+5=9. So each ratio unit stands for 180°/9=20° of angle, and the angles are ...

80° : 100°

The angles of the rhombus are 80° and 100°.

➷ Find the total data in the first row:

90 + 30 = 120

Now divide each of these values by the total:

(30/120) = 0.25

(90/120) = 0.75

It would be 0.25 in the first box and 0.75 in the second.

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Answer:

Group1 .18

Group2 = .54

Step-by-step explanation:

To find the relative frequency, you divide the number by the total number

The total number is 30+90+14+32 = 166

Category 1 Group 1 has 30 in it

The relative frequency is 30/166 = .180722892 = .18

Category 1 Group 2 has 90 in it

The relative frequency is 90/166 =.542168675=.54

Answer:

48.3 cm^2

Step-by-step explanation:

The area of the enclosing square is that of a square 15 cm on a side, so is ...

square area = (15 cm)^2 = 225 cm^2

The white area is that of a quarter-circle of radius 15 cm, so that area is ...

quarter-circle area = (1/4)πr^2 = (π/4)·(15 cm)^2 = 56.25π cm^2 ≈ 176.7 cm^2

Then the yellow area is the difference ...

yellow area = square area - quarter-circle area

= (225 cm^2) - (176.7 cm^2)

yellow area = 48.3 cm^2

The equations for the two machines are y = 5x and y = 8x, which represent their respective production rates. Over an 8 hour period, the first machine produces 40 miles of ribbon and the second produces 64 miles, resulting in a difference of 24 miles.

The two machines described in the question produce ribbon at different rates, which can be represented with two linear equations in slope-intercept form (y = mx + b) where m is the rate of production (slope) and b is the initial amount of ribbon (y-intercept, in this case 0 as the machine starts with no ribbon).

The first machine can produce 5 miles of ribbon in an hour, so its rate is 5 miles/hour. This gives the equation y = 5x.

The second machine can produce 8 miles of ribbon in an hour, leading to the equation y = 8x.

In an 8 hour period, the first machine will produce y = 5*8 = 40 miles of ribbon, while the second machine will produce y = 8*8 = 64 miles of ribbon. The difference is 64 - 40 = 24 miles.

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The first machine will make 40 miles of ribbon in 8 hours, and the second machine will make 64 miles of ribbon. The difference in length for an 8-hour period between the two machines is 24 miles.

To graph the length of ribbon each machine will make in 8 hours, we can start by determining the length each machine can make in one hour.

The first machine can make 5 miles of ribbon in an hour, so in 8 hours, it will make 8 times 5 = 40 miles of ribbon.

The second machine can make 8 miles of ribbon in an hour, so in 8 hours, it will make 8 times 8 = 64 miles of ribbon.

The slope-intercept form of an equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept. For the first machine, the equation would be y = 5x + 0, and for the second machine, the equation would be y = 8x + 0.

The difference in length between the two machines for an 8-hour period is 64 - 40 = 24 miles.

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Answer:

A ) subtract the second equation from the first equation

Step-by-step explanation:

2x + 3y = 7

2x - 4y = -5

subtracting the second equation from the first equation we get,

7y = 12

y=12/7

This is the correct option

Answer:

A ) subtract the second equation from the first equation

Step-by-step explanation:

Let's consider the following system of equations.

2x + 3y = 7

2x = 4y - 5

If we subtract the second equation from the first equation, we get:

2x + 3y - 2x = 7 - (4y - 5)

3y = 7 - 4y + 5

7y = 12

y = 12/7

Then, we can use any of the original equations and solve for x.

2x = 4y - 5

2x = 4(12/7) - 5

x = 13/14

A sample must be a group of people who are the target of the survey question

Answer:

The correct option is 1.

Step-by-step explanation:

The set of all observations is known as populate set.

A sample is a small subset of population set that is the representative of the entire population. The sample must have sufficient size and it should include all population.

A sample must be a group of people who are the target of the survey question. This statement is true.

Therefore the correct option is 1.

A sample should have different characteristics than the population. This statement is false.

A sample must be very small. This statement is false.

A sample should include only boys or only girls.  This statement is false.

Therefore options 2, 3 and 4 are incorrect.

Final answer:

To find the exponential function that passes through (-3, 80) and (-1, 20), we use the general form y = abˣ. By solving a system of equations using these points, we find that the exponential function is y = 40*2ˣ.

Explanation:

To write an exponential function that passes through the points (-3, 80) and (-1, 20), we can use the general form of an exponential function, which is y = abˣ. Here, a and b are constants we need to find. Given two points, we can set up a system of equations to solve for a and b.

Using the first point (-3, 80):
80 = a*b⁻³

Using the second point (-1, 20):
20 = a*b⁻¹

Dividing the second equation by the first gives us:
b2 = 4 which simplifies to b = 2 or b = -2. However, in exponential functions, b is positive, so we choose b = 2.
Substituting b = 2 into the second equation gives a = 40. Thus, the exponential function is y = 40*2ˣ.

Answer:

about 0.08087

Step-by-step explanation:

The statistics functions of your graphing calclulator can help you with that. It is a good idea to learn to use them.

Answer:

Your answer is

x = -4, 6 or (b)

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The solution of the equation for the value of x will be (-4,6).

The polynomial equation with the degree of two will be termed as the quadratic equation or the highest power of the variable is 2 in the quadratic equation.

The given equation is:-

=x²-2x-24

Now we will split the equation

=x²-6x+4x-24

=x(x-6)+4(x-6)

=(x-6)(x-4)

Hence the value of x will be -4 and 6.

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Answer:

  15.7 cm

Step-by-step explanation:

The length (s) of an arc of a circle of radius r with a central angle of θ radians is ...

  s = rθ

Here, the radius is given as 7.9 cm, and the arc of interest is the supplement of 66.4°, so is ...

  θ = π·(1 - 66.4/180) ≈ 1.9827 . . . . radians

Then the arc length is ...

  s = (7.9 cm)·(1.9827) ≈ 15.7 cm

Answer:

Part A:  A (6 , 11) , B (5 , 6) , C (7 , 1) , D (0 , 8)

Part B:  A (-6 , -11) , B (-5 , -6) , C (-7 , -1) , D (0 , -8)

Step-by-step explanation:

* Lets study the reflection about the two axes X and Y

- The distance between the point and the axes of reflection =

 the distance between its image and the axes

- The point and the its image are on opposite sides of the axes

- If a point (x , y) reflected about x axis, that means the point

  will move vertically

- Moving vertically means we will change the sign of the y-coordinates

∴ The image of (x , y) after reflection about x-axis is (x , -y)

- If a point (x , y) reflected about y axis, that means the point

  will move horizontally

- Moving horizontally means we will change the sign of the x-coordinates

∴ The image of (x , y) after reflection about x-axis is (-x , y)

* Now lets use the explanation above to solve our problem

- At first lets right the original point of the quadrilateral ABCD

∵ A (-6 , 11) , B (-5 , 6) , C (-7 , 1) , D (0 , 8)

Part A: The y-axis is the line of reflection

- Lets change the signs of x-coordinates in all points

∴ The new points after reflection about y-axis is:

  A (6 , 11) , B (5 , 6) , C (7 , 1) , D (0 , 8)

- Note: The point D does not change because x-coordinate is 0

            and there is no sign for the 0

Part B: The x-axis is the line of reflection

- Lets change the signs of y-coordinates in all points

∴ The new points after reflection about x-axis is:

  A (-6 , -11) , B (-5 , -6) , C (-7 , -1) , D (0 , -8)

so calculate the Volume of the water that is already in the tank

so l x w x h

4 x 18 x 12

=864cm^3 is in the tank

find the total volume of the tank:

6 x 18 x 12

=1296cm^3

and subtract the current from the total to find what you need:

1296cm^3 - 864cm^3

= 432 cm^3

you can also find how much you need by using the remaining 2cm from the height (6-4=2) and use the volume formula with 2 substituted as the height and you’ll get the same answer

The amount of water needed to fill the tank is 432 cm³.

Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.

Volume of cuboid = lwh

The tank is filled with water to a height of 4 centimeters.

The dimension of the tank is width is 18 cm, length is 12 cm, and height 6 cm.

So, the Volume of water present in the tank

= l x w x h

= 4 x 18 x 12

= 864 cm³

Now, the total Volume of tank

= 6 x 18 x 12

= 1296 cm³

So, the amount of water needed to fill the tank

= 1296 - 864

= 432 cm³

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Answer:

The altitude of the plane is 8 miles

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

tan(72°)=h/x

h=xtan(72°) -----> equation A

In the right triangle ABD

tan(55°)=h/(x+3)

h=(x+3)tan(55°) -----> equation B

equate equation A and equation B and solve for x

xtan(72°)=(x+3)tan(55°)

xtan(72°)-xtan(55°)=3tan(55°)

x[tan(72°)-tan(55°)]=3tan(55°)

x=3tan(55°)/[tan(72°)-tan(55°)]

Find the value of h

h=xtan(72°)

h=[3tan(55°)*tan(72°)]/[tan(72°)-tan(55°)]

h=8 miles

Answer:

8.0 is the right answer

Step-by-step explanation:

ur welcommmme ;)

Answer : The dimensions ​of table runner will be, 20 inch length and 4 inch width.

Step-by-step explanation :

Let the width of table runner be, x

and, the length of table runner will be, 5x

Given:

Area of table runner = [tex]80inch^2[/tex]

As we know that:

Area of rectangle = Length × Width

[tex]80inch^2=(5x)\times (x)[/tex]

[tex]80inch^2=5x^2[/tex]

[tex]x=4inch[/tex]

The width of table runner = x = 4 inch

The length of table runner = 5x = 5(4) inch = 20 inch

Therefore, the dimensions ​of table runner will be, 20 inch length and 4 inch width.

Answer:

(2, 5)

Step-by-step explanation:

Dilating 3, means that the values were multiplied by 3.  To find their original location, divide the x and y values of the new point by 3...

(6/3, 15/3) = (2, 5)

In a dilation with a factor of 3, to find the original coordinates from the dilated point (6,15), we divide each coordinate by the dilation factor. The original point A was at (2,5).

In mathematics, dilation is a geometric transformation that resizes a figure, maintaining its shape but changing its size. It involves multiplying the coordinates of each point in the figure by a constant scale factor. If the scale factor is greater than 1, the figure expands, while a scale factor between 0 and 1 results in a reduction. Dilation is commonly used in geometry to study similarity between shapes, where corresponding angles remain equal, and corresponding sides are proportional. It plays a crucial role in various mathematical concepts and applications, such as transformations, similarity, and geometric modeling.

In a dilation, the points move closer or farther away from a certain point, called the center of dilation, by a certain factor. In this case, the dilation factor is given as 3, so the original point is gained by dividing the coordinates of the image by the dilation factor. The image of point A is given as (6,15). To find the original point A, we divide both coordinates by the dilation factor.

So, the original location of point A is (2,5).

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Answer:

the answer is C.Peter walks at a rate of 13/4 miles per hour.  hope this was helpful

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

The length of the edge of the cube = 4 inches

Step-by-step explanation:

* Lets describe the cube

- It has 6 faces all of them are squares

- It has 8 vertices

- It has 12 equal edges

∵ The volume of any formal solid = area of the base × height

∵ The base of the cube is a square

∴ Area base = L × L = L² ⇒ L is the length of the edge of it

∵ All edges are equal in length

∴ Its height = L

∴ The volume of the cube = L² × L = L³

* Now we have the volume and we want to find the

 length of the edges

∵ Its volume = 64 inches³

∴ 64 = L³

* Take cube root to the both sides

∴ ∛64 = ∛(L³)

∴ L = 4 inches

* The length of the edge of the cube = 4 inches

The length of the edges of the cube is 4 inches.

Given that the volume V  is 64 cubic inches, we can set up the equation:

[tex]\[ a^3 = 64 \][/tex]

To solve for a , we take the cube root of both sides:

[tex]\[ a = \sqrt[3]{64} \][/tex]

The cube root of 64 is 4, since [tex]\( 4^3 = 4 \times 4 \times 4 = 64 \).[/tex]

Therefore, the length of the edges of the cube is 4 inches.

Answer:

a) (0.08)^6

Step-by-step explanation:

Given in the question,

[tex]\sqrt{0.08^{12} }[/tex]

As we know that

[tex]\sqrt{x} = x^{1/2}[/tex]

So,

[tex]\sqrt{0.08^{12}[/tex] = [tex]0.08^{12(1/2)}[/tex]

[tex]0.08^{12/2}[/tex]

[tex]0.08^{6}[/tex]

Answer:

  $491.37

Step-by-step explanation:

The appropriate formula for the future value of a single investment is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested (389), r is the annual rate (0.039), n is the number of compoundings per year (12), and t is the number of years (6).

Putting the given numbers into the formula, you get ...

  A = 389·(1 +.039/12)^(12·6) = 389·1.00325^72 ≈ 491.37

The total in the account after 6 years will be $491.37.

Explanation:

In a function, each x-value has one y-value.

___

That is the definition of a relation that is a function.

Final answer:

Each x-value in a function has exactly one corresponding y-value. Functions map elements of the domain to unique elements in the range, which can be represented graphically and must pass the vertical line test. The derivative in calculus, such as dy/dx, reflects the rate of change between these variables.

Explanation:

In a function, each x-value has one corresponding y-value. This is a foundational concept in mathematics that defines a relationship whereby each input (or x-value) in the function produces exactly one output (or y-value). Essentially, a function maps each element of the domain to exactly one element in the range.

An example of a function is y = f(x), which could represent a linear function like y = 3x + 2. In this case, for every x-value, there is a specific y-value determined by the function's formula. So if x were 1, then y = 3(1) + 2 = 5. The graphical representation of a function, such as its curve or line on a coordinate plane, must pass the vertical line test. That means if you draw a vertical line through any point on the graph, it should intersect the graph at no more than one point, confirming that each x-value has only one y-value.

Understanding functions is pivotal in different areas of mathematics, including calculus where the derivative of a function represents the rate of change of the y-value with respect to the x-value. In the case of the linear function y = 6+3x, the derivative dy/dx is constant at 3, implying that for every unit increase in x, y will increase by 3 units.

Answer:

  $111

Step-by-step explanation:

The bank balance is ...

  $700 × (1 + 0.05) = $735

The cost of the computer is ...

  $750 × (1 -0.20) × (1 +0.04) = $624

The remaining bank balance after paying for the computer is ...

  $735 -624 = $111

_____

When you add a percentage, you effectively multiply by the sum of 1 and that percentage. The same is true if the amount "added" is negative (as for a discounted price).

  (original amount) + (percentage)×(original amount)

Use the distributive property to factor out the original amount:

 = (original amount)×(1 + percentage)

Answer:

  1/96

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

Then ...

[tex]6^{-1}\cdot 4^{-2}=\dfrac{1}{6}\cdot\dfrac{1}{4^{2}}=\dfrac{1}{6\cdot 16}=\dfrac{1}{96}[/tex]

Answer:

A. y = 8.34x + 10

Step-by-step explanation:

The first choice is appropriate to the situation where y=10 when x=0 and where y increases by 83.4 when x increases by 10.

___

The equation of selection D is the same and is also appropriate, but the graph does not match the equation. The equations of the other choices are incorrect, as are the graphs.

The linear equation which represents the data is : y = 8.34x + c. Hence, correct option is A.

The linear equation for the graph can be expressed in the form :

b = change in y / change in x

Change in y :

Change in x :

Hence , slope , b = (83.4 /10) = 8.34

The value of the intercept, c ;

93.4 = 8.34(10) + c

93.4 = 83.4 + c

c = 10

Hence, the linear equation is :

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Answer:

y = 2/3 x -2

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

We need to solve for y

2x-3y = 6

Subtract 2x from each side

2x-2x-3y=-2x+6

-3y = -2x+6

Divide  by -3

-3y/-3 = -2/-3x+6 /-3

y = 2/3 x -2

The slope is 2/3 and the y intercept is -2

Answer:

The correct answer is 2 23/63

Step-by-step explanation:

To determine how much the plant grew, start by subtracting the starting whole number value from the ending whole number value.

4 - 1 = 3

Now do the same with the fractions. Use common denominators.

2/9 - 6/7

14/63 - 54/63

-40/63

Now add the two numbers together.

3 - 40/63 = 2 23/63

Vertex is at (-1,-7), because the |x+1| moves the graph left 1 and -7 moves the graph down 7.

Answer:

the second answer is a

Step-by-step explanation:

edge 2020

Answer:

5/18

Step-by-step explanation:

The desired fraction can be found by dividing the fraction of distance by the fraction of hours:

(1/6 distance)/(3/5 hour) = (1/6·5/3) distance/hour = 5/18 distance/hour

Then 5/18 of the distance can be covered in one hour.

Answer:

5/18

Step-by-step explanation: