Allison designs fancy boxes to fill with chocolates. The boxes are in the shape of a right square pyramid as shown, where 8y represents the
length of one side of the base of the pyramid, and 5y represents the height of one triangular face of the pyramid.
8y
The large size box must be designed to have a volume of 1,000 cubic centimeters,
Create an equation that can be used to calculate the length of the base and height of the triangular face of the box. Enter your equation in
the first response box.

Answers

Answer 1

The requreid equation that can be used to calculate the length of the base and height of the triangular face of the box is:

8y ≈ 8.4 cm

5y ≈ 5.8 cm

What is volume?

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

The formula for the volume of a square pyramid is:

V = (1/3) * base area * height

In this case, the base of the pyramid is a square with a side length of 8y, so the base area is:

base area = (8y)² = 64y²

The height of each triangular face is given as 5y, so the total height of the pyramid is 2 * 5y = 10y.

Substituting these values into the formula for volume, we get:

1000 = (1/3) * 64y² * 10y

y ≈ 1.16

Therefore, the length of the base of the pyramid is:

8y ≈ 8.4

And the height of each triangular face is:

5y ≈ 5.8 cm

So the equation that can be used to calculate the length of the base and height of the triangular face of the box is:

8y ≈ 8.4 cm

5y ≈ 5.8 cm

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Related Questions

Write the slope-intercept form of the equation for the line passing through the given pair of points. (-9, 0) and (6, 4)
explain please show work

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Hope you understand :)

calculate the reciprocal of -0.07 correct to 1 decimal place

Answers

Answer:

-14.3

Step-by-step explanation:

Use a calculator.

1/(-0.07) = -14.2857...

Answer: -14.3

The shape given below can be decomposed into which two figures? (Pick two)

Answers

Answer:

C and D

Step-by-step explanation:

I would chose this because the square will have all sides of 3 since all the sides are the same size it classifies as a square. Then a right triangle looking at the shape you would have left.

A rectangle is a four sided polygon having all the internal angles equal to 90 degrees. The shape given below can be decomposed into two figures, they are rectangle and right triangle. The correct options are A and D.

What is a trapezium?

The trapezium is defined as a quadrilateral with one pair of parallel opposite sides. The parallel sides of a trapezium are called the bases and the non-parallel sides of a trapezium are known as legs. It is also called as the trapezoid.

A trapezium is a closed shape which has four sides and four angles. Anyone pair of opposite sides of a trapezium are parallel to each other. If the legs are of equal length, then it is called the isosceless trapezium.

A triangle in which one of its interior angles is equal to 90 degrees or any one angle is a right angle is the right triangle.

Thus the correct options are A and D.

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the measure of one side of a square is x+5. which expression represent the area and perimeter of the square?

Answers

Answer:

A= x^2   P=4s

Step-by-step explanation:

Area of a square

Perimeter= 4s

Area= (the length of one side) ^2

15 players for a softball team show up for a game: (a) How many ways are there to choose 10 players to take the field? 3003 (b) How many ways are there to assign the 10 positions by selecting players from the 15 people who show up? 3003 (c) Of the 15 people who show up, 5 are women. How many ways are there to choose 10 players to take the field if at least one of these players must be a woman?

Answers

Answer:

(a) 3003 ways

(b) 10897286400 ways

(c) 3002 ways

Step-by-step explanation:

Given

[tex]n = 15[/tex] --- 15 players

Solving (a) Ways of selecting 10 players.

This implies combination.

So, we have:

[tex]r=10[/tex]

Using:

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

We have:

[tex]^{15}C_{10} = \frac{15!}{(15-10)!10!}[/tex]

[tex]^{15}C_{10} = \frac{15!}{5!10!}[/tex]

Simplify

[tex]^{15}C_{10} = \frac{15*14*13*12*11*10!}{5!10!}[/tex]

[tex]^{15}C_{10} = \frac{15*14*13*12*11}{5!}[/tex]

[tex]^{15}C_{10} = \frac{15*14*13*12*11}{5*4*3*2*1}[/tex]

[tex]^{15}C_{10} = \frac{360360}{120}[/tex]

[tex]^{15}C_{10} = 3003[/tex]

Solving (b) Ways of assigning positions to 10 players.

This implies permutation.

So, we have:

[tex]r=10[/tex]

Using:

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

We have:

[tex]^{15}P_{10} = \frac{15!}{(15-10)!}[/tex]

[tex]^{15}P_{10} = \frac{15!}{5!}[/tex]

Solve each factorial

[tex]^{15}P_{10} = \frac{1307674368000}{120}[/tex]

[tex]^{15}P_{10} = 10897286400[/tex]

Solving (c) Ways of choosing at least 1 woman

We have:

[tex]Men = 10[/tex]

[tex]Women = 5[/tex]

Ways of selecting 10 players is: (a) 3003 ways

Since the number of men are 10, there is 1 way of selecting 10 men (i.e. selection without women)

Using complement rule:

At least 1 woman = Total - No woman

[tex]At\ least\ 1\ woman = 3003 - 1[/tex]

[tex]At\ least\ 1\ woman = 3002[/tex]

Can some one please explain how to do this? 1.253 x 7.4 =

Answers

Answer:

9.2722

Step-by-step explanation:

7.400

*1.252

_____

9.2722

Its simple, plz rate 5 str, thx, and brailiest

What is an Expression?​

Answers

A feeling or emotion

Answer:

Hello, an expression are numbers, symbols, and operators grouped to show the value of something. For example, 4+5 and 45/5-2 are expressions.

Step-by-step explanation:

I hope this helped you!

3(5)+2(w-1)=
Cual es el valor de la expresión algebraica?

Answers

Answer:

distribute

2(w-1)

a(b-c)=ab-ac

(3)(5)+(2)(w)+(2)(−1)

=15+2w+−2

combine like terms

15+2w+−2

=(2w)+(15+−2)

=

2w+13

Step-by-step explanation:

https://qcv.gg/rXpglU

find the quotient 5 2/3 ÷ 3/5 leave answer as a mixed number in simplest form.​

Answers

Answer:

[tex]9\frac{4}{9}[/tex]

Step-by-step explanation:

Exact from:

[tex]\frac{85}{9}[/tex]

Decimal Form:

9.4

Mixed Number Form:

[tex]9\frac{4}{9}[/tex]

Give me Brainllest

Find the factored form of
10a + a2 = 0

Answers

Answer:

a = 0, -10

Step-by-step explanation:

I think this is correct but it may not be.

Answer:

Step-by-step explanation:

a(10+a)=0 or - i cant remember which one it was but hope this helps

The figure below has a volume of 60 cubic units. How many more cubes will it take to fill the figure?


5 cubic units


40 cubic units


55 cubic units


60 cubic units

Answers

Answer:

40 cubic units

Step-by-step explanation:

The vertices of the triangle shown are (-2, 2), (4, -1), and (-2, -3).
y
What is the area of the triangle?
O A 11 square units
OB 15 square units
o C.13 square units
O D. 17 square units

Answers

Answer: 15

Step-by-step explanation:

Make x the subject of the formula
х
+12c = 5d
63

Answers

x=5db^3-2cb^3
Workup in photo below.
Good luck

PLEASE HELP WILL GIVE BRAINLIEST

Answers

Answer:

12.5%

Step-by-step explanation:

r = (1/4)((1500/1000) - 1) = 0.125

r = 0.125 = 12.5%

D or 12.5%
Explanation: r= (1/4) ((1500/1000)-1) =0.125
r= 0.125 = 12.5%

Solve for x using
multiplication.
cross
X - 2
x3
x + 2
=
4
3
x = [?]

Answers

ANSWER: x= 14 hope this helps

Answer:

x = 14

Step-by-step explanation:

[tex] \frac{x - 2}{3} = \frac{x + 2}{4} [/tex]

=> 4(x-2) = 3(x+2) [Cross Multiplication]

=> 4x - 8 = 3x + 6

=> 4x - 3x = 8 + 6

=> x = 14 (Ans)

PLEASE HELP ME GIVING LOTS OF POINTS AND BRAINLIEST TO THE FIRST LEGIT ANSWER!!!

Meg plotted the graph below to show the relationship between the temperature of her city and the number of people at a swimming pool:

Main title on the graph is Swimming Pool Population. Graph shows 0 to 30 on x axis at increments of 5 and 0 to 12 on y axis at increments of 1. The label on the x axis is Temperature in degree C, and the label on the y axis is Number of People at the Pool. Dots are made at the ordered pairs 2.5, 1 and 5, 2 and 7.5, 2 and 7.5, 3 and 7.5, 4 and 10, 5 and 10, 6 and 12.5, 6 and 15, 7 and 15, 8 and 17.5, 5 and 17.5, 7 and 20, 9 and 22.5, 7 and 22.5, 9 and 25, 11 and 27.5, 12.

Part A: In your own words, describe the relationship between the temperature of the city and the number of people at the swimming pool. (5 points)

Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)

Answers

Answer:

As the temperature increases, the number of people at the pool increases.

Part B: I think the line best fit can be one that starts at (0,0), and goes up until (28,12). The approximate slope would be 0.42, and the y-intercept is 0.

SLOPE:

(28,12)

y / x = m

12 / 28 = 0.42

Y-INTERCEPT:

​(0,0)

= 0

Step-by-step explanation:

Find 0% of 48:

Find 100% of 48:

Find 50% of 48:

Find 25% of 48:

Find 75% of 48:

Answers

Answer:

0

48

24

12

36

Step-by-step explanation:

Using the graph, determine the coordinates of the x-intercepts of the parabola.

Answers

The result is (0 ; -32). See the 3 pictures for details.

Calculate the volume of a cuboid with length 5.6m breadth 4.1m, height 3.4m

Answers

Answer:  78.064 cubic meter

Step-by-step explanation:

volume of a cuboid=length × breadth × height.

                                =5.6*4.1*3.4

                                =78.064 cubic meter

What is the value of x?​

Answers

The horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa" See: Coordinates.

If this doesn’t answer your question, then do you have any further information?

what’s the domain of this relation?

Answers

Answer:

there is nothing here but thanks for the points

Step-by-step explanation:

Have a great rest of your day/night!

find the value of x
help pleaee

Answers

Answer:

x = 180 - 57 - 79 = 44°

Imagine you are the teacher. Explain how you would walk your student through this problem to answer this problem step by step.

Two hikers leave a cabin at the same time, one heading due south and the other headed due west. After one hour, the hiker walking south has covered 2.8 miles and the hiker walking west has covered 3.1 miles. At that moment, what is the shortest distance between the two hikers?

Answers

Answer:

Due south and due west form a right angle, and the shortest distance between any two points is a straight line. Therefore, we can apply the Pythagorean theorem and write:

3.12+2.82=x2

Here, you will need to use a calculator to simplify the left-hand side:

17.45=x2

Now use your calculator to take the square root. You will likely need to round your answer.

x=17.45−−−−√≈4.18 miles

As you can see, it will be up to you to determine that a right angle is part of the situation given in the word problem. If it isn’t, then you can’t use the Pythagorean theorem.

Step-by-step explanation:

this is my explanation

what distance will the divider be set at the scribe a 02.8" circle? .75" or 1.4" or 2.8" or 5.6"

Answers

9514 1404 393

Answer:

  (b)  1.4"

Step-by-step explanation:

A 2.8" circle is one that has a diameter of 2.8". The divider will be set to the radius, which is half the diameter.

The divider is set to 1.4".

2/3 * n = 12

im not sure what this is please help

Answers

Answer:

n= 18

Step-by-step explanation:

:)

Answer:

18

Step-by-step explanation:

[tex]\frac{2}{3} *n=12\\\frac{2}{3} *n/\frac{2}{3} =12/\frac{2}{3} \\n=18[/tex]

What are the coordinates of the vertex of the graph of the function y=-x^2+ 6x -11?
A. (3.-2)
B. (3.16)
C. (-3, -29)
D. (-3, -20)

Answers

I think the answer is A, but im sorry if its wrong

Answer:

Hi! The answer to your question is D. (-3, -20)

Step-by-step explanation:

☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆

Brainliest is greatly appreciated!

Hope this helps!!

Stay Safe!!!

- Brooklynn Deka

11. Find the sum

2 1/2 + 1 3/4=

Answers

Answer:

It should be 4.25.


The paperweight shown below is in the shape of a square pyramid.

What is the volume of this paperweight?

Answers

Answer:45

Step-by-step explanation:

V=a2h

3=62·3.75

3=45

What is the missing length?
10 km
2
area = 33 km

Answers

Areas are measured in km2, not in km.

HELP PLEASE ILL GIVE BRAINLIEST

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Answer:

The answer is H.) (A, B, C)

Step-by-step explanation:

3 is a whole number and a natural number and 4/3 is a rational number

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