A company sells confetti in boxes in the shape of a triangular
pyramid. Each box contains a volume of 240 cubic centimeters of confetti, If
the height of the box is 15 centimeters, which of the following
could be the area of the base of the box?
Volume Formula:
V number:
h of the 3-D shape number:

Answer:

D

Step-by-step explanation:

Edge 2020

The time taken by the barnacle to get back to its starting point is A = 2π seconds

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be represented as r

Now , the value of r = 1 m

And , the boat is traveling at a rate of 1 m/s

where the total path of the barnacle = circumference of the circle

So , the time taken by the barnacle to get back to its starting point A = circumference of the circle / speed of the boat

On simplifying , we get

The circumference of the circle = 2πr = 2π meters

The time taken by the barnacle to get back to its starting point A = ( 2π / 1 )

The time taken by the barnacle to get back to its starting point A = 2π seconds

Therefore , the value of A is 2π seconds

Hence , the time taken for the circular path is 2π seconds

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The complete question is attached below :

The boat is traveling at a rate of 1 meter per second. How long does it take the barnacle to get back to its starting point?

Answer: no one cares

Step-by-step explanation:

Answer:

Slope intercept: y = -3/2x + 1

Point slope: y + 2 = -3/2 * (x - 2) [Forgot to add the work for this, I will add it if you need it, feel free to ask.]

Step-by-step explanation:

m = (change in y)/change in x)

But also

m = y_2 - y_1/x_2 - x_1

So lets substitute

m = 1 - (-2)/0 - (2)

Lets find the slope

m = 3/0 - (2)

m = 3/-2

m = -3/2 (Moved the negative)

Now we find the value of b using the equation of a line.

y = mx + b

y = (-3/2) * x + b

y = (-3/2) * (2) + b

-2 = (-3/2) * (2) + b

Now we find the value of b

Lets rewrite

-3/2 * 2 + b = -2

Cancel the CF of 2

-3 + b = -2

Move the terms without b to the right

b = -2 + 3

b = 1

Now we substitute our values of the slope and y-int into y = mx + b to find the equation.

y = -3/2x + 1

Answer:

\(y=\frac{-3}{2}x-1\)

Step-by-step explanation:

Given the two points, we can use the slope formula to get the slope of our equation.

\(\frac{y_2-y_1}{x_2-x_1}=m\)

Plug in what we know

\(\frac{(1)-(-2)}{0-2}=m\)

\(m=\frac{-3}{2}\)

\(y=\frac{-3}{2}x-b\)

Plug in one of the points given and solve to find our y-intercept [b]

\(-2=\frac{-3}{2}(2)-b\)

\(b=1\)

(we already know our y-intercept since we're given what y is when x is 0 [hence (0,1)], but this is how it is done if we did not know it initially)

Final equation

\(y=\frac{-3}{2}x-1\)

Answer:

30,000

Step-by-step explanation:

hope this helps!!!

Answer:

Everything but C.

I think.

Step-by-step explanation:

Similar triangles have the same angles and ratios of side lengths.

Do not be surprised if I'm wrong about B.

Answer:

Step-by-step explanation:

In the equation y=kx+1, k is the slope and 1 is the y-intercept.

To find the slope, use the formula k=y2-y1/x2-x1. To use this formula, you need two points. The first point, point M, is given to you. The second point can be the y-intercept, point (0, 1). Now, apply the formula to find the slope: k=3-1/1-0

k=2/1

k=2

We now have the equation y=2x+1.

The next step is to graph the line.

First, graph the y-intercept. Should look something like this: (star represents point. the point is on (0, 1).)

           |

           |

           *

------------------------------

           |

           |        

Then, use the slope to find your second point: (the point is on (1, 3)).

           |    *

           |

           *

------------------------------

           |

           |        

Draw a line through those two points and you have your answer!

Answer:

A- 3 3/4

Step-by-step explanation:

15*1/4= 3 3/4......

Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001

When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.

From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.

It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.

Therefore, the number of flags is 40.

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Answer:

X intercepts = 3/2 and -1,

Bonus the Y intercept is -3

Answer:

h = 0.4 inches

Step-by-step explanation:

Given that,

The volume of the pyramid is 8 in³.

The sides of the pyramid are 5 in and 4 in.

We need to find the height of the pyramid.

The formula for the volume of pyramid is given by :

V = lbh

Where h is the height of the pyramid

So,

\(h=\dfrac{V}{lb}\\\\h=\dfrac{8}{5\times 4}\\\\h=0.4\ in\)

So, the height of the pyramid is 0.4 inches.

Answer:

Since the order of choice matters, we will permute the values.                       a bit more explanation for this:

If the order of choice did NOT matter, ABC and BCA will be counted as one since order of choice does NOT matter

Since order of choice does matter, ABC , BCA and CAB are all different possibilities for the arrangement of the same 3 letters

Since we have 3 slots:

___  ___ ___

Now, for the first slot. You can out either one if the 4 alphabets in the first slot since no slot has been used as of now

So:

_4_ ___ ___

**Keep in mind that the 4 is the possible number of values this slot can have**

Now that one slot has been used, one of the 4 alphabets has been used and since we are not allowed to repeat the same alphabets, we are left with  3 more alphabets

we can put any one of the 3 alphabets in this second slot, Hence:

_4_ _3_ ___

Now that 2 of the 4 alphabets have been used, we are left with only 2 alphabets, so there are only 2 possible alphabets for slot 3

Therefore:

_4_ _3_ _2_

Now that we know the possible alphabets for all 3 slots, we will multiply them with each other to get the total possible number of 3 - alphabet words we can make with 4 alphabets

Total possible words = 4 * 3 * 2

Total possible words = 24

We could've used the formula for Permutation as well

The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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Answer:

y=2x+24

Step-by-step explanation:

Hi there!

We are given that a line has a slope of 2 and passes through (-7, 10)

We want to write the equation of this line in slope-intercept form

Slope-intercept form is written as y=mx+b, where m is the slope and b is the y-intercept

As we are already given the slope, we can immediately substitute it in for m

So replace m with 2 in y=mx+b

y=2x + b

Now we need to find b

As the equation passes through the point (-7, 10), we can use its values to help us find the value of b

Substitute -7 as x and 10 as y

10 = 2(-7) + b

Multiply

10 = -14 + b

Add 14 to both sides

24 = b

Substitute 24 as b into the equation

y = 2x + 24

Hope this helps!

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Answer:

x=-1

Step-by-step explanation:

x+11+x+13=22

2x+24=22

2x=-2

x=-1

Answer:

the answer is 105

Step-by-step explanation:

because 5×3=15 so 15×7 =105

Answer:

If the original cost of a laptop is $199.99 and there is a 13% markup, the retail price of the laptop would be:

Retail price = original cost + (original cost * markup)

= 199.99 + (199.99 * 0.13)

= 199.99 + 25.99927

= $225.98927

Rounded to the nearest cent, the retail price of the laptop would be $225.99.

Step-by-step explanation:

Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

We have ,

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

Hence, Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

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complete question:

A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?

b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?

d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?

e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?

f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?

g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

There are 6 marbles total. Divide the number of blue marbles by the total amount of marbles.

\(\frac{2}{6}\)

Simplify

\(\frac{1}{3}\)

Answer:

  (-1, -7)

Step-by-step explanation:

You want the midpoint of segment AB with end points A(-3, -5) and B(1, -9).

The midpoint has coordinates that are the average of the end point coordinates:

  M = (A +B)/2

  M = ((-3, -5) +(1, -9))/2 = (-3+1, -5-9)/2

  M = (-2, -14)/2 = (-1, -7)

The midpoint of AB is (-1, -7).

__

Additional comment

On the graph, you notice the points are 4 units apart horizontally, and 4 units apart vertically. Dividing each of those measures in half tells you the midpoint is 2 units horizontally and vertically from either end.

  A +(2, -2) = (-3 +2, -5 -2) = (-1, -7) . . . . location of midpoint relative to A

  B +(-2, 2) = (1 -2, -9 +2) = (-1, -7) . . . . . location of midpoint relative to B

Answer:

B.

Step-by-step explanation:

Volume of balloon = 4/3πr³

= 4/3(3.14)(0.5)³

= 0.52 cubic feet

Now

A helium tank contains 50 cubic feet of helium So,

Spherical balloons = 50/0.52

= 95.4

≈ 100

Answer:

60

Step-by-step explanation:

8x6=48

3x4=12

48+12=60

Answer:

you plus them together then you get 42 out of your number you close during / N which is 3 to get your final answer thank

The diameter of the washing machine which is equivalent to the wavelength using the graph above would be = 2.5in.

To calculate the diameter of the washing machine drum, the formula that should be used is given below as follows;

V = fλ

where

V = displacement/time

F = 1/T

But;

Displacement = 10 in

Time = 2 seconds

V = 10/2 = 5 in/s

F = 1/2 = 0.5

λ = 5/0.5 = 2.5in

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The restricted domain of the function is 0≤s≤25

The equation is a(s) = 37.5s - 1.5s²  models the function represented in the table

a(s) = s(37.5 - 1.5s)

The critical points are s=0 or

37.5 - 1.5s

37.5 = 1.5s

s=25

As area can not be negative, the area should be positive

s< 0 and s>25

Therefore, restricted domain is 0≤s≤25

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Answer:

Step-by-step explanation:

Length L = 3 + W

Perimeter P = 42 in

Perimeter = 2L + 2W

plugin values:

42 = 2(3 + W) + 2W

42 = 6 + 2W + 2W

42-6 = 4W

W = 36 / 4

W = 9  

solve L by substituting the value of W=9 into the equation:

L = 3 + W

L = 3 + 9

L = 12

therefore, the dimensions of the rectangle:

                Length = 9 in

                Width = 12 in

The dimensions for the rectangle are 12 in and 9 in if the length of a rectangle is 3 inches more than its width. if the perimeter is 42 inches.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that:

The length of a rectangle is 3 inches more than its width. if the perimeter is 42 inches.

Let l be the length and w  be the width of the rectangle.

Length l = 3 + w

Perimeter P = 42 in

Perimeter = 2l + 2w

42 = 2(3 + w) + 2w

w = 36/4

w = 9 in

solve for l by substituting the value of w = 9 into the equation:

l = 3 + w

l = 3 + 9

l = 12 in

Thus, the dimensions for the rectangle are 12 in and 9 in if the length of a rectangle is 3 inches more than its width. if the perimeter is 42 inches.

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Answer:

(-1,1)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

equation form:
x=-1, y=1

have a great day and thx for your inquiry :)

By substituting each of the provided options into the given system of linear equations, it is revealed that the ordered pair (-1, 1) is a valid solution for both the equations.

The correct answer is (-1, 1)

In mathematics, a system of linear equations consists of multiple linear equations with the same variables. These equations describe various relationships among these variables, typically representing lines in a multi-dimensional space. Solving such systems involves finding values for the variables that satisfy all equations simultaneously. Methods like substitution, elimination, or matrix algebra can be used to solve these systems. These systems are fundamental in fields like physics, engineering, economics, and computer science for modeling and solving real-world problems involving multiple interconnected variables.

We can solve this problem by substituting values from the given options into the equations and checking for which option both equations are valid. The system of linear equations is: x + 4y = 3 and y = -4x - 3.

Therefore, the ordered pair that is a solution to the system of linear equations is (-1, 1).

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The 99 percent confidence interval for the true mean length of the bolt is CI = (2.8712, 3.1288)

Confidence Interval is used to tell us the degree of certainty or uncertainty that is existent in a sampling method.

The general formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

z is z-score at confidence level

s is sample standard deviation

n is sample size

We are given;

sample size; n = 36

Sample mean; x' = 3 inches

standard deviation; s = 0.3 inches

confidence level = 99%

z at 99% CL = 2.576

Thus;

CI = 3 ± 2.576(0.3/√36)

CI = 3 ± 0.1288

CI = (2.8712, 3.1288)

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Answer:

5) P (arrive) + P (not arrive) = 100%   Complements

80% + P( not arrive) = 100%    Substitute thr ralees

P ( not arraive) = 100% - 80%   Isolate the needed

P ( not arrive) = 20%

therefor, the probability of not arriving on time is:-

20%, or 0.20, or 1/5

The complements of arriving on time is not arriving on time.

The probability is equal to 100%

--------------------------------

hope it helps..

have a great day!

1. if you use 1/2 cup of sugar, you need 3/4 cup of flour. To find how many cup of flour do you need for 4 cups of sugar, you can use the next proportion:

Solving for x

You need 6 cups of flour for the first recipe.

Replacing x = 4 into the equation, we get:

You need 7 cups of flour for the first recipe.

2. The constant of proportionality of the table is got dividing the values of the variables. Taking for example, 1/2 cup of sugar and 3/4 cup of flour,

the constant is 3/2 for the first recipe.

In the second recipe, the constant is 7/4; as can be seen in the equation

The constant relates the number of flour cups needed for 1 cup of sugar