An anthill has a volume of 8792 mm3 of dirt. Its radius is 20 mm. How far does an ant have to crawl to get from the base of the cone to the top of the hill? (This is the
slant height, s, of the cone.) Answer the questions to find out.

An Anthill Has A Volume Of 8792 Mm3 Of Dirt. Its Radius Is 20 Mm. How Far Does An Ant Have To Crawl To

Answers

Answer 1

Answer:

The slope is 29 mm.

Step-by-step explanation:

What we know:

The radius of this cone is 20 mm, and the height is 21mm

s = √r^2 + h^2

s = √20^2 + 21^2

s = √400 + 441

s = √841

s = 29 mm

Answer 2

The slant height of the cone is required,

The ant would have to crawl [tex]29\ \text{mm}[/tex]

Volume of cone

V = Volume of cone = [tex]8792\ \text{mm}^3[/tex]

r = Radius of cone = 20 mm

h = Height

s = Slant height.

Volume of a cone is given by

[tex]V=\dfrac{1}{3}\pi r^2h\\\Rightarrow h=\dfrac{3V}{\pi r^2}\\\Rightarrow h=\dfrac{3\times 8792}{3.14\times 20^2}\\\Rightarrow h=21\ \text{mm}[/tex]

From Pythagoras theorem we have

[tex]s=\sqrt{r^2+h^2}\\\Rightarrow s=\sqrt{20^2+21^2}\\\Rightarrow s=29\ \text{mm}[/tex]

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Related Questions

Shanika is making a decorative tablecloth for her small circular table. The table has a radius of 40 centimeters and height of 60 centimeters. She wants the tablecloth to hang an even 10 centimeters above ground.

Which design would give Shanika what she wants?

A. a circular piece of cloth with radius of 90 cm

B. a circular piece of cloth with radius of 110 cm

C. a circular piece of cloth with radius of 100 cm

D. a circular piece of cloth with radius of 130 cm

Answers

The answer is definatly NOT D. I think that the answer is A.

The design that should  give Shanika what she wants is the radius of 90 cm.

Calculation of the design:

Since The table has a radius of 40 centimeters and height of 60 centimeters. She wants the tablecloth to hang an even 10 centimeters above ground.

So, the radius is

= 40 + 60 - 10

= 90 cm

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help plz ive been stuck on this for a while now

Answers

Answer:1.20/5

Step-by-step explanation:

Answer:

9/10 or in decimal form 0.9

Step-by-step explanation:

Square ABCD has vertices A(-4.5, 4), B(3.5, 4),C(3.5, -4), and D(-4.5, -4). What is the area of square ABCD?

Answers

Answer:

that answer is b

Step-by-step explanation:

hope this helps

The area of square ABCD would be; 64 unit sq.

What is the distance between two points ( p,q) and (x,y)?

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]    units.

Given that Square ABCD has vertices; A(-4.5, 4), B(3.5, 4),C(3.5, -4), and D(-4.5, -4).

To find the distance from two of the vertices of the square. The distance formula is as follows;

√[(x-p)² + (y-q)²]  

A(-4.5, 4), B(3.5, 4),

D = √[(x-p)² + (y-q)²]  

D = √(3.5-(-4.5))² +(4 -(4))²

D = √(3.5-(-4.5))² +(4 -(4))²

D = √(64 + 0)

D = 8

Therefore, the side of the square is 8 units.

The area of the square = side x side

= 8 x 8

= 64 unit sq.

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#SPJ2

Lexi runs the snack stand at Belleview Community Pool. This morning, she withdrew $150 from the stand's bank account to buy supplies. When the stand closed this evening, she deposited $437 from the day's sales. What was the total change in the stand's bank account relative to where it started?

Answers

Answer:

Step-by-step explanation:

Let the initial money in the account be y.

Lexi withdrew $150 from the stand's bank account to buy supplies. This will be:

= y - $150

Later, she deposited $437 from the day's sales. The money in the account will now be:

= y - $150 + $437

= y + $287

The total change in the stand's bank account relative to where it started will be the initial amount + $287.

Answer:

287

Step-by-step explanation:

help please i'll love you forever thanksssss . *btw i am going to post a lot of questions if you answer & explain I'll give you brainliest each time .*

Isabella noticed that when she doesn't study for a test, on average she makes a 45. Isabella also realizes that for every hour she studies, on average she scores an additional 7 points. Which of the following represents g, get average test score she studied for h hours?

a. 7-5h=g
b. 7+5h=g
c. 45+7h=g
d. 45-7h=g

Answers

Answer:

C. 45 + 7h = g

Step-by-step explanation:

This one would be correct because you have to add 7 points to the 45 points she would get on average without studying, without forgetting to multiply 7 by the number of hours that Isabella studied.

Example:

Let's say that Isabella studied for 3 hours. We could replace the h for the number of hours that she studied.

45 + 7(3) = g

Now you just have to solve the equation.

45 + 21 = g

Following the rules of PEMDAS, you would get rid of the parenthesis first by multiplying 7 times 3. Now you just have to add and you will have your answer for g.

g = 66

What is the equation of the line that passes through the point (6,-4) and has a
slope of -1/6

Answers

Answer:

y = -1/6x-3

hope this helps

Answer:

x+6y+18=0

Step-by-step explanation:

we have to use (y-y1)=m(x-x1)

now,(x1,y1)=(6,-4),m=-1/6

so, (y+4)=-1/6(x-6)

or,6y+24=-x+6

or,x+6y+24-6=0

x+6y+18=0 is the required equation.

I need the answer!!!! The original price of Doritos is the same at both Wal-Mart and Kroger. Jon found out that Wal-Mart had Doritos on sale at $0.50 off per bag and bought four bags. Later that day, he found out that Kroger had Doritos on sale at $1 off per bag and bought six bags. If he paid the same amount at both stores, what was the original price of Doritos?

write an equation and solve by using the distributive property, combining like terms, and eliminating the variable on one side of the equation. You must SHOW YOUR WORK!!!!

Answers

Answer:

I believe it would be $2 per bag normally.

Step-by-step explination:

If you take $2 and subtract $.50 it is $1.50. Take that multiplied by the number of bags he bought (4), would mean he spent $6 at Wal-mart.

Now $2 subtracted my the sale of $1, is $1 per bag. If he bought 6 bags at Kroger, 1 multiplied by 6, would equal 6. Meaning he spent $6 at both stores if the price was $2.

It’s the first one that I need help with

Answers

Answer:

4x-3(6x-1)=-11

Step-by-step explanation:

6x-y=1

-y=-6x+1

y=6x-1

4x-3y=-11

4x-3(6x-1)=-11

you are planning a party for 12 people and you purchase 4 bags of candy.If you have a party for 21 people,how many bags of candy should you purchase

Answers

Answer:

7

Step-by-step explanation:

one bag of candy for every three people

12 ÷ 4 = 3

21 ÷ 7 = 3

Answer:

7  

Step-by-step explanation:

Apply proportions:

People/bag of candy

[tex]\frac{12}{4}[/tex]

For 21 people

[tex]\frac{21}{x}[/tex]

Equal both expressions

[tex]\frac{12}{4} =\frac{21}{x}[/tex]

Solve for x:

[tex]x=21\frac{12}{4} \\x= \frac{21}{3} \\x=7[/tex]

You should purchase 7 bags of candy

PLSS!!!! HELP!!! ME I WILL MARK U!!!!

Answers

Answer:

562

Step-by-step explanation:

Plug in the values of x, y, and z provided.

(5(5)-1)^2-2(7)

Solve.

(25-1)^2-14

(24)^2-14

576-14

562

Answer: 562

Step-by-step explanation:

(5x+y)^2-2z

first put in the known values. (5(5)+(-1))^2-2(7)

(25+-1)^2-14

Second, do 25+-1=24

(24)^2-14

Third, do 24 squared

576-14

Subtract

562

SOME 1 HELP WITH 11 PLZZZZ

Answers

Answer: Tiffany got 45 questions right! Hope this helped.

Step-by-step explanation:

help please show steps please I don't know what to do so I want to learn not just get the answer ​

Answers

The answer is -6 I put the work under here

What is the Y-intercept and The slope of the equation?
2x+7y=14

Can someone please help me with this!!!

Slope choice:
A. 2/7
B. 7/2
C. -2/7
D. -9

Y-intercept choices
A. 2
B. 7
C. -2
D. 0

Answers

Answer:

Slope = -2/7; Y intercept = +2

Step-by-step explanation:

First, for this particular question - we want to convert the equation to slope intercept form! You may recognize it already, it looks like this:

y = mx + b

Here's how:

[tex]2x+7y=14\\2x+7y - 2x = -2x+14\\7y=-2x+14\\\frac{7y}{7} =\frac{-2x+14}{7} \\y = \frac{-2}{7}x+2[/tex]

The above shows this equation in slope intercept form: y = -2/7x + 2.

The slope of this line is -2/7 while the y intercept is 2!

*Note*: In the slope-intercept formula, m stands for the slope, and the b is the intercept!

Hope I was of assistance! Algebra can be a little difficult but you'll get it! Have a nice day and spread the love! <3

Solve 5(x+9) - 4 = 71 for x

Answers

Solving for x you would get X=6

Answer:

x = 6

Step-by-step explanation:

5 times x is 5x, 5 times 9 is 45; 5x+49-4; 49 minus 4 is 45; 5x+45 = 75; now minus 45 from each side so it would now be 5x = 30; now divide; 30/5 = 6.

If (ax^2 + 3x + 2b) - (5x^2+bx-3c)=3x^2-9, what is the value of A + B + C?

Answers

Answer:

We have the equation:

(ax^2 + 3x + 2b) - (5x^2+bx-3c)=  3x^2 - 9

First, move all to the left side.

(ax^2 + 3x + 2b) - (5x^2+bx-3c) - 3x^2 + 9 = 0

Now let's group togheter terms with the same power of x.

(a - 5 - 3)*x^2 + (3 - b)*x + (2b + 3c + 9) = 0.

This must be zero for all the values of x, then the things inside each parenthesis must be zero.

1)

a - 5 - 3 = 0

a = 3 + 5 = 8.

2)

3 - b = 0

b = 3.

3)

2b + 3c + 9 = 0

2*3 + 3c + 9 = 0

3c = -6 - 9 = -15

c = -15/3 = -5

Then we have:

a = 8, b = 3, c = -5

a + b + c = 8 + 3 - 5 = 6

Which line is steeper Line A or Line D? EXPLAIN. PLEASE HELP I WILL MARK BRAILIEST!!

Answers

It would be line A, because of the fact the it is rising at a faster rate.

Answer:

line A is steeper.

Line A´s slope is 1, while line d´s slope is 2/5

What is the slope of the graph of 3x - 3y = 6?

Answers

Answer:

pls help

Step-by-step explanation:

PLEASE HELP!!! MATH FINAL

Answers

Answer:

He Won 26 Box trolls and 11 Pikachus

Step-by-step explanation:

You subtract 37-11 which would get you 26

26 and 11...............

8. The length of an actual road is
1,000 miles. If 1 inch represents
100 miles, what is the length of
the road on the map?

Answers

Answer:

It's A.

Step-by-step explanation:

Answer:

10 inches

Step-by-step explanation:

1,000 / 100 = 10

Are these expressions equivalent?
yes or no

Answers

Answer:

yes they are equivalent

The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time.
A'(t) =???​

Answers

MARK AS BRAINLIST

Step-by-step explanation:

L = 6t+5

H = √t

A = L*H

= (6t+5) *√t = 6t√t + 5√t

A'(t) = 6t * 1/2*√t + √t * 6 + 5/2*√t

= 6t/2√t + 6√t + 5/2√t

Expression for the rate of change of the area with respect to time will be,

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex] cm per second

It's given in the question,

Length of a rectangle is given by the expression

      (6t + 5) cm

Width or height of the rectangle is given by the expression,

       [tex]\sqrt{t}[/tex] cm

Area of the rectangle is given by,

Area = Length × Height

A = (6t + 5)(√t)

A = [tex]6t^{\frac{3}{2}}+5t^\frac{1}{2}[/tex]

Now find the derivative of area (A) with respect to time (t).

[tex]\frac{dA}{dt}=\frac{d}{dt}(6t^{\frac{3}{2}}+5t^\frac{1}{2})[/tex]

A' = [tex](6\times \frac{3}{2})t^\frac{1}{2}+\frac{5}{2} t^{-\frac{1}{2}}[/tex]

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]

     Therefore, expression for the rate of change of the area will be,

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]

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Jordan invested $97,000 in an account paying an interest rate of 1.6% compounded
monthly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest year, for the value of the account to reach $109,700?

Answers

ill give u the answer hold up i gotta do the work

Answer:

t≈ 8

Step-by-step explanation:

\text{Compounded Monthly:}

Compounded Monthly:

A=P\left(1+\frac{r}{n}\right)^{nt}

A=P(1+  

n

r

​  

)  

nt

 

Compound interest formula

A=109700\hspace{35px}P=97000\hspace{35px}r=0.016\hspace{35px}n=12

A=109700P=97000r=0.016n=12

Given values

109700=

109700=

\,\,97000\left(1+\frac{0.016}{12}\right)^{12t}

97000(1+  

12

0.016

​  

)  

12t

 

Plug in values

109700=

109700=

\,\,97000(1.0013333)^{12t}

97000(1.0013333)  

12t

 

Simplify

\frac{109700}{97000}=

97000

109700

​  

=

\,\,\frac{97000(1.0013333)^{12t}}{97000}

97000

97000(1.0013333)  

12t

 

​  

 

Divide by 97000

1.1309278=

1.1309278=

\,\,1.0013333^{12t}

1.0013333  

12t

 

\log\left(1.1309278\right)=

log(1.1309278)=

\,\,\log\left(1.0013333^{\color{blue}{12t}}\right)

log(1.0013333  

12t

)

Take the log of both sides

\log\left(1.1309278\right)=

log(1.1309278)=

\,\,\color{blue}{12t}\log\left(1.0013333\right)

12tlog(1.0013333)

Bring exponent to the front

\frac{\log\left(1.1309278\right)}{\log\left(1.0013333\right)}=

log(1.0013333)

log(1.1309278)

​  

=

\,\,\frac{12t\log\left(1.0013333\right)}{\log\left(1.0013333\right)}

log(1.0013333)

12tlog(1.0013333)

​  

 

Divide both sides by log(1.0013333)

92.3402971=

92.3402971=

\,\,12t

12t

Use calculator

\frac{92.3402971}{12}=

12

92.3402971

​  

=

\,\,\frac{12t}{12}

12

12t

​  

 

Divide by 12

7.6950248=

7.6950248=

\,\,t

t

Multiply 2.89x 23.2 =​

Answers

2.89 x 23.2
289 x 232 = 67048
67.048

67.048

-2 (3x - 6) + 4 (5x - 8) = 92

Answers

Answer: x=7

Step-by-step explanation:

John sold 32 poster prints of his artwork in September for a total of $126. In October, he sold 48 prints of his artwork for $240. If the relationship between the number of poster prints and total earnings is linear, what was the cost per print expressed as a slope(# of posters sold, $posters sold for)?(complete sentence answer

Answers

Given:

In September, John sold 32 prints of his artwork for $126.

In October, he sold 48 prints of his artwork for $240.

To find:

The cost per print expressed as a slope.

Solution:

Let y be the cost of x prints.

The relationship between the number of poster prints and total earnings is linear.

In September, John sold 32 prints of his artwork for $126. So, the line passes through (32,126).

In October, he sold 48 prints of his artwork for $240. So, the line passes through (48,240).

Now, the slope of the line is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{240-126}{48-32}[/tex]

[tex]m=\dfrac{114}{16}[/tex]

[tex]m=7.125[/tex]

The slope of the linear function 7.125.

Therefore, the cost of per print is $7.125.

If you know that the product (x) of two powers is 15^13 and the quotient (÷) of the same two powers is 5, what could the two powers be? How could you verify your answer?​

Answers

Answer:

if u get it pls tell me

Step-by-step explanation:

is 54/35 a rational number?

Answers

Answer:

54/35 is a rational number!

Have a great rest of your day!

Answer:

Yes and no

Step-by-step explanation:

The number 54 is a rational number if 54 can be expressed as a ratio, as in Rational. A quotient is the result you get when you divide one number by another number. Although the 54 is good the 35 is not due to it if you had to choose if it was or not you can say yes but it determines the question.

Make Sense and Persevere A submarine
descends to of its maximum depth. Then it
descends another of its maximum depth. If it
is now at 650 feet below sea level, what is its
maximum depth?

Answers

Answer: 325 feet

Explanation: you cut the amount of feet below sea level in half since it only depended twice. And you get 325

(3x^8)(5x) simplify using Law of exponent

Answers

It would be 15x^5 if u need the steps comment

For each set of angle measurements, determine if they would form a triangle (Answer YES or NO for
each)
1. 120, 50, 10
2. 100, 91. 25
3. 90, 60, 30
4. 77, 54, 49
5. 177. 2,1

Answers

Answer:

1. yes

2. no

3. yes

4. yes

5. yes

Step-by-step explanation:

All triangles have 3 angle measurements that add up to 180

I did these all mentally so do double check :)

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