X,Y and Z are three points on a unit sphere (i.e. a sphere with radius 1). The space
distance between any pair of the three points is √2 . An ant can only
crawl on the surface of the sphere. The ant starts from point X, passes through points Y and Z, and then returns to X. What is the shortest possible distance of this trip?

Step-by-step explanation:

write what you know

A = pi x r^2

r = 6ft

Annd plug and chug

Answer:

[tex]\boxed {\boxed {\sf a \approx 113.0 \ ft^2}}[/tex]

Step-by-step explanation:

The area of a circle is the space inside the shape. The formula is:

[tex]a= \pi r^2[/tex]

We know the radius of the circle is 6 feet and we are using 3.14 for pi.

Substitute the values into the formula.

[tex]a= (3.14) \times (6 \ ft)^2[/tex]

Solve the exponent.

[tex]a= (3.14) \times 36 \ ft^2[/tex]

Multiply.

[tex]a=113.04 \ ft^2[/tex]

Let's round to the nearest tenth. The 4 in the hundredth place tells us to leave the 0 in the tenths place.

[tex]a \approx 113.0 \ ft^2[/tex]

The area of the circle is approximately 113.0 square feet.

Answer:

Sorrry i dont know

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

y = -2x

The negative slope means it goes down from left to right ( we eliminate Choice a)

Y = mx+b  b is the y intercept

The b in the above equation is 0, so it must go through zero

That means the graph of the line is B

Answer:

B

Step-by-step explanation:

Because the equation is put in y = kx form the y intercept will be at the origin (0,0)

All graphs except B do not go through the origin

So b likely graphs y = -2x

Answer:

Mars

Step-by-step explanation:

100,000,000 kilometers, write a proportion Nadia could use to create her model on the grid paper. Use the proportion to find the distance for each planet on the model.

Answer:

0.83 mi/min

Step-by-step explanation:

Start with 80 km/hr.  Convert this to the units miles/hr:

(80 km/hr)(1 mile/1.6 km) = 50 miles/hr

Next, apply the equality 60 min / 1 hr = 1 to 50 miles/hr:

50 miles.      1 hr

------------- * ------------ = 5/6 mi/min, or 0.83 mi/min

     hr          60 min

Answer:

See Below.

Step-by-step explanation:

Let the intersection point above E be K, and let the intersection point below E be J.

Since ABCD is a trapezoid:

[tex]\displaystyle AB\parallel DC[/tex]

Therefore:

[tex]\displaystyle \angle AJF\cong \angle DKF[/tex]

And:

[tex]\displaystyle \angle DFJ\cong \angle DFJ[/tex]

So, by AA-Similarity:

[tex]\displaystyle \Delta DFK\sim \Delta AFJ[/tex]

CPSTP (Corresponding Parts of Similar Triangles are Proportional):

[tex]\displaystyle \frac{KD}{JA}=\frac{FK}{FJ}[/tex]

Likewise, do the same to the other side. Since AB is parallel to DC:

[tex]\displaystyle \angle BJF\cong CKF\text{ and } \angle CFJ\cong \angle CFJ[/tex]

Hence:

[tex]\Delta CFK\sim \Delta BFJ[/tex]

By CPSTP:

[tex]\displaystyle \frac{KC}{JB}=\frac{FK}{FJ}[/tex]

Substitution:

[tex]\displaystyle \frac{KD}{JA}=\frac{KC}{JB}[/tex]

Since AB is parallel to DC:

[tex]\displaystyle \angle CDB\cong \angle ABD[/tex]

By vertical angles:

[tex]\angle DEK\cong BEJ[/tex]

Hence, by AA-Similarity:

[tex]\Delta DKE\sim \Delta BJE[/tex]

CPSTP:

[tex]\displaystyle \frac{KD}{JB}=\frac{KE}{JE}[/tex]

Likewise:

[tex]\angle DCE\cong \angle BAC[/tex]

And by vertical angles:

[tex]\displaystyle \angle CEK\cong \angle AEJ[/tex]

Hence:

[tex]\Delta CKE\sim \Delta AJE[/tex]

CPSTP:

[tex]\displaystyle \frac{KC}{JA}=\frac{KE}{JE}[/tex]

Substitution:

[tex]\displaystyle \frac{KD}{JB}=\frac{KC}{JA}[/tex]

Now, we have obtained that:

[tex]\displaystyle \frac{KD}{JA}=\frac{KC}{JB}[/tex]

And:

[tex]\displaystyle \frac{KD}{JB}=\frac{KC}{JA}[/tex]

In the second proportion, multiply both sides by JA:

[tex]\displaystyle \frac{KD\cdot JA}{JB}=KC[/tex]

In the first equation, multiply both sides by JB:

[tex]\displaystyle \frac{KD\cdot JB}{JA}=KC[/tex]

Substitute:

[tex]\displaystyle \frac{KD\cdot JA}{JB}=\frac{KD\cdot JB}{JA}[/tex]

Cross-multiply:

[tex]JB\cdot KD\cdot JB=JA \cdot KD\cdot JA[/tex]

Cancel out KD and simplify:

[tex]JB^2=JA^2[/tex]

Therefore:

[tex]JB=JA[/tex]

And using the first proportion again:

[tex]\displaystyle \frac{KD}{JA}=\frac{KC}{JA}\Rightarrow KD=KC[/tex]

Hence, EF bisects AB and DC, the bases of the trapezoid.

Answer:

8

Step-by-step explanation:

p = ?

h = 10

b = 6

Now,

p2 = h2 - b2

p2 = ( 10)2 - (6)2

p2 = 100 - 36

p2 = 64

p = root under (64)

p = 8

Answer:

13, 14, 13, 4.6, 48

Step-by-step explanation:

these are the x-values I have but I don't know hot to solve for th code.

Answer:

7.2 is your answer:)

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

because it's the exact value

Answer:

5

Step-by-step explanation:

Verticle angles are the angles opposite of each side.

Answer:

I think only 5

hope this helps

have a good day :)

Step-by-step explanation:

if you have to choose more it would be 5 and 6

Answer:

I am not sure, but I think 362 is the answer

Step-by-step explanation:

hundred digit:x

tens digit:2x

ones digit:x-1

x+2x+x-1=11

4x=12

x=3

number=362

Answer:

Blue

Step-by-step explanation:

The experimental probability (and theoretical probability) of drawing a blue marble is the highest:

[tex]\checkmark\:\text{Blue: }\frac{16}{40},\\\text{Red: }\frac{14}{40},\\\text{Yellow: }\frac{10}{40},[/tex]

Answer:

B

Step-by-step explanation:

hope it helps

Answer:

A is your answer

Answer:

yes that is a statistical question

Step-by-step explanation:

Answer:

isosceles and obtuse

Step-by-step explanation:

We have 2 sides that are equal length - isosceles

We have an angle that is greater than 90 and less than 180 - obtuse

Answer:

B. Isosceles and Obtuse

Step-by-step explanation:

Two sides of the triangle have equal length, and one angle is more than 90 degrees.

Answer: 0.3

Step-by-step explanation:

Answer:

The heavier boy would weigh 86 pounds.

Step-by-step explanation:

Let's say boy=b, the equation would be:

2b+34=138

This is because the boys would weigh the same, with an exception of 34 pounds.

But we need to find just one person's weight. So bring 34 to the other side:

2b=138-34

Solve:

2b=104

Now, we need to find b:

b=52

So one boy would weigh 52, and the other would weigh 52+34, which is 86.

The heavier boy would weigh 86 pounds.

Happy learning!

--Applepi101

Step-by-step explanation:

1st one

2nd

4th

Answer:

2√2

Step-by-step explanation:

< C = 180-15-45 = 120°

AC/sin 45° = AB/sin 120°

AC = 2√3 × sin 45° / sin 120°

= 2√3 × ½√2 / ½√3

= 2√2

Answer:

2√2

Step-by-step explanation:

Answer:

4523.89m

So for a cylinder it is radius times two. Then multiply your answer by pie 3.14 then times high.

Answer:

8 outfits with change

Step-by-step explanation:

if you add up the prices of the objects and divide it then you get 8.989

Answer:

[tex]2f \: \alpha \: d \\ 2f = kd \\ : k \: is \: a \: constant \\ 2( \frac{3}{4} ) = k \times 1 \\ k = \frac{3}{2} \\ \therefore2f = \frac{3}{2} d \\ 4f = 3d \\ f = \frac{3}{4} d[/tex]

Answer:

1.

25 of the 36 collars will be accepted. I just counted the numbers that were either "14" "15" or "16" because the company will only accept the collars that have 14-16 miligrams of medicine in them.

2. I expect the company to reject 11 of them because 25-36 = 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

Okayy, so we know that the domain for the flea collars (let's call them x for short) is:

[tex]14\leq x\leq 16[/tex]

So basically we can eliminate all of the numbers that don't fit the inequality

In this set of numbers we are looking to eliminate the 13's and the 17's

17, 14, 14, 16, 14, 15, 15, 15, 16, 14, 16, 14, 15, 15, 15, 16, 13, 13

13, 13, 13, 14, 14, 13, 17, 14, 15, 13, 14, 15, 16, 17, 14, 17, 14, 15

The bolded ones are the ones to eliminate, also that took way too long to type those :,)

Now here's what's left:

14, 14, 16, 14, 15, 15, 15, 16, 14, 16, 14, 15, 15, 15, 16

14, 14, 14, 15, 14, 15, 16, 14, 14, 15

Now we can answer the questions

A) What percent of collars would be acceptable?

To find this answer we must find the percent of collars that are left out of all of the collars we used to have

(I hope that makes somewhat sense)

To find this we need to know the number of collars we started with and the number of collars we have left

We started with 36

We have 25 left

25/36 is about

69.44 percent

This number works even though we only used 36 because the ratio of good collars to be bad collars should be consistent throughout the whole 720 collars

nExT qUeStIoN

B) How many collars

There are probably other ways to approach this, but I'll focus on a proof by induction.

The base case is that n = 1. Plugging this into the expression gets us

n^3+11n = 1^3+11(1) = 1+11 = 12

which is a multiple of 6. So that takes care of the base case.

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

Now for the inductive step, which is often a tricky thing to grasp if you're not used to it. I recommend keeping at practice to get better familiar with these types of proofs.

The idea is this: assume that k^3+11k is a multiple of 6 for some integer k > 1

Based on that assumption, we need to prove that (k+1)^3+11(k+1) is also a multiple of 6. Note how I've replaced every k with k+1. This is the next value up after k.

If we can show that the (k+1)th case works, based on the assumption, then we've effectively wrapped up the inductive proof. Think of it like a chain of dominoes. One knocks over the other to take care of every case (aka every positive integer n)

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

Let's do a bit of algebra to say

(k+1)^3+11(k+1)

(k^3+3k^2+3k+1) + 11(k+1)

k^3+3k^2+3k+1+11k+11

(k^3+11k) + (3k^2+3k+12)

(k^3+11k) + 3(k^2+k+4)

At this point, we have the k^3+11k as the first group while we have 3(k^2+k+4) as the second group. We already know that k^3+11k is a multiple of 6, so we don't need to worry about it. We just need to show that 3(k^2+k+4) is also a multiple of 6. This means we need to show k^2+k+4 is a multiple of 2, i.e. it's even.

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

If k is even, then k = 2m for some integer m

That means k^2+k+4 = (2m)^2+(2m)+4 = 4m^2+2m+4 = 2(m^2+m+2)

We can see that if k is even, then k^2+k+4 is also even.

If k is odd, then k = 2m+1 and

k^2+k+4 = (2m+1)^2+(2m+1)+4 = 4m^2+4m+1+2m+1+4 = 2(2m^2+3m+3)

That shows k^2+k+4 is even when k is odd.

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

In short, the last section shows that k^2+k+4 is always even for any integer

That then points to 3(k^2+k+4) being a multiple of 6

Which then further points to (k^3+11k) + 3(k^2+k+4) being a multiple of 6

It's a lot of work, but we've shown that (k+1)^3+11(k+1) is a multiple of 6 based on the assumption that k^3+11k is a multiple of 6.

This concludes the inductive step and overall the proof is done by this point.

Answer:

x = 10

Step-by-step explanation:

Pythagorean Theorem = a² + b² = c²

6² + 8² = c²

36 + 64 = c²

100 = c²

c = 10

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

10

Step-by-step explanation:

pythagorean thereom

6^2 + 8^2 = c^2

100 = C^2

c = 10