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Ivahew [28]
3 years ago
7

A coffee dispensary uses ⅘ of a barrel of coffee beans per batch of coffee they ship. Yesterday, the dispensary used 3 ⅕ of a ba

rrel of coffee beans. How many batches of coffee did they produce?
Mathematics
1 answer:
KengaRu [80]3 years ago
4 0

Answer:

4 batches

Step-by-step explanation:

First, you need to convert the mix number into a single fraction:

3 1/5 = 16/5 total barrels of coffee beans used

This allows us to divide the numbers easier in the next step.

Next, because each batch uses 4/5 of a barrel of beans, you need to divide 16/5 by 4/5:

(16/5) / (4/5) = 16/4 = 4 batches

(The fives cancel out because they are the same divisor.)

I hope this helps!

-TheBusinessMan

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Which angles are supplementary to each other?
Rus_ich [418]

Answer:

Angle 4 and Angle 1 are supplementary to each other.

Step-by-step explanation:

A line is 180°. Because angle 4 and angle 1 and right next to each other and they share a straight line, both of their angles should add up to 180°, making these two angles supplementary.

I hope this was helpful to you! If it was, please rate and press thanks! Have a fantastic day!

6 0
2 years ago
Please help me with this one I don’t understand. I need help with #20 thank you!
dimaraw [331]

part A)

we know that for every 1000 ft the temperature drops by 1.3.

so after 1000ft up it went down by 1.3(1)

2000ft up it went down by 1.3(2) or 2.6

3000ft up it went down by 1.3(3) or 3.9

after 10000 up it went down by 1.3(10) or 13.

part B)

well, the current temperature on the ground where the plane is sitting is -2.8°F, after 10000ft it dropped by 13°, so the temperature will just be -2.8 - 13 = -15.8°F.

8 0
3 years ago
A 20 foot ladder leaning against a wall is used to reach a window that is 17 feet above the ground. How far from the wall is the
GarryVolchara [31]

The bottom of the ladder is 10.5 feet away from the wall

Step-by-step explanation:

The given scenario forms a right triangle.

Where

The length of ladder will be the hypotenuse

The wall on which the window is situated will ebt he perpendicular and

The distance between the foot of ladder and the wall will be the base

So,

Hypotenuse = H = 20 foot

Perpendicular = P = 17 feet

Base = B = ?

Using the Pythagoras theorem

H^2=P^2+B^2\\(20)^2=(17)^2+B^2\\400=289+B^2\\400-289=B^2\\B^2=111\\Taking\ square\ root\ on\ both\ sides\\\sqrt{B^2}=\sqrt{111}\\B=10.53\\Rounding\ off\ to\ the\ nearest\ tenth\\B=10.5

The bottom of the ladder is 10.5 feet away from the wall

Keywords: Triangle, Pythagoras Theorem

Learn more about Pythagoras theorem at:

  • brainly.com/question/9532142
  • brainly.com/question/9590016

#LearnwithBrainly

8 0
2 years ago
Factorizar o descomponer en de FACTORES
Charra [1.4K]
Not sure if you’re speaking Spanish or not but yes
5 0
2 years ago
Prove for any positive integer n, n^3 +11n is a multiple of 6
suter [353]

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.

6 0
3 years ago
Read 2 more answers
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