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3 years ago

if jacob used 1/7 of a liter of water to fill 1/9 of a fish aquarium how many liters are needed to fill the aquarium

1 answer:

6 0

1/9 of the aquarium was filled with 1/7 liter

1 whole fraction of the aquarium will be filled = 1/7 ÷ 1/9

= 1/7 * 9/1 = 9/7

9/7 liters or 1 2/7 liters will be needed.

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Decide whether the change is an increase or a decrease, and find the percent change. Original number = 35; New number = 16.... P

Elodia [21]

Answer: 60 decrease or 150 decrease

Step-by-step explanation:

3 0

3 years ago

Create a Sample Space diagram and work out the probability - There is a 4 sided dice (numbers 1 to 4) and an 8 sided dice (numbe

tester [92]

Answer:

7 / 16

Step-by-step explanation:

Sample space is attached below :

Theoretical Probability of any event A

P(A) = (number of required outcome / Total number of possible outcomes)

Required outcome = sum greater than 7 = 14

Total number of possible outcomes = 32

P(sum greater than 7) = 14 / 32

P(sum greater than 7) = 7 / 16

3 0

3 years ago

In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distanc

umka21 [38]

Answer / Step-by-step explanation:

(1) Given t = 0.0588s ¹.¹²⁵

where s is the distance and t is the time to run that distance.

The second portion asks us to find the derivative of the equation when our s value is equal to 20 and interpret.

(2) First, we try to convert the unit from miles to meters

Therefore, 1 mile = 1609 meters

Then,

t = 0.0588 ( 1609 ) ¹.¹²⁵

=238 . 09

This gives us the instantaneous rate of change of seconds between every 20 meters ran.

The last portion asks us to compare this estimate to current world records. And have they been surpassed?

As of today, the fastest official record for a standard mile is held by a man from Morocco named Hichan El Guerrouj. The time was recorded at 3.43 minutes in Rome, Italy on July 7th, 1999.

Now, keep in mind that this is almost a full minute slower than the estimated time. However, how do these projections hold up against Usain Bolt, the man that is considered the fastest man in the world ?

Although, Usain Bolt does run long distances, he holds records in nearly every sprinting event that he has ever competed in.

Hence, Kennelly's estimate for the fastest mile is 238.09

(3) Now, noting that since dt / ds = 0.0588 ( 1.25 ) s ⁰.¹²⁵

Then,

dt / ds I 100 = 0.0588 (1.25) (20) ⁰.¹²⁵

= 0.1176

6 0

3 years ago

Luke shade 20 squares on his hundredths grid. Bekka shaded 30 squares on her hundredths grid.

masha68 [24]

Answer:

50 hundredths

Step-by-step explanation:

20 + 30= 50

4 0

3 years ago

A.Find a formula for

snow_lady [41]

Answer:

a) $\frac{n}{n+1}$

b) Proof in explanation.

Step-by-step explanation:

$\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4}+\cdots+\frac{1}{n(n+1)}$ .

So let's look at the last term for a minute:

$\frac{1}{n(n+1)}$

Let's use partial fractions to see if we can find a way to write this so it is more useful to us.

$\frac{1}{n(n+1)}=\frac{A}{n}+\frac{B}{n+1}$

Multiply both sides by $n(n+1)$ :

$1=A(n+1)+Bn$

Distribute:

$1=An+A+Bn$

Reorder:

$1=An+Bn+A$

Factor:

$1=n(A+B)+A$

This implies $A=1$ and $A+B=0$ which further implies that $B=-1$ .

This means we are saying that:

$\frac{1}{n(n+1)}$ can be written as $\frac{1}{n}+\frac{-1}{n+1}$

We can check by combing the fractions:

$\frac{n+1}{n(n+1)}+\frac{-n}{n(n+1)}$

$\frac{n+1-n}{n(n+1)}$

$\frac{1}{n(n+1)}$

So it does check out.

So let's rewrite our whole expression given to us using this:

$(\frac{1}{1}+\frac{-1}{2})+(\frac{1}{2}+\frac{-1}{3})+(\frac{1}{3}+\frac{-1}{4})+\cdots +(\frac{1}{n}+\frac{-1}{n+1})$

We should see that all the terms in between the first and last are being zeroed out.

That is, this sum is equal to:

$\frac{1}{1}+\frac{-1}{n+1}$

Multiply first fraction by (n+1)/(n+1) so we can combine the fractions:

$\frac{n+1}{n+1}+\frac{-1}{n+1}$

Combine fractions:

$\frac{n}{n+1}$

Proof:

Let's see what happens when n=1.

Original expression gives us $\frac{1}{1 \cdot 2}=\frac{1}{2}$ .

The expression we came up with gives us $\frac{1}{1+1}=\frac{1}{2}$ .

So it is true for the base case.

Let's assume our expression and the expression given is true for some integer k greater than 1.

We want to now show it is true for integer k+1.

So under our assumption we have:

$\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\cdots \frac{1}{k(k+1)}=\frac{k}{k+1}$

So let's add the (k+1)th term of the given series on both sides:

$\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\cdots \frac{1}{k(k+1)}+\frac{1}{(k+1)(k+2)}=\frac{k}{k+1}+\frac{1}{(k+1)(k+2)}$

(Now we are just playing with right hand side to see if we can put it in the form our solution which be if we can $\frac{k+1}{k+2}$ .)

I'm going to find a common denominator which will be (k+1)(k+2):

$\frac{k}{k+1} \cdot \frac{k+2}{k+2}+\frac{1}{(k+1)(k+2)}$

Combine the fractions:

$\frac{k(k+2)+1}{(k+1)(k+2)}$

Distribute:

$\frac{k^2+2k+1}{(k+1)(k+2)}$

Factor the numerator:

$\frac{(k+1)^2}{(k+1)(k+2)}$

Cancel a common factor of $(k+1)$

$\frac{k+1}{k+2}$

We have proven the given expression and our formula for the sum are equal for all natural numbers,n.

6 0

3 years ago