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Ira Lisetskai [31]

2 years ago

13

Question: How many miles can we paddle in 1 hour at the Los Angeles river?

1 answer:

svlad2 [7]2 years ago

6 0

Answer:

125 mph

Step-by-step explanation:

The river is going 25 mph every 20 minutes

$20$ $minutes=25$
$40$ $minutes=50$
$60$ $minutes=75$
$80$ $minutes =100$
$1$ $hour = 125$

Therefore we can paddle <u>125 miles</u> at consistent rate.

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Lori is three times as old as Michelle. In five years Michelle's age will be one half of Lori's age. How old are Lori and Michel

AURORKA [14]

Answer:

Lori's age is 15 years old and Michelle's age is 5 years old now

Step-by-step explanation:

Let

x-----> Lori's age

y ----> Michelle's age

we know that

$x=3y$ -----> equation A

$(y+5)=\frac{1}{2}(x+5)$ ----> equation B

substitute equation A in equation B and solve for y

$(y+5)=\frac{1}{2}(3y+5)$

$2y+10=(3y+5)$

$3y-2y=10-5$

$y=5$

Find the value of x

$x=3(5)=15$

therefore

Lori's age is 15 years old and Michelle's age is 5 years old now

7 0

4 years ago

The ground temperature at Brigham Airport is 17 °C. The temperature decreases by 4.9 °C for every increase of 1 kilometer above

SSSSS [86.1K]

Answer:

should be -7.5

Step-by-step explanation:

4.9×5=24.5

17-24.5=-7.5

8 0

3 years ago

At the beginning of my bike ride I feel good, so I can travel 20 miles per hour. Later, I get tired and travel only 12 miles per

Vesnalui [34]

Answer: $3\dfrac{1}{4}$ hours

Step-by-step explanation:

Let x be the time ( in hours ) you feel good and y be the time ( in hours ) that you get tired.

As per given , we have

x+y= 8

Since : $Distance = Speed\times Time$

So , we have

20x+12y=122

According to the given question , we have the following system of equations ,

$x+y= 8--------(1)\\\\20x+12y=122------------------(2)$

Multiply 12 on both sides of equation (1) , we get

$12x+12y=96------------(3)$

Eliminate equation (3) from (2) , we get

$8x=26\\\\\Rightarrow\ x=\dfrac{13}{4}=3\dfrac{1}{4}$

Hence, you felt $3\dfrac{1}{4}$ hours good.

3 0

3 years ago

A warehouse distributor of carpet keeps 6,000 yards of deluxe shag carpet in stock during a month. The average demand for carpet

Bond [772]

Answer:

The probability that a customer’s order will not be met during a month is 1.67.

Step-by-step explanation:

Given : A warehouse distributor of carpet keeps 6,000 yards of deluxe shag carpet in stock during a month. The average demand for carpet from the stores that purchase from the distributor is 4,500 yards per month, with a standard deviation of 900 yards.

To find : What is the probability that a customer’s order will not be met during a month?

Solution :

Average Mean $\mu=4500$

Sample Mean $x=6000$

Standard deviation $\sigma=900$

The formula is given by,

$Z=\frac{x-\mu}{\sigma}$

Substitute the value in the formula,

$Z=\frac{6000-4500}{900}$

$Z=\frac{1500}{900}$

$Z=1.67$

The probability that a customer’s order will not be met during a month is 1.67.

7 0

3 years ago

I need help with my math homework. The questions is: Find all solutions of the equation in the interval [0,2π).

Aleksandr-060686 [28]

Answer:

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

Step-by-step explanation:

$\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$

Let's first isolate the trig function.

Add 1 one on both sides:

$\sqrt{3} \tan(x-\frac{\pi}{8})=1$

Divide both sides by $\sqrt{3}$ :

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

Now recall $\tan(u)=\frac{\sin(u)}{\cos(u)}$ .

$\frac{1}{\sqrt{3}}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

or

$\frac{1}{\sqrt{3}}=\frac{-\frac{1}{2}}{-\frac{\sqrt{3}}{2}}$

The first ratio I have can be found using $\frac{\pi}{6}$ in the first rotation of the unit circle.

The second ratio I have can be found using $\frac{7\pi}{6}$ you can see this is on the same line as the $\frac{\pi}{6}$ so you could write $\frac{7\pi}{6}$ as $\frac{\pi}{6}+\pi$ .

So this means the following:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$

is true when $x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

where $n$ is integer.

Integers are the set containing {..,-3,-2,-1,0,1,2,3,...}.

So now we have a linear equation to solve:

$x-\frac{\pi}{8}=\frac{\pi}{6}+n \pi$

Add $\frac{\pi}{8}$ on both sides:

$x=\frac{\pi}{6}+\frac{\pi}{8}+n \pi$

Find common denominator between the first two terms on the right.

That is 24.

$x=\frac{4\pi}{24}+\frac{3\pi}{24}+n \pi$

$x=\frac{7\pi}{24}+n \pi$ (So this is for all the solutions.)

Now I just notice that it said find all the solutions in the interval $[0,2\pi)$ .

So if $\sqrt{3} \tan(x-\frac{\pi}{8})-1=0$ and we let $u=x-\frac{\pi}{8}$ , then solving for $x$ gives us:

$u+\frac{\pi}{8}=x$ ( I just added $\frac{\pi}{8}$ on both sides.)

So recall $0\le x$ .

Then $0 \le u+\frac{\pi}{8}$ .

Subtract $\frac{\pi}{8}$ on both sides:

$-\frac{\pi}{8}\le u$

Simplify:

$-\frac{\pi}{8}\le u$

$-\frac{\pi}{8}\le u$

So we want to find solutions to:

$\tan(u)=\frac{1}{\sqrt{3}}$ with the condition:

$-\frac{\pi}{8}\le u$

That's just at $\frac{\pi}{6}$ and $\frac{7\pi}{6}$

So now adding $\frac{\pi}{8}$ to both gives us the solutions to:

$\tan(x-\frac{\pi}{8})=\frac{1}{\sqrt{3}}$ in the interval:

$0\le x$ .

The solutions we are looking for are:

$\frac{\pi}{6}+\frac{\pi}{8}$ and $\frac{7\pi}{6}+\frac{\pi}{8}$

Let's simplifying:

$(\frac{1}{6}+\frac{1}{8})\pi$ and $(\frac{7}{6}+\frac{1}{8})\pi$

$\frac{7}{24}\pi$ and $\frac{31}{24}\pi$

$\frac{7\pi}{24}$ and $\frac{31\pi}{24}$

5 0

3 years ago