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2 years ago

6

Last Saturday, there were 1486 people at the Cineplex. There were about the same number of people in each of the 6 theaters. Bet

ween which two numbers does the number of people in each theater fall?

1 answer:

grigory [225]2 years ago

5 0

<span>247 and 248 I.e. 247 in two thetheatres and 248 in the other 4. Hence 1486</span>

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A specimen of aluminum having a rectangular cross section 10 mm 12.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (80

miskamm [114]

Answer:

$\epsilon = 3.958\times 10^{-3}$

Step-by-step explanation:

The Young's Module of Aluminium is $E = 69\times 10^{9}\,Pa$ . The axial stress on the specimen is:

$\sigma = \frac{F}{A_{t}}$

$\sigma = \frac{35500\,N}{(0.01\,m)\cdot (0.013\,m)}$

$\sigma = 2.731\times 10^{8}\,Pa$

The strain is derived of following expression:

$\epsilon = \frac{\sigma}{E}$

$\epsilon = \frac{2.731\times 10^{8}\,Pa}{69\times 10^{9}\,Pa}$

$\epsilon = 3.958\times 10^{-3}$

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2 years ago

Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. Which equation c

Paha777 [63]

First lets write down our starting conditions:

we have 22 gallons and it has 16% of ammonia

16% of 22 gallons is
A = 16/100*22 = 3,52 gallons

Now since only watter is evaporating that means that in second scenario after some watter evaporated there is still 3,52 gallons of ammonia. But now those 3,52 gallons of ammonia represent 24% of total mixture. So now we go other way.
24 % is 3,52 gallons
100% is x gallons

x = 100/24*3,52 = 14.667 gallons

That means that he has to evaporate
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7 0

2 years ago

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were m

aalyn [17]

This question is incomplete. Below is the complete question:

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. what is the amount of the initial deposit?

Answer: The initial deposit is $10,001

Step-by-step explanation:

To solve this we need to utilize the continuous compounding interest formula:-

Fv = Pv × e^(i × t)

Where, Fv = the future value

Pv = present value

i = the interest rate

t = the time in years

e = a mathematical constant that is usually approximated by 2.7183

In this case, the Fv = 13,231.30

i = 3.5% or 0.035

t = 8 years

e = 2.7183

Pv = ? (The unknown variable).

13,231.30 = Pv × [2.7183^(0.035 × 8)]

13,231.30 = Pv × [2.7183^(0.28)]

13,231.30 = Pv × 1.323

Pv = 13,231.30/1.323

Pv = $10000.98

= $10,001

Therefore the initial deposit is $10,001

8 0

2 years ago

Find a line that lies entirely in the set defined by the equation x2 + y2 − z2 = 1.

RUDIKE [14]

Answer:

$x=1\,,\,y=t\,,\,z=t$

Step-by-step explanation:

A line is a one-dimensional figure that has no thickness and extends infinitely in both directions.

A line segment is a line that has two end-points and a ray is a line that has one end-point.

Given equation is $x^2+y^2-z^2=1$

To find : a line that lies entirely in the set defined by the given equation.

Solution:

Take $x=1\,,\,y=t\,,\,z=t$

Check:

$L.H.S=1^2+t^2-t^2=1+0=1=R.H.S$

Therefore, $x=1\,,\,y=t\,,\,z=t$ satisfy the given equation.

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2 years ago

The area of a small pond is 78.5 yds. What is the diameter of the pond?

Zolol [24]

Answer:

Diameter of pound = 10 yd

Step-by-step explanation:

Given area of circular pond = 78.5 square yd

To find the diameter of the pond.

Solution:

The pond being circular in shape, the area of pond can be given as:

⇒ $\pi\ r^2$

where $r$ represents radius of the pond.

Thus, we have:

⇒ $\pi\ r^2=78.5$

Using $\pi=3.14$

⇒ $3.14r^2=78.5$

Solving for $r$

Dividing both sides by 3.14

⇒ $\frac{3.14r^2}{3.14}=\frac{78.5}{3.14}$

⇒ $r^2=25$

Taking square root both sides.

⇒ $\sqrt{r^2}=\sqrt{25}$

⇒ $r=\pm5$

So, radius = 5 yd, as distances are always positive.

Diameter = $2\times radius=2\times 5\ yd= 10\ yd$

Thus, diameter of pound = 10 yd

7 0

2 years ago