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Flura [38]
3 years ago
15

Two professors in the mathematics building have offices that are consecutive odd numbers with a sum of 14,600. What are the offi

cial numbers of these two professors?
Mathematics
1 answer:
Serggg [28]3 years ago
6 0

Answer: 7299, 7301

Step-by-step explanation:

x + x + 2= 14,600

2x = 14,598

x = 7,299

Therefore, the office numbers are 7299 and 7301

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A sphere is inscribed in a cylinder. Use complete sentences and geometric formulas to compare the surface area of the sphere and
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Answer:

1 : 1

Step-by-step explanation:

When a circle is inscribed in a cylinder, the height of the cylinder is equal to the diameter of the sphere and the radius of the cylinder is same as that of the sphere.

Let the radius of sphere is r.

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Surface area of sphere, A = 4πr²

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A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the
Svetlanka [38]

Answer:

The hotel charge in each city before tax was <u>$5125</u> of the first city and <u>$3625</u> of the second city.

Step-by-step explanation:

Given:

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.

The tax of the first city was 6% and the tax of the second city was 10%.

Total hotel tax paid for two cities with $670.

Now, to find the hotel charge in each city before tax.

Let the hotel charge in first city before tax be x.

And the hotel charge in second city before tax be y.

<em>So, as the hotel charge of the second city was 1500 higher than the first.</em>

<em>Thus</em>,

y=x-1500   ........(1)

<em>And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.</em>

6% of x + 10% of y = $670.

\frac{6x}{100} +\frac{10y}{100} =670

0.06x+0.10y=670

Substituting the value of y from equation (1) we get:

0.06x+0.10(x-1500)=670

0.06x+0.10x-150=670

0.16x-150=670

<em>Adding both sides by 150 we get:</em>

0.16x=820

<em>Dividing both sides by 0.16 we get:</em>

x=5125.

<em>The hotel charge in first city before tax = $5125.</em>

Now, substituting the value of x in equation (1) we get:

y=x-1500

y=5125-1500

y=3625.

<em>The hotel charge in second city before tax = $3625.</em>

Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

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3 years ago
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f(x) just means that the number in the parentheses is the x-value and if it asks for f(x) it wants the y-value at that x point
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