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Anastaziya [24]
3 years ago
7

Katrina had a bookcase that holds 200 books. She can put 20 books on each shelf. If 20% of the bookcase is empty, how many shelv

es are filled with books
Mathematics
1 answer:
Tom [10]3 years ago
5 0

Answer:

First, find 20% of the 200 books. Then, subtract that amount by the total and divide that amount by 20 to receive your answer.

Step-by-step explanation:

20 x 200

/100  = 40

Therefore, there are 40 books missing.

200-40 = 160

160/20 = 8 shelves are filled with books.

There are 10 shelves in total: 160 books are on 8 shelves and 40 books are missing for 2 shelves

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Is the expression 2 • 4 ^ x equal to the expression 8 ^ x ? Explain your answer
kkurt [141]

Answer:

It depends on the value of x

Step-by-step explanation:

If x=1, then yes

Exponents come before multiplication, so even if 2*4=8, 2*4^2 is not equal to 8.

Ex:

2*4^2=32

8^2=64

3 0
3 years ago
Suppose f(x)=x+2. Find the graph of f(1/3x)
8090 [49]

Answer:

f(x)=x+2.

f(1/3x)=1/3 x+2=(x+6)/3or x/3+2

6 0
3 years ago
A line, y = mx + b, passes through the point (10, 3) and is parallel to the line 2x+5y=12.
slava [35]

We have been given that a line y=mx+b passes through the point (10, 3) and is parallel to the line 2x+5y=12. We are asked to find the y-intercept of the line.

First of all we will rewrite our given equation in slope-intercept form as:

2x-2x+5y=12-2x

5y=-2x+12

\frac{5y}{5}=-\frac{2}{5}x+\frac{12}{5}

y=-\frac{2}{5}x+\frac{12}{5}

We know that slope of parallel lines is equal, so slope of parallel line to our given line would be -\frac{2}{5}.

Now we will use slope-intercept form of equation to find y-intercept.

y=mx+b, where,

m = Slope,

b = The y-intercept.

Let us substitute m=-\frac{2}{5} and coordinates of point (10,3) in above equation as:

3=-\frac{2}{5}(10)+b

3=-2(2)+b

3=-4+b

3+4=-4+4+b

7=b

Therefore, the y-intercept is 7 and our required equation would be y=-\frac{2}{5}x+7.

5 0
3 years ago
Express each ratio as a unit rate. 325.4 miles on 17.3 gallons<br><br><br><br> having trouble :/
kkurt [141]
Hello! I can help you with this question! To find the unit rate, we’ll have to divide total by number of units. Or in this case, miles/gallons. 325.4/17.3 is 18.809 and other numbers, or 18.81 when rounded to the nearest hundredth. If you’re looking for the answer to the nearest hundredth, the answer is 18.81 mpg. Or, if you’re looking for the answer to the nearest whole number, the answer is 19 mpg.
8 0
3 years ago
Find all points of intersection of the given curves. (Assume 0 ≤ θ ≤ 2π and r ≥ 0. Order your answers from smallest to largest θ
DerKrebs [107]

Answer:

∅1=15°,∅2=75°,∅3=105°,∅4=165°,∅5=195°,∅6=255°,∅7=285°,

∅8=345°

Step-by-step explanation:

Data

r = 8 sin(2θ), r = 4 and r=4

iqualiting; 8.sin(2∅)=4; sin(2∅)=1/2, 2∅=asin(1/2), 2∅=30°, ∅=15°

according the graph 2, the cut points are:

I quadrant:

0+15° = 15°

90°-15°=75°

II quadrant:

90°+15°=105°

180°-15°=165°

III quadrant:

180°+15°=195°

270°-15°=255°

IV quadrant:

270°+15°=285°

360°-15°=345°

No intersection whit the pole (0)

7 0
4 years ago
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