"The area of a rectangle is X^2 + 12XY + 27Y^2, and its length is (X + 9Y). Find the breadth of the rectangle."

Answers

Answer 1
Answer:

Answer:

Hi,

Step-by-step explanation:

Let's factorize the area:

x^2+12xy+27y^2\n=x^2+3xy+9xy+27y^2\n=x(x+3y)+9y(x+3y)\n=(x+3y)(x+9y)\n

The breadth of the rectangle is x+3y


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Expand the expression and combine like terms: 20(−1.5r+0.75)
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A copier prints 80 pages in 5 minutes. Which unit rate represents this ratio?

A.80 pages per 5 minutes

B.40 pages per 2.5 minutes

C.32 pages per minute

D.16 pages per minute

Answers

The correct answer is D, 16 pages per minute. A unit rate is a ratio of something to one; in this case, the ratio is 16:1, or 16 pages to 1 minute. To get the unit rate for this problem, divide both numbers by 5 to get how many pages will be printed per 1 minute. 80/5 = 16, so the copier prints 16 pages in 1 minute. Answer choices A and B are not unit rates, and answer choice C is the incorrect unit rate.

Hope this helps!

Solve the problem.If a lawn sprinkler sprays 15 feet in every direction, what is the area of the yard that gets watered?

Answers

The area of yard gets watered is 707.142 ft²

What is area?

The portion between any closed figure, and the extent of region of any plane is area.

Given that sprinkler sprays 15 feet in every direction

so it will form a circle with radius of 15ft

and area of circle is πr²

where r is radius of circle

value of π is 22/7

area = π x (15)²

area = 707.142 ft²

Hence area of sprinkled region is 707.142 ft²

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Hello,

A=πR²=3.141592...*15²=706,8583470...( ft²)
===================================

A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428?

Answers

Solution:
To evaluate for P(0.372<x<0.428) we shall proceed as follows:
z-score is given by:
z=(x-μ)/σ
thus when x=0.372:
z=(0.372-0.4)/0.028
z=-1
thus
P(x<0.372)=P(z<-1)=0.1587

when x=0.428
z=(0.428-0.4)/(0.028)=1
P(x<0.428)=P(z<1)=0.8413
thus
P(0.372<x<0.428) =P(z<1)-P(z<-1)=0.8413-0.1587=0.6826

Final answer:

To find the percentage of observations between two values in a normal distribution, we can convert the values to z-scores and use a z-table to find the corresponding areas. In this case, the percentage of observations between 0.372 and 0.428 is 68.26%.

Explanation:

To find the percentage of observations that will lie between 0.372 and 0.428 in a normal distribution with a mean of 0.40 and standard deviation of 0.028, we need to find the area under the curve between these two values.

Using a standard normal distribution table or z-table, we can convert the values to z-scores by subtracting the mean and dividing by the standard deviation. The z-score for 0.372 is (0.372 - 0.40) / 0.028 = -1, and the z-score for 0.428 is (0.428 - 0.40) / 0.028 = 1.

By looking up the corresponding area for these z-scores in the z-table, we find that the area to the left of -1 is 0.1587 and the area to the left of 1 is 0.8413. To find the percentage between -1 and 1, we subtract the smaller area from the larger area: 0.8413 - 0.1587 = 0.6826 or 68.26%.

Learn more about Normal distribution here:

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WORKKK NEEDS TO BE SHOWNNN


-3y+4=-11

Answers

-3y+4=-11
Subtract 4 from each side
-3y=-15
Then divide -3 from each side
Y=5

Which amount of time is the shortest?3 hours, 50 minutes
250 minutes
270 minutes
4 hours, 10 minutes

Answers

3hrs , 50mins = 230mins
4hrs , 10mins = 250mins

∴ 3hrs and 50mins is the shortest
the answer is the first one . I got the answer by dividing by 60 and see which answer gives me the shortest time. :) hope that help

7. Numericals(a) A box has length 50 cm, breadth 20 cm and height 10 cm, then find
(i) its surface area of base;
(ii) its volume
(1000 cm², 100000 cm3)​

Answers

Answer:

i = 1000cm2

ii = 100000cm3

Step-by-step explanation:

for q i

surface area of base = l* b

= 50* 20

1000cm^2

for q 2

volume l*b*h

= 50*20*10

= 100000cm^3

hope it will be helpfull