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2 years ago

A rectangular piece of land is 40m long and 25m wide. A path of uniform width and 426 m^2 area sorrounds

Mathematics

1 answer:

fredd [130]2 years ago

7 0

Answer:

Width of the uniform path that surrounds the piece of land = 3 m

Step-by-step explanation:

Let the width of the path that surrounds the piece of land be x.

The situation described is sketched in the attached image to this solution.

The dimension of the Length of the piece of land including the uniform path that surrounds it = (40 + 2x) m

The Breadth of the piece of land including the uniform path that surrounds it = (25 + 2x) m

The area of the piece of land including the uniform path that surrounds it

= (Area of the piece of land) + (Area of the uniform path that surrounds it)

Area of the piece of land = Length × Breadth = 40 × 25 = 1000 m²

Area of the uniform path that surrounds it = 426 m² (Given in the question)

The area of the piece of land including the uniform path that surrounds it = 1000 + 426 = 1426 m²

But the area of the piece of land including the uniform path that surrounds it is also

= (Length of the piece of land including the uniform path that surrounds it) × (Breadth of the piece of land including the uniform path that surrounds it

= (40 + 2x) + (25 + 2x)

= 1000 + 80x + 50x + 4x²

= (4x² + 130x + 1000) m²

Equation these 2 areas

4x² + 130x + 1000 = 1426

4x² + 130x - 426 = 0

Solving the quadratic equation

x = 3 or -35.5

Since the width cannot be negative,

x = 3 m

Hope this Helps!!!

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Match each set of points with the slope of the line formed by the ordered pairs.

Fynjy0 [20]

1) The slope of the point (0,0) and (2,1) is 1/2.

2) The slope of the point (0,-1) and (2,-5) is -2.

3) The slope of the point (0,7) and (2,4) is -3/2.

4) The points (-1,3) and (-1,-3) has No slope.

5) The slope of the point (1,-3) and (-1,-3) is zero.

Step-by-step explanation:

There are five set of points given in the question.

You need to find out the slope of the line formed by the points.

The formula used to find the slope of a line is given by,

Slope = $\frac{y2-y1}{x2-x1}$

1) The given points are (0,0) and (2,1)

(x1,y1) ⇒ (0,0)

(x2,y2) ⇒ (2,1)

Slope = $\frac{1-0}{2-0}$

⇒ 1/2 is the slope.

2) The given points are (0,-1) and (2,-5)

(x1,y1) ⇒ (0,-1)

(x2,y2) ⇒ (2,-5)

Slope = $\frac{-5+1}{2-0}$

⇒ $\frac{-4}{2}$

⇒ -2 is the slope.

3) The given points are (0,7) and (2,4)

(x1,y1) ⇒ (0,7)

(x2,y2) ⇒ (2,4)

Slope = $\frac{4-7}{2-0}$

⇒ -3/2 is the slope.

4) The given points are (-1,3) and (-1,-3)

(x1,y1) ⇒ (-1,3)

(x2,y2) ⇒ (-1,-3)

Slope = $\frac{-3-3}{-1+1}$

⇒ -6/0 (No slope)

If the denominator of a fraction is zero, the expression is not a legal fraction because it's overall value is undefined.

∴ There is no slope.

5) The given points are (1,-3) and (-1,-3)

(x1,y1) ⇒ (1,-3)

(x2,y2) ⇒ (-1,-3)

Slope = $\frac{-3+3}{-1-1}$

⇒ 0/-2

∴ The slope is zero.

5 0

2 years ago

Read 2 more answers

A local company makes snack-size bags of potato chips. Each day, the company produces batches of 400 snack-size bags using a pro

ioda

Answer:

Probability that a sample of 40 bags has an average weight of at least 2.02 ounces is 0.103.

Step-by-step explanation:

We are given that the company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. Assume the amount placed in each of the 400 bags is normally distributed and has a standard deviation of 0.1 ounce.

Also, sample of 40 bags are selected.

Let $\bar X$ = sample average weight

The z-score probability distribution for sample mean is given by ;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean weight of potato chips = 2 ounces

$\sigma$ = standard deviation = 0.1 ounces

n = sample of bags = 40

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, the probability that a sample of 40 bags has an average weight of at least 2.02 ounces is given by = P( $\bar X$ $\geq$ 2.02 ounces)

P( $\bar X$ $\geq$ 2.02) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\geq$ $\frac{2.02-2}{\frac{0.1}{\sqrt{40} } }$ ) = P(Z $\geq$ 1.265) = 1 - P(Z < 1.265)

= 1 - 0.89707 = 0.103

The above probability is calculated using z table by looking at value of x = 1.265 which will lie between x = 1.26 and x = 1.27 in the z table which have an area of 0.89707.

Therefore, probability that a sample of 40 bags has an average weight of at least 2.02 ounces is 0.103.

3 0

2 years ago

Organic hot dogs at the grocery store cost $2.00 each. At a major league baseball game, an organic hot dog costs $6.50. How much

ValentinkaMS [17]

325%

6.5/2 is 3.25 or

5 0

2 years ago

NEED HELP ASAP !!!!!!!

AURORKA [14]

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷Yes.

Explain: This is because if you feel normal, you might have a little bit of willpower to do something, which will effect the statistical outcome. if you are confident, you will have a higher statistical outcome. (Example: A sport game. Feeling: Normal, Confident, Random) If you feel random, you could get a really bad score or a really high score, but you don't know because it is random.

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

6 0

2 years ago

what is a decimal that is equivalent to the expression (3 x 100) + (7 x 10) + (4x1) + (6 x 0.01) + (2 x 0.001)?

-BARSIC- [3]

Answer:

374.062

Step-by-step explanation:

multiply all those and put them in the correct place.

do it just as i did my answer

3 goes first 7 goes next to 3 4 goes next to 7 add the decimal point then

put 0 since there are no tenths then put 6 then next to 6 put 2

5 0

2 years ago