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3 years ago

A square sheet of paper measures 25 centimeters on each side. What is the length of the diagonal of this paper?

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

6 0

Answer:

35.36 cm

Step-by-step explanation:

The diagonal of a square will be given by

$D=\sqrt {a^{2}+b^{2}}$

Where a is the length of one side and b is the length of another side. For a square, botj sides are equal hence the diagonal calculations will be as follows

Given that a is 25 then

$D=\sqrt {25^{2}+25^{2}}$

D=35.3553390593274

Rounding off the nearest two decimal place

D=35.36 cm

You might be interested in

Stevan wants to build a fence around a square garden that is 506.25 ft squared. How many feet of fence will he need to complete

drek231 [11]

For side length s, the area of a square is given by

... A = s²

Then the side length can be found to be

... s = √A = √(506.25 ft²) = 22.5 ft

The perimeter is the sum of the lengths of the four equal sides.

... P = 4s = 4·(22.5 ft) = 90 ft

Stevan will need 90 ft of fence to complete the job.

5 0

4 years ago

Triangle ABE is similar to triangle ACD. AED and ABC are straight lines. EB and DC are parallel. AE = 5 cm, BC = 4.5 cm, BE = 4

lianna [129]

Answer:

y = 16x/65

Step-by-step explanation:

Given:

Triangle ABE is similar to triangle ACD. AED and ABC are straight lines

EB and DC are parallel

The area of quadrilateral BCDE = xcm²

The area of triangle ABE = ycm²

Find attached the diagram from the above information.

In similar triangles, the ratio of their corresponding angles are equal.

Also, the ratio of the area of the two triangles = square of ratio of the corresponding sides of the two triangles.

Area ∆ACD/area of ∆ABE = (DC/EB)²

Area ∆ACD/area of ∆ABE = [(area of quadrilateral BCDE +

area of ∆ABE)]/(area of ∆ABE)

(x+y)/y = (DC/EB)²

(x+y)/y = (9/4)²

x+y = (81/16)y

x = (81/16)y - y

x = (81y - 16y)/16

x = 65y/16

Making y subject of formula

16x = 65y

y = 16x/65

An expression for y in terms of x:

y = 16x/65

3 0

3 years ago

Name the equation for any horizontal line of your choosing

noname [10]

Answer:

Horizontal lines have a slope of 0. Thus, in the slope-intercept equation y = mx + b, m = 0. The equation becomes y = b, where b is the y-coordinate of the y-intercept.

Step-by-step explanation:

3 0

3 years ago

An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and

dezoksy [38]

Answer:

$0.626 - 1.96\sqrt{\frac{0.626(1-0.626)}{356}}=0.549$

$0.626 + 1.96\sqrt{\frac{0.626(1-0.626)}{356}}=0.703$

The 95% confidence interval would be given by (0.549;0.703)

Step-by-step explanation:

Notation and definitions

$X=223$ number of dies that passed the inspection.

$n=356$ random sample taken

$\hat p=\frac{223}{356}=0.626$ estimated proportion of dies that passed the inspection

$p$ true population proportion of dies that passed the inspection

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: