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2 years ago

If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the square

Mathematics

2 answers:

zysi [14]2 years ago

6 0

Answer:

The perimeter of the square is $31.96\ m$

Step-by-step explanation:

we know that

The perimeter of a square is equal to

$P=4b$

where

b is the length side of the square

Step 1

Find the length side of the square

The diagonal of the square is equal to

Applying the Pythagoras Theorem

$d^{2} =b^{2}+b^{2}\\d^{2}=2b^{2}\\d=b \sqrt{2}$

In this problem we have

$d=11.3\ m$

$d=b\sqrt{2}$ ------> solve for b

$b=d/\sqrt{2}$

substitute the value of d

$b=11.3/\sqrt{2}\ m$

Step 2

Find the perimeter of the square

$P=4b$

Substitute the value of b

$P=4(11.3/\sqrt{2})=31.96\ m$

Natalija [7]2 years ago

5 0

The length of each side can be found using pythagoras theorem:-

11.3^2 = 2x^2 where x = length od each side
x = sqrt( [11.3^2 / 2)
x = 7.99 meters

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Four friends are playing a game. They randomly choose a handful of marbles from a bag. The player with the highest ratio of blue

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We are given the number of Blue and Purple Marbles for each of the four friends. So first we have to find the ratio of blue marbles to purple marbles for each of them.

A) Rosa

Number of blue marbles = 10

Number of purple marbles = 12

Ratio of blue to purple marbles = $\frac{10}{12}=0.833$

B) Chi

Number of blue marbles = 5

Number of purple marbles = 6

Ratio of blue to purple marbles = $\frac{5}{6}=0.833$

C) Alberto

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Ratio of blue to purple marbles = $\frac{5}{12}=0.417$

D) Pedro

Number of blue marbles = 10

Number of purple marbles = 6

Ratio of blue to purple marbles = $\frac{10}{6}=1.667$

From the above calculations we can see that Pedro has the highest value of ratio for blue marbles to purple marbles. Also we can see Pedro is the only one for whom the number of blue marbles is more than the number of purple marbles. So this confirms that our calculation is correct.

Thus, the player which gets to go first is Pedro.

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What is the factored form of 36x4 – 25?

gladu [14]

$36x^4 - 25=(6x^2)^2-5^2=(6x^2-5)(6x^2+5)$

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For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations

Nookie1986 [14]

Option C

The expression 20(22 - x) represents the value of the $20 traveler's checks she has.

<u>Solution:</u>

Given, For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations travelers checks in all,

We have to find how many of each denomination does she have?

Let x represent the number of $10 traveler's checks she has,

Then, $10(x) + $20(number of $20 checks) = 300

10x + 20($20 checks) = 300

x + 2(number of $20 checks) = 30 ⇒ (1)

Now let us see the given options, for value of $20 checks,

It should be in format, that, $20 x number of $20 checks

⇒ 20(total checks - $10 checks) ⇒ 20(total checks – x), as we can see only C is in that format, it is correct and total number of checks = 22.

Then, (1) ⇒ x + 2(22 – x) = 30

⇒ x + 44 – 2x = 30

⇒2x – x = 44 – 30

⇒ x = 14

So, $10 checks count = 14, then, $20 checks count = 22 – 14 = 8.

Hence, there are 14 $10 checks and 8 $20 checks, and option c is correct.

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2 years ago

The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested, however, the m

masha68 [24]

Answer:

$1.667-2.31\frac{1.803}{\sqrt{9}}=0.2789$

$1.667+2.31\frac{1.803}{\sqrt{9}}=3.055$

So on this case the 95% confidence interval would be given by (0.2789;3.055)

The 95% confidence interval to judge whether the two indeners result in different measurements is?

Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.

Step-by-step explanation:

We have the following dataset:

specimen 1 2 3 4 5 6 7 8 9

Steel Ball 51 57 61 70 68 54 65 51 53

Diamond 53 55 63 74 69 56 68 51 56

If we calculate the differences diamond-steel ball we have this datase:

d: 2, -2, 2, 4, 1, 2, 3, 0, 3

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=1.667$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.803$

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 confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=9-1=8$

Since the confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that $t_{\alpha/2}=2.31$ .

Now we have everything in order to replace into formula (1):

$1.667-2.31\frac{1.803}{\sqrt{9}}=0.2789$

$1.667+2.31\frac{1.803}{\sqrt{9}}=3.055$

So on this case the 95% confidence interval would be given by (0.2789;3.055)

The 95% confidence interval to judge whether the two indeners result in different measurements is?

Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.

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