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3 years ago

Triangle ABC has a perimiter of 22cm AB=8cm BC=5cm by calculation deduce whether triangle ABC is a right-angled triangle

Mathematics

1 answer:

Svetllana [295]3 years ago

6 0

Answer:

ABC is not a right triangle

Step-by-step explanation:

The computation is shown below:

AC is

= Perimeter - (AB + BC)

= 22 - (8+5)

= 22 - 13

= 9

Now

= 9^2 + 13^2

= 81 +169

= 250

And, the perimeter is

= 22^2

= 484

Since the amount are not equivalent therefore ABC is not a right triangle

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Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms oc

Anit [1.1K]

Answer:

a) $\hat \sigma^2 =s^2 =30^2 = 900$

b) $567.277 \leq \sigma^2 \leq 1690.224$

Rounded to the nearest number would be:

$567 \leq \sigma^2 \leq 1690$

c) $23.818 \leq \sigma \leq 41.112$

And rounded :

$23.8 \leq \sigma \leq 41.1$

Step-by-step explanation:

Data given and notation

s=30 represent the sample standard deviation

$\bar x=290$ represent the sample mean

n=20 the sample size

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

Part a

The best point of estimate for the population variance is the sample variance, so on this case:

$\hat \sigma^2 =s^2 =30^2 = 900$

Part b

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.05,19)" "=CHISQ.INV(0.95,19)". so for this case the critical values are:

$\chi^2_{\alpha/2}=30.144$

$\chi^2_{1- \alpha/2}=10.117$

And replacing into the formula for the interval we got:

$\frac{(19)(30)^2}{30.144} \leq \sigma \leq \frac{(19)(30)^2}{10.117}$

$567.277 \leq \sigma^2 \leq 1690.224$

Rounded to the nearest number would be:

$567 \leq \sigma^2 \leq 1690$

Part c

In order to find the confidence interval for the deviation we just need to take the square root for the interval of the variance, and we got:

$23.818 \leq \sigma \leq 41.112$

And rounded :

$23.8 \leq \sigma \leq 41.1$

7 0

3 years ago

A) write √3×√6 in the form of b√2 where b is the insteger<br><br>b) simplify √8×√18<br>

Bas_tet [7]

Step-by-step explanation:

a.) the given term can be written as

$\sqrt{3} \times \sqrt{3 \times 2}$

$\sqrt{3 \times 3 \times 2}$

$3 \sqrt{2}$

hence the given term is

$3 \sqrt{2}$

where b = 3

b.)

$\sqrt{8} \times \sqrt{18}$

$\sqrt{2 \times 2 \times 2} \times \sqrt{2 \times 3 \times 3}$

$\sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3}$

$12$

hence the given term is 12

4 0

3 years ago

What is the difference between a yard and a meter? give me the actual distance<br> difference in cm

valkas [14]

Answer:

The difference is 8.56 cm. ( the metre is longer than the yard).

Step-by-step explanation:

1 yard = 36 inches

= 36 * 2.54

= 91.44 cm

1 metre = 100 cm.

7 0

3 years ago

Un comerciante de algodón de azúcar gana 40 cm por cada algodón vendido pero si no lo logra venderlo pierde 50 céntimos. un día

gayaneshka [121]

Answer:

He fails to sell that day 10 cottons.

Step-by-step explanation:

We are given that a cotton candy merchant earns 40 cents for each cotton sold, but if he cannot sell it he loses 50 cents.

One day when he made 120 cottons, he made a profit of 39 soles.

Let the number of cottons merchant is able to sold be 'x' and the number of cottons merchant is not able to sold be 'y'.

So, according to the question;

The first condition states that he made 120 cottons on one day, that is;

x + y = 120

x = 120 - y ---------------------- [Equation 1]

The second condition states that merchant earns 40 cents for each cotton sold, but if he cannot sell it he loses 50 cents and due to which he made a profit of 30 soles, that is;

$0.40x - 0.50y=39$