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2 years ago

Help me on isosceles and equilateral triangles problems. Find the value of x in the triangle shown below.

Mathematics

1 answer:

trapecia [35]2 years ago

3 0

Answer:

x° = 61°

Step-by-step explanation:

Both of the "unknown" angles in the triangle are equal, since their opposite sides have equal lengths. (The triangle is isosceles.) The sum of angles in a triangle is 180°, so we have ...

58° + x° + x° = 180°

2x° = 122° . . . . subtract 58°, collect terms

x° = 61° . . . . . . . divide by 2

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3. A new process has been developed for applying pho toresist to 125-mm silicon wafers used in manufac turing integrated circu

dlinn [17]

Answer:

The null hypothesis is $H_o : \mu = 13.4000$

The alternative hypothesis is $H_a : \mu \ne 13.4000$

The null hypothesis is rejected

The 99% confidence level is $13.3930 < \mu < 13.3994$

Step-by-step explanation:

From the question we are told that

The sample size is n = 10

The population mean is $\mu = 13.4 000 \ angstroms$

The level of significance is $\alpha = 0.05$

The sample data is

13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002

Generally the sample mean is mathematically represented as

$\= x = \frac{13.3987+ 13.3957\cdots +13.4002 }{10}$

=> $\= x = 13.3962$

Generally the sample standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }$

=> $\sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 + (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2 }{10} }$

=> $\sigma =0.0039$

The null hypothesis is $H_o : \mu = 13.4000$

The alternative hypothesis is $H_a : \mu \ne 13.4000$

Generally the test statistics is mathematically represented as

$z = \frac{\= x - \mu}{\frac{\sigma}{\sqrt{n} } }$

=> $z = \frac{13.3962 - 13.4000}{\frac{0.0039}{\sqrt{10} } }$

=> $z = 3.08$

Generally the p-value is mathematically represented as

$p-value = 2P( z > 3.08)$

From the z-table $P(z > 3.08)= 0.001035$

$p-value = 2* 0.001035$

$p-value = 0.00207$

So from the obtained value we see that

$p-value < \alpha$

Hence the null hypothesis is rejected

Consider the b question

Given that the confidence level is 99% then the level of significance is

$\alpha = (100 -99)\%$

=> $\alpha = 0.01$

Generally from the normal distribution table critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 2.58 * \frac{0.0039}{\sqrt{10} }$

=> $E = 0.00318$

Generally the 99% confidence interval is mathematically represented as

$13.3962 - 0.00318 < \mu < 13.3962 + 0.00318$

=> $13.3930 < \mu < 13.3994$

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3 years ago

A pile of 15 boxes is 3 metres high. What is the depth of each box?

schepotkina [342]

Answer:

15 boxes=3m=300cm

1 box=300cm÷15

=20cm

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3 years ago

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Express the function f(x) =3x^2-6x-18 in the form a(x + h)^2=k, where a, h and k are constants.Hence state the :

ololo11 [35]

Answer:

The minimum value of f(x) is -21 and it occurs at x = 1

Step-by-step explanation:

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Factor out the greatest common factor out of the first two terms

f(x) =3(x^2-2x)-18

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-2x/2 =-1 (-1)^2 = 1

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f(x) = 3(x^2 -2x+1) -3 -18

f(x) = 3(x-1)^2 -21

This is vertex form

f(x) = a(x-h)^2 +k where (h,k) is the vertex and a is a constant

The vertex is (1,-21)

Since a > 0 this opens upward and the vertex is a minimum

The minimum value of f(x) is -21 and it occurs at x = 1

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According to the 1993 World Almanac, the number of calories a person walking at 3 mph burns per minute depends on the persons we

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150 pounds is your answer

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leonid [27]

Answer:

Step-by-step explanation:

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Help me on isosceles and equilateral triangles problems. Find the value of x in the triangle shown below.​

Help me on isosceles and equilateral triangles problems. Find the value of x in the triangle shown below.