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3 years ago

15

Solve triangle ABC

1 answer:

Goshia [24]3 years ago

4 0

That figure obviously doesn't go with this problem. It doesn't matter; this is triangle ABC labeled the usual way.

c = 10, B = 35°, C = 65°

We have two angles and a side. The third angle is obviously

A = 180° - 35°- 65° = 80°

The remaining sides are given by the Law of Sines,

$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

$a = \dfrac{c \sin A}{\sin C} = \dfrac{10 \sin 80}{\sin 65} = 10.866$

$b = \dfrac{c \sin B}{\sin C} = \dfrac{10 \sin 35}{\sin 65} = 6.328$

Answer: A=80°, a=10.9, b=6.3, third choice

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bonufazy [111]

1/2. It isn't asking for another solution, just the fraction.

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3 years ago

a student showed the steps below while solving the equation 14=log5(2x-3) by graphing. which step did the student make the 1sr e

mixer [17]

Answer:

$x= \frac{5^{14}+3}{2}$

Step-by-step explanation:

The correct steps to solve the equation are:

$14=log_5(2x-5)$

$5^{14}=5^{log_5(2x-3)}$

Because $a^{log_am}=m$

So, solving we get:

$5^{14}=2x-3$

Sum 3 on every side:

$5^{14}+3=2x-3+3\\5^{14}+3=2x$

Dividing by 2 into both sides:

$\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x$

So, the answer is $x= \frac{5^{14}+3}{2}$

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3 years ago

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:

a

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

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

The null hypothesis is rejected

b

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 $P(z > 3.08)= 0.001035$

So

$p-value = 2* 0.001035$

$p-value = 0.00207$

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

If varies inversely as . It is known that = 10 when = 3, find the value of when = 5.

Leto [7]

Answer:

y = 6

Step-by-step explanation:

If x varies inversely proportional as y.

$x=\dfrac{k}{y}$ , k is constant of proportionality

or

k = xy

When x = 3 and y = 10

k = 3×10

k = 30

Put x = 5,

$y=\dfrac{k}{x}\\\\y=\dfrac{30}{5}\\\\y=6$

So, the value of y is 6 when x is 5.

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3 years ago

Using the digits 0 to 9 at most one time each, fill in the boxes to create a three-digit number. Try to create a three-digit num

zhenek [66]

Answer:

Greatest number of factors: 360 and 720 are both divisible by 2,3,4,5,6,8,9 and 10.

Step-by-step explanation:

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3 years ago