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4 years ago

The measure of angle QPR = ???? degrees

Mathematics

1 answer:

katovenus [111]4 years ago

4 0

QPR = 1/2 (31 + 98)

Angle QPR = 64.5 degrees

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Calculate the measure of angle ADB if angle ACB is 50 degrees.

ahrayia [7]

Answer:

ADB=50°

Step-by-step explanation:

Angles subtended by the same segment are equal

4 0

3 years ago

Show that 1n^ 3 + 2n + 3n ^2 is divisible by 2 and 3 for all positive integers n.

Dmitry_Shevchenko [17]

Prove:

Using mathemetical induction:

P(n) = $n^{3}+2n+3n^{2}$

for n=1

P(n) = $1^{3}+2(1)+3(1)^{2}$ = 6

It is divisible by 2 and 3

Now, for n=k, $n > 0$

P(k) = $k^{3}+2k+3k^{2}$

Assuming P(k) is divisible by 2 and 3:

Now, for n=k+1:

P(k+1) = $(k+1)^{3}+2(k+1)+3(k+1)^{2}$

P(k+1) = $k^{3}+3k^{2}+3k+1+2k+2+3k^{2}+6k+3$

P(k+1) = $P(k)+3(k^{2}+3k+2)$

Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also

divisible by 2 and 3.

Hence, by mathematical induction, P(n) = $n^{3}+2n+3n^{2}$ is divisible by 2 and 3 for all positive integer n.

3 0

3 years ago

A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. (a) Describe the

Ivanshal [37]

Answer:

a) $\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

b) $z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

c) $z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

d) $z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

Step-by-step explanation:

For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

$\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

We want this probability:

$P(\bar X>89)$

We can use the z score formula given by:

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

And if we find the z score for 89 we got:

$z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

Part c

$P(\bar X$

We can use the z score formula given by:

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

And if we find the z score for 75.65 we got:

$z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

Part d

We want this probability:

$P(79.4 < \bar X < 89.3)$

We find the z scores:

$z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

8 0

4 years ago

PLS HELP!! ALGEBRA!!

sineoko [7]

Horizontal distance = 48'

difference in elevation = 18"-6" = 12" = 1'

Slope of the sewer line = rise/run = 1/48 = 0.0208 = 2.08%

6 0

3 years ago

Angle ABC is shown . Determine sin B. Write your answer in fraction form.<br><br> Help ASAP

Mkey [24]

Answer:

sin b would be 4/5

Step-by-step explanation:

sine is the opposite leg/the hypotenuse

7 0

3 years ago