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3 years ago

Find the indicated missing angle. Round to the nearest angle.

Mathematics

1 answer:

sladkih [1.3K]3 years ago

4 0

Answer:

The missing angle 'x' is 22.29°.

i.e. $x\:=\:22.29^{\circ \:\:}$

Step-by-step explanation:

Let 'x' be the missing angle of the triangle.

Using the formula

tan x = opp ÷ adjacent

tan x = 30 ÷ 72

tan x = 0.41

$x=\tan ^{-1}\left(0.41\right)$

$x\:=\:22.29^{\circ \:\:}$

Therefore, the missing angle 'x' is 22.29°.

i.e. $x\:=\:22.29^{\circ \:\:}$

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I WILL GIVE MORE POINTS IF I GET THE RIGHT ANSWER

shutvik [7]

Answer:

v= 6km/h - 1km/h^2 * t

Step-by-step explanation:

From the information, it seems the runner is slowing down because the speed at 1st hour is 5km/h but at 3rd hour becomes 3km/h.

If v= velocity, v0= initial speed, t= time, and the a=acceleration then the function would be:

v= v0 + a * t

To find the acceleration you need to do this equation:

acceleration= velocity1- velocity3 / t3-t1

a = (3km/h-5km/h)/ (3 hour- 1 hour)

a = (-2km/h)/2hour= -1 km/hour^2

After that, you need to find the initial speed. Try to put the 1st-hour variable into the full equation. It would look like this

v= v0 + a * t

5km/h= v0 + (-1 km/hour^2 * 1 hour)

v0= 5km/h + 1km/h

v0= 6km/h

Then the full function would be:

v= 6km/h - 1km/h^2 * t

The graph would look like a backslash(\) from 5 gradually go down to 1.

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7 0

3 years ago

A recent study focused on the number of times men and women send a WeChat message in a day. The information is summarized next.

Ratling [72]

Answer:

1)Null hypothesis: $\mu_{men}=\mu_{women}$

Alternative hypothesis: $\mu_{men} \neq \mu_{women}$

2) Two critical values are $z_{\alpha/2}=-2.58$ and $z_{1-\alpha/2}=2.58$

3) $z=-2.40$

4) $p_v =2*P(z$

5) Comparing the p value with the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and a would NOT be a significant difference in the mean number of times men and women send a Twitter message in a day.

Step-by-step explanation:

Data given and notation

$\bar X_{men}=23$ represent the mean for the sample men

$\bar X_{women}=28$ represent the mean for the sample women

$\sigma_{men}=5$ represent the population standard deviation for the sample men

$\sigma_{women}=10$ represent the population standard deviation for the sample women

$n_{men}=25$ sample size for the group men

$n_{women}=30$ sample size for the group women

t would represent the statistic (variable of interest)

$\alpha=0.01$ significance level provided

1）Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different, the system of hypothesis would be:

Null hypothesis: $\mu_{men}=\mu_{women}$

Alternative hypothesis: $\mu_{men} \neq \mu_{women}$

Since we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{men}-\bar X_{women}}{\sqrt{\frac{\sigma^2_{men}}{n_{men}}+\frac{\sigma^2_{women}}{n_{women}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

2）Determine the critical value(s).

Based on the significance level $\alpha=0.01$ and $\alpha/2=0.005$ we can find the critical values with the normal standard distribution, we are looking for values that accumulates 0.005 of the area on each tail on the normal distribution.

For this case the two values are $z_{\alpha/2}=-2.58$ and $z_{1-\alpha/2}=2.58$

3) Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

$z=\frac{23-28}{\sqrt{\frac{5^2}{25}+\frac{10^2}{30}}}}=-2.40$

4）What is the p-value for this hypothesis test?

Since is a bilateral test the p value would be:

$p_v =2*P(z$

5）Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and a would NOT be a significant difference in the mean number of times men and women send a Twitter message in a day.

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3 years ago

To the nearest hundredth, how many cm are in 12 in? (1 in = 2.54 cm)

soldier1979 [14.2K]

12 in = 30.(48) cm this is your Answer

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3 years ago

Read 2 more answers

Square root of 45 in radical form

AfilCa [17]

Answer:

3 $\sqrt{5}$

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Given

$\sqrt{45}$

= $\sqrt{9(5)}$

= $\sqrt{9}$ × $\sqrt{5}$

= 3 $\sqrt{5}$

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3 years ago

How are arithmetic and geometric means similar and how are they different?

alisha [4.7K]

Answer:

Step-by-step explanation:

Both Geometric Mean vs Arithmetic Mean are the tools to calculate the returns on investment in finance and also used in other applications such as economics, statistics

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3 years ago