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2 years ago

What is the missing angle

Mathematics

1 answer:

nalin [4]2 years ago

6 0

Answer:

x=59deg

Step-by-step explanation:

We will use tangent to find the angle because we do not know the length of the hypotenuse.

Tan(x)=opp/adj

Tan(x)=30/18

Tan(x)~59

So the last option is correct. 59deg

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Consider the following hypothesis test:

Gnom [1K]

Answer:

a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.

b. z=1.24. No, it can not be concluded that the population mean is greater than 50.

c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.

Step-by-step explanation:

We have a hypothesis test for the mean, with the hypothesis:

$H_0: \mu\leq50\\\\H_a:\mu> 50$

The sample size is n=55 and the population standard deviation is 6.

The significance level is 0.05.

We can calculate the standard error as:

$\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{55}}=0.809$

For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.

a. If the sample mean is M=52.5, the test statistic is:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{52.5-50}{0.809}=\dfrac{2.5}{0.809}=3.09$

The null hypothesis is rejected, as z>zc and falls in the rejection region.

b. If the sample mean is M=51, the test statistic is:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51-50}{0.809}=\dfrac{1}{0.809}=1.24$

The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.

c. If the sample mean is M=51.8, the test statistic is:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51.8-50}{0.809}=\dfrac{1.8}{0.809}=2.22$

The null hypothesis is rejected, as z>zc and falls in the rejection region.

8 0

3 years ago

Devora explored a secret cave. 48\text{ m}48 m48, start text, space, m, end text from the entrance, she found an empty chest wit

siniylev [52]

Answer:

82°

Step-by-step explanation:

3 0

2 years ago

Given cos t = 1/2 tan 0 find sin (t) and sec (t)

777dan777 [17]

Answer:

Sin(t) = $\frac{\sqrt{3} }{2} }$ and $sec(t) =2$

Step-by-step explanation:

The secant function is the reciprocal function of the cosine function. Therefore, given that $sec(t) = \frac{1}{cos(t)}$ then, if $cos(t) = \frac{1}{2}$ then $sec(t) =2$ .

On the other hand, if cos (t) = 1/2 ⇒ t = ± $\frac{\pi}{3}$

Then, the sin( $\frac{\pi}{3}$ ) = $\frac{\sqrt{3} }{2} }$

3 0

2 years ago

What is the area of the parallelogram?

Anarel [89]

Answer:

Step-by-step explanation:

The height is connected to the base of 16cm

Area = b * h

b = 16

h = 5

Area = b * h

Area = 16 cm * 5 cm

Area = 80 cm^2

4 0

2 years ago

Read 2 more answers

A country's population in 1990 was 134 million. In 2000 it was 139 million. Estimate the population in 2014 using the exponentia

Rainbow [258]

Answer

P = 147 million

Step by step explanation

P = Po r^t -------------(1)

Po initial population, r = rate, t = number of years

Here P = 139, Po = 134, t = 10.

Now plug in these values into the formula and find the rate r.

139 = 134r^10

r^10 = 139/134

r = (139/134)^1/10

Now we got r, now plug in the equation (1)

Let's find the population in the year 2014, here t = 24

P = 134 (139/134)^(24/10)

P = 134(139/134)^(2.4)

P = 134*1.1

P = 147.4

P = 147 million

The country's population in 2014 is 147 million (estimation).

Thank you.

7 0

2 years ago

Read 2 more answers