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3 years ago

Please help me ASAP and please show me how you did it.

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

8 0

Answer:

2. Find m

sin m˚ = 2/5

sin^-1 (2/5) = m˚

m˚ = 23.57˚

3. Sine law

$\frac{8}{sin103}=\frac{5}{sin\alpha }$

$\frac{5sin103}{8}=sin^{-1}(0.608)=37.5$

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Trimothy climbed the mountain in two days. Trimothy spent a total of 14 hours climbing the mountain. On the second day, Trimothy

stellarik [79]

Answer:

The speed in kilometers per hour with which Timothy walked on the second day is 4 km/h

Step-by-step explanation:

The time period in which Timothy climbed the mountain = 2 days

The total time Timothy spent in climbing the mountain = 14 hours

The average speed with which Timothy walked on the second day = 0.5 km/h faster than he walked the first day

The time duration Timothy walked on the second day =2 hours less than he walked on the first day

The total distance Timothy covered in the two days = 52 kilometers

Let x represent the speed in kilometers per hour with which Timothy walked on the first day and let y represent the speed in kilometers per hour with which Timothy walked on the second day

Also, let t represent the number of hours Timothy walked on the first day

Therefore, we have;

x + 0.5 = y...(1)

x × t + y × (t - 2) = 52...(2)

t + t - 2 = 14...(3)

From equation (3), we have;

t + t - 2 = 14

2·t = 14 + 2 = 16

t = 16/2 = 8

The number of hours Timothy worked on the first day, t = 8 hours, and the number of hours Timothy walked on the second day is t - 2 hours = 8 hours - 2 hours = 6 hours

From equation (1) and (2), we have;

x × t + y × (t - 2) = 52

y = x + 0.5

Which gives;

x × t + y × (t - 2) = x × t + (x + 0.5) × (t - 2) = x × 8 + (x + 0.5) × (8 - 2) = 52

x × 8 + (x + 0.5) × (8 - 2) = x × 8 + (x + 0.5) × 6 = x × 8 + 6 × x + 3 = 52

14·x + 3 = 52

x = (52 - 3)/14 = 3.5

The speed in kilometers per hour with which Timothy walked on the first day = x = 3.5 km/h

From equation (2), we have;

y = x + 0.5 = 3.5 + 0.5 = 4

y = 4

The speed in kilometers per hour with which Timothy walked on the second day = y = 4 km/h.

4 0

3 years ago

Question 1 options:Residents in Portland, Oregon think that their city has more rainfall than Seattle, Washington. To test this

dimaraw [331]

Answer:

There is no enough evidence to to support the claim that Portland has more average yearly rainfall than Seattle.

Being μ1: average rainfall in Portland, μ2: average rainfall in Seattle, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2 > 0$

P-value = 0.1290

As the P-value is bigger than the significance level, the effect is not significant and the null hypothesis failed to be rejected.

Step-by-step explanation:

We have to test the hypothesis of the difference between means.

The claim is that Portland has more average yearly rainfall than Seattle.

Being μ1: average rainfall in Portland, μ2: average rainfall in Seattle, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2 > 0$

The significance level is 0.10.

The sample for Portland, of size n1=45, has a mean of M1=37.50 and standard deviation of s1=1.82.

The sample for Seattle, of size n1=35, has a mean of M1=37.07 and standard deviation of s1=1.68.

The difference between means is:

$M_d= M_1-M_2=37.50-37.07=0.43$

The standard error for the difference between means is:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.82^2}{45}+\dfrac{1.68^2}{35}}=\sqrt{ 0.0736+0.0688 }=\sqrt{0.1424}\\\\\\s_{M_d}=0.3774$