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jarptica [38.1K]
3 years ago
11

A person of height 1.6m up to the eye level is standing at a point 2m away from the bank of the river and found an angle of elev

ation of 30°. find the width of the river.​
Mathematics
1 answer:
natima [27]3 years ago
5 0

Step-by-step explanation:

tan30° = Height of person / (Distance away from river bank + river's width) = 1/√3.

Therefore 1.6m / (2m + x) = 1/√3

By cross multiplication, 1.6√3 = 2 + x.

Hence, x ≈ 0.77m.

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Y=x+3<br> y=3x+1<br><br> A. (1,3)<br> B. (0,1)<br> O C. (0,3)<br> D. (1.4)
guajiro [1.7K]

Answer:

D: (1, 4)

Step-by-step explanation:

You can either solve by substitution or elimination. If you are timed, the fastest way is to guess and check (plug-in the answer choices)

I will be using substitution to solve this:

Step 1: Since you have y already, you can set them equal to each other

x+3 = 3x+1

3 = 2x +1

2 = 2x

x = 1

Step 2: Now you have x, plug x into one of the original equations. In this case, I will use the first one

y = 1 + 3

y = 4

Step 3: Now write your answer as a coordinate plane point

x = 1, y = 4

(1, 4)

6 0
3 years ago
Read 2 more answers
Historically, a certain region has experienced 92 thunder days annually. (A "thunder day" is day on which at least one instance
DiKsa [7]

Answer:

We conclude that the mean number of thunder days is less than 92.

Step-by-step explanation:

We are given that Historically, a certain region has experienced 92 thunder days annually.

Over the past fifteen years, the mean number of thunder days is 72 with a standard deviation of 38.

<u><em>Let </em></u>\mu<u><em> = mean number of thunder days.</em></u>

So, Null Hypothesis, H_0 : \mu \geq 92 days     {means that the mean number of thunder days is more than or equal to 92}

Alternate Hypothesis, H_A : \mu < 92 days     {means that the mean number of thunder days is less than 92}

The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;

                       T.S. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean number of thunder days = 72

             s = sample standard deviation = 38

            n = sample of years = 15

So, <u><em>test statistics</em></u>  =  \frac{72-92}{\frac{38}{\sqrt{15} } }  ~ t_1_4

                               =  -2.038

The value of z test statistics is -2.038.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -1.761 at 14 degree of freedom for left-tailed test.

Since our test statistics is less than the critical value of t as -2.038 < -1.761, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.

Therefore, we conclude that the mean number of thunder days is less than 92.

7 0
3 years ago
A set of equations is given below:
iogann1982 [59]
There are no solutions

8 0
3 years ago
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 80° mo
trasher [3.6K]

Answer:

The measure of the first angle is 50°.

Step-by-step explanation:

Let the three angles be <em>a, b, </em>and <em>c. </em>

<em />

The measure of the first angle is twice the measure of the second angle. In other words:

a=2b

The measure of the third angle is 80° more than the measure of the second angle. In other words:

c=b+80

And since the interior angles of a triangle must equal 180°:

a+b+c=180

Substitute <em>a</em> and <em>c: </em>

<em />(2b)+b+(b+80)=180<em />

Combine like terms:

4b+80=180

Subtract 80 from both sides:

4b=100

And divide both sides by four:

b=25^\circ

So, the measure of the second angle is 25°.

Since the measure of the first is twice the second, the measure of the first angle is 50°.

(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)

8 0
2 years ago
Kira needs 3,000 milligrams of zinc for a science experiment.
luda_lava [24]
The correct answer Is C
6 0
3 years ago
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