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2 years ago

Find the value of x, rounded to the nearest tenth

Mathematics

1 answer:

solmaris [256]2 years ago

5 0

Answer:

x= 8.1

Step-by-step explanation:

The given triangle is a right angle triangle.

We cannot use the Pythagoras theorem as the lengths of all sides are not known. We will use triangular ratios here to solve the given problem.

As it is clear from the diagram that x is the hypotenuse of the triangle and 11 is the length of the base. We will use a ratio in which base and hypotenuse are used.

So,

cos⁡ θ= base/hypotenuse

cos⁡ 36=x/10

0.8090=x/10

8.090=x

x=8.090

Rounding off to nearest 10

x=8.1

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It’s 3.8 inches I’m pretty sure

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2 years ago

Rita earns $10 per hour. She puts 5% of her earnings in savings. Write inequality to find how many hours Rita must work to save

Rina8888 [55]

Answer:

Rita must work 50 days to save at least $25.

Step-by-step explanation:

The amount Rita earns per hour = $10

The saving percentage = 5%

So, the savings of Rita per hour = 5% of $10

⇒5% of $10 = $\frac{5}{100} \times 10 = 0.5$

or Rita saves $0.5 per hour.

The amount she wants to save at minimum = $25

So, let she works at the minimum of k Days.

⇒ $\textrm{The number of hours she has to work} = \frac{\textrm{Amount she needs saving}}{\textrm{Amount saved in 1 hour}}$

or, $k = \frac{25}{0.5} = 50$

The number of hours she has to work = 50 days

Hence, Rita must work 50 days to save at least $25.

3 0

2 years ago

Scores on a test are normally distributed with a mean of 81.2 and a standard deviation of 3.6. What is the probability of a rand

Misha Larkins [42]

<u>Answer:</u>

The probability of a randomly selected student scoring in between 77.6 and 88.4 is 0.8185.

<u>Solution:</u>

Given, Scores on a test are normally distributed with a mean of 81.2

And a standard deviation of 3.6.

We have to find What is the probability of a randomly selected student scoring between 77.6 and 88.4?

For that we are going to subtract probability of getting more than 88.4 from probability of getting more than 77.6

Now probability of getting more than 88.4 = 1 - area of z – score of 88.4

$\mathrm{Now}, \mathrm{z}-\mathrm{score}=\frac{88.4-\mathrm{mean}}{\text {standard deviation}}=\frac{88.4-81.2}{3.6}=\frac{7.2}{3.6}=2$

So, probability of getting more than 88.4 = 1 – area of z- score(2)

= 1 – 0.9772 [using z table values]

= 0.0228.

Now probability of getting more than 77.6 = 1 - area of z – score of 77.6

$\mathrm{Now}, \mathrm{z}-\text { score }=\frac{77.6-\text { mean }}{\text { standard deviation }}=\frac{77.6-81.2}{3.6}=\frac{-3.6}{3.6}=-1$

So, probability of getting more than 77.6 = 1 – area of z- score(-1)

= 1 – 0.1587 [Using z table values]

= 0.8413

Now, probability of getting in between 77.6 and 88.4 = 0.8413 – 0.0228 = 0.8185

Hence, the probability of a randomly selected student getting in between 77.6 and 88.4 is 0.8185.

4 0

3 years ago

A boat can travel at an average speed of 10 miles per hour in still water. Traveling with the current, it can travel 6 miles in

oksano4ka [1.4K]

Answer: The speed of the current is 2 miles per hour.

Step-by-step explanation:

We know that the speed of the boat is:

S = 10 mph.

When the boat travels with the current, the speed will be:

S = 10mph + x

where x = speed of the current.

When the boat travels against the current, the speed will be:

S = 10mph - x

Now, for a given amount of time T, when the boat travels with the current, it moves a distance of 6 miles.

Then we have the equation:

(10mph + x)*T = 6mi

And against the current, in the same time the boat moves 4 mi, then:

(10 mph - x)*T = 4mi

Then we have the system of equations:

(10mph + x)*T = 6mi

(10 mph - x)*T = 4mi

Now, we can take the quotient of these two equations and get:

((10mph + x)*T)/((10 mph - x)*T) = (6mi/4mi)

(10mph + x)/(10 mph - x) = 3/2

Now we can solve this for x.

(10mph + x) = (3/2)*(10 mph - x)

10mph + x = (3/2)*10mph - (3/2)*x

x + (3/2)*x = (3/2)*10mph - 10mph

(5/2)*x = (1/2)*10mph = 5mph

x = (2/5)*5mph = 2mph.

The speed of the current is 2 miles per hour.

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