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bonufazy [111]
3 years ago
10

There are some students playing soccer. Five students decided to join the game and now there are twenty-two students playing soc

cer. How many students were originally playing soccer?
Mathematics
1 answer:
ella [17]3 years ago
3 0

Answer:

17 students

Step-by-step explanation:

Given:

There are some students playing soccer.

Five students decided to join the game and now there are twenty-two students playing soccer.

Question asked:

How many students were originally playing soccer?

Solution:

Let initially number of students playing soccer = x

As given,

<u>After joining 5 more students, there are 22 students playing soccer, the equation will be:-</u>

x+5=22

Subtracting both side by 5

x+5-5=22-5\\x=17\ students

Hence, 17 students were originally playing soccer.

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3 years ago
Can someone help me shot this problem
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Answer:

A) sin θ = 3/5

B) tan θ = 3/4

C) csc θ = 5/3

D) sec θ = 5/4

E) cot θ = 4/3

Step-by-step explanation:

We are told that cos θ = 4/5

That θ is the acute angle of a right angle triangle.

To find the remaining trigonometric functions for angle θ, we need to find the 3rd side of the triangle.

Now, the identity cos θ means adjacent/hypotenuse.

Thus, adjacent side = 4

Hypotenuse = 5

Using pythagoras theorem, we can find the third side which is called opposite;

Opposite = √(5² - 4²)

Opposite = √(25 - 16)

Opposite = √9

Opposite = 3

A) sin θ

Trigonometric ratio for sin θ is opposite/hypotenuse. Thus;

sin θ = 3/5

B) tan θ

Trigonometric ratio for tan θ is opposite/adjacent. Thus;

tan θ = 3/4

C) csc θ

Trigonometric ratio for csc θ is 1/sin θ. Thus;

csc θ = 1/(3/5)

csc θ = 5/3

D) sec θ

Trigonometric ratio for sec θ is 1/cos θ. Thus;

sec θ = 1/(4/5)

sec θ = 5/4

E) cot θ

Trigonometric ratio for cot θ is 1/tan θ. Thus;

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5 0
2 years ago
Question Help Scores of an IQ test have a​ bell-shaped distribution with a mean of 100100 and a standard deviation of 1010. Use
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Answer:

a) 95% percentage of people has an IQ score between 80 and 120.

b) 68% percentage of people has an IQ score between 90 and 110.    

c) 2.5% percentage of people has an IQ score greater than 120.          

Step-by-step explanation:

The empirical formula states that:

  • The empirical rule is known as the three-sigma rule or 68-95-99.7 rule.
  • It is a rule which states that for a normal distribution, almost all data falls within three standard deviations of the mean.
  • 68% of data falls within the first standard deviation that is \mu \pm \sigma
  • 95% of data falls within the second standard deviation that is \mu \pm 2\sigma
  • 99.7% of data falls within the third standard deviation that is \mu \pm 3\sigma

a)  percentage of people has an IQ score between 80 and 120

(80, 120) can be written as:

(80, 120) = (100-2(10), 100 + 2(10))\\= (\mu \pm 2\sigma)

Thus, it is the interval within two standard deviation from the mean.

Thus, by empirical formula, 95% percentage of people has an IQ score between 80 and 120.

b) percentage of people has an IQ score between 90 and 110

(90, 110) can be written as:

(90, 110) = (100-1(10), 100 + 1(10))\\= (\mu \pm 1\sigma)

Thus, it is the interval within one standard deviation from the mean.

Thus, by empirical formula, 68% percentage of people has an IQ score between 90 and 110.

c) P(score greater than 120)

= 1 - percentage of score less than 80 - percentage of score between 80 and 120

= 1 - (95\% + 2.5\%) = 2.5\%

From empirical formula,

2.5% percentage of people has an IQ score greater than 120.

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