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kiruha [24]
1 year ago
8

In a class of 35 students, 5 are freshmen, 8 are sophomores, 9 are juniors and 13 are seniors. If 1 student is randomly selected

, what is the probability the student is a junior
Mathematics
1 answer:
Sauron [17]1 year ago
6 0
<h3>Answer:</h3>

\displaystyle\frac{9}{35} or 25.71%.

Probability is the likelihood of an event occurring. The desired outcomes are known as successful outcomes. In this scenario, the successful outcomes are when a junior is selected. The sample size is the total number of students.

<h3>Probability as a Fraction</h3>

Simple probability (the probability of 1 event) can easily be found as a fraction. For the fraction, the number of successful outcomes should be the numerator and the sample size is the denominator.

This means that the probability of selecting a junior is \displaystyle\frac{9}{35}.

<h3>Probability as a Percentage</h3>

In this case, it is easiest to first find the probability as a fraction, but we can then convert it to a percentage if desired.

To convert to the fraction divide the numerator and denominator (I'm rounding to 4 decimal places).

  • 9/35 = 0.2571

Then, multiply this decimal by 100, which is the equivalent of moving the decimal point 2 digits to the left.

  • 0.2571 * 100 = 25.71%
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Four more than the quotient of a number and 3 is 2
Arturiano [62]

Answer:4+x/3=2

Step-by-step explanation:

4 more=4+

the quotient of a number and 3= x/3

the anwser = =2

6 0
3 years ago
I'm confused on how to do this. Please explain step by step. If you respond with just the answer I WILL report you. I would like
Tcecarenko [31]

Answer:

Exact Form:

√2−1

Decimal Form:

0.41421356

…

Step-by-step explanation:

Since  9π/8  is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

9π/8  is not an exact angle

First, rewrite the angle as the product of  1/2  and an angle where the values of the six trigonometric functions are known. In this case,  9π/8  can be rewritten as

(1/2)*  9π/8 tan ((1/2)*  9π/8)

Use the half-angle identity for tangent to simplify the expression. The formula states that  

tan (0/2)=sin(0)/1+cos(0) sin(9π/4)/1+cos(9π/4)

Simplify

Remove full rotations of  2π  until the angle is between  0  and  2π.

sin(π/4)/1+cos(9π/4)

The exact value of sin(π/4) is √2/2

√2/2/1+cos(9π/4)

Simplify the Denominator

Remove full rotations of  2π  until the angle is between  0  and  2π.√2/2/1+cos(π4)

The exact value of cos(π/4)   is  √2/2.√2/2/1+√2/2

To write  1/1  as a fraction with a common denominator, multiply by  2/2  .√2/2/1/1⋅2/2+√2/2

Write each expression with a common denominator of  2, by multiplying each by an appropriate factor of  1.

Combine.

√2/2/1⋅2/1⋅2+√2/2

Multiply 2 by 1

√2/2/1⋅2/2+√2/2

Combine the numerators over the common denominator.

√2/2/1⋅2+√2/2

Multiply 2 by 1

√2/2/2+√2/2

Multiply the numerator by the reciprocal of the denominator

√2/2  ⋅  2/2+√2

Cancel the common factor of  2  .

Factor out the greatest common factor  2

√2/2⋅1  ⋅  2⋅1/2+√2

Cancel the common factor

√2/2⋅1  ⋅  2⋅1/2+√2

Rewrite the expression.

√2/1  ⋅  1/2+√2

Simplify

Multiply  √2/1  and  1/2+√2

√2/2+√2

Multiply  √2/2+√2  by  2−√2/2−√2

Combine

√2(2−√2)/(2+√2)(2−√2)

Expand the denominator using the FOIL method.

√2(2−√2)/4−2√2+√2⋅2−√2^2

Simplify

√2(2−√2)/2

Apply the distributive property

√2⋅2+√2(−√2)/2

Move  2  to the left of the expression  √2⋅2.

2⋅√2+√2(−√2)/2

Simplify  

√2(−√2)  .

Raise  √2  to the power of  1  .

2⋅√2−(√2^1√2)/2

Raise  √2  to the power of  1  .

2⋅√2−(√2^1√2^1)/2

Use the power rule  a^m  a^n=a^m+n  to combine exponents.

2⋅√2−√2^1+1/2

Add  1  and  1  .

2⋅√2−√2^2/2

Simplify each term.

Multiply  2  by  √2  .

2√2−√2^2/2

Rewrite  √2^2  as  2  .

2√2−1⋅2/2

Multiply  −1  by  2.

2√2−2/2

Reduce the expression by cancelling the common factors.

Factor  2  out of  2√2.

2(√2)−2/2

Factor  2  out of  −2.

2(√2)+2⋅−1/2

Factor  2  out of  

2(√2)+2(−1)2(√2−1)/2

Cancel the common factors.

Factor  2  out of  2  .

2(√2−1)/2(1)

Cancel the common factor.

2(√2−1)/2⋅1

Rewrite the expression.

√2−1/1

Divide  √2−1  by  1  .

√2−1

The result can be shown in multiple forms.

Exact Form:

√2−1

Decimal Form:

0.41421356…

Hope it help. Good luck.

4 0
3 years ago
What is the area of the figure shown?
ExtremeBDS [4]

Step-by-step explanation:

3.5 \times 6 + (5 - 3.5) \times 6 \div 2 =  \\  = 21 + 9 \div 2 =  \\  = 25.5

6 0
2 years ago
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UkoKoshka [18]

9514 1404 393

Answer:

  see attached for a graph

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Step-by-step explanation:

The graph has a y-intercept of -1, which is halfway between 0 and -2. It goes up 4 units (2 vertical grid spaces) for 1 unit to the right (1 horizontal grid space). It seems to cross y = 1 at about x = 1/2.

x = 1/2 when y = 1.

4 0
2 years ago
Find the inverse of square root f(n) = n – 3.
pogonyaev

Answer:

f'(n) = n + 3

Step-by-step explanation:

Given

f(n) = n - 3

Required

The inverse

f(n) = n - 3

Replace f(n) with y

y = n - 3

Swap positions of y and n

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Replace y with f'(n)

f'(n) = n + 3

4 0
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