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3 years ago

Applications of systems of equations

1 answer:

4 0

If m= mc questions and t= t/f questions $t=125-m, 8(125-m)+14m=1300, 1000-8m+14m=1300$ ,
$\left \{ {{t+m=125} \atop {8t+14m=1300}} \right.$ ,
6m=300 ,
m=50 , t=75

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The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally dis

svlad2 [7]

Answer:

a) 11.7% of students study for more than 10 hours per week.

b) 35.6% of student spends between 7 and 9 hours studying.

c) 1.6% of students spend fewer than 3 hours studying.

d) 5% of all A students spend studying 4.0455 or less hours during a week.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 7.5 hours

Standard Deviation, σ = 2.1 hours

We are given that the distribution of amount of time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(students study for more than 10 hours per week)

P(x > 10)

$P( x > 10) = P( z > \displaystyle\frac{10 - 7.5}{2.1}) = P(z > 1.1904)$

$= 1 - P(z \leq 1.1904)$

Calculation the value from standard normal z table, we have,

$P(x > 10) = 1 - 0.883 = 0.117 = 11.7\%$

b) P(student spends between 7 and 9 hours studying.)

$P(7 \leq x \leq 9) = P(\displaystyle\frac{7 - 7.5}{2.1} \leq z \leq \displaystyle\frac{9-7.5}{2.1}) = P(-0.2380 \leq z \leq 0.7142)\\\\= P(z \leq 0.7142) - P(z < -0.2380)\\= 0.762 - 0.406 = 0.356 = 35.6\%$

$P(7 \leq x \leq 9) = 35.6\%$

c) P(students spend fewer than 3 hours studying)

$P(x < 3) = P(z < \displaystyle\frac{3-7.5}{2.1}) = P(z < -2.1428)$

Calculating the value from the standard normal table we have,

$P( x < 3) =0.016 = 1.6\%$

d) P(X < x) = 0.05

We have to find the value of x such that the probability is 0.035

$P( X < x) = P( z < \displaystyle\frac{x - 7.5}{2.1})=0.05$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 7.5}{2.1} = -1.645\\x = 4.0455$

5% of all A students spend studying 4.0455 or less hours during a week.

5 0

3 years ago

Please help me with questions 11-13 god bless

lianna [129]

#11 and #12 have no solutions, #13 has a solution which is 14

5 0

2 years ago

M< AOB + m < 96= m <139

san4es73 [151]

139 = x + (2x + 10)
139 = 3x + 10
129 = 3x
/3 /3
43 = x

Therefore

5 0

3 years ago

for a March past competition on sports day the house captain of one house cut 25 pieces of ribbon each 1/2 metre in length.what

zzz [600]

Answer:

not lenguague spanish

Step-by-step explanation:

that bad

7 0

3 years ago

The explicit rule for a sequence is given. an=4n−1 What is the recursive rule for the sequence?

Gnom [1K]

Answer:

$a_{n+1}=a_n+4$

Step-by-step explanation:

Have in mind the definition of the term $a_n=4\,n-1$ , and now work on what the term $a_{n+1}$ is based on the previous definition:

$a_{n+1} = 4\,(n+1)-1\\a_{n+1}=4\,n+4-1$

In the next step do NOT combine the numerical values, but try to identify the $a_n$ term ( $4\,n-1$ ) in the expression (notice the use of square brackets to group the relevant terms):

$a_{n+1}=4\,n+4-1\\a_{n+1}=[4\,n-1]+4\\a_{n+1}=a_n+4$

So now we have the term " $a_{n+1}$ " defined in a recursive manner based on the previous term " $a_n$ "

8 0

3 years ago