MATHEMATICS HIGH SCHOOL

There are 46 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 4 min. (Round your answers to four decimal places.)(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?(b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?

Answers

Answer 1

Answer:

Answer:

a) P ( T < 250 mins ) = 0.7695

b) P ( T > 260 mins ) = 0.1344

Step-by-step explanation:

- The RV from a sample has the following parameters that are mean = 5 mins, and standard deviation s = 4 mins.

- The entire population has n = 46 students.

- We will first compute the population mean u and population standard deviation σ as follows:

u = n*mean

u = 46*5 = 230 mins

σ = sqt ( n ) * s

σ = sqt ( 46 ) * 4

σ = 27.129 mins

- Approximating that the time taken T to grade the population of entire class follows a normal distribution with parameters u and σ as follows:

T~ N ( 230 , 27.129 )

Find:

- If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

- The total time till 6:50 PM to 11:00 PM is ( 4 hr and 10 mins ) = 250 mins.

- We will compute the Z-value as follows:

Z = ( 250 - 230 ) / 27.129

Z = 0.7372

- Then use the Z-Tables and determine the probability:

P ( T < 250 mins ) = P ( Z < 0.7372 )

P ( T < 250 mins ) = 0.7695

Find:

- If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?

- For the teacher to miss the sports report he must take more time than 6:50 PM to 11:10 P.M.

- The total time till 6:50 PM to 11:10 PM is ( 4 hr and 20 mins ) = 260 mins.

- We will compute the Z-value as follows:

Z = ( 260 - 230 ) / 27.129

Z = 1.10582

- Then use the Z-Tables and determine the probability:

P ( T > 260 mins ) = P ( Z > 1.10582 )

P ( T > 260 mins ) = 0.1344

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Answers

Answer:

The answer is B

Step-by-step explanation:

✌

Answer:

Step-by-step explanation:

You can substitute the variables for the values!

7x = 21

3y = -6

2x = 6

y = -2

21 - (-6)

----------

6 + (-2)

----

Solve for x: |2x + 12| = 18

Answers

|2x + 12| = 18

First, break down the problem into 2 equations . / 2x + 12 = 18 and -(2x + 12) = 18
Second, solve the first equation. / $2x + 12 = 18$
Subtract 12 from both sides. / $2x = 18 - 12$
Subtract 18 - 16. / $2x = 6$
Divide both sides by 2. / $x = (6)/(2)$
Simplify. / $x = 3$
Third, solve the second equation. / -(2x + 12) = 18
Simplify your brackets. / $-2x - 12 = 18$
Add 12 to both sides. / $-2x = 18 + 12$
Add 18 + 12. / $-2x = 30$
Divide both sides by -2. / $x = (30)/(-2)$
Simplify. / $x = -(30)/(2)$
Simplify. / $x = -15$
Fourth, collect the solutions. / $x = -15,3$

Answer: x = -15, 3

Solve the equation for the given variable.
Bx+Cy=D

Solve for y

Answers

Bx + Cy = D

Solve for y . . .

*subtract Bx from both sides

Bx - Bx + Cy = D - Bx

Cy = D - Bx

*now divide both sides by C

Cy/C = (D - Bx)/C

Cy/C = D/C - Bx/C

y = D/C - (B/C)x

y = -(B/C)x + D/C

Bx+Cy=D -- subtract Bx

Cy=D-Bx -- divide by C

y=(D-Bx)/C

cone A has a height of 3 meters and radius of 2 meters. Cone B has the same radius, but height og 6 meters, calculate the volume of each cone. Which conclusion is correct ? The volume of cone A is twice the volume of cone B, the volume of cone Bis ywice the volume of cone A , The volume of cone B is 4 time the volume of cone A or The volume of cone B is 3 times the volume of cone A?

Answers

Answer:

The volume of cone B is twice the volume of cone A.

Step-by-step explanation:

Cone A

Height of cone = 3 m

Radius of Cone = 2 m

Volume of cone = $(1)/(3) \pi r^(2) h$

= $(1)/(3) * 3.14 * 2^(2) (3)$

= $12.56 m^3$

Cone B

Height of cone = 6 m

Radius of Cone = 2 m

Volume of cone = $(1)/(3) \pi r^(2) h$

= $(1)/(3) * 3.14 * 2^(2) (6)$

= $25.12 m^3$

Now $12.56 * 2 = 25.12$

Thus the volume of cone B is twice the volume of cone A.

The volume of Cone B is twice the volume of Cone A.

3. Irvin cut a 47 in. wire into two pieces. The longer piece is 13 in. longer than the shorter piece. What is the length of the longer piece?_________ in.

Please Help!!!

Answers

Let's say x to the shoter piece's length, since the longer one is 13 in longer, it's length has to be x+13 in. We know the sum of these pieces is equal to 47. So let's solve:
$x+x+13=47\n 2x+13=47\n 2x=47-13\n 2x=34\n x=\frac { 34 }{ 2 } \n x=17$
the shorter piece's length 'x' is 17 , so the longer piece's length 'x+13' is : $x+13\n 17+13=30$

Answer:

30 inches.

Step-by-step explanation:

i took the test and got it correct.

Solve for d.5d+2(2-d)=3(1+d)+1
a)no solution
b)d=4
c)infinitely many solutions
d)d=-3

Answers

5d + 2(2 - d) = 3(1 + d) + 1
5d + 2(2) - 2(d) = 3(1) + 3(d) + 1
5d + 4 - 2d = 3 + 3d + 1
5d - 2d + 4 = 3d + 3 + 1
3d + 4 = 3d + 4
-3d    -3d
   4 = 4
   d = 0

$5d+2(2-d)=3(1+d)+1 \n 5d+4-2d=3+3d+1 \n 3d+4=3d+4 \n 0=0 \n \boxed{C.\ Infinitely\ many\ solutions}$

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