A downhill skier was able to move 560 meters in 25 seconds. What is the skier’s average speed? (Round your answer to the nearest tenth of a meter per second.)

Answer:

(a) The probability that the student made the​ Dean's list is 0.1655.

(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Step-by-step explanation:

The complete question is:

Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.

a) Find the probability that the student made the Dean's list.

b) Find the probability that the student came from a private high school, given that the student made the Dean's list.

c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.

Solution:

Denote the events as follows:

A = a student attended public high school

B = a student attended private high school

C = a student was home schooled

D = a student made the Dean's list

The provided information is as follows:

P (A) = 0.71

P (B) = 0.21

P (C) = 0.08

P (D|A) = 0.16

P (D|B) = 0.19

P (D|C) = 0.15

(a)

The law of total probability states that:

[tex]P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})[/tex]

Compute the probability that the student made the​ Dean's list as follows:

[tex]P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)[/tex]

         [tex]=(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655[/tex]

Thus, the probability that the student made the​ Dean's list is 0.1655.

(b)

Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:

[tex]P(B|D)=\frac{P(D|B)P(B)}{P(D)}[/tex]

             [tex]=\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411[/tex]

Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c)

Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:

[tex]P(C^{c}|D^{c})=1-P(C|D^{c})[/tex]

               [tex]=1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185[/tex]

Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Answer:

FV= $38,735.32

Step-by-step explanation:

Giving the following information:

Monthly deposit= $100

Number of periods= 18*12= 216 months

The interest rate is confusing. I will assume an interest rate of 6%. If it is not correct, just change it in the formula.

Monthly interest rate= 0.06/12= 0.005

To calculate the future value, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

FV= {100*[(1.005^216) - 1]} / 0.005

FV= $38,735.32

Answer:

(-1,3)

Step-by-step explanation:

Elimination makes solving for the system of equations much easier if it is the faster route. In this case, it is already done for you, and no multiplication is required.

First, we want to eliminate the x values completely because they are opposites and therefore cancel out. Next, you want to add the y-values and sum (20 and 10) so that you get the new equation [tex]10y=30[/tex]. To isolate you need to divide by 10 on each side which will give you [tex]y=3[/tex].

Now that you have your y-value, you can plug in your value to either of the equations and find what x is. I will use the equation 4x + 8y = 20 to solve for x. We first want to substitute in our y-value so that we get [tex]4x+8(3)=20[/tex] which is simplified to [tex]4x+24=20[/tex] now subtract by 24 on both sides to get 4x by itself to get [tex]4x=-4[/tex]. Lastly, isolate x by dividing by 4 on each side to get [tex]x=-1[/tex]

Answer: $24

Step-by-step explanation: if you divide $120 by 5 then you get $24

Answer:

p=-5

Step-by-step explanation:

3p-49+9 -49+9=-40

3p-40=8p 3p-3p=0 8p-3p=5p

-40=5p p=5

Step-by-step explanation:

Answer:

mulitply

Step-by-step explanation:

PEMDAS

mutiply

divide

add

and subtract

Answer:

D

Step-by-step explanation:

just flip the fraction

Answer:

D

Step-by-step explanation:

The reciprocal is just the fraction flipped.

Answer:  y = 5

Step-by-step explanation:

If the slope is 0, the graph of the line is a horizontal line (parallel to the x-axis).   0 slope means it is flat.

Here it passes through the y-axis  at +5 and passes through every value of x.

Answer:

try quizlet it would help:)))

Answer:

Step-by-step explanation:

The vertical distance between a senior student with a height of 160 cm and his estimated height of 157.06 cm is 2.94 cm

the angle you are looking for is 9

Answer:

Enlargement rate is 24

Step-by-step explanation:

Divide 8 by one third to get the enlargement rate. I hope this helps:)

Answer:

Which side of the original parallelogram corresponds to the 6 ft side of the enlarged parallelogram? ITS IS  x ft

What is the second step in solving the proportion? IT IS  cross multiply

What is the value of the missing measure? IT IS  1/4

Step-by-step explanation:

i got this right

Answer:

The coordinates of Bodega is B(1,-2)

The coordinates of OWL Barbershop is O(3,-1)

Step-by-step explanation:

Coordinates of House H = (-3,-4)

Coordinates of Job J= (5,0)

His first stop is at the bodega to get something to eat. The bodega is exactly halfway between his house and the school.

Let B to represent the Bodega

Now to find coordinates of Bodega we will use use mid point formula since  bodega is exactly halfway between his house and the school.

[tex]x=\frac{x_1+x_2}{2} , y = \frac{y_1+y_2}{2}\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\x=\frac{-3+5}{2} , y = \frac{-4+0}{2}\\x=1, y = -2[/tex]

So, The coordinates of Bodega is B(1,-2)

Now we are given that The OWL Barbershop location partitions the way from Wilfred’s house and job in the ratio 3:1.

Le O to represent OWL Barbershop.

We will use section formula

[tex]x=\frac{mx_2+nx_1}{m+n} , y =\frac{my_2+ny_1}{m+n}\\(x_1,y_1)=(-3,-4)\\(x_2,y_2)=(5,0)\\m:n=3:1\\x=\frac{3(5)+1(-3)}{3+1} , y =\frac{3(0)+1(-4)}{3+1}\\x=3,y=-1[/tex]

So, The coordinates of OWL Barbershop is O(3,-1)

Given:

Length of taller tree = 50 feet

Length of shorter tree = 20 feet

Length of shadow of taller tree = 18 feet

To find:

The length of shadow of shorter tree.

Solution:

Since, two trees standing side by side in the sunlight, therefore the length of trees are proportional to their shadows.

Let the length of shadow of shorter tree be x feet.

Using the given information, we get

[tex]\dfrac{50}{18}=\dfrac{20}{x}[/tex]

By cross multiplication, we get

[tex]50\times x=20\times 18[/tex]

[tex]50x=360[/tex]

[tex]x=\dfrac{360}{50}[/tex]

[tex]x=7.2[/tex]

Therefore, the length of shadow of shorter tree is 7.2 feet.

Answer:

no solution

Step-by-step explanation:

[1]    6x - 9y = 16

  [2]    2x - 3y = 7

// Solve equation [2] for the variable  x  

 [2]    2x = 3y + 7

 [2]    x = 3y/2 + 7/2

// Plug this in for variable  x  in equation [1]

  [1]    6•(3y/2+7/2) - 9y = 16

  [1]    0 = -5 =>  NO solution

No solution

Answer:

500

Step-by-step explanation:

Answer:

9.6 cm

Step-by-step explanation:

12 x .8 = 9.6cm

Answer:

1. x > 9

2. n < 5

3. b > 2

4. p < 4

5. p < -2

6. m > 0

Step-by-step explanation:

1.

x - 2 - 2 > 5

x - 4 > 5

x > 5 + 4

x > 9

2.

5 + n < 2 x 5

n < 10 - 5

n < 5

3.

50b > 100

b > 100 : 50

b > 2

4.

-5 + p + 2 < 1

p < 1 + 3

p < 4

5.

p + 6 + 8 < 12

p + 14 < 12

p < 12 - 14

p < -2

6.

80m - 64 - 2 > -66

80m > -66 + 66

m > 0:80

m > 0

Answer: Mathematical distance is defined as the amount of space between two points. This distance can be calculated using the distance formula, which is just a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the other two sides

Step-by-step explanation:

Answer : The correct option is (A) 68.

Step-by-step explanation :

As we are given that:

LN = 6x - 5

LM = x + 7

MN = 3x + 20

Now we have to determine the value of MN.

According to the question:

LN = LM + MN

Now putting all the given values in this expression, we get:

6x - 5 = (x + 7) + (3x + 20)

6x - 5 = 4x + 27

6x - 4x = 27 + 5

2x = 32

x = 16

The value of MN = 3x + 20 = 3(16) + 20 = 48 + 20 = 68

Therefore, the value of MN is 68.

Answer:

you should know you dont need help so do it by yourself. if you want the awnser you should know or you just dont pay attention in class.1234567890 is your awnser

Answer:

-3/2, -2, 0, 2.1, 7/3

Step-by-step explanation:

Please correct me if I am wrong. Thank you.

Answer:

1 1/2 kilometers

Step-by-step explanation:

She ran 1/4 of a kilometer and then ran another 10/8 kilometer.

The 5 minute rest is to throw people off, so ignore it.

10/8 can simplify to 5/4 kilometers, so you can add that to the first quarter of a kilometer she already traveled.

5/4 plus 1/4 equals 6/4.

6/4 can be simplified to 3/2 which is equal to one and one half.

1   1/2

Hope this helps!

Answer:

A, D ,E

Step-by-step explanation:

18/30

Divide the top and bottom by 6

3/5

A.15/25  Divide top and bottom by 5  = 3/5

B.6/11  cannot be simplified

C.3/4 cannot be simplified

D.3/5 cannot be simplified

E. 9/15​  divide top and bottom by 3 = 3/5

Answer:

30%

Step-by-step explanation:

250-175=75

75/250*100%= 0.3 or 30%

Answer:

(0,3)

Step-by-step explanation [0,3] indicates that the numbers are greater or equals to 0 and less than or equals to 3; while (0,3) leaves out the equal sign

Answer:

-4[tex]x^{2}[/tex] - 6

Step-by-step explanation:

First you have to add the two polynomials.  Write the first equation then line up the second equation below the first making sure to keep the columns correct.  [tex]x^{2}[/tex] goes in one column, x goes in the next column and the whole numbers go in the last column.  Also be sure to have the correct signs of those columns.  It should look like this:

                      4[tex]x^{2}[/tex]   -   x   +   1

PLUS             -6[tex]x^{2}[/tex]   +   x   -   4

                      -----------------------

                      -2[tex]x^{2}[/tex]   +  0   -   3

Note that the middle x turns to 0 because you're subtracting 1x from 1x which is 0.

You can now write the SUM as   -2[tex]x^{2}[/tex] - 3

Now they want to know what twice this sum is so multiply it by 2

                          2 ( -2[tex]x^{2}[/tex] - 3)  =  -4[tex]x^{2}[/tex]  -  6

Answer:

See below

Step-by-step explanation:

(a) the equation

(b) If f(t) = 1000000