On the first season of "The Biggest Loser",

Find the formula for df^-1/dx. f(x)=(7-x)^3

klio [65]

Here is the equation to solve the problem above:

f(x) = (7-x)^3
y = (7-x)^3

switch y and x
x = (7 - y)^3

third root of x = 7 - y
-y = 3rootx - 7

so:f′(x)=3^√x−7

7 0

3 years ago

Write the standard form of the line that passes through the given points (6,1) and (5,4)

Serggg [28]

The standard form:

$Ax+By=C$

The point-slope form:

$y-y_1=m(x-x_1)$

m - slope

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (6, 1) and (5, 4). Substitute:

$m=\dfrac{4-1}{5-6}=\dfrac{3}{-1}=-3$

$y-1=-3(x-1)$ use distributive property

$y-1=-3x+3$ add 1 to both sides

$y=-3x+4$ add 3x to both sides

$\boxed{3x+y=4}$

7 0

3 years ago

Rsm geo lol- no idea how to start or do it at all

jek_recluse [69]

Answer:

42, 138, and 138 degrees DON'T FORGET THE DEGREES SIGNS!!!!!

Step-by-step explanation:

Using vertical angles theorem, we can get another 42, 180-42, and 180-42.

So we have 42, 138, and 138

7 0

3 years ago

TODAYTHIS WEEKCREDITS$Patricia was setting up a room with tables for an event. The room had9 maple tables, 10 poplar tables, 5 c

prohojiy [21]

As in each table can seat 8 people and the probability you need to find is about the first person you can ignore this data.

Probability that the first person to enter the room will be randomly seated at a maple table:

$P(maple)=\frac{#maple\text{ }tables}{#total\text{ }tables}$

#maple tables: 9

# total tables: 9 +10 +5 +7=31

$P(maple)=\frac{9}{31}$ Then, the probability that the first person to enter the room will be randomly seated at a maple table is 9/31

3 0

1 year ago

Suppose I ask you to pick any four cards at random from a deck of 52, without replacement, and bet you one dollar that at least

Tatiana [17]

Answer:

a) No, because you have only 33.8% of chances of winning the bet.

b) No, because you have only 44.7% of chances of winning the bet.

Step-by-step explanation:

a) Of the total amount of cards (n=52 cards) there are 12 face cards (3 face cards: Jack, Queen, or King for everyone of the 4 suits: clubs, diamonds, hearts and spades).

The probabiility of losing this bet is the sum of:

- The probability of having a face card in the first turn

- The probability of having a face card in the second turn, having a non-face card in the first turn.

- The probability of having a face card in the third turn, having a non-face card in the previous turns.

- The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

1) The probability of having a face card in the first turn

In this case, the chances are 12 in 52:

$P_1=P(face\, card)=12/52=0.231$

2) The probability of having a face card in the second turn, having a non-face card in the first turn.

In this case, first we have to get a non-face card (there are 40 in the dech of 52), and then, with the rest of the cards (there are 51 left now), getting a face card:

$P_2=P(non\,face\,card)*P(face\,card)=(40/52)*(12/51)=0.769*0.235=0.181$

3) The probability of having a face card in the third turn, having a non-face card in the first and second turn.

In this case, first we have to get two consecutive non-face card, and then, with the rest of the cards, getting a face card:

$P_3=(40/52)*(39/51)*(12/50)\\\\P_3=0.769*0.765*0.240=0.141$

4) The probability of having a face card in the fourth turn, having a non-face card in the previous turns.

In this case, first we have to get three consecutive non-face card, and then, with the rest of the cards, getting a face card:

$P_4=(40/52)*(39/51)*(38/50)*(12/49)\\\\P_4=0.769*0.765*0.76*0.245=0.109$

With these four probabilities we can calculate the probability of losing this bet:

$P=P_1+P_2+P_3+P_4=0.231+0.181+0.141+0.109=0.662$

The probability of losing is 66.2%, which is the same as saying you have (1-0.662)=0.338 or 33.8% of winning chances. Losing is more probable than winning, so you should not take the bet.

b) If the bet involves 3 cards, the only difference with a) is that there is no probability of getting the face card in the fourth turn.

We can calculate the probability of losing as the sum of the first probabilities already calculated:

$P=P_1+P_2+P_3=0.231+0.181+0.141=0.553$

There is 55.3% of losing (or 44.7% of winning), so it is still not convenient to bet.

5 0

4 years ago