Find the range of these two functions? M(x)=|x+2|-1 T(x)=|2x+2|-1

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

3 0

Because of the Absolute Values, when x = -1 or -2, the overall range
is [-1, co)

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Simplify the expression.

astra-53 [7]

$a^{\log_a b}=b\\\\12^{\log_{12}24}=24$

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what is the distance between point S and U? Round to the nearest tenth of a unit? A 3.3 B 6.4 C 8.1 D 12.0

ki77a [65]

The distance between the points (d) is found using the Pythagorean theorem.

Imagine the two points as defining the hypotenuse of a right triangle. The lengths of the legs of the triangle are the horizontal distance between the points and the vertical distance between the points. The the theorem tells us
d² = 4² + 7²
d² = 16 + 49
d² = 65
d = √65 ≈ 8.1

The distance between the points is
C 8.1

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You know that the distance must be longer than the longest leg (7) and must be shorter than the sum of the two legs (4+7=11). The only answer choice between 7 and 11 is 8.1.

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2 years ago

You roll a pair of honest dice. If you roll a total of 7, you win $18; if you roll a total of 11, you win $54; if you roll any o

amm1812

Answer: -1
The negative value indicates a loss

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Explanation:

Define the three events
A = rolling a 7
B = rolling an 11
C = roll any other total (don't roll 7, don't roll 11)

There are 6 ways to roll a 7. They are
1+6 = 7
2+5 = 7
3+4 = 7
4+3 = 7
5+2 = 7
6+1 = 7
Use this to compute the probability of rolling a 7
P(A) = (number of ways to roll 7)/(number total rolls) = 6/36 = 1/6
Note: the 36 comes from 6*6 = 36 since there are 6 sides per die

There are only 2 ways to roll an 11. Those 2 ways are:
5+6 = 11
6+5 = 11
The probability for event B is P(B) = 2/36 = 1/18

Since there are 6 ways to roll a "7" and 2 ways to roll "11", there are 6+2 = 8 ways to roll either event.
This leaves 36-8 = 28 ways to roll anything else
P(C) = 28/36 = 7/9

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

In summary so far,
P(A) = 1/6
P(B) = 1/18
P(C) = 7/9

The winnings for each event, let's call it W(X), represents the prize amounts.
Any losses are negative values
W(A) = amount of winnings if event A happens
W(B) = amount of winnings if event B happens
W(C) = amount of winnings if event C happens
W(A) = 18
W(B) = 54
W(C) = -9

Multiply the probability P(X) values with the corresponding W(X) values
P(A)*W(A) = (1/6)*(18) = 3
P(B)*W(B) = (1/18)*(54) = 3
P(C)*W(C) = (7/9)*(-9) = -7

Add up those results
3+3+(-7) = -1

The expected value for this game is -1.
The player is expected to lose on average 1 dollar per game played.

Note: because the expected value is not 0, this is not a fair game.

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If x-y =8 find the value of y when x=3

DedPeter [7]

Answer: y = -5

Substitute in 3 for x.
x - y = 8 Substitution
3 - y = 8 Subtract 3 from both sides
-y = 5 Divide by -1 to both sides
y = -5 Answer!

You can also check your work.
x - y = 8
3 - (-5) = 8
3 + 5 = 8
8 = 8

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Mashcka [7]

S= 1/3t (T is one third of s)

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