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2 years ago

If we added a 4th person to the race, what is the probability of the 4th person winning the race?

Mathematics

1 answer:

lord [1]2 years ago

5 0

Answer:

1/4 chances

Step-by-step explanation:

its like rolling a dice. Six sides, Six different numbers, one will be picked

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If the side lengths of a cube are 16 feet, what is the correct way to write the expression to represent the volume of the cube i

Dmitriy789 [7]

The answer would be B

6 0

3 years ago

Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

2 years ago

Read 2 more answers

zlopas [31]

Answer:

Step-by-step explanation:

ΔABC & ΔADE are similar triangles

$\frac{AD}{AB}=\frac{DE}{BC}\\\\\frac{12}{4}=\frac{12}{x}\\$

Cross multiply,

12*x = 12*4

$x=12*\frac{4}{12}\\$

x = 1 * 4

x = 4

8 0

2 years ago

12. If n(A) = 14, n(B) = 15, and n(<br>AB) = 6, then n(AUB) is<br>

motikmotik

Answer:

given n(A) = 14

n(B) = 15

n(A∩B ) = 15

Step-by-step explanation:

now we know that ,n(AUB) = n(A)+n(B)-n(A∩B)

n(AUB) = 14+15-6 = 23.Answer

3 0

2 years ago

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2. The water level of a river was measured each day during a two-week period. The

vampirchik [111]

Step-by-step explanation:

day during a two-week period. The

graph models the linear relationship between the water level of the river in feet

and the number of days the water level was measured.

Water Level of River

The initi

Ο Ο Ο

The max

The wate

Water Level (ft)

The water

CLEAR ALL

6 8 10

Number of Days

Which statement best describes the y-intercept of the graph?

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O 3

Os Oo Or

0.8

7 0

2 years ago

Read 2 more answers