Step-by-step explanation: The probability is given by the number of times the event could happen (in this case get an "e"), over the number of all the possibilities (in this case, the six letters of the word)

Therefore, probability $\frac{letter_e}{all letter}=\frac{2}{6} =\frac{1}{3}$

5 0

3 years ago

An ornithologist has 4 bird feeders at separate locations. She wonders if birds are equally likely to visit each of the feeders.

Marianna [84]

Answer:

the x² test statistic 13.71

Option a) 13.71 is the correct answer.

Step-by-step explanation:

Given the data in the question;

Feeder 1 2 3 4

Observed visits; $o_i$ 60 90 92 58

data sample = 300

Expected $e_i$ = 300 / 4 = 75

the x² test statistic = ?

$X^2_{stat$ = ∑[ ( $o_i$ - $e_i$ )²/ $e_i$ ]

$X^2_{stat$ = [ (60 - 75)² / 75 ] + [ (90 - 75)² / 75 ] + [ (92 - 75)² / 75 ] + [ (58 - 75)² / 75 ]

$X^2_{stat$ = [ 3 ] + [ 3 ] + [ 3.8533 ] + [ 3.8533 ]

$X^2_{stat$ = 13.7066 ≈ 13.71

Therefore, the x² test statistic 13.71

Option a) 13.71 is the correct answer.

7 0

3 years ago

Martin throws a ball straight up in the air. the equation h(t) = -16t^2 + 40t + 5 gives the height of the ball, in feet, t secon

Lisa [10]

Answer:

2.62 seconds

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> he height of the ball, in feet

we have

$h(t)=-16t^2+40t+5$

we know that

When the ball hits the ground, the height is equal to zero

$-16t^2+40t+5=0$

The formula to solve a quadratic equation of the form

$at^{2} +bt+c=0$

is equal to

$t=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+40t+5=0$

$a=-16\\b=40\\c=5$

substitute in the formula

$t=\frac{-40\pm\sqrt{40^{2}-4(-16)(5)}} {2(-16)}$

$t=\frac{-40\pm\sqrt{1,920}} {-32}$

$t=\frac{-40+\sqrt{1,920}} {-32}=-0.12\ sec$

$t=\frac{-40-\sqrt{1,920}} {-32}=2.62\ sec$

therefore

The solution is t=2.62 seconds

4 0

3 years ago