Ask question

Ask question

All categories

2 years ago

15

A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times. What is the probability that t

he toast lands buttered side down?

1 answer:

kirza4 [7]2 years ago

8 0

Step-by-step explanation:

Given that,

A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times.

It means that the total number of outcomes are 17

We need to find the probability that the toast lands buttered side down. Favourable oucome is 17-6 = 11

So, probability is given by :

$P(E)=\dfrac{\text{favourable outcomes}}{\text{total no of outcomes}}$

$P(E)=\dfrac{11}{17}$

So, the probability that the toast lands buttered side down is 11/17.

You might be interested in

In △XYZ, m∠Z = 34, x = 61 cm, and z = 42 cm. Find m∠X. Round your answer to the nearest tenth of a degree.

Elza [17]

M∠X = 54.3°.

Using the Law of Sines, we have:
$\frac{\sin{Z}}{z}=\frac{\sin{X}}{x}
\\
\\\frac{\sin{34}}{42}=\frac{\sin{X}}{61}$

Cross multiplying gives us
61(sin 34) = 42(sin X)

Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X

Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X

8 0

1 year ago

According to a survey, 10% of Americans are afraid to fly. Suppose 1100 Americans are sampled. a) What is the probability that 1

JulijaS [17]

Answer:

a) 14.46%

b) 0.00%

c) 1.54%

Step-by-step explanation:

According to the survey, 10% of Americans are afraid to fly.

This means $p=0.10$ and $q=1-0.10=0.90$ .

If 1100 Americans are sampled, then the sample size is $n=1100$ .

The mean of the distribution is $\mu=np$ .

This means $\mu=1100\times 0.10=110$

The standard deviation is $\sigma=\sqrt{npq}$

We substitute the values to get:

$\sigma=\sqrt{1100\times 0.1\times 0.9}=9.95$

a) We want to find the probability that 121 or more Americans in the survey are afraid to fly.

We first apply the continuity correction factor to get: $P(X\ge121)=P(X\:>\:121-0.5)\\P(X\ge121)=P(X\:>\:120.5)$

We now convert to Z-scores to get:

$P(X\:>\:120.5)=P(z\:>\:\frac{120.5-110}{9.95})=1.06\\$

From the standard normal distribution table P(z>1.06)=0.1446

As a percentage, the probability is 14.46%

b) We want to find the probability that 165 or more Americans in the survey are afraid to fly.

We apply the CCF to get:

$P(X\ge165)=P(X\:>\:165-0.5)\\P(X\ge165)=P(X\:>\:164.5)$

We convert to z-scores:

$P(X\:>\:164.5)=P(z\:>\:\frac{164.5-110}{9.95})=5.48$

From the normal distribution, P(z>164.5)=0

c) First, 8% of 1100 is 88.

We want to find the probability that 88 or less Americans in the survey are afraid to fly.

We apply the CCF to get:

$P(X\le88)=P(X\:$

We convert to z-scores:

$P(X\:$

From the normal distribution, P(z>\:-2.16)=0.0154

As a percentage, we get 1.54%

3 0

2 years ago

The rabbit population on a small island is observed to be given by the function P(t) = 130t − 0.3t^4 + 1100 where t is the time

Montano1993 [528]

The maximum occurs when the derivative of the function is equal to zero.
$P(t)=-0.3t^{4}+130t+1100 \\ P'(t)=-1.2t^{3}+130 \\ 0=-1.2t^{3}+130 \\ 1.2t^{3}=130 \\ t^{3}= \frac{325}{3} \\ t=4.76702$
Then evaluate the function for that time to find the maximum population.
$P(t)=-0.3t^{4}+130t \\ P(4.76702)=-0.3*4.76702^{4}+130*4.76702+1100 \\ P(4.76702)=1564.79201$
Depending on the teacher, the "correct" answer will either be the exact decimal answer or the greatest integer of that value since you cannot have part of a rabbit.

7 0

2 years ago

Write the fraction or mixed number as a percent. 43/25 = %

Stels [109]

This is a fraction, so treat it like one. Divide 43 and 25 and you'll get 1.72. Multiply that decimal value by 100 and that is your percent, 172%

5 0

2 years ago

Read 2 more answers

What is the y-intercept of the function f(x) = –f(x) equals negative StartFraction 2 Over 9 EndFraction x plus StartFraction 1 O

lora16 [44]

Answer: Third option

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

Given the function f(x):

$f(x)=-\frac{2}{9}x+\frac{1}{3}$

Since $f(x)=y$ , you can rewrite it:

$y=-\frac{2}{9}x+\frac{1}{3}$

You can identify that:

$m=-\frac{2}{9}\\\\b=\frac{1}{3}$

Therefore, you can determine that the y-intercept of the given function is:

$b=\frac{1}{3}$

Observe that this matches with the third option.

3 0

2 years ago

Read 2 more answers