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2 years ago

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Franklin has three coins, two fair coins (head on one side and tail on the other side) and one two-headed coin. He randomly pick

s one and flips it twice. Suppose B stands for the event that the first result is head, and C represents the event that the second result is also head. Are B and C independent? Are B and C independent, conditioned on the event that the two-headed coin was picked?

1 answer:

Rainbow [258]2 years ago

6 0

Answer:

<h2> B and C are not independent events </h2>

Step-by-step explanation:

This is a probability question, basically on independent events.

B and C are said to be independent if the occurrence of either event does not affect the occurrence of the other.

And now considering the fact that C will always present a head any way anyhow, the occurrence

of C will affect the outcome of B and C.

<em>Hence B and C are not independent events</em>

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Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

In-s [12.5K]

Answer:

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis

Step-by-step explanation:

f(x)= $2x^{3}-26x-24$

$2x^{3}-26x-24$ =0

$2x^{3}-26x-24=0\\2x^{3}-2x-24x-24=0\\2x(x^{2} -1)-24(x+1)=0\\2x(x+1)(x-1)-24(x+1)=0\\(x+1)(2x^{2} -2x-24)=0\\=> x+1=0 => x_{1}=-1\\$

$=> 2x^{2} -2x-24=0\\=>2(x^{2} -x-12)=0\\=> x^{2} -x-12=0\\=> x^{2} -4x+3x-12=0\\=> x(x-4)+3(x-4)=0\\=> (x-4)(x+3)=0\\$

$=> x-4=0\\=> x_{2}=4\\=> x+3=0\\=>x_{3}=-3\\$

For x∈ {-∞,-3} y<0, below x-axis

x∈ {-3,-1} y>0, above x-axis

x∈ {-1,4} y<0, below x-axis

x∈ {4,∞} y>0, above x-axis

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2 years ago

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If x varies jointly as y and z, and x = 8 when y = 4 and z = 9, find z when x = 16 and y = 6. 3

Ghella [55]

Answer:

Joint variation says that:

if $x \propto y$ and $x \propto z$

then the equation is in the form of:

$x = kyz$ , where, k is the constant of variation.

As per the statement:

If x varies jointly as y and z

then by definition we have;

$x=k(yz)$ ......[1]

Solve for k;

when x = 8 , y=4 and z=9

then

Substitute these in [1] we have;

$8=k(4 \cdot 9)$

⇒ $8 = 36k$

Divide both sides by 36 we have;

$\frac{8}{3}=k$

Simplify:

$k = \frac{2}{9}$

⇒ $x = \frac{2}{9}yz$

to find z when x = 16 and y = 6

Substitute these value we have;

$16 = \frac{2}{9} \cdot 6 \cdot z$

⇒ $16 = \frac{12}{9}z$

Multiply both sides by 9 we have;

$144 = 12z$

Divide both sides by 12 we have;

12 = z

or

z = 12

Therefore, the value of z is, 12

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2 years ago

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A customer purchased a total of 16 washcloths and towels. Each washcloth cost $10.50 and each towel cost $15.00. The customer sp

IgorC [24]

Answer:

3

Step-by-step explanation:

10.50 x 3 = 31.5

15 x 13 = 195

195 + 31.5 = 226.50

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1 year ago

Ahmed is riding the elevator in a building. The building has floors above and below ground level. Ahmed uses the expression belo

cluponka [151]

Answer:

He moved 6 floors up, then moved 8 floors down. So he is now 2 floors below ground level.

I hope this helps.

Step-by-step explanation:

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2 years ago

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A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports

hichkok12 [17]

Answer:

1

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

2

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

3

$t = 3.054$

4

The p-value is $p-value = P(Z > 3.054) = 0.0011291$

5

The conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is

Step-by-step explanation:

From the question we are told that

The first sample size is $n_1 = 51$

The first sample mean is $\mu_1 = 36$

The second sample size is $n_2 = 41$

The second sample size is $\mu_2 = 25$

The first standard deviation is $\sigma _1 = 21.4 \ g$

The second standard deviation is $\sigma _2 = 12.8 \ g$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \mu_1 = \mu_ 2$

The alternative hypothesis is $H_a : \mu_1 > \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} } }$

=> $t = \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51} + \frac{ 12.8^2}{41} } }$

=> $t = 3.054$

The p-value is mathematically represented as

$p-value = P(Z > 3.054)$

Generally from the z table

$P(Z > 3.054) = 0.0011291$

=> $p-value = P(Z > 3.054) = 0.0011291$

From the values obtained we see that $p-value < \alpha$ so the null hypothesis is rejected

Thus the conclusion is

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

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2 years ago