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2 years ago

A student claims that 3x + 2y = 5xy. Use a visual representation to show whether this is true or false

Mathematics

1 answer:

Ket [755]2 years ago

7 0

Answer:

It is true, except when x = 2/5, since it is an asymptote.

Step-by-step explanation:

3x=5xy-2y

3x=y(5x-2)

3x/5x-2=y

5x-2=0 -------> 5x=2 --------> x=2/5

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Jeanne wants to start collecting coins and orders a coin collection starter kit. The kit comes with three coins chosen at random

lesya692 [45]

Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes $P_B(A)$ .

The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by
$P(A|B)= \frac{P(A \cap B)}{P(B)}$

In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.

The probability of selecting one coin is $\frac{1}{3}$

Part A:
To find the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.

P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.

Thus $P(A)= \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}$

P(B) means that the first envelope contains a quarter AND the second envelope contains a quarter

Thus $P(B)= \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Therefore, $P(A|B)=\left( \frac{ \frac{1}{27} }{ \frac{1}{9} } \right)= \frac{1}{3}$

Part B:
To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.

$P(C)= \frac{3}{3} \times \frac{2}{3} \times \frac{1}{3} = \frac{6}{27} = \frac{2}{9}$

 $P(D)= \frac{1}{3}$ 

Therefore, $P(C|D)=\left( \frac{ \frac{2}{9} }{ \frac{1}{3} } \right)= \frac{2}{3}$

3 0

2 years ago

An experiment was performed to compare the wear of two different laminated materials. Twelve pieces of material 1 were tested by

GenaCL600 [577]

Answer:

At 0.05 level of significance, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units

Step-by-step explanation:

We hypothesize that mean difference between abrasive wear of material 1 and material 2 is greater than 2.

So we write the null hypothesis $H_0 : \mu_1 - \mu_2 >2$ ,

and the alternative hypothesis $H_1: \mu_1 - \mu_2 \leq 2$ .

We will find the T-score as well as the p-value. If the p-value is less than the level of significance, we will reject the null hypothesis, i.e. we will conclude that the abrasive wear of material 1 is less than that of material 2. Otherwise, we will accept the null hypothesis.

Since the variance is unknown and assumed to be equal, we will use the pooled variance

$s_p^2 = \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} = 20.05$ ,

where $n_1 = 12, n_2 =10, s_1 =4, s_2 = 5$ .

The mean of material 1 and material 2 are $\mu_1 =85, \mu_2=81$ respectively and mean difference $d$ is equal to 4. The hypothesize difference $d_0$ is equal to 2.

To find the T-score, we use the following formula

$T = \frac{d - d_0}{\sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2} }}$

Substituting all the values into the T-score formula gives us $T = 1.04$ , and the respective p-value is equal to 0.31. This means we have enough statistical evidence not to reject the null hypothesis, and at 5% significance level, the abrasive wear of material 1 exceeds that of material 2 by more than 2 units.

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2 years ago

Antonia is keeping track of the number of pages she reads. She started the school year having already read 95 pages her book, an

cupoosta [38]

F(x) means "function of" and x represents the day number, example: day 6 would be f(6)=(20×6)+95

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2 years ago

Here is a typical statement made by the media: "Based on a recent study, pennies weigh an average of 2.5 grams with a margin of

Damm [24]

The answer is A I think

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2 years ago

Read 2 more answers

Suppose that we've decided to test Clara, who works at the Psychic Center, to see if she really has psychic abilities. While tal

mixas84 [53]

Answer:

A) 3.5

B) 1.6202

Step-by-step explanation:

In binomial distribution,

E(X) = np and Var(X) = npq while

SD (X) = √(npq)

Where n is number of cards drawn

p is probability of getting one particular shape

q = 1-p

So from the question, n = 14

p = 13/52 = 1/4

q = 1-(1/4) = 3/4

So;

A) E(x) = np = 14 x 1/4 = 3.5

B) SD (X) = √(npq) = √(14 x 1/4 x 3/4) = √(42/16) = √2.625 = 1.6202

4 0

2 years ago