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3 years ago

Write an algebraic expression for the statement.The income earned at $ 10.91 per hour for w hours....

1 answer:

5 0

This is a "rate of pay" problem. The amount earned is equal to the (rate of pay) times the (number of hours worked).

Let the income be represented by "i". Then the formula is i = ($10.91/hour)*w, where w is the number of hours worked and has the unit of measurement "hours."

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A pair of fair dice is cast. Let Edenote the event that the number landing uppermost on the first die is a 1 and let Fdenote the

iris [78.8K]

Answer:

They are not independent

Step-by-step explanation:

Given

E = Occurrence of 1 on first die

F = Sum of the uppermost occurrence in both die is 5

Required

Are E and F independent

First, we need to list the sample space of a roll of a die

$Event\ 1 = \{1,2,3,4,5,6\}$

Next, we list out the sample space of F

$Event\ 2 = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,\$

$6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}$

In (1): the sample space of E is:

$E = \{1\}$

So:

$P(E) = \frac{n(E)}{n(Event\ 1)}$

$P(E) = \frac{1}{6}$

In (2): the sample space of F is:

$F = \{5,5,5,5\}$

So:

$P(F) = \frac{n(F)}{n(Event\ 2)}$

$P(F) =\frac{4}{36}$

$P(F) =\frac{1}{9}$

For E and F to be independent:

$P(E\ and\ F) = P(E) * P(F)$

Substitute values for P(E) and P(F)

This gives:

$P(E\ and\ F) = \frac{1}{6} * \frac{1}{9}$

$P(E\ and\ F) = \frac{1}{54}$

However, the actual value of P(E and F) is 0.

This is so because $E = \{1\}$ and $F = \{5,5,5,5\}$ have 0 common elements:

So:

$P(E\ and\ F) = 0$

Compare $P(E\ and\ F) = \frac{1}{54}$ and $P(E\ and\ F) = 0$ .

These values are not equal.

Hence: the two events are not independent

6 0

3 years ago

The variables y and x^2 are directly

choli [55]

Answer:

y = $\frac{20}{21}$ x²

Step-by-step explanation:

Given that y and x² are directly proportional then the equation relating them is

y = kx² ← k is the constant of proportion

When x = 2

y = k × 2² = 4k

When x = 5

y = k × 5² = 25k

Then

25k - 4k = 20 ( difference between values is 20 )

21k = 20 ( divide both sides by 21 )

k = $\frac{20}{21}$

y = $\frac{20}{21}$ x² ← equation of proportion

6 0

2 years ago

A data set is made up of these values.

marissa [1.9K]

I think that the answe my be b

6 0

3 years ago

Read 2 more answers

Imagine that you have developed a genetic test to detect the dominant allele (A) that cause a rare genetic condition. As with mo

s344n2d4d5 [400]

Answer:

Correct option: (B) 1.495%.

Step-by-step explanation:

Denote the events as follows:

X = the test is positive.

A = a person with the dominant allele

The information given are:

$P(X|A)=1\\P (X|A^{c})=0.005\\P(A)=0.01$

According to the law of total probability the probability of an event A, conditional upon the occurrence of another event B is:

$P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

Use this law to compute the probability of person having a positive result as follows:

$P(X)=P(X|A)P(A)+P(X|A^{c})P(A^{c})\\=(1\times0.01)+(0.005\times(1-0.01))\\=0.01+0.00495\\=0.01495$

The percentage of positive result is: 0.01495 × 100 = 1.495%.

Thus, the percentage of the population will give a positive test is 1.495%.

4 0

2 years ago

Inequalities? the product of 11 and a number is less than 53 i'm confused on how to write it out

nordsb [41]

Ok, so we know that the product of means something added, and we are given that eleven and a number are less than 53. So the equation is 11+X<53.

3 0

3 years ago