A card is drawn from a standard deck of cards. What is the probability

4. As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probabilit

RUDIKE [14]

Answer:

For this case we need to check the conditions in order to use the normal approximation:

1) $np = 60*0.3= 18>10$

2) $n(1-p) = 60*(1-0.3)= 42>10$

Since both conditions are satisfied and the independence condition is assumed we can use the normal approximation given by:

$\hat p \sim N (\hat p, \sqrt{\frac{\hat p(1-\hat p)}{n}})$

The mean would be given by:

$\mu_{\hat p}=0.3$

And the deviation is given by:

$\sigma_{\hat p}= \sqrt{\frac{0.3*(1-0.3)}{60}}= 0.0592$

Step-by-step explanation:

For this case we know the following info:

n =60 represent the sample size

$\hat p = 0.3$ represent the estimated proportion of people that will buy a packet of crackers after tasting

For this case we need to check the conditions in order to use the normal approximation:

1) $np = 60*0.3= 18>10$

2) $n(1-p) = 60*(1-0.3)= 42>10$

Since both conditions are satisfied and the independence condition is assumed we can use the normal approximation given by:

$\hat p \sim N (\hat p, \sqrt{\frac{\hat p(1-\hat p)}{n}})$

The mean would be given by:

$\mu_{\hat p}=0.3$

And the deviation is given by:

$\sigma_{\hat p}= \sqrt{\frac{0.3*(1-0.3)}{60}}= 0.0592$

6 0

3 years ago

one number is 7 more than twice the other number. if the sum of the two numbers is 19, find the two numbers

topjm [15]

Answer:

4 and 15

Step-by-step explanation:

Let the two numbers be a and b.

The sum of the two is 19. Therefore:

$a+b=19$

One number (let's use a) is 7 <em>more</em> than twice the other. Thus:

$a=7+2b$

Solve for the system of equations. Substitute the second equation into the first:

$a+b=19\\(7+2b)+b=19$

Subtract 7 from both sides:

$2b+b=12$

Combine like terms:

$3b=12$

Divide by 3:

$b=4$

So, b is 4.

And since they add up to 19, this means that a is:

$a+b=19\\a+4=19\\a=15$

So our numbers are 4 and 15

And we are done :)

8 0

3 years ago

Joey throws a ball in the air. The graph shows the height of the ball on the y-axis and the time that the ball is in the air on

Yakvenalex [24]

Picture of the graph ?

6 0

3 years ago

Read 2 more answers

Element X is a radioactive isotope such that its mass decreases by 59% every day. If an experiment starts out with 390 grams of

miss Akunina [59]

Answer:

The function that represents the mass of the sample after t days is $A(t) = 390(0.41)^t$ .

The percentage rate of change per hour is of -2.46%.

Step-by-step explanation:

Exponential amount of decay:

The exponential amount of decay for an amount of a substance after t days is given by:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount, and r is the decay rate, as a decimal.

Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.

This means, respectively, that $r = 0.59, A(0) = 390$

So

$A(t) = A(0)(1-r)^t$

$A(t) = 390(1-0.59)^t$

$A(t) = 390(0.41)^t$

The function that represents the mass of the sample after t days is $A(t) = 390(0.41)^t$ .

Hourly rate of change:

Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So

-59%/24 = -2.46%

The percentage rate of change per hour is of -2.46%.

5 0

3 years ago

Find the zero of the linear function F(x)=-4x+5

Sholpan [36]

Answer:um....

Step-by-step explanation:

7 0

3 years ago