When the chef turned the new freezer on, the temperature on the internal thermometer was 2 c .

oee [108]

<span>1. The two boats picked for the trip are the steamboat and the tall ship. Let us assume that we will take the steamboat going to the island, and then we will take the tall ship for the return trip. We will then relate the distances travelled by both ships to each other.

2. We know that the steamboat takes five hours to complete the trip. The tall ship takes more time, at ten hours to complete the trip. We do not have the exact speeds of the steamboat or of the tall ship, but we do know that the tall ship is 10 knots slower than the steamboat. We likewise do not know the exact distance travelled by either ship, but we do know that both travel the same distance. We want to find out how fast each boat travels. We expect the answers to be in knots, with a difference of 10.

3. We know that distance is equivalent to the product of speed of a boat multiplied by the time of travel. For the trip going to the island, we will use the steamboat. Let its speed be x knots (equivalent to x nautical miles per hour), and let the distance going to the island be d nautical miles. Given that the time takes is 5 hours, this means that d = 5x.

4. If we let x be the speed of the boat you are taking to the island (the steamboat), then we know that the speed of the other boat (the tall ship) is 10 knots less than the steamboat's. So the speed of the tall ship (for the return trip) is (x - 10) knots.

5. Similar to part 3: we will multiply speed by time to determine the distance from the island. From part 4, we have determined that the speed of the tall ship to be used in returning is (x - 10) knots. Meanwhile, the given in the problem says that the tall ship will take 10 hours to make the trip. Therefore the distance will be equal to d = 10(x - 10) = 10x - 100 nautical miles.

6. We can assume that the distance travelled going to the island is the same distance travelled coming back. Therefore, we can equate the formula for distance from part 3 for the steamboat, to the distance from part 5 for the tall ship.
5x = 10x - 100

7. Solving for x: 5x = 10x - 100
-5x = -100
x = 20
Since x is the speed of the steamboat, x = 20 means that the steamboat's speed is 20 knots.

8. We determined in part 4 that the speed of the second boat (in our case, the tall ship) is (x - 10) knots. Since we have calculated in part 7 that the steamboat travels at x = 20 knots, then the speed of the tall ship is (x - 10) = 20 - 10 = 10 knots.</span>

7 0

2 years ago

What is the passcode for Horatio's Haunted House? : pls help fast it is due soon

guajiro [1.7K]

Answer:

cary

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

the utilities bill for the millers' home in April was $132 fourty two percent of the bills was for gas and the rest was electric

s2008m [1.1K]

The bill was $132

42% was for gas.

Multiply the total bill by 42% ( 0.42) to find the amount spent on gas:

132 x 0.42 = $55.44 was spent on gas.

Now subtract that amount from the total to find how much was spent on electricity:

132 - 55.44 = $76.56 was spent on electricity.

5 0

2 years ago

Of the 500 sample households in the previous exercise, 7 had three or more large-screen TVs. (a) The percentage of households in

likoan [24]

Answer:

a) The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

$\hat p=\frac{7}{500}=0.014$

And that represent the 1.4%.

b) And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

Step-by-step explanation:

Data given and notation

n=500 represent the random sample taken

X=7 represent the households with three or more large-screen TVs

$\hat p=\frac{7}{500}=0.014$ estimated proportion of households with three or more large-screen TVs

$\alpha=0.05$ represent the significance level (no given, but is assumed)

z would represent the statistic (variable of interest)

p= population proportion of households with three or more large-screen TVs

Part a

The percentage of households in the town with three or more largescreen TVs is estimated as :

The best estimation for the population proportion is :

$\hat p=\frac{7}{500}=0.014$

And that represent the 1.4%.

Part b

Yes is possible. We hav that $np>10$ and $n(1-p)>10$ so we have the assumption of normality to find the interval.

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.014 - 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.00370$

$0.014 + 1.96 \sqrt{\frac{0.014(1-0.014)}{500}}=0.0243$

And the 95% confidence interval would be given (0.00370;0.0243).

And the % would be between 0.37% and 2.43%.

4 0

2 years ago

Find the value of $x$ that maximizes $$f(x) = \log (-20x + 12\sqrt{x}).$$ If there is no maximum value, write "NONE".

kakasveta [241]

The function is written as:
f(x) = log(-20x + 12√x)
To find the maximum value, differentiate the equation in terms of x, then equate it to zero. The solution is as follows.

The formula for differentiation would be:
d(log u)/dx = du/u ln(10)
Thus,
d/dx = (-20 + 6/√x)/(-20x + 12√x)(ln 10) = 0
-20 + 6/√x = 0
6/√x = 20
x = (6/20)² = 9/100

Thus,
f(x) = log(-20(9/100)+ 12√(9/100)) = 0.2553

<em>The maximum value of the function is 0.2553.</em>

5 0

2 years ago