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3 years ago

Add in the indicated base. 333 (sub)5 + 30 (sub)5

1 answer:

5 0

In base 5 the place values (from right to left) are the ones place, the 5's place and the 25's place. The highest digit you can write in any column is a 4.

333 would be (3 x 25) + (3 x 5) + (3 x 1) which is 93 in base 10.
30 would be (3x5) + (0 x 1) which is 15 in base 10.
The sum of 93 and 15 is 108 in base 10.
Now lets write that in base 5 - We can have 4 25's so there will be a 4 in the 25's column. Since 4 x 25 = 100 we still have to account for 8 to get to 108.
We can have 1 five in the 5's columns since 1 x 5 is 5. Now we have 3 left over which we can place in the one's column
Final answer 333₅ + 30₅ = 413₅

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4C. Quintin is using the three different shaped

Sauron [17]

The smallest number of tiles Quintin will need in order to tile his floor is 20

The given parameters;

number of different shapes of tiles available = 3

number of each shape = 5

area of each square shape tiles, A = 2000 cm²

length of the floor, L = 10 m = 1000 cm

width of the floor, W = 6 m = 600 cm

To find:

the smallest number of tiles Quintin will need in order to tile his floor

Among the three different shapes available, total area of one is calculated as;

$A_{one \ square \ type} = 5 \times 2000 \ cm^2 = 10,000 \ cm^2$

Area of the floor is calculated as;

$A_{floor} = 1000 \ cm \times 600 \ cm = 600,000 \ cm^2$

The maximum number tiles needed (this will be possible if only one shape type is used)

$maximum \ number= \frac{Area \ of \ floor}{total \ area \ of \ one \ shape \ type} \\\\maximum \ number= \frac{600,000 \ cm^2}{10,000 \ cm^2} \\\\maximum \ number= 60$

When all the three different shape types are used we can get the smallest number of tiles needed.

The minimum or smallest number of tiles needed (this will be possible if all the 3 different shapes are used)

$3 \times \ smallest \ number = 60\\\\smallest \ number = \frac{60}{3} \\\\smallest \ number = 20$

Thus, the smallest number of tiles Quintin will need in order to tile his floor is 20

Learn more here: brainly.com/question/13877427

3 0

3 years ago

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00d

nikitadnepr [17]

For this question, we assume that 2.5% of the thermometers are rejected at both sides of the distribution because they have readings that are too low or too high.

Answer:

The "two readings that are cutoff values separating the rejected thermometers from the others" are -1.96 Celsius degrees (below which 2.5% of the readings are too low) and 1.96 Celsius degrees (above which 2.5% of the readings are too high).

Step-by-step explanation:

We can solve this question using the standard normal distribution. This is a normal distribution with mean that equals 0, $\\ \mu = 0$ , and standard deviation that equals 1, $\\ \sigma = 1$ .

And because of using the standard normal distribution, we are going to take into account the following relevant concepts:

Standardized scores or z-scores, which we can consider as the distance from the mean in standard deviations units, and the formula for them is as follows:

$\\ Z = \frac{X - \mu}{\sigma}$ [1]

A positive value indicates that the possible raw value X is above $\\ \mu$ , and a negative that the possible raw value X is below the mean.

The [cumulative] standard normal table: there exists a table where all these values correspond to a probability, and we can apply it for every possible normally distributed data as well as we first standardize the possible raw values for X using [1]. This table is called the standard normal table, and it is available in all Statistics books or on the Internet.

From the question, we have the following information about the readings on the thermometers, which is a normally distributed random variable:

Its mean, $\\ \mu = 0$ Celsius degrees.
Its standard deviation, $\\ \sigma = 1.00$ Celsius degrees.

It coincides with the parameters of the standard normal distribution, and we can find probabilities accordingly.

It is important to mention that the readings that are too low or too high in the normal distribution are at both extremes of it, one of them with values below the mean, $\\ \mu$ , and the other with values above it.

In this case, we need to find:

First, the value below which is 2.5% of the lowest values of the distribution, and

Second, the value above which is 2.5% of the highest values of the distribution.

Here, we can take advantage of the symmetry of the normal or Gaussian distributions. In this case, the value for the 2.5% of the lowest and highest values is the same in absolute value, but one is negative (that one below the mean, $\\ \mu$ ) and the other is positive (that above the mean).

Solving the Question

The value below (and above) which are the 2.5% of the lowest (the highest) values of the distribution

Because $\\ \mu = 0$ and $\\ \sigma = 1$ (and the reasons above explained), we need to find a z-score with a corresponding probability of 2.5% or 0.025.

As we know that this value is below $\\ \mu$ , it is negative (the z-score is negative). Then, we can consult the standard normal table and find the probability 0.025 that corresponds to this specific z-score.

For this, we first find the probability of 0.025 and then look at the first row and the first column of the table, and these values are (-0.06, -1.9), respectively. Therefore, the value for the z-score = -1.96, $\\ z = -1.96$ .

As we said before, the distribution in the question has $\\ \mu = 0$ and $\\ \sigma = 1$ , the same than the standard normal distribution (of course the units are in Celsius degrees in our case).

Thus, one of the cutoff value that separates the rejected thermometers is -1.96 Celsius degrees for that 2.5% of the thermometers rejected because they have readings that are too low.

And because of the symmetry of the normal distribution, z = 1.96 is the other cutoff value, that is, the other lecture is 1.96 Celsius degrees, but in this case for that 2.5% of the thermometers rejected because they have readings that are too high. That is, in the standard normal distribution, above z = 1.96, the probability is 0.025 or $\\ P(z>1.96) = 0.025$ because $\\ P(z$ .

Remember that

$\\ P(z>1.96) + P(z$

$\\ P(z>1.96) = 1 - P(z$

$\\ P(z>1.96) = 1 - 0.975$

$\\ P(z>1.96) = 0.025$

Therefore, the "two readings that are cutoff values separating the rejected thermometers from the others" are -1.96 Celsius degrees and 1.96 Celsius degrees.

The below graph shows the areas that correspond to the values below -1.96 Celsius degrees (red) (2.5% or 0.025) and the values above 1.96 Celsius degrees (blue) (2.5% or 0.025).

4 0

3 years ago

Six students eat 6 apples in 33 seconds. How long will it take nine students to eat 19 apples, if they don't cut apples into par

stepladder [879]

Answer: 104.5 seconds

Step-by-step explanation:

Hi, to answer this question we have to apply proportions:

Six students eat 6 apples in 33 seconds.

The proportion is: number of apples eaten /time

6 apples /33 seconds = 6/33

For 19 apples:

19 apples / x seconds =19/x

6/33 = 19/x

Solving for x:

x = 19 / ( 6/33)

x = 104.5 seconds

Feel free to ask for more if needed or if you did not understand something.

3 0

3 years ago

Bob is hiking down a 12-mile country trail. He could hike at 3 mph for the first two hours and then go the rest of the way at 5

Volgvan

Answer:

The first option will take a total of 3.2 hours while the second option will take just 3 hours

This shows that the second option is faster

Step-by-step explanation:

Here, we want to compare two hiking options and see the one which is faster.

At any point in time;

Distance = speed * time

In the first option, he could hike at 3 mph for two hours.

Total distance covered would be 3 * 2 = 6 miles

Distance left = 12 miles - 6 miles = 6 miles

Time taken to hike 6 miles at 5 mph will be ; 6/5 = 1.2 hours

Total time for the first type hiking = 1.2 hours + 2 hours = 3.2 hours

For the second option;

Time = distance/speed = 12 miles/4 mph = 3 hours

We can see that the second option is faster

8 0

3 years ago

Read 2 more answers

Max rented a motorbike at $465 for 5 days. If he rents the same motorbike for a week, he has to pay a total rent of $625.

garri49 [273]

The answer is simple you divide $465 from 5 then multiply

6 0

3 years ago