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2 years ago

Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?

1 answer:

5 0

When the concentration of a solution is expressed in weight percentages, that is just equal to the mass of solute over the mass of the total solution. For a solution weighing 210 grams, 5% of it is salt. That is equal to

210*0.05= 10.5 g salt

The rest of the amount, determined by difference, is the amount of solvent which is water.

water = 210-10.5 = 199.5 g salt

To solve for the new concentration, you add up 15 g to the already existing 10.5 g of salt in the solution. The water, on the other hand, remains constant.

Concentration = (15+10.5)/(210+15) = 0.1133 or 11.33%

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g Assume that the distribution of time spent on leisure activities by adults living in household with no young children is norma

OLga [1]

Answer:

"The probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day" is about 0.8749.

Step-by-step explanation:

We have here a random variable that is normally distributed, namely, the time spent on leisure activities by adults living in a household with no young children.

The normal distribution is determined by two parameters: the population mean, $\\ \mu$ , and the population standard deviation, $\\ \sigma$ . In this case, the variable follows a normal distribution with parameters $\\ \mu = 4.5$ hours per day and $\\ \sigma = 1.3$ hours per day.

We can solve this question following the next strategy:

Use the cumulative standard normal distribution to find the probability.
Find the z-score for the raw score given in the question, that is, x = 6 hours per day.
With the z-score at hand, we can find this probability using a table with the values for the cumulative standard normal distribution. This table is called the standard normal table, and it is available on the Internet or in any Statistics books. Of course, we can also find these probabilities using statistics software or spreadsheets.

We use the standard normal distribution because we can "transform" any raw score into standardized values, which represent distances from the population mean in standard deviations units, where a positive value indicates that the value is above the mean and a negative value that the value is below it. A standard normal distribution has $\\ \mu = 0$ and $\\ \sigma = 1$ .

The formula for the z-scores is as follows

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Solving the question

Using all the previous information and using formula [1], we have

x = 6 hours per day (the raw score).

$\\ \mu = 4.5$ hours per day.

$\\ \sigma = 1.3$ hours per day.

Then (without using units)

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{6 - 4.5}{1.3}$

$\\ z = \frac{1.5}{1.3}$

$\\ z = 1.15384 \approx 1.15$

We round the value of z to two decimals since most standard normal tables only have two decimals for z.

We can observe that z = 1.15, and it tells us that the value is 1.15 standard deviations units above the mean.

With this value for z, we can consult the cumulative standard normal table, and for this z = 1.15, we have a cumulative probability of 0.8749. That is, this table gives us P(z<1.15).

We can describe the procedure of finding this probability in the next way: At the left of the table, we have z = 1.1; we can follow the first line on the table until we find 0.05. With these two values, we can determine the probability obtained above, P(z<1.15) = 0.8749.

Notice that the probability for the z-score, P(z<1.15), of the raw score, P(x<6) are practically the same, $\\ P(z$ . For an exact probability, we have to use a z-score = 1.15384 (without rounding), that is, $\\ P(z$ . However, the probability is approximated since we have to round z = 1.15384 to z = 1.15 because of the use of the table.

Therefore, "the probability that the amount of time spent on leisure activities per day for a randomly selected adult from the population of interest is less than 6 hours per day" is about 0.8749.

We can see this result in the graphs below. First, for P(x<6) in $\\ N(4.5, 1.3)$ (red area), and second, using the standard normal distribution ( $\\ N(0, 1)$ ), for P(z<1.15), which corresponds with the blue shaded area.

5 0

2 years ago

A plane is flying at 1000 meters above the ground and fires a laser 60 degrees of of straight down. what is the distance the lig

juin [17]

Answer:

Step-by-step explanation:

The distance the light traveled to the ground is the range of the plane expressed as:

R = U*√2H/g

U is he velocity

H is the max height

g is the acc. due to gravity

Let us get U first using the formula

H = u²sin²Ф/2g

1000 = u²sin²60/2(9.81)

1000*19.62 = 0.8660u²

19620 = 0.8660u²

u² = 19620/0.8660

u² = 22655.88

u = √22655.88

u = 150.52m/s

Next is to get the range

R = 150.52√2(1000)/9.81

R = 150.52 √2000/9.81

R = 150.52√203.87

R = 150.52*14.28

R = 2149.16m

Hence the distance the light traveled to the ground is 2,149.16m

5 0

2 years ago

Angelo's Pizza is having a ticket raffle to raise money for new soccer uniforms. A $1 ticket gives an even chance to win $25 gif

Bingel [31]

Answer:

$1-25-15-5=44$

Step-by-step explanation:

7 0

2 years ago

A radar gun measured the speed of a baseball at 103 miles per hour. If the baseball was actually going 102.8 miles per hour, wha

zimovet [89]

Answer:

.998%

Step-by-step explanation:

102.8/103 = .9980582524

5 0

2 years ago

Read 2 more answers

N ΔCAB, if the measure of segment AB is 8 units and the measure of segment segment AC is 5 units, which of the following could b

muminat

Answer:

∴Third side = 12 units

Step-by-step explanation:

In ΔCAB, the measure of segment AB is 8 units and the measure of segment AC is 5 units.

The sum of two sides of a triangle always grater than third side.

Therefore,

(5+8)=13 units

third side<13

∴Third side = 12 units

4 0

2 years ago