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2 years ago

The area of a right triangle is 210 square inches. The height of the right triangle is 35 inches.

Mathematics

2 answers:

Ainat [17]2 years ago

8 0

Answer:

The length of the hypotenuse is $37\ in$

Step-by-step explanation:

we know that

The area of a triangle is equal to

$A=\frac{1}{2}bh$

In this problem we have

$A=210\ in^{2}$

$h=35\ in$

step 1

Find the base of triangle

substitute the values and solve for b

$210=\frac{1}{2}b(35)$

$b=210*2/35=12\ in$

step 2

Applying the Pythagoras theorem find the length of the hypotenuse

$c^{2}=35^{2}+12^{2}\\ \\c^{2}=1,369\\ \\c= 37\ in$

deff fn [24]2 years ago

7 0

35 squared + 35 squared
rad 2450
35 rad 2

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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.

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2 years ago

The quadratic function y = -10x2 + 160x - 430 models a store's daily profit (y), in dollars, for selling T-shirts priced at x do

alexdok [17]

Answer:

D,B,C,A

Step-by-step explanation:

Look at the picture

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1 year ago

Assume that the die is weighted so that the probability of a 1 is 0.1, the probability of a 2 is 0.2, the probability of a 3 is

umka2103 [35]

Answer:

The probabilities of each outcome are the following:

for X = 1 is 0.6

for X = 2 is 0.35

for X = 3 is 0.049

and for X = 4 is 0.001

Step-by-step explanation:

Let's consider X as the random variable for the sum of outcomes "S" exceeds 3, this is: $S\geq 4$

Let's now analyze and consider the ways that X equals the different values:

X = 1: I throw the dice and the result is: 4, 5 and 6.

Then: P(X=1) = P(4) + P(5) + P(6) = 0.2+0.1+0.3 = 0.6

Thus P(X=1) = 0.6

X = 2: The result after following the dice two times can be:

1 and 3, 1 an 4.... and so on until 1 and 6

2 and 2, 2 and 3... and so on until 2 and 6

3 and 1... and so on until 3 a 6

Then P(X=2) = P(1)xP(3,4,5,6) + P(2)xP(2....6) + P(3)x(1.....6)

Theory of Probability: Sum of all possible outcomes P(1)+P(2).......P(6) = 1

Then P(1......6) = 1

Then P(X=2) = P(1)x[1-P(1)-P(2)]+P(2)x[1-P(1)]+P(3) = 0.1x(1-0.1-0.2) + 0.2x(1-0.1) + 0.1 = 0.1 x 0.7 + 0.2 x 0.9 + 0.1 = 0.35

Thus P(X=2) = 0.35

X = 3: The result can be

1 and 1 and 2, 1 and 1 and 3.... until 1 and 1 and 6

1 and 2 and 1, 1 and 2 and 2..... until 1 and 2 and 6

2 and 1 and 1, 2 and 1 and 2.... until 2 and 1 and 6

Then P(X=3) = P(1)xP(1)xP(2....6) + P(1)xP(2)xP(1.....6) + P(1)xP(2)xP(1.....6)

P(X=3) = 0.1 x 0.1 x (1-0.1) + 0.1 x 0.2 x 1 + 0.2 x 0.1 x 1 = 0.01 x 0.9 + 0.2 + 0.2 = 0.049

Thus P(X=3) = 0.049

Finally, for X to be 4, I only have the following possibilities

1 and 1 and 1 and 1.... until 1 and 1 and 1 and 6

Then P(X=4) = P(1)xP(1)xP(1)xP(1.....6) = 0.1x0.1x0.1x1 = 0.001

Thus P(X=3) = 0.001

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2 years ago

The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,00

timama [110]

Answer: the probability that a randomly selected tire will have a life of exactly 47,500 miles is 0.067

Step-by-step explanation:

Since the life expectancy of a particular brand of tire is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = life expectancy of the brand of tire in miles.

µ = mean

σ = standard deviation

From the information given,

µ = 40000 miles

σ = 5000 miles

The probability that a randomly selected tire will have a life of exactly 47,500 miles

P(x = 47500)

For x = 47500,

z = (40000 - 47500)/5000 = - 1.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.067

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2 years ago

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Nitella [24]

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2 years ago

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