Evaluate the expression.
11 +4+2 = ?

Answers

Answer 1

Answer:

the answer is 11+4+2=17

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Sleeping in college. A recent article in a college newspaper stated that college students get an average of 5.5 hrs of sleep each night. A student who was skeptical about this value decided to conduct a survey by randomly sampling 25 students. On average, the sampled students slept 6.25 hours per night. Identify which value represents the sample mean and which value represents the claimed population mean.

Answers

Answer:

Sample mean = 6.25 hours per night.

Population mean = 5.5 hrs of sleep each night.

Step-by-step explanation:

A sample mean is the mean of the sample collected. The 25 students surveyed by the student is the sample. The average sleep time derived from the sample is the sample mean.

A population mean is the mean of all the population. Here the population are college students. The population mean is the mean derived from studying the sleep duration of all the population - college students

If the legs of a right triangle measure 10 meters and
24 meters, how long is the hypotenuse?

Answers

Answer:

26 meters

Step-by-step explanation:

A particular concentration of a chemical found in polluted water has been found to be lethal to 40% of the crayfish that are exposed to the concentration for 24 hours. 22 crayfish are placed in a tank containing this concentration of chemical in the water. (a) What is the probability that 13 or 17 survive?
(b) What is the probability that at least 17 survive?
(c) What is the probability that at most 16 survive?
(d) What number of crayfish are expected to survive?
(e) What is the variance in the number of crayfish that are expected to survive? No actual crayfish were harmed in the making of this question.

Answers

Answer:

a) $P(X=13)=(24C13)(0.4)^(13) (1-0.4)^(24-13)=0.0608$

$P(X=17)=(24C17)(0.4)^(17) (1-0.4)^(24-17)=0.0017$

$P(X=13 U X=17) = 0.0608+0.0017=0.0624$

b) $P(X \geq 17)=0.000427$

c) $P(X \geq 16)= 1-0.000427=0.9996$

d) $E(X)= np = 22*0.4=8.8$

e) $Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=24, p=0.4)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

3) Part a

$P(X=13)=(22C13)(0.4)^(13) (1-0.4)^(22-13)=0.0336$

$P(X=17)=(22C17)(0.4)^(17) (1-0.4)^(22-17)=0.00035$

$P(X=13 U X=17) = 0.0336+0.00035=0.0340$

4) Part b

$P(X \geq 17)=P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)$

$P(X=17)=(22C17)(0.4)^(17) (1-0.4)^(22-17)=0.00035$

$P(X=18)=(22C18)(0.4)^(18) (1-0.4)^(22-18)=0.0000651$

$P(X=19)=(22C19)(0.4)^(19) (1-0.4)^(22-19)=0.00000914$

$P(X=20)=(22C20)(0.4)^(20) (1-0.4)^(22-20)=0.000000914$

$P(X=21)=(22C21)(0.4)^(21) (1-0.4)^(22-21)=5.81x10^(-8)$

$P(X=22)=(22C22)(0.4)^(22) (1-0.4)^(22-22)=1.76x10^(-9)$

$P(X \geq 17)=0.000427$

5) Part c

$P(X \leq 16)=1-P(X>16)=1-P(X\geq 17) = 1-[P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)]$

$P(X \geq 16)= 1-0.000427=0.9996$

6) Part d

The expected value is:

$E(X)= np = 22*0.4=8.8$

7) Part e

The variance is given by:

$Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

An architect uses a scale of 2/3inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint?

Answers

Length of the wall on blueprint will be 16 inches.

Use of scale to calculate the distances or length,

Scale used by an architect on a blueprint,

$(2)/(3)\text{ inch}= 1\text{ foot}$

Scale represents the ratio of the length of the wall on blueprint and actual length,

$\frac{\text{Length on the blueprint}}{\text{Actual length}} =\frac{(2)/(3)\text{ inches}}{1\text{ feet}}$

$\frac{\text{Length on the blueprint}}{\text{Actual length}} =(2)/(3)$

If actual length of the east wall of the building = 24 feet

Substitute the value in the expression representing the ratio,

$\frac{\text{Length on the blueprint}}{24} =(2)/(3)$

Length of the blueprint = $(2)/(3)* 24$

= $16$ inches

Therefore, length of the wall on blueprint will be 16 inches.

Learn more about the use of scale to calculate the distances on map.

brainly.com/question/11276271?referrer=searchResults

Answer:

16 in.

Step-by-step explanation:

We have the ratio

$(in.)/(ft): ((2)/(3) )/(1)$

How about let's make this easier. Easier is better, right? Let's get rid of the fraction 2/3. We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of

$(in.)/(ft):(2)/(3)$

Now we need to know how many inches there would be if the number of feet is 24:

$(in.)/(ft):(2)/(3) =(x)/(24)$

Cross multiply to get

3x = 48 so

x = 16 in.

IQ scores are normally distributed with a mean of 105 and a standard deviation of 17. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample. If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.

Answers

Answer:

Mean 105

Standard deviation 1.89

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$

In this problem, we have that:

$\mu = 105, \sigma = 17$

If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.

By the Central limit theorem

mean 105

Standard deviation

$s = (17)/(√(81)) = 1.89$

What value should go in the empty boxes to complete the calculation for finding the product of 0.37 * 0.42

Answers

Answer:

0.1554

Step-by-step explanation:

.37x.42=.1554

Final answer:

To find the product of 0.37 and 0.42, multiply the numbers together. The missing digits in the empty boxes should be 5 and 4, respectively.

Explanation:

To find the product of 0.37 and 0.42, you need to multiply the two numbers together. The empty boxes represent the missing digits after the decimal point.

The first number, 0.37, has two decimal places, and the second number, 0.42, has two decimal places as well. When you multiply these two numbers, you need to make sure the total number of decimal places in the product matches the sum of the decimal places in the original numbers.

The product of 0.37 * 0.42 is 0.1554. So, the missing digits in the empty boxes should be 5 and 4, respectively.