What is the number of degrees the minute hand of a clock moves between 10:21 and 10:34 pm on the same day?

An elevator has a placard stating that the maximum capacity is 1600 lb�10 passengers. So, 10 adult male passengers can have a m

Bezzdna [24]

Answer:

1. 0.7421 = 74.21% probability the elevator is overloaded.

2. D.No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Assume that weights of males are normally distributed with a mean of 166 lb and a standard deviation of 29 lb.

This means that $\mu = 166, \sigma = 29$

Sample of 10.

This means that $n = 10, s = \frac{29}{\sqrt{10}}$

1.The probability the elevator is overloaded is?

Probability that the sample mean is above 160 pounds, which is 1 subtracted by the p-value of Z when X = 160. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{160 - 166}{\frac{29}{\sqrt{10}}}$

$Z = -0.65$

$Z = -0.65$ has a p-value of 0.2579.

1 - 0.2579 = 0.7421

0.7421 = 74.21% probability the elevator is overloaded.

2. Does this elevator appear to be safe?

High probability of the elevator being overloaded, so not safe. Correct answer is given by option D.

7 0

3 years ago

Barbara claims that her horse can do simple addition problems. She showed her horse 8 different cards with simple addition probl

Nataliya [291]

Answer:

"Yes, the chances of getting 8 correct when guessing are very low"

Step-by-step explanation:

The point diagrams show us how likely is the occurrence of an event. When casting 8 coins there is a chance to get between 1 and 8 tails.

The dot plot tells us how many times 1, 2, 3, 4, 5, 6, 7 or 8 tails were obtained. When the number of trials increases, then the value with the most points in the diagram represents the number of queues most likely to be obtained, and the value with fewer points represents the least probable number of queues that can be obtained by casting 8 times a coin .

The dot plot for the experiment shows that it is very unlikely to get 8 queues when casting 8 coins. Of 53 times, this only happened once.

Just as it is unlikely to get 8 tails when throwing 8 coins, it is also unlikely that a horse guesses the 8 correct answers of the 8 simple sum problems. Then, the horse of barbara maybe did not guess the 8 answers.

Therefore the correct answer is option A:

"Yes, the chances of getting 8 correct when guessing are very low"

3 0

3 years ago

Easy math please help multiple choice i will pick the brainliest i need this fast

Serga [27]

Answer:

I believe it would be cpctc

Step-by-step explanation:

It would be that due to the fact it is not talking about an angle so therefore it wouldn't be ASA, it also wouldn't be definition of congruent segments because that is represented using segments and as you can see it has no tick marks, which need to be seen for the definition of congruent segments. CPCTC would be correct because it stands for corresponding parts of congruent triangles are congruent and can be represented in both lines and angles, and the problem is asking about lines and how you know they are congruent.

4 0

3 years ago

Camilla and Anne work as interior decorators in the city. Camilla can decorate a home in 5 days while Anne can

love history [14]

Answer:

It will take them 4.44 days to decorate 2 homes.

Step-by-step explanation:

Given that:

Camilla can decorate a home in 5 days

Anne can complete a home in 4 days

Let,

x be the time taken by Camilla and Anne to decorate 1 home.

$\frac{1}{Camilla's time}+\frac{1}{Anne's\ time} = \frac{1}{total\ time}\\$

$\frac{1}{5}+\frac{1}{4}=\frac{1}{x}$

Taking LCM;

$\frac{4+5}{20}=\frac{1}{x}\\\\\frac{9}{20}=\frac{1}{x}\\x=\frac{20}{9}$

Time taken by Camilla and Anne to decorate 2 homes = $\frac{20}{9}*2=\frac{40}{9}$

Time taken to decorate Camilla and Anne 2 homes = 4.44 days

Hence,

It will take them 4.44 days to decorate 2 homes.

4 0

3 years ago

What is the center and radius?<br><br> X^2+y^2+6x-6y=-14

Zolol [24]

Answer:

Therefore,

$Center\ is\ C(-3,3)\\and\\Radius= 2\ units$

Step-by-step explanation:

Given:

A Equation of a Circle that is

$x^{2} +y^{2}+ 6x-6y=-14$

Which can be written as

$x^{2} +y^{2}+ 6x-6y+14=0$

To Find:

Center C( -g , -f ) = ?

radius = r =?

Solution:

General Equation of a Circle is given as

$x^{2} +y^{2}+ 2gx+2fy+c=0$

On Comparing the Given equation with the General equation we get the following values,

$2g=6\ and\ 2f=-6\ and\ c=14\\\therefore g=\frac{6}{2}=3\\ \\\therefore f=\frac{-6}{2}=-3\\$

Now, Center and Radius for above circle is given as

$C(-g,-f)=(-3,-(-3))=(-3,3)\\and\\radius = r=\sqrt{(g^{2}+f^{2}-c )} = \sqrt{(3^{2}+(-3)^{2}-14)}\\\\\therefore radius = r=\sqrt{(18-14)} \\\\\therefore radius = r=\sqrt{4}=2\ unit\\$

Therefore,

$Center\ is\ C(-3,3)\\and\\Radius= 2\ units$

6 0

4 years ago