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Elodia [21]
2 years ago
12

A set of notations (SSS, SAS, ASA and RHS) is used to describe/prove that two triangles are conjurent. For each pair of triangle

s, select the correct statement.
Mathematics
1 answer:
lana66690 [7]2 years ago
4 0

Answer:

The answer is given below

Step-by-step explanation:

The statements are not given but from this definition, you should be able to select the correct statement.

Triangles are said to be congruent if they have the same size and shape. A triangle is made up of six (three sides and three angles) but only three is usually needed to prove triangle congruence. These are:

a) Side - Side - Side (SSS): Two triangles are congruent if the length of their three sides are equal to each other.

b) Side- angle- side (SAS): If two sides and one angle of a triangle is equal to two sides and a angle of another triangle then the two triangles are congruent to each other.

c) Angle - side - angle (ASA): If two angles and a side of a triangle are equal to a corresponding two angles and a side of another triangle then the two triangles are congruenr.

d) Right angle - hypotenuse - side (RHS): If for two right angled triangles, their hypotenuse and a side (leg) are equal, then the two triangles are congruent.

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In a production process, the diameter measures of manufactured o-ring gaskets are known to be normally distributed with a mean d
Art [367]

Answer:

DIRECT WAY EXCEL

"=NORM.DIST(75,80,3,TRUE)"

And we got: P(X\leq 75)= 0.04779

OTHER WAY

P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z

And we can find this probability using the normal standard table or excel:

P(Z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:

X \sim N(80,3)  

Where \mu=80 and \sigma=3

And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:

P(X\leq 75)

One way to do this in excel is with the following formula:

"=NORM.DIST(75,80,3,TRUE)"

And we got: P(X\leq 75)= 0.04779

And the other way is use the z score formula given by:

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

If we apply this formula to our probability we got this:

P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z

And we can find this probability using the normal standard table or excel:

P(Z

3 0
2 years ago
Three students solve a challenge math problem. Every day, the number of students who solve the problem doubles. There are 384 st
attashe74 [19]

OK, so this is assuming we are considering that the first three kids to solve ARE NOT in the first day.


So we have 3 kids and it doubles

Day 1 : 6

Day 2 : 12

Day 3 : 24

Day 4 : 48

Day 5 : 96

Day 6 : 192

Day 7: 384


So it should take 7 days or a week to solve all the problems.

The equation:

(3 * 2)^x = 384


8 0
2 years ago
Read 2 more answers
A student wants to determine if pennies are really fair when flipped, meaning equally likely to land heads up or tails up. He fl
Verdich [7]

Answer:

For this case we want to determine  if pennies are really fair when flipped, meaning equally likely to land head up or tails, so then the correct system of hypothesis are:

Null hypothesis: p=0.5

Alternative hypothesis: p \neq 0.5

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

For this case we want to determine  if pennies are really fair when flipped, meaning equally likely to land head up or tails, so then the correct system of hypothesis are:

Null hypothesis: p=0.5

Alternative hypothesis: p \neq 0.5

7 0
2 years ago
The average weight of a chicken egg is 2.25 ounces with a standard deviation of 0.2 ounces. You take a random sample of a dozen
n200080 [17]

Answer:

P(\bar X

P(\bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

X \sim N(\mu,\sigma)  

And let \bar X represent the sample mean, the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

On this case  \bar X \sim N(2.25,\frac{0.2}{\sqrt{12}})

Solution to the problem

We want this probability:

P(\bar X

The best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}

If we apply this formula to our probability we got this:

P(\bar X

P(\bar X

5 0
2 years ago
a person on a tour has rupees 12000 for his daily expenses. In order to extend his journey for 2 more days he had to cut down hi
myrzilka [38]

Answer:

Duration of the tour he planned first is 8 days.

Step-by-step explanation:

Given that a person has 12000 rupees for his daily expenses.

Let x be the number of days.

Then daily expenses per day =\frac{12000}{x}

Given that number of day is increased by 2 more days, that is number of days is x+2.

New daily expense per day \frac{12000}{x+2}

Given that this new daily expenses are 300 less than original.

That is \frac{12000}{x}-\frac{12000}{x+2}=300

              \frac{12000(x+2)-12000x}{x(x+2)}=300

                  \frac{24000}{x(x+2)}=300

                  x(x+2)=\frac{24000}{300}

                    x^{2}+2x-80=0

                    (x-8)(x+10)=0

                     x=8 or -10.

Since number of days cannot be negative, duration of the tour planned=8.

7 0
2 years ago
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