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3 years ago

Please help asap, I need help with all of them.

Mathematics

1 answer:

katrin2010 [14]3 years ago

6 0

Answer:

1) Congruent

2) Congruent

3) Not Congruent

4) Congruent

5) Congruent

6) Congruent

Step-by-step explanation:

1) If you laid the triangles in the same direction, they both share the bottom angle and top angle, making it congruent. If you use this same thought process, you can figure out the rest.

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Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that

Mekhanik [1.2K]

Answer:

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

100% probability that greater than 26 out of 124 software users will call technical support.

Step-by-step explanation:

Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

It is needed that:

$np \geq 10$ and $n(1-p) \geq 10$

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Out of 124 software users

This means that $n = 124$

Assume the probability that a given software user will call technical support is 97%.

This means that $p = 0.97$

Conditions:

$np = 124*0.97 = 120.28 \geq 10$

$n(1-p) = 124*0.03 = 3.72 < 10$

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

Consider the probability that greater than 26 out of 124 software users will call technical support.

The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0$

1 - 0 = 1

100% probability that greater than 26 out of 124 software users will call technical support.

3 0

3 years ago

What is the equation of the line in the slope intercept form

Grace [21]

Answer:

Equation of line; y = - 6x

Step-by-step explanation:

As we can see from this graph, point ( 0, 0 ) lying on this graph intersects the y - axis such that it forms a y - intercept of 0;

At the same time we can note that the change in y / change in x, in other words the slope, differs by a rise of 6 / run of - 1, 6 / - 1 being a slope of - 6;

If this equation is in slope - intercept form ⇒

y = a * x + b, where a ⇒ slope, and b ⇒ y - intercept,

Equation of line; y = - 6x

7 0

3 years ago

Read 2 more answers

Five-sixths of the distance from 1 to −13

Finger [1]

The distance of 1 to -13 is 14.

Five sixths of this is (.8333*14), which equals 11.6667.

8 0

3 years ago

The value of x in the expression 2x/3 - 7 = 5 is

Andrej [43]

Answer:

The answer is X = 18

Step-by-step explanation:

2x/3 - 7 = 5

Multiply both sides if the equation by 3 : 2x - 21 = 15

Move the constant to the right hand side and change its sign : 2x = 15 + 21

Calculate 2x = 15 + 21

2x = 36

Divide both sides of the eqaution by 2 : 2x = 36

x = 18

Answer X = 18

3 0

3 years ago

Evaluate the mean of each data set mentally. 61, 71, 81, 91, 101

goldfiish [28.3K]

Answer:

Step-by-step explanation:

they each go by ten

4 0

3 years ago