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3 years ago

20 POINTS!!

Mathematics

2 answers:

VashaNatasha [74]3 years ago

8 0

Correct answer is C

Nesterboy [21]3 years ago

4 0

<span>c) dilation by a scale factor of 2; yes; The length of segment A'B' is longer than the original segment AB. </span>

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Percentage grade averages were taken across all disciplines at a particular university, and the mean average was found to be 83.

Eduardwww [97]

The answer is d 0.1730

4 0

3 years ago

5pts and whoever has the correct answer gets brainliest

USPshnik [31]

Answer:

Step-by-step explanation:

8 0

1 year ago

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 12

melamori03 [73]

Answer:

98.75% probability that every passenger who shows up can take the flight

Step-by-step explanation:

For each passenger who show up, there are only two possible outcomes. Either they can take the flight, or they do not. The probability of a passenger taking the flight is independent from other passenger. So the binomial probability distribution is used to solve this question.

However, we are working with a large sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

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 samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

The probability that a passenger does not show up is 0.10:

This means that the probability of showing up is 1-0.1 = 0.9. So $p = 0.9$

Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets

This means that $n = 125$

Using the approximation:

$\mu = E(X) = np = 125*0.9 = 112.5$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{125*0.9*0.1} = 3.354$

(a) What is the probability that every passenger who shows up can take the flight

This is $P(X \leq 120)$ , so this is the pvalue of Z when X = 120.

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

$Z = \frac{120 - 112.5}{3.354}$

$Z = 2.24$

$Z = 2.24$ has a pvalue of 0.9875

98.75% probability that every passenger who shows up can take the flight

7 0

3 years ago

A rectangle is placed around a semicircle as shown below. The length of the rectangle is 14mm. Find the area of the shaded regio

Damm [24]

Image is missing, so i have attached it

Answer:

21.07 mm²

Step-by-step explanation:

We will use the Formulas:

Area of semicircle = πr²/2

Area_rectangle = Length x width = Lw

We are given:

Length of rectangle = 14 mm

From the attached image, the diameter of the semicircle is equal to the length of the rectangle.

Thus;

diameter of semicircle = length of rectangle

Therefore,

diameter of semicircle = 14 mm

Also, from the attached image, the radius of the semicircle is equal to the width of the rectangle.

Thus;

diameter of semicircle/2 = radius of semicircle

Hence;

radius of semicircle = 14/2 = 7mm = width of rectangle

Thus;

Area of rectangle = L*w = 14 × 7 = 98 mm²

Area of semicircle = πr²/2 = π×7²/2 = 76.93 mm²

To get the area of the shaded region, we will subtract area of the semi-circle from the area of the rectangle.

Area of shaded region = Area_rectangle - Area_semicircle = 98 - 76.93 = 21.07 mm²

7 0

3 years ago

A) show that $n(2n + 1)(7n + 1)$ is divisible by 6 for all integers $n$.

goldenfox [79]

Hi,

A)
$\dfrac{n(2n+1)(7n+1)}{6} \\

= \dfrac{14n^3+9n^2+n}{6} \\

= \dfrac{12n^3+6n^2}{6} + \dfrac{2n^3+3n^2+n}{6} \\

=2n^3+n^2+ \dfrac{n(2n^2+3n+1)}{6} \\

= 2n^3+n^2+ \dfrac{n(n+1)(2n+1)}{6} \\

= 2n^3+n^2+ 1^2+2^2+3^2+...+n^2\ is\ an\ integer.
$

B)
Only if n=4*k or n=4*k+1 , k beeing an integer.

8 0

3 years ago