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3 years ago

Please help! What is the y-intercept of the line shown?

Mathematics

2 answers:

Nikitich [7]3 years ago

7 0

3 because the line crosses through the black vertical line (y axis) at (0, 3)

aliya0001 [1]3 years ago

5 0

The answer is 3
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A recent survey describes the total sleep time per night among college students as approximately Normally distributed with mean

marin [14]

Answer:

a) $\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981$

b) We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

c) $z = \frac{6.9-6.72}{0.0981}= 1.835$

And we can use the z normal table or excel and we got:

$P(Z$

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".

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

$X \sim N(6.72,1.26)$

Where $\mu=6.72$ and $\sigma=1.26$

(a) What is the standard deviation for the average time in hours? (Round your answer to four decimal places.)

For this case the sample mean have the following distirbution

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

And the deviation is given by:

$\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981$

in minutes?= (Round your answer to three decimal places.)

(b) Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean. (Round your answer to four decimal places.)

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

(c) What is the probability that your average will be below 6.9 hours? (Round your answer to four decimal places.)

For this case we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And we can find the z score for 6.9 and we got:

$z = \frac{6.9-6.72}{0.0981}= 1.835$

And we can use the z normal table or excel and we got:

$P(Z$

4 0

3 years ago

3. The sum of two numbers 49. The difference of the two numbers is 15. What is the product of the two numbers?

Alborosie

Lets set the two numbers as 'a' and 'b'

Now let us set up some equations based on the information:

sum of two numbers 49 --> a + b = 49
difference of the two numbers is 15 --> a -b =15

Equations

a + b = 49 -- equation 1

a - b = 15 -- equation 2

Solve:

(equation 1) + (equation 2)

2a = 64

a = 32 -- equation 3

(equation 3)'s value of a into (equation 2)

32 - b = 15

b = 17

The products of 'a' and 'b' is 544

Hope that helps!

3 0

2 years ago

the proper angle for a ladder is about 75 degrees. from the ground. suppose you have a 9 foot ladder. how far from the house sho

icang [17]

ANSWER:

2.33 foot

STEP-BY-STEP EXPLANATION:

We can calculate the distance from the staircase to the wall, by means of the trigonometric cosine ratio, which is the following:

$\begin{gathered} \cos \theta=\frac{\text{ adjacent}}{\text{ hypotenuse}} \\ \theta=75\text{\degree} \\ \text{ hypotenuse = 9 foot} \\ \text{adjacent = x} \end{gathered}$

Replacing and solving for x:

$\begin{gathered} \cos 75=\frac{x}{9} \\ x=9\cdot\cos 75 \\ x=2.33 \end{gathered}$

The distance would be 2.33 foot

3 0

1 year ago

Ab is perpendicular to cd how many 90 angles are formed by the intersection

Shtirlitz [24]

Only one unless it goes across than2

3 0

2 years ago

-5/4-(-1/6) help please

tiny-mole [99]

A way to add fractions that always works is to multiply each numerator by the denominator of the other, then express the sum of products over the product of the denominators.
$\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{a}{b}\cdot\dfrac{d}{d}+\dfrac{c}{d}\cdot\dfrac{b}{b}\\\\=\dfrac{ad+bc}{bd}$

Here, you have
$\dfrac{-5}{4}-\dfrac{-1}{6}=\dfrac{-5\cdot6-(-1)\cdot4}{4\cdot6}=\dfrac{-26}{24}\\\\=\dfrac{-13}{12}=-1\frac{1}{12}$

The sum is -1 1/12

3 0

3 years ago