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3 years ago

9

Karla spent 9/2 hours of her time for preparing the exam and 5/2 hours on homework per day. If she sleeps 7 hours per day, how m

any spare hours does she have?

1 answer:

Naya [18.7K]3 years ago

6 0

Answer:

2 hours if they go to school.

10 hours if they dont go to school.

Step-by-step explanation:

add up the hours.

9/2+5/2=14/2=7hours +7 hour of sleep= 14 hours.

if they go to school for 8 hours then add 8. then it =22 hours witch gives you 2 hours

if they dont go to school then you got 24-14 hours=10 hours.

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For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

So

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

So

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$

$0.855 + P(X \geq 4) = 1$

$P(X \geq 4) = 0.145$

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

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3 years ago

Numbers 50, 42, 35, 2x + 10, 2x -8, 12, 11,8 are written in descending order and their median is 25, find x.

Natalija [7]

Answer:

Step-by-step explanation:

25=mean of (5th+6th value)

25=1/2*(2x-8+2x+10)

25=1/2*4x+2

4x+2=50

4x=48

x=12

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What is the relationship among proportional relationships lines, rates of change, and slope?

sdas [7]

<span><span>
It introduces the relationship between two variables and is called correlation. Proportionality or variation is state of relationship or correlation between two variables It has two types: </span>direct variation or proportion which states both variables are positively correlation. It is when both the variables increase or decrease together. On the contrary, indirect variation or proportion indicates negative relationship or correlation. Elaborately, the opposite of what happens to direct variation. One increases with the other variables, you got it, decreases. This correlations are important to consider because you can determine and identify how two variables relates with one another. Notice x = y (direct), y=1/x (indirect)</span>

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Kaden works 5 days. The median number of hours he works is 3. The mean number of hours he works is 4.

alisha [4.7K]

Answer:

(a) 1, 2, 3, 6, 8

Step-by-step explanation:

Given

$Median = 3$

$Mean = 4$

Required

The sequence of hours worked each day

<em>See attachment for options</em>

From the question, we understand that:

$Median = 3$

This means that, the middle number is 3 (when sorted)

So, we can conclude that (b) and (c) cannot be true because their middle numbers are 6 and 5 respectively

Next, is to determine the mean of (a) and (d)

The mean of a data is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

(a)

$\bar x = \frac{1+ 2+ 3+ 6+ 8}{5}$

$\bar x = \frac{20}{5}$

$\bar x = 4$

(d)

$\bar x = \frac{1+ 2+ 3+ 4+ 5}{5}$

$\bar x = \frac{15}{5}$

$\bar x = 3$

Option (a) is true, because it has:

$Median = 3$

$Mean = 4$

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3 years ago

Graph each circle given below right the center and the radius of each circle

Paraphin [41]

Answer:

Center: (-1,8)

Radius: 1

The graph is attached.

Step-by-step explanation:

The equation of the circle has the form:

$(x -h)^{2}+(y-k)^{2}=r^{2}$

Where (h,k) is the point of the center of the circle and r is the radius of the circle.

The equation given in the problem is

$(x +1)^{2}+(y-8)^{2}=1$

Therefore:

h=-1

k=8

Then, the center is (-1,8) and radius is 1.

You can graph the circle with its center at the (-1,8) and a radius of 1 as you can see in the figure attached.

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