A brother and a sister are in the same math class. There are 8 boys and 10 girls in the class. One boy and one girl are randomly chosen. What is the probability that the brother and sister are chosen? Write your answer as a fraction in simplest form.

Hence, the sample standard deviation is:

                         1.1832

The data is given by:

8, 8, 8, 5, 9, 8, 7, 6, 6, 7, 7, 7, 7, 9, 9.

The mean of these data points is given by:

[tex]Mean(x')=\dfrac{8+8+8+5+9+8+7+6+6+7+7+7+7+9+9}{15}\\\\i.e.\\\\Mean(x')=\dfrac{111}{15}\\\\i.e.\\\\Mean(x')=7.4[/tex]

Now,

x                x-x'                   (x-x')²

8            8-7.4=0.6              0.36

8            8-7.4=0.6              0.36

8            8-7.4=0.6              0.36    

5            5-7.4= -2.4             5.76

9            9-7.4=1.6                2.56

8            8-7.4=0.6              0.36

7            7-7.4= -0.4             0.16

6            6-7.4= -1.4              1.96

6            6-7.4= -1.4              1.96

7            7-7.4= -0.4             0.16

7            7-7.4= -0.4             0.16

7            7-7.4= -0.4             0.16

7            7-7.4= -0.4             0.16

9            9-7.4=1.6                2.56

9            9-7.4=1.6                2.56

                             ∑(x-x')²=19.69          

Now the variance of the sample population is given by:

[tex]Variance=\dfrac{\sum (x-x')^2}{n-1}[/tex]

where  n is the number of data points.

Here n= 15

Hence, n-1=14

Hence, we get:

[tex]Variance=\dfrac{19.6}{14}\\\\i.e.\\\\Variance=1.4[/tex]

We know that the standard deviation is the square root of the variance.

i.e.

[tex]Standard\ deviation=\sqrt{1.4}\\\\i.e.\\\\Standard\ deviation=1.1832[/tex]

Given the derivative f '(x) ≥ 2, the function f(x) increases by at least 2 units for every increase in 'x' from 3 to 8. Therefore, the smallest possible value of f(8) is reached when the increase is exactly 2 per 'x', giving us a result of 21.

The question is about calculus, specifically related to the concept of derivatives and their role in function interval analysis. Given the information that f(3) = 11 and f '(x) ≥ 2 for 3 ≤ x ≤ 8, we are asked to find the smallest possible value of f(8).

The derivative, f '(x), represents the rate of change of the function f(x). It is mentioned that f '(x) ≥ 2, which means that the function f(x) is increasing at a rate not less than 2 units per increase in 'x' from 3 to 8.

This suggests that the smallest possible value of f(8) could be achieved by assuming that f(x) increases exactly by 2 units for every increase in 'x'. So, from x = 3 to x = 8 is a change of 5 units in 'x'. Multiply this by the rate of change 2 to obtain the total change in f(x), which is 5 * 2 = 10. Added to the initial value f(3) = 11, we get the smallest possible value for f(8) is 11 + 10 = 21.

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Since the mean waiting time is 12 minutes, the median waiting time would also be 12 minutes.

Here's how we can find the median waiting time:

Since the mean waiting time is 12 minutes, it means that if you were to add up all the waiting times of different arrivals and divide by the number of arrivals, you would get 12 minutes.

Now, for the median waiting time, we're looking for the value that falls exactly in the middle of all the waiting times.

If the distribution is symmetrical, which is often the case with waiting times, the mean and median will be the same.

Answer:

-5,5

Step-by-step explanation:

Answer:

x = ± 3 and ± 2

Step-by-step explanation:

The given quadratic equation is

[tex](x^{2}-1)^{2}-11(x^{2}-1)+24=0[/tex]

To make this question easier we will consume ( x² -1 ) = a

a² - 11a + 24 = 0

Now we can factorize this equation easily

a²- 8a - 3a + 24 = 0

a (a-8) - 3 ( a-8) = 0

( a-3 ) ( a-8 ) = 0

Therefore, a - 3 = 0 ⇒ a = 3

or               a - 8 = 0 ⇒ a = 8

Now we put the value a

when a = 3    (x² - 1) = 3

                     x² = 3 + 1 = 4

                    x = √4

                       = ± 2

when a = 8   (x² - 1) = 8

                     x² = 9

                     x = √9

                        = ± 3

Therefore, x = ± 3 and ± 2 will be the answer.

Answer:

Option C. Obtuse

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

If [tex]c^{2}=a^{2} +b^{2}[/tex] ----> is a right triangle

If [tex]c^{2}>a^{2} +b^{2}[/tex] ----> is a obtuse triangle

If [tex]c^{2}<a^{2} +b^{2}[/tex] ----> is an acute triangle

where

c is the greater side

Verify

[tex]c^{2}=26^{2}= 676[/tex]

[tex]a^{2} +b^{2}=7^{2} +24^{2}=625[/tex]

therefore

[tex]676>625[/tex]

[tex]c^{2}>a^{2} +b^{2}[/tex] -----> is a obtuse triangle

To change 0.45 to a percent, we can move the decimal point 2 places to the right and add the percent sign.

If we move the decimal 2 places to the right, we will end up with 45 and then we will add the percent sign and it will become 45%

Therefore, 0.45 to a percent is 45%

Answer:

Step-by-step explanation:

"A system of linear equations" covers a lot of territory. In Algebra 1, it usually means two linear equations in two unknowns. Each of those equations will graph as a line on a coordinate plane.

A solution is a point that satisfies all the equations. That is, it is a point that is on all the lines described by the system of equations.

The geometry of lines on a plane comes into play with regard to solutions.

MAD tells us how far, on average, all values are from the middle. So, in the example weight of elk antler pairs at Mount St Helens NVM are, on average, 2 away from the middle. On the other hand, weight of elk antler pairs at Rocky Mountain NP are, on average, 1.5 away from the middle. So, we can assure that elk antler pairs at Rocky Mountain NP weighs more than elk antler pairs at Mount St Helens NVM.

Final answer:

To convert 300mm to meters, divide 300 by 1000 because there are 1000 mm in a meter, resulting in 0.3 meters.

Explanation:

To convert millimeters to meters, we use the conversion factor that 1000 mm equals 1 m. Therefore, to convert 300mm to meters, you divide 300 mm by 1000 because there are 1000 mm in a single meter. So, let's carry out the calculation:

300 mm ÷ 1000 = 0.3 m

Thus, 300 mm is equal to 0.3 meters.