Solve -6(5+X)+(13X+1)

Answer:

To find the area of the polygon with the given vertices A(-5, 0), B(0, 10), and C(15, 0), you can use the formula for the area of a triangle when you have the coordinates of its vertices. The formula is:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

In this case, A(-5, 0), B(0, 10), and C(15, 0), so you can plug in these coordinates into the formula:

Area = 1/2 * |-5(10 - 0) + 0(0 - 0) + 15(0 - 10)|

Simplify the expression inside the absolute value:

Area = 1/2 * |-50 + 0 - 150|

Now, continue simplifying:

Area = 1/2 * |-200|

Since we're taking the absolute value, it becomes:

Area = 1/2 * 200

Now, calculate the area:

Area = 100 square units

So, the area of the polygon is 100 square units.

You can also use the distance formula, but this way is faster to me :-p

Answer: 0.9996

Step-by-step explanation:

Given : The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F.

Sample size : n=25

Let x be the random variable that represents the body temperatures of adults.

z-score :

For x= 99° F

Now, the probability that their mean body temperature is less than 99° F will be :-

Hence, the probability that their mean body temperature is less than 99° F  = 0.9996

Final answer:

To find the probability that the mean body temperature of 25 randomly selected adults is less than 99°F, we can use the Central Limit Theorem and calculate the Z-score. The mean body temperature of adults is 98.6°F with a standard deviation of 0.60°F. The sample size is 25.

Explanation:

To find the probability that the mean body temperature of 25 randomly selected adults is less than 99°F, we can use the Central Limit Theorem. According to the Central Limit Theorem, the sampling distribution of the sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the mean body temperature of adults is 98.6°F with a standard deviation of 0.60°F. The sample size is 25. So, the mean of the sampling distribution would still be 98.6°F, but the standard deviation would be 0.60°F divided by the square root of 25, which is 0.12°F.

Now, we can use the Z-score formula to find the probability that the mean body temperature is less than 99°F. The Z-score is calculated by subtracting the population mean from the desired value (99) and dividing it by the standard deviation of the sampling distribution (0.12). We can then use a Z-table or calculator to find the probability associated with the Z-score.

Learn more about Probability here:

brainly.com/question/32117953

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Answer:

Point of intersection (-11/3 , 1/3)

All distances from the vertices are

Step-by-step explanation:

The vertices of the triangle is A(-3,5) , B (1,1) and C (-7,-3)

We need to find the perpendicular bisector of the triangle first

let's take one side connecting A and B

mid point of A and B = (-1,3)

Slope of the line joining A and B = -1

slope of perpendicular to line joining A and B = 1

equation of line passing through (-1,3) with slope 1

y - 3 = 1(x-(-1))

y -3 = x+1

x-y = -4 ............(1)

similarly

mid point joining B and C = (-3,-1)

slope perpendicular to line joining B and C  =  -2

Equation of perpendicular bisector of line joining B and C =

y +1 = -2(x +3 )

y+1 = -2x -6

2x+y = -7 ..........(2)

On solving 1 and 2

x= -11/3 , y= 1/3

Distances

From A =

From B =

From C =

75/2=x/8

x=(75*8)/2

x=600/2

x=300

300 lb