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2 years ago

Find the coordinates of the midpoint of the segment whose endpoints are H(10, 1) and K(4, 7).

Mathematics

2 answers:

Oliga [24]2 years ago

5 0

The formula of a midpoint of a segment AB:

$A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\M_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)$

We have:

H(10; 1); K(4; 7)

substitute:

$M_{HK}\left(\dfrac{10+4}{2};\ \dfrac{1+7}{2}\right)\to M_{HK}\left(\dfrac{14}{2};\ \dfrac{8}{2}\right)\to M_{HK}(7;\ 4)$

Answer: (7, 4)

inn [45]2 years ago

3 0

Answer:

(7,4)

Step-by-step explanation:

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normally distributed with mean 24.6 seconds and standard deviation 0.64 seconds;the lower finishing time, the better. If the qua

marshall27 [118]

Answer:

$z=1.04$

And if we solve for a we got

$a=24.6 +1.04*0.64=25.27$

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.

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".

Solution to the problem

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

$X \sim N(24.6,0.64)$

Where $\mu=24.6$ and $\sigma=0.64$

Solution to the problem

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.15$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.04$

And if we solve for a we got

$a=24.6 +1.04*0.64=25.27$

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.

3 0

2 years ago

-x ≥ 23<br> What is the answer?

juin [17]

Answer:

x is less than or equal to -23

Step-by-step explanation:

-x is greater than or equal fo 23 divide negative on both sides

x is less than or equal to -23

(srry i don't have the inequality signs)

5 0

2 years ago

How do i find x and y?

Stells [14]

Answer:

x=90

y=67

Step-by-step explanation:

as the line that bisects the vertical angle of isosceles triangle perpendicularly bisects the base

so x=90

and sum of all sides of triangle is 180 so

90+23+y=180

therefore,y=67

6 0

3 years ago

Read 2 more answers

Help meez 40 pts use surface area formula of cylinder that is for Lateral surface area and for total surface area

jeka94

Answer:So the radius of the cylinder is 2.65 cm.

A cylinder can be defined as a solid figure that is bound by a curved surface and two flat surfaces. The surface area of a cylinder can be found by breaking it down into 2 parts:

1. The two circles that make up the caps of the cylinder.

2. The side of the cylinder, which when "unrolled" is a rectangle.

The area of each end cap can be found from the radius r of the circle, which is given by:

A = πr2

Thus the total area of the caps is 2πr2.

The area of a rectangle is given by:

A = height × width

The width is the height h of the cylinder, and the length is the distance around the end circles, or in other words the perimeter/circumference of the base/top circle and is given by:

P = 2πr

Thus the rectangle's area is rewritten as:

A = 2πr × h

Combining these parts together we will have the total surface area of a cylinder, and the final formula is given by:

A = 2πr2 + 2πrh

where:

π is Pi, approximately 3.142

r is the radius of the cylinder

h height of the cylinder

By factoring 2πr from each term we can simplify the formula to:

A = 2πr(r + h)

The lateral surface area of a cylinder is simply given by: LSA = 2πr × h.

Example 1: Find the surface area of a cylinder with a radius of 4 cm, and a height of 3 cm.

Solution:

SA = 2 × π × r2 + 2 × π × r × h

SA = 2 × 3.14 × 42 + 2 × 3.14 × 4 × 3

SA = 6.28 × 16 + 6.28 × 12

SA = 100.48 + 75.36

SA = 175.84

Surface area = 175.84 cm2

Example 2: Find the surface area of the cylinder with a radius of 5.5cm and height of 10cm.

Solution:

The radius of cylinder = 5.5 cm.

The height of cylinder = 10 cm.

The total surface area of the cylinder is therefore:

TSA = 2πr(r+h)

TSA = 11π (5.5+10)

TSA = 170.5 π

TSA = 535.6 cm2

Example 3: Find the total surface area of a cylindrical tin of radius 17 cm and height 3 cm.

Solution:

Again as in the previous example:

TSA = 2πr(r+h)

TSA = 2π× 17(17+3)

TSA = 2π×17×20

TSA = 2136.56 cm2

Example 4: Find the surface area of the cylinder with radius of 6 cm and height of 9 cm.

Solution:

The radius of cylinder: r = 6 cm

The height of cylinder: h = 9 cm

Total surface area of cylinder is therefore:

TSA = 2πr(r + h)

TSA = 12π (6+9)

TSA = 180 π

TSA = 565.56 cm2

Example 5: Find the radius of cylinder whose lateral surface area is 150 cm2 and its height is 9 cm.

Solution:

Lateral surface area of cylinder is given by:

LSA = 2πrh

Given that:

LSA = 150cm2

h = 9cm

π is the constant and its value = 3.14

Substitute the values in the formula and find the value of r by isolating it from the equation:

LSA = 2πrh

150 = 2× π × r × 9

r = 150 / (2×9× π)

r = 2.65cm

So the radius of the cylinder is 2.65 cm.

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1 year ago

Solve this equation 3+5/2x=1/2x-8

guajiro [1.7K]

Answer:

Step-by-step explanation:

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2 years ago