Answer:
The probability of a bulb lasting for at most 606 hours is 0.9032
Step-by-step explanation:
The mean lifetime of a bulb is 580 hours.
The standard deviation of the lifetime is 20 hours
We are supposed to find the probability of a bulb lasting for at most 606 hours i.e.
Formula :
Z=1.3
Refer the z table
Hence the probability of a bulb lasting for at most 606 hours is 0.9032
Step-by-step explanation:
The shape of the new pizza must meet the conditions:
- Be an irregular polygon (different sides and/or angles).
- Have at least five sides.
- Have the approximately the same area as a 14" diameter circle.
- Fit in a 14⅛" × 14⅛" square.
- Be divisible into 8-12 equal pieces.
For simplicity, I will choose a polygon with 5 sides (a pentagon), and I will use 2 right angles (a "house" shape).
Split the pentagon into a rectangle on bottom and triangle on top. If we cut the rectangle into 8 pieces like a regular pizza, and the triangle in half, we get 10 triangles.
Now we just need to figure out the dimensions. The area of a 14" circular pizza is:
A = πr²
A = π (7 in)²
A ≈ 154 in²
That means the area of each triangle slice needs to be 15.4 in². If we make the total width of the pentagon 14", then the width of each triangle is 7", and the height of each triangle is:
A = ½ bh
15.4 in² = ½ (7 in) h
h = 4.4 in
Which makes the total height of the pentagon 3h = 13.2 in.
So, our 13.2" × 14" pentagon has at least 5 sides, is irregular, has the same area as a 14" diameter circle, fits in a 14⅛" × 14⅛" square, and can be divided into 8-12 equal pieces.
Of course, there are many possible solutions. This is just one way.
Scale ratios are used to enlarge or compress a shape.
- <em>The scale factor is 13.</em>
- <em>The transformation rule is </em><em>.</em>
- <em>The mural will not distorted, because the sides are changed evenly.</em>
Given
To get the scale factor (k), we simply divide the final measurement by the scale measurement.
So, we have:
<u>For the length, we have:</u>
<u>For the width, we have:</u>
Hence, the scale factor is 13
<u>And the transformation is:</u>
This implies that, the muralist can apply for the transformation
Hence;
<em>(a) The mural will not distorted, because the sides are changed evenly.</em>
Read more about scale ratios at:
brainly.com/question/16713785
Answer:
Part 1)
part 2)
Step-by-step explanation:
Part 1)
we know that
The area of a trapezoid is equal to
In this problem we have
----> perpendicular distance between the two bases
substitute
Part 2)
we know that
The area of a kite is equal to
we have
substitute