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3 years ago

Write down the equation of a line parallel to y = 3x + 2

Mathematics

1 answer:

vichka [17]3 years ago

8 0

Answer:

y= 3x - 15

Step-by-step explanation:

parallel lines have the same slope, but different y intercepts

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In a certain manufacturing process, it is known that, on average, 1 in every 100 items is defective.

Rashid [163]

Answer:

A. 0.009899

B. 0.005624

Step-by-step explanation:

Data:

Let the probability that an item is defective = $\frac{1}{100}$

The probability that the item is not defective = $\frac{99}{100}$

The probability that the fifth item is defective = $\frac{1}{100}* \frac{98}{99}$

= 0.009899

Probability that one in 5 items is defective = 0.005624

5 0

3 years ago

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

<h3>Area of of the circle that is not covered</h3>

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

3 0

3 years ago

If you want to create a perfect curve, which tool would be most helpful?

luda_lava [24]

The most usfull tool would be a compas

4 0

3 years ago

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On one side of the balance scale, Henry placed a 6-gram weight. On the other side of the scale, he placed a ballet slipper.

olchik [2.2K]

Answer:

<u><em>A. 6,000 miligrams</em></u>

Explanation:

A <em>balance scale</em> is balanced when the weights on both sides are equal. Then, since the image shows that both sides are equal, the weight of the <em>6-gram weight</em>, placed by Henry on one side of the balance scale is equal to the weight of the <em>ballet slipper </em>placed on the other side.

Weight of the balance slipper = weight of the 6-gram weight

Weight of the balance slipper = 6 grams

<u>Conversion of units: </u>

6 grams × 1,000miligrams/1gram = 6,000 miligrams

Weight of the balance slipper = 6,000 miligrams

That is the option A.

7 0

3 years ago

Robert earns $25 per hour at work, and he works 8 hours a day. Paris earns $225 per day at work. They both work 40 hour work wee

Alisiya [41]

Answer: I believe Robert earns more

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers