Coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows 5?1/6
1/12
2/3
1/4

Answers

Answer 1

Answer: Hello,

1/2 * 1/6=1/12
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Allison is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a theme party. The can has a diameter of 3 feet and a height of 3.5 feet. How much fabric does she need? Round to the nearest square foot.
-7x-2y=-13 -3x-2y=-12 by substitution

One third of a number is 12 less than the number itself

Answers

Answer:

Step-by-step explanation:

1/3 n = n - 12 Cross multiply

n = 3(n - 12)

n = 3n -36

2n = 36

n = 36/2

n = 18

let the number = n
(1/3)n=n-12
(3)(1/3)n=(3)n-12
n=3n-36
-2n=-36
n=18

Select all the sequences of reflections that produce an image equivalent to the image r(180°, O)(△BCD).

Answers

Answer:

r(180°,0) is a rotation of 180° degrees over the origin.

Notice that this rotation moves our figure to the opposite quadrant (so a translation of two quadrants).

Then this is equivalent to:

A reflection over the x-axis followed by a reflection over the y-axis.

Or.

A reflection over the y-axis followed by a reflection over the x-axis.

There is another possible reflection, but it depends on where is our figure.

If the figure is in the first or third quadrant, a reflection over the line y = -x is equivalent to the rotation.

If the figure is in the second or third quadrant, then the reflection over the line y = x is equivalent to the rotation.

We can combine those two and write:

A reflection over the line y = (-1)^n*x.

Where n is the number associated with the quadrant where the figure is in.

Final answer:

A rotation reflection, r(180°, O)(△BCD), can be achieved by performing two reflections over intersecting lines.

If the lines intersect at an angle of 90 degrees, the combination of the two reflections would result in a 180-degree rotation.

Explanation:

The mathematical question requires knowledge of geometrical transformations, specifically, reflections.

The rotation reflection, r(180°, O)(△BCD), means the initial triangle within the plane is reflected over a point 'O' by 180 degrees.

This reflection will result in an image equivalent to a series of two reflections over intersecting lines.

In commonly accepted mathematical conventions, it is generally accepted that any rotation can be represented by two reflections over intersecting lines.

For instance, two reflections over lines intersecting at an angle ∅/2 represent a rotation by an angle ∅, hence, a rotation by 180 degrees would mean the intersecting angle is 90 degrees.

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A 19-foot piece of string is cut into two pieces so that the longer piece is 4 feet longer than twice the shorter piece. If the shorter piece is x feet long find the lengths of both peices

Answers

here,
let the longer piece be y and shorter piece be x
now,
according to the question,
x+y=19 .............................equation (1)
y=4+2x ...............................equation (2)

from equation 1
x+y=19
x+4+2x=19 substituting the value of y from equation 2
3x=19-4
x=(19-4)/3
x=5

now
substituting value of x in equation (2)
y=4+2(5)
y=4+10
y=14

so , the longer piece is 14 foot and the shorter piece is 5 foot

Final answer:

The shorter piece of string is 5 feet long and the longer piece is 14 feet long. These lengths were determined by setting up and solving an equation based on the given facts.

Explanation:

In this problem, we need to find the lengths of two sections of a 19-foot piece of stringthat was split such that the longer piece is 4 feet longer than twice the length of the shorter one. Let's denote the length of the shorter piece as 'x'. Thus, the longer piece of string is 2x+4 (twice the length of the shorter piece, plus an additional 4 feet).

Next, we set up an equation based on the information given: the sum of the lengths of the shorter and the longer sections of string equals 19 feet, so x + (2x+4) = 19. Simplify the equation to 3x + 4 = 19, subtract 4 from both sides to give 3x = 15, and then divide by 3 to solve for x, the length of the shorter piece, which is 5 feet. Therefore, the longer piece, by substituting x=5 in 2x+4, is 14 feet.

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Solve each equation mentally

Answers

Answer:

1. x=7

2. x=11

3. x=0.2

Step-by-step explanation:

The hair on your head grows 1 and a half inch per month.Is it discrete or a continous relationship ?

Answers

I would say continuous, because it keeps happening and never stops.

it is a continuous relationship because your hair keeps growing over time. If it were discrete you hair would only grow 1 1/2 inches at the very end on the month which is not the case.
Hope that makes sense(;

Alexandra is climbing a tree that is 105 feet tall. She has climbed 70 feet so far. if f= the number of feet remaining, which graph best shows this situation?

Answers

Right answer is B. If we have f equal the amount of her remaining way so f it will be the difference between the way she has gone and her finish line. So we have 70 in the approximate middle of her way and F is between 70 feet and 105 feet, so 105=70+F

Answer:

Option B is the right answer.

Step-by-step explanation:

Given is - Alexandra is climbing a tree that is 105 feet tall. She has climbed 70 feet so far.

This means Alexandra has covered 70 feet and final point is 105 feet.

f is the remaining distance;

So, $105=f+70$