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3 years ago

Find the absolute value. 1. 12 | 2. 1-91 3. 20 |-10 4.

Mathematics

1 answer:

ser-zykov [4K]3 years ago

7 0

Answer:

1. 12

2. 9

3. 20

4. 10

5. <

6. =

7. >

Step-by-step explanation:

The absolute value is the distance between that number and 0, i.e makes the number positive.

You really should pay attention in class though.

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Which expression is equivalent to -5a + 12b - c + 5a - 7b + 12c after combining like terms?

just olya [345]

Answer:

5b + 12c

Step-by-step explanation:

-5a +5 a = 0

12b-7b = 5b

12c= 12c

therefore you have the expression 5b+12c

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3 years ago

The area formula for a triangle is?

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The area of a triangle is always:

A=bh/2

Area=(base*height)/2

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4 years ago

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Select Independent or Not independent for each situation.

krok68 [10]

Answer:

1. Not Independent

2. Independent

3. Not Independent

4. Independent

Step-by-step explanation:

Independent: An event is independent if the outcome of one event doesn't effect the outcome of the other event.

Not independent : An event is Not independent if the outcome of one event effect the outcome of other event.

1. A jar contains twenty coins. Two coins are picked randomly without replacement.

Not Independent because if coins are not replaced the outcome of next event will be effected.

2. A coin is flipped three times.

Independent because when a coin is flipped once its outcome doesn't effect the outcome of the coin flipped again

3. A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.

Not Independent because if balls are not replaced the outcome of next event will be effected.

4. A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.

Independent because when the spinner is spuned once its outcome doesn't effect the outcome of the spinner spun again

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4 years ago

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The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equatio

AnnZ [28]

The motion of the hour hand of a clock is a periodic motion that repeats every 12 hours.

The equation that can be used to models the height as a function of time, based on the given options, is presented as follows; $\displaystyle \underline{ H = 0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}$

Reasons:

The given parameters are;

The variation of the height of the tip of the hour hand = 9 feet to 10 feet

At t = 0, the time = 12.00 a.m.

Required: The equation that can be used to model the height as a function of time.

Solution:

The general form of the cosine function is presented as follows;

y = a·cos(b·x - c) + d

The amplitude = a

$\displaystyle a = \mathbf{ \frac{Maximum \ value -Minimum \ value}{2}}$

Therefore;

$\displaystyle a = \frac{10 -9}{2} = 0.5$

b = The cycle speed

The period, T, is given as follows;

$\displaystyle T = \mathbf{ \frac{2 \cdot \pi}{b}}$

The period of a block, T = 12 hours

Therefore;

$\displaystyle b = \frac{2 \cdot \pi}{T}$

$\displaystyle b = \frac{2 \cdot \pi}{12} = \mathbf{ \frac{ \pi}{6}}$

$\displaystyle d = \mathbf{ \frac{Maximum \ value +Minimum \ value}{2} = \frac{10 + 9 }{2}} = 9.5$

At t = 0, H = The highest point = 10 ft.

Which gives;

$\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \times 0 -c\right) + 9.5} = 10$

$\displaystyle cos \left( -c\right) = \frac{0.5}{0.5} = 1$

-c = arcos(1) = 0

-c = 0

c = 0

The equation is therefore;

$\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}$

The above equation is the same as; <u>H = 0.5cosine (StartFraction pi Over 6 EndFraction t) + 9.5</u>

Learn more about the cosine function here:

brainly.com/question/4458343

brainly.com/question/24368105

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3 years ago

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A local hockey rink is covered by a dome in the shape of a hemi-sphere (half sphere). if the floor of the arena has a diameter o

8_murik_8 [283]

The surface area of hemisphere is given by:

$Surface Area = 2 \pi r^{2}$

Where r is radius of hemisphere.

We are given diameter = 250 ft.

We know that radius = half of diameter.

Radius of dome = 1/2 (250) = 125 ft.

Now let us plug the value of radius in the formula,

$Surface Area = 2 (3.14) (125)^{2}$

Surface Area of dome = 98125 square foot.

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3 years ago